1,1,35,44,2.582212,"\text{Not used}","int(-2/(cos(6*x + 4) - 3),x)","\frac{\sqrt{2}\,\left(3\,x-\mathrm{atan}\left(\mathrm{tan}\left(3\,x+2\right)\right)\right)}{6}+\frac{\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)\right)}{6}","Not used",1,"(2^(1/2)*(3*x - atan(tan(3*x + 2))))/6 + (2^(1/2)*atan(2^(1/2)*tan(3*x + 2)))/6","B"
2,1,16,44,2.688965,"\text{Not used}","int(-2/(sin(6*x + 4)*(cot(6*x + 4) - 3/sin(6*x + 4))),x)","\frac{\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)\right)}{6}","Not used",1,"(2^(1/2)*atan(2^(1/2)*tan(3*x + 2)))/6","B"
3,1,35,48,2.485775,"\text{Not used}","int(1/(sin(3*x + 2)^2 + 1),x)","\frac{\sqrt{2}\,\left(3\,x-\mathrm{atan}\left(\mathrm{tan}\left(3\,x+2\right)\right)\right)}{6}+\frac{\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)\right)}{6}","Not used",1,"(2^(1/2)*(3*x - atan(tan(3*x + 2))))/6 + (2^(1/2)*atan(2^(1/2)*tan(3*x + 2)))/6","B"
4,1,35,48,2.380473,"\text{Not used}","int(-1/(cos(3*x + 2)^2 - 2),x)","\frac{\sqrt{2}\,\left(3\,x-\mathrm{atan}\left(\mathrm{tan}\left(3\,x+2\right)\right)\right)}{6}+\frac{\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)\right)}{6}","Not used",1,"(2^(1/2)*(3*x - atan(tan(3*x + 2))))/6 + (2^(1/2)*atan(2^(1/2)*tan(3*x + 2)))/6","B"
5,1,35,48,2.375782,"\text{Not used}","int(1/(2*sin(3*x + 2)^2 + cos(3*x + 2)^2),x)","\frac{\sqrt{2}\,\left(3\,x-\mathrm{atan}\left(\mathrm{tan}\left(3\,x+2\right)\right)\right)}{6}+\frac{\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)\right)}{6}","Not used",1,"(2^(1/2)*(3*x - atan(tan(3*x + 2))))/6 + (2^(1/2)*atan(2^(1/2)*tan(3*x + 2)))/6","B"
6,1,16,48,2.401610,"\text{Not used}","int(1/(cos(3*x + 2)^2*(2*tan(3*x + 2)^2 + 1)),x)","\frac{\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)\right)}{6}","Not used",1,"(2^(1/2)*atan(2^(1/2)*tan(3*x + 2)))/6","B"
7,1,16,48,2.397995,"\text{Not used}","int(1/(sin(3*x + 2)^2*(cot(3*x + 2)^2 + 2)),x)","\frac{\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)\right)}{6}","Not used",1,"(2^(1/2)*atan(2^(1/2)*tan(3*x + 2)))/6","B"
8,1,16,60,2.566146,"\text{Not used}","int(-2/(3*cos(6*x + 4) - 1),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)\right)}{6}","Not used",1,"-(2^(1/2)*atanh(2^(1/2)*tan(3*x + 2)))/6","B"
9,1,16,60,2.623730,"\text{Not used}","int(-2/(sin(6*x + 4)*(3*cot(6*x + 4) - 1/sin(6*x + 4))),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)\right)}{6}","Not used",1,"-(2^(1/2)*atanh(2^(1/2)*tan(3*x + 2)))/6","B"
10,1,16,60,2.453495,"\text{Not used}","int(1/(3*sin(3*x + 2)^2 - 1),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)\right)}{6}","Not used",1,"-(2^(1/2)*atanh(2^(1/2)*tan(3*x + 2)))/6","B"
11,1,16,60,2.439998,"\text{Not used}","int(-1/(3*cos(3*x + 2)^2 - 2),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)\right)}{6}","Not used",1,"-(2^(1/2)*atanh(2^(1/2)*tan(3*x + 2)))/6","B"
12,1,16,60,2.403679,"\text{Not used}","int(1/(2*sin(3*x + 2)^2 - cos(3*x + 2)^2),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)\right)}{6}","Not used",1,"-(2^(1/2)*atanh(2^(1/2)*tan(3*x + 2)))/6","B"
13,1,16,60,2.401985,"\text{Not used}","int(1/(cos(3*x + 2)^2*(2*tan(3*x + 2)^2 - 1)),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)\right)}{6}","Not used",1,"-(2^(1/2)*atanh(2^(1/2)*tan(3*x + 2)))/6","B"
14,1,16,60,2.409538,"\text{Not used}","int(-1/(sin(3*x + 2)^2*(cot(3*x + 2)^2 - 2)),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)\right)}{6}","Not used",1,"-(2^(1/2)*atanh(2^(1/2)*tan(3*x + 2)))/6","B"
15,1,36,42,2.535979,"\text{Not used}","int(2/(cos(6*x + 4) + 3),x)","\frac{\sqrt{2}\,\left(3\,x-\mathrm{atan}\left(\mathrm{tan}\left(3\,x+2\right)\right)\right)}{6}+\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)}{2}\right)}{6}","Not used",1,"(2^(1/2)*(3*x - atan(tan(3*x + 2))))/6 + (2^(1/2)*atan((2^(1/2)*tan(3*x + 2))/2))/6","B"
16,1,17,42,2.688569,"\text{Not used}","int(2/(sin(6*x + 4)*(cot(6*x + 4) + 3/sin(6*x + 4))),x)","\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)}{2}\right)}{6}","Not used",1,"(2^(1/2)*atan((2^(1/2)*tan(3*x + 2))/2))/6","B"
17,1,36,48,2.437591,"\text{Not used}","int(-1/(sin(3*x + 2)^2 - 2),x)","\frac{\sqrt{2}\,\left(3\,x-\mathrm{atan}\left(\mathrm{tan}\left(3\,x+2\right)\right)\right)}{6}+\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)}{2}\right)}{6}","Not used",1,"(2^(1/2)*(3*x - atan(tan(3*x + 2))))/6 + (2^(1/2)*atan((2^(1/2)*tan(3*x + 2))/2))/6","B"
18,1,36,48,2.367117,"\text{Not used}","int(1/(cos(3*x + 2)^2 + 1),x)","\frac{\sqrt{2}\,\left(3\,x-\mathrm{atan}\left(\mathrm{tan}\left(3\,x+2\right)\right)\right)}{6}+\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)}{2}\right)}{6}","Not used",1,"(2^(1/2)*(3*x - atan(tan(3*x + 2))))/6 + (2^(1/2)*atan((2^(1/2)*tan(3*x + 2))/2))/6","B"
19,1,36,48,2.366998,"\text{Not used}","int(1/(sin(3*x + 2)^2 + 2*cos(3*x + 2)^2),x)","\frac{\sqrt{2}\,\left(3\,x-\mathrm{atan}\left(\mathrm{tan}\left(3\,x+2\right)\right)\right)}{6}+\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)}{2}\right)}{6}","Not used",1,"(2^(1/2)*(3*x - atan(tan(3*x + 2))))/6 + (2^(1/2)*atan((2^(1/2)*tan(3*x + 2))/2))/6","B"
20,1,17,48,2.371176,"\text{Not used}","int(1/(cos(3*x + 2)^2*(tan(3*x + 2)^2 + 2)),x)","\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)}{2}\right)}{6}","Not used",1,"(2^(1/2)*atan((2^(1/2)*tan(3*x + 2))/2))/6","B"
21,1,17,48,2.379809,"\text{Not used}","int(1/(sin(3*x + 2)^2*(2*cot(3*x + 2)^2 + 1)),x)","\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)}{2}\right)}{6}","Not used",1,"(2^(1/2)*atan((2^(1/2)*tan(3*x + 2))/2))/6","B"
22,1,17,61,2.500922,"\text{Not used}","int(-2/(3*cos(6*x + 4) + 1),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)}{2}\right)}{6}","Not used",1,"-(2^(1/2)*atanh((2^(1/2)*tan(3*x + 2))/2))/6","B"
23,1,17,61,2.713399,"\text{Not used}","int(-2/(sin(6*x + 4)*(3*cot(6*x + 4) + 1/sin(6*x + 4))),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)}{2}\right)}{6}","Not used",1,"-(2^(1/2)*atanh((2^(1/2)*tan(3*x + 2))/2))/6","B"
24,1,17,61,2.514663,"\text{Not used}","int(1/(3*sin(3*x + 2)^2 - 2),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)}{2}\right)}{6}","Not used",1,"-(2^(1/2)*atanh((2^(1/2)*tan(3*x + 2))/2))/6","B"
25,1,17,61,2.443059,"\text{Not used}","int(-1/(3*cos(3*x + 2)^2 - 1),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)}{2}\right)}{6}","Not used",1,"-(2^(1/2)*atanh((2^(1/2)*tan(3*x + 2))/2))/6","B"
26,1,17,61,2.418288,"\text{Not used}","int(1/(sin(3*x + 2)^2 - 2*cos(3*x + 2)^2),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)}{2}\right)}{6}","Not used",1,"-(2^(1/2)*atanh((2^(1/2)*tan(3*x + 2))/2))/6","B"
27,1,17,61,2.400186,"\text{Not used}","int(1/(cos(3*x + 2)^2*(tan(3*x + 2)^2 - 2)),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)}{2}\right)}{6}","Not used",1,"-(2^(1/2)*atanh((2^(1/2)*tan(3*x + 2))/2))/6","B"
28,1,17,61,2.333615,"\text{Not used}","int(-1/(sin(3*x + 2)^2*(2*cot(3*x + 2)^2 - 1)),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(3\,x+2\right)}{2}\right)}{6}","Not used",1,"-(2^(1/2)*atanh((2^(1/2)*tan(3*x + 2))/2))/6","B"
29,1,24,30,0.057133,"\text{Not used}","int((x + sin(x))^2,x)","\frac{x}{2}+2\,\sin\left(x\right)-\frac{\cos\left(x\right)\,\sin\left(x\right)}{2}-2\,x\,\cos\left(x\right)+\frac{x^3}{3}","Not used",1,"x/2 + 2*sin(x) - (cos(x)*sin(x))/2 - 2*x*cos(x) + x^3/3","B"
30,1,46,56,2.308260,"\text{Not used}","int((x + sin(x))^3,x)","5\,\cos\left(x\right)-3\,x^2\,\cos\left(x\right)-\frac{3\,{\cos\left(x\right)}^2}{4}+\frac{{\cos\left(x\right)}^3}{3}+6\,x\,\sin\left(x\right)+\frac{3\,x^2}{4}+\frac{x^4}{4}-\frac{3\,x\,\cos\left(x\right)\,\sin\left(x\right)}{2}","Not used",1,"5*cos(x) - 3*x^2*cos(x) - (3*cos(x)^2)/4 + cos(x)^3/3 + 6*x*sin(x) + (3*x^2)/4 + x^4/4 - (3*x*cos(x)*sin(x))/2","B"
31,0,-1,213,0.000000,"\text{Not used}","int(sin(a + b*x)/(c + d*x^2),x)","\int \frac{\sin\left(a+b\,x\right)}{d\,x^2+c} \,d x","Not used",1,"int(sin(a + b*x)/(c + d*x^2), x)","F"
32,0,-1,271,0.000000,"\text{Not used}","int(sin(a + b*x)/(c + d*x + e*x^2),x)","\int \frac{\sin\left(a+b\,x\right)}{e\,x^2+d\,x+c} \,d x","Not used",1,"int(sin(a + b*x)/(c + d*x + e*x^2), x)","F"
33,1,8,10,2.418687,"\text{Not used}","int(sin((x - 7)^(1/2))/(x - 7)^(1/2),x)","-2\,\cos\left(\sqrt{x-7}\right)","Not used",1,"-2*cos((x - 7)^(1/2))","B"
34,0,-1,28,0.000000,"\text{Not used}","int((sin(x)*(b - a/x^2)^(1/2))/(a - b*x^2)^(1/2),x)","\int \frac{\sin\left(x\right)\,\sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b\,x^2}} \,d x","Not used",1,"int((sin(x)*(b - a/x^2)^(1/2))/(a - b*x^2)^(1/2), x)","F"
35,1,11,12,2.398598,"\text{Not used}","int(1/(x*(sin(log(x)) + 1)),x)","-\frac{2}{\mathrm{tan}\left(\frac{\ln\left(x\right)}{2}\right)+1}","Not used",1,"-2/(tan(log(x)/2) + 1)","B"
36,0,-1,100,0.000000,"\text{Not used}","int(sin((a + b*x)/(c + d*x)),x)","\int \sin\left(\frac{a+b\,x}{c+d\,x}\right) \,d x","Not used",1,"int(sin((a + b*x)/(c + d*x)), x)","F"
37,0,-1,107,0.000000,"\text{Not used}","int(sin((a + b*x)/(c + d*x))^2,x)","\int {\sin\left(\frac{a+b\,x}{c+d\,x}\right)}^2 \,d x","Not used",1,"int(sin((a + b*x)/(c + d*x))^2, x)","F"
38,0,-1,194,0.000000,"\text{Not used}","int(sin((a + b*x)/(c + d*x))^3,x)","\int {\sin\left(\frac{a+b\,x}{c+d\,x}\right)}^3 \,d x","Not used",1,"int(sin((a + b*x)/(c + d*x))^3, x)","F"
39,0,-1,58,0.000000,"\text{Not used}","int(-sin((1 - a*x)^(1/2)/(a*x + 1)^(1/2))^3/(a^2*x^2 - 1),x)","-\int \frac{{\sin\left(\frac{\sqrt{1-a\,x}}{\sqrt{a\,x+1}}\right)}^3}{a^2\,x^2-1} \,d x","Not used",1,"-int(sin((1 - a*x)^(1/2)/(a*x + 1)^(1/2))^3/(a^2*x^2 - 1), x)","F"
40,0,-1,58,0.000000,"\text{Not used}","int(-sin((1 - a*x)^(1/2)/(a*x + 1)^(1/2))^2/(a^2*x^2 - 1),x)","-\int \frac{{\sin\left(\frac{\sqrt{1-a\,x}}{\sqrt{a\,x+1}}\right)}^2}{a^2\,x^2-1} \,d x","Not used",1,"-int(sin((1 - a*x)^(1/2)/(a*x + 1)^(1/2))^2/(a^2*x^2 - 1), x)","F"
41,0,-1,26,0.000000,"\text{Not used}","int(-sin((1 - a*x)^(1/2)/(a*x + 1)^(1/2))/(a^2*x^2 - 1),x)","-\int \frac{\sin\left(\frac{\sqrt{1-a\,x}}{\sqrt{a\,x+1}}\right)}{a^2\,x^2-1} \,d x","Not used",1,"-int(sin((1 - a*x)^(1/2)/(a*x + 1)^(1/2))/(a^2*x^2 - 1), x)","F"
42,0,-1,40,0.000000,"\text{Not used}","int(-1/(sin((1 - a*x)^(1/2)/(a*x + 1)^(1/2))*(a^2*x^2 - 1)),x)","-\int \frac{1}{\sin\left(\frac{\sqrt{1-a\,x}}{\sqrt{a\,x+1}}\right)\,\left(a^2\,x^2-1\right)} \,d x","Not used",0,"-int(1/(sin((1 - a*x)^(1/2)/(a*x + 1)^(1/2))*(a^2*x^2 - 1)), x)","F"
43,0,-1,42,0.000000,"\text{Not used}","int(-1/(sin((1 - a*x)^(1/2)/(a*x + 1)^(1/2))^2*(a^2*x^2 - 1)),x)","-\int \frac{1}{{\sin\left(\frac{\sqrt{1-a\,x}}{\sqrt{a\,x+1}}\right)}^2\,\left(a^2\,x^2-1\right)} \,d x","Not used",0,"-int(1/(sin((1 - a*x)^(1/2)/(a*x + 1)^(1/2))^2*(a^2*x^2 - 1)), x)","F"
44,1,24,30,0.049247,"\text{Not used}","int((x + cos(x))^2,x)","\frac{x}{2}+2\,\cos\left(x\right)+\frac{\cos\left(x\right)\,\sin\left(x\right)}{2}+2\,x\,\sin\left(x\right)+\frac{x^3}{3}","Not used",1,"x/2 + 2*cos(x) + (cos(x)*sin(x))/2 + 2*x*sin(x) + x^3/3","B"
45,1,48,56,0.075847,"\text{Not used}","int((x + cos(x))^3,x)","3\,x^2\,\sin\left(x\right)-\frac{16\,\sin\left(x\right)}{3}+\frac{3\,{\cos\left(x\right)}^2}{4}+\frac{{\cos\left(x\right)}^2\,\sin\left(x\right)}{3}+6\,x\,\cos\left(x\right)+\frac{3\,x^2}{4}+\frac{x^4}{4}+\frac{3\,x\,\cos\left(x\right)\,\sin\left(x\right)}{2}","Not used",1,"3*x^2*sin(x) - (16*sin(x))/3 + (3*cos(x)^2)/4 + (cos(x)^2*sin(x))/3 + 6*x*cos(x) + (3*x^2)/4 + x^4/4 + (3*x*cos(x)*sin(x))/2","B"
46,0,-1,213,0.000000,"\text{Not used}","int(cos(a + b*x)/(c + d*x^2),x)","\int \frac{\cos\left(a+b\,x\right)}{d\,x^2+c} \,d x","Not used",1,"int(cos(a + b*x)/(c + d*x^2), x)","F"
47,0,-1,271,0.000000,"\text{Not used}","int(cos(a + b*x)/(c + d*x + e*x^2),x)","\int \frac{\cos\left(a+b\,x\right)}{e\,x^2+d\,x+c} \,d x","Not used",1,"int(cos(a + b*x)/(c + d*x + e*x^2), x)","F"
48,1,8,10,2.259880,"\text{Not used}","int((x*cos((x^2 + 1)^(1/2)))/(x^2 + 1)^(1/2),x)","\sin\left(\sqrt{x^2+1}\right)","Not used",1,"sin((x^2 + 1)^(1/2))","B"
49,1,15,22,2.316310,"\text{Not used}","int((x*cos(3^(1/2)*(x^2 + 2)^(1/2)))/(x^2 + 2)^(1/2),x)","\frac{\sqrt{3}\,\sin\left(\sqrt{3\,x^2+6}\right)}{3}","Not used",1,"(3^(1/2)*sin((3*x^2 + 6)^(1/2)))/3","B"
50,1,16,24,2.349176,"\text{Not used}","int((cos((3*(2*x - 1)^2 + 6)^(1/2))*(2*x - 1))/(3*(2*x - 1)^2 + 6)^(1/2),x)","\frac{\sin\left(\sqrt{3\,{\left(2\,x-1\right)}^2+6}\right)}{6}","Not used",1,"sin((3*(2*x - 1)^2 + 6)^(1/2))/6","B"
51,0,-1,101,0.000000,"\text{Not used}","int(cos((a + b*x)/(c + d*x)),x)","\int \cos\left(\frac{a+b\,x}{c+d\,x}\right) \,d x","Not used",1,"int(cos((a + b*x)/(c + d*x)), x)","F"
52,0,-1,107,0.000000,"\text{Not used}","int(cos((a + b*x)/(c + d*x))^2,x)","\int {\cos\left(\frac{a+b\,x}{c+d\,x}\right)}^2 \,d x","Not used",1,"int(cos((a + b*x)/(c + d*x))^2, x)","F"
53,0,-1,58,0.000000,"\text{Not used}","int(-cos((1 - a*x)^(1/2)/(a*x + 1)^(1/2))^3/(a^2*x^2 - 1),x)","-\int \frac{{\cos\left(\frac{\sqrt{1-a\,x}}{\sqrt{a\,x+1}}\right)}^3}{a^2\,x^2-1} \,d x","Not used",1,"-int(cos((1 - a*x)^(1/2)/(a*x + 1)^(1/2))^3/(a^2*x^2 - 1), x)","F"
54,0,-1,58,0.000000,"\text{Not used}","int(-cos((1 - a*x)^(1/2)/(a*x + 1)^(1/2))^2/(a^2*x^2 - 1),x)","-\int \frac{{\cos\left(\frac{\sqrt{1-a\,x}}{\sqrt{a\,x+1}}\right)}^2}{a^2\,x^2-1} \,d x","Not used",1,"-int(cos((1 - a*x)^(1/2)/(a*x + 1)^(1/2))^2/(a^2*x^2 - 1), x)","F"
55,0,-1,26,0.000000,"\text{Not used}","int(-cos((1 - a*x)^(1/2)/(a*x + 1)^(1/2))/(a^2*x^2 - 1),x)","-\int \frac{\cos\left(\frac{\sqrt{1-a\,x}}{\sqrt{a\,x+1}}\right)}{a^2\,x^2-1} \,d x","Not used",1,"-int(cos((1 - a*x)^(1/2)/(a*x + 1)^(1/2))/(a^2*x^2 - 1), x)","F"
56,0,-1,40,0.000000,"\text{Not used}","int(-1/(cos((1 - a*x)^(1/2)/(a*x + 1)^(1/2))*(a^2*x^2 - 1)),x)","-\int \frac{1}{\cos\left(\frac{\sqrt{1-a\,x}}{\sqrt{a\,x+1}}\right)\,\left(a^2\,x^2-1\right)} \,d x","Not used",0,"-int(1/(cos((1 - a*x)^(1/2)/(a*x + 1)^(1/2))*(a^2*x^2 - 1)), x)","F"
57,0,-1,42,0.000000,"\text{Not used}","int(-1/(cos((1 - a*x)^(1/2)/(a*x + 1)^(1/2))^2*(a^2*x^2 - 1)),x)","-\int \frac{1}{{\cos\left(\frac{\sqrt{1-a\,x}}{\sqrt{a\,x+1}}\right)}^2\,\left(a^2\,x^2-1\right)} \,d x","Not used",0,"-int(1/(cos((1 - a*x)^(1/2)/(a*x + 1)^(1/2))^2*(a^2*x^2 - 1)), x)","F"
58,1,19,9,3.179210,"\text{Not used}","int(tan(x^(1/2))/x^(1/2),x)","-2\,\ln\left({\mathrm{e}}^{\sqrt{x}\,2{}\mathrm{i}}+1\right)+\sqrt{x}\,2{}\mathrm{i}","Not used",1,"x^(1/2)*2i - 2*log(exp(x^(1/2)*2i) + 1)","B"
59,1,20,16,2.584171,"\text{Not used}","int(tan(x^(1/2))^2/x^(1/2),x)","-2\,\sqrt{x}+\frac{4{}\mathrm{i}}{{\mathrm{e}}^{\sqrt{x}\,2{}\mathrm{i}}+1}","Not used",1,"4i/(exp(x^(1/2)*2i) + 1) - 2*x^(1/2)","B"
60,0,-1,70,0.000000,"\text{Not used}","int(x^(1/2)*tan(x^(1/2)),x)","\int \sqrt{x}\,\mathrm{tan}\left(\sqrt{x}\right) \,d x","Not used",1,"int(x^(1/2)*tan(x^(1/2)), x)","F"
61,1,21,19,2.511455,"\text{Not used}","int(x*tan(a + b*x + c*x^2) + (b*tan(a + b*x + c*x^2))/(2*c),x)","\frac{\ln\left({\mathrm{tan}\left(c\,x^2+b\,x+a\right)}^2+1\right)}{4\,c}","Not used",1,"log(tan(a + b*x + c*x^2)^2 + 1)/(4*c)","B"
62,1,20,16,2.548566,"\text{Not used}","int(cot(x^(1/2))^2/x^(1/2),x)","-2\,\sqrt{x}-\frac{4{}\mathrm{i}}{{\mathrm{e}}^{\sqrt{x}\,2{}\mathrm{i}}-1}","Not used",1,"- 4i/(exp(x^(1/2)*2i) - 1) - 2*x^(1/2)","B"
63,0,-1,92,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)/(cos(c + d*x) + 1),x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{\cos\left(c+d\,x\right)+1} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(1/2)/(cos(c + d*x) + 1), x)","F"
64,1,29,35,0.089242,"\text{Not used}","int(1/(cos(a + b*x)*cos(2*a + 2*b*x)),x)","-\frac{\mathrm{atanh}\left(\sin\left(a+b\,x\right)\right)-\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\sin\left(a+b\,x\right)\right)}{b}","Not used",1,"-(atanh(sin(a + b*x)) - 2^(1/2)*atanh(2^(1/2)*sin(a + b*x)))/b","B"
65,1,29,35,0.001994,"\text{Not used}","int(1/(cos(a + b*x)*cos(2*a + 2*b*x)),x)","-\frac{\mathrm{atanh}\left(\sin\left(a+b\,x\right)\right)-\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\sin\left(a+b\,x\right)\right)}{b}","Not used",1,"-(atanh(sin(a + b*x)) - 2^(1/2)*atanh(2^(1/2)*sin(a + b*x)))/b","B"
66,1,6,15,0.027485,"\text{Not used}","int(sin(2*x)*sin(x),x)","\frac{2\,{\sin\left(x\right)}^3}{3}","Not used",1,"(2*sin(x)^3)/3","B"
67,1,13,17,0.028750,"\text{Not used}","int(sin(3*x)*sin(x),x)","\frac{\sin\left(2\,x\right)}{4}-\frac{\sin\left(4\,x\right)}{8}","Not used",1,"sin(2*x)/4 - sin(4*x)/8","B"
68,1,13,17,0.029258,"\text{Not used}","int(sin(4*x)*sin(x),x)","\frac{\sin\left(3\,x\right)}{6}-\frac{\sin\left(5\,x\right)}{10}","Not used",1,"sin(3*x)/6 - sin(5*x)/10","B"
69,1,64,35,2.322754,"\text{Not used}","int(sin(m*x)*sin(x),x)","\left\{\begin{array}{cl} \frac{x}{2}-\frac{\sin\left(2\,x\right)}{4} & \text{\ if\ \ }m=1\\ \frac{\sin\left(2\,x\right)}{4}-\frac{x}{2} & \text{\ if\ \ }m=-1\\ \frac{\sin\left(x\,\left(m-1\right)\right)}{2\,m-2}-\frac{\sin\left(x\,\left(m+1\right)\right)}{2\,m+2} & \text{\ if\ \ }m\neq -1\wedge m\neq 1 \end{array}\right.","Not used",1,"piecewise(m == 1, x/2 - sin(2*x)/4, m == -1, - x/2 + sin(2*x)/4, m ~= -1 & m ~= 1, sin(x*(m - 1))/(2*m - 2) - sin(x*(m + 1))/(2*m + 2))","B"
70,1,9,15,0.022563,"\text{Not used}","int(cos(2*x)*sin(x),x)","\cos\left(x\right)-\frac{2\,{\cos\left(x\right)}^3}{3}","Not used",1,"cos(x) - (2*cos(x)^3)/3","B"
71,1,13,17,0.024914,"\text{Not used}","int(cos(3*x)*sin(x),x)","\frac{3\,{\cos\left(x\right)}^2}{2}-{\cos\left(x\right)}^4","Not used",1,"(3*cos(x)^2)/2 - cos(x)^4","B"
72,1,17,17,0.027896,"\text{Not used}","int(cos(4*x)*sin(x),x)","-\frac{8\,{\cos\left(x\right)}^5}{5}+\frac{8\,{\cos\left(x\right)}^3}{3}-\cos\left(x\right)","Not used",1,"(8*cos(x)^3)/3 - cos(x) - (8*cos(x)^5)/5","B"
73,1,37,35,0.099987,"\text{Not used}","int(cos(m*x)*sin(x),x)","\left\{\begin{array}{cl} \frac{{\sin\left(x\right)}^2}{2} & \text{\ if\ \ }m=-1\vee m=1\\ \frac{\cos\left(x\,\left(m-1\right)\right)}{2\,m-2}-\frac{\cos\left(x\,\left(m+1\right)\right)}{2\,m+2} & \text{\ if\ \ }m\neq -1\wedge m\neq 1 \end{array}\right.","Not used",1,"piecewise(m == -1 | m == 1, sin(x)^2/2, m ~= -1 & m ~= 1, cos(x*(m - 1))/(2*m - 2) - cos(x*(m + 1))/(2*m + 2))","B"
74,1,17,20,2.393823,"\text{Not used}","int(tan(2*x)*sin(x),x)","\frac{\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\sin\left(x\right)\right)}{2}-\sin\left(x\right)","Not used",1,"(2^(1/2)*atanh(2^(1/2)*sin(x)))/2 - sin(x)","B"
75,1,26,47,2.339408,"\text{Not used}","int(tan(3*x)*sin(x),x)","\frac{2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{3}+\frac{\mathrm{atanh}\left(2\,\sin\left(x\right)\right)}{3}-\sin\left(x\right)","Not used",1,"(2*atanh(sin(x/2)/cos(x/2)))/3 + atanh(2*sin(x))/3 - sin(x)","B"
76,1,103,71,2.561916,"\text{Not used}","int(tan(4*x)*sin(x),x)","\frac{\mathrm{atanh}\left(\frac{34\,\sin\left(x\right)\,\sqrt{\sqrt{2}+2}+24\,\sqrt{2}\,\sin\left(x\right)\,\sqrt{\sqrt{2}+2}}{41\,\sqrt{2}+58}\right)\,\sqrt{\sqrt{2}+2}}{4}-\sin\left(x\right)-\frac{\mathrm{atanh}\left(\frac{34\,\sin\left(x\right)\,\sqrt{2-\sqrt{2}}-24\,\sqrt{2}\,\sin\left(x\right)\,\sqrt{2-\sqrt{2}}}{41\,\sqrt{2}-58}\right)\,\sqrt{2-\sqrt{2}}}{4}","Not used",1,"(atanh((34*sin(x)*(2^(1/2) + 2)^(1/2) + 24*2^(1/2)*sin(x)*(2^(1/2) + 2)^(1/2))/(41*2^(1/2) + 58))*(2^(1/2) + 2)^(1/2))/4 - sin(x) - (atanh((34*sin(x)*(2 - 2^(1/2))^(1/2) - 24*2^(1/2)*sin(x)*(2 - 2^(1/2))^(1/2))/(41*2^(1/2) - 58))*(2 - 2^(1/2))^(1/2))/4","B"
77,1,107,112,2.885374,"\text{Not used}","int(tan(5*x)*sin(x),x)","\frac{2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{5}+\frac{\mathrm{atan}\left(\frac{\sin\left(x\right)\,1042{}\mathrm{i}-\sqrt{5}\,\sin\left(x\right)\,466{}\mathrm{i}}{377\,\sqrt{5}-843}\right)\,1{}\mathrm{i}}{10}-\frac{\mathrm{atanh}\left(\sin\left(x\right)-\sqrt{5}\,\sin\left(x\right)\right)}{10}-\sin\left(x\right)-\frac{\sqrt{5}\,\mathrm{atanh}\left(\sin\left(x\right)-\sqrt{5}\,\sin\left(x\right)\right)}{10}-\frac{\sqrt{5}\,\mathrm{atan}\left(\frac{\sin\left(x\right)\,1042{}\mathrm{i}-\sqrt{5}\,\sin\left(x\right)\,466{}\mathrm{i}}{377\,\sqrt{5}-843}\right)\,1{}\mathrm{i}}{10}","Not used",1,"(atan((sin(x)*1042i - 5^(1/2)*sin(x)*466i)/(377*5^(1/2) - 843))*1i)/10 - atanh(sin(x) - 5^(1/2)*sin(x))/10 + (2*atanh(sin(x/2)/cos(x/2)))/5 - sin(x) - (5^(1/2)*atanh(sin(x) - 5^(1/2)*sin(x)))/10 - (5^(1/2)*atan((sin(x)*1042i - 5^(1/2)*sin(x)*466i)/(377*5^(1/2) - 843))*1i)/10","B"
78,1,131,89,3.112602,"\text{Not used}","int(tan(6*x)*sin(x),x)","\frac{\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\sin\left(x\right)\right)}{6}-\sin\left(x\right)-\frac{\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\sin\left(x\right)-\sqrt{6}\,\sin\left(x\right)\right)}{12}-\frac{\sqrt{6}\,\mathrm{atanh}\left(\sqrt{2}\,\sin\left(x\right)-\sqrt{6}\,\sin\left(x\right)\right)}{12}+\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sin\left(x\right)\,102818{}\mathrm{i}-\sqrt{6}\,\sin\left(x\right)\,59362{}\mathrm{i}}{40545\,\sqrt{2}\,\sqrt{6}-140452}\right)\,1{}\mathrm{i}}{12}-\frac{\sqrt{6}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sin\left(x\right)\,102818{}\mathrm{i}-\sqrt{6}\,\sin\left(x\right)\,59362{}\mathrm{i}}{40545\,\sqrt{2}\,\sqrt{6}-140452}\right)\,1{}\mathrm{i}}{12}","Not used",1,"(2^(1/2)*atan((2^(1/2)*sin(x)*102818i - 6^(1/2)*sin(x)*59362i)/(40545*2^(1/2)*6^(1/2) - 140452))*1i)/12 - sin(x) - (6^(1/2)*atan((2^(1/2)*sin(x)*102818i - 6^(1/2)*sin(x)*59362i)/(40545*2^(1/2)*6^(1/2) - 140452))*1i)/12 + (2^(1/2)*atanh(2^(1/2)*sin(x)))/6 - (2^(1/2)*atanh(2^(1/2)*sin(x) - 6^(1/2)*sin(x)))/12 - (6^(1/2)*atanh(2^(1/2)*sin(x) - 6^(1/2)*sin(x)))/12","B"
79,0,-1,105,0.000000,"\text{Not used}","int(tan(n*x)*sin(x),x)","\int \mathrm{tan}\left(n\,x\right)\,\sin\left(x\right) \,d x","Not used",1,"int(tan(n*x)*sin(x), x)","F"
80,1,10,10,2.318679,"\text{Not used}","int(cot(2*x)*sin(x),x)","\sin\left(x\right)-\mathrm{atanh}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)","Not used",1,"sin(x) - atanh(tan(x/2))","B"
81,1,16,20,2.365710,"\text{Not used}","int(cot(3*x)*sin(x),x)","\sin\left(x\right)-\frac{\sqrt{3}\,\mathrm{atanh}\left(\frac{2\,\sqrt{3}\,\sin\left(x\right)}{3}\right)}{3}","Not used",1,"sin(x) - (3^(1/2)*atanh((2*3^(1/2)*sin(x))/3))/3","B"
82,1,29,28,2.378264,"\text{Not used}","int(cot(4*x)*sin(x),x)","\sin\left(x\right)-\frac{\mathrm{atanh}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{2}-\frac{\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\sin\left(x\right)\right)}{4}","Not used",1,"sin(x) - atanh(sin(x/2)/cos(x/2))/2 - (2^(1/2)*atanh(2^(1/2)*sin(x)))/4","B"
83,1,119,82,2.608943,"\text{Not used}","int(cot(5*x)*sin(x),x)","\sin\left(x\right)-\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{\frac{25\,\sqrt{2}\,\sin\left(x\right)\,\sqrt{\sqrt{5}+5}}{2}+\frac{11\,\sqrt{2}\,\sqrt{5}\,\sin\left(x\right)\,\sqrt{\sqrt{5}+5}}{2}}{20\,\sqrt{5}+45}\right)\,\sqrt{\sqrt{5}+5}}{10}+\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{\frac{25\,\sqrt{2}\,\sin\left(x\right)\,\sqrt{5-\sqrt{5}}}{2}-\frac{11\,\sqrt{2}\,\sqrt{5}\,\sin\left(x\right)\,\sqrt{5-\sqrt{5}}}{2}}{20\,\sqrt{5}-45}\right)\,\sqrt{5-\sqrt{5}}}{10}","Not used",1,"sin(x) - (2^(1/2)*atanh(((25*2^(1/2)*sin(x)*(5^(1/2) + 5)^(1/2))/2 + (11*2^(1/2)*5^(1/2)*sin(x)*(5^(1/2) + 5)^(1/2))/2)/(20*5^(1/2) + 45))*(5^(1/2) + 5)^(1/2))/10 + (2^(1/2)*atanh(((25*2^(1/2)*sin(x)*(5 - 5^(1/2))^(1/2))/2 - (11*2^(1/2)*5^(1/2)*sin(x)*(5 - 5^(1/2))^(1/2))/2)/(20*5^(1/2) - 45))*(5 - 5^(1/2))^(1/2))/10","B"
84,1,37,38,2.499630,"\text{Not used}","int(cot(6*x)*sin(x),x)","\sin\left(x\right)-\frac{\mathrm{atanh}\left(2\,\sin\left(x\right)\right)}{6}-\frac{\mathrm{atanh}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{3}-\frac{\sqrt{3}\,\mathrm{atanh}\left(\frac{2\,\sqrt{3}\,\sin\left(x\right)}{3}\right)}{6}","Not used",1,"sin(x) - atanh(2*sin(x))/6 - atanh(sin(x/2)/cos(x/2))/3 - (3^(1/2)*atanh((2*3^(1/2)*sin(x))/3))/6","B"
85,1,12,15,2.289275,"\text{Not used}","int(sin(x)/cos(2*x),x)","\frac{\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\cos\left(x\right)\right)}{2}","Not used",1,"(2^(1/2)*atanh(2^(1/2)*cos(x)))/2","B"
86,1,15,21,2.273996,"\text{Not used}","int(sin(x)/cos(3*x),x)","\frac{\ln\left(\cos\left(x\right)\right)}{3}-\frac{\ln\left({\cos\left(x\right)}^2-\frac{3}{4}\right)}{6}","Not used",1,"log(cos(x))/3 - log(cos(x)^2 - 3/4)/6","B"
87,1,112,71,0.087579,"\text{Not used}","int(sin(x)/cos(4*x),x)","\frac{\mathrm{atanh}\left(\frac{\cos\left(x\right)\,\sqrt{2-\sqrt{2}}}{64\,\left(\frac{\sqrt{2}}{128}-\frac{1}{64}\right)}-\frac{\sqrt{2}\,\cos\left(x\right)\,\sqrt{2-\sqrt{2}}}{64\,\left(\frac{\sqrt{2}}{128}-\frac{1}{64}\right)}\right)\,\sqrt{2-\sqrt{2}}}{4}-\frac{\mathrm{atanh}\left(\frac{\cos\left(x\right)\,\sqrt{\sqrt{2}+2}}{64\,\left(\frac{\sqrt{2}}{128}+\frac{1}{64}\right)}+\frac{\sqrt{2}\,\cos\left(x\right)\,\sqrt{\sqrt{2}+2}}{64\,\left(\frac{\sqrt{2}}{128}+\frac{1}{64}\right)}\right)\,\sqrt{\sqrt{2}+2}}{4}","Not used",1,"(atanh((cos(x)*(2 - 2^(1/2))^(1/2))/(64*(2^(1/2)/128 - 1/64)) - (2^(1/2)*cos(x)*(2 - 2^(1/2))^(1/2))/(64*(2^(1/2)/128 - 1/64)))*(2 - 2^(1/2))^(1/2))/4 - (atanh((cos(x)*(2^(1/2) + 2)^(1/2))/(64*(2^(1/2)/128 + 1/64)) + (2^(1/2)*cos(x)*(2^(1/2) + 2)^(1/2))/(64*(2^(1/2)/128 + 1/64)))*(2^(1/2) + 2)^(1/2))/4","B"
88,1,47,62,0.535118,"\text{Not used}","int(sin(x)/cos(5*x),x)","\ln\left({\cos\left(x\right)}^2+\frac{\sqrt{5}}{8}-\frac{5}{8}\right)\,\left(\frac{\sqrt{5}}{20}+\frac{1}{20}\right)-\ln\left({\cos\left(x\right)}^2-\frac{\sqrt{5}}{8}-\frac{5}{8}\right)\,\left(\frac{\sqrt{5}}{20}-\frac{1}{20}\right)-\frac{\ln\left(\cos\left(x\right)\right)}{5}","Not used",1,"log(cos(x)^2 + 5^(1/2)/8 - 5/8)*(5^(1/2)/20 + 1/20) - log(cos(x)^2 - 5^(1/2)/8 - 5/8)*(5^(1/2)/20 - 1/20) - log(cos(x))/5","B"
89,1,118,85,2.283161,"\text{Not used}","int(sin(x)/cos(6*x),x)","\mathrm{atanh}\left(\frac{5\,\sqrt{2}\,\cos\left(x\right)}{2097152\,\left(\frac{\sqrt{2}\,\sqrt{6}}{4194304}+\frac{1}{1048576}\right)}+\frac{3\,\sqrt{6}\,\cos\left(x\right)}{2097152\,\left(\frac{\sqrt{2}\,\sqrt{6}}{4194304}+\frac{1}{1048576}\right)}\right)\,\left(\frac{\sqrt{2}}{12}+\frac{\sqrt{6}}{12}\right)-\mathrm{atanh}\left(\frac{5\,\sqrt{2}\,\cos\left(x\right)}{2097152\,\left(\frac{\sqrt{2}\,\sqrt{6}}{4194304}-\frac{1}{1048576}\right)}-\frac{3\,\sqrt{6}\,\cos\left(x\right)}{2097152\,\left(\frac{\sqrt{2}\,\sqrt{6}}{4194304}-\frac{1}{1048576}\right)}\right)\,\left(\frac{\sqrt{2}}{12}-\frac{\sqrt{6}}{12}\right)-\frac{\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\cos\left(x\right)\right)}{6}","Not used",1,"atanh((5*2^(1/2)*cos(x))/(2097152*((2^(1/2)*6^(1/2))/4194304 + 1/1048576)) + (3*6^(1/2)*cos(x))/(2097152*((2^(1/2)*6^(1/2))/4194304 + 1/1048576)))*(2^(1/2)/12 + 6^(1/2)/12) - atanh((5*2^(1/2)*cos(x))/(2097152*((2^(1/2)*6^(1/2))/4194304 - 1/1048576)) - (3*6^(1/2)*cos(x))/(2097152*((2^(1/2)*6^(1/2))/4194304 - 1/1048576)))*(2^(1/2)/12 - 6^(1/2)/12) - (2^(1/2)*atanh(2^(1/2)*cos(x)))/6","B"
90,1,5,7,0.108736,"\text{Not used}","int(sin(x)/sin(2*x),x)","\frac{\mathrm{atanh}\left(\sin\left(x\right)\right)}{2}","Not used",1,"atanh(sin(x))/2","B"
91,1,17,45,2.792932,"\text{Not used}","int(sin(x)/sin(3*x),x)","\frac{\sqrt{3}\,\mathrm{atanh}\left(\frac{\sqrt{3}\,\sin\left(x\right)}{3\,\cos\left(x\right)}\right)}{3}","Not used",1,"(3^(1/2)*atanh((3^(1/2)*sin(x))/(3*cos(x))))/3","B"
92,1,27,26,2.433136,"\text{Not used}","int(sin(x)/sin(4*x),x)","\frac{\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\sin\left(x\right)\right)}{4}-\frac{\mathrm{atanh}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{2}","Not used",1,"(2^(1/2)*atanh(2^(1/2)*sin(x)))/4 - atanh(sin(x/2)/cos(x/2))/2","B"
93,1,217,165,2.592146,"\text{Not used}","int(sin(x)/sin(5*x),x)","\frac{\sqrt{2}\,\mathrm{atanh}\left(-\frac{34359738368\,\sqrt{2}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\sqrt{5}+5}}{1953125\,\left(\frac{90194313216\,\sqrt{5}}{1953125}-\frac{90194313216\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1953125}-\frac{201863462912\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1953125}+\frac{201863462912}{1953125}\right)}-\frac{77309411328\,\sqrt{2}\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\sqrt{5}+5}}{9765625\,\left(\frac{90194313216\,\sqrt{5}}{1953125}-\frac{90194313216\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1953125}-\frac{201863462912\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1953125}+\frac{201863462912}{1953125}\right)}\right)\,\sqrt{\sqrt{5}+5}}{10}-\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{77309411328\,\sqrt{2}\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{5-\sqrt{5}}}{9765625\,\left(\frac{90194313216\,\sqrt{5}}{1953125}-\frac{90194313216\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1953125}+\frac{201863462912\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1953125}-\frac{201863462912}{1953125}\right)}-\frac{34359738368\,\sqrt{2}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{5-\sqrt{5}}}{1953125\,\left(\frac{90194313216\,\sqrt{5}}{1953125}-\frac{90194313216\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1953125}+\frac{201863462912\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1953125}-\frac{201863462912}{1953125}\right)}\right)\,\sqrt{5-\sqrt{5}}}{10}","Not used",1,"(2^(1/2)*atanh(- (34359738368*2^(1/2)*tan(x/2)*(5^(1/2) + 5)^(1/2))/(1953125*((90194313216*5^(1/2))/1953125 - (90194313216*5^(1/2)*tan(x/2)^2)/1953125 - (201863462912*tan(x/2)^2)/1953125 + 201863462912/1953125)) - (77309411328*2^(1/2)*5^(1/2)*tan(x/2)*(5^(1/2) + 5)^(1/2))/(9765625*((90194313216*5^(1/2))/1953125 - (90194313216*5^(1/2)*tan(x/2)^2)/1953125 - (201863462912*tan(x/2)^2)/1953125 + 201863462912/1953125)))*(5^(1/2) + 5)^(1/2))/10 - (2^(1/2)*atanh((77309411328*2^(1/2)*5^(1/2)*tan(x/2)*(5 - 5^(1/2))^(1/2))/(9765625*((90194313216*5^(1/2))/1953125 - (90194313216*5^(1/2)*tan(x/2)^2)/1953125 + (201863462912*tan(x/2)^2)/1953125 - 201863462912/1953125)) - (34359738368*2^(1/2)*tan(x/2)*(5 - 5^(1/2))^(1/2))/(1953125*((90194313216*5^(1/2))/1953125 - (90194313216*5^(1/2)*tan(x/2)^2)/1953125 + (201863462912*tan(x/2)^2)/1953125 - 201863462912/1953125)))*(5 - 5^(1/2))^(1/2))/10","B"
94,1,35,36,2.459874,"\text{Not used}","int(sin(x)/sin(6*x),x)","\frac{\mathrm{atanh}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{3}+\frac{\mathrm{atanh}\left(2\,\sin\left(x\right)\right)}{6}-\frac{\sqrt{3}\,\mathrm{atanh}\left(\frac{2\,\sqrt{3}\,\sin\left(x\right)}{3}\right)}{6}","Not used",1,"atanh(sin(x/2)/cos(x/2))/3 + atanh(2*sin(x))/6 - (3^(1/2)*atanh((2*3^(1/2)*sin(x))/3))/6","B"
95,1,6,8,2.252495,"\text{Not used}","int(sin(3*x)/sin(x),x)","x+\sin\left(2\,x\right)","Not used",1,"x + sin(2*x)","B"
96,1,6,8,0.027369,"\text{Not used}","int(sin(6*x)/sin(3*x),x)","\frac{2\,\sin\left(3\,x\right)}{3}","Not used",1,"(2*sin(3*x))/3","B"
97,1,6,15,0.017959,"\text{Not used}","int(sin(2*x)*cos(x),x)","-\frac{2\,{\cos\left(x\right)}^3}{3}","Not used",1,"-(2*cos(x)^3)/3","B"
98,1,13,17,0.025534,"\text{Not used}","int(sin(3*x)*cos(x),x)","\frac{{\cos\left(x\right)}^2}{2}-{\cos\left(x\right)}^4","Not used",1,"cos(x)^2/2 - cos(x)^4","B"
99,1,14,17,0.023543,"\text{Not used}","int(sin(4*x)*cos(x),x)","-\frac{4\,{\cos\left(x\right)}^3\,\left(6\,{\cos\left(x\right)}^2-5\right)}{15}","Not used",1,"-(4*cos(x)^3*(6*cos(x)^2 - 5))/15","B"
100,1,57,35,2.285271,"\text{Not used}","int(sin(m*x)*cos(x),x)","\left\{\begin{array}{cl} \frac{{\sin\left(x\right)}^2}{2} & \text{\ if\ \ }m=1\\ \frac{{\cos\left(x\right)}^2}{2} & \text{\ if\ \ }m=-1\\ -\frac{\cos\left(x\,\left(m-1\right)\right)}{2\,m-2}-\frac{\cos\left(x\,\left(m+1\right)\right)}{2\,m+2} & \text{\ if\ \ }m\neq -1\wedge m\neq 1 \end{array}\right.","Not used",1,"piecewise(m == 1, sin(x)^2/2, m == -1, cos(x)^2/2, m ~= -1 & m ~= 1, - cos(x*(m - 1))/(2*m - 2) - cos(x*(m + 1))/(2*m + 2))","B"
101,1,9,15,0.024695,"\text{Not used}","int(cos(2*x)*cos(x),x)","\sin\left(x\right)-\frac{2\,{\sin\left(x\right)}^3}{3}","Not used",1,"sin(x) - (2*sin(x)^3)/3","B"
102,1,7,17,0.021697,"\text{Not used}","int(cos(3*x)*cos(x),x)","{\cos\left(x\right)}^3\,\sin\left(x\right)","Not used",1,"cos(x)^3*sin(x)","B"
103,1,13,17,0.024769,"\text{Not used}","int(cos(4*x)*cos(x),x)","\frac{\sin\left(3\,x\right)}{6}+\frac{\sin\left(5\,x\right)}{10}","Not used",1,"sin(3*x)/6 + sin(5*x)/10","B"
104,1,39,35,0.124489,"\text{Not used}","int(cos(m*x)*cos(x),x)","\left\{\begin{array}{cl} \frac{x}{2}+\frac{\sin\left(2\,x\right)}{4} & \text{\ if\ \ }m=-1\vee m=1\\ \frac{\sin\left(x\,\left(m-1\right)\right)}{2\,m-2}+\frac{\sin\left(x\,\left(m+1\right)\right)}{2\,m+2} & \text{\ if\ \ }m\neq -1\wedge m\neq 1 \end{array}\right.","Not used",1,"piecewise(m == -1 | m == 1, x/2 + sin(2*x)/4, m ~= -1 & m ~= 1, sin(x*(m - 1))/(2*m - 2) + sin(x*(m + 1))/(2*m + 2))","B"
105,1,42,20,2.357771,"\text{Not used}","int(tan(2*x)*cos(x),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{8\,\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{12\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-4}\right)}{2}-\frac{2}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}","Not used",1,"- (2^(1/2)*atanh((8*2^(1/2)*tan(x/2)^2)/(12*tan(x/2)^2 - 4)))/2 - 2/(tan(x/2)^2 + 1)","B"
106,1,42,21,2.312206,"\text{Not used}","int(tan(3*x)*cos(x),x)","-\frac{\sqrt{3}\,\mathrm{atanh}\left(\frac{32\,\sqrt{3}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{3\,\left(\frac{56\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{3}-\frac{8}{3}\right)}\right)}{3}-\frac{2}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}","Not used",1,"- (3^(1/2)*atanh((32*3^(1/2)*tan(x/2)^2)/(3*((56*tan(x/2)^2)/3 - 8/3))))/3 - 2/(tan(x/2)^2 + 1)","B"
107,1,295,71,2.445713,"\text{Not used}","int(tan(4*x)*cos(x),x)","-\frac{\mathrm{atanh}\left(\frac{219747975168\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\sqrt{2-\sqrt{2}}}{6098518016\,\sqrt{2}-254015438848\,\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+386664497152\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-20887633920}-\frac{15971909632\,\sqrt{2-\sqrt{2}}}{6098518016\,\sqrt{2}-254015438848\,\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+386664497152\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-20887633920}-\frac{130056978432\,\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\sqrt{2-\sqrt{2}}}{6098518016\,\sqrt{2}-254015438848\,\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+386664497152\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-20887633920}\right)\,\sqrt{2-\sqrt{2}}}{4}-\frac{2}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}-\frac{\mathrm{atanh}\left(\frac{15971909632\,\sqrt{\sqrt{2}+2}}{6098518016\,\sqrt{2}-254015438848\,\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-386664497152\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+20887633920}-\frac{219747975168\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\sqrt{\sqrt{2}+2}}{6098518016\,\sqrt{2}-254015438848\,\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-386664497152\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+20887633920}-\frac{130056978432\,\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\sqrt{\sqrt{2}+2}}{6098518016\,\sqrt{2}-254015438848\,\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-386664497152\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+20887633920}\right)\,\sqrt{\sqrt{2}+2}}{4}","Not used",1,"- (atanh((219747975168*tan(x/2)^2*(2 - 2^(1/2))^(1/2))/(6098518016*2^(1/2) - 254015438848*2^(1/2)*tan(x/2)^2 + 386664497152*tan(x/2)^2 - 20887633920) - (15971909632*(2 - 2^(1/2))^(1/2))/(6098518016*2^(1/2) - 254015438848*2^(1/2)*tan(x/2)^2 + 386664497152*tan(x/2)^2 - 20887633920) - (130056978432*2^(1/2)*tan(x/2)^2*(2 - 2^(1/2))^(1/2))/(6098518016*2^(1/2) - 254015438848*2^(1/2)*tan(x/2)^2 + 386664497152*tan(x/2)^2 - 20887633920))*(2 - 2^(1/2))^(1/2))/4 - 2/(tan(x/2)^2 + 1) - (atanh((15971909632*(2^(1/2) + 2)^(1/2))/(6098518016*2^(1/2) - 254015438848*2^(1/2)*tan(x/2)^2 - 386664497152*tan(x/2)^2 + 20887633920) - (219747975168*tan(x/2)^2*(2^(1/2) + 2)^(1/2))/(6098518016*2^(1/2) - 254015438848*2^(1/2)*tan(x/2)^2 - 386664497152*tan(x/2)^2 + 20887633920) - (130056978432*2^(1/2)*tan(x/2)^2*(2^(1/2) + 2)^(1/2))/(6098518016*2^(1/2) - 254015438848*2^(1/2)*tan(x/2)^2 - 386664497152*tan(x/2)^2 + 20887633920))*(2^(1/2) + 2)^(1/2))/4","B"
108,1,407,84,2.496784,"\text{Not used}","int(tan(5*x)*cos(x),x)","\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{18032420192256\,\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\sqrt{\sqrt{5}+5}}{\frac{8851927597056\,\sqrt{5}}{25}-\frac{676375744741376\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{25}-\frac{333433343574016\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{5}+2398739234816}-\frac{867583393792\,\sqrt{2}\,\sqrt{5}\,\sqrt{\sqrt{5}+5}}{25\,\left(\frac{8851927597056\,\sqrt{5}}{25}-\frac{676375744741376\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{25}-\frac{333433343574016\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{5}+2398739234816\right)}-\frac{3805341024256\,\sqrt{2}\,\sqrt{\sqrt{5}+5}}{5\,\left(\frac{8851927597056\,\sqrt{5}}{25}-\frac{676375744741376\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{25}-\frac{333433343574016\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{5}+2398739234816\right)}+\frac{6886980059136\,\sqrt{2}\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\sqrt{\sqrt{5}+5}}{\frac{8851927597056\,\sqrt{5}}{25}-\frac{676375744741376\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{25}-\frac{333433343574016\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{5}+2398739234816}\right)\,\sqrt{\sqrt{5}+5}}{10}-\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{867583393792\,\sqrt{2}\,\sqrt{5}\,\sqrt{5-\sqrt{5}}}{25\,\left(\frac{8851927597056\,\sqrt{5}}{25}-\frac{676375744741376\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{25}+\frac{333433343574016\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{5}-2398739234816\right)}-\frac{3805341024256\,\sqrt{2}\,\sqrt{5-\sqrt{5}}}{5\,\left(\frac{8851927597056\,\sqrt{5}}{25}-\frac{676375744741376\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{25}+\frac{333433343574016\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{5}-2398739234816\right)}+\frac{18032420192256\,\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\sqrt{5-\sqrt{5}}}{\frac{8851927597056\,\sqrt{5}}{25}-\frac{676375744741376\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{25}+\frac{333433343574016\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{5}-2398739234816}-\frac{6886980059136\,\sqrt{2}\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\sqrt{5-\sqrt{5}}}{\frac{8851927597056\,\sqrt{5}}{25}-\frac{676375744741376\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{25}+\frac{333433343574016\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{5}-2398739234816}\right)\,\sqrt{5-\sqrt{5}}}{10}-\frac{2}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}","Not used",1,"(2^(1/2)*atanh((18032420192256*2^(1/2)*tan(x/2)^2*(5^(1/2) + 5)^(1/2))/((8851927597056*5^(1/2))/25 - (676375744741376*5^(1/2)*tan(x/2)^2)/25 - (333433343574016*tan(x/2)^2)/5 + 2398739234816) - (867583393792*2^(1/2)*5^(1/2)*(5^(1/2) + 5)^(1/2))/(25*((8851927597056*5^(1/2))/25 - (676375744741376*5^(1/2)*tan(x/2)^2)/25 - (333433343574016*tan(x/2)^2)/5 + 2398739234816)) - (3805341024256*2^(1/2)*(5^(1/2) + 5)^(1/2))/(5*((8851927597056*5^(1/2))/25 - (676375744741376*5^(1/2)*tan(x/2)^2)/25 - (333433343574016*tan(x/2)^2)/5 + 2398739234816)) + (6886980059136*2^(1/2)*5^(1/2)*tan(x/2)^2*(5^(1/2) + 5)^(1/2))/((8851927597056*5^(1/2))/25 - (676375744741376*5^(1/2)*tan(x/2)^2)/25 - (333433343574016*tan(x/2)^2)/5 + 2398739234816))*(5^(1/2) + 5)^(1/2))/10 - (2^(1/2)*atanh((867583393792*2^(1/2)*5^(1/2)*(5 - 5^(1/2))^(1/2))/(25*((8851927597056*5^(1/2))/25 - (676375744741376*5^(1/2)*tan(x/2)^2)/25 + (333433343574016*tan(x/2)^2)/5 - 2398739234816)) - (3805341024256*2^(1/2)*(5 - 5^(1/2))^(1/2))/(5*((8851927597056*5^(1/2))/25 - (676375744741376*5^(1/2)*tan(x/2)^2)/25 + (333433343574016*tan(x/2)^2)/5 - 2398739234816)) + (18032420192256*2^(1/2)*tan(x/2)^2*(5 - 5^(1/2))^(1/2))/((8851927597056*5^(1/2))/25 - (676375744741376*5^(1/2)*tan(x/2)^2)/25 + (333433343574016*tan(x/2)^2)/5 - 2398739234816) - (6886980059136*2^(1/2)*5^(1/2)*tan(x/2)^2*(5 - 5^(1/2))^(1/2))/((8851927597056*5^(1/2))/25 - (676375744741376*5^(1/2)*tan(x/2)^2)/25 + (333433343574016*tan(x/2)^2)/5 - 2398739234816))*(5 - 5^(1/2))^(1/2))/10 - 2/(tan(x/2)^2 + 1)","B"
109,1,787,89,4.074111,"\text{Not used}","int(tan(6*x)*cos(x),x)","-\frac{2}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}+\frac{\sqrt{6}\,\left(\mathrm{atan}\left(\frac{\sqrt{2}\,321030945816576{}\mathrm{i}}{213254896304333030400\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-129275829262795438080\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2176593611144037376}+\frac{\sqrt{6}\,888405273481134080{}\mathrm{i}}{213254896304333030400\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-129275829262795438080\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2176593611144037376}-\frac{\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,18711054724802560{}\mathrm{i}}{213254896304333030400\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-129275829262795438080\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2176593611144037376}+\frac{\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,10905601889064960{}\mathrm{i}}{213254896304333030400\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-129275829262795438080\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2176593611144037376}-\frac{\sqrt{6}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,52765833462352287744{}\mathrm{i}}{213254896304333030400\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-129275829262795438080\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2176593611144037376}+\frac{\sqrt{6}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,87054650497106012160{}\mathrm{i}}{213254896304333030400\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-129275829262795438080\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2176593611144037376}\right)+\mathrm{atan}\left(\frac{\sqrt{2}\,1443325504589801788190484332544{}\mathrm{i}}{589232404262260650654553866240\,\sqrt{2}\,\sqrt{6}+119129717169909888440949339586560\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-34367271726987959946466862039040\,\sqrt{2}\,\sqrt{6}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-2087090309450798997834557292544}-\frac{\sqrt{6}\,852047139771204346616741888000{}\mathrm{i}}{589232404262260650654553866240\,\sqrt{2}\,\sqrt{6}+119129717169909888440949339586560\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-34367271726987959946466862039040\,\sqrt{2}\,\sqrt{6}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-2087090309450798997834557292544}-\frac{\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,84182283571305304543568582410240{}\mathrm{i}}{589232404262260650654553866240\,\sqrt{2}\,\sqrt{6}+119129717169909888440949339586560\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-34367271726987959946466862039040\,\sqrt{2}\,\sqrt{6}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-2087090309450798997834557292544}+\frac{\sqrt{6}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,48634501075236486504873424060416{}\mathrm{i}}{589232404262260650654553866240\,\sqrt{2}\,\sqrt{6}+119129717169909888440949339586560\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-34367271726987959946466862039040\,\sqrt{2}\,\sqrt{6}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-2087090309450798997834557292544}\right)\right)\,1{}\mathrm{i}}{12}-\frac{\sqrt{2}\,\left(2\,\mathrm{atan}\left(\frac{\sqrt{2}\,2276803846003180334341033033728{}\mathrm{i}}{18766876017666378997952094928896\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-3219886877884552553529320931328}-\frac{\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,13270185293778646110081740963840{}\mathrm{i}}{18766876017666378997952094928896\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-3219886877884552553529320931328}\right)-\mathrm{atan}\left(\frac{\sqrt{2}\,321030945816576{}\mathrm{i}}{213254896304333030400\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-129275829262795438080\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2176593611144037376}+\frac{\sqrt{6}\,888405273481134080{}\mathrm{i}}{213254896304333030400\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-129275829262795438080\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2176593611144037376}-\frac{\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,18711054724802560{}\mathrm{i}}{213254896304333030400\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-129275829262795438080\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2176593611144037376}+\frac{\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,10905601889064960{}\mathrm{i}}{213254896304333030400\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-129275829262795438080\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2176593611144037376}-\frac{\sqrt{6}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,52765833462352287744{}\mathrm{i}}{213254896304333030400\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-129275829262795438080\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2176593611144037376}+\frac{\sqrt{6}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,87054650497106012160{}\mathrm{i}}{213254896304333030400\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-129275829262795438080\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2176593611144037376}\right)+\mathrm{atan}\left(\frac{\sqrt{2}\,1443325504589801788190484332544{}\mathrm{i}}{589232404262260650654553866240\,\sqrt{2}\,\sqrt{6}+119129717169909888440949339586560\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-34367271726987959946466862039040\,\sqrt{2}\,\sqrt{6}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-2087090309450798997834557292544}-\frac{\sqrt{6}\,852047139771204346616741888000{}\mathrm{i}}{589232404262260650654553866240\,\sqrt{2}\,\sqrt{6}+119129717169909888440949339586560\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-34367271726987959946466862039040\,\sqrt{2}\,\sqrt{6}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-2087090309450798997834557292544}-\frac{\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,84182283571305304543568582410240{}\mathrm{i}}{589232404262260650654553866240\,\sqrt{2}\,\sqrt{6}+119129717169909888440949339586560\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-34367271726987959946466862039040\,\sqrt{2}\,\sqrt{6}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-2087090309450798997834557292544}+\frac{\sqrt{6}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,48634501075236486504873424060416{}\mathrm{i}}{589232404262260650654553866240\,\sqrt{2}\,\sqrt{6}+119129717169909888440949339586560\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-34367271726987959946466862039040\,\sqrt{2}\,\sqrt{6}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-2087090309450798997834557292544}\right)\right)\,1{}\mathrm{i}}{12}","Not used",1,"(6^(1/2)*(atan((2^(1/2)*321030945816576i)/(213254896304333030400*tan(x/2)^4 - 129275829262795438080*tan(x/2)^2 + 2176593611144037376) + (6^(1/2)*888405273481134080i)/(213254896304333030400*tan(x/2)^4 - 129275829262795438080*tan(x/2)^2 + 2176593611144037376) - (2^(1/2)*tan(x/2)^2*18711054724802560i)/(213254896304333030400*tan(x/2)^4 - 129275829262795438080*tan(x/2)^2 + 2176593611144037376) + (2^(1/2)*tan(x/2)^4*10905601889064960i)/(213254896304333030400*tan(x/2)^4 - 129275829262795438080*tan(x/2)^2 + 2176593611144037376) - (6^(1/2)*tan(x/2)^2*52765833462352287744i)/(213254896304333030400*tan(x/2)^4 - 129275829262795438080*tan(x/2)^2 + 2176593611144037376) + (6^(1/2)*tan(x/2)^4*87054650497106012160i)/(213254896304333030400*tan(x/2)^4 - 129275829262795438080*tan(x/2)^2 + 2176593611144037376)) + atan((2^(1/2)*1443325504589801788190484332544i)/(589232404262260650654553866240*2^(1/2)*6^(1/2) + 119129717169909888440949339586560*tan(x/2)^2 - 34367271726987959946466862039040*2^(1/2)*6^(1/2)*tan(x/2)^2 - 2087090309450798997834557292544) - (6^(1/2)*852047139771204346616741888000i)/(589232404262260650654553866240*2^(1/2)*6^(1/2) + 119129717169909888440949339586560*tan(x/2)^2 - 34367271726987959946466862039040*2^(1/2)*6^(1/2)*tan(x/2)^2 - 2087090309450798997834557292544) - (2^(1/2)*tan(x/2)^2*84182283571305304543568582410240i)/(589232404262260650654553866240*2^(1/2)*6^(1/2) + 119129717169909888440949339586560*tan(x/2)^2 - 34367271726987959946466862039040*2^(1/2)*6^(1/2)*tan(x/2)^2 - 2087090309450798997834557292544) + (6^(1/2)*tan(x/2)^2*48634501075236486504873424060416i)/(589232404262260650654553866240*2^(1/2)*6^(1/2) + 119129717169909888440949339586560*tan(x/2)^2 - 34367271726987959946466862039040*2^(1/2)*6^(1/2)*tan(x/2)^2 - 2087090309450798997834557292544)))*1i)/12 - 2/(tan(x/2)^2 + 1) - (2^(1/2)*(2*atan((2^(1/2)*2276803846003180334341033033728i)/(18766876017666378997952094928896*tan(x/2)^2 - 3219886877884552553529320931328) - (2^(1/2)*tan(x/2)^2*13270185293778646110081740963840i)/(18766876017666378997952094928896*tan(x/2)^2 - 3219886877884552553529320931328)) - atan((2^(1/2)*321030945816576i)/(213254896304333030400*tan(x/2)^4 - 129275829262795438080*tan(x/2)^2 + 2176593611144037376) + (6^(1/2)*888405273481134080i)/(213254896304333030400*tan(x/2)^4 - 129275829262795438080*tan(x/2)^2 + 2176593611144037376) - (2^(1/2)*tan(x/2)^2*18711054724802560i)/(213254896304333030400*tan(x/2)^4 - 129275829262795438080*tan(x/2)^2 + 2176593611144037376) + (2^(1/2)*tan(x/2)^4*10905601889064960i)/(213254896304333030400*tan(x/2)^4 - 129275829262795438080*tan(x/2)^2 + 2176593611144037376) - (6^(1/2)*tan(x/2)^2*52765833462352287744i)/(213254896304333030400*tan(x/2)^4 - 129275829262795438080*tan(x/2)^2 + 2176593611144037376) + (6^(1/2)*tan(x/2)^4*87054650497106012160i)/(213254896304333030400*tan(x/2)^4 - 129275829262795438080*tan(x/2)^2 + 2176593611144037376)) + atan((2^(1/2)*1443325504589801788190484332544i)/(589232404262260650654553866240*2^(1/2)*6^(1/2) + 119129717169909888440949339586560*tan(x/2)^2 - 34367271726987959946466862039040*2^(1/2)*6^(1/2)*tan(x/2)^2 - 2087090309450798997834557292544) - (6^(1/2)*852047139771204346616741888000i)/(589232404262260650654553866240*2^(1/2)*6^(1/2) + 119129717169909888440949339586560*tan(x/2)^2 - 34367271726987959946466862039040*2^(1/2)*6^(1/2)*tan(x/2)^2 - 2087090309450798997834557292544) - (2^(1/2)*tan(x/2)^2*84182283571305304543568582410240i)/(589232404262260650654553866240*2^(1/2)*6^(1/2) + 119129717169909888440949339586560*tan(x/2)^2 - 34367271726987959946466862039040*2^(1/2)*6^(1/2)*tan(x/2)^2 - 2087090309450798997834557292544) + (6^(1/2)*tan(x/2)^2*48634501075236486504873424060416i)/(589232404262260650654553866240*2^(1/2)*6^(1/2) + 119129717169909888440949339586560*tan(x/2)^2 - 34367271726987959946466862039040*2^(1/2)*6^(1/2)*tan(x/2)^2 - 2087090309450798997834557292544)))*1i)/12","B"
110,1,20,10,2.336314,"\text{Not used}","int(cot(2*x)*cos(x),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{2}+\frac{2}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}","Not used",1,"log(tan(x/2))/2 + 2/(tan(x/2)^2 + 1)","B"
111,1,39,45,2.369387,"\text{Not used}","int(cot(3*x)*cos(x),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{3}+\frac{\mathrm{atanh}\left(\frac{8}{183\,\left(\frac{488\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{243}-\frac{56}{81}\right)}+\frac{121}{122}\right)}{3}+\frac{2}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}","Not used",1,"log(tan(x/2))/3 + atanh(8/(183*((488*tan(x/2)^2)/243 - 56/81)) + 121/122)/3 + 2/(tan(x/2)^2 + 1)","B"
112,1,67,28,2.348879,"\text{Not used}","int(cot(4*x)*cos(x),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{4}-\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{7\,\sqrt{2}}{8\,\left(\frac{29\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{4}-\frac{5}{4}\right)}-\frac{41\,\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,\left(\frac{29\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{4}-\frac{5}{4}\right)}\right)}{4}+\frac{2}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}","Not used",1,"log(tan(x/2))/4 - (2^(1/2)*atanh((7*2^(1/2))/(8*((29*tan(x/2)^2)/4 - 5/4)) - (41*2^(1/2)*tan(x/2)^2)/(8*((29*tan(x/2)^2)/4 - 5/4))))/4 + 2/(tan(x/2)^2 + 1)","B"
113,1,611,110,3.033998,"\text{Not used}","int(cot(5*x)*cos(x),x)","\frac{\mathrm{atan}\left(-\frac{\sqrt{5}\,247887795585024{}\mathrm{i}}{1220703125\,\left(\frac{213485644414976\,\sqrt{5}}{1220703125}-\frac{2152646198689792\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}-\frac{4959229085483008\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}+\frac{110872433262592}{244140625}\right)}-\frac{95487323537408{}\mathrm{i}}{244140625\,\left(\frac{213485644414976\,\sqrt{5}}{1220703125}-\frac{2152646198689792\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}-\frac{4959229085483008\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}+\frac{110872433262592}{244140625}\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,4813499234516992{}\mathrm{i}}{1220703125\,\left(\frac{213485644414976\,\sqrt{5}}{1220703125}-\frac{2152646198689792\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}-\frac{4959229085483008\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}+\frac{110872433262592}{244140625}\right)}+\frac{\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,2217818569310208{}\mathrm{i}}{1220703125\,\left(\frac{213485644414976\,\sqrt{5}}{1220703125}-\frac{2152646198689792\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}-\frac{4959229085483008\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}+\frac{110872433262592}{244140625}\right)}\right)\,1{}\mathrm{i}}{10}+\frac{\mathrm{atan}\left(-\frac{\sqrt{5}\,247887795585024{}\mathrm{i}}{1220703125\,\left(\frac{213485644414976\,\sqrt{5}}{1220703125}-\frac{2152646198689792\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}+\frac{4959229085483008\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}-\frac{110872433262592}{244140625}\right)}+\frac{95487323537408{}\mathrm{i}}{244140625\,\left(\frac{213485644414976\,\sqrt{5}}{1220703125}-\frac{2152646198689792\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}+\frac{4959229085483008\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}-\frac{110872433262592}{244140625}\right)}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,4813499234516992{}\mathrm{i}}{1220703125\,\left(\frac{213485644414976\,\sqrt{5}}{1220703125}-\frac{2152646198689792\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}+\frac{4959229085483008\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}-\frac{110872433262592}{244140625}\right)}+\frac{\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,2217818569310208{}\mathrm{i}}{1220703125\,\left(\frac{213485644414976\,\sqrt{5}}{1220703125}-\frac{2152646198689792\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}+\frac{4959229085483008\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}-\frac{110872433262592}{244140625}\right)}\right)\,1{}\mathrm{i}}{10}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{5}+\frac{2}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}+\frac{\sqrt{5}\,\left(\mathrm{atan}\left(-\frac{\sqrt{5}\,247887795585024{}\mathrm{i}}{1220703125\,\left(\frac{213485644414976\,\sqrt{5}}{1220703125}-\frac{2152646198689792\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}-\frac{4959229085483008\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}+\frac{110872433262592}{244140625}\right)}-\frac{95487323537408{}\mathrm{i}}{244140625\,\left(\frac{213485644414976\,\sqrt{5}}{1220703125}-\frac{2152646198689792\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}-\frac{4959229085483008\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}+\frac{110872433262592}{244140625}\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,4813499234516992{}\mathrm{i}}{1220703125\,\left(\frac{213485644414976\,\sqrt{5}}{1220703125}-\frac{2152646198689792\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}-\frac{4959229085483008\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}+\frac{110872433262592}{244140625}\right)}+\frac{\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,2217818569310208{}\mathrm{i}}{1220703125\,\left(\frac{213485644414976\,\sqrt{5}}{1220703125}-\frac{2152646198689792\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}-\frac{4959229085483008\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}+\frac{110872433262592}{244140625}\right)}\right)-\mathrm{atan}\left(-\frac{\sqrt{5}\,247887795585024{}\mathrm{i}}{1220703125\,\left(\frac{213485644414976\,\sqrt{5}}{1220703125}-\frac{2152646198689792\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}+\frac{4959229085483008\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}-\frac{110872433262592}{244140625}\right)}+\frac{95487323537408{}\mathrm{i}}{244140625\,\left(\frac{213485644414976\,\sqrt{5}}{1220703125}-\frac{2152646198689792\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}+\frac{4959229085483008\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}-\frac{110872433262592}{244140625}\right)}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,4813499234516992{}\mathrm{i}}{1220703125\,\left(\frac{213485644414976\,\sqrt{5}}{1220703125}-\frac{2152646198689792\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}+\frac{4959229085483008\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}-\frac{110872433262592}{244140625}\right)}+\frac{\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,2217818569310208{}\mathrm{i}}{1220703125\,\left(\frac{213485644414976\,\sqrt{5}}{1220703125}-\frac{2152646198689792\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}+\frac{4959229085483008\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1220703125}-\frac{110872433262592}{244140625}\right)}\right)\right)\,1{}\mathrm{i}}{10}","Not used",1,"(atan((tan(x/2)^2*4813499234516992i)/(1220703125*((213485644414976*5^(1/2))/1220703125 - (2152646198689792*5^(1/2)*tan(x/2)^2)/1220703125 - (4959229085483008*tan(x/2)^2)/1220703125 + 110872433262592/244140625)) - 95487323537408i/(244140625*((213485644414976*5^(1/2))/1220703125 - (2152646198689792*5^(1/2)*tan(x/2)^2)/1220703125 - (4959229085483008*tan(x/2)^2)/1220703125 + 110872433262592/244140625)) - (5^(1/2)*247887795585024i)/(1220703125*((213485644414976*5^(1/2))/1220703125 - (2152646198689792*5^(1/2)*tan(x/2)^2)/1220703125 - (4959229085483008*tan(x/2)^2)/1220703125 + 110872433262592/244140625)) + (5^(1/2)*tan(x/2)^2*2217818569310208i)/(1220703125*((213485644414976*5^(1/2))/1220703125 - (2152646198689792*5^(1/2)*tan(x/2)^2)/1220703125 - (4959229085483008*tan(x/2)^2)/1220703125 + 110872433262592/244140625)))*1i)/10 + (atan(95487323537408i/(244140625*((213485644414976*5^(1/2))/1220703125 - (2152646198689792*5^(1/2)*tan(x/2)^2)/1220703125 + (4959229085483008*tan(x/2)^2)/1220703125 - 110872433262592/244140625)) - (5^(1/2)*247887795585024i)/(1220703125*((213485644414976*5^(1/2))/1220703125 - (2152646198689792*5^(1/2)*tan(x/2)^2)/1220703125 + (4959229085483008*tan(x/2)^2)/1220703125 - 110872433262592/244140625)) - (tan(x/2)^2*4813499234516992i)/(1220703125*((213485644414976*5^(1/2))/1220703125 - (2152646198689792*5^(1/2)*tan(x/2)^2)/1220703125 + (4959229085483008*tan(x/2)^2)/1220703125 - 110872433262592/244140625)) + (5^(1/2)*tan(x/2)^2*2217818569310208i)/(1220703125*((213485644414976*5^(1/2))/1220703125 - (2152646198689792*5^(1/2)*tan(x/2)^2)/1220703125 + (4959229085483008*tan(x/2)^2)/1220703125 - 110872433262592/244140625)))*1i)/10 + log(tan(x/2))/5 + 2/(tan(x/2)^2 + 1) + (5^(1/2)*(atan((tan(x/2)^2*4813499234516992i)/(1220703125*((213485644414976*5^(1/2))/1220703125 - (2152646198689792*5^(1/2)*tan(x/2)^2)/1220703125 - (4959229085483008*tan(x/2)^2)/1220703125 + 110872433262592/244140625)) - 95487323537408i/(244140625*((213485644414976*5^(1/2))/1220703125 - (2152646198689792*5^(1/2)*tan(x/2)^2)/1220703125 - (4959229085483008*tan(x/2)^2)/1220703125 + 110872433262592/244140625)) - (5^(1/2)*247887795585024i)/(1220703125*((213485644414976*5^(1/2))/1220703125 - (2152646198689792*5^(1/2)*tan(x/2)^2)/1220703125 - (4959229085483008*tan(x/2)^2)/1220703125 + 110872433262592/244140625)) + (5^(1/2)*tan(x/2)^2*2217818569310208i)/(1220703125*((213485644414976*5^(1/2))/1220703125 - (2152646198689792*5^(1/2)*tan(x/2)^2)/1220703125 - (4959229085483008*tan(x/2)^2)/1220703125 + 110872433262592/244140625))) - atan(95487323537408i/(244140625*((213485644414976*5^(1/2))/1220703125 - (2152646198689792*5^(1/2)*tan(x/2)^2)/1220703125 + (4959229085483008*tan(x/2)^2)/1220703125 - 110872433262592/244140625)) - (5^(1/2)*247887795585024i)/(1220703125*((213485644414976*5^(1/2))/1220703125 - (2152646198689792*5^(1/2)*tan(x/2)^2)/1220703125 + (4959229085483008*tan(x/2)^2)/1220703125 - 110872433262592/244140625)) - (tan(x/2)^2*4813499234516992i)/(1220703125*((213485644414976*5^(1/2))/1220703125 - (2152646198689792*5^(1/2)*tan(x/2)^2)/1220703125 + (4959229085483008*tan(x/2)^2)/1220703125 - 110872433262592/244140625)) + (5^(1/2)*tan(x/2)^2*2217818569310208i)/(1220703125*((213485644414976*5^(1/2))/1220703125 - (2152646198689792*5^(1/2)*tan(x/2)^2)/1220703125 + (4959229085483008*tan(x/2)^2)/1220703125 - 110872433262592/244140625))))*1i)/10","B"
114,1,86,38,2.435209,"\text{Not used}","int(cot(6*x)*cos(x),x)","\frac{\mathrm{atanh}\left(\frac{1073741824}{10761687\,\left(\frac{427973089951744\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{14348907}-\frac{47552804159488}{4782969}\right)}+\frac{797161}{797162}\right)}{6}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{6}-\frac{\sqrt{3}\,\mathrm{atanh}\left(\frac{303181204553728\,\sqrt{3}}{4782969\,\left(\frac{7314051205955584\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{4782969}-\frac{525125250187264}{4782969}\right)}-\frac{4222769432625152\,\sqrt{3}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{4782969\,\left(\frac{7314051205955584\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{4782969}-\frac{525125250187264}{4782969}\right)}\right)}{6}+\frac{2}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}","Not used",1,"atanh(1073741824/(10761687*((427973089951744*tan(x/2)^2)/14348907 - 47552804159488/4782969)) + 797161/797162)/6 + log(tan(x/2))/6 - (3^(1/2)*atanh((303181204553728*3^(1/2))/(4782969*((7314051205955584*tan(x/2)^2)/4782969 - 525125250187264/4782969)) - (4222769432625152*3^(1/2)*tan(x/2)^2)/(4782969*((7314051205955584*tan(x/2)^2)/4782969 - 525125250187264/4782969))))/6 + 2/(tan(x/2)^2 + 1)","B"
115,0,-1,92,0.000000,"\text{Not used}","int(cot(n*x)*cos(x),x)","\int \mathrm{cot}\left(n\,x\right)\,\cos\left(x\right) \,d x","Not used",1,"int(cot(n*x)*cos(x), x)","F"
116,1,12,15,0.114132,"\text{Not used}","int(cos(x)/cos(2*x),x)","\frac{\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\sin\left(x\right)\right)}{2}","Not used",1,"(2^(1/2)*atanh(2^(1/2)*sin(x)))/2","B"
117,1,16,44,2.664326,"\text{Not used}","int(cos(x)/cos(3*x),x)","\frac{\sqrt{3}\,\mathrm{atanh}\left(\frac{\sqrt{3}\,\sin\left(x\right)}{\cos\left(x\right)}\right)}{3}","Not used",1,"(3^(1/2)*atanh((3^(1/2)*sin(x))/cos(x)))/3","B"
118,1,95,71,2.271829,"\text{Not used}","int(cos(x)/cos(4*x),x)","\frac{\mathrm{atanh}\left(\frac{2\,\sin\left(x\right)\,\sqrt{\sqrt{2}+2}+2\,\sqrt{2}\,\sin\left(x\right)\,\sqrt{\sqrt{2}+2}}{\sqrt{2}+2}\right)\,\sqrt{\sqrt{2}+2}}{4}-\frac{\mathrm{atanh}\left(\frac{2\,\sin\left(x\right)\,\sqrt{2-\sqrt{2}}-2\,\sqrt{2}\,\sin\left(x\right)\,\sqrt{2-\sqrt{2}}}{\sqrt{2}-2}\right)\,\sqrt{2-\sqrt{2}}}{4}","Not used",1,"(atanh((2*sin(x)*(2^(1/2) + 2)^(1/2) + 2*2^(1/2)*sin(x)*(2^(1/2) + 2)^(1/2))/(2^(1/2) + 2))*(2^(1/2) + 2)^(1/2))/4 - (atanh((2*sin(x)*(2 - 2^(1/2))^(1/2) - 2*2^(1/2)*sin(x)*(2 - 2^(1/2))^(1/2))/(2^(1/2) - 2))*(2 - 2^(1/2))^(1/2))/4","B"
119,1,217,163,2.666847,"\text{Not used}","int(cos(x)/cos(5*x),x)","\frac{\sqrt{2}\,\mathrm{atanh}\left(-\frac{34359738368\,\sqrt{2}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{5-\sqrt{5}}}{5\,\left(\frac{124554051584\,\sqrt{5}}{25}-\frac{124554051584\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{25}-\frac{55834574848\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{5}+\frac{55834574848}{5}\right)}-\frac{77309411328\,\sqrt{2}\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{5-\sqrt{5}}}{25\,\left(\frac{124554051584\,\sqrt{5}}{25}-\frac{124554051584\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{25}-\frac{55834574848\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{5}+\frac{55834574848}{5}\right)}\right)\,\sqrt{5-\sqrt{5}}}{10}-\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{77309411328\,\sqrt{2}\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\sqrt{5}+5}}{25\,\left(\frac{124554051584\,\sqrt{5}}{25}-\frac{124554051584\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{25}+\frac{55834574848\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{5}-\frac{55834574848}{5}\right)}-\frac{34359738368\,\sqrt{2}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\sqrt{5}+5}}{5\,\left(\frac{124554051584\,\sqrt{5}}{25}-\frac{124554051584\,\sqrt{5}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{25}+\frac{55834574848\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{5}-\frac{55834574848}{5}\right)}\right)\,\sqrt{\sqrt{5}+5}}{10}","Not used",1,"(2^(1/2)*atanh(- (34359738368*2^(1/2)*tan(x/2)*(5 - 5^(1/2))^(1/2))/(5*((124554051584*5^(1/2))/25 - (124554051584*5^(1/2)*tan(x/2)^2)/25 - (55834574848*tan(x/2)^2)/5 + 55834574848/5)) - (77309411328*2^(1/2)*5^(1/2)*tan(x/2)*(5 - 5^(1/2))^(1/2))/(25*((124554051584*5^(1/2))/25 - (124554051584*5^(1/2)*tan(x/2)^2)/25 - (55834574848*tan(x/2)^2)/5 + 55834574848/5)))*(5 - 5^(1/2))^(1/2))/10 - (2^(1/2)*atanh((77309411328*2^(1/2)*5^(1/2)*tan(x/2)*(5^(1/2) + 5)^(1/2))/(25*((124554051584*5^(1/2))/25 - (124554051584*5^(1/2)*tan(x/2)^2)/25 + (55834574848*tan(x/2)^2)/5 - 55834574848/5)) - (34359738368*2^(1/2)*tan(x/2)*(5^(1/2) + 5)^(1/2))/(5*((124554051584*5^(1/2))/25 - (124554051584*5^(1/2)*tan(x/2)^2)/25 + (55834574848*tan(x/2)^2)/5 - 55834574848/5)))*(5^(1/2) + 5)^(1/2))/10","B"
120,1,118,85,2.292249,"\text{Not used}","int(cos(x)/cos(6*x),x)","\mathrm{atanh}\left(\frac{5\,\sqrt{2}\,\sin\left(x\right)}{2097152\,\left(\frac{\sqrt{2}\,\sqrt{6}}{4194304}+\frac{1}{1048576}\right)}+\frac{3\,\sqrt{6}\,\sin\left(x\right)}{2097152\,\left(\frac{\sqrt{2}\,\sqrt{6}}{4194304}+\frac{1}{1048576}\right)}\right)\,\left(\frac{\sqrt{2}}{12}+\frac{\sqrt{6}}{12}\right)-\mathrm{atanh}\left(\frac{5\,\sqrt{2}\,\sin\left(x\right)}{2097152\,\left(\frac{\sqrt{2}\,\sqrt{6}}{4194304}-\frac{1}{1048576}\right)}-\frac{3\,\sqrt{6}\,\sin\left(x\right)}{2097152\,\left(\frac{\sqrt{2}\,\sqrt{6}}{4194304}-\frac{1}{1048576}\right)}\right)\,\left(\frac{\sqrt{2}}{12}-\frac{\sqrt{6}}{12}\right)-\frac{\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\sin\left(x\right)\right)}{6}","Not used",1,"atanh((5*2^(1/2)*sin(x))/(2097152*((2^(1/2)*6^(1/2))/4194304 + 1/1048576)) + (3*6^(1/2)*sin(x))/(2097152*((2^(1/2)*6^(1/2))/4194304 + 1/1048576)))*(2^(1/2)/12 + 6^(1/2)/12) - atanh((5*2^(1/2)*sin(x))/(2097152*((2^(1/2)*6^(1/2))/4194304 - 1/1048576)) - (3*6^(1/2)*sin(x))/(2097152*((2^(1/2)*6^(1/2))/4194304 - 1/1048576)))*(2^(1/2)/12 - 6^(1/2)/12) - (2^(1/2)*atanh(2^(1/2)*sin(x)))/6","B"
121,1,10,10,2.246818,"\text{Not used}","int(cos(2*x)/cos(x),x)","2\,\sin\left(x\right)-\mathrm{atanh}\left(\sin\left(x\right)\right)","Not used",1,"2*sin(x) - atanh(sin(x))","B"
122,1,12,14,0.024679,"\text{Not used}","int(cos(4*x)/cos(2*x),x)","\sin\left(2\,x\right)-\frac{\mathrm{atanh}\left(\sin\left(2\,x\right)\right)}{2}","Not used",1,"sin(2*x) - atanh(sin(2*x))/2","B"
123,1,5,7,0.027161,"\text{Not used}","int(cos(x)/sin(2*x),x)","-\frac{\mathrm{atanh}\left(\cos\left(x\right)\right)}{2}","Not used",1,"-atanh(cos(x))/2","B"
124,1,17,21,0.103290,"\text{Not used}","int(cos(x)/sin(3*x),x)","\frac{\ln\left(\sin\left(x\right)\right)}{3}-\frac{\ln\left(\frac{1}{4}-{\cos\left(x\right)}^2\right)}{6}","Not used",1,"log(sin(x))/3 - log(1/4 - cos(x)^2)/6","B"
125,1,55,26,2.307344,"\text{Not used}","int(cos(x)/sin(4*x),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{4}+\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{41\,\sqrt{2}}{8\,\left(\frac{169\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{4}-\frac{29}{4}\right)}-\frac{239\,\sqrt{2}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,\left(\frac{169\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{4}-\frac{29}{4}\right)}\right)}{4}","Not used",1,"log(tan(x/2))/4 + (2^(1/2)*atanh((41*2^(1/2))/(8*((169*tan(x/2)^2)/4 - 29/4)) - (239*2^(1/2)*tan(x/2)^2)/(8*((169*tan(x/2)^2)/4 - 29/4))))/4","B"
126,1,51,62,2.679124,"\text{Not used}","int(cos(x)/sin(5*x),x)","\frac{\ln\left(\sin\left(x\right)\right)}{5}+\ln\left(-{\cos\left(x\right)}^2-\frac{\sqrt{5}}{8}+\frac{3}{8}\right)\,\left(\frac{\sqrt{5}}{20}-\frac{1}{20}\right)-\ln\left(-{\cos\left(x\right)}^2+\frac{\sqrt{5}}{8}+\frac{3}{8}\right)\,\left(\frac{\sqrt{5}}{20}+\frac{1}{20}\right)","Not used",1,"log(sin(x))/5 + log(3/8 - 5^(1/2)/8 - cos(x)^2)*(5^(1/2)/20 - 1/20) - log(5^(1/2)/8 - cos(x)^2 + 3/8)*(5^(1/2)/20 + 1/20)","B"
127,1,74,36,2.367530,"\text{Not used}","int(cos(x)/sin(6*x),x)","\frac{\mathrm{atanh}\left(\frac{1073741824}{10761687\,\left(\frac{427973089951744\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{14348907}-\frac{47552804159488}{4782969}\right)}+\frac{797161}{797162}\right)}{6}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{6}+\frac{\sqrt{3}\,\mathrm{atanh}\left(\frac{4222769432625152\,\sqrt{3}}{4782969\,\left(\frac{101871591633190912\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{4782969}-\frac{7314051205955584}{4782969}\right)}-\frac{19605196950732800\,\sqrt{3}\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{1594323\,\left(\frac{101871591633190912\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{4782969}-\frac{7314051205955584}{4782969}\right)}\right)}{6}","Not used",1,"atanh(1073741824/(10761687*((427973089951744*tan(x/2)^2)/14348907 - 47552804159488/4782969)) + 797161/797162)/6 + log(tan(x/2))/6 + (3^(1/2)*atanh((4222769432625152*3^(1/2))/(4782969*((101871591633190912*tan(x/2)^2)/4782969 - 7314051205955584/4782969)) - (19605196950732800*3^(1/2)*tan(x/2)^2)/(1594323*((101871591633190912*tan(x/2)^2)/4782969 - 7314051205955584/4782969))))/6","B"
128,1,57,33,0.080341,"\text{Not used}","int(cos(6*x)^3*sin(x),x)","-\frac{32768\,{\cos\left(x\right)}^{19}}{19}+\frac{147456\,{\cos\left(x\right)}^{17}}{17}-18432\,{\cos\left(x\right)}^{15}+21504\,{\cos\left(x\right)}^{13}-14976\,{\cos\left(x\right)}^{11}+6336\,{\cos\left(x\right)}^9-\frac{11112\,{\cos\left(x\right)}^7}{7}+\frac{1116\,{\cos\left(x\right)}^5}{5}-18\,{\cos\left(x\right)}^3+\cos\left(x\right)","Not used",1,"cos(x) - 18*cos(x)^3 + (1116*cos(x)^5)/5 - (11112*cos(x)^7)/7 + 6336*cos(x)^9 - 14976*cos(x)^11 + 21504*cos(x)^13 - 18432*cos(x)^15 + (147456*cos(x)^17)/17 - (32768*cos(x)^19)/19","B"
129,1,78,33,2.469267,"\text{Not used}","int(cos(6*x)^3*sin(9*x),x)","-\frac{2\,\left(135\,{\mathrm{tan}\left(\frac{3\,x}{2}\right)}^{16}-900\,{\mathrm{tan}\left(\frac{3\,x}{2}\right)}^{14}+5640\,{\mathrm{tan}\left(\frac{3\,x}{2}\right)}^{12}-13140\,{\mathrm{tan}\left(\frac{3\,x}{2}\right)}^{10}+15534\,{\mathrm{tan}\left(\frac{3\,x}{2}\right)}^8-4044\,{\mathrm{tan}\left(\frac{3\,x}{2}\right)}^6+1584\,{\mathrm{tan}\left(\frac{3\,x}{2}\right)}^4+36\,{\mathrm{tan}\left(\frac{3\,x}{2}\right)}^2+19\right)}{135\,{\left({\mathrm{tan}\left(\frac{3\,x}{2}\right)}^2+1\right)}^9}","Not used",1,"-(2*(36*tan((3*x)/2)^2 + 1584*tan((3*x)/2)^4 - 4044*tan((3*x)/2)^6 + 15534*tan((3*x)/2)^8 - 13140*tan((3*x)/2)^10 + 5640*tan((3*x)/2)^12 - 900*tan((3*x)/2)^14 + 135*tan((3*x)/2)^16 + 19))/(135*(tan((3*x)/2)^2 + 1)^9)","B"
130,1,25,25,2.289014,"\text{Not used}","int(cos(2*x)*sin(6*x)^2,x)","\frac{8\,{\sin\left(2\,x\right)}^7}{7}-\frac{12\,{\sin\left(2\,x\right)}^5}{5}+\frac{3\,{\sin\left(2\,x\right)}^3}{2}","Not used",1,"(3*sin(2*x)^3)/2 - (12*sin(2*x)^5)/5 + (8*sin(2*x)^7)/7","B"
131,1,17,23,2.486701,"\text{Not used}","int(sin(6*x)^2*cos(x),x)","\frac{\sin\left(x\right)}{2}-\frac{\sin\left(13\,x\right)}{52}-\frac{\sin\left(11\,x\right)}{44}","Not used",1,"sin(x)/2 - sin(13*x)/52 - sin(11*x)/44","B"
132,1,150,33,2.697804,"\text{Not used}","int(sin(6*x)^3*cos(x),x)","-\frac{32\,\left(305235\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{34}-9665775\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{32}+153838440\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{30}-1348695544\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{28}+7083812484\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{26}-23578828164\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{24}+51613490424\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{22}-75928491144\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{20}+75935973762\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{18}-51607368282\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{16}+23582909592\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{14}-7081614792\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{12}+1349637412\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{10}-153524484\,{\mathrm{tan}\left(\frac{x}{2}\right)}^8+9744264\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6-291384\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+1539\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+81\right)}{11305\,{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}^{19}}","Not used",1,"-(32*(1539*tan(x/2)^2 - 291384*tan(x/2)^4 + 9744264*tan(x/2)^6 - 153524484*tan(x/2)^8 + 1349637412*tan(x/2)^10 - 7081614792*tan(x/2)^12 + 23582909592*tan(x/2)^14 - 51607368282*tan(x/2)^16 + 75935973762*tan(x/2)^18 - 75928491144*tan(x/2)^20 + 51613490424*tan(x/2)^22 - 23578828164*tan(x/2)^24 + 7083812484*tan(x/2)^26 - 1348695544*tan(x/2)^28 + 153838440*tan(x/2)^30 - 9665775*tan(x/2)^32 + 305235*tan(x/2)^34 + 81))/(11305*(tan(x/2)^2 + 1)^19)","B"
133,1,198,31,3.178510,"\text{Not used}","int(cos(7*x)*sin(6*x)^3,x)","\frac{32\,\left(-96525\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{46}+8655075\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{44}-300482325\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{42}+5743927475\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{40}-67792485475\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{38}+523868412925\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{36}-2750448633075\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{34}+10084506042325\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{32}-26325778958050\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{30}+49575817586750\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{28}-67895787973650\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{26}+67896209197950\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{24}-49575456537350\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{22}+26326043727610\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{20}-10084340561350\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{18}+2750536240650\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{16}-523829476225\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{14}+67806830575\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{12}-5739623945\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{10}+301506975\,{\mathrm{tan}\left(\frac{x}{2}\right)}^8-8468775\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+120825\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+2025\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+81\right)}{3575\,{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}^{25}}","Not used",1,"(32*(2025*tan(x/2)^2 + 120825*tan(x/2)^4 - 8468775*tan(x/2)^6 + 301506975*tan(x/2)^8 - 5739623945*tan(x/2)^10 + 67806830575*tan(x/2)^12 - 523829476225*tan(x/2)^14 + 2750536240650*tan(x/2)^16 - 10084340561350*tan(x/2)^18 + 26326043727610*tan(x/2)^20 - 49575456537350*tan(x/2)^22 + 67896209197950*tan(x/2)^24 - 67895787973650*tan(x/2)^26 + 49575817586750*tan(x/2)^28 - 26325778958050*tan(x/2)^30 + 10084506042325*tan(x/2)^32 - 2750448633075*tan(x/2)^34 + 523868412925*tan(x/2)^36 - 67792485475*tan(x/2)^38 + 5743927475*tan(x/2)^40 - 300482325*tan(x/2)^42 + 8655075*tan(x/2)^44 - 96525*tan(x/2)^46 + 81))/(3575*(tan(x/2)^2 + 1)^25)","B"
134,1,25,41,2.270845,"\text{Not used}","int(cos(3*x)^2*sin(2*x)^3,x)","\frac{32\,{\cos\left(x\right)}^{12}}{3}-32\,{\cos\left(x\right)}^{10}+33\,{\cos\left(x\right)}^8-12\,{\cos\left(x\right)}^6","Not used",1,"33*cos(x)^8 - 12*cos(x)^6 - 32*cos(x)^10 + (32*cos(x)^12)/3","B"
135,1,36,27,2.476161,"\text{Not used}","int(sin(a + b*x)*sin(c + b*x),x)","\left\{\begin{array}{cl} x\,\sin\left(a\right)\,\sin\left(c\right) & \text{\ if\ \ }b=0\\ \frac{x\,\cos\left(a-c\right)}{2}-\frac{\sin\left(a+c+2\,b\,x\right)}{4\,b} & \text{\ if\ \ }b\neq 0 \end{array}\right.","Not used",1,"piecewise(b == 0, x*sin(a)*sin(c), b ~= 0, (x*cos(a - c))/2 - sin(a + c + 2*b*x)/(4*b))","B"
136,1,36,27,2.460763,"\text{Not used}","int(sin(a + b*x)*sin(c - b*x),x)","\left\{\begin{array}{cl} x\,\sin\left(a\right)\,\sin\left(c\right) & \text{\ if\ \ }b=0\\ \frac{\sin\left(a-c+2\,b\,x\right)}{4\,b}-\frac{x\,\cos\left(a+c\right)}{2} & \text{\ if\ \ }b\neq 0 \end{array}\right.","Not used",1,"piecewise(b == 0, x*sin(a)*sin(c), b ~= 0, sin(a - c + 2*b*x)/(4*b) - (x*cos(a + c))/2)","B"
137,1,36,27,2.274569,"\text{Not used}","int(cos(a + b*x)*cos(c + b*x),x)","\left\{\begin{array}{cl} x\,\cos\left(a\right)\,\cos\left(c\right) & \text{\ if\ \ }b=0\\ \frac{x\,\cos\left(a-c\right)}{2}+\frac{\sin\left(a+c+2\,b\,x\right)}{4\,b} & \text{\ if\ \ }b\neq 0 \end{array}\right.","Not used",1,"piecewise(b == 0, x*cos(a)*cos(c), b ~= 0, (x*cos(a - c))/2 + sin(a + c + 2*b*x)/(4*b))","B"
138,1,36,27,2.263894,"\text{Not used}","int(cos(a + b*x)*cos(c - b*x),x)","\left\{\begin{array}{cl} x\,\cos\left(a\right)\,\cos\left(c\right) & \text{\ if\ \ }b=0\\ \frac{\sin\left(a-c+2\,b\,x\right)}{4\,b}+\frac{x\,\cos\left(a+c\right)}{2} & \text{\ if\ \ }b\neq 0 \end{array}\right.","Not used",1,"piecewise(b == 0, x*cos(a)*cos(c), b ~= 0, sin(a - c + 2*b*x)/(4*b) + (x*cos(a + c))/2)","B"
139,1,207,39,4.988614,"\text{Not used}","int(tan(a + b*x)*tan(c + b*x),x)","-\frac{\frac{x}{2}+x\,\left({\sin\left(a-c\right)}^2-\frac{1}{2}\right)}{{\sin\left(a-c\right)}^2}-\frac{\frac{\sin\left(2\,a-2\,c\right)\,\ln\left({\sin\left(2\,a-2\,c\right)}^2\,2{}\mathrm{i}-{\sin\left(a+b\,x\right)}^2\,2{}\mathrm{i}+{\sin\left(3\,a-2\,c+b\,x\right)}^2\,2{}\mathrm{i}+\sin\left(4\,a-4\,c\right)+\sin\left(6\,a-4\,c+2\,b\,x\right)-\sin\left(2\,a+2\,b\,x\right)\right)}{2}-\frac{\sin\left(2\,a-2\,c\right)\,\ln\left({\sin\left(2\,a-2\,c\right)}^2\,2{}\mathrm{i}-{\sin\left(c+b\,x\right)}^2\,2{}\mathrm{i}+{\sin\left(2\,a-c+b\,x\right)}^2\,2{}\mathrm{i}+\sin\left(4\,a-4\,c\right)+\sin\left(4\,a-2\,c+2\,b\,x\right)-\sin\left(2\,c+2\,b\,x\right)\right)}{2}}{b\,{\sin\left(a-c\right)}^2}","Not used",1,"- (x/2 + x*(sin(a - c)^2 - 1/2))/sin(a - c)^2 - ((sin(2*a - 2*c)*log(sin(4*a - 4*c) + sin(6*a - 4*c + 2*b*x) - sin(2*a + 2*b*x) + sin(2*a - 2*c)^2*2i - sin(a + b*x)^2*2i + sin(3*a - 2*c + b*x)^2*2i))/2 - (sin(2*a - 2*c)*log(sin(4*a - 4*c) + sin(4*a - 2*c + 2*b*x) - sin(2*c + 2*b*x) + sin(2*a - 2*c)^2*2i - sin(c + b*x)^2*2i + sin(2*a - c + b*x)^2*2i))/2)/(b*sin(a - c)^2)","B"
140,1,196,34,4.998195,"\text{Not used}","int(tan(a + b*x)*tan(c - b*x),x)","\frac{\frac{x}{2}+x\,\left({\sin\left(a+c\right)}^2-\frac{1}{2}\right)}{{\sin\left(a+c\right)}^2}+\frac{\frac{\sin\left(2\,a+2\,c\right)\,\ln\left({\sin\left(2\,a+2\,c\right)}^2\,2{}\mathrm{i}-{\sin\left(a+b\,x\right)}^2\,2{}\mathrm{i}+{\sin\left(3\,a+2\,c+b\,x\right)}^2\,2{}\mathrm{i}+\sin\left(4\,a+4\,c\right)+\sin\left(6\,a+4\,c+2\,b\,x\right)-\sin\left(2\,a+2\,b\,x\right)\right)}{2}-\frac{\sin\left(2\,a+2\,c\right)\,\ln\left({\sin\left(2\,a+c+b\,x\right)}^2\,2{}\mathrm{i}+{\sin\left(2\,a+2\,c\right)}^2\,2{}\mathrm{i}-{\sin\left(c-b\,x\right)}^2\,2{}\mathrm{i}+\sin\left(4\,a+4\,c\right)+\sin\left(4\,a+2\,c+2\,b\,x\right)+\sin\left(2\,c-2\,b\,x\right)\right)}{2}}{b\,{\sin\left(a+c\right)}^2}","Not used",1,"(x/2 + x*(sin(a + c)^2 - 1/2))/sin(a + c)^2 + ((sin(2*a + 2*c)*log(sin(4*a + 4*c) + sin(6*a + 4*c + 2*b*x) - sin(2*a + 2*b*x) + sin(2*a + 2*c)^2*2i - sin(a + b*x)^2*2i + sin(3*a + 2*c + b*x)^2*2i))/2 - (sin(2*a + 2*c)*log(sin(4*a + 4*c) + sin(4*a + 2*c + 2*b*x) + sin(2*c - 2*b*x) + sin(2*a + c + b*x)^2*2i + sin(2*a + 2*c)^2*2i - sin(c - b*x)^2*2i))/2)/(b*sin(a + c)^2)","B"
141,1,207,39,4.815183,"\text{Not used}","int(cot(a + b*x)*cot(c + b*x),x)","-\frac{\frac{x}{2}+x\,\left({\sin\left(a-c\right)}^2-\frac{1}{2}\right)}{{\sin\left(a-c\right)}^2}-\frac{\frac{\sin\left(2\,a-2\,c\right)\,\ln\left({\sin\left(2\,a-2\,c\right)}^2\,2{}\mathrm{i}+{\sin\left(a+b\,x\right)}^2\,2{}\mathrm{i}-{\sin\left(3\,a-2\,c+b\,x\right)}^2\,2{}\mathrm{i}+\sin\left(4\,a-4\,c\right)-\sin\left(6\,a-4\,c+2\,b\,x\right)+\sin\left(2\,a+2\,b\,x\right)\right)}{2}-\frac{\sin\left(2\,a-2\,c\right)\,\ln\left({\sin\left(2\,a-2\,c\right)}^2\,2{}\mathrm{i}+{\sin\left(c+b\,x\right)}^2\,2{}\mathrm{i}-{\sin\left(2\,a-c+b\,x\right)}^2\,2{}\mathrm{i}+\sin\left(4\,a-4\,c\right)-\sin\left(4\,a-2\,c+2\,b\,x\right)+\sin\left(2\,c+2\,b\,x\right)\right)}{2}}{b\,{\sin\left(a-c\right)}^2}","Not used",1,"- (x/2 + x*(sin(a - c)^2 - 1/2))/sin(a - c)^2 - ((sin(2*a - 2*c)*log(sin(4*a - 4*c) - sin(6*a - 4*c + 2*b*x) + sin(2*a + 2*b*x) + sin(2*a - 2*c)^2*2i + sin(a + b*x)^2*2i - sin(3*a - 2*c + b*x)^2*2i))/2 - (sin(2*a - 2*c)*log(sin(4*a - 4*c) - sin(4*a - 2*c + 2*b*x) + sin(2*c + 2*b*x) + sin(2*a - 2*c)^2*2i + sin(c + b*x)^2*2i - sin(2*a - c + b*x)^2*2i))/2)/(b*sin(a - c)^2)","B"
142,1,200,34,5.054813,"\text{Not used}","int(cot(a + b*x)*cot(c - b*x),x)","\frac{\frac{x}{2}+x\,\left({\sin\left(a+c\right)}^2-\frac{1}{2}\right)}{{\sin\left(a+c\right)}^2}+\frac{\frac{\sin\left(2\,a+2\,c\right)\,\ln\left({\sin\left(2\,a+2\,c\right)}^2\,2{}\mathrm{i}+{\sin\left(a+b\,x\right)}^2\,2{}\mathrm{i}-{\sin\left(3\,a+2\,c+b\,x\right)}^2\,2{}\mathrm{i}+\sin\left(4\,a+4\,c\right)-\sin\left(6\,a+4\,c+2\,b\,x\right)+\sin\left(2\,a+2\,b\,x\right)\right)}{2}-\frac{\sin\left(2\,a+2\,c\right)\,\ln\left(-{\sin\left(2\,a+c+b\,x\right)}^2\,2{}\mathrm{i}+{\sin\left(2\,a+2\,c\right)}^2\,2{}\mathrm{i}+{\sin\left(c-b\,x\right)}^2\,2{}\mathrm{i}+\sin\left(4\,a+4\,c\right)-\sin\left(4\,a+2\,c+2\,b\,x\right)-\sin\left(2\,c-2\,b\,x\right)\right)}{2}}{b\,{\sin\left(a+c\right)}^2}","Not used",1,"(x/2 + x*(sin(a + c)^2 - 1/2))/sin(a + c)^2 + ((sin(2*a + 2*c)*log(sin(4*a + 4*c) - sin(6*a + 4*c + 2*b*x) + sin(2*a + 2*b*x) + sin(2*a + 2*c)^2*2i + sin(a + b*x)^2*2i - sin(3*a + 2*c + b*x)^2*2i))/2 - (sin(2*a + 2*c)*log(sin(4*a + 4*c) - sin(4*a + 2*c + 2*b*x) - sin(2*c - 2*b*x) - sin(2*a + c + b*x)^2*2i + sin(2*a + 2*c)^2*2i + sin(c - b*x)^2*2i))/2)/(b*sin(a + c)^2)","B"
143,1,249,36,7.836504,"\text{Not used}","int(1/(cos(a + b*x)*cos(c + b*x)),x)","\frac{2\,\sqrt{-{\mathrm{e}}^{a\,2{}\mathrm{i}-c\,2{}\mathrm{i}}}\,\left(\ln\left(-\frac{2\,\sqrt{-{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{-c\,2{}\mathrm{i}}}\,\left(4\,b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{-c\,2{}\mathrm{i}}+2\,b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}+2\,b\,{\mathrm{e}}^{a\,4{}\mathrm{i}}\,{\mathrm{e}}^{-c\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}\right)}{b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{-c\,2{}\mathrm{i}}-1\right)}+{\mathrm{e}}^{a\,1{}\mathrm{i}}\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{-c\,1{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}\,4{}\mathrm{i}\right)-\ln\left(-\frac{2\,\sqrt{-{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{-c\,2{}\mathrm{i}}}\,\left(4\,b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{-c\,2{}\mathrm{i}}+2\,b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}+2\,b\,{\mathrm{e}}^{a\,4{}\mathrm{i}}\,{\mathrm{e}}^{-c\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}\right)}{b-b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{-c\,2{}\mathrm{i}}}+{\mathrm{e}}^{a\,1{}\mathrm{i}}\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{-c\,1{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}\,4{}\mathrm{i}\right)\right)}{b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}-c\,2{}\mathrm{i}}-1\right)}","Not used",1,"(2*(-exp(a*2i - c*2i))^(1/2)*(log(exp(a*1i)*exp(a*2i)*exp(-c*1i)*exp(b*x*2i)*4i - (2*(-exp(a*2i)*exp(-c*2i))^(1/2)*(4*b*exp(a*2i)*exp(-c*2i) + 2*b*exp(a*2i)*exp(b*x*2i) + 2*b*exp(a*4i)*exp(-c*2i)*exp(b*x*2i)))/(b*(exp(a*2i)*exp(-c*2i) - 1))) - log(exp(a*1i)*exp(a*2i)*exp(-c*1i)*exp(b*x*2i)*4i - (2*(-exp(a*2i)*exp(-c*2i))^(1/2)*(4*b*exp(a*2i)*exp(-c*2i) + 2*b*exp(a*2i)*exp(b*x*2i) + 2*b*exp(a*4i)*exp(-c*2i)*exp(b*x*2i)))/(b - b*exp(a*2i)*exp(-c*2i)))))/(b*(exp(a*2i - c*2i) - 1))","B"
144,1,249,33,7.728401,"\text{Not used}","int(1/(cos(a + b*x)*cos(c - b*x)),x)","\frac{2\,\sqrt{-{\mathrm{e}}^{a\,2{}\mathrm{i}+c\,2{}\mathrm{i}}}\,\left(\ln\left(-\frac{2\,\sqrt{-{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{c\,2{}\mathrm{i}}}\,\left(4\,b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{c\,2{}\mathrm{i}}+2\,b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}+2\,b\,{\mathrm{e}}^{a\,4{}\mathrm{i}}\,{\mathrm{e}}^{c\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}\right)}{b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{c\,2{}\mathrm{i}}-1\right)}+{\mathrm{e}}^{a\,1{}\mathrm{i}}\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{c\,1{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}\,4{}\mathrm{i}\right)-\ln\left(-\frac{2\,\sqrt{-{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{c\,2{}\mathrm{i}}}\,\left(4\,b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{c\,2{}\mathrm{i}}+2\,b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}+2\,b\,{\mathrm{e}}^{a\,4{}\mathrm{i}}\,{\mathrm{e}}^{c\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}\right)}{b-b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{c\,2{}\mathrm{i}}}+{\mathrm{e}}^{a\,1{}\mathrm{i}}\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{c\,1{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}\,4{}\mathrm{i}\right)\right)}{b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+c\,2{}\mathrm{i}}-1\right)}","Not used",1,"(2*(-exp(a*2i + c*2i))^(1/2)*(log(exp(a*1i)*exp(a*2i)*exp(c*1i)*exp(b*x*2i)*4i - (2*(-exp(a*2i)*exp(c*2i))^(1/2)*(4*b*exp(a*2i)*exp(c*2i) + 2*b*exp(a*2i)*exp(b*x*2i) + 2*b*exp(a*4i)*exp(c*2i)*exp(b*x*2i)))/(b*(exp(a*2i)*exp(c*2i) - 1))) - log(exp(a*1i)*exp(a*2i)*exp(c*1i)*exp(b*x*2i)*4i - (2*(-exp(a*2i)*exp(c*2i))^(1/2)*(4*b*exp(a*2i)*exp(c*2i) + 2*b*exp(a*2i)*exp(b*x*2i) + 2*b*exp(a*4i)*exp(c*2i)*exp(b*x*2i)))/(b - b*exp(a*2i)*exp(c*2i)))))/(b*(exp(a*2i + c*2i) - 1))","B"
145,1,249,36,7.774497,"\text{Not used}","int(1/(sin(a + b*x)*sin(c + b*x)),x)","\frac{2\,\sqrt{-{\mathrm{e}}^{a\,2{}\mathrm{i}-c\,2{}\mathrm{i}}}\,\left(\ln\left(\frac{2\,\sqrt{-{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{-c\,2{}\mathrm{i}}}\,\left(-4\,b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{-c\,2{}\mathrm{i}}+2\,b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}+2\,b\,{\mathrm{e}}^{a\,4{}\mathrm{i}}\,{\mathrm{e}}^{-c\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}\right)}{b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{-c\,2{}\mathrm{i}}-1\right)}-{\mathrm{e}}^{a\,1{}\mathrm{i}}\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{-c\,1{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}\,4{}\mathrm{i}\right)-\ln\left(\frac{2\,\sqrt{-{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{-c\,2{}\mathrm{i}}}\,\left(-4\,b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{-c\,2{}\mathrm{i}}+2\,b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}+2\,b\,{\mathrm{e}}^{a\,4{}\mathrm{i}}\,{\mathrm{e}}^{-c\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}\right)}{b-b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{-c\,2{}\mathrm{i}}}-{\mathrm{e}}^{a\,1{}\mathrm{i}}\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{-c\,1{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}\,4{}\mathrm{i}\right)\right)}{b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}-c\,2{}\mathrm{i}}-1\right)}","Not used",1,"(2*(-exp(a*2i - c*2i))^(1/2)*(log((2*(-exp(a*2i)*exp(-c*2i))^(1/2)*(2*b*exp(a*2i)*exp(b*x*2i) - 4*b*exp(a*2i)*exp(-c*2i) + 2*b*exp(a*4i)*exp(-c*2i)*exp(b*x*2i)))/(b*(exp(a*2i)*exp(-c*2i) - 1)) - exp(a*1i)*exp(a*2i)*exp(-c*1i)*exp(b*x*2i)*4i) - log((2*(-exp(a*2i)*exp(-c*2i))^(1/2)*(2*b*exp(a*2i)*exp(b*x*2i) - 4*b*exp(a*2i)*exp(-c*2i) + 2*b*exp(a*4i)*exp(-c*2i)*exp(b*x*2i)))/(b - b*exp(a*2i)*exp(-c*2i)) - exp(a*1i)*exp(a*2i)*exp(-c*1i)*exp(b*x*2i)*4i)))/(b*(exp(a*2i - c*2i) - 1))","B"
146,1,249,33,7.872801,"\text{Not used}","int(1/(sin(a + b*x)*sin(c - b*x)),x)","\frac{2\,\sqrt{-{\mathrm{e}}^{a\,2{}\mathrm{i}+c\,2{}\mathrm{i}}}\,\left(\ln\left(\frac{2\,\sqrt{-{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{c\,2{}\mathrm{i}}}\,\left(-4\,b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{c\,2{}\mathrm{i}}+2\,b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}+2\,b\,{\mathrm{e}}^{a\,4{}\mathrm{i}}\,{\mathrm{e}}^{c\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}\right)}{b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{c\,2{}\mathrm{i}}-1\right)}+{\mathrm{e}}^{a\,1{}\mathrm{i}}\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{c\,1{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}\,4{}\mathrm{i}\right)-\ln\left(\frac{2\,\sqrt{-{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{c\,2{}\mathrm{i}}}\,\left(-4\,b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{c\,2{}\mathrm{i}}+2\,b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}+2\,b\,{\mathrm{e}}^{a\,4{}\mathrm{i}}\,{\mathrm{e}}^{c\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}\right)}{b-b\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{c\,2{}\mathrm{i}}}+{\mathrm{e}}^{a\,1{}\mathrm{i}}\,{\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{c\,1{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}\,4{}\mathrm{i}\right)\right)}{b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+c\,2{}\mathrm{i}}-1\right)}","Not used",1,"(2*(-exp(a*2i + c*2i))^(1/2)*(log((2*(-exp(a*2i)*exp(c*2i))^(1/2)*(2*b*exp(a*2i)*exp(b*x*2i) - 4*b*exp(a*2i)*exp(c*2i) + 2*b*exp(a*4i)*exp(c*2i)*exp(b*x*2i)))/(b*(exp(a*2i)*exp(c*2i) - 1)) + exp(a*1i)*exp(a*2i)*exp(c*1i)*exp(b*x*2i)*4i) - log((2*(-exp(a*2i)*exp(c*2i))^(1/2)*(2*b*exp(a*2i)*exp(b*x*2i) - 4*b*exp(a*2i)*exp(c*2i) + 2*b*exp(a*4i)*exp(c*2i)*exp(b*x*2i)))/(b - b*exp(a*2i)*exp(c*2i)) + exp(a*1i)*exp(a*2i)*exp(c*1i)*exp(b*x*2i)*4i)))/(b*(exp(a*2i + c*2i) - 1))","B"
147,1,20,13,2.562247,"\text{Not used}","int((sin(x)*tan(x))^(1/2),x)","-\frac{2\,\sin\left(x\right)}{\sqrt{\frac{1}{\cos\left(x\right)}}\,\sqrt{1-{\cos\left(x\right)}^2}}","Not used",1,"-(2*sin(x))/((1/cos(x))^(1/2)*(1 - cos(x)^2)^(1/2))","B"
148,0,-1,31,0.000000,"\text{Not used}","int((sin(x)*tan(x))^(3/2),x)","\int {\left(\sin\left(x\right)\,\mathrm{tan}\left(x\right)\right)}^{3/2} \,d x","Not used",1,"int((sin(x)*tan(x))^(3/2), x)","F"
149,0,-1,50,0.000000,"\text{Not used}","int((sin(x)*tan(x))^(5/2),x)","\int {\left(\sin\left(x\right)\,\mathrm{tan}\left(x\right)\right)}^{5/2} \,d x","Not used",1,"int((sin(x)*tan(x))^(5/2), x)","F"
150,1,18,13,2.653250,"\text{Not used}","int((cos(x)*cot(x))^(1/2),x)","\frac{2\,\left|\cos\left(x\right)\right|\,{\sin\left(x\right)}^{3/2}}{\left|\sin\left(x\right)\right|\,\cos\left(x\right)}","Not used",1,"(2*abs(cos(x))*sin(x)^(3/2))/(abs(sin(x))*cos(x))","B"
151,0,-1,31,0.000000,"\text{Not used}","int((cos(x)*cot(x))^(3/2),x)","\int {\left(\cos\left(x\right)\,\mathrm{cot}\left(x\right)\right)}^{3/2} \,d x","Not used",1,"int((cos(x)*cot(x))^(3/2), x)","F"
152,0,-1,50,0.000000,"\text{Not used}","int((cos(x)*cot(x))^(5/2),x)","\int {\left(\cos\left(x\right)\,\mathrm{cot}\left(x\right)\right)}^{5/2} \,d x","Not used",1,"int((cos(x)*cot(x))^(5/2), x)","F"
153,0,-1,58,0.000000,"\text{Not used}","int((x*cos(x))/(a + b*sin(x))^2,x)","\int \frac{x\,\cos\left(x\right)}{{\left(a+b\,\sin\left(x\right)\right)}^2} \,d x","Not used",1,"int((x*cos(x))/(a + b*sin(x))^2, x)","F"
154,0,-1,85,0.000000,"\text{Not used}","int((x*cos(x))/(a + b*sin(x))^3,x)","\int \frac{x\,\cos\left(x\right)}{{\left(a+b\,\sin\left(x\right)\right)}^3} \,d x","Not used",1,"int((x*cos(x))/(a + b*sin(x))^3, x)","F"
155,1,132,59,3.292402,"\text{Not used}","int((x*sin(x))/(a + b*cos(x))^2,x)","\frac{2\,x\,{\mathrm{e}}^{x\,1{}\mathrm{i}}}{b\,\left(2\,a\,{\mathrm{e}}^{x\,1{}\mathrm{i}}+2\,b\,{\mathrm{e}}^{x\,1{}\mathrm{i}}\,\cos\left(x\right)\right)}+\frac{\ln\left(2\,{\mathrm{e}}^{x\,1{}\mathrm{i}}-\frac{\left(b+a\,{\mathrm{e}}^{x\,1{}\mathrm{i}}\right)\,2{}\mathrm{i}}{\sqrt{a+b}\,\sqrt{b-a}}\right)}{b\,\sqrt{a+b}\,\sqrt{b-a}}-\frac{\ln\left(2\,{\mathrm{e}}^{x\,1{}\mathrm{i}}+\frac{\left(b+a\,{\mathrm{e}}^{x\,1{}\mathrm{i}}\right)\,2{}\mathrm{i}}{\sqrt{a+b}\,\sqrt{b-a}}\right)}{b\,\sqrt{a+b}\,\sqrt{b-a}}","Not used",1,"(2*x*exp(x*1i))/(b*(2*a*exp(x*1i) + 2*b*exp(x*1i)*cos(x))) + log(2*exp(x*1i) - ((b + a*exp(x*1i))*2i)/((a + b)^(1/2)*(b - a)^(1/2)))/(b*(a + b)^(1/2)*(b - a)^(1/2)) - log(2*exp(x*1i) + ((b + a*exp(x*1i))*2i)/((a + b)^(1/2)*(b - a)^(1/2)))/(b*(a + b)^(1/2)*(b - a)^(1/2))","B"
156,0,-1,88,0.000000,"\text{Not used}","int((x*sin(x))/(a + b*cos(x))^3,x)","\int \frac{x\,\sin\left(x\right)}{{\left(a+b\,\cos\left(x\right)\right)}^3} \,d x","Not used",1,"int((x*sin(x))/(a + b*cos(x))^3, x)","F"
157,0,-1,50,0.000000,"\text{Not used}","int(x/(cos(x)^2*(a + b*tan(x))^2),x)","\int \frac{x}{{\cos\left(x\right)}^2\,{\left(a+b\,\mathrm{tan}\left(x\right)\right)}^2} \,d x","Not used",1,"int(x/(cos(x)^2*(a + b*tan(x))^2), x)","F"
158,0,-1,50,0.000000,"\text{Not used}","int(x/(sin(x)^2*(a + b*cot(x))^2),x)","\int \frac{x}{{\sin\left(x\right)}^2\,{\left(a+b\,\mathrm{cot}\left(x\right)\right)}^2} \,d x","Not used",1,"int(x/(sin(x)^2*(a + b*cot(x))^2), x)","F"
159,1,24,32,2.560371,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b*tan(c + d*x)^2)),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\mathrm{tan}\left(c+d\,x\right)}{\sqrt{a}}\right)}{\sqrt{a}\,\sqrt{b}\,d}","Not used",1,"atan((b^(1/2)*tan(c + d*x))/a^(1/2))/(a^(1/2)*b^(1/2)*d)","B"
160,0,-1,211,0.000000,"\text{Not used}","int(x/(cos(c + d*x)^2*(a + b*tan(c + d*x)^2)),x)","\int \frac{x}{{\cos\left(c+d\,x\right)}^2\,\left(b\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\right)} \,d x","Not used",1,"int(x/(cos(c + d*x)^2*(a + b*tan(c + d*x)^2)), x)","F"
161,0,-1,337,0.000000,"\text{Not used}","int(x^2/(cos(c + d*x)^2*(a + b*tan(c + d*x)^2)),x)","\int \frac{x^2}{{\cos\left(c+d\,x\right)}^2\,\left(b\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\right)} \,d x","Not used",1,"int(x^2/(cos(c + d*x)^2*(a + b*tan(c + d*x)^2)), x)","F"
162,1,45,40,2.596872,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + c/cos(c + d*x)^2 + b*tan(c + d*x)^2)),x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(b+c\right)}{\sqrt{a\,b+a\,c+b\,c+c^2}}\right)}{d\,\sqrt{a\,b+a\,c+b\,c+c^2}}","Not used",1,"atan((tan(c + d*x)*(b + c))/(a*b + a*c + b*c + c^2)^(1/2))/(d*(a*b + a*c + b*c + c^2)^(1/2))","B"
163,0,-1,267,0.000000,"\text{Not used}","int(x/(cos(c + d*x)^2*(a + c/cos(c + d*x)^2 + b*tan(c + d*x)^2)),x)","\int \frac{x}{{\cos\left(c+d\,x\right)}^2\,\left(a+\frac{c}{{\cos\left(c+d\,x\right)}^2}+b\,{\mathrm{tan}\left(c+d\,x\right)}^2\right)} \,d x","Not used",1,"int(x/(cos(c + d*x)^2*(a + c/cos(c + d*x)^2 + b*tan(c + d*x)^2)), x)","F"
164,0,-1,407,0.000000,"\text{Not used}","int(x^2/(cos(c + d*x)^2*(a + c/cos(c + d*x)^2 + b*tan(c + d*x)^2)),x)","\int \frac{x^2}{{\cos\left(c+d\,x\right)}^2\,\left(a+\frac{c}{{\cos\left(c+d\,x\right)}^2}+b\,{\mathrm{tan}\left(c+d\,x\right)}^2\right)} \,d x","Not used",1,"int(x^2/(cos(c + d*x)^2*(a + c/cos(c + d*x)^2 + b*tan(c + d*x)^2)), x)","F"
165,1,111,155,3.052849,"\text{Not used}","int(x^3*(a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(1/2),x)","-\frac{\sqrt{-a\,\left(\sin\left(e+f\,x\right)-1\right)}\,\sqrt{c\,\left(\sin\left(e+f\,x\right)+1\right)}\,\left(6\,\cos\left(2\,e+2\,f\,x\right)-3\,f^2\,x^2+6\,f\,x\,\sin\left(2\,e+2\,f\,x\right)-3\,f^2\,x^2\,\cos\left(2\,e+2\,f\,x\right)-f^3\,x^3\,\sin\left(2\,e+2\,f\,x\right)+6\right)}{f^4\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-((-a*(sin(e + f*x) - 1))^(1/2)*(c*(sin(e + f*x) + 1))^(1/2)*(6*cos(2*e + 2*f*x) - 3*f^2*x^2 + 6*f*x*sin(2*e + 2*f*x) - 3*f^2*x^2*cos(2*e + 2*f*x) - f^3*x^3*sin(2*e + 2*f*x) + 6))/(f^4*(cos(2*e + 2*f*x) + 1))","B"
166,1,86,118,2.807581,"\text{Not used}","int(x^2*(a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(1/2),x)","\frac{\sqrt{-a\,\left(\sin\left(e+f\,x\right)-1\right)}\,\sqrt{c\,\left(\sin\left(e+f\,x\right)+1\right)}\,\left(2\,f\,x-2\,\sin\left(2\,e+2\,f\,x\right)+2\,f\,x\,\left(2\,{\cos\left(e+f\,x\right)}^2-1\right)+f^2\,x^2\,\sin\left(2\,e+2\,f\,x\right)\right)}{2\,f^3\,{\cos\left(e+f\,x\right)}^2}","Not used",1,"((-a*(sin(e + f*x) - 1))^(1/2)*(c*(sin(e + f*x) + 1))^(1/2)*(2*f*x - 2*sin(2*e + 2*f*x) + 2*f*x*(2*cos(e + f*x)^2 - 1) + f^2*x^2*sin(2*e + 2*f*x)))/(2*f^3*cos(e + f*x)^2)","B"
167,1,61,74,2.692050,"\text{Not used}","int(x*(a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(1/2),x)","\frac{\sqrt{-a\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(2\,{\cos\left(e+f\,x\right)}^2+f\,x\,\sin\left(2\,e+2\,f\,x\right)\right)\,\sqrt{c\,\left(\sin\left(e+f\,x\right)+1\right)}}{2\,f^2\,{\cos\left(e+f\,x\right)}^2}","Not used",1,"((-a*(sin(e + f*x) - 1))^(1/2)*(2*cos(e + f*x)^2 + f*x*sin(2*e + 2*f*x))*(c*(sin(e + f*x) + 1))^(1/2))/(2*f^2*cos(e + f*x)^2)","B"
168,0,-1,86,0.000000,"\text{Not used}","int(((a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(1/2))/x,x)","\int \frac{\sqrt{a-a\,\sin\left(e+f\,x\right)}\,\sqrt{c+c\,\sin\left(e+f\,x\right)}}{x} \,d x","Not used",1,"int(((a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(1/2))/x, x)","F"
169,0,-1,123,0.000000,"\text{Not used}","int(((a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(1/2))/x^2,x)","\int \frac{\sqrt{a-a\,\sin\left(e+f\,x\right)}\,\sqrt{c+c\,\sin\left(e+f\,x\right)}}{x^2} \,d x","Not used",1,"int(((a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(1/2))/x^2, x)","F"
170,0,-1,176,0.000000,"\text{Not used}","int(((a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(1/2))/x^3,x)","\int \frac{\sqrt{a-a\,\sin\left(e+f\,x\right)}\,\sqrt{c+c\,\sin\left(e+f\,x\right)}}{x^3} \,d x","Not used",1,"int(((a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(1/2))/x^3, x)","F"
171,1,216,393,4.147235,"\text{Not used}","int(x^3*(a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(3/2),x)","-\frac{c\,\sqrt{-a\,\left(\sin\left(e+f\,x\right)-1\right)}\,\sqrt{c\,\left(\sin\left(e+f\,x\right)+1\right)}\,\left(3\,\sin\left(e+f\,x\right)+96\,\cos\left(2\,e+2\,f\,x\right)+3\,\sin\left(3\,e+3\,f\,x\right)-48\,f^2\,x^2-6\,f\,x\,\cos\left(3\,e+3\,f\,x\right)+96\,f\,x\,\sin\left(2\,e+2\,f\,x\right)+4\,f^3\,x^3\,\cos\left(e+f\,x\right)-6\,f^2\,x^2\,\sin\left(e+f\,x\right)-6\,f\,x\,\cos\left(e+f\,x\right)-48\,f^2\,x^2\,\cos\left(2\,e+2\,f\,x\right)+4\,f^3\,x^3\,\cos\left(3\,e+3\,f\,x\right)-6\,f^2\,x^2\,\sin\left(3\,e+3\,f\,x\right)-16\,f^3\,x^3\,\sin\left(2\,e+2\,f\,x\right)+96\right)}{16\,f^4\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(c*(-a*(sin(e + f*x) - 1))^(1/2)*(c*(sin(e + f*x) + 1))^(1/2)*(3*sin(e + f*x) + 96*cos(2*e + 2*f*x) + 3*sin(3*e + 3*f*x) - 48*f^2*x^2 - 6*f*x*cos(3*e + 3*f*x) + 96*f*x*sin(2*e + 2*f*x) + 4*f^3*x^3*cos(e + f*x) - 6*f^2*x^2*sin(e + f*x) - 6*f*x*cos(e + f*x) - 48*f^2*x^2*cos(2*e + 2*f*x) + 4*f^3*x^3*cos(3*e + 3*f*x) - 6*f^2*x^2*sin(3*e + 3*f*x) - 16*f^3*x^3*sin(2*e + 2*f*x) + 96))/(16*f^4*(cos(2*e + 2*f*x) + 1))","B"
172,1,159,265,3.765453,"\text{Not used}","int(x^2*(a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(3/2),x)","\frac{c\,\sqrt{-a\,\left(\sin\left(e+f\,x\right)-1\right)}\,\sqrt{c\,\left(\sin\left(e+f\,x\right)+1\right)}\,\left(\cos\left(e+f\,x\right)+\cos\left(3\,e+3\,f\,x\right)-16\,\sin\left(2\,e+2\,f\,x\right)+16\,f\,x+16\,f\,x\,\cos\left(2\,e+2\,f\,x\right)+2\,f\,x\,\sin\left(3\,e+3\,f\,x\right)-2\,f^2\,x^2\,\cos\left(e+f\,x\right)+2\,f\,x\,\sin\left(e+f\,x\right)-2\,f^2\,x^2\,\cos\left(3\,e+3\,f\,x\right)+8\,f^2\,x^2\,\sin\left(2\,e+2\,f\,x\right)\right)}{8\,f^3\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"(c*(-a*(sin(e + f*x) - 1))^(1/2)*(c*(sin(e + f*x) + 1))^(1/2)*(cos(e + f*x) + cos(3*e + 3*f*x) - 16*sin(2*e + 2*f*x) + 16*f*x + 16*f*x*cos(2*e + 2*f*x) + 2*f*x*sin(3*e + 3*f*x) - 2*f^2*x^2*cos(e + f*x) + 2*f*x*sin(e + f*x) - 2*f^2*x^2*cos(3*e + 3*f*x) + 8*f^2*x^2*sin(2*e + 2*f*x)))/(8*f^3*(cos(2*e + 2*f*x) + 1))","B"
173,1,123,168,1.205591,"\text{Not used}","int(x*(a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(3/2),x)","-\frac{c\,\sqrt{-a\,\left(\sin\left(e+f\,x\right)-1\right)}\,\sqrt{c\,\left(\sin\left(e+f\,x\right)+1\right)}\,\left(-16\,{\sin\left(e+f\,x\right)}^2+\sin\left(e+f\,x\right)+\sin\left(3\,e+3\,f\,x\right)+8\,f\,x\,\sin\left(2\,e+2\,f\,x\right)+2\,f\,x\,\left(2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)+2\,f\,x\,\left(2\,{\sin\left(\frac{3\,e}{2}+\frac{3\,f\,x}{2}\right)}^2-1\right)+16\right)}{8\,f^2\,\left(2\,{\sin\left(e+f\,x\right)}^2-2\right)}","Not used",1,"-(c*(-a*(sin(e + f*x) - 1))^(1/2)*(c*(sin(e + f*x) + 1))^(1/2)*(sin(e + f*x) + sin(3*e + 3*f*x) - 16*sin(e + f*x)^2 + 8*f*x*sin(2*e + 2*f*x) + 2*f*x*(2*sin(e/2 + (f*x)/2)^2 - 1) + 2*f*x*(2*sin((3*e)/2 + (3*f*x)/2)^2 - 1) + 16))/(8*f^2*(2*sin(e + f*x)^2 - 2))","B"
174,0,-1,186,0.000000,"\text{Not used}","int(((a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(3/2))/x,x)","\int \frac{\sqrt{a-a\,\sin\left(e+f\,x\right)}\,{\left(c+c\,\sin\left(e+f\,x\right)\right)}^{3/2}}{x} \,d x","Not used",1,"int(((a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(3/2))/x, x)","F"
175,0,-1,273,0.000000,"\text{Not used}","int(((a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(3/2))/x^2,x)","\int \frac{\sqrt{a-a\,\sin\left(e+f\,x\right)}\,{\left(c+c\,\sin\left(e+f\,x\right)\right)}^{3/2}}{x^2} \,d x","Not used",1,"int(((a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(3/2))/x^2, x)","F"
176,0,-1,385,0.000000,"\text{Not used}","int(((a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(3/2))/x^3,x)","\int \frac{\sqrt{a-a\,\sin\left(e+f\,x\right)}\,{\left(c+c\,\sin\left(e+f\,x\right)\right)}^{3/2}}{x^3} \,d x","Not used",1,"int(((a - a*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))^(3/2))/x^3, x)","F"
177,0,-1,767,0.000000,"\text{Not used}","int(((g + h*x)^3*(a - a*sin(e + f*x))^(1/2))/(c + c*sin(e + f*x))^(1/2),x)","\int \frac{{\left(g+h\,x\right)}^3\,\sqrt{a-a\,\sin\left(e+f\,x\right)}}{\sqrt{c+c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((g + h*x)^3*(a - a*sin(e + f*x))^(1/2))/(c + c*sin(e + f*x))^(1/2), x)","F"
178,0,-1,555,0.000000,"\text{Not used}","int(((g + h*x)^2*(a - a*sin(e + f*x))^(1/2))/(c + c*sin(e + f*x))^(1/2),x)","\int \frac{{\left(g+h\,x\right)}^2\,\sqrt{a-a\,\sin\left(e+f\,x\right)}}{\sqrt{c+c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((g + h*x)^2*(a - a*sin(e + f*x))^(1/2))/(c + c*sin(e + f*x))^(1/2), x)","F"
179,0,-1,355,0.000000,"\text{Not used}","int(((g + h*x)*(a - a*sin(e + f*x))^(1/2))/(c + c*sin(e + f*x))^(1/2),x)","\int \frac{\left(g+h\,x\right)\,\sqrt{a-a\,\sin\left(e+f\,x\right)}}{\sqrt{c+c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((g + h*x)*(a - a*sin(e + f*x))^(1/2))/(c + c*sin(e + f*x))^(1/2), x)","F"
180,0,-1,110,0.000000,"\text{Not used}","int((a - a*sin(e + f*x))^(1/2)/((g + h*x)*(c + c*sin(e + f*x))^(1/2)),x)","\int \frac{\sqrt{a-a\,\sin\left(e+f\,x\right)}}{\left(g+h\,x\right)\,\sqrt{c+c\,\sin\left(e+f\,x\right)}} \,d x","Not used",0,"int((a - a*sin(e + f*x))^(1/2)/((g + h*x)*(c + c*sin(e + f*x))^(1/2)), x)","F"
181,0,-1,536,0.000000,"\text{Not used}","int((x^3*(a - a*sin(e + f*x))^(1/2))/(c + c*sin(e + f*x))^(3/2),x)","\int \frac{x^3\,\sqrt{a-a\,\sin\left(e+f\,x\right)}}{{\left(c+c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((x^3*(a - a*sin(e + f*x))^(1/2))/(c + c*sin(e + f*x))^(3/2), x)","F"
182,0,-1,280,0.000000,"\text{Not used}","int((x^2*(a - a*sin(e + f*x))^(1/2))/(c + c*sin(e + f*x))^(3/2),x)","\int \frac{x^2\,\sqrt{a-a\,\sin\left(e+f\,x\right)}}{{\left(c+c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((x^2*(a - a*sin(e + f*x))^(1/2))/(c + c*sin(e + f*x))^(3/2), x)","F"
183,1,88,171,3.315692,"\text{Not used}","int((x*(a - a*sin(e + f*x))^(1/2))/(c + c*sin(e + f*x))^(3/2),x)","-\frac{\sqrt{-a\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(\cos\left(2\,e+2\,f\,x\right)+2\,f\,x\,\cos\left(e+f\,x\right)+1-\cos\left(e+f\,x\right)\,2{}\mathrm{i}-\sin\left(2\,e+2\,f\,x\right)\,1{}\mathrm{i}\right)}{c\,f^2\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)\,\sqrt{c\,\left(\sin\left(e+f\,x\right)+1\right)}}","Not used",1,"-((-a*(sin(e + f*x) - 1))^(1/2)*(cos(2*e + 2*f*x) - cos(e + f*x)*2i - sin(2*e + 2*f*x)*1i + 2*f*x*cos(e + f*x) + 1))/(c*f^2*(cos(2*e + 2*f*x) + 1)*(c*(sin(e + f*x) + 1))^(1/2))","B"
184,0,-1,300,0.000000,"\text{Not used}","int((z^2*(cos(z) + 1)^(1/2))/(1 - cos(z))^(1/2),z)","\int \frac{z^2\,\sqrt{\cos\left(z\right)+1}}{\sqrt{1-\cos\left(z\right)}} \,d z","Not used",1,"int((z^2*(cos(z) + 1)^(1/2))/(1 - cos(z))^(1/2), z)","F"
185,1,54,18,2.475670,"\text{Not used}","int((a + a*cos(x))*(A + B/cos(x)),x)","2\,A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)+2\,B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)+2\,B\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)+A\,a\,\sin\left(x\right)","Not used",1,"2*A*a*atan(sin(x/2)/cos(x/2)) + 2*B*a*atan(sin(x/2)/cos(x/2)) + 2*B*a*atanh(sin(x/2)/cos(x/2)) + A*a*sin(x)","B"
186,1,403,57,2.463591,"\text{Not used}","int((a + a*cos(x))^2*(A + B/cos(x)),x)","\frac{\left(3\,A\,a^2+2\,B\,a^2\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+\left(5\,A\,a^2+2\,B\,a^2\right)\,\mathrm{tan}\left(\frac{x}{2}\right)}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}+a^2\,\mathrm{atan}\left(\frac{216\,A^3\,a^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{216\,A^3\,a^6+864\,A^2\,B\,a^6+1248\,A\,B^2\,a^6+640\,B^3\,a^6}+\frac{640\,B^3\,a^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{216\,A^3\,a^6+864\,A^2\,B\,a^6+1248\,A\,B^2\,a^6+640\,B^3\,a^6}+\frac{1248\,A\,B^2\,a^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{216\,A^3\,a^6+864\,A^2\,B\,a^6+1248\,A\,B^2\,a^6+640\,B^3\,a^6}+\frac{864\,A^2\,B\,a^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{216\,A^3\,a^6+864\,A^2\,B\,a^6+1248\,A\,B^2\,a^6+640\,B^3\,a^6}\right)\,\left(3\,A+4\,B\right)+2\,B\,a^2\,\mathrm{atanh}\left(\frac{320\,B^3\,a^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{144\,A^2\,B\,a^6+384\,A\,B^2\,a^6+320\,B^3\,a^6}+\frac{384\,A\,B^2\,a^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{144\,A^2\,B\,a^6+384\,A\,B^2\,a^6+320\,B^3\,a^6}+\frac{144\,A^2\,B\,a^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{144\,A^2\,B\,a^6+384\,A\,B^2\,a^6+320\,B^3\,a^6}\right)","Not used",1,"(tan(x/2)^3*(3*A*a^2 + 2*B*a^2) + tan(x/2)*(5*A*a^2 + 2*B*a^2))/(2*tan(x/2)^2 + tan(x/2)^4 + 1) + a^2*atan((216*A^3*a^6*tan(x/2))/(216*A^3*a^6 + 640*B^3*a^6 + 1248*A*B^2*a^6 + 864*A^2*B*a^6) + (640*B^3*a^6*tan(x/2))/(216*A^3*a^6 + 640*B^3*a^6 + 1248*A*B^2*a^6 + 864*A^2*B*a^6) + (1248*A*B^2*a^6*tan(x/2))/(216*A^3*a^6 + 640*B^3*a^6 + 1248*A*B^2*a^6 + 864*A^2*B*a^6) + (864*A^2*B*a^6*tan(x/2))/(216*A^3*a^6 + 640*B^3*a^6 + 1248*A*B^2*a^6 + 864*A^2*B*a^6))*(3*A + 4*B) + 2*B*a^2*atanh((320*B^3*a^6*tan(x/2))/(320*B^3*a^6 + 384*A*B^2*a^6 + 144*A^2*B*a^6) + (384*A*B^2*a^6*tan(x/2))/(320*B^3*a^6 + 384*A*B^2*a^6 + 144*A^2*B*a^6) + (144*A^2*B*a^6*tan(x/2))/(320*B^3*a^6 + 384*A*B^2*a^6 + 144*A^2*B*a^6))","B"
187,1,431,75,2.476785,"\text{Not used}","int((a + a*cos(x))^3*(A + B/cos(x)),x)","\frac{\left(5\,A\,a^3+5\,B\,a^3\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+\left(\frac{40\,A\,a^3}{3}+12\,B\,a^3\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+\left(11\,A\,a^3+7\,B\,a^3\right)\,\mathrm{tan}\left(\frac{x}{2}\right)}{{\mathrm{tan}\left(\frac{x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}+a^3\,\mathrm{atan}\left(\frac{1000\,A^3\,a^9\,\mathrm{tan}\left(\frac{x}{2}\right)}{1000\,A^3\,a^9+4200\,A^2\,B\,a^9+6040\,A\,B^2\,a^9+2968\,B^3\,a^9}+\frac{2968\,B^3\,a^9\,\mathrm{tan}\left(\frac{x}{2}\right)}{1000\,A^3\,a^9+4200\,A^2\,B\,a^9+6040\,A\,B^2\,a^9+2968\,B^3\,a^9}+\frac{6040\,A\,B^2\,a^9\,\mathrm{tan}\left(\frac{x}{2}\right)}{1000\,A^3\,a^9+4200\,A^2\,B\,a^9+6040\,A\,B^2\,a^9+2968\,B^3\,a^9}+\frac{4200\,A^2\,B\,a^9\,\mathrm{tan}\left(\frac{x}{2}\right)}{1000\,A^3\,a^9+4200\,A^2\,B\,a^9+6040\,A\,B^2\,a^9+2968\,B^3\,a^9}\right)\,\left(5\,A+7\,B\right)+2\,B\,a^3\,\mathrm{atanh}\left(\frac{848\,B^3\,a^9\,\mathrm{tan}\left(\frac{x}{2}\right)}{400\,A^2\,B\,a^9+1120\,A\,B^2\,a^9+848\,B^3\,a^9}+\frac{1120\,A\,B^2\,a^9\,\mathrm{tan}\left(\frac{x}{2}\right)}{400\,A^2\,B\,a^9+1120\,A\,B^2\,a^9+848\,B^3\,a^9}+\frac{400\,A^2\,B\,a^9\,\mathrm{tan}\left(\frac{x}{2}\right)}{400\,A^2\,B\,a^9+1120\,A\,B^2\,a^9+848\,B^3\,a^9}\right)","Not used",1,"(tan(x/2)^5*(5*A*a^3 + 5*B*a^3) + tan(x/2)^3*((40*A*a^3)/3 + 12*B*a^3) + tan(x/2)*(11*A*a^3 + 7*B*a^3))/(3*tan(x/2)^2 + 3*tan(x/2)^4 + tan(x/2)^6 + 1) + a^3*atan((1000*A^3*a^9*tan(x/2))/(1000*A^3*a^9 + 2968*B^3*a^9 + 6040*A*B^2*a^9 + 4200*A^2*B*a^9) + (2968*B^3*a^9*tan(x/2))/(1000*A^3*a^9 + 2968*B^3*a^9 + 6040*A*B^2*a^9 + 4200*A^2*B*a^9) + (6040*A*B^2*a^9*tan(x/2))/(1000*A^3*a^9 + 2968*B^3*a^9 + 6040*A*B^2*a^9 + 4200*A^2*B*a^9) + (4200*A^2*B*a^9*tan(x/2))/(1000*A^3*a^9 + 2968*B^3*a^9 + 6040*A*B^2*a^9 + 4200*A^2*B*a^9))*(5*A + 7*B) + 2*B*a^3*atanh((848*B^3*a^9*tan(x/2))/(848*B^3*a^9 + 1120*A*B^2*a^9 + 400*A^2*B*a^9) + (1120*A*B^2*a^9*tan(x/2))/(848*B^3*a^9 + 1120*A*B^2*a^9 + 400*A^2*B*a^9) + (400*A^2*B*a^9*tan(x/2))/(848*B^3*a^9 + 1120*A*B^2*a^9 + 400*A^2*B*a^9))","B"
188,1,460,104,2.523450,"\text{Not used}","int((a + a*cos(x))^4*(A + B/cos(x)),x)","\frac{\left(\frac{35\,A\,a^4}{4}+10\,B\,a^4\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7+\left(\frac{385\,A\,a^4}{12}+\frac{106\,B\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+\left(\frac{511\,A\,a^4}{12}+\frac{130\,B\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+\left(\frac{93\,A\,a^4}{4}+18\,B\,a^4\right)\,\mathrm{tan}\left(\frac{x}{2}\right)}{{\mathrm{tan}\left(\frac{x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}+\frac{a^4\,\mathrm{atan}\left(\frac{42875\,A^3\,a^{12}\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,\left(\frac{42875\,A^3\,a^{12}}{8}+22050\,A^2\,B\,a^{12}+30520\,A\,B^2\,a^{12}+14208\,B^3\,a^{12}\right)}+\frac{14208\,B^3\,a^{12}\,\mathrm{tan}\left(\frac{x}{2}\right)}{\frac{42875\,A^3\,a^{12}}{8}+22050\,A^2\,B\,a^{12}+30520\,A\,B^2\,a^{12}+14208\,B^3\,a^{12}}+\frac{30520\,A\,B^2\,a^{12}\,\mathrm{tan}\left(\frac{x}{2}\right)}{\frac{42875\,A^3\,a^{12}}{8}+22050\,A^2\,B\,a^{12}+30520\,A\,B^2\,a^{12}+14208\,B^3\,a^{12}}+\frac{22050\,A^2\,B\,a^{12}\,\mathrm{tan}\left(\frac{x}{2}\right)}{\frac{42875\,A^3\,a^{12}}{8}+22050\,A^2\,B\,a^{12}+30520\,A\,B^2\,a^{12}+14208\,B^3\,a^{12}}\right)\,\left(35\,A+48\,B\right)}{4}+2\,B\,a^4\,\mathrm{atanh}\left(\frac{2368\,B^3\,a^{12}\,\mathrm{tan}\left(\frac{x}{2}\right)}{1225\,A^2\,B\,a^{12}+3360\,A\,B^2\,a^{12}+2368\,B^3\,a^{12}}+\frac{3360\,A\,B^2\,a^{12}\,\mathrm{tan}\left(\frac{x}{2}\right)}{1225\,A^2\,B\,a^{12}+3360\,A\,B^2\,a^{12}+2368\,B^3\,a^{12}}+\frac{1225\,A^2\,B\,a^{12}\,\mathrm{tan}\left(\frac{x}{2}\right)}{1225\,A^2\,B\,a^{12}+3360\,A\,B^2\,a^{12}+2368\,B^3\,a^{12}}\right)","Not used",1,"(tan(x/2)^7*((35*A*a^4)/4 + 10*B*a^4) + tan(x/2)^5*((385*A*a^4)/12 + (106*B*a^4)/3) + tan(x/2)^3*((511*A*a^4)/12 + (130*B*a^4)/3) + tan(x/2)*((93*A*a^4)/4 + 18*B*a^4))/(4*tan(x/2)^2 + 6*tan(x/2)^4 + 4*tan(x/2)^6 + tan(x/2)^8 + 1) + (a^4*atan((42875*A^3*a^12*tan(x/2))/(8*((42875*A^3*a^12)/8 + 14208*B^3*a^12 + 30520*A*B^2*a^12 + 22050*A^2*B*a^12)) + (14208*B^3*a^12*tan(x/2))/((42875*A^3*a^12)/8 + 14208*B^3*a^12 + 30520*A*B^2*a^12 + 22050*A^2*B*a^12) + (30520*A*B^2*a^12*tan(x/2))/((42875*A^3*a^12)/8 + 14208*B^3*a^12 + 30520*A*B^2*a^12 + 22050*A^2*B*a^12) + (22050*A^2*B*a^12*tan(x/2))/((42875*A^3*a^12)/8 + 14208*B^3*a^12 + 30520*A*B^2*a^12 + 22050*A^2*B*a^12))*(35*A + 48*B))/4 + 2*B*a^4*atanh((2368*B^3*a^12*tan(x/2))/(2368*B^3*a^12 + 3360*A*B^2*a^12 + 1225*A^2*B*a^12) + (3360*A*B^2*a^12*tan(x/2))/(2368*B^3*a^12 + 3360*A*B^2*a^12 + 1225*A^2*B*a^12) + (1225*A^2*B*a^12*tan(x/2))/(2368*B^3*a^12 + 3360*A*B^2*a^12 + 1225*A^2*B*a^12))","B"
189,1,25,25,2.363648,"\text{Not used}","int((A + B/cos(x))/(a + a*cos(x)),x)","\frac{2\,B\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A-B\right)}{a}","Not used",1,"(2*B*atanh(tan(x/2)))/a + (tan(x/2)*(A - B))/a","B"
190,1,50,48,2.349442,"\text{Not used}","int((A + B/cos(x))/(a + a*cos(x))^2,x)","\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{A-B}{2\,a^2}-\frac{B}{a^2}\right)+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(A-B\right)}{6\,a^2}+\frac{2\,B\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a^2}","Not used",1,"tan(x/2)*((A - B)/(2*a^2) - B/a^2) + (tan(x/2)^3*(A - B))/(6*a^2) + (2*B*atanh(tan(x/2)))/a^2","B"
191,1,92,75,2.365627,"\text{Not used}","int((A + B/cos(x))/(a + a*cos(x))^3,x)","{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(\frac{A-B}{12\,a^3}+\frac{A-3\,B}{12\,a^3}\right)+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{A-B}{4\,a^3}+\frac{A-3\,B}{4\,a^3}-\frac{A+3\,B}{4\,a^3}\right)+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(A-B\right)}{20\,a^3}+\frac{2\,B\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a^3}","Not used",1,"tan(x/2)^3*((A - B)/(12*a^3) + (A - 3*B)/(12*a^3)) + tan(x/2)*((A - B)/(4*a^3) + (A - 3*B)/(4*a^3) - (A + 3*B)/(4*a^3)) + (tan(x/2)^5*(A - B))/(20*a^3) + (2*B*atanh(tan(x/2)))/a^3","B"
192,1,140,96,2.339666,"\text{Not used}","int((A + B/cos(x))/(a + a*cos(x))^4,x)","\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{A-B}{8\,a^4}-\frac{3\,B}{4\,a^4}+\frac{2\,A-4\,B}{8\,a^4}-\frac{2\,A+4\,B}{8\,a^4}\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(\frac{A-B}{40\,a^4}+\frac{2\,A-4\,B}{40\,a^4}\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(\frac{A-B}{24\,a^4}-\frac{B}{4\,a^4}+\frac{2\,A-4\,B}{24\,a^4}\right)+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^7\,\left(A-B\right)}{56\,a^4}+\frac{2\,B\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a^4}","Not used",1,"tan(x/2)*((A - B)/(8*a^4) - (3*B)/(4*a^4) + (2*A - 4*B)/(8*a^4) - (2*A + 4*B)/(8*a^4)) + tan(x/2)^5*((A - B)/(40*a^4) + (2*A - 4*B)/(40*a^4)) + tan(x/2)^3*((A - B)/(24*a^4) - B/(4*a^4) + (2*A - 4*B)/(24*a^4)) + (tan(x/2)^7*(A - B))/(56*a^4) + (2*B*atanh(tan(x/2)))/a^4","B"
193,0,-1,98,0.000000,"\text{Not used}","int((a + a*cos(x))^(5/2)*(A + B/cos(x)),x)","\int {\left(a+a\,\cos\left(x\right)\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(x\right)}\right) \,d x","Not used",1,"int((a + a*cos(x))^(5/2)*(A + B/cos(x)), x)","F"
194,0,-1,72,0.000000,"\text{Not used}","int((a + a*cos(x))^(3/2)*(A + B/cos(x)),x)","\int {\left(a+a\,\cos\left(x\right)\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(x\right)}\right) \,d x","Not used",1,"int((a + a*cos(x))^(3/2)*(A + B/cos(x)), x)","F"
195,0,-1,44,0.000000,"\text{Not used}","int((a + a*cos(x))^(1/2)*(A + B/cos(x)),x)","\int \sqrt{a+a\,\cos\left(x\right)}\,\left(A+\frac{B}{\cos\left(x\right)}\right) \,d x","Not used",1,"int((a + a*cos(x))^(1/2)*(A + B/cos(x)), x)","F"
196,0,-1,68,0.000000,"\text{Not used}","int((A + B/cos(x))/(a + a*cos(x))^(1/2),x)","\int \frac{A+\frac{B}{\cos\left(x\right)}}{\sqrt{a+a\,\cos\left(x\right)}} \,d x","Not used",1,"int((A + B/cos(x))/(a + a*cos(x))^(1/2), x)","F"
197,0,-1,92,0.000000,"\text{Not used}","int((A + B/cos(x))/(a + a*cos(x))^(3/2),x)","\int \frac{A+\frac{B}{\cos\left(x\right)}}{{\left(a+a\,\cos\left(x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(x))/(a + a*cos(x))^(3/2), x)","F"
198,0,-1,120,0.000000,"\text{Not used}","int((A + B/cos(x))/(a + a*cos(x))^(5/2),x)","\int \frac{A+\frac{B}{\cos\left(x\right)}}{{\left(a+a\,\cos\left(x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(x))/(a + a*cos(x))^(5/2), x)","F"
199,0,-1,25,0.000000,"\text{Not used}","int((x*(b + a*sin(x)))/(a + b*sin(x))^2,x)","\int \frac{x\,\left(b+a\,\sin\left(x\right)\right)}{{\left(a+b\,\sin\left(x\right)\right)}^2} \,d x","Not used",1,"int((x*(b + a*sin(x)))/(a + b*sin(x))^2, x)","F"
200,1,68,24,2.744962,"\text{Not used}","int((x*(b + a*cos(x)))/(a + b*cos(x))^2,x)","\frac{\ln\left(b+2\,a\,{\mathrm{e}}^{x\,1{}\mathrm{i}}+b\,{\mathrm{e}}^{x\,2{}\mathrm{i}}\right)}{b}-\frac{x\,2{}\mathrm{i}}{b}+\frac{x\,2{}\mathrm{i}+\frac{a\,x\,{\mathrm{e}}^{x\,1{}\mathrm{i}}\,2{}\mathrm{i}}{b}}{b+2\,a\,{\mathrm{e}}^{x\,1{}\mathrm{i}}+b\,{\mathrm{e}}^{x\,2{}\mathrm{i}}}","Not used",1,"log(b + 2*a*exp(x*1i) + b*exp(x*2i))/b - (x*2i)/b + (x*2i + (a*x*exp(x*1i)*2i)/b)/(b + 2*a*exp(x*1i) + b*exp(x*2i))","B"
201,1,8,8,2.307112,"\text{Not used}","int(-(sin(x)^2 + 1)/(sin(x)^2 - 1),x)","2\,\mathrm{tan}\left(x\right)-x","Not used",1,"2*tan(x) - x","B"
202,1,26,36,2.323686,"\text{Not used}","int(-(sin(x)^2 - 1)/(sin(x)^2 + 1),x)","\sqrt{2}\,\left(x-\mathrm{atan}\left(\mathrm{tan}\left(x\right)\right)\right)-x+\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,\mathrm{tan}\left(x\right)\right)","Not used",1,"2^(1/2)*(x - atan(tan(x))) - x + 2^(1/2)*atan(2^(1/2)*tan(x))","B"
203,1,8,8,2.286593,"\text{Not used}","int(-(cos(x)^2 + 1)/(cos(x)^2 - 1),x)","-x-2\,\mathrm{cot}\left(x\right)","Not used",1,"- x - 2*cot(x)","B"
204,1,27,37,2.285987,"\text{Not used}","int(-(cos(x)^2 - 1)/(cos(x)^2 + 1),x)","\sqrt{2}\,\left(x-\mathrm{atan}\left(\mathrm{tan}\left(x\right)\right)\right)-x+\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)}{2}\right)","Not used",1,"2^(1/2)*(x - atan(tan(x))) - x + 2^(1/2)*atan((2^(1/2)*tan(x))/2)","B"
205,1,13,14,2.474343,"\text{Not used}","int((sin(x)^2 + c^2/d^2 - 1)/(c + d*cos(x)),x)","\frac{c\,x-d\,\sin\left(x\right)}{d^2}","Not used",1,"(c*x - d*sin(x))/d^2","B"
206,1,2429,105,4.042628,"\text{Not used}","int((a + b*sin(x)^2)/(c + d*cos(x)),x)","\frac{b\,c^2\,d\,\sin\left(x\right)}{d^4-c^2\,d^2}-\frac{b\,d^3\,\sin\left(x\right)}{d^4-c^2\,d^2}-\frac{2\,b\,c^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{d^4-c^2\,d^2}+\frac{2\,b\,c\,d^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{d^4-c^2\,d^2}-\frac{a\,d^2\,\mathrm{atan}\left(\frac{a^2\,d^7\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-b^2\,c^5\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}-b^2\,c^7\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+b^2\,d^7\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-a^2\,c\,d^4\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}+a^2\,c\,d^6\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-b^2\,c\,d^4\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}+b^2\,c\,d^6\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-a^2\,c^2\,d^5\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-a^2\,c^3\,d^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-b^2\,c^2\,d^5\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+b^2\,c^3\,d^2\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,4{}\mathrm{i}-b^2\,c^3\,d^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}+b^2\,c^4\,d^3\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+b^2\,c^5\,d^2\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,5{}\mathrm{i}+a\,b\,d^7\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-a\,b\,c\,d^4\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,4{}\mathrm{i}+a\,b\,c\,d^6\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-a\,b\,c^2\,d^5\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}+a\,b\,c^3\,d^2\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,4{}\mathrm{i}-a\,b\,c^3\,d^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}+a\,b\,c^4\,d^3\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+a\,b\,c^5\,d^2\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{\cos\left(\frac{x}{2}\right)\,a^2\,c^4\,d^4-2\,\cos\left(\frac{x}{2}\right)\,a^2\,c^2\,d^6+\cos\left(\frac{x}{2}\right)\,a^2\,d^8-2\,\cos\left(\frac{x}{2}\right)\,a\,b\,c^6\,d^2+6\,\cos\left(\frac{x}{2}\right)\,a\,b\,c^4\,d^4-6\,\cos\left(\frac{x}{2}\right)\,a\,b\,c^2\,d^6+2\,\cos\left(\frac{x}{2}\right)\,a\,b\,d^8-\cos\left(\frac{x}{2}\right)\,b^2\,c^6\,d^2+3\,\cos\left(\frac{x}{2}\right)\,b^2\,c^4\,d^4-3\,\cos\left(\frac{x}{2}\right)\,b^2\,c^2\,d^6+\cos\left(\frac{x}{2}\right)\,b^2\,d^8}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{d^4-c^2\,d^2}+\frac{b\,c^2\,\mathrm{atan}\left(\frac{a^2\,d^7\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-b^2\,c^5\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}-b^2\,c^7\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+b^2\,d^7\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-a^2\,c\,d^4\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}+a^2\,c\,d^6\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-b^2\,c\,d^4\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}+b^2\,c\,d^6\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-a^2\,c^2\,d^5\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-a^2\,c^3\,d^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-b^2\,c^2\,d^5\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+b^2\,c^3\,d^2\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,4{}\mathrm{i}-b^2\,c^3\,d^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}+b^2\,c^4\,d^3\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+b^2\,c^5\,d^2\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,5{}\mathrm{i}+a\,b\,d^7\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-a\,b\,c\,d^4\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,4{}\mathrm{i}+a\,b\,c\,d^6\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-a\,b\,c^2\,d^5\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}+a\,b\,c^3\,d^2\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,4{}\mathrm{i}-a\,b\,c^3\,d^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}+a\,b\,c^4\,d^3\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+a\,b\,c^5\,d^2\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{\cos\left(\frac{x}{2}\right)\,a^2\,c^4\,d^4-2\,\cos\left(\frac{x}{2}\right)\,a^2\,c^2\,d^6+\cos\left(\frac{x}{2}\right)\,a^2\,d^8-2\,\cos\left(\frac{x}{2}\right)\,a\,b\,c^6\,d^2+6\,\cos\left(\frac{x}{2}\right)\,a\,b\,c^4\,d^4-6\,\cos\left(\frac{x}{2}\right)\,a\,b\,c^2\,d^6+2\,\cos\left(\frac{x}{2}\right)\,a\,b\,d^8-\cos\left(\frac{x}{2}\right)\,b^2\,c^6\,d^2+3\,\cos\left(\frac{x}{2}\right)\,b^2\,c^4\,d^4-3\,\cos\left(\frac{x}{2}\right)\,b^2\,c^2\,d^6+\cos\left(\frac{x}{2}\right)\,b^2\,d^8}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{d^4-c^2\,d^2}-\frac{b\,d^2\,\mathrm{atan}\left(\frac{a^2\,d^7\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-b^2\,c^5\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}-b^2\,c^7\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+b^2\,d^7\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-a^2\,c\,d^4\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}+a^2\,c\,d^6\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-b^2\,c\,d^4\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}+b^2\,c\,d^6\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-a^2\,c^2\,d^5\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-a^2\,c^3\,d^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-b^2\,c^2\,d^5\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+b^2\,c^3\,d^2\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,4{}\mathrm{i}-b^2\,c^3\,d^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}+b^2\,c^4\,d^3\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+b^2\,c^5\,d^2\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,5{}\mathrm{i}+a\,b\,d^7\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-a\,b\,c\,d^4\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,4{}\mathrm{i}+a\,b\,c\,d^6\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-a\,b\,c^2\,d^5\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}+a\,b\,c^3\,d^2\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,4{}\mathrm{i}-a\,b\,c^3\,d^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}+a\,b\,c^4\,d^3\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+a\,b\,c^5\,d^2\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{\cos\left(\frac{x}{2}\right)\,a^2\,c^4\,d^4-2\,\cos\left(\frac{x}{2}\right)\,a^2\,c^2\,d^6+\cos\left(\frac{x}{2}\right)\,a^2\,d^8-2\,\cos\left(\frac{x}{2}\right)\,a\,b\,c^6\,d^2+6\,\cos\left(\frac{x}{2}\right)\,a\,b\,c^4\,d^4-6\,\cos\left(\frac{x}{2}\right)\,a\,b\,c^2\,d^6+2\,\cos\left(\frac{x}{2}\right)\,a\,b\,d^8-\cos\left(\frac{x}{2}\right)\,b^2\,c^6\,d^2+3\,\cos\left(\frac{x}{2}\right)\,b^2\,c^4\,d^4-3\,\cos\left(\frac{x}{2}\right)\,b^2\,c^2\,d^6+\cos\left(\frac{x}{2}\right)\,b^2\,d^8}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{d^4-c^2\,d^2}","Not used",1,"(b*c^2*d*sin(x))/(d^4 - c^2*d^2) - (b*d^3*sin(x))/(d^4 - c^2*d^2) - (2*b*c^3*atan(sin(x/2)/cos(x/2)))/(d^4 - c^2*d^2) - (a*d^2*atan((a^2*d^7*sin(x/2)*(d^2 - c^2)^(1/2)*1i - b^2*c^5*sin(x/2)*(d^2 - c^2)^(3/2)*2i - b^2*c^7*sin(x/2)*(d^2 - c^2)^(1/2)*2i + b^2*d^7*sin(x/2)*(d^2 - c^2)^(1/2)*1i - a^2*c*d^4*sin(x/2)*(d^2 - c^2)^(3/2)*2i + a^2*c*d^6*sin(x/2)*(d^2 - c^2)^(1/2)*1i - b^2*c*d^4*sin(x/2)*(d^2 - c^2)^(3/2)*2i + b^2*c*d^6*sin(x/2)*(d^2 - c^2)^(1/2)*1i - a^2*c^2*d^5*sin(x/2)*(d^2 - c^2)^(1/2)*1i - a^2*c^3*d^4*sin(x/2)*(d^2 - c^2)^(1/2)*1i - b^2*c^2*d^5*sin(x/2)*(d^2 - c^2)^(1/2)*2i + b^2*c^3*d^2*sin(x/2)*(d^2 - c^2)^(3/2)*4i - b^2*c^3*d^4*sin(x/2)*(d^2 - c^2)^(1/2)*4i + b^2*c^4*d^3*sin(x/2)*(d^2 - c^2)^(1/2)*1i + b^2*c^5*d^2*sin(x/2)*(d^2 - c^2)^(1/2)*5i + a*b*d^7*sin(x/2)*(d^2 - c^2)^(1/2)*2i - a*b*c*d^4*sin(x/2)*(d^2 - c^2)^(3/2)*4i + a*b*c*d^6*sin(x/2)*(d^2 - c^2)^(1/2)*2i - a*b*c^2*d^5*sin(x/2)*(d^2 - c^2)^(1/2)*4i + a*b*c^3*d^2*sin(x/2)*(d^2 - c^2)^(3/2)*4i - a*b*c^3*d^4*sin(x/2)*(d^2 - c^2)^(1/2)*4i + a*b*c^4*d^3*sin(x/2)*(d^2 - c^2)^(1/2)*2i + a*b*c^5*d^2*sin(x/2)*(d^2 - c^2)^(1/2)*2i)/(a^2*d^8*cos(x/2) + b^2*d^8*cos(x/2) + 2*a*b*d^8*cos(x/2) - 2*a^2*c^2*d^6*cos(x/2) + a^2*c^4*d^4*cos(x/2) - 3*b^2*c^2*d^6*cos(x/2) + 3*b^2*c^4*d^4*cos(x/2) - b^2*c^6*d^2*cos(x/2) - 6*a*b*c^2*d^6*cos(x/2) + 6*a*b*c^4*d^4*cos(x/2) - 2*a*b*c^6*d^2*cos(x/2)))*(d^2 - c^2)^(1/2)*2i)/(d^4 - c^2*d^2) + (b*c^2*atan((a^2*d^7*sin(x/2)*(d^2 - c^2)^(1/2)*1i - b^2*c^5*sin(x/2)*(d^2 - c^2)^(3/2)*2i - b^2*c^7*sin(x/2)*(d^2 - c^2)^(1/2)*2i + b^2*d^7*sin(x/2)*(d^2 - c^2)^(1/2)*1i - a^2*c*d^4*sin(x/2)*(d^2 - c^2)^(3/2)*2i + a^2*c*d^6*sin(x/2)*(d^2 - c^2)^(1/2)*1i - b^2*c*d^4*sin(x/2)*(d^2 - c^2)^(3/2)*2i + b^2*c*d^6*sin(x/2)*(d^2 - c^2)^(1/2)*1i - a^2*c^2*d^5*sin(x/2)*(d^2 - c^2)^(1/2)*1i - a^2*c^3*d^4*sin(x/2)*(d^2 - c^2)^(1/2)*1i - b^2*c^2*d^5*sin(x/2)*(d^2 - c^2)^(1/2)*2i + b^2*c^3*d^2*sin(x/2)*(d^2 - c^2)^(3/2)*4i - b^2*c^3*d^4*sin(x/2)*(d^2 - c^2)^(1/2)*4i + b^2*c^4*d^3*sin(x/2)*(d^2 - c^2)^(1/2)*1i + b^2*c^5*d^2*sin(x/2)*(d^2 - c^2)^(1/2)*5i + a*b*d^7*sin(x/2)*(d^2 - c^2)^(1/2)*2i - a*b*c*d^4*sin(x/2)*(d^2 - c^2)^(3/2)*4i + a*b*c*d^6*sin(x/2)*(d^2 - c^2)^(1/2)*2i - a*b*c^2*d^5*sin(x/2)*(d^2 - c^2)^(1/2)*4i + a*b*c^3*d^2*sin(x/2)*(d^2 - c^2)^(3/2)*4i - a*b*c^3*d^4*sin(x/2)*(d^2 - c^2)^(1/2)*4i + a*b*c^4*d^3*sin(x/2)*(d^2 - c^2)^(1/2)*2i + a*b*c^5*d^2*sin(x/2)*(d^2 - c^2)^(1/2)*2i)/(a^2*d^8*cos(x/2) + b^2*d^8*cos(x/2) + 2*a*b*d^8*cos(x/2) - 2*a^2*c^2*d^6*cos(x/2) + a^2*c^4*d^4*cos(x/2) - 3*b^2*c^2*d^6*cos(x/2) + 3*b^2*c^4*d^4*cos(x/2) - b^2*c^6*d^2*cos(x/2) - 6*a*b*c^2*d^6*cos(x/2) + 6*a*b*c^4*d^4*cos(x/2) - 2*a*b*c^6*d^2*cos(x/2)))*(d^2 - c^2)^(1/2)*2i)/(d^4 - c^2*d^2) - (b*d^2*atan((a^2*d^7*sin(x/2)*(d^2 - c^2)^(1/2)*1i - b^2*c^5*sin(x/2)*(d^2 - c^2)^(3/2)*2i - b^2*c^7*sin(x/2)*(d^2 - c^2)^(1/2)*2i + b^2*d^7*sin(x/2)*(d^2 - c^2)^(1/2)*1i - a^2*c*d^4*sin(x/2)*(d^2 - c^2)^(3/2)*2i + a^2*c*d^6*sin(x/2)*(d^2 - c^2)^(1/2)*1i - b^2*c*d^4*sin(x/2)*(d^2 - c^2)^(3/2)*2i + b^2*c*d^6*sin(x/2)*(d^2 - c^2)^(1/2)*1i - a^2*c^2*d^5*sin(x/2)*(d^2 - c^2)^(1/2)*1i - a^2*c^3*d^4*sin(x/2)*(d^2 - c^2)^(1/2)*1i - b^2*c^2*d^5*sin(x/2)*(d^2 - c^2)^(1/2)*2i + b^2*c^3*d^2*sin(x/2)*(d^2 - c^2)^(3/2)*4i - b^2*c^3*d^4*sin(x/2)*(d^2 - c^2)^(1/2)*4i + b^2*c^4*d^3*sin(x/2)*(d^2 - c^2)^(1/2)*1i + b^2*c^5*d^2*sin(x/2)*(d^2 - c^2)^(1/2)*5i + a*b*d^7*sin(x/2)*(d^2 - c^2)^(1/2)*2i - a*b*c*d^4*sin(x/2)*(d^2 - c^2)^(3/2)*4i + a*b*c*d^6*sin(x/2)*(d^2 - c^2)^(1/2)*2i - a*b*c^2*d^5*sin(x/2)*(d^2 - c^2)^(1/2)*4i + a*b*c^3*d^2*sin(x/2)*(d^2 - c^2)^(3/2)*4i - a*b*c^3*d^4*sin(x/2)*(d^2 - c^2)^(1/2)*4i + a*b*c^4*d^3*sin(x/2)*(d^2 - c^2)^(1/2)*2i + a*b*c^5*d^2*sin(x/2)*(d^2 - c^2)^(1/2)*2i)/(a^2*d^8*cos(x/2) + b^2*d^8*cos(x/2) + 2*a*b*d^8*cos(x/2) - 2*a^2*c^2*d^6*cos(x/2) + a^2*c^4*d^4*cos(x/2) - 3*b^2*c^2*d^6*cos(x/2) + 3*b^2*c^4*d^4*cos(x/2) - b^2*c^6*d^2*cos(x/2) - 6*a*b*c^2*d^6*cos(x/2) + 6*a*b*c^4*d^4*cos(x/2) - 2*a*b*c^6*d^2*cos(x/2)))*(d^2 - c^2)^(1/2)*2i)/(d^4 - c^2*d^2) + (2*b*c*d^2*atan(sin(x/2)/cos(x/2)))/(d^4 - c^2*d^2)","B"
207,1,242,57,2.427400,"\text{Not used}","int((a + b*sin(x)^2)/(c + c*cos(x)^2),x)","\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,a^3\,\mathrm{tan}\left(x\right)}{2\,\left(a^3+6\,a^2\,b+10\,a\,b^2+4\,b^3\right)}+\frac{2\,\sqrt{2}\,b^3\,\mathrm{tan}\left(x\right)}{a^3+6\,a^2\,b+10\,a\,b^2+4\,b^3}+\frac{5\,\sqrt{2}\,a\,b^2\,\mathrm{tan}\left(x\right)}{a^3+6\,a^2\,b+10\,a\,b^2+4\,b^3}+\frac{3\,\sqrt{2}\,a^2\,b\,\mathrm{tan}\left(x\right)}{a^3+6\,a^2\,b+10\,a\,b^2+4\,b^3}\right)\,\left(a+2\,b\right)}{2\,c}-\frac{b\,\mathrm{atan}\left(\frac{4\,b^3\,\mathrm{tan}\left(x\right)}{2\,a^2\,b+8\,a\,b^2+4\,b^3}+\frac{8\,a\,b^2\,\mathrm{tan}\left(x\right)}{2\,a^2\,b+8\,a\,b^2+4\,b^3}+\frac{2\,a^2\,b\,\mathrm{tan}\left(x\right)}{2\,a^2\,b+8\,a\,b^2+4\,b^3}\right)}{c}","Not used",1,"(2^(1/2)*atan((2^(1/2)*a^3*tan(x))/(2*(10*a*b^2 + 6*a^2*b + a^3 + 4*b^3)) + (2*2^(1/2)*b^3*tan(x))/(10*a*b^2 + 6*a^2*b + a^3 + 4*b^3) + (5*2^(1/2)*a*b^2*tan(x))/(10*a*b^2 + 6*a^2*b + a^3 + 4*b^3) + (3*2^(1/2)*a^2*b*tan(x))/(10*a*b^2 + 6*a^2*b + a^3 + 4*b^3))*(a + 2*b))/(2*c) - (b*atan((4*b^3*tan(x))/(8*a*b^2 + 2*a^2*b + 4*b^3) + (8*a*b^2*tan(x))/(8*a*b^2 + 2*a^2*b + 4*b^3) + (2*a^2*b*tan(x))/(8*a*b^2 + 2*a^2*b + 4*b^3)))/c","B"
208,1,13,15,2.308682,"\text{Not used}","int((a + b*sin(x)^2)/(c - c*cos(x)^2),x)","\frac{b\,x-a\,\mathrm{cot}\left(x\right)}{c}","Not used",1,"(b*x - a*cot(x))/c","B"
209,1,1987,49,2.848202,"\text{Not used}","int((a + b*sin(x)^2)/(c + d*cos(x)^2),x)","-\frac{b\,c^2\,x}{c^2\,d+c\,d^2}-\frac{b\,c\,d\,x}{c^2\,d+c\,d^2}-\frac{a\,d\,\mathrm{atan}\left(\frac{a^2\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,1{}\mathrm{i}+b^2\,c^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+b^2\,c^5\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+b^2\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,1{}\mathrm{i}+a^2\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+a^2\,c\,d^4\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}+b^2\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,4{}\mathrm{i}+b^2\,c\,d^4\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}+b^2\,c^2\,d\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,5{}\mathrm{i}+b^2\,c^4\,d\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,6{}\mathrm{i}+a^2\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+a^2\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}+b^2\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,4{}\mathrm{i}+b^2\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,7{}\mathrm{i}+a\,b\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+a\,b\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,6{}\mathrm{i}+a\,b\,c\,d^4\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+a\,b\,c^2\,d\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,4{}\mathrm{i}+a\,b\,c^4\,d\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+a\,b\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,6{}\mathrm{i}+a\,b\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,6{}\mathrm{i}}{a^2\,c^4\,d^2+2\,a^2\,c^3\,d^3+a^2\,c^2\,d^4+2\,a\,b\,c^5\,d+6\,a\,b\,c^4\,d^2+6\,a\,b\,c^3\,d^3+2\,a\,b\,c^2\,d^4+b^2\,c^5\,d+3\,b^2\,c^4\,d^2+3\,b^2\,c^3\,d^3+b^2\,c^2\,d^4}\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}}{c^2\,d+c\,d^2}-\frac{b\,c\,\mathrm{atan}\left(\frac{a^2\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,1{}\mathrm{i}+b^2\,c^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+b^2\,c^5\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+b^2\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,1{}\mathrm{i}+a^2\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+a^2\,c\,d^4\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}+b^2\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,4{}\mathrm{i}+b^2\,c\,d^4\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}+b^2\,c^2\,d\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,5{}\mathrm{i}+b^2\,c^4\,d\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,6{}\mathrm{i}+a^2\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+a^2\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}+b^2\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,4{}\mathrm{i}+b^2\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,7{}\mathrm{i}+a\,b\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+a\,b\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,6{}\mathrm{i}+a\,b\,c\,d^4\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+a\,b\,c^2\,d\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,4{}\mathrm{i}+a\,b\,c^4\,d\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+a\,b\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,6{}\mathrm{i}+a\,b\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,6{}\mathrm{i}}{a^2\,c^4\,d^2+2\,a^2\,c^3\,d^3+a^2\,c^2\,d^4+2\,a\,b\,c^5\,d+6\,a\,b\,c^4\,d^2+6\,a\,b\,c^3\,d^3+2\,a\,b\,c^2\,d^4+b^2\,c^5\,d+3\,b^2\,c^4\,d^2+3\,b^2\,c^3\,d^3+b^2\,c^2\,d^4}\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}}{c^2\,d+c\,d^2}-\frac{b\,d\,\mathrm{atan}\left(\frac{a^2\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,1{}\mathrm{i}+b^2\,c^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+b^2\,c^5\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+b^2\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,1{}\mathrm{i}+a^2\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+a^2\,c\,d^4\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}+b^2\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,4{}\mathrm{i}+b^2\,c\,d^4\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}+b^2\,c^2\,d\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,5{}\mathrm{i}+b^2\,c^4\,d\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,6{}\mathrm{i}+a^2\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+a^2\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}+b^2\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,4{}\mathrm{i}+b^2\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,7{}\mathrm{i}+a\,b\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+a\,b\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,6{}\mathrm{i}+a\,b\,c\,d^4\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+a\,b\,c^2\,d\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,4{}\mathrm{i}+a\,b\,c^4\,d\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+a\,b\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,6{}\mathrm{i}+a\,b\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,6{}\mathrm{i}}{a^2\,c^4\,d^2+2\,a^2\,c^3\,d^3+a^2\,c^2\,d^4+2\,a\,b\,c^5\,d+6\,a\,b\,c^4\,d^2+6\,a\,b\,c^3\,d^3+2\,a\,b\,c^2\,d^4+b^2\,c^5\,d+3\,b^2\,c^4\,d^2+3\,b^2\,c^3\,d^3+b^2\,c^2\,d^4}\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}}{c^2\,d+c\,d^2}","Not used",1,"- (b*c^2*x)/(c*d^2 + c^2*d) - (a*d*atan((a^2*d^3*tan(x)*(- c*d - c^2)^(3/2)*1i + b^2*c^3*tan(x)*(- c*d - c^2)^(3/2)*2i + b^2*c^5*tan(x)*(- c*d - c^2)^(1/2)*2i + b^2*d^3*tan(x)*(- c*d - c^2)^(3/2)*1i + a^2*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*2i + a^2*c*d^4*tan(x)*(- c*d - c^2)^(1/2)*1i + b^2*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*4i + b^2*c*d^4*tan(x)*(- c*d - c^2)^(1/2)*1i + b^2*c^2*d*tan(x)*(- c*d - c^2)^(3/2)*5i + b^2*c^4*d*tan(x)*(- c*d - c^2)^(1/2)*6i + a^2*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*2i + a^2*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*1i + b^2*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*4i + b^2*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*7i + a*b*d^3*tan(x)*(- c*d - c^2)^(3/2)*2i + a*b*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*6i + a*b*c*d^4*tan(x)*(- c*d - c^2)^(1/2)*2i + a*b*c^2*d*tan(x)*(- c*d - c^2)^(3/2)*4i + a*b*c^4*d*tan(x)*(- c*d - c^2)^(1/2)*2i + a*b*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*6i + a*b*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*6i)/(b^2*c^5*d + a^2*c^2*d^4 + 2*a^2*c^3*d^3 + a^2*c^4*d^2 + b^2*c^2*d^4 + 3*b^2*c^3*d^3 + 3*b^2*c^4*d^2 + 2*a*b*c^5*d + 2*a*b*c^2*d^4 + 6*a*b*c^3*d^3 + 6*a*b*c^4*d^2))*(- c*d - c^2)^(1/2)*1i)/(c*d^2 + c^2*d) - (b*c*atan((a^2*d^3*tan(x)*(- c*d - c^2)^(3/2)*1i + b^2*c^3*tan(x)*(- c*d - c^2)^(3/2)*2i + b^2*c^5*tan(x)*(- c*d - c^2)^(1/2)*2i + b^2*d^3*tan(x)*(- c*d - c^2)^(3/2)*1i + a^2*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*2i + a^2*c*d^4*tan(x)*(- c*d - c^2)^(1/2)*1i + b^2*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*4i + b^2*c*d^4*tan(x)*(- c*d - c^2)^(1/2)*1i + b^2*c^2*d*tan(x)*(- c*d - c^2)^(3/2)*5i + b^2*c^4*d*tan(x)*(- c*d - c^2)^(1/2)*6i + a^2*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*2i + a^2*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*1i + b^2*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*4i + b^2*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*7i + a*b*d^3*tan(x)*(- c*d - c^2)^(3/2)*2i + a*b*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*6i + a*b*c*d^4*tan(x)*(- c*d - c^2)^(1/2)*2i + a*b*c^2*d*tan(x)*(- c*d - c^2)^(3/2)*4i + a*b*c^4*d*tan(x)*(- c*d - c^2)^(1/2)*2i + a*b*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*6i + a*b*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*6i)/(b^2*c^5*d + a^2*c^2*d^4 + 2*a^2*c^3*d^3 + a^2*c^4*d^2 + b^2*c^2*d^4 + 3*b^2*c^3*d^3 + 3*b^2*c^4*d^2 + 2*a*b*c^5*d + 2*a*b*c^2*d^4 + 6*a*b*c^3*d^3 + 6*a*b*c^4*d^2))*(- c*d - c^2)^(1/2)*1i)/(c*d^2 + c^2*d) - (b*d*atan((a^2*d^3*tan(x)*(- c*d - c^2)^(3/2)*1i + b^2*c^3*tan(x)*(- c*d - c^2)^(3/2)*2i + b^2*c^5*tan(x)*(- c*d - c^2)^(1/2)*2i + b^2*d^3*tan(x)*(- c*d - c^2)^(3/2)*1i + a^2*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*2i + a^2*c*d^4*tan(x)*(- c*d - c^2)^(1/2)*1i + b^2*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*4i + b^2*c*d^4*tan(x)*(- c*d - c^2)^(1/2)*1i + b^2*c^2*d*tan(x)*(- c*d - c^2)^(3/2)*5i + b^2*c^4*d*tan(x)*(- c*d - c^2)^(1/2)*6i + a^2*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*2i + a^2*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*1i + b^2*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*4i + b^2*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*7i + a*b*d^3*tan(x)*(- c*d - c^2)^(3/2)*2i + a*b*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*6i + a*b*c*d^4*tan(x)*(- c*d - c^2)^(1/2)*2i + a*b*c^2*d*tan(x)*(- c*d - c^2)^(3/2)*4i + a*b*c^4*d*tan(x)*(- c*d - c^2)^(1/2)*2i + a*b*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*6i + a*b*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*6i)/(b^2*c^5*d + a^2*c^2*d^4 + 2*a^2*c^3*d^3 + a^2*c^4*d^2 + b^2*c^2*d^4 + 3*b^2*c^3*d^3 + 3*b^2*c^4*d^2 + 2*a*b*c^5*d + 2*a*b*c^2*d^4 + 6*a*b*c^3*d^3 + 6*a*b*c^4*d^2))*(- c*d - c^2)^(1/2)*1i)/(c*d^2 + c^2*d) - (b*c*d*x)/(c*d^2 + c^2*d)","B"
210,1,13,13,2.460848,"\text{Not used}","int((cos(x)^2 + c^2/d^2 - 1)/(c + d*sin(x)),x)","\frac{\cos\left(x\right)}{d}+\frac{c\,x}{d^2}","Not used",1,"cos(x)/d + (c*x)/d^2","B"
211,1,1646,100,5.150263,"\text{Not used}","int((a + b*cos(x)^2)/(c + d*sin(x)),x)","\frac{2\,b}{d\,\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}+\frac{2\,b\,c\,\mathrm{atan}\left(\frac{64\,b^3\,c^2\,\mathrm{tan}\left(\frac{x}{2}\right)}{64\,b^3\,c^2+128\,a\,b^2\,c^2+64\,a^2\,b\,c^2-\frac{64\,b^3\,c^4}{d^2}-\frac{128\,a\,b^2\,c^4}{d^2}}-\frac{64\,b^3\,c^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{64\,a^2\,b\,c^2\,d^2-128\,a\,b^2\,c^4+128\,a\,b^2\,c^2\,d^2-64\,b^3\,c^4+64\,b^3\,c^2\,d^2}-\frac{128\,a\,b^2\,c^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{64\,a^2\,b\,c^2\,d^2-128\,a\,b^2\,c^4+128\,a\,b^2\,c^2\,d^2-64\,b^3\,c^4+64\,b^3\,c^2\,d^2}+\frac{128\,a\,b^2\,c^2\,\mathrm{tan}\left(\frac{x}{2}\right)}{64\,b^3\,c^2+128\,a\,b^2\,c^2+64\,a^2\,b\,c^2-\frac{64\,b^3\,c^4}{d^2}-\frac{128\,a\,b^2\,c^4}{d^2}}+\frac{64\,a^2\,b\,c^2\,\mathrm{tan}\left(\frac{x}{2}\right)}{64\,b^3\,c^2+128\,a\,b^2\,c^2+64\,a^2\,b\,c^2-\frac{64\,b^3\,c^4}{d^2}-\frac{128\,a\,b^2\,c^4}{d^2}}\right)}{d^2}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,\left(\frac{32\,b^2\,c^4}{d}-\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2\,c\,d^5-2\,a\,b\,c^3\,d^3+2\,a\,b\,c\,d^5+2\,b^2\,c^5\,d-4\,b^2\,c^3\,d^3+b^2\,c\,d^5\right)}{d^3}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,\left(32\,a\,c^2\,d^2+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a\,c\,d^6-2\,b\,c^3\,d^4+2\,b\,c\,d^6\right)}{d^3}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,\left(32\,c^2\,d^3+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,c\,d^7-2\,c^3\,d^5\right)}{d^3}\right)\,\left(a\,d^2-b\,c^2+b\,d^2\right)}{d^4-c^2\,d^2}\right)\,\left(a\,d^2-b\,c^2+b\,d^2\right)}{d^4-c^2\,d^2}\right)\,\left(a\,d^2-b\,c^2+b\,d^2\right)\,1{}\mathrm{i}}{d^4-c^2\,d^2}-\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2\,c\,d^5-2\,a\,b\,c^3\,d^3+2\,a\,b\,c\,d^5+2\,b^2\,c^5\,d-4\,b^2\,c^3\,d^3+b^2\,c\,d^5\right)}{d^3}-\frac{32\,b^2\,c^4}{d}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,\left(32\,a\,c^2\,d^2+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a\,c\,d^6-2\,b\,c^3\,d^4+2\,b\,c\,d^6\right)}{d^3}-\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,\left(32\,c^2\,d^3+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,c\,d^7-2\,c^3\,d^5\right)}{d^3}\right)\,\left(a\,d^2-b\,c^2+b\,d^2\right)}{d^4-c^2\,d^2}\right)\,\left(a\,d^2-b\,c^2+b\,d^2\right)}{d^4-c^2\,d^2}\right)\,\left(a\,d^2-b\,c^2+b\,d^2\right)\,1{}\mathrm{i}}{d^4-c^2\,d^2}}{\frac{64\,\left(a^2\,b\,c^2\,d^2-a\,b^2\,c^4+2\,a\,b^2\,c^2\,d^2-b^3\,c^4+b^3\,c^2\,d^2\right)}{d^2}+\frac{64\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,b^3\,c^5+2\,b^3\,c^3\,d^2+2\,a\,b^2\,c^3\,d^2\right)}{d^3}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,\left(\frac{32\,b^2\,c^4}{d}-\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2\,c\,d^5-2\,a\,b\,c^3\,d^3+2\,a\,b\,c\,d^5+2\,b^2\,c^5\,d-4\,b^2\,c^3\,d^3+b^2\,c\,d^5\right)}{d^3}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,\left(32\,a\,c^2\,d^2+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a\,c\,d^6-2\,b\,c^3\,d^4+2\,b\,c\,d^6\right)}{d^3}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,\left(32\,c^2\,d^3+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,c\,d^7-2\,c^3\,d^5\right)}{d^3}\right)\,\left(a\,d^2-b\,c^2+b\,d^2\right)}{d^4-c^2\,d^2}\right)\,\left(a\,d^2-b\,c^2+b\,d^2\right)}{d^4-c^2\,d^2}\right)\,\left(a\,d^2-b\,c^2+b\,d^2\right)}{d^4-c^2\,d^2}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2\,c\,d^5-2\,a\,b\,c^3\,d^3+2\,a\,b\,c\,d^5+2\,b^2\,c^5\,d-4\,b^2\,c^3\,d^3+b^2\,c\,d^5\right)}{d^3}-\frac{32\,b^2\,c^4}{d}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,\left(32\,a\,c^2\,d^2+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a\,c\,d^6-2\,b\,c^3\,d^4+2\,b\,c\,d^6\right)}{d^3}-\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,\left(32\,c^2\,d^3+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,c\,d^7-2\,c^3\,d^5\right)}{d^3}\right)\,\left(a\,d^2-b\,c^2+b\,d^2\right)}{d^4-c^2\,d^2}\right)\,\left(a\,d^2-b\,c^2+b\,d^2\right)}{d^4-c^2\,d^2}\right)\,\left(a\,d^2-b\,c^2+b\,d^2\right)}{d^4-c^2\,d^2}}\right)\,\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,\left(a\,d^2-b\,c^2+b\,d^2\right)\,2{}\mathrm{i}}{d^4-c^2\,d^2}","Not used",1,"(2*b)/(d*(tan(x/2)^2 + 1)) - (atan((((-(c + d)*(c - d))^(1/2)*((32*b^2*c^4)/d - (32*tan(x/2)*(a^2*c*d^5 + b^2*c*d^5 + 2*b^2*c^5*d - 4*b^2*c^3*d^3 + 2*a*b*c*d^5 - 2*a*b*c^3*d^3))/d^3 + ((-(c + d)*(c - d))^(1/2)*(32*a*c^2*d^2 + (32*tan(x/2)*(2*a*c*d^6 - 2*b*c^3*d^4 + 2*b*c*d^6))/d^3 + ((-(c + d)*(c - d))^(1/2)*(32*c^2*d^3 + (32*tan(x/2)*(3*c*d^7 - 2*c^3*d^5))/d^3)*(a*d^2 - b*c^2 + b*d^2))/(d^4 - c^2*d^2))*(a*d^2 - b*c^2 + b*d^2))/(d^4 - c^2*d^2))*(a*d^2 - b*c^2 + b*d^2)*1i)/(d^4 - c^2*d^2) - ((-(c + d)*(c - d))^(1/2)*((32*tan(x/2)*(a^2*c*d^5 + b^2*c*d^5 + 2*b^2*c^5*d - 4*b^2*c^3*d^3 + 2*a*b*c*d^5 - 2*a*b*c^3*d^3))/d^3 - (32*b^2*c^4)/d + ((-(c + d)*(c - d))^(1/2)*(32*a*c^2*d^2 + (32*tan(x/2)*(2*a*c*d^6 - 2*b*c^3*d^4 + 2*b*c*d^6))/d^3 - ((-(c + d)*(c - d))^(1/2)*(32*c^2*d^3 + (32*tan(x/2)*(3*c*d^7 - 2*c^3*d^5))/d^3)*(a*d^2 - b*c^2 + b*d^2))/(d^4 - c^2*d^2))*(a*d^2 - b*c^2 + b*d^2))/(d^4 - c^2*d^2))*(a*d^2 - b*c^2 + b*d^2)*1i)/(d^4 - c^2*d^2))/((64*(b^3*c^2*d^2 - a*b^2*c^4 - b^3*c^4 + 2*a*b^2*c^2*d^2 + a^2*b*c^2*d^2))/d^2 + (64*tan(x/2)*(2*b^3*c^3*d^2 - 2*b^3*c^5 + 2*a*b^2*c^3*d^2))/d^3 + ((-(c + d)*(c - d))^(1/2)*((32*b^2*c^4)/d - (32*tan(x/2)*(a^2*c*d^5 + b^2*c*d^5 + 2*b^2*c^5*d - 4*b^2*c^3*d^3 + 2*a*b*c*d^5 - 2*a*b*c^3*d^3))/d^3 + ((-(c + d)*(c - d))^(1/2)*(32*a*c^2*d^2 + (32*tan(x/2)*(2*a*c*d^6 - 2*b*c^3*d^4 + 2*b*c*d^6))/d^3 + ((-(c + d)*(c - d))^(1/2)*(32*c^2*d^3 + (32*tan(x/2)*(3*c*d^7 - 2*c^3*d^5))/d^3)*(a*d^2 - b*c^2 + b*d^2))/(d^4 - c^2*d^2))*(a*d^2 - b*c^2 + b*d^2))/(d^4 - c^2*d^2))*(a*d^2 - b*c^2 + b*d^2))/(d^4 - c^2*d^2) + ((-(c + d)*(c - d))^(1/2)*((32*tan(x/2)*(a^2*c*d^5 + b^2*c*d^5 + 2*b^2*c^5*d - 4*b^2*c^3*d^3 + 2*a*b*c*d^5 - 2*a*b*c^3*d^3))/d^3 - (32*b^2*c^4)/d + ((-(c + d)*(c - d))^(1/2)*(32*a*c^2*d^2 + (32*tan(x/2)*(2*a*c*d^6 - 2*b*c^3*d^4 + 2*b*c*d^6))/d^3 - ((-(c + d)*(c - d))^(1/2)*(32*c^2*d^3 + (32*tan(x/2)*(3*c*d^7 - 2*c^3*d^5))/d^3)*(a*d^2 - b*c^2 + b*d^2))/(d^4 - c^2*d^2))*(a*d^2 - b*c^2 + b*d^2))/(d^4 - c^2*d^2))*(a*d^2 - b*c^2 + b*d^2))/(d^4 - c^2*d^2)))*(-(c + d)*(c - d))^(1/2)*(a*d^2 - b*c^2 + b*d^2)*2i)/(d^4 - c^2*d^2) + (2*b*c*atan((64*b^3*c^2*tan(x/2))/(64*b^3*c^2 + 128*a*b^2*c^2 + 64*a^2*b*c^2 - (64*b^3*c^4)/d^2 - (128*a*b^2*c^4)/d^2) - (64*b^3*c^4*tan(x/2))/(64*b^3*c^2*d^2 - 128*a*b^2*c^4 - 64*b^3*c^4 + 128*a*b^2*c^2*d^2 + 64*a^2*b*c^2*d^2) - (128*a*b^2*c^4*tan(x/2))/(64*b^3*c^2*d^2 - 128*a*b^2*c^4 - 64*b^3*c^4 + 128*a*b^2*c^2*d^2 + 64*a^2*b*c^2*d^2) + (128*a*b^2*c^2*tan(x/2))/(64*b^3*c^2 + 128*a*b^2*c^2 + 64*a^2*b*c^2 - (64*b^3*c^4)/d^2 - (128*a*b^2*c^4)/d^2) + (64*a^2*b*c^2*tan(x/2))/(64*b^3*c^2 + 128*a*b^2*c^2 + 64*a^2*b*c^2 - (64*b^3*c^4)/d^2 - (128*a*b^2*c^4)/d^2)))/d^2","B"
212,1,249,56,2.386687,"\text{Not used}","int((a + b*cos(x)^2)/(c + c*sin(x)^2),x)","\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{4\,\sqrt{2}\,a^3\,\mathrm{tan}\left(x\right)}{4\,a^3+24\,a^2\,b+40\,a\,b^2+16\,b^3}+\frac{16\,\sqrt{2}\,b^3\,\mathrm{tan}\left(x\right)}{4\,a^3+24\,a^2\,b+40\,a\,b^2+16\,b^3}+\frac{40\,\sqrt{2}\,a\,b^2\,\mathrm{tan}\left(x\right)}{4\,a^3+24\,a^2\,b+40\,a\,b^2+16\,b^3}+\frac{24\,\sqrt{2}\,a^2\,b\,\mathrm{tan}\left(x\right)}{4\,a^3+24\,a^2\,b+40\,a\,b^2+16\,b^3}\right)\,\left(a+2\,b\right)}{2\,c}-\frac{b\,\mathrm{atan}\left(\frac{8\,b^3\,\mathrm{tan}\left(x\right)}{4\,a^2\,b+16\,a\,b^2+8\,b^3}+\frac{16\,a\,b^2\,\mathrm{tan}\left(x\right)}{4\,a^2\,b+16\,a\,b^2+8\,b^3}+\frac{4\,a^2\,b\,\mathrm{tan}\left(x\right)}{4\,a^2\,b+16\,a\,b^2+8\,b^3}\right)}{c}","Not used",1,"(2^(1/2)*atan((4*2^(1/2)*a^3*tan(x))/(40*a*b^2 + 24*a^2*b + 4*a^3 + 16*b^3) + (16*2^(1/2)*b^3*tan(x))/(40*a*b^2 + 24*a^2*b + 4*a^3 + 16*b^3) + (40*2^(1/2)*a*b^2*tan(x))/(40*a*b^2 + 24*a^2*b + 4*a^3 + 16*b^3) + (24*2^(1/2)*a^2*b*tan(x))/(40*a*b^2 + 24*a^2*b + 4*a^3 + 16*b^3))*(a + 2*b))/(2*c) - (b*atan((8*b^3*tan(x))/(16*a*b^2 + 4*a^2*b + 8*b^3) + (16*a*b^2*tan(x))/(16*a*b^2 + 4*a^2*b + 8*b^3) + (4*a^2*b*tan(x))/(16*a*b^2 + 4*a^2*b + 8*b^3)))/c","B"
213,1,12,14,2.314501,"\text{Not used}","int((a + b*cos(x)^2)/(c - c*sin(x)^2),x)","\frac{b\,x+a\,\mathrm{tan}\left(x\right)}{c}","Not used",1,"(b*x + a*tan(x))/c","B"
214,1,1774,49,2.945724,"\text{Not used}","int((a + b*cos(x)^2)/(c + d*sin(x)^2),x)","-\frac{b\,c^2\,x}{c^2\,d+c\,d^2}-\frac{b\,c\,d\,x}{c^2\,d+c\,d^2}-\frac{a\,d\,\mathrm{atan}\left(\frac{a^2\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,1{}\mathrm{i}+b^2\,c^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+b^2\,c^5\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+b^2\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,1{}\mathrm{i}+a^2\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+b^2\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,4{}\mathrm{i}+b^2\,c^2\,d\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,5{}\mathrm{i}+b^2\,c^4\,d\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,6{}\mathrm{i}+a^2\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}+a^2\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}+b^2\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+b^2\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,6{}\mathrm{i}+a\,b\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+a\,b\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,6{}\mathrm{i}+a\,b\,c^2\,d\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,4{}\mathrm{i}+a\,b\,c^4\,d\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+a\,b\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+a\,b\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,4{}\mathrm{i}}{a^2\,c^4\,d^2+2\,a^2\,c^3\,d^3+a^2\,c^2\,d^4+2\,a\,b\,c^5\,d+6\,a\,b\,c^4\,d^2+6\,a\,b\,c^3\,d^3+2\,a\,b\,c^2\,d^4+b^2\,c^5\,d+3\,b^2\,c^4\,d^2+3\,b^2\,c^3\,d^3+b^2\,c^2\,d^4}\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}}{c^2\,d+c\,d^2}-\frac{b\,c\,\mathrm{atan}\left(\frac{a^2\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,1{}\mathrm{i}+b^2\,c^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+b^2\,c^5\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+b^2\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,1{}\mathrm{i}+a^2\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+b^2\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,4{}\mathrm{i}+b^2\,c^2\,d\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,5{}\mathrm{i}+b^2\,c^4\,d\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,6{}\mathrm{i}+a^2\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}+a^2\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}+b^2\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+b^2\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,6{}\mathrm{i}+a\,b\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+a\,b\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,6{}\mathrm{i}+a\,b\,c^2\,d\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,4{}\mathrm{i}+a\,b\,c^4\,d\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+a\,b\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+a\,b\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,4{}\mathrm{i}}{a^2\,c^4\,d^2+2\,a^2\,c^3\,d^3+a^2\,c^2\,d^4+2\,a\,b\,c^5\,d+6\,a\,b\,c^4\,d^2+6\,a\,b\,c^3\,d^3+2\,a\,b\,c^2\,d^4+b^2\,c^5\,d+3\,b^2\,c^4\,d^2+3\,b^2\,c^3\,d^3+b^2\,c^2\,d^4}\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}}{c^2\,d+c\,d^2}-\frac{b\,d\,\mathrm{atan}\left(\frac{a^2\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,1{}\mathrm{i}+b^2\,c^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+b^2\,c^5\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+b^2\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,1{}\mathrm{i}+a^2\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+b^2\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,4{}\mathrm{i}+b^2\,c^2\,d\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,5{}\mathrm{i}+b^2\,c^4\,d\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,6{}\mathrm{i}+a^2\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}+a^2\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}+b^2\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+b^2\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,6{}\mathrm{i}+a\,b\,d^3\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,2{}\mathrm{i}+a\,b\,c\,d^2\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,6{}\mathrm{i}+a\,b\,c^2\,d\,\mathrm{tan}\left(x\right)\,{\left(-c^2-d\,c\right)}^{3/2}\,4{}\mathrm{i}+a\,b\,c^4\,d\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+a\,b\,c^2\,d^3\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,2{}\mathrm{i}+a\,b\,c^3\,d^2\,\mathrm{tan}\left(x\right)\,\sqrt{-c^2-d\,c}\,4{}\mathrm{i}}{a^2\,c^4\,d^2+2\,a^2\,c^3\,d^3+a^2\,c^2\,d^4+2\,a\,b\,c^5\,d+6\,a\,b\,c^4\,d^2+6\,a\,b\,c^3\,d^3+2\,a\,b\,c^2\,d^4+b^2\,c^5\,d+3\,b^2\,c^4\,d^2+3\,b^2\,c^3\,d^3+b^2\,c^2\,d^4}\right)\,\sqrt{-c^2-d\,c}\,1{}\mathrm{i}}{c^2\,d+c\,d^2}","Not used",1,"- (b*c^2*x)/(c*d^2 + c^2*d) - (a*d*atan((a^2*d^3*tan(x)*(- c*d - c^2)^(3/2)*1i + b^2*c^3*tan(x)*(- c*d - c^2)^(3/2)*2i + b^2*c^5*tan(x)*(- c*d - c^2)^(1/2)*2i + b^2*d^3*tan(x)*(- c*d - c^2)^(3/2)*1i + a^2*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*2i + b^2*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*4i + b^2*c^2*d*tan(x)*(- c*d - c^2)^(3/2)*5i + b^2*c^4*d*tan(x)*(- c*d - c^2)^(1/2)*6i + a^2*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*1i + a^2*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*1i + b^2*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*2i + b^2*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*6i + a*b*d^3*tan(x)*(- c*d - c^2)^(3/2)*2i + a*b*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*6i + a*b*c^2*d*tan(x)*(- c*d - c^2)^(3/2)*4i + a*b*c^4*d*tan(x)*(- c*d - c^2)^(1/2)*2i + a*b*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*2i + a*b*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*4i)/(b^2*c^5*d + a^2*c^2*d^4 + 2*a^2*c^3*d^3 + a^2*c^4*d^2 + b^2*c^2*d^4 + 3*b^2*c^3*d^3 + 3*b^2*c^4*d^2 + 2*a*b*c^5*d + 2*a*b*c^2*d^4 + 6*a*b*c^3*d^3 + 6*a*b*c^4*d^2))*(- c*d - c^2)^(1/2)*1i)/(c*d^2 + c^2*d) - (b*c*atan((a^2*d^3*tan(x)*(- c*d - c^2)^(3/2)*1i + b^2*c^3*tan(x)*(- c*d - c^2)^(3/2)*2i + b^2*c^5*tan(x)*(- c*d - c^2)^(1/2)*2i + b^2*d^3*tan(x)*(- c*d - c^2)^(3/2)*1i + a^2*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*2i + b^2*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*4i + b^2*c^2*d*tan(x)*(- c*d - c^2)^(3/2)*5i + b^2*c^4*d*tan(x)*(- c*d - c^2)^(1/2)*6i + a^2*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*1i + a^2*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*1i + b^2*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*2i + b^2*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*6i + a*b*d^3*tan(x)*(- c*d - c^2)^(3/2)*2i + a*b*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*6i + a*b*c^2*d*tan(x)*(- c*d - c^2)^(3/2)*4i + a*b*c^4*d*tan(x)*(- c*d - c^2)^(1/2)*2i + a*b*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*2i + a*b*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*4i)/(b^2*c^5*d + a^2*c^2*d^4 + 2*a^2*c^3*d^3 + a^2*c^4*d^2 + b^2*c^2*d^4 + 3*b^2*c^3*d^3 + 3*b^2*c^4*d^2 + 2*a*b*c^5*d + 2*a*b*c^2*d^4 + 6*a*b*c^3*d^3 + 6*a*b*c^4*d^2))*(- c*d - c^2)^(1/2)*1i)/(c*d^2 + c^2*d) - (b*d*atan((a^2*d^3*tan(x)*(- c*d - c^2)^(3/2)*1i + b^2*c^3*tan(x)*(- c*d - c^2)^(3/2)*2i + b^2*c^5*tan(x)*(- c*d - c^2)^(1/2)*2i + b^2*d^3*tan(x)*(- c*d - c^2)^(3/2)*1i + a^2*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*2i + b^2*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*4i + b^2*c^2*d*tan(x)*(- c*d - c^2)^(3/2)*5i + b^2*c^4*d*tan(x)*(- c*d - c^2)^(1/2)*6i + a^2*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*1i + a^2*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*1i + b^2*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*2i + b^2*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*6i + a*b*d^3*tan(x)*(- c*d - c^2)^(3/2)*2i + a*b*c*d^2*tan(x)*(- c*d - c^2)^(3/2)*6i + a*b*c^2*d*tan(x)*(- c*d - c^2)^(3/2)*4i + a*b*c^4*d*tan(x)*(- c*d - c^2)^(1/2)*2i + a*b*c^2*d^3*tan(x)*(- c*d - c^2)^(1/2)*2i + a*b*c^3*d^2*tan(x)*(- c*d - c^2)^(1/2)*4i)/(b^2*c^5*d + a^2*c^2*d^4 + 2*a^2*c^3*d^3 + a^2*c^4*d^2 + b^2*c^2*d^4 + 3*b^2*c^3*d^3 + 3*b^2*c^4*d^2 + 2*a*b*c^5*d + 2*a*b*c^2*d^4 + 6*a*b*c^3*d^3 + 6*a*b*c^4*d^2))*(- c*d - c^2)^(1/2)*1i)/(c*d^2 + c^2*d) - (b*c*d*x)/(c*d^2 + c^2*d)","B"
215,1,1302,74,3.513582,"\text{Not used}","int((a + b/cos(x)^2)/(c + d*cos(x)),x)","\frac{b\,c^3\,\sin\left(x\right)}{c^4\,\cos\left(x\right)-c^2\,d^2\,\cos\left(x\right)}-\frac{b\,c\,d^2\,\sin\left(x\right)}{c^4\,\cos\left(x\right)-c^2\,d^2\,\cos\left(x\right)}+\frac{2\,b\,d^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\cos\left(x\right)}{c^4\,\cos\left(x\right)-c^2\,d^2\,\cos\left(x\right)}-\frac{2\,b\,c^2\,d\,\mathrm{atanh}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\cos\left(x\right)}{c^4\,\cos\left(x\right)-c^2\,d^2\,\cos\left(x\right)}+\frac{a\,c^2\,\mathrm{atan}\left(\frac{a^2\,c^7\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+b^2\,d^5\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}-b^2\,d^7\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+a^2\,c^4\,d\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}+a^2\,c^6\,d\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-a^2\,c^4\,d^3\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-a^2\,c^5\,d^2\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+b^2\,c^2\,d^5\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,3{}\mathrm{i}-b^2\,c^3\,d^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-b^2\,c^4\,d^3\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+b^2\,c^5\,d^2\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+a\,b\,c^2\,d^3\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,4{}\mathrm{i}-a\,b\,c^2\,d^5\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-a\,b\,c^3\,d^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+a\,b\,c^4\,d^3\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+a\,b\,c^5\,d^2\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{\cos\left(\frac{x}{2}\right)\,a^2\,c^8-2\,\cos\left(\frac{x}{2}\right)\,a^2\,c^6\,d^2+\cos\left(\frac{x}{2}\right)\,a^2\,c^4\,d^4+2\,\cos\left(\frac{x}{2}\right)\,a\,b\,c^6\,d^2-4\,\cos\left(\frac{x}{2}\right)\,a\,b\,c^4\,d^4+2\,\cos\left(\frac{x}{2}\right)\,a\,b\,c^2\,d^6+\cos\left(\frac{x}{2}\right)\,b^2\,c^6\,d^2-2\,\cos\left(\frac{x}{2}\right)\,b^2\,c^4\,d^4+\cos\left(\frac{x}{2}\right)\,b^2\,c^2\,d^6}\right)\,\cos\left(x\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{c^4\,\cos\left(x\right)-c^2\,d^2\,\cos\left(x\right)}+\frac{b\,d^2\,\mathrm{atan}\left(\frac{a^2\,c^7\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+b^2\,d^5\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}-b^2\,d^7\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+a^2\,c^4\,d\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}+a^2\,c^6\,d\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-a^2\,c^4\,d^3\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-a^2\,c^5\,d^2\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+b^2\,c^2\,d^5\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,3{}\mathrm{i}-b^2\,c^3\,d^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-b^2\,c^4\,d^3\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+b^2\,c^5\,d^2\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+a\,b\,c^2\,d^3\,\sin\left(\frac{x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,4{}\mathrm{i}-a\,b\,c^2\,d^5\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-a\,b\,c^3\,d^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+a\,b\,c^4\,d^3\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+a\,b\,c^5\,d^2\,\sin\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{\cos\left(\frac{x}{2}\right)\,a^2\,c^8-2\,\cos\left(\frac{x}{2}\right)\,a^2\,c^6\,d^2+\cos\left(\frac{x}{2}\right)\,a^2\,c^4\,d^4+2\,\cos\left(\frac{x}{2}\right)\,a\,b\,c^6\,d^2-4\,\cos\left(\frac{x}{2}\right)\,a\,b\,c^4\,d^4+2\,\cos\left(\frac{x}{2}\right)\,a\,b\,c^2\,d^6+\cos\left(\frac{x}{2}\right)\,b^2\,c^6\,d^2-2\,\cos\left(\frac{x}{2}\right)\,b^2\,c^4\,d^4+\cos\left(\frac{x}{2}\right)\,b^2\,c^2\,d^6}\right)\,\cos\left(x\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{c^4\,\cos\left(x\right)-c^2\,d^2\,\cos\left(x\right)}","Not used",1,"(b*c^3*sin(x))/(c^4*cos(x) - c^2*d^2*cos(x)) - (b*c*d^2*sin(x))/(c^4*cos(x) - c^2*d^2*cos(x)) + (2*b*d^3*atanh(sin(x/2)/cos(x/2))*cos(x))/(c^4*cos(x) - c^2*d^2*cos(x)) + (a*c^2*atan((a^2*c^7*sin(x/2)*(d^2 - c^2)^(1/2)*1i + b^2*d^5*sin(x/2)*(d^2 - c^2)^(3/2)*2i - b^2*d^7*sin(x/2)*(d^2 - c^2)^(1/2)*2i + a^2*c^4*d*sin(x/2)*(d^2 - c^2)^(3/2)*2i + a^2*c^6*d*sin(x/2)*(d^2 - c^2)^(1/2)*1i - a^2*c^4*d^3*sin(x/2)*(d^2 - c^2)^(1/2)*1i - a^2*c^5*d^2*sin(x/2)*(d^2 - c^2)^(1/2)*1i + b^2*c^2*d^5*sin(x/2)*(d^2 - c^2)^(1/2)*3i - b^2*c^3*d^4*sin(x/2)*(d^2 - c^2)^(1/2)*1i - b^2*c^4*d^3*sin(x/2)*(d^2 - c^2)^(1/2)*1i + b^2*c^5*d^2*sin(x/2)*(d^2 - c^2)^(1/2)*1i + a*b*c^2*d^3*sin(x/2)*(d^2 - c^2)^(3/2)*4i - a*b*c^2*d^5*sin(x/2)*(d^2 - c^2)^(1/2)*2i - a*b*c^3*d^4*sin(x/2)*(d^2 - c^2)^(1/2)*2i + a*b*c^4*d^3*sin(x/2)*(d^2 - c^2)^(1/2)*2i + a*b*c^5*d^2*sin(x/2)*(d^2 - c^2)^(1/2)*2i)/(a^2*c^8*cos(x/2) + a^2*c^4*d^4*cos(x/2) - 2*a^2*c^6*d^2*cos(x/2) + b^2*c^2*d^6*cos(x/2) - 2*b^2*c^4*d^4*cos(x/2) + b^2*c^6*d^2*cos(x/2) + 2*a*b*c^2*d^6*cos(x/2) - 4*a*b*c^4*d^4*cos(x/2) + 2*a*b*c^6*d^2*cos(x/2)))*cos(x)*(d^2 - c^2)^(1/2)*2i)/(c^4*cos(x) - c^2*d^2*cos(x)) + (b*d^2*atan((a^2*c^7*sin(x/2)*(d^2 - c^2)^(1/2)*1i + b^2*d^5*sin(x/2)*(d^2 - c^2)^(3/2)*2i - b^2*d^7*sin(x/2)*(d^2 - c^2)^(1/2)*2i + a^2*c^4*d*sin(x/2)*(d^2 - c^2)^(3/2)*2i + a^2*c^6*d*sin(x/2)*(d^2 - c^2)^(1/2)*1i - a^2*c^4*d^3*sin(x/2)*(d^2 - c^2)^(1/2)*1i - a^2*c^5*d^2*sin(x/2)*(d^2 - c^2)^(1/2)*1i + b^2*c^2*d^5*sin(x/2)*(d^2 - c^2)^(1/2)*3i - b^2*c^3*d^4*sin(x/2)*(d^2 - c^2)^(1/2)*1i - b^2*c^4*d^3*sin(x/2)*(d^2 - c^2)^(1/2)*1i + b^2*c^5*d^2*sin(x/2)*(d^2 - c^2)^(1/2)*1i + a*b*c^2*d^3*sin(x/2)*(d^2 - c^2)^(3/2)*4i - a*b*c^2*d^5*sin(x/2)*(d^2 - c^2)^(1/2)*2i - a*b*c^3*d^4*sin(x/2)*(d^2 - c^2)^(1/2)*2i + a*b*c^4*d^3*sin(x/2)*(d^2 - c^2)^(1/2)*2i + a*b*c^5*d^2*sin(x/2)*(d^2 - c^2)^(1/2)*2i)/(a^2*c^8*cos(x/2) + a^2*c^4*d^4*cos(x/2) - 2*a^2*c^6*d^2*cos(x/2) + b^2*c^2*d^6*cos(x/2) - 2*b^2*c^4*d^4*cos(x/2) + b^2*c^6*d^2*cos(x/2) + 2*a*b*c^2*d^6*cos(x/2) - 4*a*b*c^4*d^4*cos(x/2) + 2*a*b*c^6*d^2*cos(x/2)))*cos(x)*(d^2 - c^2)^(1/2)*2i)/(c^4*cos(x) - c^2*d^2*cos(x)) - (2*b*c^2*d*atanh(sin(x/2)/cos(x/2))*cos(x))/(c^4*cos(x) - c^2*d^2*cos(x))","B"
216,1,463,72,2.831515,"\text{Not used}","int((a + b/sin(x)^2)/(c + d*sin(x)),x)","\frac{b\,d^3\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-b\,c^2\,d\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)+a\,c^2\,\mathrm{atan}\left(\frac{a\,c^3\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+b\,d^3\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}+b\,c\,d^2\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+a\,c^2\,d\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-b\,c^2\,d\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}}{4\,b\,d^4\,\mathrm{tan}\left(\frac{x}{2}\right)-a\,c^4\,\mathrm{tan}\left(\frac{x}{2}\right)+a\,c^3\,d+2\,b\,c\,d^3-b\,c^3\,d+2\,a\,c^2\,d^2\,\mathrm{tan}\left(\frac{x}{2}\right)-3\,b\,c^2\,d^2\,\mathrm{tan}\left(\frac{x}{2}\right)}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+b\,d^2\,\mathrm{atan}\left(\frac{a\,c^3\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+b\,d^3\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}+b\,c\,d^2\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+a\,c^2\,d\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-b\,c^2\,d\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}}{4\,b\,d^4\,\mathrm{tan}\left(\frac{x}{2}\right)-a\,c^4\,\mathrm{tan}\left(\frac{x}{2}\right)+a\,c^3\,d+2\,b\,c\,d^3-b\,c^3\,d+2\,a\,c^2\,d^2\,\mathrm{tan}\left(\frac{x}{2}\right)-3\,b\,c^2\,d^2\,\mathrm{tan}\left(\frac{x}{2}\right)}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{c^4-c^2\,d^2}-\frac{b\,c^3-b\,c\,d^2}{c^4\,\mathrm{tan}\left(x\right)-c^2\,d^2\,\mathrm{tan}\left(x\right)}","Not used",1,"(b*d^3*log(tan(x/2)) + a*c^2*atan((a*c^3*(d^2 - c^2)^(1/2)*1i + b*d^3*tan(x/2)*(d^2 - c^2)^(1/2)*4i + b*c*d^2*(d^2 - c^2)^(1/2)*2i + a*c^2*d*tan(x/2)*(d^2 - c^2)^(1/2)*2i - b*c^2*d*tan(x/2)*(d^2 - c^2)^(1/2)*1i)/(4*b*d^4*tan(x/2) - a*c^4*tan(x/2) + a*c^3*d + 2*b*c*d^3 - b*c^3*d + 2*a*c^2*d^2*tan(x/2) - 3*b*c^2*d^2*tan(x/2)))*(d^2 - c^2)^(1/2)*2i + b*d^2*atan((a*c^3*(d^2 - c^2)^(1/2)*1i + b*d^3*tan(x/2)*(d^2 - c^2)^(1/2)*4i + b*c*d^2*(d^2 - c^2)^(1/2)*2i + a*c^2*d*tan(x/2)*(d^2 - c^2)^(1/2)*2i - b*c^2*d*tan(x/2)*(d^2 - c^2)^(1/2)*1i)/(4*b*d^4*tan(x/2) - a*c^4*tan(x/2) + a*c^3*d + 2*b*c*d^3 - b*c^3*d + 2*a*c^2*d^2*tan(x/2) - 3*b*c^2*d^2*tan(x/2)))*(d^2 - c^2)^(1/2)*2i - b*c^2*d*log(tan(x/2)))/(c^4 - c^2*d^2) - (b*c^3 - b*c*d^2)/(c^4*tan(x) - c^2*d^2*tan(x))","B"
217,0,-1,136,0.000000,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^n,x)","\int {\left(a\,\cos\left(c+d\,x\right)+b\,\sin\left(c+d\,x\right)\right)}^n \,d x","Not used",1,"int((a*cos(c + d*x) + b*sin(c + d*x))^n, x)","F"
218,0,-1,95,0.000000,"\text{Not used}","int((2*cos(c + d*x) + 3*sin(c + d*x))^n,x)","\int {\left(2\,\cos\left(c+d\,x\right)+3\,\sin\left(c+d\,x\right)\right)}^n \,d x","Not used",1,"int((2*cos(c + d*x) + 3*sin(c + d*x))^n, x)","F"
219,1,422,127,6.158017,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^7,x)","-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(70\,a^6\,b-140\,a^4\,b^3+224\,a^2\,b^5\right)-2\,a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{424\,a^7}{35}+\frac{912\,a^5\,b^2}{5}-192\,a^3\,b^4+128\,a\,b^6\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(42\,a^6\,b-56\,a^4\,b^3+\frac{336\,a^2\,b^5}{5}+\frac{96\,b^7}{5}\right)+2\,a^6\,b+\frac{32\,b^7}{35}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{86\,a^7}{5}-\frac{224\,a^5\,b^2}{5}+224\,a^3\,b^4\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{86\,a^7}{5}-\frac{224\,a^5\,b^2}{5}+224\,a^3\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(28\,a^4\,b^3+\frac{112\,a^2\,b^5}{5}+\frac{32\,b^7}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(280\,a^4\,b^3-112\,a^2\,b^5+32\,b^7\right)+\frac{16\,a^2\,b^5}{5}+4\,a^4\,b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a^7+56\,a^5\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(4\,a^7+56\,a^5\,b^2\right)-2\,a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+140\,a^4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+14\,a^6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^7}","Not used",1,"-(tan(c/2 + (d*x)/2)^8*(70*a^6*b + 224*a^2*b^5 - 140*a^4*b^3) - 2*a^7*tan(c/2 + (d*x)/2)^13 - tan(c/2 + (d*x)/2)^7*(128*a*b^6 + (424*a^7)/35 - 192*a^3*b^4 + (912*a^5*b^2)/5) + tan(c/2 + (d*x)/2)^4*(42*a^6*b + (96*b^7)/5 + (336*a^2*b^5)/5 - 56*a^4*b^3) + 2*a^6*b + (32*b^7)/35 - tan(c/2 + (d*x)/2)^5*((86*a^7)/5 + 224*a^3*b^4 - (224*a^5*b^2)/5) - tan(c/2 + (d*x)/2)^9*((86*a^7)/5 + 224*a^3*b^4 - (224*a^5*b^2)/5) + tan(c/2 + (d*x)/2)^2*((32*b^7)/5 + (112*a^2*b^5)/5 + 28*a^4*b^3) + tan(c/2 + (d*x)/2)^6*(32*b^7 - 112*a^2*b^5 + 280*a^4*b^3) + (16*a^2*b^5)/5 + 4*a^4*b^3 - tan(c/2 + (d*x)/2)^3*(4*a^7 + 56*a^5*b^2) - tan(c/2 + (d*x)/2)^11*(4*a^7 + 56*a^5*b^2) - 2*a^7*tan(c/2 + (d*x)/2) + 140*a^4*b^3*tan(c/2 + (d*x)/2)^10 + 14*a^6*b*tan(c/2 + (d*x)/2)^12)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
220,1,519,161,4.117420,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^6,x)","\frac{5\,\mathrm{atan}\left(\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2+b^2\right)}^3}{8\,\left(\frac{5\,a^6}{8}+\frac{15\,a^4\,b^2}{8}+\frac{15\,a^2\,b^4}{8}+\frac{5\,b^6}{8}\right)}\right)\,{\left(a^2+b^2\right)}^3}{8\,d}-\frac{5\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,{\left(a^2+b^2\right)}^3}{8\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(40\,a^5\,b-\frac{160\,a^3\,b^3}{3}+64\,a\,b^5\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-\frac{11\,a^6}{8}+\frac{15\,a^4\,b^2}{8}+\frac{15\,a^2\,b^4}{8}+\frac{5\,b^6}{8}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(-\frac{11\,a^6}{8}+\frac{15\,a^4\,b^2}{8}+\frac{15\,a^2\,b^4}{8}+\frac{5\,b^6}{8}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{5\,a^6}{24}-\frac{235\,a^4\,b^2}{8}+\frac{85\,a^2\,b^4}{8}+\frac{85\,b^6}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{5\,a^6}{24}-\frac{235\,a^4\,b^2}{8}+\frac{85\,a^2\,b^4}{8}+\frac{85\,b^6}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{15\,a^6}{4}-\frac{195\,a^4\,b^2}{4}+\frac{285\,a^2\,b^4}{4}-\frac{33\,b^6}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{15\,a^6}{4}-\frac{195\,a^4\,b^2}{4}+\frac{285\,a^2\,b^4}{4}-\frac{33\,b^6}{4}\right)+80\,a^3\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+80\,a^3\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+12\,a^5\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+12\,a^5\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(5*atan((5*tan(c/2 + (d*x)/2)*(a^2 + b^2)^3)/(8*((5*a^6)/8 + (5*b^6)/8 + (15*a^2*b^4)/8 + (15*a^4*b^2)/8)))*(a^2 + b^2)^3)/(8*d) - (5*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(a^2 + b^2)^3)/(8*d) + (tan(c/2 + (d*x)/2)^6*(64*a*b^5 + 40*a^5*b - (160*a^3*b^3)/3) - tan(c/2 + (d*x)/2)*((5*b^6)/8 - (11*a^6)/8 + (15*a^2*b^4)/8 + (15*a^4*b^2)/8) + tan(c/2 + (d*x)/2)^11*((5*b^6)/8 - (11*a^6)/8 + (15*a^2*b^4)/8 + (15*a^4*b^2)/8) - tan(c/2 + (d*x)/2)^3*((5*a^6)/24 + (85*b^6)/24 + (85*a^2*b^4)/8 - (235*a^4*b^2)/8) + tan(c/2 + (d*x)/2)^9*((5*a^6)/24 + (85*b^6)/24 + (85*a^2*b^4)/8 - (235*a^4*b^2)/8) + tan(c/2 + (d*x)/2)^5*((15*a^6)/4 - (33*b^6)/4 + (285*a^2*b^4)/4 - (195*a^4*b^2)/4) - tan(c/2 + (d*x)/2)^7*((15*a^6)/4 - (33*b^6)/4 + (285*a^2*b^4)/4 - (195*a^4*b^2)/4) + 80*a^3*b^3*tan(c/2 + (d*x)/2)^4 + 80*a^3*b^3*tan(c/2 + (d*x)/2)^8 + 12*a^5*b*tan(c/2 + (d*x)/2)^2 + 12*a^5*b*tan(c/2 + (d*x)/2)^10)/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1))","B"
221,1,248,94,2.720399,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^5,x)","\frac{2\,\left(\frac{3\,\sin\left(c+d\,x\right)\,a^5\,{\cos\left(c+d\,x\right)}^4}{2}+2\,\sin\left(c+d\,x\right)\,a^5\,{\cos\left(c+d\,x\right)}^2+4\,\sin\left(c+d\,x\right)\,a^5-\frac{15\,a^4\,b\,{\cos\left(c+d\,x\right)}^5}{2}-15\,\sin\left(c+d\,x\right)\,a^3\,b^2\,{\cos\left(c+d\,x\right)}^4+5\,\sin\left(c+d\,x\right)\,a^3\,b^2\,{\cos\left(c+d\,x\right)}^2+10\,\sin\left(c+d\,x\right)\,a^3\,b^2+15\,a^2\,b^3\,{\cos\left(c+d\,x\right)}^5-25\,a^2\,b^3\,{\cos\left(c+d\,x\right)}^3+\frac{15\,\sin\left(c+d\,x\right)\,a\,b^4\,{\cos\left(c+d\,x\right)}^4}{2}-15\,\sin\left(c+d\,x\right)\,a\,b^4\,{\cos\left(c+d\,x\right)}^2+\frac{15\,\sin\left(c+d\,x\right)\,a\,b^4}{2}-\frac{3\,b^5\,{\cos\left(c+d\,x\right)}^5}{2}+5\,b^5\,{\cos\left(c+d\,x\right)}^3-\frac{15\,b^5\,\cos\left(c+d\,x\right)}{2}\right)}{15\,d}","Not used",1,"(2*(4*a^5*sin(c + d*x) - (15*b^5*cos(c + d*x))/2 + 5*b^5*cos(c + d*x)^3 - (3*b^5*cos(c + d*x)^5)/2 - (15*a^4*b*cos(c + d*x)^5)/2 + 2*a^5*cos(c + d*x)^2*sin(c + d*x) + (3*a^5*cos(c + d*x)^4*sin(c + d*x))/2 + 10*a^3*b^2*sin(c + d*x) - 25*a^2*b^3*cos(c + d*x)^3 + 15*a^2*b^3*cos(c + d*x)^5 + (15*a*b^4*sin(c + d*x))/2 + 5*a^3*b^2*cos(c + d*x)^2*sin(c + d*x) - 15*a^3*b^2*cos(c + d*x)^4*sin(c + d*x) - 15*a*b^4*cos(c + d*x)^2*sin(c + d*x) + (15*a*b^4*cos(c + d*x)^4*sin(c + d*x))/2))/(15*d)","B"
222,1,320,108,3.460540,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^4,x)","\frac{3\,\mathrm{atan}\left(\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2+b^2\right)}^2}{4\,\left(\frac{3\,a^4}{4}+\frac{3\,a^2\,b^2}{2}+\frac{3\,b^4}{4}\right)}\right)\,{\left(a^2+b^2\right)}^2}{4\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-\frac{5\,a^4}{4}+\frac{3\,a^2\,b^2}{2}+\frac{3\,b^4}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{3\,a^4}{4}-\frac{21\,a^2\,b^2}{2}+\frac{11\,b^4}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{3\,a^4}{4}-\frac{21\,a^2\,b^2}{2}+\frac{11\,b^4}{4}\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-\frac{5\,a^4}{4}+\frac{3\,a^2\,b^2}{2}+\frac{3\,b^4}{4}\right)+8\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+16\,a\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{3\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,{\left(a^2+b^2\right)}^2}{4\,d}","Not used",1,"(3*atan((3*tan(c/2 + (d*x)/2)*(a^2 + b^2)^2)/(4*((3*a^4)/4 + (3*b^4)/4 + (3*a^2*b^2)/2)))*(a^2 + b^2)^2)/(4*d) + (tan(c/2 + (d*x)/2)^7*((3*b^4)/4 - (5*a^4)/4 + (3*a^2*b^2)/2) - tan(c/2 + (d*x)/2)^3*((3*a^4)/4 + (11*b^4)/4 - (21*a^2*b^2)/2) + tan(c/2 + (d*x)/2)^5*((3*a^4)/4 + (11*b^4)/4 - (21*a^2*b^2)/2) - tan(c/2 + (d*x)/2)*((3*b^4)/4 - (5*a^4)/4 + (3*a^2*b^2)/2) + 8*a^3*b*tan(c/2 + (d*x)/2)^2 + 16*a*b^3*tan(c/2 + (d*x)/2)^4 + 8*a^3*b*tan(c/2 + (d*x)/2)^6)/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (3*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(a^2 + b^2)^2)/(4*d)","B"
223,1,104,58,2.480197,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^3,x)","\frac{\frac{\sin\left(c+d\,x\right)\,a^3\,{\cos\left(c+d\,x\right)}^2}{3}+\frac{2\,\sin\left(c+d\,x\right)\,a^3}{3}-a^2\,b\,{\cos\left(c+d\,x\right)}^3-\sin\left(c+d\,x\right)\,a\,b^2\,{\cos\left(c+d\,x\right)}^2+\sin\left(c+d\,x\right)\,a\,b^2+\frac{b^3\,{\cos\left(c+d\,x\right)}^3}{3}-b^3\,\cos\left(c+d\,x\right)}{d}","Not used",1,"((2*a^3*sin(c + d*x))/3 - b^3*cos(c + d*x) + (b^3*cos(c + d*x)^3)/3 - a^2*b*cos(c + d*x)^3 + (a^3*cos(c + d*x)^2*sin(c + d*x))/3 + a*b^2*sin(c + d*x) - a*b^2*cos(c + d*x)^2*sin(c + d*x))/d","B"
224,1,63,55,2.417612,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^2,x)","\frac{a^2\,x}{2}+\frac{b^2\,x}{2}+\frac{a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}-\frac{b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}-\frac{a\,b\,\cos\left(2\,c+2\,d\,x\right)}{2\,d}","Not used",1,"(a^2*x)/2 + (b^2*x)/2 + (a^2*sin(2*c + 2*d*x))/(4*d) - (b^2*sin(2*c + 2*d*x))/(4*d) - (a*b*cos(2*c + 2*d*x))/(2*d)","B"
225,1,38,24,2.323950,"\text{Not used}","int(a*cos(c + d*x) + b*sin(c + d*x),x)","-\frac{2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"-(2*cos(c/2 + (d*x)/2)*(b*cos(c/2 + (d*x)/2) - a*sin(c/2 + (d*x)/2)))/d","B"
226,1,39,47,2.800958,"\text{Not used}","int(1/(a*cos(c + d*x) + b*sin(c + d*x)),x)","-\frac{2\,\mathrm{atanh}\left(\frac{b-a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{d\,\sqrt{a^2+b^2}}","Not used",1,"-(2*atanh((b - a*tan(c/2 + (d*x)/2))/(a^2 + b^2)^(1/2)))/(d*(a^2 + b^2)^(1/2))","B"
227,1,47,32,2.342115,"\text{Not used}","int(1/(a*cos(c + d*x) + b*sin(c + d*x))^2,x)","\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}","Not used",1,"(2*tan(c/2 + (d*x)/2))/(a*d*(a + 2*b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^2))","B"
228,1,260,103,4.554539,"\text{Not used}","int(1/(a*cos(c + d*x) + b*sin(c + d*x))^3,x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-2\,b^2\right)}{a\,\left(a^2+b^2\right)}-\frac{b}{a^2+b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2+2\,b^2\right)}{a\,\left(a^2+b^2\right)}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2-2\,b^2\right)}{a^2\,\left(a^2+b^2\right)}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-4\,b^2\right)+a^2-4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{\mathrm{atanh}\left(\frac{\left(2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{2\,a^2\,b+2\,b^3}{a^2+b^2}\right)\,\left(\frac{a^2}{2}+\frac{b^2}{2}\right)}{{\left(a^2+b^2\right)}^{3/2}}\right)}{d\,{\left(a^2+b^2\right)}^{3/2}}","Not used",1,"((tan(c/2 + (d*x)/2)*(a^2 - 2*b^2))/(a*(a^2 + b^2)) - b/(a^2 + b^2) + (tan(c/2 + (d*x)/2)^3*(a^2 + 2*b^2))/(a*(a^2 + b^2)) + (b*tan(c/2 + (d*x)/2)^2*(a^2 - 2*b^2))/(a^2*(a^2 + b^2)))/(d*(a^2*tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)^2*(2*a^2 - 4*b^2) + a^2 - 4*a*b*tan(c/2 + (d*x)/2)^3 + 4*a*b*tan(c/2 + (d*x)/2))) + atanh(((2*a*tan(c/2 + (d*x)/2) - (2*a^2*b + 2*b^3)/(a^2 + b^2))*(a^2/2 + b^2/2))/(a^2 + b^2)^(3/2))/(d*(a^2 + b^2)^(3/2))","B"
229,1,222,98,3.115509,"\text{Not used}","int(1/(a*cos(c + d*x) + b*sin(c + d*x))^4,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{a}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2-2\,b^2\right)}{3\,a^3}+\frac{4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^2}-\frac{4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{a^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a\,b^2-3\,a^3\right)-a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12\,a\,b^2-3\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(12\,a^2\,b-8\,b^3\right)+a^3+6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^5)/a + (2*tan(c/2 + (d*x)/2))/a - (4*tan(c/2 + (d*x)/2)^3*(a^2 - 2*b^2))/(3*a^3) + (4*b*tan(c/2 + (d*x)/2)^2)/a^2 - (4*b*tan(c/2 + (d*x)/2)^4)/a^2)/(d*(tan(c/2 + (d*x)/2)^2*(12*a*b^2 - 3*a^3) - a^3*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^4*(12*a*b^2 - 3*a^3) - tan(c/2 + (d*x)/2)^3*(12*a^2*b - 8*b^3) + a^3 + 6*a^2*b*tan(c/2 + (d*x)/2) + 6*a^2*b*tan(c/2 + (d*x)/2)^5))","B"
230,1,719,156,6.093041,"\text{Not used}","int(1/(a*cos(c + d*x) + b*sin(c + d*x))^5,x)","-\frac{\frac{5\,a^2\,b+2\,b^3}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^4\,b+16\,a^2\,b^3+8\,b^5\right)}{4\,a^2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-23\,a^4\,b+64\,a^2\,b^3+24\,b^5\right)}{4\,a^2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-5\,a^4+24\,a^2\,b^2+8\,b^4\right)}{4\,a\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,a^6-36\,a^4\,b^2+56\,a^2\,b^4+32\,b^6\right)}{4\,a^3\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^6+84\,a^4\,b^2-56\,a^2\,b^4-32\,b^6\right)}{4\,a^3\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(5\,a^4+16\,a^2\,b^2+8\,b^4\right)}{4\,a\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(5\,a^2\,b+2\,b^3\right)\,\left(3\,a^4-24\,a^2\,b^2+8\,b^4\right)}{4\,a^4\,\left(a^4+2\,a^2\,b^2+b^4\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^4-48\,a^2\,b^2+16\,b^4\right)+a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+a^4-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^4-24\,a^2\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^4-24\,a^2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(32\,a\,b^3-24\,a^3\,b\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(32\,a\,b^3-24\,a^3\,b\right)+8\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-8\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\right)}+\frac{\mathrm{atan}\left(\frac{-1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5+a^4\,b\,1{}\mathrm{i}-2{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^2+a^2\,b^3\,2{}\mathrm{i}-1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^4+b^5\,1{}\mathrm{i}}{{\left(a^2+b^2\right)}^{5/2}}\right)\,3{}\mathrm{i}}{4\,d\,{\left(a^2+b^2\right)}^{5/2}}","Not used",1,"(atan((a^4*b*1i + b^5*1i + a^2*b^3*2i - a^5*tan(c/2 + (d*x)/2)*1i - a*b^4*tan(c/2 + (d*x)/2)*1i - a^3*b^2*tan(c/2 + (d*x)/2)*2i)/(a^2 + b^2)^(5/2))*3i)/(4*d*(a^2 + b^2)^(5/2)) - ((5*a^2*b + 2*b^3)/(4*(a^4 + b^4 + 2*a^2*b^2)) + (3*tan(c/2 + (d*x)/2)^6*(a^4*b + 8*b^5 + 16*a^2*b^3))/(4*a^2*(a^4 + b^4 + 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^2*(24*b^5 - 23*a^4*b + 64*a^2*b^3))/(4*a^2*(a^4 + b^4 + 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)*(8*b^4 - 5*a^4 + 24*a^2*b^2))/(4*a*(a^4 + b^4 + 2*a^2*b^2)) - (tan(c/2 + (d*x)/2)^5*(3*a^6 + 32*b^6 + 56*a^2*b^4 - 36*a^4*b^2))/(4*a^3*(a^4 + b^4 + 2*a^2*b^2)) - (tan(c/2 + (d*x)/2)^3*(3*a^6 - 32*b^6 - 56*a^2*b^4 + 84*a^4*b^2))/(4*a^3*(a^4 + b^4 + 2*a^2*b^2)) - (tan(c/2 + (d*x)/2)^7*(5*a^4 + 8*b^4 + 16*a^2*b^2))/(4*a*(a^4 + b^4 + 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^4*(5*a^2*b + 2*b^3)*(3*a^4 + 8*b^4 - 24*a^2*b^2))/(4*a^4*(a^4 + b^4 + 2*a^2*b^2)))/(d*(tan(c/2 + (d*x)/2)^4*(6*a^4 + 16*b^4 - 48*a^2*b^2) + a^4*tan(c/2 + (d*x)/2)^8 + a^4 - tan(c/2 + (d*x)/2)^2*(4*a^4 - 24*a^2*b^2) - tan(c/2 + (d*x)/2)^6*(4*a^4 - 24*a^2*b^2) + tan(c/2 + (d*x)/2)^3*(32*a*b^3 - 24*a^3*b) - tan(c/2 + (d*x)/2)^5*(32*a*b^3 - 24*a^3*b) + 8*a^3*b*tan(c/2 + (d*x)/2) - 8*a^3*b*tan(c/2 + (d*x)/2)^7))","B"
231,1,470,151,5.150786,"\text{Not used}","int(1/(a*cos(c + d*x) + b*sin(c + d*x))^6,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{a}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}-\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(7\,a^2\,b-6\,b^3\right)}{3\,a^4}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(7\,a^2\,b-6\,b^3\right)}{3\,a^4}-\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2-6\,b^2\right)}{3\,a^3}-\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(a^2-6\,b^2\right)}{3\,a^3}+\frac{8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^2}-\frac{8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{a^2}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(29\,a^4-112\,a^2\,b^2+24\,b^4\right)}{15\,a^5}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(10\,a^5-120\,a^3\,b^2+80\,a\,b^4\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(40\,a^4\,b-80\,a^2\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(40\,a^4\,b-80\,a^2\,b^3\right)-a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(10\,a^5-120\,a^3\,b^2+80\,a\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(60\,a^4\,b-160\,a^2\,b^3+32\,b^5\right)+a^5-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(5\,a^5-40\,a^3\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(5\,a^5-40\,a^3\,b^2\right)+10\,a^4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^9)/a + (2*tan(c/2 + (d*x)/2))/a - (8*tan(c/2 + (d*x)/2)^4*(7*a^2*b - 6*b^3))/(3*a^4) + (8*tan(c/2 + (d*x)/2)^6*(7*a^2*b - 6*b^3))/(3*a^4) - (8*tan(c/2 + (d*x)/2)^3*(a^2 - 6*b^2))/(3*a^3) - (8*tan(c/2 + (d*x)/2)^7*(a^2 - 6*b^2))/(3*a^3) + (8*b*tan(c/2 + (d*x)/2)^2)/a^2 - (8*b*tan(c/2 + (d*x)/2)^8)/a^2 + (4*tan(c/2 + (d*x)/2)^5*(29*a^4 + 24*b^4 - 112*a^2*b^2))/(15*a^5))/(d*(tan(c/2 + (d*x)/2)^4*(80*a*b^4 + 10*a^5 - 120*a^3*b^2) - tan(c/2 + (d*x)/2)^3*(40*a^4*b - 80*a^2*b^3) - tan(c/2 + (d*x)/2)^7*(40*a^4*b - 80*a^2*b^3) - a^5*tan(c/2 + (d*x)/2)^10 - tan(c/2 + (d*x)/2)^6*(80*a*b^4 + 10*a^5 - 120*a^3*b^2) + tan(c/2 + (d*x)/2)^5*(60*a^4*b + 32*b^5 - 160*a^2*b^3) + a^5 - tan(c/2 + (d*x)/2)^2*(5*a^5 - 40*a^3*b^2) + tan(c/2 + (d*x)/2)^8*(5*a^5 - 40*a^3*b^2) + 10*a^4*b*tan(c/2 + (d*x)/2) + 10*a^4*b*tan(c/2 + (d*x)/2)^9))","B"
232,0,-1,186,0.000000,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^(7/2),x)","\int {\left(a\,\cos\left(c+d\,x\right)+b\,\sin\left(c+d\,x\right)\right)}^{7/2} \,d x","Not used",1,"int((a*cos(c + d*x) + b*sin(c + d*x))^(7/2), x)","F"
233,0,-1,131,0.000000,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^(5/2),x)","\int {\left(a\,\cos\left(c+d\,x\right)+b\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a*cos(c + d*x) + b*sin(c + d*x))^(5/2), x)","F"
234,0,-1,131,0.000000,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^(3/2),x)","\int {\left(a\,\cos\left(c+d\,x\right)+b\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a*cos(c + d*x) + b*sin(c + d*x))^(3/2), x)","F"
235,0,-1,75,0.000000,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^(1/2),x)","\int \sqrt{a\,\cos\left(c+d\,x\right)+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((a*cos(c + d*x) + b*sin(c + d*x))^(1/2), x)","F"
236,0,-1,75,0.000000,"\text{Not used}","int(1/(a*cos(c + d*x) + b*sin(c + d*x))^(1/2),x)","\int \frac{1}{\sqrt{a\,\cos\left(c+d\,x\right)+b\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(a*cos(c + d*x) + b*sin(c + d*x))^(1/2), x)","F"
237,0,-1,138,0.000000,"\text{Not used}","int(1/(a*cos(c + d*x) + b*sin(c + d*x))^(3/2),x)","\int \frac{1}{{\left(a\,\cos\left(c+d\,x\right)+b\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(a*cos(c + d*x) + b*sin(c + d*x))^(3/2), x)","F"
238,0,-1,142,0.000000,"\text{Not used}","int(1/(a*cos(c + d*x) + b*sin(c + d*x))^(5/2),x)","\int \frac{1}{{\left(a\,\cos\left(c+d\,x\right)+b\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(a*cos(c + d*x) + b*sin(c + d*x))^(5/2), x)","F"
239,0,-1,197,0.000000,"\text{Not used}","int(1/(a*cos(c + d*x) + b*sin(c + d*x))^(7/2),x)","\int \frac{1}{{\left(a\,\cos\left(c+d\,x\right)+b\,\sin\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(1/(a*cos(c + d*x) + b*sin(c + d*x))^(7/2), x)","F"
240,0,-1,120,0.000000,"\text{Not used}","int((2*cos(c + d*x) + 3*sin(c + d*x))^(7/2),x)","\int {\left(2\,\cos\left(c+d\,x\right)+3\,\sin\left(c+d\,x\right)\right)}^{7/2} \,d x","Not used",1,"int((2*cos(c + d*x) + 3*sin(c + d*x))^(7/2), x)","F"
241,0,-1,75,0.000000,"\text{Not used}","int((2*cos(c + d*x) + 3*sin(c + d*x))^(5/2),x)","\int {\left(2\,\cos\left(c+d\,x\right)+3\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((2*cos(c + d*x) + 3*sin(c + d*x))^(5/2), x)","F"
242,0,-1,75,0.000000,"\text{Not used}","int((2*cos(c + d*x) + 3*sin(c + d*x))^(3/2),x)","\int {\left(2\,\cos\left(c+d\,x\right)+3\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((2*cos(c + d*x) + 3*sin(c + d*x))^(3/2), x)","F"
243,0,-1,27,0.000000,"\text{Not used}","int((2*cos(c + d*x) + 3*sin(c + d*x))^(1/2),x)","\int \sqrt{2\,\cos\left(c+d\,x\right)+3\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((2*cos(c + d*x) + 3*sin(c + d*x))^(1/2), x)","F"
244,0,-1,27,0.000000,"\text{Not used}","int(1/(2*cos(c + d*x) + 3*sin(c + d*x))^(1/2),x)","\int \frac{1}{\sqrt{2\,\cos\left(c+d\,x\right)+3\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(2*cos(c + d*x) + 3*sin(c + d*x))^(1/2), x)","F"
245,0,-1,73,0.000000,"\text{Not used}","int(1/(2*cos(c + d*x) + 3*sin(c + d*x))^(3/2),x)","\int \frac{1}{{\left(2\,\cos\left(c+d\,x\right)+3\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(2*cos(c + d*x) + 3*sin(c + d*x))^(3/2), x)","F"
246,0,-1,75,0.000000,"\text{Not used}","int(1/(2*cos(c + d*x) + 3*sin(c + d*x))^(5/2),x)","\int \frac{1}{{\left(2\,\cos\left(c+d\,x\right)+3\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(2*cos(c + d*x) + 3*sin(c + d*x))^(5/2), x)","F"
247,0,-1,120,0.000000,"\text{Not used}","int(1/(2*cos(c + d*x) + 3*sin(c + d*x))^(7/2),x)","\int \frac{1}{{\left(2\,\cos\left(c+d\,x\right)+3\,\sin\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(1/(2*cos(c + d*x) + 3*sin(c + d*x))^(7/2), x)","F"
248,0,-1,32,0.000000,"\text{Not used}","int((a*cos(c + d*x) + a*sin(c + d*x)*1i)^n,x)","\int {\left(a\,\cos\left(c+d\,x\right)+a\,\sin\left(c+d\,x\right)\,1{}\mathrm{i}\right)}^n \,d x","Not used",1,"int((a*cos(c + d*x) + a*sin(c + d*x)*1i)^n, x)","F"
249,1,84,31,2.554811,"\text{Not used}","int((a*cos(c + d*x) + a*sin(c + d*x)*1i)^4,x)","-\frac{2\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,4{}\mathrm{i}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4{}\mathrm{i}+1\right)}","Not used",1,"-(2*a^4*tan(c/2 + (d*x)/2)*(tan(c/2 + (d*x)/2)^2 - 1))/(d*(tan(c/2 + (d*x)/2)^3*4i - 6*tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)*4i + tan(c/2 + (d*x)/2)^4 + 1))","B"
250,1,66,31,2.465205,"\text{Not used}","int((a*cos(c + d*x) + a*sin(c + d*x)*1i)^3,x)","-\frac{2\,a^3\,\left(3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}{3\,d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,3{}\mathrm{i}+3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)}","Not used",1,"-(2*a^3*(3*tan(c/2 + (d*x)/2)^2 - 1))/(3*d*(3*tan(c/2 + (d*x)/2) - tan(c/2 + (d*x)/2)^2*3i - tan(c/2 + (d*x)/2)^3 + 1i))","B"
251,1,44,31,2.424515,"\text{Not used}","int((a*cos(c + d*x) + a*sin(c + d*x)*1i)^2,x)","-\frac{2\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,2{}\mathrm{i}-1\right)}","Not used",1,"-(2*a^2*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)*2i + tan(c/2 + (d*x)/2)^2 - 1))","B"
252,1,20,26,2.389152,"\text{Not used}","int(a*cos(c + d*x) + a*sin(c + d*x)*1i,x)","\frac{2\,a}{d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)}","Not used",1,"(2*a)/(d*(tan(c/2 + (d*x)/2) + 1i))","B"
253,1,25,29,2.388898,"\text{Not used}","int(1/(a*cos(c + d*x) + a*sin(c + d*x)*1i),x)","\frac{2{}\mathrm{i}}{a\,d\,\left(1+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}\right)}","Not used",1,"2i/(a*d*(tan(c/2 + (d*x)/2)*1i + 1))","B"
254,1,31,31,2.411872,"\text{Not used}","int(1/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^2,x)","-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)}^2}","Not used",1,"-(2*tan(c/2 + (d*x)/2))/(a^2*d*(tan(c/2 + (d*x)/2) - 1i)^2)","B"
255,1,68,31,2.464979,"\text{Not used}","int(1/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^3,x)","-\frac{2\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,3{}\mathrm{i}-\mathrm{i}\right)}{3\,a^3\,d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,1{}\mathrm{i}-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3{}\mathrm{i}+1\right)}","Not used",1,"-(2*(tan(c/2 + (d*x)/2)^2*3i - 1i))/(3*a^3*d*(tan(c/2 + (d*x)/2)*3i - 3*tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)^3*1i + 1))","B"
256,1,91,31,2.557536,"\text{Not used}","int(1/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^4,x)","-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,1{}\mathrm{i}-\mathrm{i}\right)}{a^4\,d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,1{}\mathrm{i}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,6{}\mathrm{i}-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)}","Not used",1,"-(2*tan(c/2 + (d*x)/2)*(tan(c/2 + (d*x)/2)^2*1i - 1i))/(a^4*d*(4*tan(c/2 + (d*x)/2)^3 - tan(c/2 + (d*x)/2)^2*6i - 4*tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^4*1i + 1i))","B"
257,1,35,33,0.431680,"\text{Not used}","int((a*cos(c + d*x) + a*sin(c + d*x)*1i)^(5/2),x)","-\frac{a^2\,{\mathrm{e}}^{c\,2{}\mathrm{i}}\,{\mathrm{e}}^{d\,x\,2{}\mathrm{i}}\,\sqrt{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}}\,{\mathrm{e}}^{d\,x\,1{}\mathrm{i}}}\,2{}\mathrm{i}}{5\,d}","Not used",1,"-(a^2*exp(c*2i)*exp(d*x*2i)*(a*exp(c*1i)*exp(d*x*1i))^(1/2)*2i)/(5*d)","B"
258,1,33,33,2.378204,"\text{Not used}","int((a*cos(c + d*x) + a*sin(c + d*x)*1i)^(3/2),x)","-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}}\,{\mathrm{e}}^{d\,x\,1{}\mathrm{i}}\,\sqrt{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}}\,{\mathrm{e}}^{d\,x\,1{}\mathrm{i}}}\,2{}\mathrm{i}}{3\,d}","Not used",1,"-(a*exp(c*1i)*exp(d*x*1i)*(a*exp(c*1i)*exp(d*x*1i))^(1/2)*2i)/(3*d)","B"
259,0,-1,31,0.000000,"\text{Not used}","int((a*cos(c + d*x) + a*sin(c + d*x)*1i)^(1/2),x)","\int \sqrt{a\,\cos\left(c+d\,x\right)+a\,\sin\left(c+d\,x\right)\,1{}\mathrm{i}} \,d x","Not used",1,"int((a*cos(c + d*x) + a*sin(c + d*x)*1i)^(1/2), x)","F"
260,0,-1,31,0.000000,"\text{Not used}","int(1/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^(1/2),x)","\int \frac{1}{\sqrt{a\,\cos\left(c+d\,x\right)+a\,\sin\left(c+d\,x\right)\,1{}\mathrm{i}}} \,d x","Not used",1,"int(1/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^(1/2), x)","F"
261,0,-1,33,0.000000,"\text{Not used}","int(1/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^(3/2),x)","\int \frac{1}{{\left(a\,\cos\left(c+d\,x\right)+a\,\sin\left(c+d\,x\right)\,1{}\mathrm{i}\right)}^{3/2}} \,d x","Not used",1,"int(1/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^(3/2), x)","F"
262,0,-1,33,0.000000,"\text{Not used}","int(1/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^(5/2),x)","\int \frac{1}{{\left(a\,\cos\left(c+d\,x\right)+a\,\sin\left(c+d\,x\right)\,1{}\mathrm{i}\right)}^{5/2}} \,d x","Not used",1,"int(1/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^(5/2), x)","F"
263,1,272,149,2.882651,"\text{Not used}","int((b*tan(x) + a/cos(x))^5,x)","\frac{\left(\frac{5\,a^5}{4}+\frac{5\,a^3\,b^2}{2}-\frac{15\,a\,b^4}{4}\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7+\left(10\,a^4\,b-2\,b^5\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+\left(\frac{3\,a^5}{4}+\frac{35\,a^3\,b^2}{2}+\frac{55\,a\,b^4}{4}\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+\left(40\,a^2\,b^3+8\,b^5\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+\left(\frac{3\,a^5}{4}+\frac{35\,a^3\,b^2}{2}+\frac{55\,a\,b^4}{4}\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+\left(10\,a^4\,b-2\,b^5\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\left(\frac{5\,a^5}{4}+\frac{5\,a^3\,b^2}{2}-\frac{15\,a\,b^4}{4}\right)\,\mathrm{tan}\left(\frac{x}{2}\right)}{{\mathrm{tan}\left(\frac{x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}+b^5\,\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)\,{\left(a+b\right)}^3\,\left(3\,a^2-9\,a\,b+8\,b^2\right)}{8}+\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)\,{\left(a-b\right)}^3\,\left(\frac{3\,a^2}{8}+\frac{9\,a\,b}{8}+b^2\right)","Not used",1,"(tan(x/2)^2*(10*a^4*b - 2*b^5) + tan(x/2)^6*(10*a^4*b - 2*b^5) + tan(x/2)^4*(8*b^5 + 40*a^2*b^3) + tan(x/2)*((5*a^5)/4 - (15*a*b^4)/4 + (5*a^3*b^2)/2) + tan(x/2)^7*((5*a^5)/4 - (15*a*b^4)/4 + (5*a^3*b^2)/2) + tan(x/2)^3*((55*a*b^4)/4 + (3*a^5)/4 + (35*a^3*b^2)/2) + tan(x/2)^5*((55*a*b^4)/4 + (3*a^5)/4 + (35*a^3*b^2)/2))/(6*tan(x/2)^4 - 4*tan(x/2)^2 - 4*tan(x/2)^6 + tan(x/2)^8 + 1) + b^5*log(tan(x/2)^2 + 1) - (log(tan(x/2) - 1)*(a + b)^3*(3*a^2 - 9*a*b + 8*b^2))/8 + log(tan(x/2) + 1)*(a - b)^3*((9*a*b)/8 + (3*a^2)/8 + b^2)","B"
264,1,115,100,2.531800,"\text{Not used}","int((b*tan(x) + a/cos(x))^4,x)","b^4\,x-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^4-2\,b^4\right)-\frac{16\,a\,b^3}{3}+\frac{8\,a^3\,b}{3}+{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(-\frac{4\,a^4}{3}+16\,a^2\,b^2+\frac{20\,b^4}{3}\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(2\,a^4-2\,b^4\right)+16\,a\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+8\,a^3\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2-1\right)}^3}","Not used",1,"b^4*x - (tan(x/2)*(2*a^4 - 2*b^4) - (16*a*b^3)/3 + (8*a^3*b)/3 + tan(x/2)^3*((20*b^4)/3 - (4*a^4)/3 + 16*a^2*b^2) + tan(x/2)^5*(2*a^4 - 2*b^4) + 16*a*b^3*tan(x/2)^2 + 8*a^3*b*tan(x/2)^4)/(tan(x/2)^2 - 1)^3","B"
265,1,126,75,2.503170,"\text{Not used}","int((b*tan(x) + a/cos(x))^3,x)","\frac{\left(a^3+3\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+\left(6\,a^2\,b+2\,b^3\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\left(a^3+3\,a\,b^2\right)\,\mathrm{tan}\left(\frac{x}{2}\right)}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}-b^3\,\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)\,{\left(a+b\right)}^2\,\left(a-2\,b\right)}{2}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)\,{\left(a-b\right)}^2\,\left(a+2\,b\right)}{2}","Not used",1,"(tan(x/2)^2*(6*a^2*b + 2*b^3) + tan(x/2)*(3*a*b^2 + a^3) + tan(x/2)^3*(3*a*b^2 + a^3))/(tan(x/2)^4 - 2*tan(x/2)^2 + 1) - b^3*log(tan(x/2)^2 + 1) - (log(tan(x/2) - 1)*(a + b)^2*(a - 2*b))/2 + (log(tan(x/2) + 1)*(a - b)^2*(a + 2*b))/2","B"
266,1,40,27,2.380004,"\text{Not used}","int((b*tan(x) + a/cos(x))^2,x)","-\frac{4\,a\,b+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^2+2\,b^2\right)}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2-1}-b^2\,x","Not used",1,"- (4*a*b + tan(x/2)*(2*a^2 + 2*b^2))/(tan(x/2)^2 - 1) - b^2*x","B"
267,1,37,12,2.493044,"\text{Not used}","int(b*tan(x) + a/cos(x),x)","b\,\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)-\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)\,\left(a+b\right)+\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)\,\left(a-b\right)","Not used",1,"b*log(tan(x/2)^2 + 1) - log(tan(x/2) - 1)*(a + b) + log(tan(x/2) + 1)*(a - b)","B"
268,1,55,11,3.792126,"\text{Not used}","int(1/(b*tan(x) + a/cos(x)),x)","\frac{2\,\mathrm{atanh}\left(\frac{b\,\left(2\,a^3\,\sin\left(x\right)+\frac{5\,a^2\,b}{2}-b^3-\frac{a^2\,b\,\cos\left(2\,x\right)}{2}\right)}{{\left(2\,a^2+\sin\left(x\right)\,a\,b-b^2\right)}^2}\right)}{b}","Not used",1,"(2*atanh((b*(2*a^3*sin(x) + (5*a^2*b)/2 - b^3 - (a^2*b*cos(2*x))/2))/(2*a^2 - b^2 + a*b*sin(x))^2))/b","B"
269,1,604,66,2.806177,"\text{Not used}","int(1/(b*tan(x) + a/cos(x))^2,x)","-\frac{x}{b^2}-\frac{\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)}{a}+\frac{2}{b}}{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{32\,a^2}{b}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a\,b^3-2\,a^3\,b\right)}{b^3}+\frac{a\,\left(32\,a\,b^2+64\,a^2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{a\,\left(32\,a^2\,b^3+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a\,b^7-2\,a^3\,b^5\right)}{b^3}\right)}{b^2\,\sqrt{b^2-a^2}}\right)}{b^2\,\sqrt{b^2-a^2}}\right)\,1{}\mathrm{i}}{b^2\,\sqrt{b^2-a^2}}+\frac{a\,\left(\frac{32\,a^2}{b}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a\,b^3-2\,a^3\,b\right)}{b^3}-\frac{a\,\left(32\,a\,b^2+64\,a^2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{a\,\left(32\,a^2\,b^3+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a\,b^7-2\,a^3\,b^5\right)}{b^3}\right)}{b^2\,\sqrt{b^2-a^2}}\right)}{b^2\,\sqrt{b^2-a^2}}\right)\,1{}\mathrm{i}}{b^2\,\sqrt{b^2-a^2}}}{\frac{128\,a^2\,\mathrm{tan}\left(\frac{x}{2}\right)}{b^3}+\frac{a\,\left(\frac{32\,a^2}{b}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a\,b^3-2\,a^3\,b\right)}{b^3}+\frac{a\,\left(32\,a\,b^2+64\,a^2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{a\,\left(32\,a^2\,b^3+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a\,b^7-2\,a^3\,b^5\right)}{b^3}\right)}{b^2\,\sqrt{b^2-a^2}}\right)}{b^2\,\sqrt{b^2-a^2}}\right)}{b^2\,\sqrt{b^2-a^2}}-\frac{a\,\left(\frac{32\,a^2}{b}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a\,b^3-2\,a^3\,b\right)}{b^3}-\frac{a\,\left(32\,a\,b^2+64\,a^2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{a\,\left(32\,a^2\,b^3+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a\,b^7-2\,a^3\,b^5\right)}{b^3}\right)}{b^2\,\sqrt{b^2-a^2}}\right)}{b^2\,\sqrt{b^2-a^2}}\right)}{b^2\,\sqrt{b^2-a^2}}}\right)\,2{}\mathrm{i}}{b^2\,\sqrt{b^2-a^2}}","Not used",1,"- x/b^2 - ((2*tan(x/2))/a + 2/b)/(a + 2*b*tan(x/2) + a*tan(x/2)^2) - (a*atan(((a*((32*a^2)/b + (32*tan(x/2)*(2*a*b^3 - 2*a^3*b))/b^3 + (a*(32*a*b^2 + 64*a^2*b*tan(x/2) + (a*(32*a^2*b^3 + (32*tan(x/2)*(3*a*b^7 - 2*a^3*b^5))/b^3))/(b^2*(b^2 - a^2)^(1/2))))/(b^2*(b^2 - a^2)^(1/2)))*1i)/(b^2*(b^2 - a^2)^(1/2)) + (a*((32*a^2)/b + (32*tan(x/2)*(2*a*b^3 - 2*a^3*b))/b^3 - (a*(32*a*b^2 + 64*a^2*b*tan(x/2) - (a*(32*a^2*b^3 + (32*tan(x/2)*(3*a*b^7 - 2*a^3*b^5))/b^3))/(b^2*(b^2 - a^2)^(1/2))))/(b^2*(b^2 - a^2)^(1/2)))*1i)/(b^2*(b^2 - a^2)^(1/2)))/((128*a^2*tan(x/2))/b^3 + (a*((32*a^2)/b + (32*tan(x/2)*(2*a*b^3 - 2*a^3*b))/b^3 + (a*(32*a*b^2 + 64*a^2*b*tan(x/2) + (a*(32*a^2*b^3 + (32*tan(x/2)*(3*a*b^7 - 2*a^3*b^5))/b^3))/(b^2*(b^2 - a^2)^(1/2))))/(b^2*(b^2 - a^2)^(1/2))))/(b^2*(b^2 - a^2)^(1/2)) - (a*((32*a^2)/b + (32*tan(x/2)*(2*a*b^3 - 2*a^3*b))/b^3 - (a*(32*a*b^2 + 64*a^2*b*tan(x/2) - (a*(32*a^2*b^3 + (32*tan(x/2)*(3*a*b^7 - 2*a^3*b^5))/b^3))/(b^2*(b^2 - a^2)^(1/2))))/(b^2*(b^2 - a^2)^(1/2))))/(b^2*(b^2 - a^2)^(1/2))))*2i)/(b^2*(b^2 - a^2)^(1/2))","B"
270,1,106,51,2.698158,"\text{Not used}","int(1/(b*tan(x) + a/cos(x))^3,x)","\frac{2\,a^3\,b\,\sin\left(x\right)+3\,a^2\,b^2\,{\sin\left(x\right)}^2+2\,a\,b^3\,\sin\left(x\right)+b^4\,{\sin\left(x\right)}^2}{2\,a^4\,b^3+4\,a^3\,b^4\,\sin\left(x\right)+2\,a^2\,b^5\,{\sin\left(x\right)}^2}-\frac{2\,\mathrm{atanh}\left(\frac{b^2+a\,\sin\left(x\right)\,b}{2\,a^2+\sin\left(x\right)\,a\,b-b^2}\right)}{b^3}","Not used",1,"(b^4*sin(x)^2 + 3*a^2*b^2*sin(x)^2 + 2*a*b^3*sin(x) + 2*a^3*b*sin(x))/(2*a^4*b^3 + 2*a^2*b^5*sin(x)^2 + 4*a^3*b^4*sin(x)) - (2*atanh((b^2 + a*b*sin(x))/(2*a^2 - b^2 + a*b*sin(x))))/b^3","B"
271,1,2782,156,6.372973,"\text{Not used}","int(1/(b*tan(x) + a/cos(x))^4,x)","\frac{\frac{6\,a^4-5\,a^2\,b^2+2\,b^4}{3\,b^3\,\left(a^2-b^2\right)}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(11\,a^4-8\,a^2\,b^2+2\,b^4\right)}{a\,b^2\,\left(a^2-b^2\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(a^4-2\,a^2\,b^2+2\,b^4\right)}{a\,b^2\,\left(a^2-b^2\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(2\,a^6+3\,a^4\,b^2-4\,a^2\,b^4+4\,b^6\right)}{a^2\,b^3\,\left(a^2-b^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^6+8\,a^4\,b^2-7\,a^2\,b^4+2\,b^6\right)}{a^2\,b^3\,\left(a^2-b^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(3\,a^2+2\,b^2\right)\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{3\,a^3\,b^2\,\left(a^2-b^2\right)}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(3\,a^3+12\,a\,b^2\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(3\,a^3+12\,a\,b^2\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(12\,a^2\,b+8\,b^3\right)+a^3+a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+6\,a^2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+6\,a^2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}+\frac{2\,\mathrm{atan}\left(\frac{48\,a^3\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)}{\frac{176\,a^3\,b^{15}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{160\,a^5\,b^{13}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{48\,a^7\,b^{11}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{64\,a\,b^{17}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}}-\frac{64\,a\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{\frac{176\,a^3\,b^{15}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{160\,a^5\,b^{13}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{48\,a^7\,b^{11}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{64\,a\,b^{17}}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}}\right)}{b^4}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,a^6\,b^3-8\,a^4\,b^5+4\,a^2\,b^7\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^3+28\,a^5\,b^5-29\,a^3\,b^7+8\,a\,b^9\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,a^5\,b^8-6\,a^3\,b^{10}+4\,a\,b^{12}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^6\,b^8-20\,a^4\,b^{10}+12\,a^2\,b^{12}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{a\,\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)}{2\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,1{}\mathrm{i}}{2\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}+\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,a^6\,b^3-8\,a^4\,b^5+4\,a^2\,b^7\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^3+28\,a^5\,b^5-29\,a^3\,b^7+8\,a\,b^9\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,a^5\,b^8-6\,a^3\,b^{10}+4\,a\,b^{12}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^6\,b^8-20\,a^4\,b^{10}+12\,a^2\,b^{12}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{a\,\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)}{2\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,1{}\mathrm{i}}{2\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}}{\frac{16\,\left(2\,a^5-3\,a^3\,b^2\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{16\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^6-20\,a^4\,b^2+12\,a^2\,b^4\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,a^6\,b^3-8\,a^4\,b^5+4\,a^2\,b^7\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^3+28\,a^5\,b^5-29\,a^3\,b^7+8\,a\,b^9\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,a^5\,b^8-6\,a^3\,b^{10}+4\,a\,b^{12}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^6\,b^8-20\,a^4\,b^{10}+12\,a^2\,b^{12}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{a\,\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)}{2\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)}{2\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}+\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,a^6\,b^3-8\,a^4\,b^5+4\,a^2\,b^7\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^3+28\,a^5\,b^5-29\,a^3\,b^7+8\,a\,b^9\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,a^5\,b^8-6\,a^3\,b^{10}+4\,a\,b^{12}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^6\,b^8-20\,a^4\,b^{10}+12\,a^2\,b^{12}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{a\,\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)}{2\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)}{2\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}","Not used",1,"((6*a^4 + 2*b^4 - 5*a^2*b^2)/(3*b^3*(a^2 - b^2)) + (tan(x/2)*(11*a^4 + 2*b^4 - 8*a^2*b^2))/(a*b^2*(a^2 - b^2)) + (tan(x/2)^5*(a^4 + 2*b^4 - 2*a^2*b^2))/(a*b^2*(a^2 - b^2)) + (tan(x/2)^4*(2*a^6 + 4*b^6 - 4*a^2*b^4 + 3*a^4*b^2))/(a^2*b^3*(a^2 - b^2)) + (2*tan(x/2)^2*(2*a^6 + 2*b^6 - 7*a^2*b^4 + 8*a^4*b^2))/(a^2*b^3*(a^2 - b^2)) + (2*tan(x/2)^3*(3*a^2 + 2*b^2)*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(3*a^3*b^2*(a^2 - b^2)))/(tan(x/2)^2*(12*a*b^2 + 3*a^3) + tan(x/2)^4*(12*a*b^2 + 3*a^3) + tan(x/2)^3*(12*a^2*b + 8*b^3) + a^3 + a^3*tan(x/2)^6 + 6*a^2*b*tan(x/2)^5 + 6*a^2*b*tan(x/2)) + (2*atan((48*a^3*b^3*tan(x/2))/((176*a^3*b^15)/(b^12 - 2*a^2*b^10 + a^4*b^8) - (160*a^5*b^13)/(b^12 - 2*a^2*b^10 + a^4*b^8) + (48*a^7*b^11)/(b^12 - 2*a^2*b^10 + a^4*b^8) - (64*a*b^17)/(b^12 - 2*a^2*b^10 + a^4*b^8)) - (64*a*b^5*tan(x/2))/((176*a^3*b^15)/(b^12 - 2*a^2*b^10 + a^4*b^8) - (160*a^5*b^13)/(b^12 - 2*a^2*b^10 + a^4*b^8) + (48*a^7*b^11)/(b^12 - 2*a^2*b^10 + a^4*b^8) - (64*a*b^17)/(b^12 - 2*a^2*b^10 + a^4*b^8))))/b^4 + (a*atan(((a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^2*b^7 - 8*a^4*b^5 + 4*a^6*b^3))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(8*a*b^9 - 29*a^3*b^7 + 28*a^5*b^5 - 8*a^7*b^3))/(b^13 - 2*a^2*b^11 + a^4*b^9) - (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a*b^12 - 6*a^3*b^10 + 2*a^5*b^8))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(12*a^2*b^12 - 20*a^4*b^10 + 8*a^6*b^8))/(b^13 - 2*a^2*b^11 + a^4*b^9) - (a*((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(2*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))))/(2*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*1i)/(2*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)) + (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^2*b^7 - 8*a^4*b^5 + 4*a^6*b^3))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(8*a*b^9 - 29*a^3*b^7 + 28*a^5*b^5 - 8*a^7*b^3))/(b^13 - 2*a^2*b^11 + a^4*b^9) + (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a*b^12 - 6*a^3*b^10 + 2*a^5*b^8))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(12*a^2*b^12 - 20*a^4*b^10 + 8*a^6*b^8))/(b^13 - 2*a^2*b^11 + a^4*b^9) + (a*((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(2*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))))/(2*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*1i)/(2*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))/((16*(2*a^5 - 3*a^3*b^2))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (16*tan(x/2)*(8*a^6 + 12*a^2*b^4 - 20*a^4*b^2))/(b^13 - 2*a^2*b^11 + a^4*b^9) - (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^2*b^7 - 8*a^4*b^5 + 4*a^6*b^3))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(8*a*b^9 - 29*a^3*b^7 + 28*a^5*b^5 - 8*a^7*b^3))/(b^13 - 2*a^2*b^11 + a^4*b^9) - (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a*b^12 - 6*a^3*b^10 + 2*a^5*b^8))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(12*a^2*b^12 - 20*a^4*b^10 + 8*a^6*b^8))/(b^13 - 2*a^2*b^11 + a^4*b^9) - (a*((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(2*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))))/(2*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))))/(2*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)) + (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^2*b^7 - 8*a^4*b^5 + 4*a^6*b^3))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(8*a*b^9 - 29*a^3*b^7 + 28*a^5*b^5 - 8*a^7*b^3))/(b^13 - 2*a^2*b^11 + a^4*b^9) + (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a*b^12 - 6*a^3*b^10 + 2*a^5*b^8))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(12*a^2*b^12 - 20*a^4*b^10 + 8*a^6*b^8))/(b^13 - 2*a^2*b^11 + a^4*b^9) + (a*((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(2*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))))/(2*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))))/(2*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)","B"
272,1,541,101,3.836928,"\text{Not used}","int(1/(b*tan(x) + a/cos(x))^5,x)","\frac{2\,\mathrm{atanh}\left(\frac{16\,a}{\frac{32\,a^3}{b^2}-16\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-16\,a+\frac{32\,a^2\,\mathrm{tan}\left(\frac{x}{2}\right)}{b}+\frac{32\,a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{b^2}}+\frac{16\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{\frac{32\,a^3}{b^2}-16\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-16\,a+\frac{32\,a^2\,\mathrm{tan}\left(\frac{x}{2}\right)}{b}+\frac{32\,a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{b^2}}+\frac{32\,a^2\,\mathrm{tan}\left(\frac{x}{2}\right)}{32\,a^2\,\mathrm{tan}\left(\frac{x}{2}\right)-16\,a\,b+\frac{32\,a^3}{b}+\frac{32\,a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{b}-16\,a\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}\right)}{b^5}-\frac{\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(7\,a^4-3\,b^4\right)}{a^2\,b^3}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6\,\left(7\,a^4-3\,b^4\right)}{a^2\,b^3}+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^4-b^4\right)}{a\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7\,\left(a^4-b^4\right)}{a\,b^4}+\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(21\,a^6+25\,a^4\,b^2-7\,a^2\,b^4-3\,b^6\right)}{3\,a^4\,b^3}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(9\,a^6+52\,a^4\,b^2-a^2\,b^4-12\,b^6\right)}{3\,a^3\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(9\,a^6+52\,a^4\,b^2-a^2\,b^4-12\,b^6\right)}{3\,a^3\,b^4}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(4\,a^4+24\,a^2\,b^2\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^6\,\left(4\,a^4+24\,a^2\,b^2\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(24\,a^3\,b+32\,a\,b^3\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(24\,a^3\,b+32\,a\,b^3\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(6\,a^4+48\,a^2\,b^2+16\,b^4\right)+a^4+a^4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^8+8\,a^3\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7+8\,a^3\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}","Not used",1,"(2*atanh((16*a)/((32*a^3)/b^2 - 16*a*tan(x/2)^2 - 16*a + (32*a^2*tan(x/2))/b + (32*a^3*tan(x/2)^2)/b^2) + (16*a*tan(x/2)^2)/((32*a^3)/b^2 - 16*a*tan(x/2)^2 - 16*a + (32*a^2*tan(x/2))/b + (32*a^3*tan(x/2)^2)/b^2) + (32*a^2*tan(x/2))/(32*a^2*tan(x/2) - 16*a*b + (32*a^3)/b + (32*a^3*tan(x/2)^2)/b - 16*a*b*tan(x/2)^2)))/b^5 - ((2*tan(x/2)^2*(7*a^4 - 3*b^4))/(a^2*b^3) + (2*tan(x/2)^6*(7*a^4 - 3*b^4))/(a^2*b^3) + (2*tan(x/2)*(a^4 - b^4))/(a*b^4) + (2*tan(x/2)^7*(a^4 - b^4))/(a*b^4) + (4*tan(x/2)^4*(21*a^6 - 3*b^6 - 7*a^2*b^4 + 25*a^4*b^2))/(3*a^4*b^3) + (2*tan(x/2)^3*(9*a^6 - 12*b^6 - a^2*b^4 + 52*a^4*b^2))/(3*a^3*b^4) + (2*tan(x/2)^5*(9*a^6 - 12*b^6 - a^2*b^4 + 52*a^4*b^2))/(3*a^3*b^4))/(tan(x/2)^2*(4*a^4 + 24*a^2*b^2) + tan(x/2)^6*(4*a^4 + 24*a^2*b^2) + tan(x/2)^3*(32*a*b^3 + 24*a^3*b) + tan(x/2)^5*(32*a*b^3 + 24*a^3*b) + tan(x/2)^4*(6*a^4 + 16*b^4 + 48*a^2*b^2) + a^4 + a^4*tan(x/2)^8 + 8*a^3*b*tan(x/2)^7 + 8*a^3*b*tan(x/2))","B"
273,1,59,30,2.437584,"\text{Not used}","int((tan(x) + 1/cos(x))^5,x)","\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)-2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)+\frac{8\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-4\,\mathrm{tan}\left(\frac{x}{2}\right)+1}","Not used",1,"log(tan(x/2)^2 + 1) - 2*log(tan(x/2) - 1) + (8*tan(x/2)^2)/(6*tan(x/2)^2 - 4*tan(x/2) - 4*tan(x/2)^3 + tan(x/2)^4 + 1)","B"
274,1,20,30,2.372645,"\text{Not used}","int((tan(x) + 1/cos(x))^4,x)","x-\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{8}{3}}{{\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)}^3}","Not used",1,"x - (8*tan(x/2) - 8/3)/(tan(x/2) - 1)^3","B"
275,1,43,18,2.395054,"\text{Not used}","int((tan(x) + 1/cos(x))^3,x)","2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)-\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)+\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2-2\,\mathrm{tan}\left(\frac{x}{2}\right)+1}","Not used",1,"2*log(tan(x/2) - 1) - log(tan(x/2)^2 + 1) + (4*tan(x/2))/(tan(x/2)^2 - 2*tan(x/2) + 1)","B"
276,1,14,16,2.357031,"\text{Not used}","int((tan(x) + 1/cos(x))^2,x)","-x-\frac{4}{\mathrm{tan}\left(\frac{x}{2}\right)-1}","Not used",1,"- x - 4/(tan(x/2) - 1)","B"
277,1,19,13,2.398912,"\text{Not used}","int(tan(x) + 1/cos(x),x)","\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)-2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)","Not used",1,"log(tan(x/2)^2 + 1) - 2*log(tan(x/2) - 1)","B"
278,1,21,5,2.776500,"\text{Not used}","int(1/(tan(x) + 1/cos(x)),x)","2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)-\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)","Not used",1,"2*log(tan(x/2) + 1) - log(tan(x/2)^2 + 1)","B"
279,1,14,14,2.341741,"\text{Not used}","int(1/(tan(x) + 1/cos(x))^2,x)","-x-\frac{4}{\mathrm{tan}\left(\frac{x}{2}\right)+1}","Not used",1,"- x - 4/(tan(x/2) + 1)","B"
280,1,41,16,2.359313,"\text{Not used}","int(1/(tan(x) + 1/cos(x))^3,x)","\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)-2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)+\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{x}{2}\right)+1}","Not used",1,"log(tan(x/2)^2 + 1) - 2*log(tan(x/2) + 1) + (4*tan(x/2))/(2*tan(x/2) + tan(x/2)^2 + 1)","B"
281,1,19,26,2.340219,"\text{Not used}","int(1/(tan(x) + 1/cos(x))^4,x)","x+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{8}{3}}{{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^3}","Not used",1,"x + (8*tan(x/2) + 8/3)/(tan(x/2) + 1)^3","B"
282,1,61,22,2.379422,"\text{Not used}","int(1/(tan(x) + 1/cos(x))^5,x)","2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)-\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)-\frac{8\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+4\,\mathrm{tan}\left(\frac{x}{2}\right)+1}","Not used",1,"2*log(tan(x/2) + 1) - log(tan(x/2)^2 + 1) - (8*tan(x/2)^2)/(4*tan(x/2) + 6*tan(x/2)^2 + 4*tan(x/2)^3 + tan(x/2)^4 + 1)","B"
283,1,174,152,2.580342,"\text{Not used}","int((b/sin(x) + a*cot(x))^5,x)","{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(\frac{5\,\left(a+b\right)\,{\left(a-b\right)}^4}{32}+\frac{{\left(a-b\right)}^5}{32}\right)-\frac{\frac{5\,a\,b^4}{4}+\frac{5\,a^4\,b}{4}-{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(3\,a^5+10\,a^4\,b+10\,a^3\,b^2-5\,a\,b^4-2\,b^5\right)+\frac{a^5}{4}+\frac{b^5}{4}+\frac{5\,a^2\,b^3}{2}+\frac{5\,a^3\,b^2}{2}}{16\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}-a^5\,\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)+\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(a^5+\frac{15\,a^4\,b}{8}-\frac{5\,a^2\,b^3}{4}+\frac{3\,b^5}{8}\right)-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,{\left(a-b\right)}^5}{64}","Not used",1,"tan(x/2)^2*((5*(a + b)*(a - b)^4)/32 + (a - b)^5/32) - ((5*a*b^4)/4 + (5*a^4*b)/4 - tan(x/2)^2*(10*a^4*b - 5*a*b^4 + 3*a^5 - 2*b^5 + 10*a^3*b^2) + a^5/4 + b^5/4 + (5*a^2*b^3)/2 + (5*a^3*b^2)/2)/(16*tan(x/2)^4) - a^5*log(tan(x/2)^2 + 1) + log(tan(x/2))*((15*a^4*b)/8 + a^5 + (3*b^5)/8 - (5*a^2*b^3)/4) - (tan(x/2)^4*(a - b)^5)/64","B"
284,1,127,101,2.530382,"\text{Not used}","int((b/sin(x) + a*cot(x))^4,x)","a^4\,x-\frac{\frac{4\,a\,b^3}{3}+\frac{4\,a^3\,b}{3}-{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(5\,a^4+12\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3-3\,b^4\right)+\frac{a^4}{3}+\frac{b^4}{3}+2\,a^2\,b^2}{8\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{\left(a+b\right)\,{\left(a-b\right)}^3}{2}+\frac{{\left(a-b\right)}^4}{8}\right)+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,{\left(a-b\right)}^4}{24}","Not used",1,"a^4*x - ((4*a*b^3)/3 + (4*a^3*b)/3 - tan(x/2)^2*(12*a^3*b - 4*a*b^3 + 5*a^4 - 3*b^4 + 6*a^2*b^2) + a^4/3 + b^4/3 + 2*a^2*b^2)/(8*tan(x/2)^3) - tan(x/2)*(((a + b)*(a - b)^3)/2 + (a - b)^4/8) + (tan(x/2)^3*(a - b)^4)/24","B"
285,1,82,77,2.448156,"\text{Not used}","int((b/sin(x) + a*cot(x))^3,x)","a^3\,\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)-\frac{\frac{a^3}{8}+\frac{3\,a^2\,b}{8}+\frac{3\,a\,b^2}{8}+\frac{b^3}{8}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}-\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(a^3+\frac{3\,a^2\,b}{2}-\frac{b^3}{2}\right)-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,{\left(a-b\right)}^3}{8}","Not used",1,"a^3*log(tan(x/2)^2 + 1) - ((3*a*b^2)/8 + (3*a^2*b)/8 + a^3/8 + b^3/8)/tan(x/2)^2 - log(tan(x/2))*((3*a^2*b)/2 + a^3 - b^3/2) - (tan(x/2)^2*(a - b)^3)/8","B"
286,1,30,29,2.417204,"\text{Not used}","int((b/sin(x) + a*cot(x))^2,x)","-\frac{\cos\left(x\right)\,a^2+2\,a\,b+\cos\left(x\right)\,b^2}{\sin\left(x\right)}-a^2\,x","Not used",1,"- (2*a*b + a^2*cos(x) + b^2*cos(x))/sin(x) - a^2*x","B"
287,1,27,12,2.408027,"\text{Not used}","int(b/sin(x) + a*cot(x),x)","a\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-a\,\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)+b\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)","Not used",1,"a*log(tan(x/2)) - a*log(tan(x/2)^2 + 1) + b*log(tan(x/2))","B"
288,1,36,12,3.282996,"\text{Not used}","int(1/(b/sin(x) + a*cot(x)),x)","\frac{\mathrm{atan}\left(\frac{a\,{\sin\left(\frac{x}{2}\right)}^2}{-1{}\mathrm{i}\,a\,{\sin\left(\frac{x}{2}\right)}^2+a\,1{}\mathrm{i}+b\,1{}\mathrm{i}}\right)\,2{}\mathrm{i}}{a}","Not used",1,"(atan((a*sin(x/2)^2)/(a*1i + b*1i - a*sin(x/2)^2*1i))*2i)/a","B"
289,1,440,67,3.043579,"\text{Not used}","int(1/(b/sin(x) + a*cot(x))^2,x)","\frac{a^3\,\sin\left(x\right)+b^2\,\left(-a\,\sin\left(x\right)+\mathrm{atan}\left(\frac{-a^5\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+b^3\,\sin\left(\frac{x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}+b^5\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+a^4\,b\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-a^2\,b^3\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,3{}\mathrm{i}+a^3\,b^2\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}}{\cos\left(\frac{x}{2}\right)\,a^6-2\,\cos\left(\frac{x}{2}\right)\,a^4\,b^2+\cos\left(\frac{x}{2}\right)\,a^2\,b^4}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}\right)+a\,b\,\mathrm{atan}\left(\frac{-a^5\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+b^3\,\sin\left(\frac{x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}+b^5\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+a^4\,b\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-a^2\,b^3\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,3{}\mathrm{i}+a^3\,b^2\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}}{\cos\left(\frac{x}{2}\right)\,a^6-2\,\cos\left(\frac{x}{2}\right)\,a^4\,b^2+\cos\left(\frac{x}{2}\right)\,a^2\,b^4}\right)\,\cos\left(x\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{\cos\left(x\right)\,a^5+a^4\,b-\cos\left(x\right)\,a^3\,b^2-a^2\,b^3}-\frac{2\,\mathrm{atan}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{a^2}","Not used",1,"(a^3*sin(x) + b^2*(atan((b^3*sin(x/2)*(a^2 - b^2)^(3/2)*2i - a^5*sin(x/2)*(a^2 - b^2)^(1/2)*1i + b^5*sin(x/2)*(a^2 - b^2)^(1/2)*2i + a^4*b*sin(x/2)*(a^2 - b^2)^(1/2)*1i - a^2*b^3*sin(x/2)*(a^2 - b^2)^(1/2)*3i + a^3*b^2*sin(x/2)*(a^2 - b^2)^(1/2)*1i)/(a^6*cos(x/2) + a^2*b^4*cos(x/2) - 2*a^4*b^2*cos(x/2)))*(a^2 - b^2)^(1/2)*2i - a*sin(x)) + a*b*atan((b^3*sin(x/2)*(a^2 - b^2)^(3/2)*2i - a^5*sin(x/2)*(a^2 - b^2)^(1/2)*1i + b^5*sin(x/2)*(a^2 - b^2)^(1/2)*2i + a^4*b*sin(x/2)*(a^2 - b^2)^(1/2)*1i - a^2*b^3*sin(x/2)*(a^2 - b^2)^(1/2)*3i + a^3*b^2*sin(x/2)*(a^2 - b^2)^(1/2)*1i)/(a^6*cos(x/2) + a^2*b^4*cos(x/2) - 2*a^4*b^2*cos(x/2)))*cos(x)*(a^2 - b^2)^(1/2)*2i)/(a^4*b - a^2*b^3 + a^5*cos(x) - a^3*b^2*cos(x)) - (2*atan(sin(x/2)/cos(x/2)))/a^2","B"
290,1,311,50,2.770457,"\text{Not used}","int(1/(b/sin(x) + a*cot(x))^3,x)","\frac{\frac{2\,\left(b^2+a\,b\right)}{a^2\,\left(a-b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a-b\right)}{a^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+2\,a\,b-{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+a^2+b^2}-\frac{2\,\mathrm{atanh}\left(\frac{32\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{\frac{32\,b^3}{a^3}-\frac{32\,b^2}{a^2}-\frac{32\,b}{a}+\frac{32\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a}-\frac{64\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^2}+\frac{32\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^3}+32}-\frac{64\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{32\,a-32\,b+32\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-\frac{32\,b^2}{a}+\frac{32\,b^3}{a^2}-\frac{64\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a}+\frac{32\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^2}}+\frac{32\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{32\,a^2-32\,a\,b-32\,b^2-64\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\frac{32\,b^3}{a}+\frac{32\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a}+32\,a\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}\right)}{a^3}","Not used",1,"((2*(a*b + b^2))/(a^2*(a - b)) + (2*tan(x/2)^2*(a - b))/a^2)/(tan(x/2)^4*(a^2 - 2*a*b + b^2) + 2*a*b - tan(x/2)^2*(2*a^2 - 2*b^2) + a^2 + b^2) - (2*atanh((32*tan(x/2)^2)/((32*b^3)/a^3 - (32*b^2)/a^2 - (32*b)/a + (32*b*tan(x/2)^2)/a - (64*b^2*tan(x/2)^2)/a^2 + (32*b^3*tan(x/2)^2)/a^3 + 32) - (64*b*tan(x/2)^2)/(32*a - 32*b + 32*b*tan(x/2)^2 - (32*b^2)/a + (32*b^3)/a^2 - (64*b^2*tan(x/2)^2)/a + (32*b^3*tan(x/2)^2)/a^2) + (32*b^2*tan(x/2)^2)/(32*a^2 - 32*a*b - 32*b^2 - 64*b^2*tan(x/2)^2 + (32*b^3)/a + (32*b^3*tan(x/2)^2)/a + 32*a*b*tan(x/2)^2)))/a^3","B"
291,1,3068,159,8.245598,"\text{Not used}","int(1/(b/sin(x) + a*cot(x))^4,x)","\frac{2\,\mathrm{atan}\left(\frac{\frac{\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a^6-8\,a^5\,b+5\,a^4\,b^2+16\,a^3\,b^3-16\,a^2\,b^4-8\,a\,b^5+8\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(\frac{8\,\left(-4\,a^{13}+6\,a^{12}\,b+6\,a^{11}\,b^2-10\,a^{10}\,b^3-2\,a^9\,b^4+4\,a^8\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)\,8{}\mathrm{i}}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,1{}\mathrm{i}}{a^4}}{a^4}-\frac{-\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a^6-8\,a^5\,b+5\,a^4\,b^2+16\,a^3\,b^3-16\,a^2\,b^4-8\,a\,b^5+8\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(\frac{8\,\left(-4\,a^{13}+6\,a^{12}\,b+6\,a^{11}\,b^2-10\,a^{10}\,b^3-2\,a^9\,b^4+4\,a^8\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)\,8{}\mathrm{i}}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,1{}\mathrm{i}}{a^4}}{a^4}}{\frac{16\,\left(6\,a^4\,b+3\,a^3\,b^2-10\,a^2\,b^3-2\,a\,b^4+4\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a^6-8\,a^5\,b+5\,a^4\,b^2+16\,a^3\,b^3-16\,a^2\,b^4-8\,a\,b^5+8\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(\frac{8\,\left(-4\,a^{13}+6\,a^{12}\,b+6\,a^{11}\,b^2-10\,a^{10}\,b^3-2\,a^9\,b^4+4\,a^8\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)\,8{}\mathrm{i}}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,1{}\mathrm{i}}{a^4}\right)\,1{}\mathrm{i}}{a^4}+\frac{\left(-\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a^6-8\,a^5\,b+5\,a^4\,b^2+16\,a^3\,b^3-16\,a^2\,b^4-8\,a\,b^5+8\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(\frac{8\,\left(-4\,a^{13}+6\,a^{12}\,b+6\,a^{11}\,b^2-10\,a^{10}\,b^3-2\,a^9\,b^4+4\,a^8\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)\,8{}\mathrm{i}}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,1{}\mathrm{i}}{a^4}\right)\,1{}\mathrm{i}}{a^4}}\right)}{a^4}+\frac{\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(5\,a^2-3\,b^2\right)}{3\,a^3}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a+b\right)\,\left(-2\,a^2+a\,b+2\,b^2\right)}{a^3\,b-a^4}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(-2\,a^3+a^2\,b+3\,a\,b^2-2\,b^3\right)}{a^3\,\left(a+b\right)}}{3\,a\,b^2-{\mathrm{tan}\left(\frac{x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)+3\,a^2\,b+{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)-{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)+a^3+b^3}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(3\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a^6-8\,a^5\,b+5\,a^4\,b^2+16\,a^3\,b^3-16\,a^2\,b^4-8\,a\,b^5+8\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b\,\left(\frac{8\,\left(-4\,a^{13}+6\,a^{12}\,b+6\,a^{11}\,b^2-10\,a^{10}\,b^3-2\,a^9\,b^4+4\,a^8\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{4\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,1{}\mathrm{i}}{2\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}+\frac{b\,\left(3\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a^6-8\,a^5\,b+5\,a^4\,b^2+16\,a^3\,b^3-16\,a^2\,b^4-8\,a\,b^5+8\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b\,\left(\frac{8\,\left(-4\,a^{13}+6\,a^{12}\,b+6\,a^{11}\,b^2-10\,a^{10}\,b^3-2\,a^9\,b^4+4\,a^8\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{4\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,1{}\mathrm{i}}{2\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}}{\frac{16\,\left(6\,a^4\,b+3\,a^3\,b^2-10\,a^2\,b^3-2\,a\,b^4+4\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{b\,\left(3\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a^6-8\,a^5\,b+5\,a^4\,b^2+16\,a^3\,b^3-16\,a^2\,b^4-8\,a\,b^5+8\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b\,\left(\frac{8\,\left(-4\,a^{13}+6\,a^{12}\,b+6\,a^{11}\,b^2-10\,a^{10}\,b^3-2\,a^9\,b^4+4\,a^8\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{4\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)}{2\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}-\frac{b\,\left(3\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a^6-8\,a^5\,b+5\,a^4\,b^2+16\,a^3\,b^3-16\,a^2\,b^4-8\,a\,b^5+8\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b\,\left(\frac{8\,\left(-4\,a^{13}+6\,a^{12}\,b+6\,a^{11}\,b^2-10\,a^{10}\,b^3-2\,a^9\,b^4+4\,a^8\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{4\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)}{2\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}","Not used",1,"(2*atan((((((8*(6*a^12*b - 4*a^13 + 4*a^8*b^5 - 2*a^9*b^4 - 10*a^10*b^3 + 6*a^11*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (tan(x/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2)*8i)/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*1i)/a^4 + (8*tan(x/2)*(4*a^6 - 8*a^5*b - 8*a*b^5 + 8*b^6 - 16*a^2*b^4 + 16*a^3*b^3 + 5*a^4*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2))/a^4 - ((((8*(6*a^12*b - 4*a^13 + 4*a^8*b^5 - 2*a^9*b^4 - 10*a^10*b^3 + 6*a^11*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (tan(x/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2)*8i)/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*1i)/a^4 - (8*tan(x/2)*(4*a^6 - 8*a^5*b - 8*a*b^5 + 8*b^6 - 16*a^2*b^4 + 16*a^3*b^3 + 5*a^4*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2))/a^4)/((16*(6*a^4*b - 2*a*b^4 + 4*b^5 - 10*a^2*b^3 + 3*a^3*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (((((8*(6*a^12*b - 4*a^13 + 4*a^8*b^5 - 2*a^9*b^4 - 10*a^10*b^3 + 6*a^11*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (tan(x/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2)*8i)/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*1i)/a^4 + (8*tan(x/2)*(4*a^6 - 8*a^5*b - 8*a*b^5 + 8*b^6 - 16*a^2*b^4 + 16*a^3*b^3 + 5*a^4*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2))*1i)/a^4 + (((((8*(6*a^12*b - 4*a^13 + 4*a^8*b^5 - 2*a^9*b^4 - 10*a^10*b^3 + 6*a^11*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (tan(x/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2)*8i)/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*1i)/a^4 - (8*tan(x/2)*(4*a^6 - 8*a^5*b - 8*a*b^5 + 8*b^6 - 16*a^2*b^4 + 16*a^3*b^3 + 5*a^4*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2))*1i)/a^4)))/a^4 + ((4*tan(x/2)^3*(5*a^2 - 3*b^2))/(3*a^3) - (tan(x/2)*(a + b)*(a*b - 2*a^2 + 2*b^2))/(a^3*b - a^4) + (tan(x/2)^5*(3*a*b^2 + a^2*b - 2*a^3 - 2*b^3))/(a^3*(a + b)))/(3*a*b^2 - tan(x/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3) + 3*a^2*b + tan(x/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) - tan(x/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) + a^3 + b^3) + (b*atan(((b*(3*a^2 - 2*b^2)*((a + b)^3*(a - b)^3)^(1/2)*((8*tan(x/2)*(4*a^6 - 8*a^5*b - 8*a*b^5 + 8*b^6 - 16*a^2*b^4 + 16*a^3*b^3 + 5*a^4*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b*((8*(6*a^12*b - 4*a^13 + 4*a^8*b^5 - 2*a^9*b^4 - 10*a^10*b^3 + 6*a^11*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (4*b*tan(x/2)*(3*a^2 - 2*b^2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*a^2 - 2*b^2)*((a + b)^3*(a - b)^3)^(1/2))/(2*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*1i)/(2*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)) + (b*(3*a^2 - 2*b^2)*((a + b)^3*(a - b)^3)^(1/2)*((8*tan(x/2)*(4*a^6 - 8*a^5*b - 8*a*b^5 + 8*b^6 - 16*a^2*b^4 + 16*a^3*b^3 + 5*a^4*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b*((8*(6*a^12*b - 4*a^13 + 4*a^8*b^5 - 2*a^9*b^4 - 10*a^10*b^3 + 6*a^11*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (4*b*tan(x/2)*(3*a^2 - 2*b^2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*a^2 - 2*b^2)*((a + b)^3*(a - b)^3)^(1/2))/(2*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*1i)/(2*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))/((16*(6*a^4*b - 2*a*b^4 + 4*b^5 - 10*a^2*b^3 + 3*a^3*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (b*(3*a^2 - 2*b^2)*((a + b)^3*(a - b)^3)^(1/2)*((8*tan(x/2)*(4*a^6 - 8*a^5*b - 8*a*b^5 + 8*b^6 - 16*a^2*b^4 + 16*a^3*b^3 + 5*a^4*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b*((8*(6*a^12*b - 4*a^13 + 4*a^8*b^5 - 2*a^9*b^4 - 10*a^10*b^3 + 6*a^11*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (4*b*tan(x/2)*(3*a^2 - 2*b^2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*a^2 - 2*b^2)*((a + b)^3*(a - b)^3)^(1/2))/(2*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))))/(2*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)) - (b*(3*a^2 - 2*b^2)*((a + b)^3*(a - b)^3)^(1/2)*((8*tan(x/2)*(4*a^6 - 8*a^5*b - 8*a*b^5 + 8*b^6 - 16*a^2*b^4 + 16*a^3*b^3 + 5*a^4*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b*((8*(6*a^12*b - 4*a^13 + 4*a^8*b^5 - 2*a^9*b^4 - 10*a^10*b^3 + 6*a^11*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (4*b*tan(x/2)*(3*a^2 - 2*b^2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*a^2 - 2*b^2)*((a + b)^3*(a - b)^3)^(1/2))/(2*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))))/(2*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))))*(3*a^2 - 2*b^2)*((a + b)^3*(a - b)^3)^(1/2)*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)","B"
292,1,538,100,3.680235,"\text{Not used}","int(1/(b/sin(x) + a*cot(x))^5,x)","\frac{2\,\mathrm{atanh}\left(\frac{32\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{\frac{32\,b^3}{a^3}-\frac{32\,b^2}{a^2}-\frac{32\,b}{a}+\frac{32\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a}-\frac{64\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^2}+\frac{32\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^3}+32}-\frac{64\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{32\,a-32\,b+32\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-\frac{32\,b^2}{a}+\frac{32\,b^3}{a^2}-\frac{64\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a}+\frac{32\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^2}}+\frac{32\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{32\,a^2-32\,a\,b-32\,b^2-64\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\frac{32\,b^3}{a}+\frac{32\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a}+32\,a\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}\right)}{a^5}-\frac{\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}{a^4}+\frac{2\,\left(5\,a^4\,b+10\,a^3\,b^2+2\,a^2\,b^3-6\,a\,b^4-3\,b^5\right)}{3\,a^4\,{\left(a-b\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(-4\,a^3+5\,a^2\,b+2\,a\,b^2-3\,b^3\right)}{a^4}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(3\,a^4-14\,a^3\,b-20\,a^2\,b^2+6\,a\,b^3+9\,b^4\right)}{3\,a^4\,\left(a-b\right)}}{4\,a\,b^3+4\,a^3\,b+{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(6\,a^4-12\,a^2\,b^2+6\,b^4\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(-4\,a^4-8\,a^3\,b+8\,a\,b^3+4\,b^4\right)-{\mathrm{tan}\left(\frac{x}{2}\right)}^6\,\left(4\,a^4-8\,a^3\,b+8\,a\,b^3-4\,b^4\right)+a^4+b^4+{\mathrm{tan}\left(\frac{x}{2}\right)}^8\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)+6\,a^2\,b^2}","Not used",1,"(2*atanh((32*tan(x/2)^2)/((32*b^3)/a^3 - (32*b^2)/a^2 - (32*b)/a + (32*b*tan(x/2)^2)/a - (64*b^2*tan(x/2)^2)/a^2 + (32*b^3*tan(x/2)^2)/a^3 + 32) - (64*b*tan(x/2)^2)/(32*a - 32*b + 32*b*tan(x/2)^2 - (32*b^2)/a + (32*b^3)/a^2 - (64*b^2*tan(x/2)^2)/a + (32*b^3*tan(x/2)^2)/a^2) + (32*b^2*tan(x/2)^2)/(32*a^2 - 32*a*b - 32*b^2 - 64*b^2*tan(x/2)^2 + (32*b^3)/a + (32*b^3*tan(x/2)^2)/a + 32*a*b*tan(x/2)^2)))/a^5 - ((2*tan(x/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))/a^4 + (2*(5*a^4*b - 6*a*b^4 - 3*b^5 + 2*a^2*b^3 + 10*a^3*b^2))/(3*a^4*(a - b)^2) + (2*tan(x/2)^4*(2*a*b^2 + 5*a^2*b - 4*a^3 - 3*b^3))/a^4 + (2*tan(x/2)^2*(6*a*b^3 - 14*a^3*b + 3*a^4 + 9*b^4 - 20*a^2*b^2))/(3*a^4*(a - b)))/(4*a*b^3 + 4*a^3*b + tan(x/2)^4*(6*a^4 + 6*b^4 - 12*a^2*b^2) + tan(x/2)^2*(8*a*b^3 - 8*a^3*b - 4*a^4 + 4*b^4) - tan(x/2)^6*(8*a*b^3 - 8*a^3*b + 4*a^4 - 4*b^4) + a^4 + b^4 + tan(x/2)^8*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2) + 6*a^2*b^2)","B"
293,1,34,28,2.417431,"\text{Not used}","int((cot(x) + 1/sin(x))^5,x)","2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2-\frac{1}{2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4}","Not used",1,"2*log(tan(x/2)) - log(tan(x/2)^2 + 1) + (tan(x/2)^2 - 1/2)/tan(x/2)^4","B"
294,1,16,30,2.413155,"\text{Not used}","int((cot(x) + 1/sin(x))^4,x)","-\frac{2\,{\mathrm{cot}\left(\frac{x}{2}\right)}^3}{3}+2\,\mathrm{cot}\left(\frac{x}{2}\right)+x","Not used",1,"x + 2*cot(x/2) - (2*cot(x/2)^3)/3","B"
295,1,25,20,2.385118,"\text{Not used}","int((cot(x) + 1/sin(x))^3,x)","\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)-2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-\frac{1}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}","Not used",1,"log(tan(x/2)^2 + 1) - 2*log(tan(x/2)) - 1/tan(x/2)^2","B"
296,1,10,16,2.403776,"\text{Not used}","int((cot(x) + 1/sin(x))^2,x)","-x-2\,\mathrm{cot}\left(\frac{x}{2}\right)","Not used",1,"- x - 2*cot(x/2)","B"
297,1,19,9,2.409056,"\text{Not used}","int(cot(x) + 1/sin(x),x)","2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)","Not used",1,"2*log(tan(x/2)) - log(tan(x/2)^2 + 1)","B"
298,1,9,7,2.857200,"\text{Not used}","int(1/(cot(x) + 1/sin(x)),x)","\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)","Not used",1,"log(tan(x/2)^2 + 1)","B"
299,1,10,14,2.406954,"\text{Not used}","int(1/(cot(x) + 1/sin(x))^2,x)","2\,\mathrm{tan}\left(\frac{x}{2}\right)-x","Not used",1,"2*tan(x/2) - x","B"
300,1,18,14,2.345310,"\text{Not used}","int(1/(cot(x) + 1/sin(x))^3,x)","{\mathrm{tan}\left(\frac{x}{2}\right)}^2-\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)","Not used",1,"tan(x/2)^2 - log(tan(x/2)^2 + 1)","B"
301,1,16,26,2.371248,"\text{Not used}","int(1/(cot(x) + 1/sin(x))^4,x)","\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{3}-2\,\mathrm{tan}\left(\frac{x}{2}\right)+x","Not used",1,"x - 2*tan(x/2) + (2*tan(x/2)^3)/3","B"
302,1,26,24,2.408110,"\text{Not used}","int(1/(cot(x) + 1/sin(x))^5,x)","\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)-{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{2}","Not used",1,"log(tan(x/2)^2 + 1) - tan(x/2)^2 + tan(x/2)^4/2","B"
303,1,59,44,2.494394,"\text{Not used}","int((sin(x) - 1/sin(x))^4,x)","\frac{\frac{{\cos\left(x\right)}^7}{4}+\frac{7\,{\cos\left(x\right)}^5}{8}-\frac{35\,{\cos\left(x\right)}^3}{6}+\frac{35\,\cos\left(x\right)}{8}}{\sin\left(x\right)-{\cos\left(x\right)}^2\,\sin\left(x\right)}-\frac{\frac{35\,x}{8}-\frac{35\,x\,{\cos\left(x\right)}^2}{8}}{{\cos\left(x\right)}^2-1}","Not used",1,"((35*cos(x))/8 - (35*cos(x)^3)/6 + (7*cos(x)^5)/8 + cos(x)^7/4)/(sin(x) - cos(x)^2*sin(x)) - ((35*x)/8 - (35*x*cos(x)^2)/8)/(cos(x)^2 - 1)","B"
304,1,75,34,2.487504,"\text{Not used}","int(-(sin(x) - 1/sin(x))^3,x)","\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8}-\frac{\frac{49\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6}{8}+\frac{67\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{8}+\frac{121\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{24}+\frac{1}{8}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^8+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+{\mathrm{tan}\left(\frac{x}{2}\right)}^2}-\frac{5\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{2}","Not used",1,"tan(x/2)^2/8 - ((121*tan(x/2)^2)/24 + (67*tan(x/2)^4)/8 + (49*tan(x/2)^6)/8 + 1/8)/(tan(x/2)^2 + 3*tan(x/2)^4 + 3*tan(x/2)^6 + tan(x/2)^8) - (5*log(tan(x/2)))/2","B"
305,1,21,22,2.404088,"\text{Not used}","int((sin(x) - 1/sin(x))^2,x)","-\frac{3\,x}{2}-\frac{\frac{3\,\cos\left(x\right)}{2}-\frac{{\cos\left(x\right)}^3}{2}}{\sin\left(x\right)}","Not used",1,"- (3*x)/2 - ((3*cos(x))/2 - cos(x)^3/2)/sin(x)","B"
306,1,8,8,0.020992,"\text{Not used}","int(1/sin(x) - sin(x),x)","\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)+\cos\left(x\right)","Not used",1,"log(tan(x/2)) + cos(x)","B"
307,1,12,2,2.461513,"\text{Not used}","int(-1/(sin(x) - 1/sin(x)),x)","-\frac{2}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2-1}","Not used",1,"-2/(tan(x/2)^2 - 1)","B"
308,1,6,8,2.405660,"\text{Not used}","int(1/(sin(x) - 1/sin(x))^2,x)","\frac{{\mathrm{tan}\left(x\right)}^3}{3}","Not used",1,"tan(x)^3/3","B"
309,1,13,17,2.546564,"\text{Not used}","int(-1/(sin(x) - 1/sin(x))^3,x)","\frac{1}{5\,{\cos\left(x\right)}^5}-\frac{1}{3\,{\cos\left(x\right)}^3}","Not used",1,"1/(5*cos(x)^5) - 1/(3*cos(x)^3)","B"
310,1,23,17,2.565797,"\text{Not used}","int(1/(sin(x) - 1/sin(x))^4,x)","\frac{2\,{\cos\left(x\right)}^2\,{\sin\left(x\right)}^5+5\,{\sin\left(x\right)}^5}{35\,{\cos\left(x\right)}^7}","Not used",1,"(5*sin(x)^5 + 2*cos(x)^2*sin(x)^5)/(35*cos(x)^7)","B"
311,1,19,25,2.944372,"\text{Not used}","int(-1/(sin(x) - 1/sin(x))^5,x)","\frac{1}{5\,{\cos\left(x\right)}^5}-\frac{2}{7\,{\cos\left(x\right)}^7}+\frac{1}{9\,{\cos\left(x\right)}^9}","Not used",1,"1/(5*cos(x)^5) - 2/(7*cos(x)^7) + 1/(9*cos(x)^9)","B"
312,1,33,25,2.914585,"\text{Not used}","int(1/(sin(x) - 1/sin(x))^6,x)","\frac{8\,{\cos\left(x\right)}^4\,{\sin\left(x\right)}^7+28\,{\cos\left(x\right)}^2\,{\sin\left(x\right)}^7+63\,{\sin\left(x\right)}^7}{693\,{\cos\left(x\right)}^{11}}","Not used",1,"(63*sin(x)^7 + 28*cos(x)^2*sin(x)^7 + 8*cos(x)^4*sin(x)^7)/(693*cos(x)^11)","B"
313,1,25,33,3.538022,"\text{Not used}","int(-1/(sin(x) - 1/sin(x))^7,x)","\frac{1}{3\,{\cos\left(x\right)}^9}-\frac{1}{7\,{\cos\left(x\right)}^7}-\frac{3}{11\,{\cos\left(x\right)}^{11}}+\frac{1}{13\,{\cos\left(x\right)}^{13}}","Not used",1,"1/(3*cos(x)^9) - 1/(7*cos(x)^7) - 3/(11*cos(x)^11) + 1/(13*cos(x)^13)","B"
314,0,-1,73,0.000000,"\text{Not used}","int((1/sin(x) - sin(x))^(7/2),x)","\int {\left(\frac{1}{\sin\left(x\right)}-\sin\left(x\right)\right)}^{7/2} \,d x","Not used",1,"int((1/sin(x) - sin(x))^(7/2), x)","F"
315,0,-1,50,0.000000,"\text{Not used}","int((1/sin(x) - sin(x))^(5/2),x)","\int {\left(\frac{1}{\sin\left(x\right)}-\sin\left(x\right)\right)}^{5/2} \,d x","Not used",1,"int((1/sin(x) - sin(x))^(5/2), x)","F"
316,0,-1,31,0.000000,"\text{Not used}","int((1/sin(x) - sin(x))^(3/2),x)","\int {\left(\frac{1}{\sin\left(x\right)}-\sin\left(x\right)\right)}^{3/2} \,d x","Not used",1,"int((1/sin(x) - sin(x))^(3/2), x)","F"
317,1,15,13,2.483287,"\text{Not used}","int((1/sin(x) - sin(x))^(1/2),x)","\frac{2\,\left|\cos\left(x\right)\right|}{\cos\left(x\right)\,\sqrt{\frac{1}{\sin\left(x\right)}}}","Not used",1,"(2*abs(cos(x)))/(cos(x)*(1/sin(x))^(1/2))","B"
318,0,-1,60,0.000000,"\text{Not used}","int(1/(1/sin(x) - sin(x))^(1/2),x)","\int \frac{1}{\sqrt{\frac{1}{\sin\left(x\right)}-\sin\left(x\right)}} \,d x","Not used",1,"int(1/(1/sin(x) - sin(x))^(1/2), x)","F"
319,0,-1,80,0.000000,"\text{Not used}","int(1/(1/sin(x) - sin(x))^(3/2),x)","\int \frac{1}{{\left(\frac{1}{\sin\left(x\right)}-\sin\left(x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(1/sin(x) - sin(x))^(3/2), x)","F"
320,0,-1,99,0.000000,"\text{Not used}","int(1/(1/sin(x) - sin(x))^(5/2),x)","\int \frac{1}{{\left(\frac{1}{\sin\left(x\right)}-\sin\left(x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(1/sin(x) - sin(x))^(5/2), x)","F"
321,0,-1,118,0.000000,"\text{Not used}","int(1/(1/sin(x) - sin(x))^(7/2),x)","\int \frac{1}{{\left(\frac{1}{\sin\left(x\right)}-\sin\left(x\right)\right)}^{7/2}} \,d x","Not used",1,"int(1/(1/sin(x) - sin(x))^(7/2), x)","F"
322,1,80,44,2.573251,"\text{Not used}","int((cos(x) - 1/cos(x))^4,x)","\frac{35\,x}{8}+\frac{\frac{35\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{13}}{4}+\frac{35\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{11}}{6}-\frac{329\,{\mathrm{tan}\left(\frac{x}{2}\right)}^9}{12}-17\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7-\frac{329\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{12}+\frac{35\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{6}+\frac{35\,\mathrm{tan}\left(\frac{x}{2}\right)}{4}}{{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2-1\right)}^3\,{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}^4}","Not used",1,"(35*x)/8 + ((35*tan(x/2))/4 + (35*tan(x/2)^3)/6 - (329*tan(x/2)^5)/12 - 17*tan(x/2)^7 - (329*tan(x/2)^9)/12 + (35*tan(x/2)^11)/6 + (35*tan(x/2)^13)/4)/((tan(x/2)^2 - 1)^3*(tan(x/2)^2 + 1)^4)","B"
323,1,68,34,2.464240,"\text{Not used}","int(-(cos(x) - 1/cos(x))^3,x)","\frac{5\,{\mathrm{tan}\left(\frac{x}{2}\right)}^9+\frac{20\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7}{3}-\frac{22\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{3}+\frac{20\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{3}+5\,\mathrm{tan}\left(\frac{x}{2}\right)}{{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2-1\right)}^2\,{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}^3}-5\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)","Not used",1,"(5*tan(x/2) + (20*tan(x/2)^3)/3 - (22*tan(x/2)^5)/3 + (20*tan(x/2)^7)/3 + 5*tan(x/2)^9)/((tan(x/2)^2 - 1)^2*(tan(x/2)^2 + 1)^3) - 5*atanh(tan(x/2))","B"
324,1,49,22,2.410260,"\text{Not used}","int((cos(x) - 1/cos(x))^2,x)","-\frac{3\,x}{2}-\frac{3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+3\,\mathrm{tan}\left(\frac{x}{2}\right)}{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2-1\right)\,{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}^2}","Not used",1,"- (3*x)/2 - (3*tan(x/2) + 2*tan(x/2)^3 + 3*tan(x/2)^5)/((tan(x/2)^2 - 1)*(tan(x/2)^2 + 1)^2)","B"
325,1,14,8,2.299510,"\text{Not used}","int(1/cos(x) - cos(x),x)","\ln\left(\mathrm{tan}\left(\frac{x}{2}+\frac{\pi }{4}\right)\right)-\sin\left(x\right)","Not used",1,"log(tan(x/2 + pi/4)) - sin(x)","B"
326,1,6,4,2.368155,"\text{Not used}","int(-1/(cos(x) - 1/cos(x)),x)","-\frac{1}{\sin\left(x\right)}","Not used",1,"-1/sin(x)","B"
327,1,6,8,2.450210,"\text{Not used}","int(1/(cos(x) - 1/cos(x))^2,x)","-\frac{{\mathrm{cot}\left(x\right)}^3}{3}","Not used",1,"-cot(x)^3/3","B"
328,1,14,17,2.381557,"\text{Not used}","int(-1/(cos(x) - 1/cos(x))^3,x)","\frac{5\,{\sin\left(x\right)}^2-3}{15\,{\sin\left(x\right)}^5}","Not used",1,"(5*sin(x)^2 - 3)/(15*sin(x)^5)","B"
329,1,16,17,2.430542,"\text{Not used}","int(1/(cos(x) - 1/cos(x))^4,x)","\frac{{\cos\left(x\right)}^5\,\left(\cos\left(2\,x\right)-6\right)}{35\,{\sin\left(x\right)}^7}","Not used",1,"(cos(x)^5*(cos(2*x) - 6))/(35*sin(x)^7)","B"
330,1,20,25,2.421159,"\text{Not used}","int(-1/(cos(x) - 1/cos(x))^5,x)","-\frac{63\,{\sin\left(x\right)}^4-90\,{\sin\left(x\right)}^2+35}{315\,{\sin\left(x\right)}^9}","Not used",1,"-(63*sin(x)^4 - 90*sin(x)^2 + 35)/(315*sin(x)^9)","B"
331,1,46,25,2.446269,"\text{Not used}","int(1/(cos(x) - 1/cos(x))^6,x)","-\frac{80\,{\cos\left(x\right)}^7-18\,{\cos\left(x\right)}^7\,\left(2\,{\cos\left(x\right)}^2-1\right)+{\cos\left(x\right)}^7\,\left(2\,{\left(2\,{\cos\left(x\right)}^2-1\right)}^2-1\right)}{693\,{\sin\left(x\right)}^{11}}","Not used",1,"-(80*cos(x)^7 - 18*cos(x)^7*(2*cos(x)^2 - 1) + cos(x)^7*(2*(2*cos(x)^2 - 1)^2 - 1))/(693*sin(x)^11)","B"
332,1,109,33,2.506429,"\text{Not used}","int(-1/(cos(x) - 1/cos(x))^7,x)","-\frac{{\mathrm{cot}\left(\frac{x}{2}\right)}^{13}}{106496}+\frac{{\mathrm{cot}\left(\frac{x}{2}\right)}^{11}}{90112}+\frac{{\mathrm{cot}\left(\frac{x}{2}\right)}^9}{12288}-\frac{3\,{\mathrm{cot}\left(\frac{x}{2}\right)}^7}{28672}-\frac{3\,{\mathrm{cot}\left(\frac{x}{2}\right)}^5}{8192}+\frac{5\,{\mathrm{cot}\left(\frac{x}{2}\right)}^3}{8192}+\frac{5\,\mathrm{cot}\left(\frac{x}{2}\right)}{2048}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^{13}}{106496}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^{11}}{90112}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^9}{12288}-\frac{3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7}{28672}-\frac{3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{8192}+\frac{5\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{8192}+\frac{5\,\mathrm{tan}\left(\frac{x}{2}\right)}{2048}","Not used",1,"(5*cot(x/2))/2048 + (5*tan(x/2))/2048 + (5*cot(x/2)^3)/8192 - (3*cot(x/2)^5)/8192 - (3*cot(x/2)^7)/28672 + cot(x/2)^9/12288 + cot(x/2)^11/90112 - cot(x/2)^13/106496 + (5*tan(x/2)^3)/8192 - (3*tan(x/2)^5)/8192 - (3*tan(x/2)^7)/28672 + tan(x/2)^9/12288 + tan(x/2)^11/90112 - tan(x/2)^13/106496","B"
333,0,-1,73,0.000000,"\text{Not used}","int((1/cos(x) - cos(x))^(7/2),x)","\int {\left(\frac{1}{\cos\left(x\right)}-\cos\left(x\right)\right)}^{7/2} \,d x","Not used",1,"int((1/cos(x) - cos(x))^(7/2), x)","F"
334,0,-1,50,0.000000,"\text{Not used}","int((1/cos(x) - cos(x))^(5/2),x)","\int {\left(\frac{1}{\cos\left(x\right)}-\cos\left(x\right)\right)}^{5/2} \,d x","Not used",1,"int((1/cos(x) - cos(x))^(5/2), x)","F"
335,0,-1,31,0.000000,"\text{Not used}","int((1/cos(x) - cos(x))^(3/2),x)","\int {\left(\frac{1}{\cos\left(x\right)}-\cos\left(x\right)\right)}^{3/2} \,d x","Not used",1,"int((1/cos(x) - cos(x))^(3/2), x)","F"
336,1,20,13,2.423705,"\text{Not used}","int((1/cos(x) - cos(x))^(1/2),x)","-\frac{2\,\sin\left(x\right)}{\sqrt{\frac{1}{\cos\left(x\right)}}\,\sqrt{1-{\cos\left(x\right)}^2}}","Not used",1,"-(2*sin(x))/((1/cos(x))^(1/2)*(1 - cos(x)^2)^(1/2))","B"
337,0,-1,52,0.000000,"\text{Not used}","int(1/(1/cos(x) - cos(x))^(1/2),x)","\int \frac{1}{\sqrt{\frac{1}{\cos\left(x\right)}-\cos\left(x\right)}} \,d x","Not used",1,"int(1/(1/cos(x) - cos(x))^(1/2), x)","F"
338,0,-1,72,0.000000,"\text{Not used}","int(1/(1/cos(x) - cos(x))^(3/2),x)","\int \frac{1}{{\left(\frac{1}{\cos\left(x\right)}-\cos\left(x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(1/cos(x) - cos(x))^(3/2), x)","F"
339,0,-1,91,0.000000,"\text{Not used}","int(1/(1/cos(x) - cos(x))^(5/2),x)","\int \frac{1}{{\left(\frac{1}{\cos\left(x\right)}-\cos\left(x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(1/cos(x) - cos(x))^(5/2), x)","F"
340,0,-1,110,0.000000,"\text{Not used}","int(1/(1/cos(x) - cos(x))^(7/2),x)","\int \frac{1}{{\left(\frac{1}{\cos\left(x\right)}-\cos\left(x\right)\right)}^{7/2}} \,d x","Not used",1,"int(1/(1/cos(x) - cos(x))^(7/2), x)","F"
341,1,88,55,2.538634,"\text{Not used}","int((sin(x) + tan(x))^4,x)","-\frac{61\,x}{8}-4\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-\frac{\frac{45\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{13}}{4}+\frac{29\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{11}}{6}-\frac{455\,{\mathrm{tan}\left(\frac{x}{2}\right)}^9}{12}-15\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7+\frac{179\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{4}+\frac{31\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{2}+\frac{77\,\mathrm{tan}\left(\frac{x}{2}\right)}{4}}{{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2-1\right)}^3\,{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}^4}","Not used",1,"- (61*x)/8 - 4*atanh(tan(x/2)) - ((77*tan(x/2))/4 + (31*tan(x/2)^3)/2 + (179*tan(x/2)^5)/4 - 15*tan(x/2)^7 - (455*tan(x/2)^9)/12 + (29*tan(x/2)^11)/6 + (45*tan(x/2)^13)/4)/((tan(x/2)^2 - 1)^3*(tan(x/2)^2 + 1)^4)","B"
342,1,65,38,2.449567,"\text{Not used}","int((sin(x) + tan(x))^3,x)","4\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2\right)+\frac{-4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+\frac{20\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{3}+\frac{20\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{3}+\frac{32}{3}}{{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2-1\right)}^2\,{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}^3}","Not used",1,"4*atanh(tan(x/2)^2) + ((20*tan(x/2)^2)/3 + (20*tan(x/2)^4)/3 - 4*tan(x/2)^6 - 4*tan(x/2)^8 + 32/3)/((tan(x/2)^2 - 1)^2*(tan(x/2)^2 + 1)^3)","B"
343,1,61,25,2.422667,"\text{Not used}","int((sin(x) + tan(x))^2,x)","4\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-\frac{x}{2}+\frac{5\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3-3\,\mathrm{tan}\left(\frac{x}{2}\right)}{-{\mathrm{tan}\left(\frac{x}{2}\right)}^6-{\mathrm{tan}\left(\frac{x}{2}\right)}^4+{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}","Not used",1,"4*atanh(tan(x/2)) - x/2 + (6*tan(x/2)^3 - 3*tan(x/2) + 5*tan(x/2)^5)/(tan(x/2)^2 - tan(x/2)^4 - tan(x/2)^6 + 1)","B"
344,1,22,10,2.399464,"\text{Not used}","int(sin(x) + tan(x),x)","2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2\right)-\frac{2}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}","Not used",1,"2*atanh(tan(x/2)^2) - 2/(tan(x/2)^2 + 1)","B"
345,1,16,24,2.466677,"\text{Not used}","int(1/(sin(x) + tan(x)),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{2}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{4}","Not used",1,"log(tan(x/2))/2 - tan(x/2)^2/4","B"
346,1,40,33,2.393103,"\text{Not used}","int(1/(sin(x) + tan(x))^2,x)","-\frac{8\,{\cos\left(\frac{x}{2}\right)}^6-4\,{\cos\left(\frac{x}{2}\right)}^4+14\,{\cos\left(\frac{x}{2}\right)}^2-3}{120\,{\cos\left(\frac{x}{2}\right)}^5\,\sin\left(\frac{x}{2}\right)}","Not used",1,"-(14*cos(x/2)^2 - 4*cos(x/2)^4 + 8*cos(x/2)^6 - 3)/(120*cos(x/2)^5*sin(x/2))","B"
347,1,48,60,2.385903,"\text{Not used}","int(1/(sin(x) + tan(x))^3,x)","\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{64}-\frac{1}{64\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{32}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{32}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^6}{192}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^8}{256}","Not used",1,"tan(x/2)^4/64 - 1/(64*tan(x/2)^2) - tan(x/2)^2/32 - log(tan(x/2))/32 + tan(x/2)^6/192 - tan(x/2)^8/256","B"
348,1,87,65,2.453250,"\text{Not used}","int(1/(sin(x) + tan(x))^4,x)","-\frac{15616\,{\cos\left(\frac{x}{2}\right)}^{14}-23424\,{\cos\left(\frac{x}{2}\right)}^{12}+5856\,{\cos\left(\frac{x}{2}\right)}^{10}+976\,{\cos\left(\frac{x}{2}\right)}^8+7296\,{\cos\left(\frac{x}{2}\right)}^6-7440\,{\cos\left(\frac{x}{2}\right)}^4+2590\,{\cos\left(\frac{x}{2}\right)}^2-315}{443520\,\left({\cos\left(\frac{x}{2}\right)}^{11}\,\sin\left(\frac{x}{2}\right)-{\cos\left(\frac{x}{2}\right)}^{13}\,\sin\left(\frac{x}{2}\right)\right)}","Not used",1,"-(2590*cos(x/2)^2 - 7440*cos(x/2)^4 + 7296*cos(x/2)^6 + 976*cos(x/2)^8 + 5856*cos(x/2)^10 - 23424*cos(x/2)^12 + 15616*cos(x/2)^14 - 315)/(443520*(cos(x/2)^11*sin(x/2) - cos(x/2)^13*sin(x/2)))","B"
349,1,695,74,7.017088,"\text{Not used}","int((A + C*sin(x))/(b*cos(x) + c*sin(x)),x)","-\ln\left(-32\,A\,C^2\,b^2-\frac{\left(A\,\sqrt{{\left(b^2+c^2\right)}^3}+C\,b^3+C\,b\,c^2\right)\,\left(64\,A^2\,b^2\,c+32\,C^2\,b^2\,c-32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A^2\,b^2-A^2\,c^2-4\,A\,C\,b\,c+2\,C^2\,c^2\right)+64\,A\,C\,b^3+\frac{\left(A\,\sqrt{{\left(b^2+c^2\right)}^3}+C\,b^3+C\,b\,c^2\right)\,\left(32\,A\,b^4+32\,A\,b^2\,c^2+32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,C\,b^3+2\,A\,b^2\,c+C\,b\,c^2+2\,A\,c^3\right)-32\,C\,b\,c^3+64\,C\,b^3\,c-\frac{96\,b\,c\,\left(b+c\,\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(A\,\sqrt{{\left(b^2+c^2\right)}^3}+C\,b^3+C\,b\,c^2\right)}{b^2+c^2}\right)}{{\left(b^2+c^2\right)}^2}\right)}{{\left(b^2+c^2\right)}^2}-32\,A^2\,C\,b\,c-32\,C\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-b\,A^2+2\,c\,A\,C+2\,b\,C^2\right)\right)\,\left(\frac{C\,b}{b^2+c^2}+\frac{A\,\sqrt{{\left(b^2+c^2\right)}^3}}{{\left(b^2+c^2\right)}^2}\right)-\ln\left(-32\,A\,C^2\,b^2-\frac{\left(C\,b^3-A\,\sqrt{{\left(b^2+c^2\right)}^3}+C\,b\,c^2\right)\,\left(64\,A^2\,b^2\,c+32\,C^2\,b^2\,c-32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A^2\,b^2-A^2\,c^2-4\,A\,C\,b\,c+2\,C^2\,c^2\right)+64\,A\,C\,b^3+\frac{\left(C\,b^3-A\,\sqrt{{\left(b^2+c^2\right)}^3}+C\,b\,c^2\right)\,\left(32\,A\,b^4+32\,A\,b^2\,c^2+32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,C\,b^3+2\,A\,b^2\,c+C\,b\,c^2+2\,A\,c^3\right)-32\,C\,b\,c^3+64\,C\,b^3\,c-\frac{96\,b\,c\,\left(b+c\,\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(C\,b^3-A\,\sqrt{{\left(b^2+c^2\right)}^3}+C\,b\,c^2\right)}{b^2+c^2}\right)}{{\left(b^2+c^2\right)}^2}\right)}{{\left(b^2+c^2\right)}^2}-32\,A^2\,C\,b\,c-32\,C\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-b\,A^2+2\,c\,A\,C+2\,b\,C^2\right)\right)\,\left(\frac{C\,b}{b^2+c^2}-\frac{A\,\sqrt{{\left(b^2+c^2\right)}^3}}{{\left(b^2+c^2\right)}^2}\right)+\frac{C\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)}{b-c\,1{}\mathrm{i}}+\frac{C\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,1{}\mathrm{i}}{-c+b\,1{}\mathrm{i}}","Not used",1,"(C*log(tan(x/2) + 1i))/(b - c*1i) - log(- 32*A*C^2*b^2 - ((C*b^3 - A*((b^2 + c^2)^3)^(1/2) + C*b*c^2)*(64*A^2*b^2*c + 32*C^2*b^2*c - 32*b*tan(x/2)*(A^2*b^2 - A^2*c^2 + 2*C^2*c^2 - 4*A*C*b*c) + 64*A*C*b^3 + ((C*b^3 - A*((b^2 + c^2)^3)^(1/2) + C*b*c^2)*(32*A*b^4 + 32*A*b^2*c^2 + 32*b*tan(x/2)*(2*A*c^3 - 2*C*b^3 + 2*A*b^2*c + C*b*c^2) - 32*C*b*c^3 + 64*C*b^3*c - (96*b*c*(b + c*tan(x/2))*(C*b^3 - A*((b^2 + c^2)^3)^(1/2) + C*b*c^2))/(b^2 + c^2)))/(b^2 + c^2)^2))/(b^2 + c^2)^2 - 32*A^2*C*b*c - 32*C*b*tan(x/2)*(2*C^2*b - A^2*b + 2*A*C*c))*((C*b)/(b^2 + c^2) - (A*((b^2 + c^2)^3)^(1/2))/(b^2 + c^2)^2) - log(- 32*A*C^2*b^2 - ((A*((b^2 + c^2)^3)^(1/2) + C*b^3 + C*b*c^2)*(64*A^2*b^2*c + 32*C^2*b^2*c - 32*b*tan(x/2)*(A^2*b^2 - A^2*c^2 + 2*C^2*c^2 - 4*A*C*b*c) + 64*A*C*b^3 + ((A*((b^2 + c^2)^3)^(1/2) + C*b^3 + C*b*c^2)*(32*A*b^4 + 32*A*b^2*c^2 + 32*b*tan(x/2)*(2*A*c^3 - 2*C*b^3 + 2*A*b^2*c + C*b*c^2) - 32*C*b*c^3 + 64*C*b^3*c - (96*b*c*(b + c*tan(x/2))*(A*((b^2 + c^2)^3)^(1/2) + C*b^3 + C*b*c^2))/(b^2 + c^2)))/(b^2 + c^2)^2))/(b^2 + c^2)^2 - 32*A^2*C*b*c - 32*C*b*tan(x/2)*(2*C^2*b - A^2*b + 2*A*C*c))*((C*b)/(b^2 + c^2) + (A*((b^2 + c^2)^3)^(1/2))/(b^2 + c^2)^2) + (C*log(tan(x/2) - 1i)*1i)/(b*1i - c)","B"
350,1,105,75,2.583128,"\text{Not used}","int((A + C*sin(x))/(b*cos(x) + c*sin(x))^2,x)","\frac{\frac{2\,C\,b}{b^2+c^2}+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A\,b^2+C\,b\,c+A\,c^2\right)}{b\,\left(b^2+c^2\right)}}{-b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,c\,\mathrm{tan}\left(\frac{x}{2}\right)+b}-\frac{2\,C\,c\,\mathrm{atanh}\left(\frac{2\,c-2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{2\,\sqrt{b^2+c^2}}\right)}{{\left(b^2+c^2\right)}^{3/2}}","Not used",1,"((2*C*b)/(b^2 + c^2) + (2*tan(x/2)*(A*b^2 + A*c^2 + C*b*c))/(b*(b^2 + c^2)))/(b + 2*c*tan(x/2) - b*tan(x/2)^2) - (2*C*c*atanh((2*c - 2*b*tan(x/2))/(2*(b^2 + c^2)^(1/2))))/(b^2 + c^2)^(3/2)","B"
351,1,227,116,2.855622,"\text{Not used}","int((A + C*sin(x))/(b*cos(x) + c*sin(x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(A\,b^2+2\,A\,c^2\right)}{b\,\left(b^2+c^2\right)}-\frac{A\,c}{b^2+c^2}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,C\,b^3+A\,b^2\,c+2\,C\,b\,c^2-2\,A\,c^3\right)}{b^2\,\left(b^2+c^2\right)}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A\,b^2-2\,A\,c^2\right)}{b\,\left(b^2+c^2\right)}}{b^2-{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,b^2-4\,c^2\right)+b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,b\,c\,\mathrm{tan}\left(\frac{x}{2}\right)-4\,b\,c\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}+\frac{A\,\mathrm{atan}\left(\frac{b^2\,c\,1{}\mathrm{i}+c^3\,1{}\mathrm{i}-b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(b^2+c^2\right)\,1{}\mathrm{i}}{{\left(b^2+c^2\right)}^{3/2}}\right)\,1{}\mathrm{i}}{{\left(b^2+c^2\right)}^{3/2}}","Not used",1,"((tan(x/2)^3*(A*b^2 + 2*A*c^2))/(b*(b^2 + c^2)) - (A*c)/(b^2 + c^2) + (tan(x/2)^2*(2*C*b^3 - 2*A*c^3 + A*b^2*c + 2*C*b*c^2))/(b^2*(b^2 + c^2)) + (tan(x/2)*(A*b^2 - 2*A*c^2))/(b*(b^2 + c^2)))/(b^2 - tan(x/2)^2*(2*b^2 - 4*c^2) + b^2*tan(x/2)^4 + 4*b*c*tan(x/2) - 4*b*c*tan(x/2)^3) + (A*atan((b^2*c*1i + c^3*1i - b*tan(x/2)*(b^2 + c^2)*1i)/(b^2 + c^2)^(3/2))*1i)/(b^2 + c^2)^(3/2)","B"
352,1,692,73,6.525286,"\text{Not used}","int((A + B*cos(x))/(b*cos(x) + c*sin(x)),x)","\ln\left(32\,A^2\,B\,b^2-32\,A\,B^2\,b^2-\frac{\left(A\,\sqrt{{\left(b^2+c^2\right)}^3}+B\,c^3+B\,b^2\,c\right)\,\left(32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A^2\,b^2-A^2\,c^2+4\,A\,B\,c^2+B^2\,b^2-3\,B^2\,c^2\right)-64\,A^2\,b^2\,c-32\,B^2\,b^2\,c+\frac{\left(A\,\sqrt{{\left(b^2+c^2\right)}^3}+B\,c^3+B\,b^2\,c\right)\,\left(32\,A\,b^4+32\,B\,b^4+32\,A\,b^2\,c^2-64\,B\,b^2\,c^2+32\,b\,c\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,A\,b^2+2\,A\,c^2+4\,B\,b^2+B\,c^2\right)+\frac{96\,b\,c\,\left(b+c\,\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(A\,\sqrt{{\left(b^2+c^2\right)}^3}+B\,c^3+B\,b^2\,c\right)}{b^2+c^2}\right)}{{\left(b^2+c^2\right)}^2}+64\,A\,B\,b^2\,c\right)}{{\left(b^2+c^2\right)}^2}+32\,B\,b\,c\,\mathrm{tan}\left(\frac{x}{2}\right)\,{\left(A-B\right)}^2\right)\,\left(\frac{B\,c}{b^2+c^2}+\frac{A\,\sqrt{{\left(b^2+c^2\right)}^3}}{{\left(b^2+c^2\right)}^2}\right)+\ln\left(32\,A^2\,B\,b^2-32\,A\,B^2\,b^2-\frac{\left(B\,c^3-A\,\sqrt{{\left(b^2+c^2\right)}^3}+B\,b^2\,c\right)\,\left(32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A^2\,b^2-A^2\,c^2+4\,A\,B\,c^2+B^2\,b^2-3\,B^2\,c^2\right)-64\,A^2\,b^2\,c-32\,B^2\,b^2\,c+\frac{\left(B\,c^3-A\,\sqrt{{\left(b^2+c^2\right)}^3}+B\,b^2\,c\right)\,\left(32\,A\,b^4+32\,B\,b^4+32\,A\,b^2\,c^2-64\,B\,b^2\,c^2+32\,b\,c\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,A\,b^2+2\,A\,c^2+4\,B\,b^2+B\,c^2\right)+\frac{96\,b\,c\,\left(b+c\,\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(B\,c^3-A\,\sqrt{{\left(b^2+c^2\right)}^3}+B\,b^2\,c\right)}{b^2+c^2}\right)}{{\left(b^2+c^2\right)}^2}+64\,A\,B\,b^2\,c\right)}{{\left(b^2+c^2\right)}^2}+32\,B\,b\,c\,\mathrm{tan}\left(\frac{x}{2}\right)\,{\left(A-B\right)}^2\right)\,\left(\frac{B\,c}{b^2+c^2}-\frac{A\,\sqrt{{\left(b^2+c^2\right)}^3}}{{\left(b^2+c^2\right)}^2}\right)-\frac{B\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,1{}\mathrm{i}}{b+c\,1{}\mathrm{i}}-\frac{B\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)}{c+b\,1{}\mathrm{i}}","Not used",1,"log(32*A^2*B*b^2 - 32*A*B^2*b^2 - ((A*((b^2 + c^2)^3)^(1/2) + B*c^3 + B*b^2*c)*(32*b*tan(x/2)*(A^2*b^2 - A^2*c^2 + B^2*b^2 - 3*B^2*c^2 + 4*A*B*c^2) - 64*A^2*b^2*c - 32*B^2*b^2*c + ((A*((b^2 + c^2)^3)^(1/2) + B*c^3 + B*b^2*c)*(32*A*b^4 + 32*B*b^4 + 32*A*b^2*c^2 - 64*B*b^2*c^2 + 32*b*c*tan(x/2)*(2*A*b^2 + 2*A*c^2 + 4*B*b^2 + B*c^2) + (96*b*c*(b + c*tan(x/2))*(A*((b^2 + c^2)^3)^(1/2) + B*c^3 + B*b^2*c))/(b^2 + c^2)))/(b^2 + c^2)^2 + 64*A*B*b^2*c))/(b^2 + c^2)^2 + 32*B*b*c*tan(x/2)*(A - B)^2)*((B*c)/(b^2 + c^2) + (A*((b^2 + c^2)^3)^(1/2))/(b^2 + c^2)^2) + log(32*A^2*B*b^2 - 32*A*B^2*b^2 - ((B*c^3 - A*((b^2 + c^2)^3)^(1/2) + B*b^2*c)*(32*b*tan(x/2)*(A^2*b^2 - A^2*c^2 + B^2*b^2 - 3*B^2*c^2 + 4*A*B*c^2) - 64*A^2*b^2*c - 32*B^2*b^2*c + ((B*c^3 - A*((b^2 + c^2)^3)^(1/2) + B*b^2*c)*(32*A*b^4 + 32*B*b^4 + 32*A*b^2*c^2 - 64*B*b^2*c^2 + 32*b*c*tan(x/2)*(2*A*b^2 + 2*A*c^2 + 4*B*b^2 + B*c^2) + (96*b*c*(b + c*tan(x/2))*(B*c^3 - A*((b^2 + c^2)^3)^(1/2) + B*b^2*c))/(b^2 + c^2)))/(b^2 + c^2)^2 + 64*A*B*b^2*c))/(b^2 + c^2)^2 + 32*B*b*c*tan(x/2)*(A - B)^2)*((B*c)/(b^2 + c^2) - (A*((b^2 + c^2)^3)^(1/2))/(b^2 + c^2)^2) - (B*log(tan(x/2) - 1i)*1i)/(b + c*1i) - (B*log(tan(x/2) + 1i))/(b*1i + c)","B"
353,1,126,76,2.623361,"\text{Not used}","int((A + B*cos(x))/(b*cos(x) + c*sin(x))^2,x)","-\frac{\frac{2\,B\,c}{b^2+c^2}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A\,b^2+A\,c^2-B\,c^2\right)}{b\,\left(b^2+c^2\right)}}{-b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,c\,\mathrm{tan}\left(\frac{x}{2}\right)+b}+\frac{B\,b\,\mathrm{atan}\left(\frac{b^2\,c\,1{}\mathrm{i}+c^3\,1{}\mathrm{i}-b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(b^2+c^2\right)\,1{}\mathrm{i}}{{\left(b^2+c^2\right)}^{3/2}}\right)\,2{}\mathrm{i}}{{\left(b^2+c^2\right)}^{3/2}}","Not used",1,"(B*b*atan((b^2*c*1i + c^3*1i - b*tan(x/2)*(b^2 + c^2)*1i)/(b^2 + c^2)^(3/2))*2i)/(b^2 + c^2)^(3/2) - ((2*B*c)/(b^2 + c^2) - (2*tan(x/2)*(A*b^2 + A*c^2 - B*c^2))/(b*(b^2 + c^2)))/(b + 2*c*tan(x/2) - b*tan(x/2)^2)","B"
354,1,251,116,2.878965,"\text{Not used}","int((A + B*cos(x))/(b*cos(x) + c*sin(x))^3,x)","\frac{\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A\,b^2-2\,A\,c^2+2\,B\,b^2+2\,B\,c^2\right)}{b\,\left(b^2+c^2\right)}-\frac{A\,c}{b^2+c^2}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,B\,c^3-2\,A\,c^3+A\,b^2\,c+2\,B\,b^2\,c\right)}{b^2\,\left(b^2+c^2\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(A\,b^2+2\,A\,c^2-2\,B\,b^2-2\,B\,c^2\right)}{b\,\left(b^2+c^2\right)}}{b^2-{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,b^2-4\,c^2\right)+b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,b\,c\,\mathrm{tan}\left(\frac{x}{2}\right)-4\,b\,c\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}+\frac{A\,\mathrm{atan}\left(\frac{b^2\,c\,1{}\mathrm{i}+c^3\,1{}\mathrm{i}-b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(b^2+c^2\right)\,1{}\mathrm{i}}{{\left(b^2+c^2\right)}^{3/2}}\right)\,1{}\mathrm{i}}{{\left(b^2+c^2\right)}^{3/2}}","Not used",1,"((tan(x/2)*(A*b^2 - 2*A*c^2 + 2*B*b^2 + 2*B*c^2))/(b*(b^2 + c^2)) - (A*c)/(b^2 + c^2) + (tan(x/2)^2*(2*B*c^3 - 2*A*c^3 + A*b^2*c + 2*B*b^2*c))/(b^2*(b^2 + c^2)) + (tan(x/2)^3*(A*b^2 + 2*A*c^2 - 2*B*b^2 - 2*B*c^2))/(b*(b^2 + c^2)))/(b^2 - tan(x/2)^2*(2*b^2 - 4*c^2) + b^2*tan(x/2)^4 + 4*b*c*tan(x/2) - 4*b*c*tan(x/2)^3) + (A*atan((b^2*c*1i + c^3*1i - b*tan(x/2)*(b^2 + c^2)*1i)/(b^2 + c^2)^(3/2))*1i)/(b^2 + c^2)^(3/2)","B"
355,1,522,246,7.319499,"\text{Not used}","int((b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^4,x)","\frac{35\,\mathrm{atan}\left(\frac{35\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,{\left(b^2+c^2\right)}^2}{4\,\left(\frac{35\,b^4}{4}+\frac{35\,b^2\,c^2}{2}+\frac{35\,c^4}{4}\right)}\right)\,{\left(b^2+c^2\right)}^2}{4\,e}-\frac{35\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\right)-\frac{e\,x}{2}\right)\,{\left(b^2+c^2\right)}^2}{4\,e}+\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(\left(16\,b^3+8\,b\,c^2\right)\,\sqrt{b^2+c^2}+\frac{29\,b^4}{4}-\frac{27\,c^4}{4}-\frac{3\,b^2\,c^2}{2}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6\,\left(24\,b\,c^3+32\,b^3\,c-\left(32\,b^2\,c+8\,c^3\right)\,\sqrt{b^2+c^2}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(64\,b\,c^3+48\,b^3\,c-\left(48\,b^2\,c+40\,c^3\right)\,\sqrt{b^2+c^2}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(24\,b\,c^3+32\,b^3\,c-\left(32\,b^2\,c+\frac{136\,c^3}{3}\right)\,\sqrt{b^2+c^2}\right)-\left(16\,b^2\,c+\frac{40\,c^3}{3}\right)\,\sqrt{b^2+c^2}+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^7\,\left(\left(16\,b^3+8\,b\,c^2\right)\,\sqrt{b^2+c^2}-\frac{29\,b^4}{4}+\frac{27\,c^4}{4}+\frac{3\,b^2\,c^2}{2}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(\left(\frac{112\,b^3}{3}+56\,b\,c^2\right)\,\sqrt{b^2+c^2}+\frac{21\,b^4}{4}-\frac{35\,c^4}{4}+\frac{21\,b^2\,c^2}{2}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(\left(\frac{112\,b^3}{3}+56\,b\,c^2\right)\,\sqrt{b^2+c^2}-\frac{21\,b^4}{4}+\frac{35\,c^4}{4}-\frac{21\,b^2\,c^2}{2}\right)}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+1\right)}","Not used",1,"(35*atan((35*tan(d/2 + (e*x)/2)*(b^2 + c^2)^2)/(4*((35*b^4)/4 + (35*c^4)/4 + (35*b^2*c^2)/2)))*(b^2 + c^2)^2)/(4*e) - (35*(atan(tan(d/2 + (e*x)/2)) - (e*x)/2)*(b^2 + c^2)^2)/(4*e) + (tan(d/2 + (e*x)/2)*((8*b*c^2 + 16*b^3)*(b^2 + c^2)^(1/2) + (29*b^4)/4 - (27*c^4)/4 - (3*b^2*c^2)/2) + tan(d/2 + (e*x)/2)^6*(24*b*c^3 + 32*b^3*c - (32*b^2*c + 8*c^3)*(b^2 + c^2)^(1/2)) + tan(d/2 + (e*x)/2)^4*(64*b*c^3 + 48*b^3*c - (48*b^2*c + 40*c^3)*(b^2 + c^2)^(1/2)) + tan(d/2 + (e*x)/2)^2*(24*b*c^3 + 32*b^3*c - (32*b^2*c + (136*c^3)/3)*(b^2 + c^2)^(1/2)) - (16*b^2*c + (40*c^3)/3)*(b^2 + c^2)^(1/2) + tan(d/2 + (e*x)/2)^7*((8*b*c^2 + 16*b^3)*(b^2 + c^2)^(1/2) - (29*b^4)/4 + (27*c^4)/4 + (3*b^2*c^2)/2) + tan(d/2 + (e*x)/2)^3*((56*b*c^2 + (112*b^3)/3)*(b^2 + c^2)^(1/2) + (21*b^4)/4 - (35*c^4)/4 + (21*b^2*c^2)/2) + tan(d/2 + (e*x)/2)^5*((56*b*c^2 + (112*b^3)/3)*(b^2 + c^2)^(1/2) - (21*b^4)/4 + (35*c^4)/4 - (21*b^2*c^2)/2))/(e*(4*tan(d/2 + (e*x)/2)^2 + 6*tan(d/2 + (e*x)/2)^4 + 4*tan(d/2 + (e*x)/2)^6 + tan(d/2 + (e*x)/2)^8 + 1))","B"
356,1,261,178,7.324258,"\text{Not used}","int((b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^3,x)","\frac{5\,x\,{\left(b^2+c^2\right)}^{3/2}}{2}-\frac{8\,b^2\,c-\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(\left(3\,b^2-3\,c^2\right)\,\sqrt{b^2+c^2}+6\,b\,c^2+8\,b^3\right)-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(\frac{40\,b^3}{3}+20\,b\,c^2\right)+\frac{22\,c^3}{3}-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(6\,b\,c^2-\left(3\,b^2-3\,c^2\right)\,\sqrt{b^2+c^2}+8\,b^3\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(12\,b^2\,c+6\,c^3-12\,b\,c\,\sqrt{b^2+c^2}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(12\,b^2\,c+16\,c^3-12\,b\,c\,\sqrt{b^2+c^2}\right)}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+1\right)}","Not used",1,"(5*x*(b^2 + c^2)^(3/2))/2 - (8*b^2*c - tan(d/2 + (e*x)/2)*((3*b^2 - 3*c^2)*(b^2 + c^2)^(1/2) + 6*b*c^2 + 8*b^3) - tan(d/2 + (e*x)/2)^3*(20*b*c^2 + (40*b^3)/3) + (22*c^3)/3 - tan(d/2 + (e*x)/2)^5*(6*b*c^2 - (3*b^2 - 3*c^2)*(b^2 + c^2)^(1/2) + 8*b^3) + tan(d/2 + (e*x)/2)^4*(12*b^2*c + 6*c^3 - 12*b*c*(b^2 + c^2)^(1/2)) + tan(d/2 + (e*x)/2)^2*(12*b^2*c + 16*c^3 - 12*b*c*(b^2 + c^2)^(1/2)))/(e*(3*tan(d/2 + (e*x)/2)^2 + 3*tan(d/2 + (e*x)/2)^4 + tan(d/2 + (e*x)/2)^6 + 1))","B"
357,1,100,116,3.075132,"\text{Not used}","int((b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^2,x)","\frac{b^2\,\sin\left(2\,d+2\,e\,x\right)-c^2\,\sin\left(2\,d+2\,e\,x\right)+16\,c\,{\sin\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\sqrt{b^2+c^2}+8\,b\,\sin\left(d+e\,x\right)\,\sqrt{b^2+c^2}+4\,b\,c\,{\sin\left(d+e\,x\right)}^2+6\,b^2\,e\,x+6\,c^2\,e\,x}{4\,e}","Not used",1,"(b^2*sin(2*d + 2*e*x) - c^2*sin(2*d + 2*e*x) + 16*c*sin(d/2 + (e*x)/2)^2*(b^2 + c^2)^(1/2) + 8*b*sin(d + e*x)*(b^2 + c^2)^(1/2) + 4*b*c*sin(d + e*x)^2 + 6*b^2*e*x + 6*c^2*e*x)/(4*e)","B"
358,1,48,37,2.672360,"\text{Not used}","int(b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2),x)","x\,\sqrt{b^2+c^2}-\frac{2\,c-2\,b\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+1\right)}","Not used",1,"x*(b^2 + c^2)^(1/2) - (2*c - 2*b*tan(d/2 + (e*x)/2))/(e*(tan(d/2 + (e*x)/2)^2 + 1))","B"
359,1,38,49,2.823849,"\text{Not used}","int(1/(b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2)),x)","\frac{2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{e\,\left(b+\sqrt{b^2+c^2}+c\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\right)}","Not used",1,"(2*tan(d/2 + (e*x)/2))/(e*(b + (b^2 + c^2)^(1/2) + c*tan(d/2 + (e*x)/2)))","B"
360,1,274,129,3.672924,"\text{Not used}","int(1/(b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^2,x)","-\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(\frac{4\,b^2+2\,c^2}{c^4}+\frac{4\,b\,\sqrt{b^2+c^2}}{c^4}\right)+\frac{\frac{16\,b^4}{3}+\frac{20\,b^2\,c^2}{3}+\frac{4\,c^4}{3}}{c^6}+\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(\frac{8\,b^3+6\,b\,c^2}{c^5}+\frac{\left(8\,b^2+2\,c^2\right)\,\sqrt{b^2+c^2}}{c^5}\right)+\frac{\left(\frac{16\,b^3}{3}+4\,b\,c^2\right)\,\sqrt{b^2+c^2}}{c^6}}{e\,\left(\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(\frac{6\,b^2+3\,c^2}{c^2}+\frac{6\,b\,\sqrt{b^2+c^2}}{c^2}\right)+\frac{4\,b^3+3\,b\,c^2}{c^3}+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(\frac{3\,\sqrt{b^2+c^2}}{c}+\frac{3\,b}{c}\right)+\frac{\left(4\,b^2+c^2\right)\,\sqrt{b^2+c^2}}{c^3}\right)}","Not used",1,"-(tan(d/2 + (e*x)/2)^2*((4*b^2 + 2*c^2)/c^4 + (4*b*(b^2 + c^2)^(1/2))/c^4) + ((16*b^4)/3 + (4*c^4)/3 + (20*b^2*c^2)/3)/c^6 + tan(d/2 + (e*x)/2)*((6*b*c^2 + 8*b^3)/c^5 + ((8*b^2 + 2*c^2)*(b^2 + c^2)^(1/2))/c^5) + ((4*b*c^2 + (16*b^3)/3)*(b^2 + c^2)^(1/2))/c^6)/(e*(tan(d/2 + (e*x)/2)*((6*b^2 + 3*c^2)/c^2 + (6*b*(b^2 + c^2)^(1/2))/c^2) + (3*b*c^2 + 4*b^3)/c^3 + tan(d/2 + (e*x)/2)^3 + tan(d/2 + (e*x)/2)^2*((3*(b^2 + c^2)^(1/2))/c + (3*b)/c) + ((4*b^2 + c^2)*(b^2 + c^2)^(1/2))/c^3))","B"
361,1,592,191,8.120028,"\text{Not used}","int(1/(b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^3,x)","-\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(\frac{32\,b^4+32\,b^2\,c^2+4\,c^4}{c^7}+\frac{\left(32\,b^3+16\,b\,c^2\right)\,\sqrt{b^2+c^2}}{c^7}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(\frac{8\,b^3+6\,b\,c^2}{c^6}+\frac{\left(8\,b^2+2\,c^2\right)\,\sqrt{b^2+c^2}}{c^6}\right)+\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(\frac{64\,b^6+\frac{304\,b^4\,c^2}{3}+\frac{124\,b^2\,c^4}{3}+\frac{8\,c^6}{3}}{c^9}+\frac{\sqrt{b^2+c^2}\,\left(64\,b^5+\frac{208\,b^3\,c^2}{3}+\frac{44\,b\,c^4}{3}\right)}{c^9}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(\frac{64\,b^5+\frac{256\,b^3\,c^2}{3}+24\,b\,c^4}{c^8}+\frac{\sqrt{b^2+c^2}\,\left(64\,b^4+\frac{160\,b^2\,c^2}{3}+\frac{16\,c^4}{3}\right)}{c^8}\right)+\frac{\frac{128\,b^7}{5}+\frac{704\,b^5\,c^2}{15}+\frac{80\,b^3\,c^4}{3}+\frac{14\,b\,c^6}{3}}{c^{10}}+\frac{\sqrt{b^2+c^2}\,\left(\frac{128\,b^6}{5}+\frac{512\,b^4\,c^2}{15}+\frac{64\,b^2\,c^4}{5}+\frac{14\,c^6}{15}\right)}{c^{10}}}{e\,\left(\frac{16\,b^5+20\,b^3\,c^2+5\,b\,c^4}{c^5}+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(\frac{40\,b^3+30\,b\,c^2}{c^3}+\frac{\left(40\,b^2+10\,c^2\right)\,\sqrt{b^2+c^2}}{c^3}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(\frac{20\,b^2+10\,c^2}{c^2}+\frac{20\,b\,\sqrt{b^2+c^2}}{c^2}\right)+\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(\frac{40\,b^4+40\,b^2\,c^2+5\,c^4}{c^4}+\frac{\left(40\,b^3+20\,b\,c^2\right)\,\sqrt{b^2+c^2}}{c^4}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(\frac{5\,\sqrt{b^2+c^2}}{c}+\frac{5\,b}{c}\right)+\frac{\sqrt{b^2+c^2}\,\left(16\,b^4+12\,b^2\,c^2+c^4\right)}{c^5}\right)}","Not used",1,"-(tan(d/2 + (e*x)/2)^3*((32*b^4 + 4*c^4 + 32*b^2*c^2)/c^7 + ((16*b*c^2 + 32*b^3)*(b^2 + c^2)^(1/2))/c^7) + tan(d/2 + (e*x)/2)^4*((6*b*c^2 + 8*b^3)/c^6 + ((8*b^2 + 2*c^2)*(b^2 + c^2)^(1/2))/c^6) + tan(d/2 + (e*x)/2)*((64*b^6 + (8*c^6)/3 + (124*b^2*c^4)/3 + (304*b^4*c^2)/3)/c^9 + ((b^2 + c^2)^(1/2)*((44*b*c^4)/3 + 64*b^5 + (208*b^3*c^2)/3))/c^9) + tan(d/2 + (e*x)/2)^2*((24*b*c^4 + 64*b^5 + (256*b^3*c^2)/3)/c^8 + ((b^2 + c^2)^(1/2)*(64*b^4 + (16*c^4)/3 + (160*b^2*c^2)/3))/c^8) + ((14*b*c^6)/3 + (128*b^7)/5 + (80*b^3*c^4)/3 + (704*b^5*c^2)/15)/c^10 + ((b^2 + c^2)^(1/2)*((128*b^6)/5 + (14*c^6)/15 + (64*b^2*c^4)/5 + (512*b^4*c^2)/15))/c^10)/(e*((5*b*c^4 + 16*b^5 + 20*b^3*c^2)/c^5 + tan(d/2 + (e*x)/2)^2*((30*b*c^2 + 40*b^3)/c^3 + ((40*b^2 + 10*c^2)*(b^2 + c^2)^(1/2))/c^3) + tan(d/2 + (e*x)/2)^5 + tan(d/2 + (e*x)/2)^3*((20*b^2 + 10*c^2)/c^2 + (20*b*(b^2 + c^2)^(1/2))/c^2) + tan(d/2 + (e*x)/2)*((40*b^4 + 5*c^4 + 40*b^2*c^2)/c^4 + ((20*b*c^2 + 40*b^3)*(b^2 + c^2)^(1/2))/c^4) + tan(d/2 + (e*x)/2)^4*((5*(b^2 + c^2)^(1/2))/c + (5*b)/c) + ((b^2 + c^2)^(1/2)*(16*b^4 + c^4 + 12*b^2*c^2))/c^5))","B"
362,1,1004,259,12.306202,"\text{Not used}","int(1/(b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^4,x)","-\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6\,\left(\frac{16\,b^4+16\,b^2\,c^2+2\,c^4}{c^8}+\frac{\left(16\,b^3+8\,b\,c^2\right)\,\sqrt{b^2+c^2}}{c^8}\right)+\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(\frac{512\,b^9+\frac{5888\,b^7\,c^2}{5}+\frac{4576\,b^5\,c^4}{5}+\frac{1352\,b^3\,c^6}{5}+\frac{114\,b\,c^8}{5}}{c^{13}}+\frac{\sqrt{b^2+c^2}\,\left(512\,b^8+\frac{4608\,b^6\,c^2}{5}+\frac{2592\,b^4\,c^4}{5}+\frac{472\,b^2\,c^6}{5}+\frac{14\,c^8}{5}\right)}{c^{13}}\right)+\frac{\frac{1024\,b^{10}}{7}+\frac{13056\,b^8\,c^2}{35}+\frac{11776\,b^6\,c^4}{35}+\frac{4496\,b^4\,c^6}{35}+\frac{136\,b^2\,c^8}{7}+\frac{24\,c^{10}}{35}}{c^{14}}+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(\frac{768\,b^8+\frac{7872\,b^6\,c^2}{5}+\frac{5136\,b^4\,c^4}{5}+\frac{1116\,b^2\,c^6}{5}+\frac{42\,c^8}{5}}{c^{12}}+\frac{\sqrt{b^2+c^2}\,\left(768\,b^7+\frac{5952\,b^5\,c^2}{5}+528\,b^3\,c^4+60\,b\,c^6\right)}{c^{12}}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(\frac{640\,b^7+1152\,b^5\,c^2+600\,b^3\,c^4+80\,b\,c^6}{c^{11}}+\frac{\sqrt{b^2+c^2}\,\left(640\,b^6+832\,b^4\,c^2+264\,b^2\,c^4+12\,c^6\right)}{c^{11}}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(\frac{320\,b^6+496\,b^4\,c^2+196\,b^2\,c^4+12\,c^6}{c^{10}}+\frac{\sqrt{b^2+c^2}\,\left(320\,b^5+336\,b^3\,c^2+68\,b\,c^4\right)}{c^{10}}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(\frac{96\,b^5+120\,b^3\,c^2+30\,b\,c^4}{c^9}+\frac{\sqrt{b^2+c^2}\,\left(96\,b^4+72\,b^2\,c^2+6\,c^4\right)}{c^9}\right)+\frac{\sqrt{b^2+c^2}\,\left(\frac{1024\,b^9}{7}+\frac{10496\,b^7\,c^2}{35}+\frac{1024\,b^5\,c^4}{5}+\frac{272\,b^3\,c^6}{5}+\frac{24\,b\,c^8}{5}\right)}{c^{14}}}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(\frac{280\,b^4+280\,b^2\,c^2+35\,c^4}{c^4}+\frac{\left(280\,b^3+140\,b\,c^2\right)\,\sqrt{b^2+c^2}}{c^4}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(\frac{140\,b^3+105\,b\,c^2}{c^3}+\frac{\left(140\,b^2+35\,c^2\right)\,\sqrt{b^2+c^2}}{c^3}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^7+\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(\frac{224\,b^6+336\,b^4\,c^2+126\,b^2\,c^4+7\,c^6}{c^6}+\frac{\sqrt{b^2+c^2}\,\left(224\,b^5+224\,b^3\,c^2+42\,b\,c^4\right)}{c^6}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(\frac{42\,b^2+21\,c^2}{c^2}+\frac{42\,b\,\sqrt{b^2+c^2}}{c^2}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6\,\left(\frac{7\,\sqrt{b^2+c^2}}{c}+\frac{7\,b}{c}\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(\frac{336\,b^5+420\,b^3\,c^2+105\,b\,c^4}{c^5}+\frac{\sqrt{b^2+c^2}\,\left(336\,b^4+252\,b^2\,c^2+21\,c^4\right)}{c^5}\right)+\frac{64\,b^7+112\,b^5\,c^2+56\,b^3\,c^4+7\,b\,c^6}{c^7}+\frac{\sqrt{b^2+c^2}\,\left(64\,b^6+80\,b^4\,c^2+24\,b^2\,c^4+c^6\right)}{c^7}\right)}","Not used",1,"-(tan(d/2 + (e*x)/2)^6*((16*b^4 + 2*c^4 + 16*b^2*c^2)/c^8 + ((8*b*c^2 + 16*b^3)*(b^2 + c^2)^(1/2))/c^8) + tan(d/2 + (e*x)/2)*(((114*b*c^8)/5 + 512*b^9 + (1352*b^3*c^6)/5 + (4576*b^5*c^4)/5 + (5888*b^7*c^2)/5)/c^13 + ((b^2 + c^2)^(1/2)*(512*b^8 + (14*c^8)/5 + (472*b^2*c^6)/5 + (2592*b^4*c^4)/5 + (4608*b^6*c^2)/5))/c^13) + ((1024*b^10)/7 + (24*c^10)/35 + (136*b^2*c^8)/7 + (4496*b^4*c^6)/35 + (11776*b^6*c^4)/35 + (13056*b^8*c^2)/35)/c^14 + tan(d/2 + (e*x)/2)^2*((768*b^8 + (42*c^8)/5 + (1116*b^2*c^6)/5 + (5136*b^4*c^4)/5 + (7872*b^6*c^2)/5)/c^12 + ((b^2 + c^2)^(1/2)*(60*b*c^6 + 768*b^7 + 528*b^3*c^4 + (5952*b^5*c^2)/5))/c^12) + tan(d/2 + (e*x)/2)^3*((80*b*c^6 + 640*b^7 + 600*b^3*c^4 + 1152*b^5*c^2)/c^11 + ((b^2 + c^2)^(1/2)*(640*b^6 + 12*c^6 + 264*b^2*c^4 + 832*b^4*c^2))/c^11) + tan(d/2 + (e*x)/2)^4*((320*b^6 + 12*c^6 + 196*b^2*c^4 + 496*b^4*c^2)/c^10 + ((b^2 + c^2)^(1/2)*(68*b*c^4 + 320*b^5 + 336*b^3*c^2))/c^10) + tan(d/2 + (e*x)/2)^5*((30*b*c^4 + 96*b^5 + 120*b^3*c^2)/c^9 + ((b^2 + c^2)^(1/2)*(96*b^4 + 6*c^4 + 72*b^2*c^2))/c^9) + ((b^2 + c^2)^(1/2)*((24*b*c^8)/5 + (1024*b^9)/7 + (272*b^3*c^6)/5 + (1024*b^5*c^4)/5 + (10496*b^7*c^2)/35))/c^14)/(e*(tan(d/2 + (e*x)/2)^3*((280*b^4 + 35*c^4 + 280*b^2*c^2)/c^4 + ((140*b*c^2 + 280*b^3)*(b^2 + c^2)^(1/2))/c^4) + tan(d/2 + (e*x)/2)^4*((105*b*c^2 + 140*b^3)/c^3 + ((140*b^2 + 35*c^2)*(b^2 + c^2)^(1/2))/c^3) + tan(d/2 + (e*x)/2)^7 + tan(d/2 + (e*x)/2)*((224*b^6 + 7*c^6 + 126*b^2*c^4 + 336*b^4*c^2)/c^6 + ((b^2 + c^2)^(1/2)*(42*b*c^4 + 224*b^5 + 224*b^3*c^2))/c^6) + tan(d/2 + (e*x)/2)^5*((42*b^2 + 21*c^2)/c^2 + (42*b*(b^2 + c^2)^(1/2))/c^2) + tan(d/2 + (e*x)/2)^6*((7*(b^2 + c^2)^(1/2))/c + (7*b)/c) + tan(d/2 + (e*x)/2)^2*((105*b*c^4 + 336*b^5 + 420*b^3*c^2)/c^5 + ((b^2 + c^2)^(1/2)*(336*b^4 + 21*c^4 + 252*b^2*c^2))/c^5) + (7*b*c^6 + 64*b^7 + 56*b^3*c^4 + 112*b^5*c^2)/c^7 + ((b^2 + c^2)^(1/2)*(64*b^6 + c^6 + 24*b^2*c^4 + 80*b^4*c^2))/c^7))","B"
363,1,239,157,2.574610,"\text{Not used}","int((2*a + 2*a*cos(d + e*x) + 2*c*sin(d + e*x))^3,x)","20\,a^3\,x-\frac{32\,c^3\,{\cos\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4}{e}+\frac{64\,c^3\,{\cos\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6}{3\,e}+12\,a\,c^2\,x-\frac{64\,a^2\,c\,{\cos\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6}{e}+\frac{40\,a^3\,\cos\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\sin\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{e}+\frac{80\,a^3\,{\cos\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\sin\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{3\,e}+\frac{64\,a^3\,{\cos\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\sin\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{3\,e}+\frac{16\,a\,c^2\,{\cos\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\sin\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{e}-\frac{64\,a\,c^2\,{\cos\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\sin\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{e}+\frac{24\,a\,c^2\,\cos\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\sin\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{e}","Not used",1,"20*a^3*x - (32*c^3*cos(d/2 + (e*x)/2)^4)/e + (64*c^3*cos(d/2 + (e*x)/2)^6)/(3*e) + 12*a*c^2*x - (64*a^2*c*cos(d/2 + (e*x)/2)^6)/e + (40*a^3*cos(d/2 + (e*x)/2)*sin(d/2 + (e*x)/2))/e + (80*a^3*cos(d/2 + (e*x)/2)^3*sin(d/2 + (e*x)/2))/(3*e) + (64*a^3*cos(d/2 + (e*x)/2)^5*sin(d/2 + (e*x)/2))/(3*e) + (16*a*c^2*cos(d/2 + (e*x)/2)^3*sin(d/2 + (e*x)/2))/e - (64*a*c^2*cos(d/2 + (e*x)/2)^5*sin(d/2 + (e*x)/2))/e + (24*a*c^2*cos(d/2 + (e*x)/2)*sin(d/2 + (e*x)/2))/e","B"
364,1,96,81,3.213236,"\text{Not used}","int((2*a + 2*a*cos(d + e*x) + 2*c*sin(d + e*x))^2,x)","\frac{x\,\left(12\,a^2+4\,c^2\right)}{2}+\frac{\left(12\,a^2+4\,c^2\right)\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3+\left(20\,a^2-4\,c^2\right)\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)-16\,a\,c}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+1\right)}","Not used",1,"(x*(12*a^2 + 4*c^2))/2 + (tan(d/2 + (e*x)/2)^3*(12*a^2 + 4*c^2) - 16*a*c + tan(d/2 + (e*x)/2)*(20*a^2 - 4*c^2))/(e*(2*tan(d/2 + (e*x)/2)^2 + tan(d/2 + (e*x)/2)^4 + 1))","B"
365,1,29,29,2.428279,"\text{Not used}","int(2*a + 2*a*cos(d + e*x) + 2*c*sin(d + e*x),x)","2\,a\,x-\frac{2\,c\,\cos\left(d+e\,x\right)}{e}+\frac{2\,a\,\sin\left(d+e\,x\right)}{e}","Not used",1,"2*a*x - (2*c*cos(d + e*x))/e + (2*a*sin(d + e*x))/e","B"
366,1,22,25,2.819771,"\text{Not used}","int(1/(2*a + 2*a*cos(d + e*x) + 2*c*sin(d + e*x)),x)","\frac{\ln\left(a+c\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\right)}{2\,c\,e}","Not used",1,"log(a + c*tan(d/2 + (e*x)/2))/(2*c*e)","B"
367,1,79,75,2.478804,"\text{Not used}","int(1/(2*a + 2*a*cos(d + e*x) + 2*c*sin(d + e*x))^2,x)","\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{8\,c^2\,e}-\frac{a\,\ln\left(a+c\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\right)}{4\,c^3\,e}-\frac{a^2+c^2}{c\,e\,\left(8\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,c^3+8\,a\,c^2\right)}","Not used",1,"tan(d/2 + (e*x)/2)/(8*c^2*e) - (a*log(a + c*tan(d/2 + (e*x)/2)))/(4*c^3*e) - (a^2 + c^2)/(c*e*(8*a*c^2 + 8*c^3*tan(d/2 + (e*x)/2)))","B"
368,1,162,134,2.481067,"\text{Not used}","int(1/(2*a + 2*a*cos(d + e*x) + 2*c*sin(d + e*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2}{64\,c^3\,e}+\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(4\,a^3+4\,a\,c^2\right)+\frac{7\,a^4+6\,a^2\,c^2-c^4}{2\,c}}{e\,\left(32\,a^2\,c^4+64\,a\,c^5\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+32\,c^6\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\right)}-\frac{3\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{32\,c^4\,e}+\frac{\ln\left(a+c\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\right)\,\left(3\,a^2+c^2\right)}{16\,c^5\,e}","Not used",1,"tan(d/2 + (e*x)/2)^2/(64*c^3*e) + (tan(d/2 + (e*x)/2)*(4*a*c^2 + 4*a^3) + (7*a^4 - c^4 + 6*a^2*c^2)/(2*c))/(e*(32*c^6*tan(d/2 + (e*x)/2)^2 + 32*a^2*c^4 + 64*a*c^5*tan(d/2 + (e*x)/2))) - (3*a*tan(d/2 + (e*x)/2))/(32*c^4*e) + (log(a + c*tan(d/2 + (e*x)/2))*(3*a^2 + c^2))/(16*c^5*e)","B"
369,1,260,207,2.526255,"\text{Not used}","int(1/(2*a + 2*a*cos(d + e*x) + 2*c*sin(d + e*x))^4,x)","\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3}{384\,c^4\,e}+\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(\frac{3}{128\,c^4}+\frac{5\,a^2}{64\,c^6}\right)}{e}-\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(27\,a^5+30\,a^3\,c^2+3\,a\,c^4\right)+\frac{37\,a^6+39\,a^4\,c^2+3\,a^2\,c^4+c^6}{3\,c}+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(15\,a^4\,c+18\,a^2\,c^3+3\,c^5\right)}{e\,\left(128\,a^3\,c^6+384\,a^2\,c^7\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+384\,a\,c^8\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+128\,c^9\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\right)}-\frac{a\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2}{64\,c^5\,e}-\frac{\ln\left(a+c\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\right)\,\left(5\,a^3+3\,a\,c^2\right)}{32\,c^7\,e}","Not used",1,"tan(d/2 + (e*x)/2)^3/(384*c^4*e) + (tan(d/2 + (e*x)/2)*(3/(128*c^4) + (5*a^2)/(64*c^6)))/e - (tan(d/2 + (e*x)/2)*(3*a*c^4 + 27*a^5 + 30*a^3*c^2) + (37*a^6 + c^6 + 3*a^2*c^4 + 39*a^4*c^2)/(3*c) + tan(d/2 + (e*x)/2)^2*(15*a^4*c + 3*c^5 + 18*a^2*c^3))/(e*(128*c^9*tan(d/2 + (e*x)/2)^3 + 128*a^3*c^6 + 384*a^2*c^7*tan(d/2 + (e*x)/2) + 384*a*c^8*tan(d/2 + (e*x)/2)^2)) - (a*tan(d/2 + (e*x)/2)^2)/(64*c^5*e) - (log(a + c*tan(d/2 + (e*x)/2))*(3*a*c^2 + 5*a^3))/(32*c^7*e)","B"
370,1,20,23,2.487970,"\text{Not used}","int(1/(2*a + 2*a*cos(d + e*x) + 2*a*sin(d + e*x)),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+1\right)}{2\,a\,e}","Not used",1,"log(tan(d/2 + (e*x)/2) + 1)/(2*a*e)","B"
371,1,59,75,2.454334,"\text{Not used}","int(1/(2*a + 2*a*cos(d + e*x) + 2*a*sin(d + e*x))^2,x)","\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{8\,a^2\,e}-\frac{\ln\left(\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+1\right)}{4\,a^2\,e}-\frac{1}{4\,a^2\,e\,\left(\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+1\right)}","Not used",1,"tan(d/2 + (e*x)/2)/(8*a^2*e) - log(tan(d/2 + (e*x)/2) + 1)/(4*a^2*e) - 1/(4*a^2*e*(tan(d/2 + (e*x)/2) + 1))","B"
372,1,90,123,2.445793,"\text{Not used}","int(1/(2*a + 2*a*cos(d + e*x) + 2*a*sin(d + e*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2}{64\,a^3\,e}+\frac{\ln\left(\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+1\right)}{4\,a^3\,e}-\frac{3\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{32\,a^3\,e}+\frac{\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{4}+\frac{3}{16}}{a^3\,e\,{\left(\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+1\right)}^2}","Not used",1,"tan(d/2 + (e*x)/2)^2/(64*a^3*e) + log(tan(d/2 + (e*x)/2) + 1)/(4*a^3*e) - (3*tan(d/2 + (e*x)/2))/(32*a^3*e) + (tan(d/2 + (e*x)/2)/4 + 3/16)/(a^3*e*(tan(d/2 + (e*x)/2) + 1)^2)","B"
373,1,161,168,2.440652,"\text{Not used}","int(1/(2*a + 2*a*cos(d + e*x) + 2*a*sin(d + e*x))^4,x)","\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3}{384\,a^4\,e}-\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2}{64\,a^4\,e}-\frac{\ln\left(\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+1\right)}{4\,a^4\,e}+\frac{13\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{128\,a^4\,e}-\frac{9\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+15\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+\frac{20}{3}}{e\,\left(32\,a^4\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3+96\,a^4\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+96\,a^4\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+32\,a^4\right)}","Not used",1,"tan(d/2 + (e*x)/2)^3/(384*a^4*e) - tan(d/2 + (e*x)/2)^2/(64*a^4*e) - log(tan(d/2 + (e*x)/2) + 1)/(4*a^4*e) + (13*tan(d/2 + (e*x)/2))/(128*a^4*e) - (15*tan(d/2 + (e*x)/2) + 9*tan(d/2 + (e*x)/2)^2 + 20/3)/(e*(96*a^4*tan(d/2 + (e*x)/2)^2 + 32*a^4*tan(d/2 + (e*x)/2)^3 + 32*a^4 + 96*a^4*tan(d/2 + (e*x)/2)))","B"
374,1,258,157,3.213785,"\text{Not used}","int((2*a - 2*a*cos(d + e*x) + 2*c*sin(d + e*x))^3,x)","\frac{8\,a\,\mathrm{atan}\left(\frac{8\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(5\,a^2+3\,c^2\right)}{40\,a^3+24\,a\,c^2}\right)\,\left(5\,a^2+3\,c^2\right)}{e}-\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(40\,a^3+24\,a\,c^2\right)+64\,a^2\,c-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(24\,a\,c^2-88\,a^3\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(\frac{320\,a^3}{3}+64\,a\,c^2\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(192\,a^2\,c+32\,c^3\right)+\frac{32\,c^3}{3}+192\,a^2\,c\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+1\right)}-\frac{8\,a\,\left(5\,a^2+3\,c^2\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\right)-\frac{e\,x}{2}\right)}{e}","Not used",1,"(8*a*atan((8*a*tan(d/2 + (e*x)/2)*(5*a^2 + 3*c^2))/(24*a*c^2 + 40*a^3))*(5*a^2 + 3*c^2))/e - (tan(d/2 + (e*x)/2)*(24*a*c^2 + 40*a^3) + 64*a^2*c - tan(d/2 + (e*x)/2)^5*(24*a*c^2 - 88*a^3) + tan(d/2 + (e*x)/2)^3*(64*a*c^2 + (320*a^3)/3) + tan(d/2 + (e*x)/2)^2*(192*a^2*c + 32*c^3) + (32*c^3)/3 + 192*a^2*c*tan(d/2 + (e*x)/2)^4)/(e*(3*tan(d/2 + (e*x)/2)^2 + 3*tan(d/2 + (e*x)/2)^4 + tan(d/2 + (e*x)/2)^6 + 1)) - (8*a*(5*a^2 + 3*c^2)*(atan(tan(d/2 + (e*x)/2)) - (e*x)/2))/e","B"
375,1,84,81,2.504162,"\text{Not used}","int((2*a - 2*a*cos(d + e*x) + 2*c*sin(d + e*x))^2,x)","\frac{a^2\,\sin\left(2\,d+2\,e\,x\right)-8\,a^2\,\sin\left(d+e\,x\right)-c^2\,\sin\left(2\,d+2\,e\,x\right)+16\,a\,c\,{\sin\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2-4\,a\,c\,{\sin\left(d+e\,x\right)}^2+6\,a^2\,e\,x+2\,c^2\,e\,x}{e}","Not used",1,"(a^2*sin(2*d + 2*e*x) - 8*a^2*sin(d + e*x) - c^2*sin(2*d + 2*e*x) + 16*a*c*sin(d/2 + (e*x)/2)^2 - 4*a*c*sin(d + e*x)^2 + 6*a^2*e*x + 2*c^2*e*x)/e","B"
376,1,29,29,2.428724,"\text{Not used}","int(2*a - 2*a*cos(d + e*x) + 2*c*sin(d + e*x),x)","2\,a\,x-\frac{2\,c\,\cos\left(d+e\,x\right)}{e}-\frac{2\,a\,\sin\left(d+e\,x\right)}{e}","Not used",1,"2*a*x - (2*c*cos(d + e*x))/e - (2*a*sin(d + e*x))/e","B"
377,1,26,25,2.617255,"\text{Not used}","int(1/(2*a - 2*a*cos(d + e*x) + 2*c*sin(d + e*x)),x)","-\frac{\mathrm{atanh}\left(\frac{2\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{c}+1\right)}{c\,e}","Not used",1,"-atanh((2*a*tan(d/2 + (e*x)/2))/c + 1)/(c*e)","B"
378,1,91,75,2.546324,"\text{Not used}","int(1/(2*a - 2*a*cos(d + e*x) + 2*c*sin(d + e*x))^2,x)","\frac{a\,\mathrm{atanh}\left(\frac{2\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{c}+1\right)}{2\,c^3\,e}-\frac{\frac{1}{c}+\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a^2+c^2\right)}{a\,c^2}}{e\,\left(8\,a\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+8\,c\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\right)}","Not used",1,"(a*atanh((2*a*tan(d/2 + (e*x)/2))/c + 1))/(2*c^3*e) - (1/c + (tan(d/2 + (e*x)/2)*(2*a^2 + c^2))/(a*c^2))/(e*(8*c*tan(d/2 + (e*x)/2) + 8*a*tan(d/2 + (e*x)/2)^2))","B"
379,1,186,134,4.467555,"\text{Not used}","int(1/(2*a - 2*a*cos(d + e*x) + 2*c*sin(d + e*x))^3,x)","\frac{\frac{2\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{c^2}-\frac{1}{2\,c}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(6\,a^4+2\,a^2\,c^2-c^4\right)}{a\,c^4}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(18\,a^4+6\,a^2\,c^2-c^4\right)}{2\,a^2\,c^3}}{e\,\left(32\,a^2\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4+64\,a\,c\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3+32\,c^2\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\right)}-\frac{\mathrm{atanh}\left(\frac{2\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{c}+1\right)\,\left(3\,a^2+c^2\right)}{8\,c^5\,e}","Not used",1,"((2*a*tan(d/2 + (e*x)/2))/c^2 - 1/(2*c) + (tan(d/2 + (e*x)/2)^3*(6*a^4 - c^4 + 2*a^2*c^2))/(a*c^4) + (tan(d/2 + (e*x)/2)^2*(18*a^4 - c^4 + 6*a^2*c^2))/(2*a^2*c^3))/(e*(32*a^2*tan(d/2 + (e*x)/2)^4 + 32*c^2*tan(d/2 + (e*x)/2)^2 + 64*a*c*tan(d/2 + (e*x)/2)^3)) - (atanh((2*a*tan(d/2 + (e*x)/2))/c + 1)*(3*a^2 + c^2))/(8*c^5*e)","B"
380,1,301,207,6.050526,"\text{Not used}","int(1/(2*a - 2*a*cos(d + e*x) + 2*c*sin(d + e*x))^4,x)","\frac{a\,\mathrm{atanh}\left(\frac{a\,\left(c+2\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\right)\,\left(5\,a^2+3\,c^2\right)}{c\,\left(5\,a^3+3\,a\,c^2\right)}\right)\,\left(5\,a^2+3\,c^2\right)}{16\,c^7\,e}-\frac{\frac{1}{3\,c}-\frac{a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{c^2}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(5\,a^2+3\,c^2\right)}{c^3}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(110\,a^6+66\,a^4\,c^2+3\,a^2\,c^4+c^6\right)}{3\,a^3\,c^4}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(20\,a^6+12\,a^4\,c^2+c^6\right)}{a\,c^6}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(50\,a^6+30\,a^4\,c^2+c^6\right)}{a^2\,c^5}}{e\,\left(128\,a^3\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6+384\,a^2\,c\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5+384\,a\,c^2\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4+128\,c^3\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\right)}","Not used",1,"(a*atanh((a*(c + 2*a*tan(d/2 + (e*x)/2))*(5*a^2 + 3*c^2))/(c*(3*a*c^2 + 5*a^3)))*(5*a^2 + 3*c^2))/(16*c^7*e) - (1/(3*c) - (a*tan(d/2 + (e*x)/2))/c^2 + (tan(d/2 + (e*x)/2)^2*(5*a^2 + 3*c^2))/c^3 + (tan(d/2 + (e*x)/2)^3*(110*a^6 + c^6 + 3*a^2*c^4 + 66*a^4*c^2))/(3*a^3*c^4) + (tan(d/2 + (e*x)/2)^5*(20*a^6 + c^6 + 12*a^4*c^2))/(a*c^6) + (tan(d/2 + (e*x)/2)^4*(50*a^6 + c^6 + 30*a^4*c^2))/(a^2*c^5))/(e*(128*a^3*tan(d/2 + (e*x)/2)^6 + 128*c^3*tan(d/2 + (e*x)/2)^3 + 384*a*c^2*tan(d/2 + (e*x)/2)^4 + 384*a^2*c*tan(d/2 + (e*x)/2)^5))","B"
381,1,292,157,3.602845,"\text{Not used}","int((2*a + 2*b*cos(d + e*x) + 2*a*sin(d + e*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(24\,a^3+48\,a^2\,b-24\,a\,b^2+16\,b^3\right)-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(48\,a^3-96\,a^2\,b+48\,a\,b^2\right)-16\,a\,b^2+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(96\,a^2\,b-128\,a^3\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(160\,a^2\,b+\frac{32\,b^3}{3}\right)-\frac{176\,a^3}{3}+\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-24\,a^3+48\,a^2\,b+24\,a\,b^2+16\,b^3\right)}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+1\right)}+\frac{8\,a\,\mathrm{atan}\left(\frac{8\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(5\,a^2+3\,b^2\right)}{40\,a^3+24\,a\,b^2}\right)\,\left(5\,a^2+3\,b^2\right)}{e}-\frac{8\,a\,\left(5\,a^2+3\,b^2\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\right)-\frac{e\,x}{2}\right)}{e}","Not used",1,"(tan(d/2 + (e*x)/2)^5*(48*a^2*b - 24*a*b^2 + 24*a^3 + 16*b^3) - tan(d/2 + (e*x)/2)^4*(48*a*b^2 - 96*a^2*b + 48*a^3) - 16*a*b^2 + tan(d/2 + (e*x)/2)^2*(96*a^2*b - 128*a^3) + tan(d/2 + (e*x)/2)^3*(160*a^2*b + (32*b^3)/3) - (176*a^3)/3 + tan(d/2 + (e*x)/2)*(24*a*b^2 + 48*a^2*b - 24*a^3 + 16*b^3))/(e*(3*tan(d/2 + (e*x)/2)^2 + 3*tan(d/2 + (e*x)/2)^4 + tan(d/2 + (e*x)/2)^6 + 1)) + (8*a*atan((8*a*tan(d/2 + (e*x)/2)*(5*a^2 + 3*b^2))/(24*a*b^2 + 40*a^3))*(5*a^2 + 3*b^2))/e - (8*a*(5*a^2 + 3*b^2)*(atan(tan(d/2 + (e*x)/2)) - (e*x)/2))/e","B"
382,1,127,81,3.718377,"\text{Not used}","int((2*a + 2*b*cos(d + e*x) + 2*a*sin(d + e*x))^2,x)","\frac{x\,\left(12\,a^2+4\,b^2\right)}{2}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(16\,a\,b-16\,a^2\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(4\,a^2+16\,a\,b-4\,b^2\right)-16\,a^2+\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-4\,a^2+16\,a\,b+4\,b^2\right)}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+1\right)}","Not used",1,"(x*(12*a^2 + 4*b^2))/2 + (tan(d/2 + (e*x)/2)^2*(16*a*b - 16*a^2) + tan(d/2 + (e*x)/2)^3*(16*a*b + 4*a^2 - 4*b^2) - 16*a^2 + tan(d/2 + (e*x)/2)*(16*a*b - 4*a^2 + 4*b^2))/(e*(2*tan(d/2 + (e*x)/2)^2 + tan(d/2 + (e*x)/2)^4 + 1))","B"
383,1,29,29,2.440037,"\text{Not used}","int(2*a + 2*b*cos(d + e*x) + 2*a*sin(d + e*x),x)","2\,a\,x-\frac{2\,a\,\cos\left(d+e\,x\right)}{e}+\frac{2\,b\,\sin\left(d+e\,x\right)}{e}","Not used",1,"2*a*x - (2*a*cos(d + e*x))/e + (2*b*sin(d + e*x))/e","B"
384,1,33,33,2.830256,"\text{Not used}","int(1/(2*a + 2*b*cos(d + e*x) + 2*a*sin(d + e*x)),x)","-\frac{\mathrm{atanh}\left(\frac{a+\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a-2\,b\right)}{2}}{b}\right)}{b\,e}","Not used",1,"-atanh((a + (tan(d/2 + (e*x)/2)*(2*a - 2*b))/2)/b)/(b*e)","B"
385,1,126,83,2.720801,"\text{Not used}","int(1/(2*a + 2*b*cos(d + e*x) + 2*a*sin(d + e*x))^2,x)","\frac{a\,\mathrm{atanh}\left(\frac{a+\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a-2\,b\right)}{2}}{b}\right)}{2\,b^3\,e}-\frac{\frac{a^2}{b^2\,\left(a-b\right)}+\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(a^2-a\,b+b^2\right)}{b^2\,\left(a-b\right)}}{e\,\left(\left(2\,a-2\,b\right)\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+4\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+2\,a+2\,b\right)}","Not used",1,"(a*atanh((a + (tan(d/2 + (e*x)/2)*(2*a - 2*b))/2)/b))/(2*b^3*e) - (a^2/(b^2*(a - b)) + (tan(d/2 + (e*x)/2)*(a^2 - a*b + b^2))/(b^2*(a - b)))/(e*(2*a + 2*b + tan(d/2 + (e*x)/2)^2*(2*a - 2*b) + 4*a*tan(d/2 + (e*x)/2)))","B"
386,1,360,142,6.445004,"\text{Not used}","int(1/(2*a + 2*b*cos(d + e*x) + 2*a*sin(d + e*x))^3,x)","-\frac{\frac{-3\,a^5+4\,a^3\,b^2+a\,b^4}{2\,b^4\,{\left(a-b\right)}^2}+\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-9\,a^5+9\,a^4\,b+2\,a^3\,b^2-2\,a^2\,b^3+5\,a\,b^4-b^5\right)}{2\,b^4\,{\left(a-b\right)}^2}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(-3\,a^4+6\,a^3\,b-4\,a^2\,b^2+2\,a\,b^3+b^4\right)}{2\,b^4\,\left(a-b\right)}-\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(9\,a^5-18\,a^4\,b+12\,a^3\,b^2-6\,a^2\,b^3+a\,b^4\right)}{2\,b^4\,{\left(a-b\right)}^2}}{e\,\left(8\,a\,b+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(24\,a^2-8\,b^2\right)-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(16\,a\,b-16\,a^2\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(4\,a^2-8\,a\,b+4\,b^2\right)+4\,a^2+4\,b^2+\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(16\,a^2+16\,b\,a\right)\right)}-\frac{\mathrm{atanh}\left(\frac{2\,a+\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a-2\,b\right)}{2\,b}\right)\,\left(3\,a^2+b^2\right)}{8\,b^5\,e}","Not used",1,"- ((a*b^4 - 3*a^5 + 4*a^3*b^2)/(2*b^4*(a - b)^2) + (tan(d/2 + (e*x)/2)*(5*a*b^4 + 9*a^4*b - 9*a^5 - b^5 - 2*a^2*b^3 + 2*a^3*b^2))/(2*b^4*(a - b)^2) + (tan(d/2 + (e*x)/2)^3*(2*a*b^3 + 6*a^3*b - 3*a^4 + b^4 - 4*a^2*b^2))/(2*b^4*(a - b)) - (tan(d/2 + (e*x)/2)^2*(a*b^4 - 18*a^4*b + 9*a^5 - 6*a^2*b^3 + 12*a^3*b^2))/(2*b^4*(a - b)^2))/(e*(8*a*b + tan(d/2 + (e*x)/2)^2*(24*a^2 - 8*b^2) - tan(d/2 + (e*x)/2)^3*(16*a*b - 16*a^2) + tan(d/2 + (e*x)/2)^4*(4*a^2 - 8*a*b + 4*b^2) + 4*a^2 + 4*b^2 + tan(d/2 + (e*x)/2)*(16*a*b + 16*a^2))) - (atanh((2*a + tan(d/2 + (e*x)/2)*(2*a - 2*b))/(2*b))*(3*a^2 + b^2))/(8*b^5*e)","B"
387,1,730,215,7.217049,"\text{Not used}","int(1/(2*a + 2*b*cos(d + e*x) + 2*a*sin(d + e*x))^4,x)","\frac{a\,\mathrm{atanh}\left(\frac{a\,\left(2\,a+\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a-2\,b\right)\right)\,\left(5\,a^2+3\,b^2\right)}{2\,b\,\left(5\,a^3+3\,a\,b^2\right)}\right)\,\left(5\,a^2+3\,b^2\right)}{16\,b^7\,e}-\frac{\frac{15\,a^8-31\,a^6\,b^2+9\,a^4\,b^4+15\,a^2\,b^6}{6\,b^6\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(25\,a^8-50\,a^7\,b+20\,a^6\,b^2+10\,a^5\,b^3-17\,a^4\,b^4+24\,a^3\,b^5-10\,a^2\,b^6+2\,a\,b^7\right)}{b^6\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(25\,a^7-75\,a^6\,b+90\,a^5\,b^2-70\,a^4\,b^3+45\,a^3\,b^4-15\,a^2\,b^5+4\,a\,b^6\right)}{2\,b^6\,{\left(a-b\right)}^2}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(75\,a^8-225\,a^7\,b+250\,a^6\,b^2-150\,a^5\,b^3+63\,a^4\,b^4+11\,a^3\,b^5-24\,a^2\,b^6+6\,a\,b^7-2\,b^8\right)}{3\,b^6\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(5\,a^6-15\,a^5\,b+18\,a^4\,b^2-14\,a^3\,b^3+9\,a^2\,b^4-3\,a\,b^5+2\,b^6\right)}{2\,b^6\,\left(a-b\right)}+\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(25\,a^8-25\,a^7\,b-25\,a^6\,b^2+25\,a^5\,b^3-13\,a^4\,b^4+13\,a^3\,b^5+11\,a^2\,b^6-5\,a\,b^7+2\,b^8\right)}{2\,b^6\,{\left(a-b\right)}^3}}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(48\,a^3-96\,a^2\,b+48\,a\,b^2\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6\,\left(8\,a^3-24\,a^2\,b+24\,a\,b^2-8\,b^3\right)-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(-120\,a^3-120\,a^2\,b+24\,a\,b^2+24\,b^3\right)-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(-120\,a^3+120\,a^2\,b+24\,a\,b^2-24\,b^3\right)+24\,a\,b^2+24\,a^2\,b-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(96\,a\,b^2-160\,a^3\right)+\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(48\,a^3+96\,a^2\,b+48\,a\,b^2\right)+8\,a^3+8\,b^3\right)}","Not used",1,"(a*atanh((a*(2*a + tan(d/2 + (e*x)/2)*(2*a - 2*b))*(5*a^2 + 3*b^2))/(2*b*(3*a*b^2 + 5*a^3)))*(5*a^2 + 3*b^2))/(16*b^7*e) - ((15*a^8 + 15*a^2*b^6 + 9*a^4*b^4 - 31*a^6*b^2)/(6*b^6*(a - b)^3) + (tan(d/2 + (e*x)/2)^2*(2*a*b^7 - 50*a^7*b + 25*a^8 - 10*a^2*b^6 + 24*a^3*b^5 - 17*a^4*b^4 + 10*a^5*b^3 + 20*a^6*b^2))/(b^6*(a - b)^3) + (tan(d/2 + (e*x)/2)^4*(4*a*b^6 - 75*a^6*b + 25*a^7 - 15*a^2*b^5 + 45*a^3*b^4 - 70*a^4*b^3 + 90*a^5*b^2))/(2*b^6*(a - b)^2) + (tan(d/2 + (e*x)/2)^3*(6*a*b^7 - 225*a^7*b + 75*a^8 - 2*b^8 - 24*a^2*b^6 + 11*a^3*b^5 + 63*a^4*b^4 - 150*a^5*b^3 + 250*a^6*b^2))/(3*b^6*(a - b)^3) + (tan(d/2 + (e*x)/2)^5*(5*a^6 - 15*a^5*b - 3*a*b^5 + 2*b^6 + 9*a^2*b^4 - 14*a^3*b^3 + 18*a^4*b^2))/(2*b^6*(a - b)) + (tan(d/2 + (e*x)/2)*(25*a^8 - 25*a^7*b - 5*a*b^7 + 2*b^8 + 11*a^2*b^6 + 13*a^3*b^5 - 13*a^4*b^4 + 25*a^5*b^3 - 25*a^6*b^2))/(2*b^6*(a - b)^3))/(e*(tan(d/2 + (e*x)/2)^5*(48*a*b^2 - 96*a^2*b + 48*a^3) + tan(d/2 + (e*x)/2)^6*(24*a*b^2 - 24*a^2*b + 8*a^3 - 8*b^3) - tan(d/2 + (e*x)/2)^2*(24*a*b^2 - 120*a^2*b - 120*a^3 + 24*b^3) - tan(d/2 + (e*x)/2)^4*(24*a*b^2 + 120*a^2*b - 120*a^3 - 24*b^3) + 24*a*b^2 + 24*a^2*b - tan(d/2 + (e*x)/2)^3*(96*a*b^2 - 160*a^3) + tan(d/2 + (e*x)/2)*(48*a*b^2 + 96*a^2*b + 48*a^3) + 8*a^3 + 8*b^3))","B"
388,1,292,157,3.439161,"\text{Not used}","int((2*a + 2*b*cos(d + e*x) - 2*a*sin(d + e*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(48\,a^3-96\,a^2\,b+48\,a\,b^2\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(24\,a^3+48\,a^2\,b-24\,a\,b^2+16\,b^3\right)+16\,a\,b^2-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(96\,a^2\,b-128\,a^3\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(160\,a^2\,b+\frac{32\,b^3}{3}\right)+\frac{176\,a^3}{3}+\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-24\,a^3+48\,a^2\,b+24\,a\,b^2+16\,b^3\right)}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+1\right)}+\frac{8\,a\,\mathrm{atan}\left(\frac{8\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(5\,a^2+3\,b^2\right)}{40\,a^3+24\,a\,b^2}\right)\,\left(5\,a^2+3\,b^2\right)}{e}-\frac{8\,a\,\left(5\,a^2+3\,b^2\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\right)-\frac{e\,x}{2}\right)}{e}","Not used",1,"(tan(d/2 + (e*x)/2)^4*(48*a*b^2 - 96*a^2*b + 48*a^3) + tan(d/2 + (e*x)/2)^5*(48*a^2*b - 24*a*b^2 + 24*a^3 + 16*b^3) + 16*a*b^2 - tan(d/2 + (e*x)/2)^2*(96*a^2*b - 128*a^3) + tan(d/2 + (e*x)/2)^3*(160*a^2*b + (32*b^3)/3) + (176*a^3)/3 + tan(d/2 + (e*x)/2)*(24*a*b^2 + 48*a^2*b - 24*a^3 + 16*b^3))/(e*(3*tan(d/2 + (e*x)/2)^2 + 3*tan(d/2 + (e*x)/2)^4 + tan(d/2 + (e*x)/2)^6 + 1)) + (8*a*atan((8*a*tan(d/2 + (e*x)/2)*(5*a^2 + 3*b^2))/(24*a*b^2 + 40*a^3))*(5*a^2 + 3*b^2))/e - (8*a*(5*a^2 + 3*b^2)*(atan(tan(d/2 + (e*x)/2)) - (e*x)/2))/e","B"
389,1,128,81,3.742882,"\text{Not used}","int((2*a + 2*b*cos(d + e*x) - 2*a*sin(d + e*x))^2,x)","\frac{x\,\left(12\,a^2+4\,b^2\right)}{2}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(4\,a^2+16\,a\,b-4\,b^2\right)-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(16\,a\,b-16\,a^2\right)+16\,a^2+\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-4\,a^2+16\,a\,b+4\,b^2\right)}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+1\right)}","Not used",1,"(x*(12*a^2 + 4*b^2))/2 + (tan(d/2 + (e*x)/2)^3*(16*a*b + 4*a^2 - 4*b^2) - tan(d/2 + (e*x)/2)^2*(16*a*b - 16*a^2) + 16*a^2 + tan(d/2 + (e*x)/2)*(16*a*b - 4*a^2 + 4*b^2))/(e*(2*tan(d/2 + (e*x)/2)^2 + tan(d/2 + (e*x)/2)^4 + 1))","B"
390,1,29,29,2.444640,"\text{Not used}","int(2*a + 2*b*cos(d + e*x) - 2*a*sin(d + e*x),x)","2\,a\,x+\frac{2\,a\,\cos\left(d+e\,x\right)}{e}+\frac{2\,b\,\sin\left(d+e\,x\right)}{e}","Not used",1,"2*a*x + (2*a*cos(d + e*x))/e + (2*b*sin(d + e*x))/e","B"
391,1,32,33,2.739463,"\text{Not used}","int(1/(2*a + 2*b*cos(d + e*x) - 2*a*sin(d + e*x)),x)","\frac{\mathrm{atanh}\left(\frac{a-\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a-2\,b\right)}{2}}{b}\right)}{b\,e}","Not used",1,"atanh((a - (tan(d/2 + (e*x)/2)*(2*a - 2*b))/2)/b)/(b*e)","B"
392,1,126,83,2.737630,"\text{Not used}","int(1/(2*a + 2*b*cos(d + e*x) - 2*a*sin(d + e*x))^2,x)","\frac{\frac{a^2}{b^2\,\left(a-b\right)}-\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(a^2-a\,b+b^2\right)}{b^2\,\left(a-b\right)}}{e\,\left(\left(2\,a-2\,b\right)\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2-4\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+2\,a+2\,b\right)}-\frac{a\,\mathrm{atanh}\left(\frac{a-\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a-2\,b\right)}{2}}{b}\right)}{2\,b^3\,e}","Not used",1,"(a^2/(b^2*(a - b)) - (tan(d/2 + (e*x)/2)*(a^2 - a*b + b^2))/(b^2*(a - b)))/(e*(2*a + 2*b + tan(d/2 + (e*x)/2)^2*(2*a - 2*b) - 4*a*tan(d/2 + (e*x)/2))) - (a*atanh((a - (tan(d/2 + (e*x)/2)*(2*a - 2*b))/2)/b))/(2*b^3*e)","B"
393,1,361,142,6.481796,"\text{Not used}","int(1/(2*a + 2*b*cos(d + e*x) - 2*a*sin(d + e*x))^3,x)","\frac{\mathrm{atanh}\left(\frac{2\,a-\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a-2\,b\right)}{2\,b}\right)\,\left(3\,a^2+b^2\right)}{8\,b^5\,e}-\frac{\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-9\,a^5+9\,a^4\,b+2\,a^3\,b^2-2\,a^2\,b^3+5\,a\,b^4-b^5\right)}{2\,b^4\,{\left(a-b\right)}^2}-\frac{-3\,a^5+4\,a^3\,b^2+a\,b^4}{2\,b^4\,{\left(a-b\right)}^2}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(-3\,a^4+6\,a^3\,b-4\,a^2\,b^2+2\,a\,b^3+b^4\right)}{2\,b^4\,\left(a-b\right)}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(9\,a^5-18\,a^4\,b+12\,a^3\,b^2-6\,a^2\,b^3+a\,b^4\right)}{2\,b^4\,{\left(a-b\right)}^2}}{e\,\left(8\,a\,b+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(24\,a^2-8\,b^2\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(16\,a\,b-16\,a^2\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(4\,a^2-8\,a\,b+4\,b^2\right)+4\,a^2+4\,b^2-\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(16\,a^2+16\,b\,a\right)\right)}","Not used",1,"(atanh((2*a - tan(d/2 + (e*x)/2)*(2*a - 2*b))/(2*b))*(3*a^2 + b^2))/(8*b^5*e) - ((tan(d/2 + (e*x)/2)*(5*a*b^4 + 9*a^4*b - 9*a^5 - b^5 - 2*a^2*b^3 + 2*a^3*b^2))/(2*b^4*(a - b)^2) - (a*b^4 - 3*a^5 + 4*a^3*b^2)/(2*b^4*(a - b)^2) + (tan(d/2 + (e*x)/2)^3*(2*a*b^3 + 6*a^3*b - 3*a^4 + b^4 - 4*a^2*b^2))/(2*b^4*(a - b)) + (tan(d/2 + (e*x)/2)^2*(a*b^4 - 18*a^4*b + 9*a^5 - 6*a^2*b^3 + 12*a^3*b^2))/(2*b^4*(a - b)^2))/(e*(8*a*b + tan(d/2 + (e*x)/2)^2*(24*a^2 - 8*b^2) + tan(d/2 + (e*x)/2)^3*(16*a*b - 16*a^2) + tan(d/2 + (e*x)/2)^4*(4*a^2 - 8*a*b + 4*b^2) + 4*a^2 + 4*b^2 - tan(d/2 + (e*x)/2)*(16*a*b + 16*a^2)))","B"
394,1,731,215,7.088301,"\text{Not used}","int(1/(2*a + 2*b*cos(d + e*x) - 2*a*sin(d + e*x))^4,x)","\frac{\frac{15\,a^8-31\,a^6\,b^2+9\,a^4\,b^4+15\,a^2\,b^6}{6\,b^6\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(25\,a^8-50\,a^7\,b+20\,a^6\,b^2+10\,a^5\,b^3-17\,a^4\,b^4+24\,a^3\,b^5-10\,a^2\,b^6+2\,a\,b^7\right)}{b^6\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(25\,a^7-75\,a^6\,b+90\,a^5\,b^2-70\,a^4\,b^3+45\,a^3\,b^4-15\,a^2\,b^5+4\,a\,b^6\right)}{2\,b^6\,{\left(a-b\right)}^2}-\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(75\,a^8-225\,a^7\,b+250\,a^6\,b^2-150\,a^5\,b^3+63\,a^4\,b^4+11\,a^3\,b^5-24\,a^2\,b^6+6\,a\,b^7-2\,b^8\right)}{3\,b^6\,{\left(a-b\right)}^3}-\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(5\,a^6-15\,a^5\,b+18\,a^4\,b^2-14\,a^3\,b^3+9\,a^2\,b^4-3\,a\,b^5+2\,b^6\right)}{2\,b^6\,\left(a-b\right)}-\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(25\,a^8-25\,a^7\,b-25\,a^6\,b^2+25\,a^5\,b^3-13\,a^4\,b^4+13\,a^3\,b^5+11\,a^2\,b^6-5\,a\,b^7+2\,b^8\right)}{2\,b^6\,{\left(a-b\right)}^3}}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6\,\left(8\,a^3-24\,a^2\,b+24\,a\,b^2-8\,b^3\right)-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(48\,a^3-96\,a^2\,b+48\,a\,b^2\right)-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(-120\,a^3-120\,a^2\,b+24\,a\,b^2+24\,b^3\right)-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(-120\,a^3+120\,a^2\,b+24\,a\,b^2-24\,b^3\right)+24\,a\,b^2+24\,a^2\,b+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(96\,a\,b^2-160\,a^3\right)-\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(48\,a^3+96\,a^2\,b+48\,a\,b^2\right)+8\,a^3+8\,b^3\right)}-\frac{a\,\mathrm{atanh}\left(\frac{a\,\left(2\,a-\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a-2\,b\right)\right)\,\left(5\,a^2+3\,b^2\right)}{2\,b\,\left(5\,a^3+3\,a\,b^2\right)}\right)\,\left(5\,a^2+3\,b^2\right)}{16\,b^7\,e}","Not used",1,"((15*a^8 + 15*a^2*b^6 + 9*a^4*b^4 - 31*a^6*b^2)/(6*b^6*(a - b)^3) + (tan(d/2 + (e*x)/2)^2*(2*a*b^7 - 50*a^7*b + 25*a^8 - 10*a^2*b^6 + 24*a^3*b^5 - 17*a^4*b^4 + 10*a^5*b^3 + 20*a^6*b^2))/(b^6*(a - b)^3) + (tan(d/2 + (e*x)/2)^4*(4*a*b^6 - 75*a^6*b + 25*a^7 - 15*a^2*b^5 + 45*a^3*b^4 - 70*a^4*b^3 + 90*a^5*b^2))/(2*b^6*(a - b)^2) - (tan(d/2 + (e*x)/2)^3*(6*a*b^7 - 225*a^7*b + 75*a^8 - 2*b^8 - 24*a^2*b^6 + 11*a^3*b^5 + 63*a^4*b^4 - 150*a^5*b^3 + 250*a^6*b^2))/(3*b^6*(a - b)^3) - (tan(d/2 + (e*x)/2)^5*(5*a^6 - 15*a^5*b - 3*a*b^5 + 2*b^6 + 9*a^2*b^4 - 14*a^3*b^3 + 18*a^4*b^2))/(2*b^6*(a - b)) - (tan(d/2 + (e*x)/2)*(25*a^8 - 25*a^7*b - 5*a*b^7 + 2*b^8 + 11*a^2*b^6 + 13*a^3*b^5 - 13*a^4*b^4 + 25*a^5*b^3 - 25*a^6*b^2))/(2*b^6*(a - b)^3))/(e*(tan(d/2 + (e*x)/2)^6*(24*a*b^2 - 24*a^2*b + 8*a^3 - 8*b^3) - tan(d/2 + (e*x)/2)^5*(48*a*b^2 - 96*a^2*b + 48*a^3) - tan(d/2 + (e*x)/2)^2*(24*a*b^2 - 120*a^2*b - 120*a^3 + 24*b^3) - tan(d/2 + (e*x)/2)^4*(24*a*b^2 + 120*a^2*b - 120*a^3 - 24*b^3) + 24*a*b^2 + 24*a^2*b + tan(d/2 + (e*x)/2)^3*(96*a*b^2 - 160*a^3) - tan(d/2 + (e*x)/2)*(48*a*b^2 + 96*a^2*b + 48*a^3) + 8*a^3 + 8*b^3)) - (a*atanh((a*(2*a - tan(d/2 + (e*x)/2)*(2*a - 2*b))*(5*a^2 + 3*b^2))/(2*b*(3*a*b^2 + 5*a^3)))*(5*a^2 + 3*b^2))/(16*b^7*e)","B"
395,1,376,260,3.374469,"\text{Not used}","int((a + b*cos(d + e*x) + c*sin(d + e*x))^4,x)","\frac{6\,b^4\,\sin\left(2\,d+2\,e\,x\right)+\frac{3\,b^4\,\sin\left(4\,d+4\,e\,x\right)}{4}-6\,c^4\,\sin\left(2\,d+2\,e\,x\right)+\frac{3\,c^4\,\sin\left(4\,d+4\,e\,x\right)}{4}+8\,a\,c^3\,\cos\left(3\,d+3\,e\,x\right)-12\,b\,c^3\,\cos\left(2\,d+2\,e\,x\right)-12\,b^3\,c\,\cos\left(2\,d+2\,e\,x\right)+3\,b\,c^3\,\cos\left(4\,d+4\,e\,x\right)-3\,b^3\,c\,\cos\left(4\,d+4\,e\,x\right)+8\,a\,b^3\,\sin\left(3\,d+3\,e\,x\right)+36\,a^2\,b^2\,\sin\left(2\,d+2\,e\,x\right)-36\,a^2\,c^2\,\sin\left(2\,d+2\,e\,x\right)-\frac{9\,b^2\,c^2\,\sin\left(4\,d+4\,e\,x\right)}{2}-72\,a\,c^3\,\cos\left(d+e\,x\right)-96\,a^3\,c\,\cos\left(d+e\,x\right)+72\,a\,b^3\,\sin\left(d+e\,x\right)+96\,a^3\,b\,\sin\left(d+e\,x\right)+24\,a^4\,e\,x+9\,b^4\,e\,x+9\,c^4\,e\,x-72\,a\,b^2\,c\,\cos\left(d+e\,x\right)+72\,a\,b\,c^2\,\sin\left(d+e\,x\right)-72\,a^2\,b\,c\,\cos\left(2\,d+2\,e\,x\right)-24\,a\,b^2\,c\,\cos\left(3\,d+3\,e\,x\right)-24\,a\,b\,c^2\,\sin\left(3\,d+3\,e\,x\right)+72\,a^2\,b^2\,e\,x+72\,a^2\,c^2\,e\,x+18\,b^2\,c^2\,e\,x}{24\,e}","Not used",1,"(6*b^4*sin(2*d + 2*e*x) + (3*b^4*sin(4*d + 4*e*x))/4 - 6*c^4*sin(2*d + 2*e*x) + (3*c^4*sin(4*d + 4*e*x))/4 + 8*a*c^3*cos(3*d + 3*e*x) - 12*b*c^3*cos(2*d + 2*e*x) - 12*b^3*c*cos(2*d + 2*e*x) + 3*b*c^3*cos(4*d + 4*e*x) - 3*b^3*c*cos(4*d + 4*e*x) + 8*a*b^3*sin(3*d + 3*e*x) + 36*a^2*b^2*sin(2*d + 2*e*x) - 36*a^2*c^2*sin(2*d + 2*e*x) - (9*b^2*c^2*sin(4*d + 4*e*x))/2 - 72*a*c^3*cos(d + e*x) - 96*a^3*c*cos(d + e*x) + 72*a*b^3*sin(d + e*x) + 96*a^3*b*sin(d + e*x) + 24*a^4*e*x + 9*b^4*e*x + 9*c^4*e*x - 72*a*b^2*c*cos(d + e*x) + 72*a*b*c^2*sin(d + e*x) - 72*a^2*b*c*cos(2*d + 2*e*x) - 24*a*b^2*c*cos(3*d + 3*e*x) - 24*a*b*c^2*sin(3*d + 3*e*x) + 72*a^2*b^2*e*x + 72*a^2*c^2*e*x + 18*b^2*c^2*e*x)/(24*e)","B"
396,1,333,170,3.699884,"\text{Not used}","int((a + b*cos(d + e*x) + c*sin(d + e*x))^3,x)","\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a^2+3\,b^2+3\,c^2\right)}{2\,a^3+3\,a\,b^2+3\,a\,c^2}\right)\,\left(2\,a^2+3\,b^2+3\,c^2\right)}{e}-\frac{a\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\right)-\frac{e\,x}{2}\right)\,\left(2\,a^2+3\,b^2+3\,c^2\right)}{e}-\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(12\,a^2\,c-12\,b\,a\,c+4\,c^3\right)-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(12\,a^2\,b+\frac{4\,b^3}{3}+8\,b\,c^2\right)-\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(6\,a^2\,b+3\,a\,b^2-3\,a\,c^2+2\,b^3\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(6\,c\,a^2-12\,c\,a\,b+6\,c\,b^2\right)+6\,a^2\,c+2\,b^2\,c-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(6\,a^2\,b-3\,a\,b^2+3\,a\,c^2+2\,b^3\right)+\frac{4\,c^3}{3}}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+1\right)}","Not used",1,"(a*atan((a*tan(d/2 + (e*x)/2)*(2*a^2 + 3*b^2 + 3*c^2))/(3*a*b^2 + 3*a*c^2 + 2*a^3))*(2*a^2 + 3*b^2 + 3*c^2))/e - (a*(atan(tan(d/2 + (e*x)/2)) - (e*x)/2)*(2*a^2 + 3*b^2 + 3*c^2))/e - (tan(d/2 + (e*x)/2)^2*(12*a^2*c + 4*c^3 - 12*a*b*c) - tan(d/2 + (e*x)/2)^3*(12*a^2*b + 8*b*c^2 + (4*b^3)/3) - tan(d/2 + (e*x)/2)*(3*a*b^2 + 6*a^2*b - 3*a*c^2 + 2*b^3) + tan(d/2 + (e*x)/2)^4*(6*a^2*c + 6*b^2*c - 12*a*b*c) + 6*a^2*c + 2*b^2*c - tan(d/2 + (e*x)/2)^5*(6*a^2*b - 3*a*b^2 + 3*a*c^2 + 2*b^3) + (4*c^3)/3)/(e*(3*tan(d/2 + (e*x)/2)^2 + 3*tan(d/2 + (e*x)/2)^4 + tan(d/2 + (e*x)/2)^6 + 1))","B"
397,1,125,91,3.784028,"\text{Not used}","int((a + b*cos(d + e*x) + c*sin(d + e*x))^2,x)","\frac{x\,\left(2\,a^2+b^2+c^2\right)}{2}-\frac{\left(b^2-4\,a\,b-c^2\right)\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3+\left(4\,a\,c-4\,b\,c\right)\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+\left(-b^2-4\,a\,b+c^2\right)\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+4\,a\,c}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+1\right)}","Not used",1,"(x*(2*a^2 + b^2 + c^2))/2 - (4*a*c + tan(d/2 + (e*x)/2)^2*(4*a*c - 4*b*c) - tan(d/2 + (e*x)/2)*(4*a*b + b^2 - c^2) - tan(d/2 + (e*x)/2)^3*(4*a*b - b^2 + c^2))/(e*(2*tan(d/2 + (e*x)/2)^2 + tan(d/2 + (e*x)/2)^4 + 1))","B"
398,1,40,27,2.505901,"\text{Not used}","int(a + b*cos(d + e*x) + c*sin(d + e*x),x)","a\,x-\frac{2\,c-2\,b\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+1\right)}","Not used",1,"a*x - (2*c - 2*b*tan(d/2 + (e*x)/2))/(e*(tan(d/2 + (e*x)/2)^2 + 1))","B"
399,1,75,61,4.011361,"\text{Not used}","int(1/(a + b*cos(d + e*x) + c*sin(d + e*x)),x)","\frac{2\,\mathrm{atan}\left(\frac{c}{\sqrt{a^2-b^2-c^2}}+\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a-2\,b\right)}{2\,\sqrt{a^2-b^2-c^2}}\right)}{e\,\sqrt{a^2-b^2-c^2}}","Not used",1,"(2*atan(c/(a^2 - b^2 - c^2)^(1/2) + (tan(d/2 + (e*x)/2)*(2*a - 2*b))/(2*(a^2 - b^2 - c^2)^(1/2))))/(e*(a^2 - b^2 - c^2)^(1/2))","B"
400,1,195,121,3.057222,"\text{Not used}","int(1/(a + b*cos(d + e*x) + c*sin(d + e*x))^2,x)","\frac{2\,a\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a-2\,b\right)+\frac{2\,\left(-a^2\,c+b^2\,c+c^3\right)}{-a^2+b^2+c^2}}{2\,\sqrt{-a^2+b^2+c^2}}\right)}{e\,{\left(-a^2+b^2+c^2\right)}^{3/2}}-\frac{\frac{2\,a\,c}{\left(a-b\right)\,\left(-a^2+b^2+c^2\right)}+\frac{2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(b^2-a\,b+c^2\right)}{\left(a-b\right)\,\left(-a^2+b^2+c^2\right)}}{e\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+2\,c\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+a+b\right)}","Not used",1,"(2*a*atanh((tan(d/2 + (e*x)/2)*(2*a - 2*b) + (2*(b^2*c - a^2*c + c^3))/(b^2 - a^2 + c^2))/(2*(b^2 - a^2 + c^2)^(1/2))))/(e*(b^2 - a^2 + c^2)^(3/2)) - ((2*a*c)/((a - b)*(b^2 - a^2 + c^2)) + (2*tan(d/2 + (e*x)/2)*(b^2 - a*b + c^2))/((a - b)*(b^2 - a^2 + c^2)))/(e*(a + b + tan(d/2 + (e*x)/2)^2*(a - b) + 2*c*tan(d/2 + (e*x)/2)))","B"
401,1,700,197,6.055265,"\text{Not used}","int(1/(a + b*cos(d + e*x) + c*sin(d + e*x))^3,x)","-\frac{\frac{-4\,a^4\,c+3\,a^2\,b^2\,c+a^2\,c^3+b^4\,c+b^2\,c^3}{{\left(a-b\right)}^2\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}+\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(4\,a^4\,b-5\,a^3\,b^2-11\,a^3\,c^2-3\,a^2\,b^3+3\,a^2\,b\,c^2+5\,a\,b^4+7\,a\,b^2\,c^2+2\,a\,c^4-b^5+b^3\,c^2+2\,b\,c^4\right)}{{\left(a-b\right)}^2\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(-4\,a^4\,c+12\,a^3\,b\,c-13\,a^2\,b^2\,c-7\,a^2\,c^3+6\,a\,b^3\,c+6\,a\,b\,c^3-b^4\,c+b^2\,c^3+2\,c^5\right)}{{\left(a-b\right)}^2\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(4\,a^3\,b-7\,a^2\,b^2-5\,a^2\,c^2+2\,a\,b^3+2\,a\,b\,c^2+b^4+3\,b^2\,c^2+2\,c^4\right)}{\left(a-b\right)\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}}{e\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(4\,a\,c-4\,b\,c\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2+4\,c^2\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2+\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(4\,a\,c+4\,b\,c\right)\right)}-\frac{\mathrm{atanh}\left(\frac{a^4\,c-2\,a^2\,b^2\,c-2\,a^2\,c^3+b^4\,c+2\,b^2\,c^3+c^5}{{\left(-a^2+b^2+c^2\right)}^{5/2}}+\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}{2\,{\left(-a^2+b^2+c^2\right)}^{5/2}}\right)\,\left(2\,a^2+b^2+c^2\right)}{e\,{\left(-a^2+b^2+c^2\right)}^{5/2}}","Not used",1,"- ((b^4*c - 4*a^4*c + a^2*c^3 + b^2*c^3 + 3*a^2*b^2*c)/((a - b)^2*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)) + (tan(d/2 + (e*x)/2)*(5*a*b^4 + 4*a^4*b + 2*a*c^4 + 2*b*c^4 - b^5 - 3*a^2*b^3 - 5*a^3*b^2 - 11*a^3*c^2 + b^3*c^2 + 7*a*b^2*c^2 + 3*a^2*b*c^2))/((a - b)^2*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)) + (tan(d/2 + (e*x)/2)^2*(2*c^5 - b^4*c - 4*a^4*c - 7*a^2*c^3 + b^2*c^3 - 13*a^2*b^2*c + 6*a*b*c^3 + 6*a*b^3*c + 12*a^3*b*c))/((a - b)^2*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)) + (tan(d/2 + (e*x)/2)^3*(2*a*b^3 + 4*a^3*b + b^4 + 2*c^4 - 7*a^2*b^2 - 5*a^2*c^2 + 3*b^2*c^2 + 2*a*b*c^2))/((a - b)*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)))/(e*(2*a*b + tan(d/2 + (e*x)/2)^3*(4*a*c - 4*b*c) + tan(d/2 + (e*x)/2)^2*(2*a^2 - 2*b^2 + 4*c^2) + tan(d/2 + (e*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2 + tan(d/2 + (e*x)/2)*(4*a*c + 4*b*c))) - (atanh((a^4*c + b^4*c + c^5 - 2*a^2*c^3 + 2*b^2*c^3 - 2*a^2*b^2*c)/(b^2 - a^2 + c^2)^(5/2) + (tan(d/2 + (e*x)/2)*(2*a - 2*b)*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2))/(2*(b^2 - a^2 + c^2)^(5/2)))*(2*a^2 + b^2 + c^2))/(e*(b^2 - a^2 + c^2)^(5/2))","B"
402,1,1946,292,4.806388,"\text{Not used}","int(1/(a + b*cos(d + e*x) + c*sin(d + e*x))^4,x)","\frac{a\,\mathrm{atanh}\left(\frac{a\,\left(2\,a^2+3\,b^2+3\,c^2\right)\,\left(-2\,a^6\,c+6\,a^4\,b^2\,c+6\,a^4\,c^3-6\,a^2\,b^4\,c-12\,a^2\,b^2\,c^3-6\,a^2\,c^5+2\,b^6\,c+6\,b^4\,c^3+6\,b^2\,c^5+2\,c^7\right)}{2\,{\left(-a^2+b^2+c^2\right)}^{7/2}\,\left(2\,a^3+3\,a\,b^2+3\,a\,c^2\right)}+\frac{a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(2\,a^2+3\,b^2+3\,c^2\right)\,\left(-a^6+3\,a^4\,b^2+3\,a^4\,c^2-3\,a^2\,b^4-6\,a^2\,b^2\,c^2-3\,a^2\,c^4+b^6+3\,b^4\,c^2+3\,b^2\,c^4+c^6\right)}{2\,{\left(-a^2+b^2+c^2\right)}^{7/2}\,\left(2\,a^3+3\,a\,b^2+3\,a\,c^2\right)}\right)\,\left(2\,a^2+3\,b^2+3\,c^2\right)}{e\,{\left(-a^2+b^2+c^2\right)}^{7/2}}-\frac{\frac{18\,a^7\,c-21\,a^5\,b^2\,c-5\,a^5\,c^3-12\,a^3\,b^4\,c-16\,a^3\,b^2\,c^3+2\,a^3\,c^5+15\,a\,b^6\,c+21\,a\,b^4\,c^3+6\,a\,b^2\,c^5}{3\,{\left(a-b\right)}^3\,\left(-a^6+3\,a^4\,b^2+3\,a^4\,c^2-3\,a^2\,b^4-6\,a^2\,b^2\,c^2-3\,a^2\,c^4+b^6+3\,b^4\,c^2+3\,b^2\,c^4+c^6\right)}+\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-6\,a^7\,b+9\,a^6\,b^2+27\,a^6\,c^2+7\,a^5\,b^3-9\,a^5\,b\,c^2-16\,a^4\,b^4-30\,a^4\,b^2\,c^2-4\,a^4\,c^4+4\,a^3\,b^5-14\,a^3\,b\,c^4+5\,a^2\,b^6-3\,a^2\,b^4\,c^2-6\,a^2\,b^2\,c^4+2\,a^2\,c^6-5\,a\,b^7+9\,a\,b^5\,c^2+18\,a\,b^3\,c^4+4\,a\,b\,c^6+2\,b^8+6\,b^6\,c^2+6\,b^4\,c^4+2\,b^2\,c^6\right)}{{\left(a-b\right)}^3\,\left(-a^6+3\,a^4\,b^2+3\,a^4\,c^2-3\,a^2\,b^4-6\,a^2\,b^2\,c^2-3\,a^2\,c^4+b^6+3\,b^4\,c^2+3\,b^2\,c^4+c^6\right)}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(6\,a^6\,c-30\,a^5\,b\,c+57\,a^4\,b^2\,c+27\,a^4\,c^3-55\,a^3\,b^3\,c-45\,a^3\,b\,c^3+33\,a^2\,b^4\,c+21\,a^2\,b^2\,c^3-12\,a^2\,c^5-15\,a\,b^5\,c-15\,a\,b^3\,c^3+4\,b^6\,c+12\,b^4\,c^3+12\,b^2\,c^5+4\,c^7\right)}{{\left(a-b\right)}^2\,\left(-a^6+3\,a^4\,b^2+3\,a^4\,c^2-3\,a^2\,b^4-6\,a^2\,b^2\,c^2-3\,a^2\,c^4+b^6+3\,b^4\,c^2+3\,b^2\,c^4+c^6\right)}-\frac{2\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(18\,a^7\,b-54\,a^6\,b^2-54\,a^6\,c^2+38\,a^5\,b^3+120\,a^5\,b\,c^2+30\,a^4\,b^4-81\,a^4\,b^2\,c^2-21\,a^4\,c^4-50\,a^3\,b^5+61\,a^3\,b^3\,c^2+81\,a^3\,b\,c^4+22\,a^2\,b^6-87\,a^2\,b^4\,c^2-105\,a^2\,b^2\,c^4+4\,a^2\,c^6-6\,a\,b^7+39\,a\,b^5\,c^2+51\,a\,b^3\,c^4+6\,a\,b\,c^6+2\,b^8+2\,b^6\,c^2-6\,b^4\,c^4-10\,b^2\,c^6-4\,c^8\right)}{3\,{\left(a-b\right)}^3\,\left(-a^6+3\,a^4\,b^2+3\,a^4\,c^2-3\,a^2\,b^4-6\,a^2\,b^2\,c^2-3\,a^2\,c^4+b^6+3\,b^4\,c^2+3\,b^2\,c^4+c^6\right)}-\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(6\,a^5\,b-15\,a^4\,b^2-9\,a^4\,c^2+11\,a^3\,b^3+9\,a^3\,b\,c^2-3\,a^2\,b^4+3\,a^2\,b^2\,c^2+6\,a^2\,c^4+3\,a\,b^5+3\,a\,b^3\,c^2-2\,b^6-6\,b^4\,c^2-6\,b^2\,c^4-2\,c^6\right)}{\left(a-b\right)\,\left(-a^6+3\,a^4\,b^2+3\,a^4\,c^2-3\,a^2\,b^4-6\,a^2\,b^2\,c^2-3\,a^2\,c^4+b^6+3\,b^4\,c^2+3\,b^2\,c^4+c^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(6\,a^7\,c-18\,a^6\,b\,c+18\,a^5\,b^2\,c+20\,a^5\,c^3-2\,a^4\,b^3\,c-22\,a^4\,b\,c^3-14\,a^3\,b^4\,c-7\,a^3\,b^2\,c^3-3\,a^3\,c^5+18\,a^2\,b^5\,c+6\,a^2\,b^3\,c^3-12\,a^2\,b\,c^5-10\,a\,b^6\,c-3\,a\,b^4\,c^3+9\,a\,b^2\,c^5+2\,a\,c^7+2\,b^7\,c+6\,b^5\,c^3+6\,b^3\,c^5+2\,b\,c^7\right)}{{\left(a-b\right)}^3\,\left(-a^6+3\,a^4\,b^2+3\,a^4\,c^2-3\,a^2\,b^4-6\,a^2\,b^2\,c^2-3\,a^2\,c^4+b^6+3\,b^4\,c^2+3\,b^2\,c^4+c^6\right)}}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(12\,a^2\,c-12\,b^2\,c+8\,c^3\right)+\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(6\,c\,a^2+12\,c\,a\,b+6\,c\,b^2\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(3\,a^3+3\,a^2\,b-3\,a\,b^2+12\,a\,c^2-3\,b^3+12\,b\,c^2\right)-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-12\,a\,c^2-3\,b^3+12\,b\,c^2\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(6\,c\,a^2-12\,c\,a\,b+6\,c\,b^2\right)+3\,a\,b^2+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}","Not used",1,"(a*atanh((a*(2*a^2 + 3*b^2 + 3*c^2)*(2*b^6*c - 2*a^6*c + 2*c^7 - 6*a^2*c^5 + 6*a^4*c^3 + 6*b^2*c^5 + 6*b^4*c^3 - 6*a^2*b^4*c + 6*a^4*b^2*c - 12*a^2*b^2*c^3))/(2*(b^2 - a^2 + c^2)^(7/2)*(3*a*b^2 + 3*a*c^2 + 2*a^3)) + (a*tan(d/2 + (e*x)/2)*(2*a - 2*b)*(2*a^2 + 3*b^2 + 3*c^2)*(b^6 - a^6 + c^6 - 3*a^2*b^4 + 3*a^4*b^2 - 3*a^2*c^4 + 3*a^4*c^2 + 3*b^2*c^4 + 3*b^4*c^2 - 6*a^2*b^2*c^2))/(2*(b^2 - a^2 + c^2)^(7/2)*(3*a*b^2 + 3*a*c^2 + 2*a^3)))*(2*a^2 + 3*b^2 + 3*c^2))/(e*(b^2 - a^2 + c^2)^(7/2)) - ((18*a^7*c + 2*a^3*c^5 - 5*a^5*c^3 + 6*a*b^2*c^5 + 21*a*b^4*c^3 - 12*a^3*b^4*c - 21*a^5*b^2*c - 16*a^3*b^2*c^3 + 15*a*b^6*c)/(3*(a - b)^3*(b^6 - a^6 + c^6 - 3*a^2*b^4 + 3*a^4*b^2 - 3*a^2*c^4 + 3*a^4*c^2 + 3*b^2*c^4 + 3*b^4*c^2 - 6*a^2*b^2*c^2)) + (tan(d/2 + (e*x)/2)*(2*b^8 - 6*a^7*b - 5*a*b^7 + 5*a^2*b^6 + 4*a^3*b^5 - 16*a^4*b^4 + 7*a^5*b^3 + 9*a^6*b^2 + 2*a^2*c^6 - 4*a^4*c^4 + 27*a^6*c^2 + 2*b^2*c^6 + 6*b^4*c^4 + 6*b^6*c^2 + 18*a*b^3*c^4 + 9*a*b^5*c^2 - 14*a^3*b*c^4 - 9*a^5*b*c^2 - 6*a^2*b^2*c^4 - 3*a^2*b^4*c^2 - 30*a^4*b^2*c^2 + 4*a*b*c^6))/((a - b)^3*(b^6 - a^6 + c^6 - 3*a^2*b^4 + 3*a^4*b^2 - 3*a^2*c^4 + 3*a^4*c^2 + 3*b^2*c^4 + 3*b^4*c^2 - 6*a^2*b^2*c^2)) + (tan(d/2 + (e*x)/2)^4*(6*a^6*c + 4*b^6*c + 4*c^7 - 12*a^2*c^5 + 27*a^4*c^3 + 12*b^2*c^5 + 12*b^4*c^3 - 15*a*b^3*c^3 + 33*a^2*b^4*c - 45*a^3*b*c^3 - 55*a^3*b^3*c + 57*a^4*b^2*c + 21*a^2*b^2*c^3 - 15*a*b^5*c - 30*a^5*b*c))/((a - b)^2*(b^6 - a^6 + c^6 - 3*a^2*b^4 + 3*a^4*b^2 - 3*a^2*c^4 + 3*a^4*c^2 + 3*b^2*c^4 + 3*b^4*c^2 - 6*a^2*b^2*c^2)) - (2*tan(d/2 + (e*x)/2)^3*(18*a^7*b - 6*a*b^7 + 2*b^8 - 4*c^8 + 22*a^2*b^6 - 50*a^3*b^5 + 30*a^4*b^4 + 38*a^5*b^3 - 54*a^6*b^2 + 4*a^2*c^6 - 21*a^4*c^4 - 54*a^6*c^2 - 10*b^2*c^6 - 6*b^4*c^4 + 2*b^6*c^2 + 51*a*b^3*c^4 + 39*a*b^5*c^2 + 81*a^3*b*c^4 + 120*a^5*b*c^2 - 105*a^2*b^2*c^4 - 87*a^2*b^4*c^2 + 61*a^3*b^3*c^2 - 81*a^4*b^2*c^2 + 6*a*b*c^6))/(3*(a - b)^3*(b^6 - a^6 + c^6 - 3*a^2*b^4 + 3*a^4*b^2 - 3*a^2*c^4 + 3*a^4*c^2 + 3*b^2*c^4 + 3*b^4*c^2 - 6*a^2*b^2*c^2)) - (tan(d/2 + (e*x)/2)^5*(3*a*b^5 + 6*a^5*b - 2*b^6 - 2*c^6 - 3*a^2*b^4 + 11*a^3*b^3 - 15*a^4*b^2 + 6*a^2*c^4 - 9*a^4*c^2 - 6*b^2*c^4 - 6*b^4*c^2 + 3*a*b^3*c^2 + 9*a^3*b*c^2 + 3*a^2*b^2*c^2))/((a - b)*(b^6 - a^6 + c^6 - 3*a^2*b^4 + 3*a^4*b^2 - 3*a^2*c^4 + 3*a^4*c^2 + 3*b^2*c^4 + 3*b^4*c^2 - 6*a^2*b^2*c^2)) + (2*tan(d/2 + (e*x)/2)^2*(2*a*c^7 + 6*a^7*c + 2*b*c^7 + 2*b^7*c - 3*a^3*c^5 + 20*a^5*c^3 + 6*b^3*c^5 + 6*b^5*c^3 + 9*a*b^2*c^5 - 3*a*b^4*c^3 - 12*a^2*b*c^5 + 18*a^2*b^5*c - 14*a^3*b^4*c - 22*a^4*b*c^3 - 2*a^4*b^3*c + 18*a^5*b^2*c + 6*a^2*b^3*c^3 - 7*a^3*b^2*c^3 - 10*a*b^6*c - 18*a^6*b*c))/((a - b)^3*(b^6 - a^6 + c^6 - 3*a^2*b^4 + 3*a^4*b^2 - 3*a^2*c^4 + 3*a^4*c^2 + 3*b^2*c^4 + 3*b^4*c^2 - 6*a^2*b^2*c^2)))/(e*(tan(d/2 + (e*x)/2)^3*(12*a^2*c - 12*b^2*c + 8*c^3) + tan(d/2 + (e*x)/2)*(6*a^2*c + 6*b^2*c + 12*a*b*c) + tan(d/2 + (e*x)/2)^2*(3*a^2*b - 3*a*b^2 + 12*a*c^2 + 12*b*c^2 + 3*a^3 - 3*b^3) - tan(d/2 + (e*x)/2)^4*(3*a*b^2 + 3*a^2*b - 12*a*c^2 + 12*b*c^2 - 3*a^3 - 3*b^3) + tan(d/2 + (e*x)/2)^5*(6*a^2*c + 6*b^2*c - 12*a*b*c) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 + tan(d/2 + (e*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3)))","B"
403,0,-1,185,0.000000,"\text{Not used}","int((3*cos(d + e*x) + 5*sin(d + e*x) + 2)^(5/2),x)","\int {\left(3\,\cos\left(d+e\,x\right)+5\,\sin\left(d+e\,x\right)+2\right)}^{5/2} \,d x","Not used",1,"int((3*cos(d + e*x) + 5*sin(d + e*x) + 2)^(5/2), x)","F"
404,0,-1,139,0.000000,"\text{Not used}","int((3*cos(d + e*x) + 5*sin(d + e*x) + 2)^(3/2),x)","\int {\left(3\,\cos\left(d+e\,x\right)+5\,\sin\left(d+e\,x\right)+2\right)}^{3/2} \,d x","Not used",1,"int((3*cos(d + e*x) + 5*sin(d + e*x) + 2)^(3/2), x)","F"
405,0,-1,45,0.000000,"\text{Not used}","int((3*cos(d + e*x) + 5*sin(d + e*x) + 2)^(1/2),x)","\int \sqrt{3\,\cos\left(d+e\,x\right)+5\,\sin\left(d+e\,x\right)+2} \,d x","Not used",1,"int((3*cos(d + e*x) + 5*sin(d + e*x) + 2)^(1/2), x)","F"
406,0,-1,45,0.000000,"\text{Not used}","int(1/(3*cos(d + e*x) + 5*sin(d + e*x) + 2)^(1/2),x)","\int \frac{1}{\sqrt{3\,\cos\left(d+e\,x\right)+5\,\sin\left(d+e\,x\right)+2}} \,d x","Not used",1,"int(1/(3*cos(d + e*x) + 5*sin(d + e*x) + 2)^(1/2), x)","F"
407,0,-1,94,0.000000,"\text{Not used}","int(1/(3*cos(d + e*x) + 5*sin(d + e*x) + 2)^(3/2),x)","\int \frac{1}{{\left(3\,\cos\left(d+e\,x\right)+5\,\sin\left(d+e\,x\right)+2\right)}^{3/2}} \,d x","Not used",1,"int(1/(3*cos(d + e*x) + 5*sin(d + e*x) + 2)^(3/2), x)","F"
408,0,-1,187,0.000000,"\text{Not used}","int(1/(3*cos(d + e*x) + 5*sin(d + e*x) + 2)^(5/2),x)","\int \frac{1}{{\left(3\,\cos\left(d+e\,x\right)+5\,\sin\left(d+e\,x\right)+2\right)}^{5/2}} \,d x","Not used",1,"int(1/(3*cos(d + e*x) + 5*sin(d + e*x) + 2)^(5/2), x)","F"
409,0,-1,233,0.000000,"\text{Not used}","int(1/(3*cos(d + e*x) + 5*sin(d + e*x) + 2)^(7/2),x)","\int \frac{1}{{\left(3\,\cos\left(d+e\,x\right)+5\,\sin\left(d+e\,x\right)+2\right)}^{7/2}} \,d x","Not used",1,"int(1/(3*cos(d + e*x) + 5*sin(d + e*x) + 2)^(7/2), x)","F"
410,0,-1,347,0.000000,"\text{Not used}","int((a + b*cos(d + e*x) + c*sin(d + e*x))^(5/2),x)","\int {\left(a+b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + b*cos(d + e*x) + c*sin(d + e*x))^(5/2), x)","F"
411,0,-1,283,0.000000,"\text{Not used}","int((a + b*cos(d + e*x) + c*sin(d + e*x))^(3/2),x)","\int {\left(a+b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + b*cos(d + e*x) + c*sin(d + e*x))^(3/2), x)","F"
412,0,-1,108,0.000000,"\text{Not used}","int((a + b*cos(d + e*x) + c*sin(d + e*x))^(1/2),x)","\int \sqrt{a+b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)} \,d x","Not used",1,"int((a + b*cos(d + e*x) + c*sin(d + e*x))^(1/2), x)","F"
413,0,-1,108,0.000000,"\text{Not used}","int(1/(a + b*cos(d + e*x) + c*sin(d + e*x))^(1/2),x)","\int \frac{1}{\sqrt{a+b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)}} \,d x","Not used",1,"int(1/(a + b*cos(d + e*x) + c*sin(d + e*x))^(1/2), x)","F"
414,0,-1,186,0.000000,"\text{Not used}","int(1/(a + b*cos(d + e*x) + c*sin(d + e*x))^(3/2),x)","\int \frac{1}{{\left(a+b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(a + b*cos(d + e*x) + c*sin(d + e*x))^(3/2), x)","F"
415,0,-1,382,0.000000,"\text{Not used}","int(1/(a + b*cos(d + e*x) + c*sin(d + e*x))^(5/2),x)","\int \frac{1}{{\left(a+b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(a + b*cos(d + e*x) + c*sin(d + e*x))^(5/2), x)","F"
416,0,-1,490,0.000000,"\text{Not used}","int(1/(a + b*cos(d + e*x) + c*sin(d + e*x))^(7/2),x)","\int \frac{1}{{\left(a+b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(1/(a + b*cos(d + e*x) + c*sin(d + e*x))^(7/2), x)","F"
417,0,-1,139,0.000000,"\text{Not used}","int((4*cos(d + e*x) + 3*sin(d + e*x) + 5)^(5/2),x)","\int {\left(4\,\cos\left(d+e\,x\right)+3\,\sin\left(d+e\,x\right)+5\right)}^{5/2} \,d x","Not used",1,"int((4*cos(d + e*x) + 3*sin(d + e*x) + 5)^(5/2), x)","F"
418,0,-1,93,0.000000,"\text{Not used}","int((4*cos(d + e*x) + 3*sin(d + e*x) + 5)^(3/2),x)","\int {\left(4\,\cos\left(d+e\,x\right)+3\,\sin\left(d+e\,x\right)+5\right)}^{3/2} \,d x","Not used",1,"int((4*cos(d + e*x) + 3*sin(d + e*x) + 5)^(3/2), x)","F"
419,1,39,44,0.309933,"\text{Not used}","int((4*cos(d + e*x) + 3*sin(d + e*x) + 5)^(1/2),x)","-\frac{2\,\sqrt{5}\,\left(3\,\cos\left(d+e\,x\right)-4\,\sin\left(d+e\,x\right)\right)}{5\,e\,\sqrt{\cos\left(d-\mathrm{atan}\left(\frac{3}{4}\right)+e\,x\right)+1}}","Not used",1,"-(2*5^(1/2)*(3*cos(d + e*x) - 4*sin(d + e*x)))/(5*e*(cos(d - atan(3/4) + e*x) + 1)^(1/2))","B"
420,0,-1,48,0.000000,"\text{Not used}","int(1/(4*cos(d + e*x) + 3*sin(d + e*x) + 5)^(1/2),x)","\int \frac{1}{\sqrt{4\,\cos\left(d+e\,x\right)+3\,\sin\left(d+e\,x\right)+5}} \,d x","Not used",1,"int(1/(4*cos(d + e*x) + 3*sin(d + e*x) + 5)^(1/2), x)","F"
421,0,-1,96,0.000000,"\text{Not used}","int(1/(4*cos(d + e*x) + 3*sin(d + e*x) + 5)^(3/2),x)","\int \frac{1}{{\left(4\,\cos\left(d+e\,x\right)+3\,\sin\left(d+e\,x\right)+5\right)}^{3/2}} \,d x","Not used",1,"int(1/(4*cos(d + e*x) + 3*sin(d + e*x) + 5)^(3/2), x)","F"
422,0,-1,142,0.000000,"\text{Not used}","int(1/(4*cos(d + e*x) + 3*sin(d + e*x) + 5)^(5/2),x)","\int \frac{1}{{\left(4\,\cos\left(d+e\,x\right)+3\,\sin\left(d+e\,x\right)+5\right)}^{5/2}} \,d x","Not used",1,"int(1/(4*cos(d + e*x) + 3*sin(d + e*x) + 5)^(5/2), x)","F"
423,0,-1,185,0.000000,"\text{Not used}","int((4*cos(d + e*x) + 3*sin(d + e*x) - 5)^(7/2),x)","\int {\left(4\,\cos\left(d+e\,x\right)+3\,\sin\left(d+e\,x\right)-5\right)}^{7/2} \,d x","Not used",1,"int((4*cos(d + e*x) + 3*sin(d + e*x) - 5)^(7/2), x)","F"
424,0,-1,139,0.000000,"\text{Not used}","int((4*cos(d + e*x) + 3*sin(d + e*x) - 5)^(5/2),x)","\int {\left(4\,\cos\left(d+e\,x\right)+3\,\sin\left(d+e\,x\right)-5\right)}^{5/2} \,d x","Not used",1,"int((4*cos(d + e*x) + 3*sin(d + e*x) - 5)^(5/2), x)","F"
425,0,-1,93,0.000000,"\text{Not used}","int((4*cos(d + e*x) + 3*sin(d + e*x) - 5)^(3/2),x)","\int {\left(4\,\cos\left(d+e\,x\right)+3\,\sin\left(d+e\,x\right)-5\right)}^{3/2} \,d x","Not used",1,"int((4*cos(d + e*x) + 3*sin(d + e*x) - 5)^(3/2), x)","F"
426,1,39,44,0.423252,"\text{Not used}","int((4*cos(d + e*x) + 3*sin(d + e*x) - 5)^(1/2),x)","-\frac{2\,\sqrt{5}\,\left(3\,\cos\left(d+e\,x\right)-4\,\sin\left(d+e\,x\right)\right)}{5\,e\,\sqrt{\cos\left(d-\mathrm{atan}\left(\frac{3}{4}\right)+e\,x\right)-1}}","Not used",1,"-(2*5^(1/2)*(3*cos(d + e*x) - 4*sin(d + e*x)))/(5*e*(cos(d - atan(3/4) + e*x) - 1)^(1/2))","B"
427,0,-1,49,0.000000,"\text{Not used}","int(1/(4*cos(d + e*x) + 3*sin(d + e*x) - 5)^(1/2),x)","\int \frac{1}{\sqrt{4\,\cos\left(d+e\,x\right)+3\,\sin\left(d+e\,x\right)-5}} \,d x","Not used",1,"int(1/(4*cos(d + e*x) + 3*sin(d + e*x) - 5)^(1/2), x)","F"
428,0,-1,96,0.000000,"\text{Not used}","int(1/(4*cos(d + e*x) + 3*sin(d + e*x) - 5)^(3/2),x)","\int \frac{1}{{\left(4\,\cos\left(d+e\,x\right)+3\,\sin\left(d+e\,x\right)-5\right)}^{3/2}} \,d x","Not used",1,"int(1/(4*cos(d + e*x) + 3*sin(d + e*x) - 5)^(3/2), x)","F"
429,0,-1,142,0.000000,"\text{Not used}","int(1/(4*cos(d + e*x) + 3*sin(d + e*x) - 5)^(5/2),x)","\int \frac{1}{{\left(4\,\cos\left(d+e\,x\right)+3\,\sin\left(d+e\,x\right)-5\right)}^{5/2}} \,d x","Not used",1,"int(1/(4*cos(d + e*x) + 3*sin(d + e*x) - 5)^(5/2), x)","F"
430,0,-1,258,0.000000,"\text{Not used}","int((b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^(7/2),x)","\int {\left(b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)+\sqrt{b^2+c^2}\right)}^{7/2} \,d x","Not used",1,"int((b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^(7/2), x)","F"
431,0,-1,190,0.000000,"\text{Not used}","int((b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^(5/2),x)","\int {\left(b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)+\sqrt{b^2+c^2}\right)}^{5/2} \,d x","Not used",1,"int((b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^(5/2), x)","F"
432,0,-1,126,0.000000,"\text{Not used}","int((b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^(3/2),x)","\int {\left(b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)+\sqrt{b^2+c^2}\right)}^{3/2} \,d x","Not used",1,"int((b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^(3/2), x)","F"
433,0,-1,55,0.000000,"\text{Not used}","int((b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^(1/2),x)","\int \sqrt{b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)+\sqrt{b^2+c^2}} \,d x","Not used",1,"int((b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^(1/2), x)","F"
434,0,-1,88,0.000000,"\text{Not used}","int(1/(b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^(1/2),x)","\int \frac{1}{\sqrt{b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)+\sqrt{b^2+c^2}}} \,d x","Not used",1,"int(1/(b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^(1/2), x)","F"
435,0,-1,160,0.000000,"\text{Not used}","int(1/(b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^(3/2),x)","\int \frac{1}{{\left(b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)+\sqrt{b^2+c^2}\right)}^{3/2}} \,d x","Not used",1,"int(1/(b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^(3/2), x)","F"
436,0,-1,226,0.000000,"\text{Not used}","int(1/(b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^(5/2),x)","\int \frac{1}{{\left(b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)+\sqrt{b^2+c^2}\right)}^{5/2}} \,d x","Not used",1,"int(1/(b*cos(d + e*x) + c*sin(d + e*x) + (b^2 + c^2)^(1/2))^(5/2), x)","F"
437,0,-1,196,0.000000,"\text{Not used}","int((b*cos(d + e*x) + c*sin(d + e*x) - (b^2 + c^2)^(1/2))^(5/2),x)","\int {\left(b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)-\sqrt{b^2+c^2}\right)}^{5/2} \,d x","Not used",1,"int((b*cos(d + e*x) + c*sin(d + e*x) - (b^2 + c^2)^(1/2))^(5/2), x)","F"
438,0,-1,130,0.000000,"\text{Not used}","int((b*cos(d + e*x) + c*sin(d + e*x) - (b^2 + c^2)^(1/2))^(3/2),x)","\int {\left(b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)-\sqrt{b^2+c^2}\right)}^{3/2} \,d x","Not used",1,"int((b*cos(d + e*x) + c*sin(d + e*x) - (b^2 + c^2)^(1/2))^(3/2), x)","F"
439,0,-1,57,0.000000,"\text{Not used}","int((b*cos(d + e*x) + c*sin(d + e*x) - (b^2 + c^2)^(1/2))^(1/2),x)","\int \sqrt{b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)-\sqrt{b^2+c^2}} \,d x","Not used",1,"int((b*cos(d + e*x) + c*sin(d + e*x) - (b^2 + c^2)^(1/2))^(1/2), x)","F"
440,0,-1,91,0.000000,"\text{Not used}","int(1/(b*cos(d + e*x) + c*sin(d + e*x) - (b^2 + c^2)^(1/2))^(1/2),x)","\int \frac{1}{\sqrt{b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)-\sqrt{b^2+c^2}}} \,d x","Not used",1,"int(1/(b*cos(d + e*x) + c*sin(d + e*x) - (b^2 + c^2)^(1/2))^(1/2), x)","F"
441,0,-1,164,0.000000,"\text{Not used}","int(1/(b*cos(d + e*x) + c*sin(d + e*x) - (b^2 + c^2)^(1/2))^(3/2),x)","\int \frac{1}{{\left(b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)-\sqrt{b^2+c^2}\right)}^{3/2}} \,d x","Not used",1,"int(1/(b*cos(d + e*x) + c*sin(d + e*x) - (b^2 + c^2)^(1/2))^(3/2), x)","F"
442,0,-1,232,0.000000,"\text{Not used}","int(1/(b*cos(d + e*x) + c*sin(d + e*x) - (b^2 + c^2)^(1/2))^(5/2),x)","\int \frac{1}{{\left(b\,\cos\left(d+e\,x\right)+c\,\sin\left(d+e\,x\right)-\sqrt{b^2+c^2}\right)}^{5/2}} \,d x","Not used",1,"int(1/(b*cos(d + e*x) + c*sin(d + e*x) - (b^2 + c^2)^(1/2))^(5/2), x)","F"
443,1,950,101,11.444080,"\text{Not used}","int(sin(x)/(a + b*cos(x) + c*sin(x)),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)}{b-c\,1{}\mathrm{i}}+\frac{\ln\left(64\,\mathrm{tan}\left(\frac{x}{2}\right)\,{\left(a-b\right)}^2-\frac{\left(a^2\,b-b\,c^2-b^3+a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(32\,a^2\,c+32\,b^2\,c-64\,a\,b\,c+64\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(-a^2+b\,a+c^2\right)+\frac{\left(a^2\,b-b\,c^2-b^3+a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(32\,b\,c^3-32\,a\,c^3-64\,b^3\,c+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(-2\,b^3+2\,a\,b^2+b\,c^2-2\,a\,c^2\right)+128\,a\,b^2\,c-64\,a^2\,b\,c+\frac{32\,\left(a-b\right)\,\left(a^2\,b-b\,c^2-b^3+a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^2-4\,a^2\,b\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,c^2-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^3+a\,b^2\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b\,c^2+a\,c^3+3\,b^3\,c+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2\,c^2+3\,b\,c^3+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,c^4\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)\,\left(b\,\left(a^2-c^2\right)-b^3+a\,c\,\sqrt{-a^2+b^2+c^2}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}-\frac{\ln\left(64\,\mathrm{tan}\left(\frac{x}{2}\right)\,{\left(a-b\right)}^2+\frac{\left(b\,c^2-a^2\,b+b^3+a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(32\,a^2\,c+32\,b^2\,c-64\,a\,b\,c+64\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(-a^2+b\,a+c^2\right)+\frac{\left(b\,c^2-a^2\,b+b^3+a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(32\,a\,c^3-32\,b\,c^3+64\,b^3\,c-32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(-2\,b^3+2\,a\,b^2+b\,c^2-2\,a\,c^2\right)-128\,a\,b^2\,c+64\,a^2\,b\,c+\frac{32\,\left(a-b\right)\,\left(b\,c^2-a^2\,b+b^3+a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^2-4\,a^2\,b\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,c^2-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^3+a\,b^2\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b\,c^2+a\,c^3+3\,b^3\,c+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2\,c^2+3\,b\,c^3+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,c^4\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)\,\left(b^3-b\,\left(a^2-c^2\right)+a\,c\,\sqrt{-a^2+b^2+c^2}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,1{}\mathrm{i}}{-c+b\,1{}\mathrm{i}}","Not used",1,"log(tan(x/2) + 1i)/(b - c*1i) + (log(tan(x/2) - 1i)*1i)/(b*1i - c) + (log(64*tan(x/2)*(a - b)^2 - ((a^2*b - b*c^2 - b^3 + a*c*(b^2 - a^2 + c^2)^(1/2))*(32*a^2*c + 32*b^2*c - 64*a*b*c + 64*tan(x/2)*(a - b)*(a*b - a^2 + c^2) + ((a^2*b - b*c^2 - b^3 + a*c*(b^2 - a^2 + c^2)^(1/2))*(32*b*c^3 - 32*a*c^3 - 64*b^3*c + 32*tan(x/2)*(a - b)*(2*a*b^2 - 2*a*c^2 + b*c^2 - 2*b^3) + 128*a*b^2*c - 64*a^2*b*c + (32*(a - b)*(a^2*b - b*c^2 - b^3 + a*c*(b^2 - a^2 + c^2)^(1/2))*(3*c^4*tan(x/2) + a*c^3 + 3*b*c^3 + 3*b^3*c + 2*a^2*b^2*tan(x/2) - 2*a^2*c^2*tan(x/2) + 3*b^2*c^2*tan(x/2) - 2*a*b^3*tan(x/2) + a*b^2*c - 4*a^2*b*c - 2*a*b*c^2*tan(x/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2)))*(b*(a^2 - c^2) - b^3 + a*c*(b^2 - a^2 + c^2)^(1/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2)) - (log(64*tan(x/2)*(a - b)^2 + ((b*c^2 - a^2*b + b^3 + a*c*(b^2 - a^2 + c^2)^(1/2))*(32*a^2*c + 32*b^2*c - 64*a*b*c + 64*tan(x/2)*(a - b)*(a*b - a^2 + c^2) + ((b*c^2 - a^2*b + b^3 + a*c*(b^2 - a^2 + c^2)^(1/2))*(32*a*c^3 - 32*b*c^3 + 64*b^3*c - 32*tan(x/2)*(a - b)*(2*a*b^2 - 2*a*c^2 + b*c^2 - 2*b^3) - 128*a*b^2*c + 64*a^2*b*c + (32*(a - b)*(b*c^2 - a^2*b + b^3 + a*c*(b^2 - a^2 + c^2)^(1/2))*(3*c^4*tan(x/2) + a*c^3 + 3*b*c^3 + 3*b^3*c + 2*a^2*b^2*tan(x/2) - 2*a^2*c^2*tan(x/2) + 3*b^2*c^2*tan(x/2) - 2*a*b^3*tan(x/2) + a*b^2*c - 4*a^2*b*c - 2*a*b*c^2*tan(x/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2)))*(b^3 - b*(a^2 - c^2) + a*c*(b^2 - a^2 + c^2)^(1/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2))","B"
444,1,34,22,2.788642,"\text{Not used}","int(sin(x)/(cos(x) + sin(x) + 1),x)","-\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)+\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)+\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)","Not used",1,"log(tan(x/2) - 1i)*(1/2 - 1i/2) - log(tan(x/2) + 1) + log(tan(x/2) + 1i)*(1/2 + 1i/2)","B"
445,1,988,97,13.029473,"\text{Not used}","int(1/(a + b*tan(x) + c/cos(x)),x)","\frac{\ln\left(32\,a\,c-32\,c^2+32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-c\right)+\frac{\left(32\,a^2\,b-32\,b\,c^2+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-c\right)\,\left(-a^2+2\,a\,c+3\,b^2-2\,c^2\right)-\frac{\left(a^2\,b-b\,c^2+b^3+a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(32\,a^4-64\,a^3\,c-64\,a^2\,b^2+32\,a^2\,c^2-32\,b^2\,c^2+96\,a\,b^2\,c+32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-c\right)\,\left(4\,a^2-4\,c\,a+b^2\right)+\frac{32\,\left(a-c\right)\,\left(a^2\,b-b\,c^2+b^3+a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(3\,a^3\,b-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^3\,c+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^2+a^2\,b\,c+2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,c^2+3\,a\,b^3-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^2\,c-4\,a\,b\,c^2+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^4+b^3\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2\,c^2\right)}{\left(a^2+b^2\right)\,\left(a^2+b^2-c^2\right)}\right)}{\left(a^2+b^2\right)\,\left(a^2+b^2-c^2\right)}\right)\,\left(a^2\,b-b\,c^2+b^3+a\,c\,\sqrt{a^2+b^2-c^2}\right)}{\left(a^2+b^2\right)\,\left(a^2+b^2-c^2\right)}\right)\,\left(b\,\left(a^2-c^2\right)+b^3+a\,c\,\sqrt{a^2+b^2-c^2}\right)}{c^2\,\left(a^2+b^2-c^2\right)+{\left(a^2+b^2-c^2\right)}^2}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)}{b+a\,1{}\mathrm{i}}+\frac{\ln\left(32\,a\,c-32\,c^2+32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-c\right)+\frac{\left(32\,a^2\,b-32\,b\,c^2+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-c\right)\,\left(-a^2+2\,a\,c+3\,b^2-2\,c^2\right)-\frac{\left(a^2\,b-b\,c^2+b^3-a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(32\,a^4-64\,a^3\,c-64\,a^2\,b^2+32\,a^2\,c^2-32\,b^2\,c^2+96\,a\,b^2\,c+32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-c\right)\,\left(4\,a^2-4\,c\,a+b^2\right)+\frac{32\,\left(a-c\right)\,\left(a^2\,b-b\,c^2+b^3-a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(3\,a^3\,b-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^3\,c+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^2+a^2\,b\,c+2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,c^2+3\,a\,b^3-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^2\,c-4\,a\,b\,c^2+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^4+b^3\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2\,c^2\right)}{\left(a^2+b^2\right)\,\left(a^2+b^2-c^2\right)}\right)}{\left(a^2+b^2\right)\,\left(a^2+b^2-c^2\right)}\right)\,\left(a^2\,b-b\,c^2+b^3-a\,c\,\sqrt{a^2+b^2-c^2}\right)}{\left(a^2+b^2\right)\,\left(a^2+b^2-c^2\right)}\right)\,\left(b\,\left(a^2-c^2\right)+b^3-a\,c\,\sqrt{a^2+b^2-c^2}\right)}{c^2\,\left(a^2+b^2-c^2\right)+{\left(a^2+b^2-c^2\right)}^2}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,1{}\mathrm{i}}{a+b\,1{}\mathrm{i}}","Not used",1,"(log(32*a*c - 32*c^2 + 32*b*tan(x/2)*(a - c) + ((32*a^2*b - 32*b*c^2 + 32*tan(x/2)*(a - c)*(2*a*c - a^2 + 3*b^2 - 2*c^2) - ((a^2*b - b*c^2 + b^3 + a*c*(a^2 + b^2 - c^2)^(1/2))*(32*a^4 - 64*a^3*c - 64*a^2*b^2 + 32*a^2*c^2 - 32*b^2*c^2 + 96*a*b^2*c + 32*b*tan(x/2)*(a - c)*(4*a^2 - 4*a*c + b^2) + (32*(a - c)*(a^2*b - b*c^2 + b^3 + a*c*(a^2 + b^2 - c^2)^(1/2))*(3*b^4*tan(x/2) + 3*a*b^3 + 3*a^3*b + b^3*c + 3*a^2*b^2*tan(x/2) + 2*a^2*c^2*tan(x/2) - 2*b^2*c^2*tan(x/2) - 2*a^3*c*tan(x/2) - 4*a*b*c^2 + a^2*b*c - 2*a*b^2*c*tan(x/2)))/((a^2 + b^2)*(a^2 + b^2 - c^2))))/((a^2 + b^2)*(a^2 + b^2 - c^2)))*(a^2*b - b*c^2 + b^3 + a*c*(a^2 + b^2 - c^2)^(1/2)))/((a^2 + b^2)*(a^2 + b^2 - c^2)))*(b*(a^2 - c^2) + b^3 + a*c*(a^2 + b^2 - c^2)^(1/2)))/(c^2*(a^2 + b^2 - c^2) + (a^2 + b^2 - c^2)^2) - log(tan(x/2) + 1i)/(a*1i + b) - (log(tan(x/2) - 1i)*1i)/(a + b*1i) + (log(32*a*c - 32*c^2 + 32*b*tan(x/2)*(a - c) + ((32*a^2*b - 32*b*c^2 + 32*tan(x/2)*(a - c)*(2*a*c - a^2 + 3*b^2 - 2*c^2) - ((a^2*b - b*c^2 + b^3 - a*c*(a^2 + b^2 - c^2)^(1/2))*(32*a^4 - 64*a^3*c - 64*a^2*b^2 + 32*a^2*c^2 - 32*b^2*c^2 + 96*a*b^2*c + 32*b*tan(x/2)*(a - c)*(4*a^2 - 4*a*c + b^2) + (32*(a - c)*(a^2*b - b*c^2 + b^3 - a*c*(a^2 + b^2 - c^2)^(1/2))*(3*b^4*tan(x/2) + 3*a*b^3 + 3*a^3*b + b^3*c + 3*a^2*b^2*tan(x/2) + 2*a^2*c^2*tan(x/2) - 2*b^2*c^2*tan(x/2) - 2*a^3*c*tan(x/2) - 4*a*b*c^2 + a^2*b*c - 2*a*b^2*c*tan(x/2)))/((a^2 + b^2)*(a^2 + b^2 - c^2))))/((a^2 + b^2)*(a^2 + b^2 - c^2)))*(a^2*b - b*c^2 + b^3 - a*c*(a^2 + b^2 - c^2)^(1/2)))/((a^2 + b^2)*(a^2 + b^2 - c^2)))*(b*(a^2 - c^2) + b^3 - a*c*(a^2 + b^2 - c^2)^(1/2)))/(c^2*(a^2 + b^2 - c^2) + (a^2 + b^2 - c^2)^2)","B"
446,1,47,51,2.776740,"\text{Not used}","int(1/(cos(x)*(a + b*tan(x) + c/cos(x))),x)","-\frac{2\,\mathrm{atanh}\left(\frac{b-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a-2\,c\right)}{2}}{\sqrt{a^2+b^2-c^2}}\right)}{\sqrt{a^2+b^2-c^2}}","Not used",1,"-(2*atanh((b - (tan(x/2)*(2*a - 2*c))/2)/(a^2 + b^2 - c^2)^(1/2)))/(a^2 + b^2 - c^2)^(1/2)","B"
447,1,977,142,11.437354,"\text{Not used}","int(1/(cos(x)^2*(a + b*tan(x) + c/cos(x))),x)","\frac{\ln\left(32\,a\,c-32\,a^2-32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-c\right)-\frac{\left(a^2\,b-b\,c^2+b^3+a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(32\,a^2\,b-32\,b\,c^2+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-c\right)\,\left(2\,a^2-2\,a\,c+3\,b^2+c^2\right)-\frac{\left(a^2\,b-b\,c^2+b^3+a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(32\,c^4-64\,a\,c^3+32\,a^2\,b^2+32\,a^2\,c^2+64\,b^2\,c^2-96\,a\,b^2\,c+32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-c\right)\,\left(b^2-4\,c^2+4\,a\,c\right)+\frac{32\,\left(a-c\right)\,\left(a^2\,b-b\,c^2+b^3+a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^2+4\,a^2\,b\,c+2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,c^2+a\,b^3+2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^2\,c-a\,b\,c^2-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,c^3+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^4+3\,b^3\,c-3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2\,c^2-3\,b\,c^3\right)}{\left(b^2-c^2\right)\,\left(a^2+b^2-c^2\right)}\right)}{\left(b^2-c^2\right)\,\left(a^2+b^2-c^2\right)}\right)}{\left(b^2-c^2\right)\,\left(a^2+b^2-c^2\right)}\right)\,\left(b\,\left(a^2-c^2\right)+b^3+a\,c\,\sqrt{a^2+b^2-c^2}\right)}{\left(b^2-c^2\right)\,\left(a^2+b^2-c^2\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)}{b+c}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}{b-c}+\frac{\ln\left(32\,a\,c-32\,a^2-32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-c\right)-\frac{\left(a^2\,b-b\,c^2+b^3-a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(32\,a^2\,b-32\,b\,c^2+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-c\right)\,\left(2\,a^2-2\,a\,c+3\,b^2+c^2\right)-\frac{\left(a^2\,b-b\,c^2+b^3-a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(32\,c^4-64\,a\,c^3+32\,a^2\,b^2+32\,a^2\,c^2+64\,b^2\,c^2-96\,a\,b^2\,c+32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-c\right)\,\left(b^2-4\,c^2+4\,a\,c\right)+\frac{32\,\left(a-c\right)\,\left(a^2\,b-b\,c^2+b^3-a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^2+4\,a^2\,b\,c+2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,c^2+a\,b^3+2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^2\,c-a\,b\,c^2-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,c^3+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^4+3\,b^3\,c-3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2\,c^2-3\,b\,c^3\right)}{\left(b^2-c^2\right)\,\left(a^2+b^2-c^2\right)}\right)}{\left(b^2-c^2\right)\,\left(a^2+b^2-c^2\right)}\right)}{\left(b^2-c^2\right)\,\left(a^2+b^2-c^2\right)}\right)\,\left(b\,\left(a^2-c^2\right)+b^3-a\,c\,\sqrt{a^2+b^2-c^2}\right)}{\left(b^2-c^2\right)\,\left(a^2+b^2-c^2\right)}","Not used",1,"(log(32*a*c - 32*a^2 - 32*b*tan(x/2)*(a - c) - ((a^2*b - b*c^2 + b^3 + a*c*(a^2 + b^2 - c^2)^(1/2))*(32*a^2*b - 32*b*c^2 + 32*tan(x/2)*(a - c)*(2*a^2 - 2*a*c + 3*b^2 + c^2) - ((a^2*b - b*c^2 + b^3 + a*c*(a^2 + b^2 - c^2)^(1/2))*(32*c^4 - 64*a*c^3 + 32*a^2*b^2 + 32*a^2*c^2 + 64*b^2*c^2 - 96*a*b^2*c + 32*b*tan(x/2)*(a - c)*(4*a*c + b^2 - 4*c^2) + (32*(a - c)*(a^2*b - b*c^2 + b^3 + a*c*(a^2 + b^2 - c^2)^(1/2))*(3*b^4*tan(x/2) + a*b^3 - 3*b*c^3 + 3*b^3*c + 2*a^2*b^2*tan(x/2) + 2*a^2*c^2*tan(x/2) - 3*b^2*c^2*tan(x/2) - 2*a*c^3*tan(x/2) - a*b*c^2 + 4*a^2*b*c + 2*a*b^2*c*tan(x/2)))/((b^2 - c^2)*(a^2 + b^2 - c^2))))/((b^2 - c^2)*(a^2 + b^2 - c^2))))/((b^2 - c^2)*(a^2 + b^2 - c^2)))*(b*(a^2 - c^2) + b^3 + a*c*(a^2 + b^2 - c^2)^(1/2)))/((b^2 - c^2)*(a^2 + b^2 - c^2)) - log(tan(x/2) - 1)/(b + c) - log(tan(x/2) + 1)/(b - c) + (log(32*a*c - 32*a^2 - 32*b*tan(x/2)*(a - c) - ((a^2*b - b*c^2 + b^3 - a*c*(a^2 + b^2 - c^2)^(1/2))*(32*a^2*b - 32*b*c^2 + 32*tan(x/2)*(a - c)*(2*a^2 - 2*a*c + 3*b^2 + c^2) - ((a^2*b - b*c^2 + b^3 - a*c*(a^2 + b^2 - c^2)^(1/2))*(32*c^4 - 64*a*c^3 + 32*a^2*b^2 + 32*a^2*c^2 + 64*b^2*c^2 - 96*a*b^2*c + 32*b*tan(x/2)*(a - c)*(4*a*c + b^2 - 4*c^2) + (32*(a - c)*(a^2*b - b*c^2 + b^3 - a*c*(a^2 + b^2 - c^2)^(1/2))*(3*b^4*tan(x/2) + a*b^3 - 3*b*c^3 + 3*b^3*c + 2*a^2*b^2*tan(x/2) + 2*a^2*c^2*tan(x/2) - 3*b^2*c^2*tan(x/2) - 2*a*c^3*tan(x/2) - a*b*c^2 + 4*a^2*b*c + 2*a*b^2*c*tan(x/2)))/((b^2 - c^2)*(a^2 + b^2 - c^2))))/((b^2 - c^2)*(a^2 + b^2 - c^2))))/((b^2 - c^2)*(a^2 + b^2 - c^2)))*(b*(a^2 - c^2) + b^3 - a*c*(a^2 + b^2 - c^2)^(1/2)))/((b^2 - c^2)*(a^2 + b^2 - c^2))","B"
448,0,-1,371,0.000000,"\text{Not used}","int((a + c*tan(d + e*x) + b/cos(d + e*x))^(3/2)/(1/cos(d + e*x))^(3/2),x)","\int \frac{{\left(a+c\,\mathrm{tan}\left(d+e\,x\right)+\frac{b}{\cos\left(d+e\,x\right)}\right)}^{3/2}}{{\left(\frac{1}{\cos\left(d+e\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((a + c*tan(d + e*x) + b/cos(d + e*x))^(3/2)/(1/cos(d + e*x))^(3/2), x)","F"
449,0,-1,118,0.000000,"\text{Not used}","int((a + c*tan(d + e*x) + b/cos(d + e*x))^(1/2)/(1/cos(d + e*x))^(1/2),x)","\int \frac{\sqrt{a+c\,\mathrm{tan}\left(d+e\,x\right)+\frac{b}{\cos\left(d+e\,x\right)}}}{\sqrt{\frac{1}{\cos\left(d+e\,x\right)}}} \,d x","Not used",1,"int((a + c*tan(d + e*x) + b/cos(d + e*x))^(1/2)/(1/cos(d + e*x))^(1/2), x)","F"
450,0,-1,118,0.000000,"\text{Not used}","int((1/cos(d + e*x))^(1/2)/(a + c*tan(d + e*x) + b/cos(d + e*x))^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(d+e\,x\right)}}}{\sqrt{a+c\,\mathrm{tan}\left(d+e\,x\right)+\frac{b}{\cos\left(d+e\,x\right)}}} \,d x","Not used",1,"int((1/cos(d + e*x))^(1/2)/(a + c*tan(d + e*x) + b/cos(d + e*x))^(1/2), x)","F"
451,0,-1,240,0.000000,"\text{Not used}","int((1/cos(d + e*x))^(3/2)/(a + c*tan(d + e*x) + b/cos(d + e*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(d+e\,x\right)}\right)}^{3/2}}{{\left(a+c\,\mathrm{tan}\left(d+e\,x\right)+\frac{b}{\cos\left(d+e\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((1/cos(d + e*x))^(3/2)/(a + c*tan(d + e*x) + b/cos(d + e*x))^(3/2), x)","F"
452,0,-1,492,0.000000,"\text{Not used}","int((1/cos(d + e*x))^(5/2)/(a + c*tan(d + e*x) + b/cos(d + e*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(d+e\,x\right)}\right)}^{5/2}}{{\left(a+c\,\mathrm{tan}\left(d+e\,x\right)+\frac{b}{\cos\left(d+e\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((1/cos(d + e*x))^(5/2)/(a + c*tan(d + e*x) + b/cos(d + e*x))^(5/2), x)","F"
453,0,-1,371,0.000000,"\text{Not used}","int(cos(d + e*x)^(3/2)*(a + c*tan(d + e*x) + b/cos(d + e*x))^(3/2),x)","\int {\cos\left(d+e\,x\right)}^{3/2}\,{\left(a+c\,\mathrm{tan}\left(d+e\,x\right)+\frac{b}{\cos\left(d+e\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(d + e*x)^(3/2)*(a + c*tan(d + e*x) + b/cos(d + e*x))^(3/2), x)","F"
454,0,-1,118,0.000000,"\text{Not used}","int(cos(d + e*x)^(1/2)*(a + c*tan(d + e*x) + b/cos(d + e*x))^(1/2),x)","\int \sqrt{\cos\left(d+e\,x\right)}\,\sqrt{a+c\,\mathrm{tan}\left(d+e\,x\right)+\frac{b}{\cos\left(d+e\,x\right)}} \,d x","Not used",1,"int(cos(d + e*x)^(1/2)*(a + c*tan(d + e*x) + b/cos(d + e*x))^(1/2), x)","F"
455,0,-1,118,0.000000,"\text{Not used}","int(1/(cos(d + e*x)^(1/2)*(a + c*tan(d + e*x) + b/cos(d + e*x))^(1/2)),x)","\int \frac{1}{\sqrt{\cos\left(d+e\,x\right)}\,\sqrt{a+c\,\mathrm{tan}\left(d+e\,x\right)+\frac{b}{\cos\left(d+e\,x\right)}}} \,d x","Not used",1,"int(1/(cos(d + e*x)^(1/2)*(a + c*tan(d + e*x) + b/cos(d + e*x))^(1/2)), x)","F"
456,0,-1,240,0.000000,"\text{Not used}","int(1/(cos(d + e*x)^(3/2)*(a + c*tan(d + e*x) + b/cos(d + e*x))^(3/2)),x)","\int \frac{1}{{\cos\left(d+e\,x\right)}^{3/2}\,{\left(a+c\,\mathrm{tan}\left(d+e\,x\right)+\frac{b}{\cos\left(d+e\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(d + e*x)^(3/2)*(a + c*tan(d + e*x) + b/cos(d + e*x))^(3/2)), x)","F"
457,0,-1,492,0.000000,"\text{Not used}","int(1/(cos(d + e*x)^(5/2)*(a + c*tan(d + e*x) + b/cos(d + e*x))^(5/2)),x)","\int \frac{1}{{\cos\left(d+e\,x\right)}^{5/2}\,{\left(a+c\,\mathrm{tan}\left(d+e\,x\right)+\frac{b}{\cos\left(d+e\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(d + e*x)^(5/2)*(a + c*tan(d + e*x) + b/cos(d + e*x))^(5/2)), x)","F"
458,1,965,98,13.762303,"\text{Not used}","int(1/(a + c/sin(x) + b*cot(x)),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)}{b+a\,1{}\mathrm{i}}-\frac{\ln\left(-64\,\mathrm{tan}\left(\frac{x}{2}\right)\,{\left(b-c\right)}^2-\frac{\left(a^2\,b-b\,c^2+b^3+a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(32\,a\,b^2+32\,a\,c^2-64\,a\,b\,c-64\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(b-c\right)\,\left(a^2-c^2+b\,c\right)+\frac{\left(a^2\,b-b\,c^2+b^3+a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(64\,a\,b^3-32\,a^3\,b+32\,a^3\,c+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(b-c\right)\,\left(a^2\,b-2\,c\,a^2-2\,b^3+2\,c\,b^2\right)+64\,a\,b\,c^2-128\,a\,b^2\,c-\frac{32\,\left(b-c\right)\,\left(a^2\,b-b\,c^2+b^3+a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(3\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^4+3\,a^3\,b+a^3\,c+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^2-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,c^2+3\,a\,b^3+a\,b^2\,c-4\,a\,b\,c^2-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^3\,c+2\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2\,c^2\right)}{\left(a^2+b^2\right)\,\left(a^2+b^2-c^2\right)}\right)}{\left(a^2+b^2\right)\,\left(a^2+b^2-c^2\right)}\right)}{\left(a^2+b^2\right)\,\left(a^2+b^2-c^2\right)}\right)\,\left(b\,\left(a^2-c^2\right)+b^3+a\,c\,\sqrt{a^2+b^2-c^2}\right)}{c^2\,\left(a^2+b^2-c^2\right)+{\left(a^2+b^2-c^2\right)}^2}-\frac{\ln\left(-64\,\mathrm{tan}\left(\frac{x}{2}\right)\,{\left(b-c\right)}^2-\frac{\left(a^2\,b-b\,c^2+b^3-a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(32\,a\,b^2+32\,a\,c^2-64\,a\,b\,c-64\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(b-c\right)\,\left(a^2-c^2+b\,c\right)+\frac{\left(a^2\,b-b\,c^2+b^3-a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(64\,a\,b^3-32\,a^3\,b+32\,a^3\,c+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(b-c\right)\,\left(a^2\,b-2\,c\,a^2-2\,b^3+2\,c\,b^2\right)+64\,a\,b\,c^2-128\,a\,b^2\,c-\frac{32\,\left(b-c\right)\,\left(a^2\,b-b\,c^2+b^3-a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(3\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^4+3\,a^3\,b+a^3\,c+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^2-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,c^2+3\,a\,b^3+a\,b^2\,c-4\,a\,b\,c^2-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^3\,c+2\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2\,c^2\right)}{\left(a^2+b^2\right)\,\left(a^2+b^2-c^2\right)}\right)}{\left(a^2+b^2\right)\,\left(a^2+b^2-c^2\right)}\right)}{\left(a^2+b^2\right)\,\left(a^2+b^2-c^2\right)}\right)\,\left(b\,\left(a^2-c^2\right)+b^3-a\,c\,\sqrt{a^2+b^2-c^2}\right)}{c^2\,\left(a^2+b^2-c^2\right)+{\left(a^2+b^2-c^2\right)}^2}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)\,1{}\mathrm{i}}{a+b\,1{}\mathrm{i}}","Not used",1,"log(tan(x/2) - 1i)/(a*1i + b) + (log(tan(x/2) + 1i)*1i)/(a + b*1i) - (log(- 64*tan(x/2)*(b - c)^2 - ((a^2*b - b*c^2 + b^3 + a*c*(a^2 + b^2 - c^2)^(1/2))*(32*a*b^2 + 32*a*c^2 - 64*a*b*c - 64*tan(x/2)*(b - c)*(b*c + a^2 - c^2) + ((a^2*b - b*c^2 + b^3 + a*c*(a^2 + b^2 - c^2)^(1/2))*(64*a*b^3 - 32*a^3*b + 32*a^3*c + 32*tan(x/2)*(b - c)*(a^2*b - 2*a^2*c + 2*b^2*c - 2*b^3) + 64*a*b*c^2 - 128*a*b^2*c - (32*(b - c)*(a^2*b - b*c^2 + b^3 + a*c*(a^2 + b^2 - c^2)^(1/2))*(3*a^4*tan(x/2) + 3*a*b^3 + 3*a^3*b + a^3*c + 3*a^2*b^2*tan(x/2) - 2*a^2*c^2*tan(x/2) + 2*b^2*c^2*tan(x/2) - 2*b^3*c*tan(x/2) - 4*a*b*c^2 + a*b^2*c - 2*a^2*b*c*tan(x/2)))/((a^2 + b^2)*(a^2 + b^2 - c^2))))/((a^2 + b^2)*(a^2 + b^2 - c^2))))/((a^2 + b^2)*(a^2 + b^2 - c^2)))*(b*(a^2 - c^2) + b^3 + a*c*(a^2 + b^2 - c^2)^(1/2)))/(c^2*(a^2 + b^2 - c^2) + (a^2 + b^2 - c^2)^2) - (log(- 64*tan(x/2)*(b - c)^2 - ((a^2*b - b*c^2 + b^3 - a*c*(a^2 + b^2 - c^2)^(1/2))*(32*a*b^2 + 32*a*c^2 - 64*a*b*c - 64*tan(x/2)*(b - c)*(b*c + a^2 - c^2) + ((a^2*b - b*c^2 + b^3 - a*c*(a^2 + b^2 - c^2)^(1/2))*(64*a*b^3 - 32*a^3*b + 32*a^3*c + 32*tan(x/2)*(b - c)*(a^2*b - 2*a^2*c + 2*b^2*c - 2*b^3) + 64*a*b*c^2 - 128*a*b^2*c - (32*(b - c)*(a^2*b - b*c^2 + b^3 - a*c*(a^2 + b^2 - c^2)^(1/2))*(3*a^4*tan(x/2) + 3*a*b^3 + 3*a^3*b + a^3*c + 3*a^2*b^2*tan(x/2) - 2*a^2*c^2*tan(x/2) + 2*b^2*c^2*tan(x/2) - 2*b^3*c*tan(x/2) - 4*a*b*c^2 + a*b^2*c - 2*a^2*b*c*tan(x/2)))/((a^2 + b^2)*(a^2 + b^2 - c^2))))/((a^2 + b^2)*(a^2 + b^2 - c^2))))/((a^2 + b^2)*(a^2 + b^2 - c^2)))*(b*(a^2 - c^2) + b^3 - a*c*(a^2 + b^2 - c^2)^(1/2)))/(c^2*(a^2 + b^2 - c^2) + (a^2 + b^2 - c^2)^2)","B"
459,1,47,51,2.786855,"\text{Not used}","int(1/(sin(x)*(a + c/sin(x) + b*cot(x))),x)","-\frac{2\,\mathrm{atanh}\left(\frac{a-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,b-2\,c\right)}{2}}{\sqrt{a^2+b^2-c^2}}\right)}{\sqrt{a^2+b^2-c^2}}","Not used",1,"-(2*atanh((a - (tan(x/2)*(2*b - 2*c))/2)/(a^2 + b^2 - c^2)^(1/2)))/(a^2 + b^2 - c^2)^(1/2)","B"
460,1,531,120,8.698244,"\text{Not used}","int(1/(sin(x)^2*(a + c/sin(x) + b*cot(x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{b+c}-\frac{\ln\left(2\,a-2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^2-8\,b^2+6\,b\,c+2\,c^2\right)-4\,a\,c+\frac{2\,\left(b-c\right)\,\left(a^2\,b-b\,c^2+b^3+a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(4\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2+a\,b+a\,c+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2-3\,\mathrm{tan}\left(\frac{x}{2}\right)\,c^2\right)}{\left(b^2-c^2\right)\,\left(a^2+b^2-c^2\right)}\right)\,\left(a^2\,b-b\,c^2+b^3+a\,c\,\sqrt{a^2+b^2-c^2}\right)}{\left(b^2-c^2\right)\,\left(a^2+b^2-c^2\right)}\right)\,\left(b\,\left(a^2-c^2\right)+b^3+a\,c\,\sqrt{a^2+b^2-c^2}\right)}{\left(b^2-c^2\right)\,\left(a^2+b^2-c^2\right)}-\frac{\ln\left(2\,a-2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^2-8\,b^2+6\,b\,c+2\,c^2\right)-4\,a\,c+\frac{2\,\left(b-c\right)\,\left(a^2\,b-b\,c^2+b^3-a\,c\,\sqrt{a^2+b^2-c^2}\right)\,\left(4\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2+a\,b+a\,c+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2-3\,\mathrm{tan}\left(\frac{x}{2}\right)\,c^2\right)}{\left(b^2-c^2\right)\,\left(a^2+b^2-c^2\right)}\right)\,\left(a^2\,b-b\,c^2+b^3-a\,c\,\sqrt{a^2+b^2-c^2}\right)}{\left(b^2-c^2\right)\,\left(a^2+b^2-c^2\right)}\right)\,\left(b\,\left(a^2-c^2\right)+b^3-a\,c\,\sqrt{a^2+b^2-c^2}\right)}{\left(b^2-c^2\right)\,\left(a^2+b^2-c^2\right)}","Not used",1,"log(tan(x/2))/(b + c) - (log(2*a - 2*b*tan(x/2) - ((tan(x/2)*(6*b*c - 8*a^2 - 8*b^2 + 2*c^2) - 4*a*c + (2*(b - c)*(a^2*b - b*c^2 + b^3 + a*c*(a^2 + b^2 - c^2)^(1/2))*(a*b + a*c + 4*a^2*tan(x/2) + 3*b^2*tan(x/2) - 3*c^2*tan(x/2)))/((b^2 - c^2)*(a^2 + b^2 - c^2)))*(a^2*b - b*c^2 + b^3 + a*c*(a^2 + b^2 - c^2)^(1/2)))/((b^2 - c^2)*(a^2 + b^2 - c^2)))*(b*(a^2 - c^2) + b^3 + a*c*(a^2 + b^2 - c^2)^(1/2)))/((b^2 - c^2)*(a^2 + b^2 - c^2)) - (log(2*a - 2*b*tan(x/2) - ((tan(x/2)*(6*b*c - 8*a^2 - 8*b^2 + 2*c^2) - 4*a*c + (2*(b - c)*(a^2*b - b*c^2 + b^3 - a*c*(a^2 + b^2 - c^2)^(1/2))*(a*b + a*c + 4*a^2*tan(x/2) + 3*b^2*tan(x/2) - 3*c^2*tan(x/2)))/((b^2 - c^2)*(a^2 + b^2 - c^2)))*(a^2*b - b*c^2 + b^3 - a*c*(a^2 + b^2 - c^2)^(1/2)))/((b^2 - c^2)*(a^2 + b^2 - c^2)))*(b*(a^2 - c^2) + b^3 - a*c*(a^2 + b^2 - c^2)^(1/2)))/((b^2 - c^2)*(a^2 + b^2 - c^2))","B"
461,1,9,21,3.141268,"\text{Not used}","int(1/(sin(x)*(2*cot(x) + 3/sin(x) + 2)),x)","2\,\mathrm{atan}\left(\mathrm{tan}\left(\frac{x}{2}\right)+2\right)","Not used",1,"2*atan(tan(x/2) + 2)","B"
462,0,-1,371,0.000000,"\text{Not used}","int((a + c*cot(d + e*x) + b/sin(d + e*x))^(3/2)/(1/sin(d + e*x))^(3/2),x)","\int \frac{{\left(a+c\,\mathrm{cot}\left(d+e\,x\right)+\frac{b}{\sin\left(d+e\,x\right)}\right)}^{3/2}}{{\left(\frac{1}{\sin\left(d+e\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((a + c*cot(d + e*x) + b/sin(d + e*x))^(3/2)/(1/sin(d + e*x))^(3/2), x)","F"
463,0,-1,118,0.000000,"\text{Not used}","int((a + c*cot(d + e*x) + b/sin(d + e*x))^(1/2)/(1/sin(d + e*x))^(1/2),x)","\int \frac{\sqrt{a+c\,\mathrm{cot}\left(d+e\,x\right)+\frac{b}{\sin\left(d+e\,x\right)}}}{\sqrt{\frac{1}{\sin\left(d+e\,x\right)}}} \,d x","Not used",1,"int((a + c*cot(d + e*x) + b/sin(d + e*x))^(1/2)/(1/sin(d + e*x))^(1/2), x)","F"
464,0,-1,118,0.000000,"\text{Not used}","int((1/sin(d + e*x))^(1/2)/(a + c*cot(d + e*x) + b/sin(d + e*x))^(1/2),x)","\int \frac{\sqrt{\frac{1}{\sin\left(d+e\,x\right)}}}{\sqrt{a+c\,\mathrm{cot}\left(d+e\,x\right)+\frac{b}{\sin\left(d+e\,x\right)}}} \,d x","Not used",1,"int((1/sin(d + e*x))^(1/2)/(a + c*cot(d + e*x) + b/sin(d + e*x))^(1/2), x)","F"
465,0,-1,240,0.000000,"\text{Not used}","int((1/sin(d + e*x))^(3/2)/(a + c*cot(d + e*x) + b/sin(d + e*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\sin\left(d+e\,x\right)}\right)}^{3/2}}{{\left(a+c\,\mathrm{cot}\left(d+e\,x\right)+\frac{b}{\sin\left(d+e\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((1/sin(d + e*x))^(3/2)/(a + c*cot(d + e*x) + b/sin(d + e*x))^(3/2), x)","F"
466,0,-1,492,0.000000,"\text{Not used}","int((1/sin(d + e*x))^(5/2)/(a + c*cot(d + e*x) + b/sin(d + e*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\sin\left(d+e\,x\right)}\right)}^{5/2}}{{\left(a+c\,\mathrm{cot}\left(d+e\,x\right)+\frac{b}{\sin\left(d+e\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((1/sin(d + e*x))^(5/2)/(a + c*cot(d + e*x) + b/sin(d + e*x))^(5/2), x)","F"
467,0,-1,371,0.000000,"\text{Not used}","int(sin(d + e*x)^(3/2)*(a + c*cot(d + e*x) + b/sin(d + e*x))^(3/2),x)","\int {\sin\left(d+e\,x\right)}^{3/2}\,{\left(a+c\,\mathrm{cot}\left(d+e\,x\right)+\frac{b}{\sin\left(d+e\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(sin(d + e*x)^(3/2)*(a + c*cot(d + e*x) + b/sin(d + e*x))^(3/2), x)","F"
468,0,-1,118,0.000000,"\text{Not used}","int(sin(d + e*x)^(1/2)*(a + c*cot(d + e*x) + b/sin(d + e*x))^(1/2),x)","\int \sqrt{\sin\left(d+e\,x\right)}\,\sqrt{a+c\,\mathrm{cot}\left(d+e\,x\right)+\frac{b}{\sin\left(d+e\,x\right)}} \,d x","Not used",1,"int(sin(d + e*x)^(1/2)*(a + c*cot(d + e*x) + b/sin(d + e*x))^(1/2), x)","F"
469,0,-1,118,0.000000,"\text{Not used}","int(1/(sin(d + e*x)^(1/2)*(a + c*cot(d + e*x) + b/sin(d + e*x))^(1/2)),x)","\int \frac{1}{\sqrt{\sin\left(d+e\,x\right)}\,\sqrt{a+c\,\mathrm{cot}\left(d+e\,x\right)+\frac{b}{\sin\left(d+e\,x\right)}}} \,d x","Not used",1,"int(1/(sin(d + e*x)^(1/2)*(a + c*cot(d + e*x) + b/sin(d + e*x))^(1/2)), x)","F"
470,0,-1,240,0.000000,"\text{Not used}","int(1/(sin(d + e*x)^(3/2)*(a + c*cot(d + e*x) + b/sin(d + e*x))^(3/2)),x)","\int \frac{1}{{\sin\left(d+e\,x\right)}^{3/2}\,{\left(a+c\,\mathrm{cot}\left(d+e\,x\right)+\frac{b}{\sin\left(d+e\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(1/(sin(d + e*x)^(3/2)*(a + c*cot(d + e*x) + b/sin(d + e*x))^(3/2)), x)","F"
471,0,-1,492,0.000000,"\text{Not used}","int(1/(sin(d + e*x)^(5/2)*(a + c*cot(d + e*x) + b/sin(d + e*x))^(5/2)),x)","\int \frac{1}{{\sin\left(d+e\,x\right)}^{5/2}\,{\left(a+c\,\mathrm{cot}\left(d+e\,x\right)+\frac{b}{\sin\left(d+e\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(1/(sin(d + e*x)^(5/2)*(a + c*cot(d + e*x) + b/sin(d + e*x))^(5/2)), x)","F"
472,1,1,1,2.644980,"\text{Not used}","int(1/(cos(x)^2 + sin(x)^2),x)","x","Not used",1,"x","B"
473,1,1,1,2.629590,"\text{Not used}","int(1/(cos(x)^2 + sin(x)^2)^2,x)","x","Not used",1,"x","B"
474,1,1,1,2.594240,"\text{Not used}","int(1/(cos(x)^2 + sin(x)^2)^3,x)","x","Not used",1,"x","B"
475,1,3,11,2.904976,"\text{Not used}","int(1/(cos(x)^2 - sin(x)^2),x)","\mathrm{atanh}\left(\mathrm{tan}\left(x\right)\right)","Not used",1,"atanh(tan(x))","B"
476,1,6,13,2.632909,"\text{Not used}","int(1/(cos(x)^2 - sin(x)^2)^2,x)","\frac{\mathrm{tan}\left(2\,x\right)}{2}","Not used",1,"tan(2*x)/2","B"
477,1,32,32,2.651069,"\text{Not used}","int(1/(cos(x)^2 - sin(x)^2)^3,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(x\right)\right)}{2}+\frac{\frac{{\mathrm{tan}\left(x\right)}^3}{2}+\frac{\mathrm{tan}\left(x\right)}{2}}{{\mathrm{tan}\left(x\right)}^4-2\,{\mathrm{tan}\left(x\right)}^2+1}","Not used",1,"atanh(tan(x))/2 + (tan(x)/2 + tan(x)^3/2)/(tan(x)^4 - 2*tan(x)^2 + 1)","B"
478,1,9,9,2.834256,"\text{Not used}","int(1/(cos(x)^2 + a^2*sin(x)^2),x)","\frac{\mathrm{atan}\left(a\,\mathrm{tan}\left(x\right)\right)}{a}","Not used",1,"atan(a*tan(x))/a","B"
479,1,11,11,2.832231,"\text{Not used}","int(1/(sin(x)^2 + b^2*cos(x)^2),x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(x\right)}{b}\right)}{b}","Not used",1,"atan(tan(x)/b)/b","B"
480,1,15,15,2.845454,"\text{Not used}","int(1/(b^2*cos(x)^2 + a^2*sin(x)^2),x)","\frac{\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(x\right)}{b}\right)}{a\,b}","Not used",1,"atan((a*tan(x))/b)/(a*b)","B"
481,1,36,53,2.758893,"\text{Not used}","int(1/(3*sin(2*x + 1)^2 + 4*cos(2*x + 1)^2),x)","\frac{\sqrt{3}\,\left(2\,x-\mathrm{atan}\left(\mathrm{tan}\left(2\,x+1\right)\right)\right)}{12}+\frac{\sqrt{3}\,\mathrm{atan}\left(\frac{\sqrt{3}\,\mathrm{tan}\left(2\,x+1\right)}{2}\right)}{12}","Not used",1,"(3^(1/2)*(2*x - atan(tan(2*x + 1))))/12 + (3^(1/2)*atan((3^(1/2)*tan(2*x + 1))/2))/12","B"
482,1,51,43,2.729728,"\text{Not used}","int(sin(x)^2/(b*sin(x)^2 + a*cos(x)^2),x)","\left\{\begin{array}{cl} \frac{2\,x-\sin\left(2\,x\right)}{4\,b} & \text{\ if\ \ }a=b\\ -\frac{x-\frac{\sqrt{a}\,\mathrm{atan}\left(\frac{\sqrt{b}\,\mathrm{tan}\left(x\right)}{\sqrt{a}}\right)}{\sqrt{b}}}{a-b} & \text{\ if\ \ }a\neq b \end{array}\right.","Not used",1,"piecewise(a == b, (2*x - sin(2*x))/(4*b), a ~= b, -(x - (a^(1/2)*atan((b^(1/2)*tan(x))/a^(1/2)))/b^(1/2))/(a - b))","B"
483,1,48,43,2.672141,"\text{Not used}","int(cos(x)^2/(b*sin(x)^2 + a*cos(x)^2),x)","\left\{\begin{array}{cl} \frac{2\,x+\sin\left(2\,x\right)}{4\,b} & \text{\ if\ \ }a=b\\ \frac{x-\frac{\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,\mathrm{tan}\left(x\right)}{\sqrt{a}}\right)}{\sqrt{a}}}{a-b} & \text{\ if\ \ }a\neq b \end{array}\right.","Not used",1,"piecewise(a == b, (2*x + sin(2*x))/(4*b), a ~= b, (x - (b^(1/2)*atan((b^(1/2)*tan(x))/a^(1/2)))/a^(1/2))/(a - b))","B"
484,1,15,36,2.652443,"\text{Not used}","int(1/(1/cos(x)^2 + tan(x)^2),x)","\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,\mathrm{tan}\left(x\right)\right)-x","Not used",1,"2^(1/2)*atan(2^(1/2)*tan(x)) - x","B"
485,1,27,49,2.664076,"\text{Not used}","int(1/(1/cos(x)^2 + tan(x)^2)^2,x)","x+\frac{\mathrm{tan}\left(x\right)}{2\,\left({\mathrm{tan}\left(x\right)}^2+\frac{1}{2}\right)}-\frac{\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,\mathrm{tan}\left(x\right)\right)}{2}","Not used",1,"x + tan(x)/(2*(tan(x)^2 + 1/2)) - (2^(1/2)*atan(2^(1/2)*tan(x)))/2","B"
486,1,40,74,2.697711,"\text{Not used}","int(1/(1/cos(x)^2 + tan(x)^2)^3,x)","\frac{\frac{\mathrm{tan}\left(x\right)}{16}-\frac{{\mathrm{tan}\left(x\right)}^3}{8}}{{\mathrm{tan}\left(x\right)}^4+{\mathrm{tan}\left(x\right)}^2+\frac{1}{4}}-x+\frac{7\,\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,\mathrm{tan}\left(x\right)\right)}{8}","Not used",1,"(tan(x)/16 - tan(x)^3/8)/(tan(x)^2 + tan(x)^4 + 1/4) - x + (7*2^(1/2)*atan(2^(1/2)*tan(x)))/8","B"
487,1,1,1,2.745504,"\text{Not used}","int(1/(1/cos(x)^2 - tan(x)^2),x)","x","Not used",1,"x","B"
488,1,1,1,2.581258,"\text{Not used}","int(1/(1/cos(x)^2 - tan(x)^2)^2,x)","x","Not used",1,"x","B"
489,1,1,1,2.571083,"\text{Not used}","int(1/(1/cos(x)^2 - tan(x)^2)^3,x)","x","Not used",1,"x","B"
490,1,16,37,2.713236,"\text{Not used}","int(1/(cot(x)^2 + 1/sin(x)^2),x)","\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)}{2}\right)-x","Not used",1,"2^(1/2)*atan((2^(1/2)*tan(x))/2) - x","B"
491,1,27,47,2.687645,"\text{Not used}","int(1/(cot(x)^2 + 1/sin(x)^2)^2,x)","x-\frac{\mathrm{tan}\left(x\right)}{{\mathrm{tan}\left(x\right)}^2+2}-\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)}{2}\right)}{2}","Not used",1,"x - tan(x)/(tan(x)^2 + 2) - (2^(1/2)*atan((2^(1/2)*tan(x))/2))/2","B"
492,1,43,72,2.682825,"\text{Not used}","int(1/(cot(x)^2 + 1/sin(x)^2)^3,x)","\frac{\frac{\mathrm{tan}\left(x\right)}{2}-\frac{{\mathrm{tan}\left(x\right)}^3}{4}}{{\mathrm{tan}\left(x\right)}^4+4\,{\mathrm{tan}\left(x\right)}^2+4}-x+\frac{7\,\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)}{2}\right)}{8}","Not used",1,"(tan(x)/2 - tan(x)^3/4)/(4*tan(x)^2 + tan(x)^4 + 4) - x + (7*2^(1/2)*atan((2^(1/2)*tan(x))/2))/8","B"
493,1,3,3,2.729018,"\text{Not used}","int(1/(cot(x)^2 - 1/sin(x)^2),x)","-x","Not used",1,"-x","B"
494,1,1,1,2.649942,"\text{Not used}","int(1/(cot(x)^2 - 1/sin(x)^2)^2,x)","x","Not used",1,"x","B"
495,1,3,3,2.615292,"\text{Not used}","int(1/(cot(x)^2 - 1/sin(x)^2)^3,x)","-x","Not used",1,"-x","B"
496,1,43,33,2.854601,"\text{Not used}","int(1/(a + c*sin(x)^2 + b*cos(x)^2),x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(x\right)\,\left(2\,a+2\,c\right)}{2\,\sqrt{a\,b+a\,c+b\,c+a^2}}\right)}{\sqrt{a\,b+a\,c+b\,c+a^2}}","Not used",1,"atan((tan(x)*(2*a + 2*c))/(2*(a*b + a*c + b*c + a^2)^(1/2)))/(a*b + a*c + b*c + a^2)^(1/2)","B"
497,0,-1,239,0.000000,"\text{Not used}","int(x/(a + c*sin(x)^2 + b*cos(x)^2),x)","\int \frac{x}{b\,{\cos\left(x\right)}^2+c\,{\sin\left(x\right)}^2+a} \,d x","Not used",1,"int(x/(a + c*sin(x)^2 + b*cos(x)^2), x)","F"
498,0,-1,365,0.000000,"\text{Not used}","int(x^2/(a + c*sin(x)^2 + b*cos(x)^2),x)","\int \frac{x^2}{b\,{\cos\left(x\right)}^2+c\,{\sin\left(x\right)}^2+a} \,d x","Not used",1,"int(x^2/(a + c*sin(x)^2 + b*cos(x)^2), x)","F"
499,1,456,195,4.489792,"\text{Not used}","int((a + b*sin(d + e*x))*(b^2 + a^2*sin(d + e*x)^2 + 2*a*b*sin(d + e*x))^2,x)","\frac{3\,a\,\mathrm{atan}\left(\frac{3\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(a^4+12\,a^2\,b^2+8\,b^4\right)}{4\,\left(\frac{3\,a^5}{4}+9\,a^3\,b^2+6\,a\,b^4\right)}\right)\,\left(a^4+12\,a^2\,b^2+8\,b^4\right)}{4\,e}-\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(\frac{3\,a^5}{4}+9\,a^3\,b^2+4\,a\,b^4\right)-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^9\,\left(\frac{3\,a^5}{4}+9\,a^3\,b^2+4\,a\,b^4\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(\frac{7\,a^5}{2}+26\,a^3\,b^2+8\,a\,b^4\right)-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^7\,\left(\frac{7\,a^5}{2}+26\,a^3\,b^2+8\,a\,b^4\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6\,\left(16\,a^4\,b+56\,a^2\,b^3+8\,b^5\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(32\,a^4\,b+72\,a^2\,b^3+8\,b^5\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(48\,a^4\,b+104\,a^2\,b^3+12\,b^5\right)+\frac{32\,a^4\,b}{5}+2\,b^5+16\,a^2\,b^3+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^8\,\left(8\,a^2\,b^3+2\,b^5\right)}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+1\right)}-\frac{3\,a\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\right)-\frac{e\,x}{2}\right)\,\left(a^4+12\,a^2\,b^2+8\,b^4\right)}{4\,e}","Not used",1,"(3*a*atan((3*a*tan(d/2 + (e*x)/2)*(a^4 + 8*b^4 + 12*a^2*b^2))/(4*(6*a*b^4 + (3*a^5)/4 + 9*a^3*b^2)))*(a^4 + 8*b^4 + 12*a^2*b^2))/(4*e) - (tan(d/2 + (e*x)/2)*(4*a*b^4 + (3*a^5)/4 + 9*a^3*b^2) - tan(d/2 + (e*x)/2)^9*(4*a*b^4 + (3*a^5)/4 + 9*a^3*b^2) + tan(d/2 + (e*x)/2)^3*(8*a*b^4 + (7*a^5)/2 + 26*a^3*b^2) - tan(d/2 + (e*x)/2)^7*(8*a*b^4 + (7*a^5)/2 + 26*a^3*b^2) + tan(d/2 + (e*x)/2)^6*(16*a^4*b + 8*b^5 + 56*a^2*b^3) + tan(d/2 + (e*x)/2)^2*(32*a^4*b + 8*b^5 + 72*a^2*b^3) + tan(d/2 + (e*x)/2)^4*(48*a^4*b + 12*b^5 + 104*a^2*b^3) + (32*a^4*b)/5 + 2*b^5 + 16*a^2*b^3 + tan(d/2 + (e*x)/2)^8*(2*b^5 + 8*a^2*b^3))/(e*(5*tan(d/2 + (e*x)/2)^2 + 10*tan(d/2 + (e*x)/2)^4 + 10*tan(d/2 + (e*x)/2)^6 + 5*tan(d/2 + (e*x)/2)^8 + tan(d/2 + (e*x)/2)^10 + 1)) - (3*a*(atan(tan(d/2 + (e*x)/2)) - (e*x)/2)*(a^4 + 8*b^4 + 12*a^2*b^2))/(4*e)","B"
500,1,88,109,2.897782,"\text{Not used}","int((a + b*sin(d + e*x))*(b^2 + a^2*sin(d + e*x)^2 + 2*a*b*sin(d + e*x)),x)","-\frac{6\,b^3\,\cos\left(d+e\,x\right)+\frac{3\,a^3\,\sin\left(2\,d+2\,e\,x\right)}{2}-\frac{a^2\,b\,\cos\left(3\,d+3\,e\,x\right)}{2}+3\,a\,b^2\,\sin\left(2\,d+2\,e\,x\right)+\frac{33\,a^2\,b\,\cos\left(d+e\,x\right)}{2}-3\,a^3\,e\,x-12\,a\,b^2\,e\,x}{6\,e}","Not used",1,"-(6*b^3*cos(d + e*x) + (3*a^3*sin(2*d + 2*e*x))/2 - (a^2*b*cos(3*d + 3*e*x))/2 + 3*a*b^2*sin(2*d + 2*e*x) + (33*a^2*b*cos(d + e*x))/2 - 3*a^3*e*x - 12*a*b^2*e*x)/(6*e)","B"
501,1,39,23,2.840712,"\text{Not used}","int((a + b*sin(d + e*x))/(b^2 + a^2*sin(d + e*x)^2 + 2*a*b*sin(d + e*x)),x)","-\frac{a\,\sin\left(d+e\,x\right)+b\,\left(\cos\left(d+e\,x\right)+1\right)}{b\,e\,\left(b+a\,\sin\left(d+e\,x\right)\right)}","Not used",1,"-(a*sin(d + e*x) + b*(cos(d + e*x) + 1))/(b*e*(b + a*sin(d + e*x)))","B"
502,1,497,157,6.062935,"\text{Not used}","int((a + b*sin(d + e*x))/(b^2 + a^2*sin(d + e*x)^2 + 2*a*b*sin(d + e*x))^2,x)","\frac{2\,a\,b\,\mathrm{atanh}\left(\frac{\left(2\,a+2\,b\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{2\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}\right)}{e\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}-\frac{\frac{2\,\left(a^4-a^2\,b^2+3\,b^4\right)}{3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{4\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(a^6+3\,a^2\,b^4+b^6\right)}{b^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{2\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(2\,a^6-3\,a^4\,b^2+5\,a^2\,b^4+b^6\right)}{b^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{2\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(a^4+4\,b^4\right)}{b\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{2\,a\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(a^4-2\,a^2\,b^2+2\,b^4\right)}{b\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{4\,a\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(2\,a^2+3\,b^2\right)\,\left(a^4-a^2\,b^2+3\,b^4\right)}{3\,b^3\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{e\,\left(b^3\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(8\,a^3+12\,a\,b^2\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(12\,a^2\,b+3\,b^3\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(12\,a^2\,b+3\,b^3\right)+b^3+6\,a\,b^2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+6\,a\,b^2\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\right)}","Not used",1,"(2*a*b*atanh(((2*a + 2*b*tan(d/2 + (e*x)/2))*(a^4 + b^4 - 2*a^2*b^2))/(2*(a + b)^(5/2)*(a - b)^(5/2))))/(e*(a + b)^(5/2)*(a - b)^(5/2)) - ((2*(a^4 + 3*b^4 - a^2*b^2))/(3*(a^4 + b^4 - 2*a^2*b^2)) + (4*tan(d/2 + (e*x)/2)^2*(a^6 + b^6 + 3*a^2*b^4))/(b^2*(a^4 + b^4 - 2*a^2*b^2)) + (2*tan(d/2 + (e*x)/2)^4*(2*a^6 + b^6 + 5*a^2*b^4 - 3*a^4*b^2))/(b^2*(a^4 + b^4 - 2*a^2*b^2)) + (2*a*tan(d/2 + (e*x)/2)*(a^4 + 4*b^4))/(b*(a^4 + b^4 - 2*a^2*b^2)) + (2*a*tan(d/2 + (e*x)/2)^5*(a^4 + 2*b^4 - 2*a^2*b^2))/(b*(a^4 + b^4 - 2*a^2*b^2)) + (4*a*tan(d/2 + (e*x)/2)^3*(2*a^2 + 3*b^2)*(a^4 + 3*b^4 - a^2*b^2))/(3*b^3*(a^4 + b^4 - 2*a^2*b^2)))/(e*(b^3*tan(d/2 + (e*x)/2)^6 + tan(d/2 + (e*x)/2)^3*(12*a*b^2 + 8*a^3) + tan(d/2 + (e*x)/2)^2*(12*a^2*b + 3*b^3) + tan(d/2 + (e*x)/2)^4*(12*a^2*b + 3*b^3) + b^3 + 6*a*b^2*tan(d/2 + (e*x)/2) + 6*a*b^2*tan(d/2 + (e*x)/2)^5))","B"
503,1,10465,242,17.109005,"\text{Not used}","int((d + e*sin(x))/(a + c*sin(x)^2 + b*sin(x)),x)","\mathrm{atan}\left(\frac{\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(256\,a^4\,c-64\,a^3\,b^2+768\,a^3\,c^2-576\,a^2\,b^2\,c+512\,a^2\,c^3+96\,a\,b^4-128\,a\,b^2\,c^2\right)+32\,a^2\,b^3+128\,a^2\,b\,c^2-32\,a\,b^3\,c-128\,a^3\,b\,c\right)+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-256\,e\,a^3\,c+64\,e\,a^2\,b^2+256\,d\,a^2\,b\,c-256\,e\,a^2\,c^2-64\,d\,a\,b^3+64\,e\,a\,b^2\,c\right)-32\,a^2\,b^2\,d+128\,a^2\,c^2\,d+32\,a\,b^3\,e+128\,a^3\,c\,d-32\,a\,b^2\,c\,d-128\,a^2\,b\,c\,e\right)-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^3\,e^2-64\,a^2\,b\,d\,e-64\,a^2\,c\,d^2+128\,a^2\,c\,e^2+32\,a\,b^2\,d^2-64\,a\,b^2\,e^2+128\,a\,b\,c\,d\,e-128\,a\,c^2\,d^2\right)+32\,a^2\,b\,e^2+32\,a\,b\,c\,d^2-128\,a^2\,c\,d\,e\right)\,1{}\mathrm{i}+\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(256\,a^4\,c-64\,a^3\,b^2+768\,a^3\,c^2-576\,a^2\,b^2\,c+512\,a^2\,c^3+96\,a\,b^4-128\,a\,b^2\,c^2\right)+32\,a^2\,b^3+128\,a^2\,b\,c^2-32\,a\,b^3\,c-128\,a^3\,b\,c\right)-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-256\,e\,a^3\,c+64\,e\,a^2\,b^2+256\,d\,a^2\,b\,c-256\,e\,a^2\,c^2-64\,d\,a\,b^3+64\,e\,a\,b^2\,c\right)+32\,a^2\,b^2\,d-128\,a^2\,c^2\,d-32\,a\,b^3\,e-128\,a^3\,c\,d+32\,a\,b^2\,c\,d+128\,a^2\,b\,c\,e\right)-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^3\,e^2-64\,a^2\,b\,d\,e-64\,a^2\,c\,d^2+128\,a^2\,c\,e^2+32\,a\,b^2\,d^2-64\,a\,b^2\,e^2+128\,a\,b\,c\,d\,e-128\,a\,c^2\,d^2\right)+32\,a^2\,b\,e^2+32\,a\,b\,c\,d^2-128\,a^2\,c\,d\,e\right)\,1{}\mathrm{i}}{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^2\,e^3+64\,c\,a\,d^2\,e-64\,b\,a\,d\,e^2\right)+\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(256\,a^4\,c-64\,a^3\,b^2+768\,a^3\,c^2-576\,a^2\,b^2\,c+512\,a^2\,c^3+96\,a\,b^4-128\,a\,b^2\,c^2\right)+32\,a^2\,b^3+128\,a^2\,b\,c^2-32\,a\,b^3\,c-128\,a^3\,b\,c\right)+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-256\,e\,a^3\,c+64\,e\,a^2\,b^2+256\,d\,a^2\,b\,c-256\,e\,a^2\,c^2-64\,d\,a\,b^3+64\,e\,a\,b^2\,c\right)-32\,a^2\,b^2\,d+128\,a^2\,c^2\,d+32\,a\,b^3\,e+128\,a^3\,c\,d-32\,a\,b^2\,c\,d-128\,a^2\,b\,c\,e\right)-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^3\,e^2-64\,a^2\,b\,d\,e-64\,a^2\,c\,d^2+128\,a^2\,c\,e^2+32\,a\,b^2\,d^2-64\,a\,b^2\,e^2+128\,a\,b\,c\,d\,e-128\,a\,c^2\,d^2\right)+32\,a^2\,b\,e^2+32\,a\,b\,c\,d^2-128\,a^2\,c\,d\,e\right)-\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(256\,a^4\,c-64\,a^3\,b^2+768\,a^3\,c^2-576\,a^2\,b^2\,c+512\,a^2\,c^3+96\,a\,b^4-128\,a\,b^2\,c^2\right)+32\,a^2\,b^3+128\,a^2\,b\,c^2-32\,a\,b^3\,c-128\,a^3\,b\,c\right)-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-256\,e\,a^3\,c+64\,e\,a^2\,b^2+256\,d\,a^2\,b\,c-256\,e\,a^2\,c^2-64\,d\,a\,b^3+64\,e\,a\,b^2\,c\right)+32\,a^2\,b^2\,d-128\,a^2\,c^2\,d-32\,a\,b^3\,e-128\,a^3\,c\,d+32\,a\,b^2\,c\,d+128\,a^2\,b\,c\,e\right)-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^3\,e^2-64\,a^2\,b\,d\,e-64\,a^2\,c\,d^2+128\,a^2\,c\,e^2+32\,a\,b^2\,d^2-64\,a\,b^2\,e^2+128\,a\,b\,c\,d\,e-128\,a\,c^2\,d^2\right)+32\,a^2\,b\,e^2+32\,a\,b\,c\,d^2-128\,a^2\,c\,d\,e\right)+64\,a^2\,d\,e^2+64\,a\,c\,d^3-64\,a\,b\,d^2\,e}\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(256\,a^4\,c-64\,a^3\,b^2+768\,a^3\,c^2-576\,a^2\,b^2\,c+512\,a^2\,c^3+96\,a\,b^4-128\,a\,b^2\,c^2\right)+32\,a^2\,b^3+128\,a^2\,b\,c^2-32\,a\,b^3\,c-128\,a^3\,b\,c\right)+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-256\,e\,a^3\,c+64\,e\,a^2\,b^2+256\,d\,a^2\,b\,c-256\,e\,a^2\,c^2-64\,d\,a\,b^3+64\,e\,a\,b^2\,c\right)-32\,a^2\,b^2\,d+128\,a^2\,c^2\,d+32\,a\,b^3\,e+128\,a^3\,c\,d-32\,a\,b^2\,c\,d-128\,a^2\,b\,c\,e\right)-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^3\,e^2-64\,a^2\,b\,d\,e-64\,a^2\,c\,d^2+128\,a^2\,c\,e^2+32\,a\,b^2\,d^2-64\,a\,b^2\,e^2+128\,a\,b\,c\,d\,e-128\,a\,c^2\,d^2\right)+32\,a^2\,b\,e^2+32\,a\,b\,c\,d^2-128\,a^2\,c\,d\,e\right)\,1{}\mathrm{i}+\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(256\,a^4\,c-64\,a^3\,b^2+768\,a^3\,c^2-576\,a^2\,b^2\,c+512\,a^2\,c^3+96\,a\,b^4-128\,a\,b^2\,c^2\right)+32\,a^2\,b^3+128\,a^2\,b\,c^2-32\,a\,b^3\,c-128\,a^3\,b\,c\right)-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-256\,e\,a^3\,c+64\,e\,a^2\,b^2+256\,d\,a^2\,b\,c-256\,e\,a^2\,c^2-64\,d\,a\,b^3+64\,e\,a\,b^2\,c\right)+32\,a^2\,b^2\,d-128\,a^2\,c^2\,d-32\,a\,b^3\,e-128\,a^3\,c\,d+32\,a\,b^2\,c\,d+128\,a^2\,b\,c\,e\right)-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^3\,e^2-64\,a^2\,b\,d\,e-64\,a^2\,c\,d^2+128\,a^2\,c\,e^2+32\,a\,b^2\,d^2-64\,a\,b^2\,e^2+128\,a\,b\,c\,d\,e-128\,a\,c^2\,d^2\right)+32\,a^2\,b\,e^2+32\,a\,b\,c\,d^2-128\,a^2\,c\,d\,e\right)\,1{}\mathrm{i}}{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^2\,e^3+64\,c\,a\,d^2\,e-64\,b\,a\,d\,e^2\right)+\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(256\,a^4\,c-64\,a^3\,b^2+768\,a^3\,c^2-576\,a^2\,b^2\,c+512\,a^2\,c^3+96\,a\,b^4-128\,a\,b^2\,c^2\right)+32\,a^2\,b^3+128\,a^2\,b\,c^2-32\,a\,b^3\,c-128\,a^3\,b\,c\right)+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-256\,e\,a^3\,c+64\,e\,a^2\,b^2+256\,d\,a^2\,b\,c-256\,e\,a^2\,c^2-64\,d\,a\,b^3+64\,e\,a\,b^2\,c\right)-32\,a^2\,b^2\,d+128\,a^2\,c^2\,d+32\,a\,b^3\,e+128\,a^3\,c\,d-32\,a\,b^2\,c\,d-128\,a^2\,b\,c\,e\right)-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^3\,e^2-64\,a^2\,b\,d\,e-64\,a^2\,c\,d^2+128\,a^2\,c\,e^2+32\,a\,b^2\,d^2-64\,a\,b^2\,e^2+128\,a\,b\,c\,d\,e-128\,a\,c^2\,d^2\right)+32\,a^2\,b\,e^2+32\,a\,b\,c\,d^2-128\,a^2\,c\,d\,e\right)-\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(256\,a^4\,c-64\,a^3\,b^2+768\,a^3\,c^2-576\,a^2\,b^2\,c+512\,a^2\,c^3+96\,a\,b^4-128\,a\,b^2\,c^2\right)+32\,a^2\,b^3+128\,a^2\,b\,c^2-32\,a\,b^3\,c-128\,a^3\,b\,c\right)-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-256\,e\,a^3\,c+64\,e\,a^2\,b^2+256\,d\,a^2\,b\,c-256\,e\,a^2\,c^2-64\,d\,a\,b^3+64\,e\,a\,b^2\,c\right)+32\,a^2\,b^2\,d-128\,a^2\,c^2\,d-32\,a\,b^3\,e-128\,a^3\,c\,d+32\,a\,b^2\,c\,d+128\,a^2\,b\,c\,e\right)-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^3\,e^2-64\,a^2\,b\,d\,e-64\,a^2\,c\,d^2+128\,a^2\,c\,e^2+32\,a\,b^2\,d^2-64\,a\,b^2\,e^2+128\,a\,b\,c\,d\,e-128\,a\,c^2\,d^2\right)+32\,a^2\,b\,e^2+32\,a\,b\,c\,d^2-128\,a^2\,c\,d\,e\right)+64\,a^2\,d\,e^2+64\,a\,c\,d^3-64\,a\,b\,d^2\,e}\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,2{}\mathrm{i}","Not used",1,"atan(((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(tan(x/2)*(96*a*b^4 + 256*a^4*c - 64*a^3*b^2 + 512*a^2*c^3 + 768*a^3*c^2 - 128*a*b^2*c^2 - 576*a^2*b^2*c) + 32*a^2*b^3 + 128*a^2*b*c^2 - 32*a*b^3*c - 128*a^3*b*c) + tan(x/2)*(64*a^2*b^2*e - 256*a^2*c^2*e - 64*a*b^3*d - 256*a^3*c*e + 256*a^2*b*c*d + 64*a*b^2*c*e) - 32*a^2*b^2*d + 128*a^2*c^2*d + 32*a*b^3*e + 128*a^3*c*d - 32*a*b^2*c*d - 128*a^2*b*c*e) - tan(x/2)*(64*a^3*e^2 + 32*a*b^2*d^2 - 64*a*b^2*e^2 - 128*a*c^2*d^2 - 64*a^2*c*d^2 + 128*a^2*c*e^2 - 64*a^2*b*d*e + 128*a*b*c*d*e) + 32*a^2*b*e^2 + 32*a*b*c*d^2 - 128*a^2*c*d*e)*1i + (-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(tan(x/2)*(96*a*b^4 + 256*a^4*c - 64*a^3*b^2 + 512*a^2*c^3 + 768*a^3*c^2 - 128*a*b^2*c^2 - 576*a^2*b^2*c) + 32*a^2*b^3 + 128*a^2*b*c^2 - 32*a*b^3*c - 128*a^3*b*c) - tan(x/2)*(64*a^2*b^2*e - 256*a^2*c^2*e - 64*a*b^3*d - 256*a^3*c*e + 256*a^2*b*c*d + 64*a*b^2*c*e) + 32*a^2*b^2*d - 128*a^2*c^2*d - 32*a*b^3*e - 128*a^3*c*d + 32*a*b^2*c*d + 128*a^2*b*c*e) - tan(x/2)*(64*a^3*e^2 + 32*a*b^2*d^2 - 64*a*b^2*e^2 - 128*a*c^2*d^2 - 64*a^2*c*d^2 + 128*a^2*c*e^2 - 64*a^2*b*d*e + 128*a*b*c*d*e) + 32*a^2*b*e^2 + 32*a*b*c*d^2 - 128*a^2*c*d*e)*1i)/(2*tan(x/2)*(64*a^2*e^3 - 64*a*b*d*e^2 + 64*a*c*d^2*e) + (-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(tan(x/2)*(96*a*b^4 + 256*a^4*c - 64*a^3*b^2 + 512*a^2*c^3 + 768*a^3*c^2 - 128*a*b^2*c^2 - 576*a^2*b^2*c) + 32*a^2*b^3 + 128*a^2*b*c^2 - 32*a*b^3*c - 128*a^3*b*c) + tan(x/2)*(64*a^2*b^2*e - 256*a^2*c^2*e - 64*a*b^3*d - 256*a^3*c*e + 256*a^2*b*c*d + 64*a*b^2*c*e) - 32*a^2*b^2*d + 128*a^2*c^2*d + 32*a*b^3*e + 128*a^3*c*d - 32*a*b^2*c*d - 128*a^2*b*c*e) - tan(x/2)*(64*a^3*e^2 + 32*a*b^2*d^2 - 64*a*b^2*e^2 - 128*a*c^2*d^2 - 64*a^2*c*d^2 + 128*a^2*c*e^2 - 64*a^2*b*d*e + 128*a*b*c*d*e) + 32*a^2*b*e^2 + 32*a*b*c*d^2 - 128*a^2*c*d*e) - (-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(tan(x/2)*(96*a*b^4 + 256*a^4*c - 64*a^3*b^2 + 512*a^2*c^3 + 768*a^3*c^2 - 128*a*b^2*c^2 - 576*a^2*b^2*c) + 32*a^2*b^3 + 128*a^2*b*c^2 - 32*a*b^3*c - 128*a^3*b*c) - tan(x/2)*(64*a^2*b^2*e - 256*a^2*c^2*e - 64*a*b^3*d - 256*a^3*c*e + 256*a^2*b*c*d + 64*a*b^2*c*e) + 32*a^2*b^2*d - 128*a^2*c^2*d - 32*a*b^3*e - 128*a^3*c*d + 32*a*b^2*c*d + 128*a^2*b*c*e) - tan(x/2)*(64*a^3*e^2 + 32*a*b^2*d^2 - 64*a*b^2*e^2 - 128*a*c^2*d^2 - 64*a^2*c*d^2 + 128*a^2*c*e^2 - 64*a^2*b*d*e + 128*a*b*c*d*e) + 32*a^2*b*e^2 + 32*a*b*c*d^2 - 128*a^2*c*d*e) + 64*a^2*d*e^2 + 64*a*c*d^3 - 64*a*b*d^2*e))*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*2i + atan(((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(tan(x/2)*(96*a*b^4 + 256*a^4*c - 64*a^3*b^2 + 512*a^2*c^3 + 768*a^3*c^2 - 128*a*b^2*c^2 - 576*a^2*b^2*c) + 32*a^2*b^3 + 128*a^2*b*c^2 - 32*a*b^3*c - 128*a^3*b*c) + tan(x/2)*(64*a^2*b^2*e - 256*a^2*c^2*e - 64*a*b^3*d - 256*a^3*c*e + 256*a^2*b*c*d + 64*a*b^2*c*e) - 32*a^2*b^2*d + 128*a^2*c^2*d + 32*a*b^3*e + 128*a^3*c*d - 32*a*b^2*c*d - 128*a^2*b*c*e) - tan(x/2)*(64*a^3*e^2 + 32*a*b^2*d^2 - 64*a*b^2*e^2 - 128*a*c^2*d^2 - 64*a^2*c*d^2 + 128*a^2*c*e^2 - 64*a^2*b*d*e + 128*a*b*c*d*e) + 32*a^2*b*e^2 + 32*a*b*c*d^2 - 128*a^2*c*d*e)*1i + (-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(tan(x/2)*(96*a*b^4 + 256*a^4*c - 64*a^3*b^2 + 512*a^2*c^3 + 768*a^3*c^2 - 128*a*b^2*c^2 - 576*a^2*b^2*c) + 32*a^2*b^3 + 128*a^2*b*c^2 - 32*a*b^3*c - 128*a^3*b*c) - tan(x/2)*(64*a^2*b^2*e - 256*a^2*c^2*e - 64*a*b^3*d - 256*a^3*c*e + 256*a^2*b*c*d + 64*a*b^2*c*e) + 32*a^2*b^2*d - 128*a^2*c^2*d - 32*a*b^3*e - 128*a^3*c*d + 32*a*b^2*c*d + 128*a^2*b*c*e) - tan(x/2)*(64*a^3*e^2 + 32*a*b^2*d^2 - 64*a*b^2*e^2 - 128*a*c^2*d^2 - 64*a^2*c*d^2 + 128*a^2*c*e^2 - 64*a^2*b*d*e + 128*a*b*c*d*e) + 32*a^2*b*e^2 + 32*a*b*c*d^2 - 128*a^2*c*d*e)*1i)/(2*tan(x/2)*(64*a^2*e^3 - 64*a*b*d*e^2 + 64*a*c*d^2*e) + (-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(tan(x/2)*(96*a*b^4 + 256*a^4*c - 64*a^3*b^2 + 512*a^2*c^3 + 768*a^3*c^2 - 128*a*b^2*c^2 - 576*a^2*b^2*c) + 32*a^2*b^3 + 128*a^2*b*c^2 - 32*a*b^3*c - 128*a^3*b*c) + tan(x/2)*(64*a^2*b^2*e - 256*a^2*c^2*e - 64*a*b^3*d - 256*a^3*c*e + 256*a^2*b*c*d + 64*a*b^2*c*e) - 32*a^2*b^2*d + 128*a^2*c^2*d + 32*a*b^3*e + 128*a^3*c*d - 32*a*b^2*c*d - 128*a^2*b*c*e) - tan(x/2)*(64*a^3*e^2 + 32*a*b^2*d^2 - 64*a*b^2*e^2 - 128*a*c^2*d^2 - 64*a^2*c*d^2 + 128*a^2*c*e^2 - 64*a^2*b*d*e + 128*a*b*c*d*e) + 32*a^2*b*e^2 + 32*a*b*c*d^2 - 128*a^2*c*d*e) - (-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(tan(x/2)*(96*a*b^4 + 256*a^4*c - 64*a^3*b^2 + 512*a^2*c^3 + 768*a^3*c^2 - 128*a*b^2*c^2 - 576*a^2*b^2*c) + 32*a^2*b^3 + 128*a^2*b*c^2 - 32*a*b^3*c - 128*a^3*b*c) - tan(x/2)*(64*a^2*b^2*e - 256*a^2*c^2*e - 64*a*b^3*d - 256*a^3*c*e + 256*a^2*b*c*d + 64*a*b^2*c*e) + 32*a^2*b^2*d - 128*a^2*c^2*d - 32*a*b^3*e - 128*a^3*c*d + 32*a*b^2*c*d + 128*a^2*b*c*e) - tan(x/2)*(64*a^3*e^2 + 32*a*b^2*d^2 - 64*a*b^2*e^2 - 128*a*c^2*d^2 - 64*a^2*c*d^2 + 128*a^2*c*e^2 - 64*a^2*b*d*e + 128*a*b*c*d*e) + 32*a^2*b*e^2 + 32*a*b*c*d^2 - 128*a^2*c*d*e) + 64*a^2*d*e^2 + 64*a*c*d^3 - 64*a*b*d^2*e))*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*2i","B"
504,0,-1,331,0.000000,"\text{Not used}","int((a + b*sin(d + e*x))*(b^2 + a^2*sin(d + e*x)^2 + 2*a*b*sin(d + e*x))^(3/2),x)","\int \left(a+b\,\sin\left(d+e\,x\right)\right)\,{\left(a^2\,{\sin\left(d+e\,x\right)}^2+2\,a\,b\,\sin\left(d+e\,x\right)+b^2\right)}^{3/2} \,d x","Not used",1,"int((a + b*sin(d + e*x))*(b^2 + a^2*sin(d + e*x)^2 + 2*a*b*sin(d + e*x))^(3/2), x)","F"
505,0,-1,185,0.000000,"\text{Not used}","int((a + b*sin(d + e*x))*(b^2 + a^2*sin(d + e*x)^2 + 2*a*b*sin(d + e*x))^(1/2),x)","\int \left(a+b\,\sin\left(d+e\,x\right)\right)\,\sqrt{a^2\,{\sin\left(d+e\,x\right)}^2+2\,a\,b\,\sin\left(d+e\,x\right)+b^2} \,d x","Not used",1,"int((a + b*sin(d + e*x))*(b^2 + a^2*sin(d + e*x)^2 + 2*a*b*sin(d + e*x))^(1/2), x)","F"
506,0,-1,137,0.000000,"\text{Not used}","int((a + b*sin(d + e*x))/(b^2 + a^2*sin(d + e*x)^2 + 2*a*b*sin(d + e*x))^(1/2),x)","\int \frac{a+b\,\sin\left(d+e\,x\right)}{\sqrt{a^2\,{\sin\left(d+e\,x\right)}^2+2\,a\,b\,\sin\left(d+e\,x\right)+b^2}} \,d x","Not used",1,"int((a + b*sin(d + e*x))/(b^2 + a^2*sin(d + e*x)^2 + 2*a*b*sin(d + e*x))^(1/2), x)","F"
507,0,-1,239,0.000000,"\text{Not used}","int((a + b*sin(d + e*x))/(b^2 + a^2*sin(d + e*x)^2 + 2*a*b*sin(d + e*x))^(3/2),x)","\int \frac{a+b\,\sin\left(d+e\,x\right)}{{\left(a^2\,{\sin\left(d+e\,x\right)}^2+2\,a\,b\,\sin\left(d+e\,x\right)+b^2\right)}^{3/2}} \,d x","Not used",1,"int((a + b*sin(d + e*x))/(b^2 + a^2*sin(d + e*x)^2 + 2*a*b*sin(d + e*x))^(3/2), x)","F"
508,1,24,11,2.936542,"\text{Not used}","int((a + b*cos(x))/(a^2*cos(x)^2 + b^2 + 2*a*b*cos(x)),x)","\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)}{\left(b-a\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+a+b}","Not used",1,"(2*tan(x/2))/(a + b - tan(x/2)^2*(a - b))","B"
509,1,11781,246,16.768919,"\text{Not used}","int((d + e*cos(x))/(a + b*cos(x) + c*cos(x)^2),x)","-\mathrm{atan}\left(\frac{\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(256\,a^2\,c^2\,d-32\,b^4\,e-32\,a^2\,b^2\,d-32\,a^2\,b^2\,e-32\,b^4\,d+256\,a^2\,c^2\,e-32\,b^2\,c^2\,d-32\,b^2\,c^2\,e+\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(-256\,a^4\,c+64\,a^3\,b^2+512\,a^3\,b\,c-256\,a^3\,c^2-128\,a^2\,b^3-192\,a^2\,b^2\,c+256\,a^2\,c^3+64\,a\,b^4+192\,a\,b^2\,c^2-512\,a\,b\,c^3+256\,a\,c^4-64\,b^4\,c+128\,b^3\,c^2-64\,b^2\,c^3\right)+64\,a\,b^3\,d+64\,a\,b^3\,e+128\,a\,c^3\,d+128\,a^3\,c\,d+128\,a\,c^3\,e+128\,a^3\,c\,e+64\,b^3\,c\,d+64\,b^3\,c\,e-256\,a\,b\,c^2\,d+64\,a\,b^2\,c\,d-256\,a^2\,b\,c\,d-256\,a\,b\,c^2\,e+64\,a\,b^2\,c\,e-256\,a^2\,b\,c\,e\right)+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^3\,e^2-64\,a^2\,b\,d\,e-128\,a^2\,b\,e^2-64\,a^2\,c\,d^2+256\,a^2\,c\,d\,e+32\,a\,b^2\,d^2+64\,a\,b^2\,d\,e+96\,a\,b^2\,e^2-384\,a\,b\,c\,d\,e+256\,a\,c^2\,d\,e-64\,a\,c^2\,e^2-32\,b^3\,d^2-32\,b^3\,e^2+96\,b^2\,c\,d^2+64\,b^2\,c\,d\,e+32\,b^2\,c\,e^2-128\,b\,c^2\,d^2-64\,b\,c^2\,d\,e+64\,c^3\,d^2\right)\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,1{}\mathrm{i}-\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(256\,a^2\,c^2\,d-32\,b^4\,e-32\,a^2\,b^2\,d-32\,a^2\,b^2\,e-32\,b^4\,d+256\,a^2\,c^2\,e-32\,b^2\,c^2\,d-32\,b^2\,c^2\,e-\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(-256\,a^4\,c+64\,a^3\,b^2+512\,a^3\,b\,c-256\,a^3\,c^2-128\,a^2\,b^3-192\,a^2\,b^2\,c+256\,a^2\,c^3+64\,a\,b^4+192\,a\,b^2\,c^2-512\,a\,b\,c^3+256\,a\,c^4-64\,b^4\,c+128\,b^3\,c^2-64\,b^2\,c^3\right)+64\,a\,b^3\,d+64\,a\,b^3\,e+128\,a\,c^3\,d+128\,a^3\,c\,d+128\,a\,c^3\,e+128\,a^3\,c\,e+64\,b^3\,c\,d+64\,b^3\,c\,e-256\,a\,b\,c^2\,d+64\,a\,b^2\,c\,d-256\,a^2\,b\,c\,d-256\,a\,b\,c^2\,e+64\,a\,b^2\,c\,e-256\,a^2\,b\,c\,e\right)-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^3\,e^2-64\,a^2\,b\,d\,e-128\,a^2\,b\,e^2-64\,a^2\,c\,d^2+256\,a^2\,c\,d\,e+32\,a\,b^2\,d^2+64\,a\,b^2\,d\,e+96\,a\,b^2\,e^2-384\,a\,b\,c\,d\,e+256\,a\,c^2\,d\,e-64\,a\,c^2\,e^2-32\,b^3\,d^2-32\,b^3\,e^2+96\,b^2\,c\,d^2+64\,b^2\,c\,d\,e+32\,b^2\,c\,e^2-128\,b\,c^2\,d^2-64\,b\,c^2\,d\,e+64\,c^3\,d^2\right)\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,1{}\mathrm{i}}{\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(256\,a^2\,c^2\,d-32\,b^4\,e-32\,a^2\,b^2\,d-32\,a^2\,b^2\,e-32\,b^4\,d+256\,a^2\,c^2\,e-32\,b^2\,c^2\,d-32\,b^2\,c^2\,e+\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(-256\,a^4\,c+64\,a^3\,b^2+512\,a^3\,b\,c-256\,a^3\,c^2-128\,a^2\,b^3-192\,a^2\,b^2\,c+256\,a^2\,c^3+64\,a\,b^4+192\,a\,b^2\,c^2-512\,a\,b\,c^3+256\,a\,c^4-64\,b^4\,c+128\,b^3\,c^2-64\,b^2\,c^3\right)+64\,a\,b^3\,d+64\,a\,b^3\,e+128\,a\,c^3\,d+128\,a^3\,c\,d+128\,a\,c^3\,e+128\,a^3\,c\,e+64\,b^3\,c\,d+64\,b^3\,c\,e-256\,a\,b\,c^2\,d+64\,a\,b^2\,c\,d-256\,a^2\,b\,c\,d-256\,a\,b\,c^2\,e+64\,a\,b^2\,c\,e-256\,a^2\,b\,c\,e\right)+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^3\,e^2-64\,a^2\,b\,d\,e-128\,a^2\,b\,e^2-64\,a^2\,c\,d^2+256\,a^2\,c\,d\,e+32\,a\,b^2\,d^2+64\,a\,b^2\,d\,e+96\,a\,b^2\,e^2-384\,a\,b\,c\,d\,e+256\,a\,c^2\,d\,e-64\,a\,c^2\,e^2-32\,b^3\,d^2-32\,b^3\,e^2+96\,b^2\,c\,d^2+64\,b^2\,c\,d\,e+32\,b^2\,c\,e^2-128\,b\,c^2\,d^2-64\,b\,c^2\,d\,e+64\,c^3\,d^2\right)\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}+\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(256\,a^2\,c^2\,d-32\,b^4\,e-32\,a^2\,b^2\,d-32\,a^2\,b^2\,e-32\,b^4\,d+256\,a^2\,c^2\,e-32\,b^2\,c^2\,d-32\,b^2\,c^2\,e-\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(-256\,a^4\,c+64\,a^3\,b^2+512\,a^3\,b\,c-256\,a^3\,c^2-128\,a^2\,b^3-192\,a^2\,b^2\,c+256\,a^2\,c^3+64\,a\,b^4+192\,a\,b^2\,c^2-512\,a\,b\,c^3+256\,a\,c^4-64\,b^4\,c+128\,b^3\,c^2-64\,b^2\,c^3\right)+64\,a\,b^3\,d+64\,a\,b^3\,e+128\,a\,c^3\,d+128\,a^3\,c\,d+128\,a\,c^3\,e+128\,a^3\,c\,e+64\,b^3\,c\,d+64\,b^3\,c\,e-256\,a\,b\,c^2\,d+64\,a\,b^2\,c\,d-256\,a^2\,b\,c\,d-256\,a\,b\,c^2\,e+64\,a\,b^2\,c\,e-256\,a^2\,b\,c\,e\right)-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^3\,e^2-64\,a^2\,b\,d\,e-128\,a^2\,b\,e^2-64\,a^2\,c\,d^2+256\,a^2\,c\,d\,e+32\,a\,b^2\,d^2+64\,a\,b^2\,d\,e+96\,a\,b^2\,e^2-384\,a\,b\,c\,d\,e+256\,a\,c^2\,d\,e-64\,a\,c^2\,e^2-32\,b^3\,d^2-32\,b^3\,e^2+96\,b^2\,c\,d^2+64\,b^2\,c\,d\,e+32\,b^2\,c\,e^2-128\,b\,c^2\,d^2-64\,b\,c^2\,d\,e+64\,c^3\,d^2\right)\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}-64\,a^2\,e^3+64\,c^2\,d^3+64\,a^2\,d\,e^2-64\,b^2\,d\,e^2+64\,b^2\,d^2\,e-64\,c^2\,d^2\,e+64\,a\,b\,e^3+64\,a\,c\,d^3-64\,a\,c\,e^3-64\,b\,c\,d^3-64\,a\,b\,d^2\,e+64\,a\,c\,d\,e^2-64\,a\,c\,d^2\,e+64\,b\,c\,d\,e^2}\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2+b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2+b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e-2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e-2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(256\,a^2\,c^2\,d-32\,b^4\,e-32\,a^2\,b^2\,d-32\,a^2\,b^2\,e-32\,b^4\,d+256\,a^2\,c^2\,e-32\,b^2\,c^2\,d-32\,b^2\,c^2\,e+\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(-256\,a^4\,c+64\,a^3\,b^2+512\,a^3\,b\,c-256\,a^3\,c^2-128\,a^2\,b^3-192\,a^2\,b^2\,c+256\,a^2\,c^3+64\,a\,b^4+192\,a\,b^2\,c^2-512\,a\,b\,c^3+256\,a\,c^4-64\,b^4\,c+128\,b^3\,c^2-64\,b^2\,c^3\right)+64\,a\,b^3\,d+64\,a\,b^3\,e+128\,a\,c^3\,d+128\,a^3\,c\,d+128\,a\,c^3\,e+128\,a^3\,c\,e+64\,b^3\,c\,d+64\,b^3\,c\,e-256\,a\,b\,c^2\,d+64\,a\,b^2\,c\,d-256\,a^2\,b\,c\,d-256\,a\,b\,c^2\,e+64\,a\,b^2\,c\,e-256\,a^2\,b\,c\,e\right)+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^3\,e^2-64\,a^2\,b\,d\,e-128\,a^2\,b\,e^2-64\,a^2\,c\,d^2+256\,a^2\,c\,d\,e+32\,a\,b^2\,d^2+64\,a\,b^2\,d\,e+96\,a\,b^2\,e^2-384\,a\,b\,c\,d\,e+256\,a\,c^2\,d\,e-64\,a\,c^2\,e^2-32\,b^3\,d^2-32\,b^3\,e^2+96\,b^2\,c\,d^2+64\,b^2\,c\,d\,e+32\,b^2\,c\,e^2-128\,b\,c^2\,d^2-64\,b\,c^2\,d\,e+64\,c^3\,d^2\right)\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,1{}\mathrm{i}-\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(256\,a^2\,c^2\,d-32\,b^4\,e-32\,a^2\,b^2\,d-32\,a^2\,b^2\,e-32\,b^4\,d+256\,a^2\,c^2\,e-32\,b^2\,c^2\,d-32\,b^2\,c^2\,e-\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(-256\,a^4\,c+64\,a^3\,b^2+512\,a^3\,b\,c-256\,a^3\,c^2-128\,a^2\,b^3-192\,a^2\,b^2\,c+256\,a^2\,c^3+64\,a\,b^4+192\,a\,b^2\,c^2-512\,a\,b\,c^3+256\,a\,c^4-64\,b^4\,c+128\,b^3\,c^2-64\,b^2\,c^3\right)+64\,a\,b^3\,d+64\,a\,b^3\,e+128\,a\,c^3\,d+128\,a^3\,c\,d+128\,a\,c^3\,e+128\,a^3\,c\,e+64\,b^3\,c\,d+64\,b^3\,c\,e-256\,a\,b\,c^2\,d+64\,a\,b^2\,c\,d-256\,a^2\,b\,c\,d-256\,a\,b\,c^2\,e+64\,a\,b^2\,c\,e-256\,a^2\,b\,c\,e\right)-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^3\,e^2-64\,a^2\,b\,d\,e-128\,a^2\,b\,e^2-64\,a^2\,c\,d^2+256\,a^2\,c\,d\,e+32\,a\,b^2\,d^2+64\,a\,b^2\,d\,e+96\,a\,b^2\,e^2-384\,a\,b\,c\,d\,e+256\,a\,c^2\,d\,e-64\,a\,c^2\,e^2-32\,b^3\,d^2-32\,b^3\,e^2+96\,b^2\,c\,d^2+64\,b^2\,c\,d\,e+32\,b^2\,c\,e^2-128\,b\,c^2\,d^2-64\,b\,c^2\,d\,e+64\,c^3\,d^2\right)\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,1{}\mathrm{i}}{\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(256\,a^2\,c^2\,d-32\,b^4\,e-32\,a^2\,b^2\,d-32\,a^2\,b^2\,e-32\,b^4\,d+256\,a^2\,c^2\,e-32\,b^2\,c^2\,d-32\,b^2\,c^2\,e+\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(-256\,a^4\,c+64\,a^3\,b^2+512\,a^3\,b\,c-256\,a^3\,c^2-128\,a^2\,b^3-192\,a^2\,b^2\,c+256\,a^2\,c^3+64\,a\,b^4+192\,a\,b^2\,c^2-512\,a\,b\,c^3+256\,a\,c^4-64\,b^4\,c+128\,b^3\,c^2-64\,b^2\,c^3\right)+64\,a\,b^3\,d+64\,a\,b^3\,e+128\,a\,c^3\,d+128\,a^3\,c\,d+128\,a\,c^3\,e+128\,a^3\,c\,e+64\,b^3\,c\,d+64\,b^3\,c\,e-256\,a\,b\,c^2\,d+64\,a\,b^2\,c\,d-256\,a^2\,b\,c\,d-256\,a\,b\,c^2\,e+64\,a\,b^2\,c\,e-256\,a^2\,b\,c\,e\right)+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^3\,e^2-64\,a^2\,b\,d\,e-128\,a^2\,b\,e^2-64\,a^2\,c\,d^2+256\,a^2\,c\,d\,e+32\,a\,b^2\,d^2+64\,a\,b^2\,d\,e+96\,a\,b^2\,e^2-384\,a\,b\,c\,d\,e+256\,a\,c^2\,d\,e-64\,a\,c^2\,e^2-32\,b^3\,d^2-32\,b^3\,e^2+96\,b^2\,c\,d^2+64\,b^2\,c\,d\,e+32\,b^2\,c\,e^2-128\,b\,c^2\,d^2-64\,b\,c^2\,d\,e+64\,c^3\,d^2\right)\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}+\left(\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(256\,a^2\,c^2\,d-32\,b^4\,e-32\,a^2\,b^2\,d-32\,a^2\,b^2\,e-32\,b^4\,d+256\,a^2\,c^2\,e-32\,b^2\,c^2\,d-32\,b^2\,c^2\,e-\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,\left(-256\,a^4\,c+64\,a^3\,b^2+512\,a^3\,b\,c-256\,a^3\,c^2-128\,a^2\,b^3-192\,a^2\,b^2\,c+256\,a^2\,c^3+64\,a\,b^4+192\,a\,b^2\,c^2-512\,a\,b\,c^3+256\,a\,c^4-64\,b^4\,c+128\,b^3\,c^2-64\,b^2\,c^3\right)+64\,a\,b^3\,d+64\,a\,b^3\,e+128\,a\,c^3\,d+128\,a^3\,c\,d+128\,a\,c^3\,e+128\,a^3\,c\,e+64\,b^3\,c\,d+64\,b^3\,c\,e-256\,a\,b\,c^2\,d+64\,a\,b^2\,c\,d-256\,a^2\,b\,c\,d-256\,a\,b\,c^2\,e+64\,a\,b^2\,c\,e-256\,a^2\,b\,c\,e\right)-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^3\,e^2-64\,a^2\,b\,d\,e-128\,a^2\,b\,e^2-64\,a^2\,c\,d^2+256\,a^2\,c\,d\,e+32\,a\,b^2\,d^2+64\,a\,b^2\,d\,e+96\,a\,b^2\,e^2-384\,a\,b\,c\,d\,e+256\,a\,c^2\,d\,e-64\,a\,c^2\,e^2-32\,b^3\,d^2-32\,b^3\,e^2+96\,b^2\,c\,d^2+64\,b^2\,c\,d\,e+32\,b^2\,c\,e^2-128\,b\,c^2\,d^2-64\,b\,c^2\,d\,e+64\,c^3\,d^2\right)\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}-64\,a^2\,e^3+64\,c^2\,d^3+64\,a^2\,d\,e^2-64\,b^2\,d\,e^2+64\,b^2\,d^2\,e-64\,c^2\,d^2\,e+64\,a\,b\,e^3+64\,a\,c\,d^3-64\,a\,c\,e^3-64\,b\,c\,d^3-64\,a\,b\,d^2\,e+64\,a\,c\,d\,e^2-64\,a\,c\,d^2\,e+64\,b\,c\,d\,e^2}\right)\,\sqrt{-\frac{b^4\,d^2-b^4\,e^2+8\,a\,c^3\,d^2-b\,d^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,a^3\,c\,e^2-b\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a^2\,b^2\,e^2+8\,a^2\,c^2\,d^2-8\,a^2\,c^2\,e^2-2\,b^2\,c^2\,d^2-2\,a\,b^3\,d\,e+2\,a\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e+2\,c\,d\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-6\,a\,b^2\,c\,d^2+6\,a\,b^2\,c\,e^2-8\,a\,b\,c^2\,d\,e+8\,a^2\,b\,c\,d\,e}{2\,\left(16\,a^4\,c^2-8\,a^3\,b^2\,c+32\,a^3\,c^3+a^2\,b^4-32\,a^2\,b^2\,c^2+16\,a^2\,c^4+10\,a\,b^4\,c-8\,a\,b^2\,c^3-b^6+b^4\,c^2\right)}}\,2{}\mathrm{i}","Not used",1,"- atan((((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(256*a^2*c^2*d - 32*b^4*e - 32*a^2*b^2*d - 32*a^2*b^2*e - 32*b^4*d + 256*a^2*c^2*e - 32*b^2*c^2*d - 32*b^2*c^2*e + tan(x/2)*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(64*a*b^4 + 256*a*c^4 - 256*a^4*c - 64*b^4*c - 128*a^2*b^3 + 64*a^3*b^2 + 256*a^2*c^3 - 256*a^3*c^2 - 64*b^2*c^3 + 128*b^3*c^2 + 192*a*b^2*c^2 - 192*a^2*b^2*c - 512*a*b*c^3 + 512*a^3*b*c) + 64*a*b^3*d + 64*a*b^3*e + 128*a*c^3*d + 128*a^3*c*d + 128*a*c^3*e + 128*a^3*c*e + 64*b^3*c*d + 64*b^3*c*e - 256*a*b*c^2*d + 64*a*b^2*c*d - 256*a^2*b*c*d - 256*a*b*c^2*e + 64*a*b^2*c*e - 256*a^2*b*c*e) + tan(x/2)*(64*a^3*e^2 - 32*b^3*d^2 - 32*b^3*e^2 + 64*c^3*d^2 + 32*a*b^2*d^2 + 96*a*b^2*e^2 - 128*a^2*b*e^2 - 64*a^2*c*d^2 - 64*a*c^2*e^2 - 128*b*c^2*d^2 + 96*b^2*c*d^2 + 32*b^2*c*e^2 + 64*a*b^2*d*e - 64*a^2*b*d*e + 256*a*c^2*d*e + 256*a^2*c*d*e - 64*b*c^2*d*e + 64*b^2*c*d*e - 384*a*b*c*d*e))*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*1i - ((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(256*a^2*c^2*d - 32*b^4*e - 32*a^2*b^2*d - 32*a^2*b^2*e - 32*b^4*d + 256*a^2*c^2*e - 32*b^2*c^2*d - 32*b^2*c^2*e - tan(x/2)*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(64*a*b^4 + 256*a*c^4 - 256*a^4*c - 64*b^4*c - 128*a^2*b^3 + 64*a^3*b^2 + 256*a^2*c^3 - 256*a^3*c^2 - 64*b^2*c^3 + 128*b^3*c^2 + 192*a*b^2*c^2 - 192*a^2*b^2*c - 512*a*b*c^3 + 512*a^3*b*c) + 64*a*b^3*d + 64*a*b^3*e + 128*a*c^3*d + 128*a^3*c*d + 128*a*c^3*e + 128*a^3*c*e + 64*b^3*c*d + 64*b^3*c*e - 256*a*b*c^2*d + 64*a*b^2*c*d - 256*a^2*b*c*d - 256*a*b*c^2*e + 64*a*b^2*c*e - 256*a^2*b*c*e) - tan(x/2)*(64*a^3*e^2 - 32*b^3*d^2 - 32*b^3*e^2 + 64*c^3*d^2 + 32*a*b^2*d^2 + 96*a*b^2*e^2 - 128*a^2*b*e^2 - 64*a^2*c*d^2 - 64*a*c^2*e^2 - 128*b*c^2*d^2 + 96*b^2*c*d^2 + 32*b^2*c*e^2 + 64*a*b^2*d*e - 64*a^2*b*d*e + 256*a*c^2*d*e + 256*a^2*c*d*e - 64*b*c^2*d*e + 64*b^2*c*d*e - 384*a*b*c*d*e))*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*1i)/(((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(256*a^2*c^2*d - 32*b^4*e - 32*a^2*b^2*d - 32*a^2*b^2*e - 32*b^4*d + 256*a^2*c^2*e - 32*b^2*c^2*d - 32*b^2*c^2*e + tan(x/2)*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(64*a*b^4 + 256*a*c^4 - 256*a^4*c - 64*b^4*c - 128*a^2*b^3 + 64*a^3*b^2 + 256*a^2*c^3 - 256*a^3*c^2 - 64*b^2*c^3 + 128*b^3*c^2 + 192*a*b^2*c^2 - 192*a^2*b^2*c - 512*a*b*c^3 + 512*a^3*b*c) + 64*a*b^3*d + 64*a*b^3*e + 128*a*c^3*d + 128*a^3*c*d + 128*a*c^3*e + 128*a^3*c*e + 64*b^3*c*d + 64*b^3*c*e - 256*a*b*c^2*d + 64*a*b^2*c*d - 256*a^2*b*c*d - 256*a*b*c^2*e + 64*a*b^2*c*e - 256*a^2*b*c*e) + tan(x/2)*(64*a^3*e^2 - 32*b^3*d^2 - 32*b^3*e^2 + 64*c^3*d^2 + 32*a*b^2*d^2 + 96*a*b^2*e^2 - 128*a^2*b*e^2 - 64*a^2*c*d^2 - 64*a*c^2*e^2 - 128*b*c^2*d^2 + 96*b^2*c*d^2 + 32*b^2*c*e^2 + 64*a*b^2*d*e - 64*a^2*b*d*e + 256*a*c^2*d*e + 256*a^2*c*d*e - 64*b*c^2*d*e + 64*b^2*c*d*e - 384*a*b*c*d*e))*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2) + ((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(256*a^2*c^2*d - 32*b^4*e - 32*a^2*b^2*d - 32*a^2*b^2*e - 32*b^4*d + 256*a^2*c^2*e - 32*b^2*c^2*d - 32*b^2*c^2*e - tan(x/2)*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(64*a*b^4 + 256*a*c^4 - 256*a^4*c - 64*b^4*c - 128*a^2*b^3 + 64*a^3*b^2 + 256*a^2*c^3 - 256*a^3*c^2 - 64*b^2*c^3 + 128*b^3*c^2 + 192*a*b^2*c^2 - 192*a^2*b^2*c - 512*a*b*c^3 + 512*a^3*b*c) + 64*a*b^3*d + 64*a*b^3*e + 128*a*c^3*d + 128*a^3*c*d + 128*a*c^3*e + 128*a^3*c*e + 64*b^3*c*d + 64*b^3*c*e - 256*a*b*c^2*d + 64*a*b^2*c*d - 256*a^2*b*c*d - 256*a*b*c^2*e + 64*a*b^2*c*e - 256*a^2*b*c*e) - tan(x/2)*(64*a^3*e^2 - 32*b^3*d^2 - 32*b^3*e^2 + 64*c^3*d^2 + 32*a*b^2*d^2 + 96*a*b^2*e^2 - 128*a^2*b*e^2 - 64*a^2*c*d^2 - 64*a*c^2*e^2 - 128*b*c^2*d^2 + 96*b^2*c*d^2 + 32*b^2*c*e^2 + 64*a*b^2*d*e - 64*a^2*b*d*e + 256*a*c^2*d*e + 256*a^2*c*d*e - 64*b*c^2*d*e + 64*b^2*c*d*e - 384*a*b*c*d*e))*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2) - 64*a^2*e^3 + 64*c^2*d^3 + 64*a^2*d*e^2 - 64*b^2*d*e^2 + 64*b^2*d^2*e - 64*c^2*d^2*e + 64*a*b*e^3 + 64*a*c*d^3 - 64*a*c*e^3 - 64*b*c*d^3 - 64*a*b*d^2*e + 64*a*c*d*e^2 - 64*a*c*d^2*e + 64*b*c*d*e^2))*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 + b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e - 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e - 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*2i - atan((((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(256*a^2*c^2*d - 32*b^4*e - 32*a^2*b^2*d - 32*a^2*b^2*e - 32*b^4*d + 256*a^2*c^2*e - 32*b^2*c^2*d - 32*b^2*c^2*e + tan(x/2)*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(64*a*b^4 + 256*a*c^4 - 256*a^4*c - 64*b^4*c - 128*a^2*b^3 + 64*a^3*b^2 + 256*a^2*c^3 - 256*a^3*c^2 - 64*b^2*c^3 + 128*b^3*c^2 + 192*a*b^2*c^2 - 192*a^2*b^2*c - 512*a*b*c^3 + 512*a^3*b*c) + 64*a*b^3*d + 64*a*b^3*e + 128*a*c^3*d + 128*a^3*c*d + 128*a*c^3*e + 128*a^3*c*e + 64*b^3*c*d + 64*b^3*c*e - 256*a*b*c^2*d + 64*a*b^2*c*d - 256*a^2*b*c*d - 256*a*b*c^2*e + 64*a*b^2*c*e - 256*a^2*b*c*e) + tan(x/2)*(64*a^3*e^2 - 32*b^3*d^2 - 32*b^3*e^2 + 64*c^3*d^2 + 32*a*b^2*d^2 + 96*a*b^2*e^2 - 128*a^2*b*e^2 - 64*a^2*c*d^2 - 64*a*c^2*e^2 - 128*b*c^2*d^2 + 96*b^2*c*d^2 + 32*b^2*c*e^2 + 64*a*b^2*d*e - 64*a^2*b*d*e + 256*a*c^2*d*e + 256*a^2*c*d*e - 64*b*c^2*d*e + 64*b^2*c*d*e - 384*a*b*c*d*e))*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*1i - ((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(256*a^2*c^2*d - 32*b^4*e - 32*a^2*b^2*d - 32*a^2*b^2*e - 32*b^4*d + 256*a^2*c^2*e - 32*b^2*c^2*d - 32*b^2*c^2*e - tan(x/2)*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(64*a*b^4 + 256*a*c^4 - 256*a^4*c - 64*b^4*c - 128*a^2*b^3 + 64*a^3*b^2 + 256*a^2*c^3 - 256*a^3*c^2 - 64*b^2*c^3 + 128*b^3*c^2 + 192*a*b^2*c^2 - 192*a^2*b^2*c - 512*a*b*c^3 + 512*a^3*b*c) + 64*a*b^3*d + 64*a*b^3*e + 128*a*c^3*d + 128*a^3*c*d + 128*a*c^3*e + 128*a^3*c*e + 64*b^3*c*d + 64*b^3*c*e - 256*a*b*c^2*d + 64*a*b^2*c*d - 256*a^2*b*c*d - 256*a*b*c^2*e + 64*a*b^2*c*e - 256*a^2*b*c*e) - tan(x/2)*(64*a^3*e^2 - 32*b^3*d^2 - 32*b^3*e^2 + 64*c^3*d^2 + 32*a*b^2*d^2 + 96*a*b^2*e^2 - 128*a^2*b*e^2 - 64*a^2*c*d^2 - 64*a*c^2*e^2 - 128*b*c^2*d^2 + 96*b^2*c*d^2 + 32*b^2*c*e^2 + 64*a*b^2*d*e - 64*a^2*b*d*e + 256*a*c^2*d*e + 256*a^2*c*d*e - 64*b*c^2*d*e + 64*b^2*c*d*e - 384*a*b*c*d*e))*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*1i)/(((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(256*a^2*c^2*d - 32*b^4*e - 32*a^2*b^2*d - 32*a^2*b^2*e - 32*b^4*d + 256*a^2*c^2*e - 32*b^2*c^2*d - 32*b^2*c^2*e + tan(x/2)*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(64*a*b^4 + 256*a*c^4 - 256*a^4*c - 64*b^4*c - 128*a^2*b^3 + 64*a^3*b^2 + 256*a^2*c^3 - 256*a^3*c^2 - 64*b^2*c^3 + 128*b^3*c^2 + 192*a*b^2*c^2 - 192*a^2*b^2*c - 512*a*b*c^3 + 512*a^3*b*c) + 64*a*b^3*d + 64*a*b^3*e + 128*a*c^3*d + 128*a^3*c*d + 128*a*c^3*e + 128*a^3*c*e + 64*b^3*c*d + 64*b^3*c*e - 256*a*b*c^2*d + 64*a*b^2*c*d - 256*a^2*b*c*d - 256*a*b*c^2*e + 64*a*b^2*c*e - 256*a^2*b*c*e) + tan(x/2)*(64*a^3*e^2 - 32*b^3*d^2 - 32*b^3*e^2 + 64*c^3*d^2 + 32*a*b^2*d^2 + 96*a*b^2*e^2 - 128*a^2*b*e^2 - 64*a^2*c*d^2 - 64*a*c^2*e^2 - 128*b*c^2*d^2 + 96*b^2*c*d^2 + 32*b^2*c*e^2 + 64*a*b^2*d*e - 64*a^2*b*d*e + 256*a*c^2*d*e + 256*a^2*c*d*e - 64*b*c^2*d*e + 64*b^2*c*d*e - 384*a*b*c*d*e))*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2) + ((-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(256*a^2*c^2*d - 32*b^4*e - 32*a^2*b^2*d - 32*a^2*b^2*e - 32*b^4*d + 256*a^2*c^2*e - 32*b^2*c^2*d - 32*b^2*c^2*e - tan(x/2)*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*(64*a*b^4 + 256*a*c^4 - 256*a^4*c - 64*b^4*c - 128*a^2*b^3 + 64*a^3*b^2 + 256*a^2*c^3 - 256*a^3*c^2 - 64*b^2*c^3 + 128*b^3*c^2 + 192*a*b^2*c^2 - 192*a^2*b^2*c - 512*a*b*c^3 + 512*a^3*b*c) + 64*a*b^3*d + 64*a*b^3*e + 128*a*c^3*d + 128*a^3*c*d + 128*a*c^3*e + 128*a^3*c*e + 64*b^3*c*d + 64*b^3*c*e - 256*a*b*c^2*d + 64*a*b^2*c*d - 256*a^2*b*c*d - 256*a*b*c^2*e + 64*a*b^2*c*e - 256*a^2*b*c*e) - tan(x/2)*(64*a^3*e^2 - 32*b^3*d^2 - 32*b^3*e^2 + 64*c^3*d^2 + 32*a*b^2*d^2 + 96*a*b^2*e^2 - 128*a^2*b*e^2 - 64*a^2*c*d^2 - 64*a*c^2*e^2 - 128*b*c^2*d^2 + 96*b^2*c*d^2 + 32*b^2*c*e^2 + 64*a*b^2*d*e - 64*a^2*b*d*e + 256*a*c^2*d*e + 256*a^2*c*d*e - 64*b*c^2*d*e + 64*b^2*c*d*e - 384*a*b*c*d*e))*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2) - 64*a^2*e^3 + 64*c^2*d^3 + 64*a^2*d*e^2 - 64*b^2*d*e^2 + 64*b^2*d^2*e - 64*c^2*d^2*e + 64*a*b*e^3 + 64*a*c*d^3 - 64*a*c*e^3 - 64*b*c*d^3 - 64*a*b*d^2*e + 64*a*c*d*e^2 - 64*a*c*d^2*e + 64*b*c*d*e^2))*(-(b^4*d^2 - b^4*e^2 + 8*a*c^3*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a^3*c*e^2 - b*e^2*(-(4*a*c - b^2)^3)^(1/2) + 2*a^2*b^2*e^2 + 8*a^2*c^2*d^2 - 8*a^2*c^2*e^2 - 2*b^2*c^2*d^2 - 2*a*b^3*d*e + 2*a*d*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e + 2*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^2*c*d^2 + 6*a*b^2*c*e^2 - 8*a*b*c^2*d*e + 8*a^2*b*c*d*e)/(2*(a^2*b^4 - b^6 + 16*a^2*c^4 + 32*a^3*c^3 + 16*a^4*c^2 + b^4*c^2 - 8*a*b^2*c^3 - 8*a^3*b^2*c - 32*a^2*b^2*c^2 + 10*a*b^4*c)))^(1/2)*2i","B"
510,1,205,144,2.854240,"\text{Not used}","int((a + b*tan(d + e*x))*(b^2 + a^2*tan(d + e*x)^2 + 2*a*b*tan(d + e*x))^2,x)","\frac{{\mathrm{tan}\left(d+e\,x\right)}^3\,\left(\frac{a^5}{3}+\frac{4\,a^3\,b^2}{3}\right)}{e}+\frac{\mathrm{tan}\left(d+e\,x\right)\,\left(-a^5+2\,a^3\,b^2+4\,a\,b^4\right)}{e}-\frac{\ln\left({\mathrm{tan}\left(d+e\,x\right)}^2+1\right)\,\left(\frac{3\,a^4\,b}{2}+a^2\,b^3-\frac{b^5}{2}\right)}{e}+\frac{{\mathrm{tan}\left(d+e\,x\right)}^2\,\left(\frac{3\,a^4\,b}{2}+3\,a^2\,b^3\right)}{e}+\frac{a^4\,b\,{\mathrm{tan}\left(d+e\,x\right)}^4}{4\,e}-\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(d+e\,x\right)\,\left(a^2-3\,b^2\right)\,\left(a^2+b^2\right)}{-a^5+2\,a^3\,b^2+3\,a\,b^4}\right)\,\left(a^2-3\,b^2\right)\,\left(a^2+b^2\right)}{e}","Not used",1,"(tan(d + e*x)^3*(a^5/3 + (4*a^3*b^2)/3))/e + (tan(d + e*x)*(4*a*b^4 - a^5 + 2*a^3*b^2))/e - (log(tan(d + e*x)^2 + 1)*((3*a^4*b)/2 - b^5/2 + a^2*b^3))/e + (tan(d + e*x)^2*((3*a^4*b)/2 + 3*a^2*b^3))/e + (a^4*b*tan(d + e*x)^4)/(4*e) - (a*atan((a*tan(d + e*x)*(a^2 - 3*b^2)*(a^2 + b^2))/(3*a*b^4 - a^5 + 2*a^3*b^2))*(a^2 - 3*b^2)*(a^2 + b^2))/e","B"
511,1,105,72,2.769658,"\text{Not used}","int((a + b*tan(d + e*x))*(b^2 + a^2*tan(d + e*x)^2 + 2*a*b*tan(d + e*x)),x)","\frac{\mathrm{tan}\left(d+e\,x\right)\,\left(a^3+2\,a\,b^2\right)}{e}+\frac{\ln\left({\mathrm{tan}\left(d+e\,x\right)}^2+1\right)\,\left(\frac{a^2\,b}{2}+\frac{b^3}{2}\right)}{e}+\frac{a^2\,b\,{\mathrm{tan}\left(d+e\,x\right)}^2}{2\,e}-\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(d+e\,x\right)\,\left(a^2+b^2\right)}{a^3+a\,b^2}\right)\,\left(a^2+b^2\right)}{e}","Not used",1,"(tan(d + e*x)*(2*a*b^2 + a^3))/e + (log(tan(d + e*x)^2 + 1)*((a^2*b)/2 + b^3/2))/e + (a^2*b*tan(d + e*x)^2)/(2*e) - (a*atan((a*tan(d + e*x)*(a^2 + b^2))/(a*b^2 + a^3))*(a^2 + b^2))/e","B"
512,1,152,101,3.088970,"\text{Not used}","int((a + b*tan(d + e*x))/(b^2 + a^2*tan(d + e*x)^2 + 2*a*b*tan(d + e*x)),x)","\frac{b\,\ln\left(b+a\,\mathrm{tan}\left(d+e\,x\right)\right)\,\left(3\,a^2-b^2\right)}{e\,{\left(a^2+b^2\right)}^2}-\frac{\ln\left(\mathrm{tan}\left(d+e\,x\right)+1{}\mathrm{i}\right)\,\left(a-b\,1{}\mathrm{i}\right)}{2\,e\,\left(-a^2\,1{}\mathrm{i}+2\,a\,b+b^2\,1{}\mathrm{i}\right)}-\frac{a^2-b^2}{e\,\left(a^2+b^2\right)\,\left(b+a\,\mathrm{tan}\left(d+e\,x\right)\right)}-\frac{\ln\left(\mathrm{tan}\left(d+e\,x\right)-\mathrm{i}\right)\,\left(a+b\,1{}\mathrm{i}\right)}{2\,e\,\left(a^2\,1{}\mathrm{i}+2\,a\,b-b^2\,1{}\mathrm{i}\right)}","Not used",1,"(b*log(b + a*tan(d + e*x))*(3*a^2 - b^2))/(e*(a^2 + b^2)^2) - (log(tan(d + e*x) + 1i)*(a - b*1i))/(2*e*(2*a*b - a^2*1i + b^2*1i)) - (a^2 - b^2)/(e*(a^2 + b^2)*(b + a*tan(d + e*x))) - (log(tan(d + e*x) - 1i)*(a + b*1i))/(2*e*(2*a*b + a^2*1i - b^2*1i))","B"
513,1,388,197,3.261491,"\text{Not used}","int((a + b*tan(d + e*x))/(b^2 + a^2*tan(d + e*x)^2 + 2*a*b*tan(d + e*x))^2,x)","\frac{\frac{{\mathrm{tan}\left(d+e\,x\right)}^2\,\left(a^6-6\,a^4\,b^2+a^2\,b^4\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{2\,a^6+5\,a^4\,b^2+40\,a^2\,b^4-11\,b^6}{6\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{\mathrm{tan}\left(d+e\,x\right)\,\left(a^5\,b-26\,a^3\,b^3+5\,a\,b^5\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}}{e\,\left(a^3\,{\mathrm{tan}\left(d+e\,x\right)}^3+3\,a^2\,b\,{\mathrm{tan}\left(d+e\,x\right)}^2+3\,a\,b^2\,\mathrm{tan}\left(d+e\,x\right)+b^3\right)}-\frac{\ln\left(b+a\,\mathrm{tan}\left(d+e\,x\right)\right)\,\left(\frac{5\,b}{{\left(a^2+b^2\right)}^2}-\frac{20\,b^3}{{\left(a^2+b^2\right)}^3}+\frac{16\,b^5}{{\left(a^2+b^2\right)}^4}\right)}{e}+\frac{\ln\left(\mathrm{tan}\left(d+e\,x\right)-\mathrm{i}\right)\,\left(a+b\,1{}\mathrm{i}\right)}{2\,e\,\left(a^4\,1{}\mathrm{i}+4\,a^3\,b-a^2\,b^2\,6{}\mathrm{i}-4\,a\,b^3+b^4\,1{}\mathrm{i}\right)}-\frac{\ln\left(\mathrm{tan}\left(d+e\,x\right)+1{}\mathrm{i}\right)\,\left(a-b\,1{}\mathrm{i}\right)}{2\,e\,\left(a^4\,1{}\mathrm{i}-4\,a^3\,b-a^2\,b^2\,6{}\mathrm{i}+4\,a\,b^3+b^4\,1{}\mathrm{i}\right)}","Not used",1,"((tan(d + e*x)^2*(a^6 + a^2*b^4 - 6*a^4*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (2*a^6 - 11*b^6 + 40*a^2*b^4 + 5*a^4*b^2)/(6*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (tan(d + e*x)*(5*a*b^5 + a^5*b - 26*a^3*b^3))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))/(e*(b^3 + a^3*tan(d + e*x)^3 + 3*a^2*b*tan(d + e*x)^2 + 3*a*b^2*tan(d + e*x))) - (log(b + a*tan(d + e*x))*((5*b)/(a^2 + b^2)^2 - (20*b^3)/(a^2 + b^2)^3 + (16*b^5)/(a^2 + b^2)^4))/e + (log(tan(d + e*x) - 1i)*(a + b*1i))/(2*e*(4*a^3*b - 4*a*b^3 + a^4*1i + b^4*1i - a^2*b^2*6i)) - (log(tan(d + e*x) + 1i)*(a - b*1i))/(2*e*(4*a*b^3 - 4*a^3*b + a^4*1i + b^4*1i - a^2*b^2*6i))","B"
514,0,-1,284,0.000000,"\text{Not used}","int((a + b*tan(d + e*x))*(b^2 + a^2*tan(d + e*x)^2 + 2*a*b*tan(d + e*x))^(3/2),x)","\int \left(a+b\,\mathrm{tan}\left(d+e\,x\right)\right)\,{\left(a^2\,{\mathrm{tan}\left(d+e\,x\right)}^2+2\,a\,b\,\mathrm{tan}\left(d+e\,x\right)+b^2\right)}^{3/2} \,d x","Not used",1,"int((a + b*tan(d + e*x))*(b^2 + a^2*tan(d + e*x)^2 + 2*a*b*tan(d + e*x))^(3/2), x)","F"
515,0,-1,122,0.000000,"\text{Not used}","int((a + b*tan(d + e*x))*(b^2 + a^2*tan(d + e*x)^2 + 2*a*b*tan(d + e*x))^(1/2),x)","\int \left(a+b\,\mathrm{tan}\left(d+e\,x\right)\right)\,\sqrt{a^2\,{\mathrm{tan}\left(d+e\,x\right)}^2+2\,a\,b\,\mathrm{tan}\left(d+e\,x\right)+b^2} \,d x","Not used",1,"int((a + b*tan(d + e*x))*(b^2 + a^2*tan(d + e*x)^2 + 2*a*b*tan(d + e*x))^(1/2), x)","F"
516,0,-1,138,0.000000,"\text{Not used}","int((a + b*tan(d + e*x))/(b^2 + a^2*tan(d + e*x)^2 + 2*a*b*tan(d + e*x))^(1/2),x)","\int \frac{a+b\,\mathrm{tan}\left(d+e\,x\right)}{\sqrt{a^2\,{\mathrm{tan}\left(d+e\,x\right)}^2+2\,a\,b\,\mathrm{tan}\left(d+e\,x\right)+b^2}} \,d x","Not used",1,"int((a + b*tan(d + e*x))/(b^2 + a^2*tan(d + e*x)^2 + 2*a*b*tan(d + e*x))^(1/2), x)","F"
517,0,-1,316,0.000000,"\text{Not used}","int((a + b*tan(d + e*x))/(b^2 + a^2*tan(d + e*x)^2 + 2*a*b*tan(d + e*x))^(3/2),x)","\int \frac{a+b\,\mathrm{tan}\left(d+e\,x\right)}{{\left(a^2\,{\mathrm{tan}\left(d+e\,x\right)}^2+2\,a\,b\,\mathrm{tan}\left(d+e\,x\right)+b^2\right)}^{3/2}} \,d x","Not used",1,"int((a + b*tan(d + e*x))/(b^2 + a^2*tan(d + e*x)^2 + 2*a*b*tan(d + e*x))^(3/2), x)","F"
518,1,323,184,3.304320,"\text{Not used}","int((a + b/cos(d + e*x))*(b^2 + a^2/cos(d + e*x)^2 + (2*a*b)/cos(d + e*x))^2,x)","\frac{2\,a^5\,\sin\left(d+e\,x\right)}{3\,e\,\cos\left(d+e\,x\right)}+\frac{a^5\,\sin\left(d+e\,x\right)}{3\,e\,{\cos\left(d+e\,x\right)}^3}+\frac{2\,a\,b^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{\cos\left(\frac{d}{2}+\frac{e\,x}{2}\right)}\right)}{e}+\frac{4\,a\,b^4\,\sin\left(d+e\,x\right)}{e\,\cos\left(d+e\,x\right)}+\frac{19\,a^4\,b\,\sin\left(d+e\,x\right)}{8\,e\,{\cos\left(d+e\,x\right)}^2}+\frac{a^4\,b\,\sin\left(d+e\,x\right)}{4\,e\,{\cos\left(d+e\,x\right)}^4}+\frac{26\,a^3\,b^2\,\sin\left(d+e\,x\right)}{3\,e\,\cos\left(d+e\,x\right)}+\frac{3\,a^2\,b^3\,\sin\left(d+e\,x\right)}{e\,{\cos\left(d+e\,x\right)}^2}+\frac{4\,a^3\,b^2\,\sin\left(d+e\,x\right)}{3\,e\,{\cos\left(d+e\,x\right)}^3}-\frac{b^5\,\mathrm{atan}\left(\frac{\sin\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{d}{2}+\frac{e\,x}{2}\right)}\right)\,2{}\mathrm{i}}{e}-\frac{a^2\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{d}{2}+\frac{e\,x}{2}\right)}\right)\,14{}\mathrm{i}}{e}-\frac{a^4\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{d}{2}+\frac{e\,x}{2}\right)}\right)\,19{}\mathrm{i}}{4\,e}","Not used",1,"(2*a^5*sin(d + e*x))/(3*e*cos(d + e*x)) - (b^5*atan((sin(d/2 + (e*x)/2)*1i)/cos(d/2 + (e*x)/2))*2i)/e + (a^5*sin(d + e*x))/(3*e*cos(d + e*x)^3) - (a^2*b^3*atan((sin(d/2 + (e*x)/2)*1i)/cos(d/2 + (e*x)/2))*14i)/e + (2*a*b^4*atan(sin(d/2 + (e*x)/2)/cos(d/2 + (e*x)/2)))/e - (a^4*b*atan((sin(d/2 + (e*x)/2)*1i)/cos(d/2 + (e*x)/2))*19i)/(4*e) + (4*a*b^4*sin(d + e*x))/(e*cos(d + e*x)) + (19*a^4*b*sin(d + e*x))/(8*e*cos(d + e*x)^2) + (a^4*b*sin(d + e*x))/(4*e*cos(d + e*x)^4) + (26*a^3*b^2*sin(d + e*x))/(3*e*cos(d + e*x)) + (3*a^2*b^3*sin(d + e*x))/(e*cos(d + e*x)^2) + (4*a^3*b^2*sin(d + e*x))/(3*e*cos(d + e*x)^3)","B"
519,1,160,76,2.908021,"\text{Not used}","int((a + b/cos(d + e*x))*(b^2 + a^2/cos(d + e*x)^2 + (2*a*b)/cos(d + e*x)),x)","\frac{2\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{\cos\left(\frac{d}{2}+\frac{e\,x}{2}\right)}\right)}{e}+\frac{a^3\,\sin\left(d+e\,x\right)}{e\,\cos\left(d+e\,x\right)}+\frac{2\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{\cos\left(\frac{d}{2}+\frac{e\,x}{2}\right)}\right)}{e}+\frac{5\,a^2\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{\cos\left(\frac{d}{2}+\frac{e\,x}{2}\right)}\right)}{e}+\frac{2\,a\,b^2\,\sin\left(d+e\,x\right)}{e\,\cos\left(d+e\,x\right)}+\frac{a^2\,b\,\sin\left(d+e\,x\right)}{2\,e\,{\cos\left(d+e\,x\right)}^2}","Not used",1,"(2*b^3*atanh(sin(d/2 + (e*x)/2)/cos(d/2 + (e*x)/2)))/e + (a^3*sin(d + e*x))/(e*cos(d + e*x)) + (2*a*b^2*atan(sin(d/2 + (e*x)/2)/cos(d/2 + (e*x)/2)))/e + (5*a^2*b*atanh(sin(d/2 + (e*x)/2)/cos(d/2 + (e*x)/2)))/e + (2*a*b^2*sin(d + e*x))/(e*cos(d + e*x)) + (a^2*b*sin(d + e*x))/(2*e*cos(d + e*x)^2)","B"
520,1,444,92,3.023475,"\text{Not used}","int((a + b/cos(d + e*x))/(b^2 + a^2/cos(d + e*x)^2 + (2*a*b)/cos(d + e*x)),x)","\frac{2\,\mathrm{atanh}\left(\frac{64\,a^3\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\sqrt{b^2-a^2}}{64\,a^4-128\,a^3\,b+128\,a\,b^3-64\,b^4}-\frac{192\,a^2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\sqrt{b^2-a^2}}{128\,a\,b^2-128\,a^3-64\,b^3+\frac{64\,a^4}{b}}+\frac{192\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\sqrt{b^2-a^2}}{128\,a\,b-64\,b^2-\frac{128\,a^3}{b}+\frac{64\,a^4}{b^2}}-\frac{64\,b\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\sqrt{b^2-a^2}}{128\,a\,b-64\,b^2-\frac{128\,a^3}{b}+\frac{64\,a^4}{b^2}}\right)\,\sqrt{b^2-a^2}}{b^2\,e}-\frac{2\,a\,\mathrm{atan}\left(\frac{64\,a^2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{64\,a\,b-64\,a^2-\frac{64\,a^3}{b}+\frac{64\,a^4}{b^2}}+\frac{64\,a^3\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{64\,a\,b^2-64\,a^2\,b-64\,a^3+\frac{64\,a^4}{b}}-\frac{64\,a^4\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{64\,a^4-64\,a^3\,b-64\,a^2\,b^2+64\,a\,b^3}-\frac{64\,a\,b\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{64\,a\,b-64\,a^2-\frac{64\,a^3}{b}+\frac{64\,a^4}{b^2}}\right)}{b^2\,e}-\frac{2\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}{b\,e\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+a+b\right)}","Not used",1,"(2*atanh((64*a^3*tan(d/2 + (e*x)/2)*(b^2 - a^2)^(1/2))/(128*a*b^3 - 128*a^3*b + 64*a^4 - 64*b^4) - (192*a^2*tan(d/2 + (e*x)/2)*(b^2 - a^2)^(1/2))/(128*a*b^2 - 128*a^3 - 64*b^3 + (64*a^4)/b) + (192*a*tan(d/2 + (e*x)/2)*(b^2 - a^2)^(1/2))/(128*a*b - 64*b^2 - (128*a^3)/b + (64*a^4)/b^2) - (64*b*tan(d/2 + (e*x)/2)*(b^2 - a^2)^(1/2))/(128*a*b - 64*b^2 - (128*a^3)/b + (64*a^4)/b^2))*(b^2 - a^2)^(1/2))/(b^2*e) - (2*a*atan((64*a^2*tan(d/2 + (e*x)/2))/(64*a*b - 64*a^2 - (64*a^3)/b + (64*a^4)/b^2) + (64*a^3*tan(d/2 + (e*x)/2))/(64*a*b^2 - 64*a^2*b - 64*a^3 + (64*a^4)/b) - (64*a^4*tan(d/2 + (e*x)/2))/(64*a*b^3 - 64*a^3*b + 64*a^4 - 64*a^2*b^2) - (64*a*b*tan(d/2 + (e*x)/2))/(64*a*b - 64*a^2 - (64*a^3)/b + (64*a^4)/b^2)))/(b^2*e) - (2*a*tan(d/2 + (e*x)/2))/(b*e*(a + b + tan(d/2 + (e*x)/2)^2*(a - b)))","B"
521,1,5469,230,11.473141,"\text{Not used}","int((a + b/cos(d + e*x))/(b^2 + a^2/cos(d + e*x)^2 + (2*a*b)/cos(d + e*x))^2,x)","-\frac{\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a^5+a^4\,b-4\,a^3\,b^2-3\,a^2\,b^3+6\,a\,b^4\right)}{a^2\,b^3-2\,a\,b^4+b^5}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(2\,a^5-a^4\,b-4\,a^3\,b^2+3\,a^2\,b^3+6\,a\,b^4\right)}{b^3\,{\left(a+b\right)}^2}+\frac{4\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(3\,a^5-8\,a^3\,b^2+9\,a\,b^4\right)}{3\,\left(a\,b^3-b^4\right)\,\left(a+b\right)}}{e\,\left(3\,a\,b^2-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}-\frac{2\,a\,\mathrm{atan}\left(\frac{\frac{a\,\left(-\frac{8\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-8\,a^{12}+8\,a^{11}\,b+32\,a^{10}\,b^2-32\,a^9\,b^3-45\,a^8\,b^4+48\,a^7\,b^5+30\,a^6\,b^6-32\,a^5\,b^7-17\,a^4\,b^8+8\,a^3\,b^9+8\,a^2\,b^{10}-4\,b^{12}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{a\,\left(\frac{8\,\left(-4\,a^{10}\,b^8+2\,a^9\,b^9+18\,a^8\,b^{10}-10\,a^7\,b^{11}-30\,a^6\,b^{12}+14\,a^5\,b^{13}+26\,a^4\,b^{14}-6\,a^3\,b^{15}-14\,a^2\,b^{16}+4\,b^{18}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)\,8{}\mathrm{i}}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,1{}\mathrm{i}}{b^4}\right)}{b^4}-\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-8\,a^{12}+8\,a^{11}\,b+32\,a^{10}\,b^2-32\,a^9\,b^3-45\,a^8\,b^4+48\,a^7\,b^5+30\,a^6\,b^6-32\,a^5\,b^7-17\,a^4\,b^8+8\,a^3\,b^9+8\,a^2\,b^{10}-4\,b^{12}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{a\,\left(\frac{8\,\left(-4\,a^{10}\,b^8+2\,a^9\,b^9+18\,a^8\,b^{10}-10\,a^7\,b^{11}-30\,a^6\,b^{12}+14\,a^5\,b^{13}+26\,a^4\,b^{14}-6\,a^3\,b^{15}-14\,a^2\,b^{16}+4\,b^{18}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)\,8{}\mathrm{i}}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,1{}\mathrm{i}}{b^4}\right)}{b^4}}{-\frac{16\,\left(4\,a^{12}-2\,a^{11}\,b-18\,a^{10}\,b^2+7\,a^9\,b^3+30\,a^8\,b^4-12\,a^7\,b^5-26\,a^6\,b^6+15\,a^5\,b^7+14\,a^4\,b^8-8\,a^3\,b^9-4\,a^2\,b^{10}+4\,a\,b^{11}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{a\,\left(-\frac{8\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-8\,a^{12}+8\,a^{11}\,b+32\,a^{10}\,b^2-32\,a^9\,b^3-45\,a^8\,b^4+48\,a^7\,b^5+30\,a^6\,b^6-32\,a^5\,b^7-17\,a^4\,b^8+8\,a^3\,b^9+8\,a^2\,b^{10}-4\,b^{12}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{a\,\left(\frac{8\,\left(-4\,a^{10}\,b^8+2\,a^9\,b^9+18\,a^8\,b^{10}-10\,a^7\,b^{11}-30\,a^6\,b^{12}+14\,a^5\,b^{13}+26\,a^4\,b^{14}-6\,a^3\,b^{15}-14\,a^2\,b^{16}+4\,b^{18}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)\,8{}\mathrm{i}}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,1{}\mathrm{i}}{b^4}\right)\,1{}\mathrm{i}}{b^4}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-8\,a^{12}+8\,a^{11}\,b+32\,a^{10}\,b^2-32\,a^9\,b^3-45\,a^8\,b^4+48\,a^7\,b^5+30\,a^6\,b^6-32\,a^5\,b^7-17\,a^4\,b^8+8\,a^3\,b^9+8\,a^2\,b^{10}-4\,b^{12}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{a\,\left(\frac{8\,\left(-4\,a^{10}\,b^8+2\,a^9\,b^9+18\,a^8\,b^{10}-10\,a^7\,b^{11}-30\,a^6\,b^{12}+14\,a^5\,b^{13}+26\,a^4\,b^{14}-6\,a^3\,b^{15}-14\,a^2\,b^{16}+4\,b^{18}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)\,8{}\mathrm{i}}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,1{}\mathrm{i}}{b^4}\right)\,1{}\mathrm{i}}{b^4}}\right)}{b^4\,e}-\frac{\mathrm{atan}\left(\frac{\frac{\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-8\,a^{12}+8\,a^{11}\,b+32\,a^{10}\,b^2-32\,a^9\,b^3-45\,a^8\,b^4+48\,a^7\,b^5+30\,a^6\,b^6-32\,a^5\,b^7-17\,a^4\,b^8+8\,a^3\,b^9+8\,a^2\,b^{10}-4\,b^{12}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\left(\frac{8\,\left(-4\,a^{10}\,b^8+2\,a^9\,b^9+18\,a^8\,b^{10}-10\,a^7\,b^{11}-30\,a^6\,b^{12}+14\,a^5\,b^{13}+26\,a^4\,b^{14}-6\,a^3\,b^{15}-14\,a^2\,b^{16}+4\,b^{18}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{4\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-a^2\,b^2+b^4\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-a^2\,b^2+b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(2\,a^4-a^2\,b^2+b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}+\frac{\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-8\,a^{12}+8\,a^{11}\,b+32\,a^{10}\,b^2-32\,a^9\,b^3-45\,a^8\,b^4+48\,a^7\,b^5+30\,a^6\,b^6-32\,a^5\,b^7-17\,a^4\,b^8+8\,a^3\,b^9+8\,a^2\,b^{10}-4\,b^{12}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{\left(\frac{8\,\left(-4\,a^{10}\,b^8+2\,a^9\,b^9+18\,a^8\,b^{10}-10\,a^7\,b^{11}-30\,a^6\,b^{12}+14\,a^5\,b^{13}+26\,a^4\,b^{14}-6\,a^3\,b^{15}-14\,a^2\,b^{16}+4\,b^{18}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{4\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-a^2\,b^2+b^4\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-a^2\,b^2+b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(2\,a^4-a^2\,b^2+b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}{\frac{16\,\left(4\,a^{12}-2\,a^{11}\,b-18\,a^{10}\,b^2+7\,a^9\,b^3+30\,a^8\,b^4-12\,a^7\,b^5-26\,a^6\,b^6+15\,a^5\,b^7+14\,a^4\,b^8-8\,a^3\,b^9-4\,a^2\,b^{10}+4\,a\,b^{11}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-8\,a^{12}+8\,a^{11}\,b+32\,a^{10}\,b^2-32\,a^9\,b^3-45\,a^8\,b^4+48\,a^7\,b^5+30\,a^6\,b^6-32\,a^5\,b^7-17\,a^4\,b^8+8\,a^3\,b^9+8\,a^2\,b^{10}-4\,b^{12}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\left(\frac{8\,\left(-4\,a^{10}\,b^8+2\,a^9\,b^9+18\,a^8\,b^{10}-10\,a^7\,b^{11}-30\,a^6\,b^{12}+14\,a^5\,b^{13}+26\,a^4\,b^{14}-6\,a^3\,b^{15}-14\,a^2\,b^{16}+4\,b^{18}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{4\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-a^2\,b^2+b^4\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-a^2\,b^2+b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(2\,a^4-a^2\,b^2+b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}-\frac{\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-8\,a^{12}+8\,a^{11}\,b+32\,a^{10}\,b^2-32\,a^9\,b^3-45\,a^8\,b^4+48\,a^7\,b^5+30\,a^6\,b^6-32\,a^5\,b^7-17\,a^4\,b^8+8\,a^3\,b^9+8\,a^2\,b^{10}-4\,b^{12}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{\left(\frac{8\,\left(-4\,a^{10}\,b^8+2\,a^9\,b^9+18\,a^8\,b^{10}-10\,a^7\,b^{11}-30\,a^6\,b^{12}+14\,a^5\,b^{13}+26\,a^4\,b^{14}-6\,a^3\,b^{15}-14\,a^2\,b^{16}+4\,b^{18}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{4\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-a^2\,b^2+b^4\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-a^2\,b^2+b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(2\,a^4-a^2\,b^2+b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}\right)\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-a^2\,b^2+b^4\right)\,1{}\mathrm{i}}{e\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}","Not used",1,"- ((tan(d/2 + (e*x)/2)*(6*a*b^4 + a^4*b + 2*a^5 - 3*a^2*b^3 - 4*a^3*b^2))/(b^5 - 2*a*b^4 + a^2*b^3) + (tan(d/2 + (e*x)/2)^5*(6*a*b^4 - a^4*b + 2*a^5 + 3*a^2*b^3 - 4*a^3*b^2))/(b^3*(a + b)^2) + (4*tan(d/2 + (e*x)/2)^3*(9*a*b^4 + 3*a^5 - 8*a^3*b^2))/(3*(a*b^3 - b^4)*(a + b)))/(e*(3*a*b^2 - tan(d/2 + (e*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) - tan(d/2 + (e*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) + 3*a^2*b + a^3 + b^3 + tan(d/2 + (e*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) - (2*a*atan(((a*((a*((8*(4*b^18 - 14*a^2*b^16 - 6*a^3*b^15 + 26*a^4*b^14 + 14*a^5*b^13 - 30*a^6*b^12 - 10*a^7*b^11 + 18*a^8*b^10 + 2*a^9*b^9 - 4*a^10*b^8))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (a*tan(d/2 + (e*x)/2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8)*8i)/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*1i)/b^4 - (8*tan(d/2 + (e*x)/2)*(8*a^11*b - 8*a^12 - 4*b^12 + 8*a^2*b^10 + 8*a^3*b^9 - 17*a^4*b^8 - 32*a^5*b^7 + 30*a^6*b^6 + 48*a^7*b^5 - 45*a^8*b^4 - 32*a^9*b^3 + 32*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))/b^4 - (a*((a*((8*(4*b^18 - 14*a^2*b^16 - 6*a^3*b^15 + 26*a^4*b^14 + 14*a^5*b^13 - 30*a^6*b^12 - 10*a^7*b^11 + 18*a^8*b^10 + 2*a^9*b^9 - 4*a^10*b^8))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (a*tan(d/2 + (e*x)/2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8)*8i)/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*1i)/b^4 + (8*tan(d/2 + (e*x)/2)*(8*a^11*b - 8*a^12 - 4*b^12 + 8*a^2*b^10 + 8*a^3*b^9 - 17*a^4*b^8 - 32*a^5*b^7 + 30*a^6*b^6 + 48*a^7*b^5 - 45*a^8*b^4 - 32*a^9*b^3 + 32*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))/b^4)/((a*((a*((8*(4*b^18 - 14*a^2*b^16 - 6*a^3*b^15 + 26*a^4*b^14 + 14*a^5*b^13 - 30*a^6*b^12 - 10*a^7*b^11 + 18*a^8*b^10 + 2*a^9*b^9 - 4*a^10*b^8))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (a*tan(d/2 + (e*x)/2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8)*8i)/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*1i)/b^4 - (8*tan(d/2 + (e*x)/2)*(8*a^11*b - 8*a^12 - 4*b^12 + 8*a^2*b^10 + 8*a^3*b^9 - 17*a^4*b^8 - 32*a^5*b^7 + 30*a^6*b^6 + 48*a^7*b^5 - 45*a^8*b^4 - 32*a^9*b^3 + 32*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6))*1i)/b^4 - (16*(4*a*b^11 - 2*a^11*b + 4*a^12 - 4*a^2*b^10 - 8*a^3*b^9 + 14*a^4*b^8 + 15*a^5*b^7 - 26*a^6*b^6 - 12*a^7*b^5 + 30*a^8*b^4 + 7*a^9*b^3 - 18*a^10*b^2))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (a*((a*((8*(4*b^18 - 14*a^2*b^16 - 6*a^3*b^15 + 26*a^4*b^14 + 14*a^5*b^13 - 30*a^6*b^12 - 10*a^7*b^11 + 18*a^8*b^10 + 2*a^9*b^9 - 4*a^10*b^8))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (a*tan(d/2 + (e*x)/2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8)*8i)/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*1i)/b^4 + (8*tan(d/2 + (e*x)/2)*(8*a^11*b - 8*a^12 - 4*b^12 + 8*a^2*b^10 + 8*a^3*b^9 - 17*a^4*b^8 - 32*a^5*b^7 + 30*a^6*b^6 + 48*a^7*b^5 - 45*a^8*b^4 - 32*a^9*b^3 + 32*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6))*1i)/b^4)))/(b^4*e) - (atan((((a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(d/2 + (e*x)/2)*(8*a^11*b - 8*a^12 - 4*b^12 + 8*a^2*b^10 + 8*a^3*b^9 - 17*a^4*b^8 - 32*a^5*b^7 + 30*a^6*b^6 + 48*a^7*b^5 - 45*a^8*b^4 - 32*a^9*b^3 + 32*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (((8*(4*b^18 - 14*a^2*b^16 - 6*a^3*b^15 + 26*a^4*b^14 + 14*a^5*b^13 - 30*a^6*b^12 - 10*a^7*b^11 + 18*a^8*b^10 + 2*a^9*b^9 - 4*a^10*b^8))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (4*tan(d/2 + (e*x)/2)*(a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + b^4 - a^2*b^2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + b^4 - a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(2*a^4 + b^4 - a^2*b^2)*1i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) + ((a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(d/2 + (e*x)/2)*(8*a^11*b - 8*a^12 - 4*b^12 + 8*a^2*b^10 + 8*a^3*b^9 - 17*a^4*b^8 - 32*a^5*b^7 + 30*a^6*b^6 + 48*a^7*b^5 - 45*a^8*b^4 - 32*a^9*b^3 + 32*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (((8*(4*b^18 - 14*a^2*b^16 - 6*a^3*b^15 + 26*a^4*b^14 + 14*a^5*b^13 - 30*a^6*b^12 - 10*a^7*b^11 + 18*a^8*b^10 + 2*a^9*b^9 - 4*a^10*b^8))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (4*tan(d/2 + (e*x)/2)*(a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + b^4 - a^2*b^2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + b^4 - a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(2*a^4 + b^4 - a^2*b^2)*1i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))/((16*(4*a*b^11 - 2*a^11*b + 4*a^12 - 4*a^2*b^10 - 8*a^3*b^9 + 14*a^4*b^8 + 15*a^5*b^7 - 26*a^6*b^6 - 12*a^7*b^5 + 30*a^8*b^4 + 7*a^9*b^3 - 18*a^10*b^2))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + ((a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(d/2 + (e*x)/2)*(8*a^11*b - 8*a^12 - 4*b^12 + 8*a^2*b^10 + 8*a^3*b^9 - 17*a^4*b^8 - 32*a^5*b^7 + 30*a^6*b^6 + 48*a^7*b^5 - 45*a^8*b^4 - 32*a^9*b^3 + 32*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (((8*(4*b^18 - 14*a^2*b^16 - 6*a^3*b^15 + 26*a^4*b^14 + 14*a^5*b^13 - 30*a^6*b^12 - 10*a^7*b^11 + 18*a^8*b^10 + 2*a^9*b^9 - 4*a^10*b^8))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (4*tan(d/2 + (e*x)/2)*(a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + b^4 - a^2*b^2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + b^4 - a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(2*a^4 + b^4 - a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) - ((a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(d/2 + (e*x)/2)*(8*a^11*b - 8*a^12 - 4*b^12 + 8*a^2*b^10 + 8*a^3*b^9 - 17*a^4*b^8 - 32*a^5*b^7 + 30*a^6*b^6 + 48*a^7*b^5 - 45*a^8*b^4 - 32*a^9*b^3 + 32*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (((8*(4*b^18 - 14*a^2*b^16 - 6*a^3*b^15 + 26*a^4*b^14 + 14*a^5*b^13 - 30*a^6*b^12 - 10*a^7*b^11 + 18*a^8*b^10 + 2*a^9*b^9 - 4*a^10*b^8))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (4*tan(d/2 + (e*x)/2)*(a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + b^4 - a^2*b^2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + b^4 - a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(2*a^4 + b^4 - a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))))*(a^2 - 2*b^2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + b^4 - a^2*b^2)*1i)/(e*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))","B"
522,0,-1,359,0.000000,"\text{Not used}","int((a + b/cos(d + e*x))*(b^2 + a^2/cos(d + e*x)^2 + (2*a*b)/cos(d + e*x))^(3/2),x)","\int \left(a+\frac{b}{\cos\left(d+e\,x\right)}\right)\,{\left(b^2+\frac{a^2}{{\cos\left(d+e\,x\right)}^2}+\frac{2\,a\,b}{\cos\left(d+e\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((a + b/cos(d + e*x))*(b^2 + a^2/cos(d + e*x)^2 + (2*a*b)/cos(d + e*x))^(3/2), x)","F"
523,0,-1,173,0.000000,"\text{Not used}","int((a + b/cos(d + e*x))*(b^2 + a^2/cos(d + e*x)^2 + (2*a*b)/cos(d + e*x))^(1/2),x)","\int \left(a+\frac{b}{\cos\left(d+e\,x\right)}\right)\,\sqrt{b^2+\frac{a^2}{{\cos\left(d+e\,x\right)}^2}+\frac{2\,a\,b}{\cos\left(d+e\,x\right)}} \,d x","Not used",1,"int((a + b/cos(d + e*x))*(b^2 + a^2/cos(d + e*x)^2 + (2*a*b)/cos(d + e*x))^(1/2), x)","F"
524,0,-1,142,0.000000,"\text{Not used}","int((a + b/cos(d + e*x))/(b^2 + a^2/cos(d + e*x)^2 + (2*a*b)/cos(d + e*x))^(1/2),x)","\int \frac{a+\frac{b}{\cos\left(d+e\,x\right)}}{\sqrt{b^2+\frac{a^2}{{\cos\left(d+e\,x\right)}^2}+\frac{2\,a\,b}{\cos\left(d+e\,x\right)}}} \,d x","Not used",1,"int((a + b/cos(d + e*x))/(b^2 + a^2/cos(d + e*x)^2 + (2*a*b)/cos(d + e*x))^(1/2), x)","F"
525,0,-1,330,0.000000,"\text{Not used}","int((a + b/cos(d + e*x))/(b^2 + a^2/cos(d + e*x)^2 + (2*a*b)/cos(d + e*x))^(3/2),x)","\int \frac{a+\frac{b}{\cos\left(d+e\,x\right)}}{{\left(b^2+\frac{a^2}{{\cos\left(d+e\,x\right)}^2}+\frac{2\,a\,b}{\cos\left(d+e\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((a + b/cos(d + e*x))/(b^2 + a^2/cos(d + e*x)^2 + (2*a*b)/cos(d + e*x))^(3/2), x)","F"
526,1,16,17,2.760088,"\text{Not used}","int((cos(x) - sin(x)*1i)/(cos(x) + sin(x)*1i),x)","-\frac{\cos\left(x\right)}{-\sin\left(x\right)+\cos\left(x\right)\,1{}\mathrm{i}}","Not used",1,"-cos(x)/(cos(x)*1i - sin(x))","B"
527,1,13,17,2.744889,"\text{Not used}","int((cos(x) + sin(x)*1i)/(cos(x) - sin(x)*1i),x)","\frac{\sin\left(x\right)}{\cos\left(x\right)-\sin\left(x\right)\,1{}\mathrm{i}}","Not used",1,"sin(x)/(cos(x) - sin(x)*1i)","B"
528,1,32,6,2.918065,"\text{Not used}","int((cos(x) - sin(x))/(cos(x) + sin(x)),x)","2\,\mathrm{atanh}\left(\frac{128\,\mathrm{tan}\left(\frac{x}{2}\right)+128}{16\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+32\,\mathrm{tan}\left(\frac{x}{2}\right)+48}-3\right)","Not used",1,"2*atanh((128*tan(x/2) + 128)/(32*tan(x/2) + 16*tan(x/2)^2 + 48) - 3)","B"
529,1,1976,47,12.819231,"\text{Not used}","int((B*cos(x) + C*sin(x))/(b*cos(x) + c*sin(x)),x)","\frac{\ln\left(-b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,c\,\mathrm{tan}\left(\frac{x}{2}\right)+b\right)\,\left(B\,c-C\,b\right)}{b^2+c^2}-\frac{\ln\left(\frac{1}{\cos\left(x\right)+1}\right)\,\left(2\,B\,c-2\,C\,b\right)}{2\,\left(b^2+c^2\right)}+\frac{2\,\mathrm{atan}\left(\frac{\left(\frac{\left(32\,B\,C^2\,b^2-\frac{\left(2\,B\,c-2\,C\,b\right)\,\left(\frac{\left(2\,B\,c-2\,C\,b\right)\,\left(64\,B\,b^2\,c^2-32\,B\,b^4+32\,C\,b\,c^3-64\,C\,b^3\,c+\frac{\left(2\,B\,c-2\,C\,b\right)\,\left(96\,b^4\,c+96\,b^2\,c^3\right)}{2\,\left(b^2+c^2\right)}\right)}{2\,\left(b^2+c^2\right)}-32\,C^2\,b^2\,c-32\,B^2\,b^2\,c+64\,B\,C\,b^3+64\,B\,C\,b\,c^2\right)}{2\,\left(b^2+c^2\right)}+\frac{\left(B\,b+C\,c\right)\,\left(\frac{\left(B\,b+C\,c\right)\,\left(64\,B\,b^2\,c^2-32\,B\,b^4+32\,C\,b\,c^3-64\,C\,b^3\,c+\frac{\left(2\,B\,c-2\,C\,b\right)\,\left(96\,b^4\,c+96\,b^2\,c^3\right)}{2\,\left(b^2+c^2\right)}\right)}{b^2+c^2}+\frac{\left(B\,b+C\,c\right)\,\left(2\,B\,c-2\,C\,b\right)\,\left(96\,b^4\,c+96\,b^2\,c^3\right)}{2\,{\left(b^2+c^2\right)}^2}\right)}{b^2+c^2}-32\,B^2\,C\,b\,c+\frac{{\left(B\,b+C\,c\right)}^2\,\left(2\,B\,c-2\,C\,b\right)\,\left(96\,b^4\,c+96\,b^2\,c^3\right)}{2\,{\left(b^2+c^2\right)}^3}\right)\,\left(-6\,B^2\,b^3\,c+12\,B^2\,b\,c^3+4\,B\,C\,b^4-28\,B\,C\,b^2\,c^2+4\,B\,C\,c^4+12\,C^2\,b^3\,c-6\,C^2\,b\,c^3\right)}{{\left(b^2+c^2\right)}^2\,{\left(B^2\,b^2+4\,B^2\,c^2-6\,B\,C\,b\,c+4\,C^2\,b^2+C^2\,c^2\right)}^2}-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{\left(32\,B^3\,b\,c-32\,B^2\,C\,b^2-64\,C^3\,b^2+\frac{\left(2\,B\,c-2\,C\,b\right)\,\left(32\,B^2\,b^3-96\,B^2\,b\,c^2+64\,C^2\,b\,c^2-\frac{\left(2\,B\,c-2\,C\,b\right)\,\left(32\,C\,b^2\,c^2-64\,C\,b^4+32\,B\,b\,c^3+128\,B\,b^3\,c-\frac{\left(2\,B\,c-2\,C\,b\right)\,\left(96\,b^3\,c^2+96\,b\,c^4\right)}{2\,\left(b^2+c^2\right)}\right)}{2\,\left(b^2+c^2\right)}+192\,B\,C\,b^2\,c\right)}{2\,\left(b^2+c^2\right)}+\frac{\left(B\,b+C\,c\right)\,\left(\frac{\left(B\,b+C\,c\right)\,\left(32\,C\,b^2\,c^2-64\,C\,b^4+32\,B\,b\,c^3+128\,B\,b^3\,c-\frac{\left(2\,B\,c-2\,C\,b\right)\,\left(96\,b^3\,c^2+96\,b\,c^4\right)}{2\,\left(b^2+c^2\right)}\right)}{b^2+c^2}-\frac{\left(B\,b+C\,c\right)\,\left(2\,B\,c-2\,C\,b\right)\,\left(96\,b^3\,c^2+96\,b\,c^4\right)}{2\,{\left(b^2+c^2\right)}^2}\right)}{b^2+c^2}+64\,B\,C^2\,b\,c-\frac{{\left(B\,b+C\,c\right)}^2\,\left(2\,B\,c-2\,C\,b\right)\,\left(96\,b^3\,c^2+96\,b\,c^4\right)}{2\,{\left(b^2+c^2\right)}^3}\right)\,\left(-6\,B^2\,b^3\,c+12\,B^2\,b\,c^3+4\,B\,C\,b^4-28\,B\,C\,b^2\,c^2+4\,B\,C\,c^4+12\,C^2\,b^3\,c-6\,C^2\,b\,c^3\right)}{{\left(b^2+c^2\right)}^2\,{\left(B^2\,b^2+4\,B^2\,c^2-6\,B\,C\,b\,c+4\,C^2\,b^2+C^2\,c^2\right)}^2}+\frac{\left(\frac{{\left(B\,b+C\,c\right)}^3\,\left(96\,b^3\,c^2+96\,b\,c^4\right)}{{\left(b^2+c^2\right)}^3}-\frac{\left(B\,b+C\,c\right)\,\left(32\,B^2\,b^3-96\,B^2\,b\,c^2+64\,C^2\,b\,c^2-\frac{\left(2\,B\,c-2\,C\,b\right)\,\left(32\,C\,b^2\,c^2-64\,C\,b^4+32\,B\,b\,c^3+128\,B\,b^3\,c-\frac{\left(2\,B\,c-2\,C\,b\right)\,\left(96\,b^3\,c^2+96\,b\,c^4\right)}{2\,\left(b^2+c^2\right)}\right)}{2\,\left(b^2+c^2\right)}+192\,B\,C\,b^2\,c\right)}{b^2+c^2}+\frac{\left(2\,B\,c-2\,C\,b\right)\,\left(\frac{\left(B\,b+C\,c\right)\,\left(32\,C\,b^2\,c^2-64\,C\,b^4+32\,B\,b\,c^3+128\,B\,b^3\,c-\frac{\left(2\,B\,c-2\,C\,b\right)\,\left(96\,b^3\,c^2+96\,b\,c^4\right)}{2\,\left(b^2+c^2\right)}\right)}{b^2+c^2}-\frac{\left(B\,b+C\,c\right)\,\left(2\,B\,c-2\,C\,b\right)\,\left(96\,b^3\,c^2+96\,b\,c^4\right)}{2\,{\left(b^2+c^2\right)}^2}\right)}{2\,\left(b^2+c^2\right)}\right)\,\left(B^2\,b^4-13\,B^2\,b^2\,c^2+4\,B^2\,c^4+18\,B\,C\,b^3\,c-18\,B\,C\,b\,c^3-4\,C^2\,b^4+13\,C^2\,b^2\,c^2-C^2\,c^4\right)}{{\left(b^2+c^2\right)}^2\,{\left(B^2\,b^2+4\,B^2\,c^2-6\,B\,C\,b\,c+4\,C^2\,b^2+C^2\,c^2\right)}^2}\right)+\frac{\left(\frac{\left(B\,b+C\,c\right)\,\left(\frac{\left(2\,B\,c-2\,C\,b\right)\,\left(64\,B\,b^2\,c^2-32\,B\,b^4+32\,C\,b\,c^3-64\,C\,b^3\,c+\frac{\left(2\,B\,c-2\,C\,b\right)\,\left(96\,b^4\,c+96\,b^2\,c^3\right)}{2\,\left(b^2+c^2\right)}\right)}{2\,\left(b^2+c^2\right)}-32\,C^2\,b^2\,c-32\,B^2\,b^2\,c+64\,B\,C\,b^3+64\,B\,C\,b\,c^2\right)}{b^2+c^2}-\frac{{\left(B\,b+C\,c\right)}^3\,\left(96\,b^4\,c+96\,b^2\,c^3\right)}{{\left(b^2+c^2\right)}^3}+\frac{\left(2\,B\,c-2\,C\,b\right)\,\left(\frac{\left(B\,b+C\,c\right)\,\left(64\,B\,b^2\,c^2-32\,B\,b^4+32\,C\,b\,c^3-64\,C\,b^3\,c+\frac{\left(2\,B\,c-2\,C\,b\right)\,\left(96\,b^4\,c+96\,b^2\,c^3\right)}{2\,\left(b^2+c^2\right)}\right)}{b^2+c^2}+\frac{\left(B\,b+C\,c\right)\,\left(2\,B\,c-2\,C\,b\right)\,\left(96\,b^4\,c+96\,b^2\,c^3\right)}{2\,{\left(b^2+c^2\right)}^2}\right)}{2\,\left(b^2+c^2\right)}\right)\,\left(B^2\,b^4-13\,B^2\,b^2\,c^2+4\,B^2\,c^4+18\,B\,C\,b^3\,c-18\,B\,C\,b\,c^3-4\,C^2\,b^4+13\,C^2\,b^2\,c^2-C^2\,c^4\right)}{{\left(b^2+c^2\right)}^2\,{\left(B^2\,b^2+4\,B^2\,c^2-6\,B\,C\,b\,c+4\,C^2\,b^2+C^2\,c^2\right)}^2}\right)\,\left(b^4+2\,b^2\,c^2+c^4\right)}{32\,B\,b^2+32\,C\,c\,b}\right)\,\left(B\,b+C\,c\right)}{b^2+c^2}","Not used",1,"(log(b + 2*c*tan(x/2) - b*tan(x/2)^2)*(B*c - C*b))/(b^2 + c^2) - (log(1/(cos(x) + 1))*(2*B*c - 2*C*b))/(2*(b^2 + c^2)) + (2*atan(((((32*B*C^2*b^2 - ((2*B*c - 2*C*b)*(((2*B*c - 2*C*b)*(64*B*b^2*c^2 - 32*B*b^4 + 32*C*b*c^3 - 64*C*b^3*c + ((2*B*c - 2*C*b)*(96*b^4*c + 96*b^2*c^3))/(2*(b^2 + c^2))))/(2*(b^2 + c^2)) - 32*C^2*b^2*c - 32*B^2*b^2*c + 64*B*C*b^3 + 64*B*C*b*c^2))/(2*(b^2 + c^2)) + ((B*b + C*c)*(((B*b + C*c)*(64*B*b^2*c^2 - 32*B*b^4 + 32*C*b*c^3 - 64*C*b^3*c + ((2*B*c - 2*C*b)*(96*b^4*c + 96*b^2*c^3))/(2*(b^2 + c^2))))/(b^2 + c^2) + ((B*b + C*c)*(2*B*c - 2*C*b)*(96*b^4*c + 96*b^2*c^3))/(2*(b^2 + c^2)^2)))/(b^2 + c^2) - 32*B^2*C*b*c + ((B*b + C*c)^2*(2*B*c - 2*C*b)*(96*b^4*c + 96*b^2*c^3))/(2*(b^2 + c^2)^3))*(12*B^2*b*c^3 - 6*B^2*b^3*c - 6*C^2*b*c^3 + 12*C^2*b^3*c + 4*B*C*b^4 + 4*B*C*c^4 - 28*B*C*b^2*c^2))/((b^2 + c^2)^2*(B^2*b^2 + 4*B^2*c^2 + 4*C^2*b^2 + C^2*c^2 - 6*B*C*b*c)^2) - tan(x/2)*(((32*B^3*b*c - 32*B^2*C*b^2 - 64*C^3*b^2 + ((2*B*c - 2*C*b)*(32*B^2*b^3 - 96*B^2*b*c^2 + 64*C^2*b*c^2 - ((2*B*c - 2*C*b)*(32*C*b^2*c^2 - 64*C*b^4 + 32*B*b*c^3 + 128*B*b^3*c - ((2*B*c - 2*C*b)*(96*b*c^4 + 96*b^3*c^2))/(2*(b^2 + c^2))))/(2*(b^2 + c^2)) + 192*B*C*b^2*c))/(2*(b^2 + c^2)) + ((B*b + C*c)*(((B*b + C*c)*(32*C*b^2*c^2 - 64*C*b^4 + 32*B*b*c^3 + 128*B*b^3*c - ((2*B*c - 2*C*b)*(96*b*c^4 + 96*b^3*c^2))/(2*(b^2 + c^2))))/(b^2 + c^2) - ((B*b + C*c)*(2*B*c - 2*C*b)*(96*b*c^4 + 96*b^3*c^2))/(2*(b^2 + c^2)^2)))/(b^2 + c^2) + 64*B*C^2*b*c - ((B*b + C*c)^2*(2*B*c - 2*C*b)*(96*b*c^4 + 96*b^3*c^2))/(2*(b^2 + c^2)^3))*(12*B^2*b*c^3 - 6*B^2*b^3*c - 6*C^2*b*c^3 + 12*C^2*b^3*c + 4*B*C*b^4 + 4*B*C*c^4 - 28*B*C*b^2*c^2))/((b^2 + c^2)^2*(B^2*b^2 + 4*B^2*c^2 + 4*C^2*b^2 + C^2*c^2 - 6*B*C*b*c)^2) + ((((B*b + C*c)^3*(96*b*c^4 + 96*b^3*c^2))/(b^2 + c^2)^3 - ((B*b + C*c)*(32*B^2*b^3 - 96*B^2*b*c^2 + 64*C^2*b*c^2 - ((2*B*c - 2*C*b)*(32*C*b^2*c^2 - 64*C*b^4 + 32*B*b*c^3 + 128*B*b^3*c - ((2*B*c - 2*C*b)*(96*b*c^4 + 96*b^3*c^2))/(2*(b^2 + c^2))))/(2*(b^2 + c^2)) + 192*B*C*b^2*c))/(b^2 + c^2) + ((2*B*c - 2*C*b)*(((B*b + C*c)*(32*C*b^2*c^2 - 64*C*b^4 + 32*B*b*c^3 + 128*B*b^3*c - ((2*B*c - 2*C*b)*(96*b*c^4 + 96*b^3*c^2))/(2*(b^2 + c^2))))/(b^2 + c^2) - ((B*b + C*c)*(2*B*c - 2*C*b)*(96*b*c^4 + 96*b^3*c^2))/(2*(b^2 + c^2)^2)))/(2*(b^2 + c^2)))*(B^2*b^4 + 4*B^2*c^4 - 4*C^2*b^4 - C^2*c^4 - 13*B^2*b^2*c^2 + 13*C^2*b^2*c^2 - 18*B*C*b*c^3 + 18*B*C*b^3*c))/((b^2 + c^2)^2*(B^2*b^2 + 4*B^2*c^2 + 4*C^2*b^2 + C^2*c^2 - 6*B*C*b*c)^2)) + ((((B*b + C*c)*(((2*B*c - 2*C*b)*(64*B*b^2*c^2 - 32*B*b^4 + 32*C*b*c^3 - 64*C*b^3*c + ((2*B*c - 2*C*b)*(96*b^4*c + 96*b^2*c^3))/(2*(b^2 + c^2))))/(2*(b^2 + c^2)) - 32*C^2*b^2*c - 32*B^2*b^2*c + 64*B*C*b^3 + 64*B*C*b*c^2))/(b^2 + c^2) - ((B*b + C*c)^3*(96*b^4*c + 96*b^2*c^3))/(b^2 + c^2)^3 + ((2*B*c - 2*C*b)*(((B*b + C*c)*(64*B*b^2*c^2 - 32*B*b^4 + 32*C*b*c^3 - 64*C*b^3*c + ((2*B*c - 2*C*b)*(96*b^4*c + 96*b^2*c^3))/(2*(b^2 + c^2))))/(b^2 + c^2) + ((B*b + C*c)*(2*B*c - 2*C*b)*(96*b^4*c + 96*b^2*c^3))/(2*(b^2 + c^2)^2)))/(2*(b^2 + c^2)))*(B^2*b^4 + 4*B^2*c^4 - 4*C^2*b^4 - C^2*c^4 - 13*B^2*b^2*c^2 + 13*C^2*b^2*c^2 - 18*B*C*b*c^3 + 18*B*C*b^3*c))/((b^2 + c^2)^2*(B^2*b^2 + 4*B^2*c^2 + 4*C^2*b^2 + C^2*c^2 - 6*B*C*b*c)^2))*(b^4 + c^4 + 2*b^2*c^2))/(32*B*b^2 + 32*C*b*c))*(B*b + C*c))/(b^2 + c^2)","B"
530,1,129,74,3.007032,"\text{Not used}","int((B*cos(x) + C*sin(x))/(b*cos(x) + c*sin(x))^2,x)","-\frac{\frac{2\,\left(B\,c-C\,b\right)}{b^2+c^2}+\frac{2\,c\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(B\,c-C\,b\right)}{b\,\left(b^2+c^2\right)}}{-b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,c\,\mathrm{tan}\left(\frac{x}{2}\right)+b}+\frac{\mathrm{atan}\left(\frac{b^2\,c\,1{}\mathrm{i}+c^3\,1{}\mathrm{i}-b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(b^2+c^2\right)\,1{}\mathrm{i}}{{\left(b^2+c^2\right)}^{3/2}}\right)\,\left(B\,b+C\,c\right)\,2{}\mathrm{i}}{{\left(b^2+c^2\right)}^{3/2}}","Not used",1,"(atan((b^2*c*1i + c^3*1i - b*tan(x/2)*(b^2 + c^2)*1i)/(b^2 + c^2)^(3/2))*(B*b + C*c)*2i)/(b^2 + c^2)^(3/2) - ((2*(B*c - C*b))/(b^2 + c^2) + (2*c*tan(x/2)*(B*c - C*b))/(b*(b^2 + c^2)))/(b + 2*c*tan(x/2) - b*tan(x/2)^2)","B"
531,1,95,66,2.823102,"\text{Not used}","int((B*cos(x) + C*sin(x))/(b*cos(x) + c*sin(x))^3,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(B\,c+C\,b\right)}{b^2}-\frac{2\,B\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{b}+\frac{2\,B\,\mathrm{tan}\left(\frac{x}{2}\right)}{b}}{b^2-{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,b^2-4\,c^2\right)+b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,b\,c\,\mathrm{tan}\left(\frac{x}{2}\right)-4\,b\,c\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}","Not used",1,"((2*tan(x/2)^2*(B*c + C*b))/b^2 - (2*B*tan(x/2)^3)/b + (2*B*tan(x/2))/b)/(b^2 - tan(x/2)^2*(2*b^2 - 4*c^2) + b^2*tan(x/2)^4 + 4*b*c*tan(x/2) - 4*b*c*tan(x/2)^3)","B"
532,1,1099,84,9.406403,"\text{Not used}","int((A + B*cos(x) + C*sin(x))/(b*cos(x) + c*sin(x)),x)","\ln\left(32\,A^2\,B\,b^2-32\,A\,B^2\,b^2-32\,A\,C^2\,b^2-32\,B\,C^2\,b^2+32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(c\,A^2\,B+b\,A^2\,C-2\,c\,A\,B^2-2\,c\,A\,C^2+c\,B^3-b\,B^2\,C+2\,c\,B\,C^2-2\,b\,C^3\right)-\frac{\left(A\,\sqrt{{\left(b^2+c^2\right)}^3}+B\,c^3-C\,b^3+B\,b^2\,c-C\,b\,c^2\right)\,\left(32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A^2\,b^2-A^2\,c^2+4\,A\,B\,c^2-4\,A\,C\,b\,c+B^2\,b^2-3\,B^2\,c^2+6\,B\,C\,b\,c+2\,C^2\,c^2\right)-32\,B^2\,b^2\,c-32\,C^2\,b^2\,c-64\,A^2\,b^2\,c-64\,A\,C\,b^3+64\,B\,C\,b^3+\frac{\left(A\,\sqrt{{\left(b^2+c^2\right)}^3}+B\,c^3-C\,b^3+B\,b^2\,c-C\,b\,c^2\right)\,\left(32\,A\,b^4+32\,B\,b^4+32\,A\,b^2\,c^2-64\,B\,b^2\,c^2-32\,C\,b\,c^3+64\,C\,b^3\,c+32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,A\,c^3+B\,c^3-2\,C\,b^3+2\,A\,b^2\,c+4\,B\,b^2\,c+C\,b\,c^2\right)+\frac{96\,b\,c\,\left(b+c\,\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(A\,\sqrt{{\left(b^2+c^2\right)}^3}+B\,c^3-C\,b^3+B\,b^2\,c-C\,b\,c^2\right)}{b^2+c^2}\right)}{{\left(b^2+c^2\right)}^2}+64\,A\,B\,b^2\,c+64\,B\,C\,b\,c^2\right)}{{\left(b^2+c^2\right)}^2}-32\,A^2\,C\,b\,c+32\,B^2\,C\,b\,c\right)\,\left(\frac{B\,c-C\,b}{b^2+c^2}+\frac{A\,\sqrt{{\left(b^2+c^2\right)}^3}}{{\left(b^2+c^2\right)}^2}\right)+\ln\left(32\,A^2\,B\,b^2-32\,A\,B^2\,b^2-32\,A\,C^2\,b^2-32\,B\,C^2\,b^2+32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(c\,A^2\,B+b\,A^2\,C-2\,c\,A\,B^2-2\,c\,A\,C^2+c\,B^3-b\,B^2\,C+2\,c\,B\,C^2-2\,b\,C^3\right)-\frac{\left(A\,\sqrt{{\left(b^2+c^2\right)}^3}-B\,c^3+C\,b^3-B\,b^2\,c+C\,b\,c^2\right)\,\left(64\,A^2\,b^2\,c+32\,B^2\,b^2\,c+32\,C^2\,b^2\,c-32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A^2\,b^2-A^2\,c^2+4\,A\,B\,c^2-4\,A\,C\,b\,c+B^2\,b^2-3\,B^2\,c^2+6\,B\,C\,b\,c+2\,C^2\,c^2\right)+64\,A\,C\,b^3-64\,B\,C\,b^3+\frac{\left(A\,\sqrt{{\left(b^2+c^2\right)}^3}-B\,c^3+C\,b^3-B\,b^2\,c+C\,b\,c^2\right)\,\left(32\,A\,b^4+32\,B\,b^4+32\,A\,b^2\,c^2-64\,B\,b^2\,c^2-32\,C\,b\,c^3+64\,C\,b^3\,c+32\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,A\,c^3+B\,c^3-2\,C\,b^3+2\,A\,b^2\,c+4\,B\,b^2\,c+C\,b\,c^2\right)-\frac{96\,b\,c\,\left(b+c\,\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(A\,\sqrt{{\left(b^2+c^2\right)}^3}-B\,c^3+C\,b^3-B\,b^2\,c+C\,b\,c^2\right)}{b^2+c^2}\right)}{{\left(b^2+c^2\right)}^2}-64\,A\,B\,b^2\,c-64\,B\,C\,b\,c^2\right)}{{\left(b^2+c^2\right)}^2}-32\,A^2\,C\,b\,c+32\,B^2\,C\,b\,c\right)\,\left(\frac{B\,c-C\,b}{b^2+c^2}-\frac{A\,\sqrt{{\left(b^2+c^2\right)}^3}}{{\left(b^2+c^2\right)}^2}\right)-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)\,\left(B-C\,1{}\mathrm{i}\right)}{c+b\,1{}\mathrm{i}}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,\left(B+C\,1{}\mathrm{i}\right)}{-c+b\,1{}\mathrm{i}}","Not used",1,"log(32*A^2*B*b^2 - 32*A*B^2*b^2 - 32*A*C^2*b^2 - 32*B*C^2*b^2 + 32*b*tan(x/2)*(B^3*c - 2*C^3*b - 2*A*B^2*c + A^2*B*c + A^2*C*b - 2*A*C^2*c - B^2*C*b + 2*B*C^2*c) - ((A*((b^2 + c^2)^3)^(1/2) + B*c^3 - C*b^3 + B*b^2*c - C*b*c^2)*(32*b*tan(x/2)*(A^2*b^2 - A^2*c^2 + B^2*b^2 - 3*B^2*c^2 + 2*C^2*c^2 + 4*A*B*c^2 - 4*A*C*b*c + 6*B*C*b*c) - 32*B^2*b^2*c - 32*C^2*b^2*c - 64*A^2*b^2*c - 64*A*C*b^3 + 64*B*C*b^3 + ((A*((b^2 + c^2)^3)^(1/2) + B*c^3 - C*b^3 + B*b^2*c - C*b*c^2)*(32*A*b^4 + 32*B*b^4 + 32*A*b^2*c^2 - 64*B*b^2*c^2 - 32*C*b*c^3 + 64*C*b^3*c + 32*b*tan(x/2)*(2*A*c^3 + B*c^3 - 2*C*b^3 + 2*A*b^2*c + 4*B*b^2*c + C*b*c^2) + (96*b*c*(b + c*tan(x/2))*(A*((b^2 + c^2)^3)^(1/2) + B*c^3 - C*b^3 + B*b^2*c - C*b*c^2))/(b^2 + c^2)))/(b^2 + c^2)^2 + 64*A*B*b^2*c + 64*B*C*b*c^2))/(b^2 + c^2)^2 - 32*A^2*C*b*c + 32*B^2*C*b*c)*((B*c - C*b)/(b^2 + c^2) + (A*((b^2 + c^2)^3)^(1/2))/(b^2 + c^2)^2) + log(32*A^2*B*b^2 - 32*A*B^2*b^2 - 32*A*C^2*b^2 - 32*B*C^2*b^2 + 32*b*tan(x/2)*(B^3*c - 2*C^3*b - 2*A*B^2*c + A^2*B*c + A^2*C*b - 2*A*C^2*c - B^2*C*b + 2*B*C^2*c) - ((A*((b^2 + c^2)^3)^(1/2) - B*c^3 + C*b^3 - B*b^2*c + C*b*c^2)*(64*A^2*b^2*c + 32*B^2*b^2*c + 32*C^2*b^2*c - 32*b*tan(x/2)*(A^2*b^2 - A^2*c^2 + B^2*b^2 - 3*B^2*c^2 + 2*C^2*c^2 + 4*A*B*c^2 - 4*A*C*b*c + 6*B*C*b*c) + 64*A*C*b^3 - 64*B*C*b^3 + ((A*((b^2 + c^2)^3)^(1/2) - B*c^3 + C*b^3 - B*b^2*c + C*b*c^2)*(32*A*b^4 + 32*B*b^4 + 32*A*b^2*c^2 - 64*B*b^2*c^2 - 32*C*b*c^3 + 64*C*b^3*c + 32*b*tan(x/2)*(2*A*c^3 + B*c^3 - 2*C*b^3 + 2*A*b^2*c + 4*B*b^2*c + C*b*c^2) - (96*b*c*(b + c*tan(x/2))*(A*((b^2 + c^2)^3)^(1/2) - B*c^3 + C*b^3 - B*b^2*c + C*b*c^2))/(b^2 + c^2)))/(b^2 + c^2)^2 - 64*A*B*b^2*c - 64*B*C*b*c^2))/(b^2 + c^2)^2 - 32*A^2*C*b*c + 32*B^2*C*b*c)*((B*c - C*b)/(b^2 + c^2) - (A*((b^2 + c^2)^3)^(1/2))/(b^2 + c^2)^2) - (log(tan(x/2) + 1i)*(B - C*1i))/(b*1i + c) + (log(tan(x/2) - 1i)*(B + C*1i))/(b*1i - c)","B"
533,1,141,85,3.051015,"\text{Not used}","int((A + B*cos(x) + C*sin(x))/(b*cos(x) + c*sin(x))^2,x)","-\frac{\frac{2\,\left(B\,c-C\,b\right)}{b^2+c^2}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A\,b^2+A\,c^2-B\,c^2+C\,b\,c\right)}{b\,\left(b^2+c^2\right)}}{-b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,c\,\mathrm{tan}\left(\frac{x}{2}\right)+b}+\frac{\mathrm{atan}\left(\frac{b^2\,c\,1{}\mathrm{i}+c^3\,1{}\mathrm{i}-b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(b^2+c^2\right)\,1{}\mathrm{i}}{{\left(b^2+c^2\right)}^{3/2}}\right)\,\left(B\,b+C\,c\right)\,2{}\mathrm{i}}{{\left(b^2+c^2\right)}^{3/2}}","Not used",1,"(atan((b^2*c*1i + c^3*1i - b*tan(x/2)*(b^2 + c^2)*1i)/(b^2 + c^2)^(3/2))*(B*b + C*c)*2i)/(b^2 + c^2)^(3/2) - ((2*(B*c - C*b))/(b^2 + c^2) - (2*tan(x/2)*(A*b^2 + A*c^2 - B*c^2 + C*b*c))/(b*(b^2 + c^2)))/(b + 2*c*tan(x/2) - b*tan(x/2)^2)","B"
534,1,264,129,3.438889,"\text{Not used}","int((A + B*cos(x) + C*sin(x))/(b*cos(x) + c*sin(x))^3,x)","\frac{\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A\,b^2-2\,A\,c^2+2\,B\,b^2+2\,B\,c^2\right)}{b\,\left(b^2+c^2\right)}-\frac{A\,c}{b^2+c^2}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,B\,c^3-2\,A\,c^3+2\,C\,b^3+A\,b^2\,c+2\,B\,b^2\,c+2\,C\,b\,c^2\right)}{b^2\,\left(b^2+c^2\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(A\,b^2+2\,A\,c^2-2\,B\,b^2-2\,B\,c^2\right)}{b\,\left(b^2+c^2\right)}}{b^2-{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,b^2-4\,c^2\right)+b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,b\,c\,\mathrm{tan}\left(\frac{x}{2}\right)-4\,b\,c\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}+\frac{A\,\mathrm{atan}\left(\frac{b^2\,c\,1{}\mathrm{i}+c^3\,1{}\mathrm{i}-b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(b^2+c^2\right)\,1{}\mathrm{i}}{{\left(b^2+c^2\right)}^{3/2}}\right)\,1{}\mathrm{i}}{{\left(b^2+c^2\right)}^{3/2}}","Not used",1,"((tan(x/2)*(A*b^2 - 2*A*c^2 + 2*B*b^2 + 2*B*c^2))/(b*(b^2 + c^2)) - (A*c)/(b^2 + c^2) + (tan(x/2)^2*(2*B*c^3 - 2*A*c^3 + 2*C*b^3 + A*b^2*c + 2*B*b^2*c + 2*C*b*c^2))/(b^2*(b^2 + c^2)) + (tan(x/2)^3*(A*b^2 + 2*A*c^2 - 2*B*b^2 - 2*B*c^2))/(b*(b^2 + c^2)))/(b^2 - tan(x/2)^2*(2*b^2 - 4*c^2) + b^2*tan(x/2)^4 + 4*b*c*tan(x/2) - 4*b*c*tan(x/2)^3) + (A*atan((b^2*c*1i + c^3*1i - b*tan(x/2)*(b^2 + c^2)*1i)/(b^2 + c^2)^(3/2))*1i)/(b^2 + c^2)^(3/2)","B"
535,1,1709,115,25.561035,"\text{Not used}","int((A + B*cos(x))/(a + b*cos(x) + c*sin(x)),x)","\frac{\ln\left(32\,B^3\,a^2-32\,A\,B^2\,a^2+32\,A\,B^2\,b^2-32\,A^2\,B\,b^2-32\,B^3\,a\,b+32\,A^2\,B\,a\,b-\frac{\left(B\,c^3+A\,b^2\,\sqrt{-a^2+b^2+c^2}-B\,a^2\,c+A\,c^2\,\sqrt{-a^2+b^2+c^2}+B\,b^2\,c-B\,a\,b\,\sqrt{-a^2+b^2+c^2}\right)\,\left(64\,A^2\,b^2\,c-32\,B^2\,a^2\,c+32\,B^2\,b^2\,c+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(A^2\,b^2-A^2\,c^2-2\,A\,B\,a\,b+4\,A\,B\,c^2+2\,B^2\,a^2-2\,B^2\,a\,b+B^2\,b^2-3\,B^2\,c^2\right)+64\,A\,B\,a^2\,c-64\,A\,B\,b^2\,c-64\,A^2\,a\,b\,c+\frac{\left(B\,c^3+A\,b^2\,\sqrt{-a^2+b^2+c^2}-B\,a^2\,c+A\,c^2\,\sqrt{-a^2+b^2+c^2}+B\,b^2\,c-B\,a\,b\,\sqrt{-a^2+b^2+c^2}\right)\,\left(32\,A\,a^2\,c^2-32\,B\,b^4-32\,A\,a^2\,b^2-32\,A\,b^4-32\,B\,a^2\,b^2-32\,A\,b^2\,c^2+32\,B\,a^2\,c^2+64\,B\,b^2\,c^2+64\,A\,a\,b^3+64\,B\,a\,b^3-96\,B\,a\,b\,c^2+32\,c\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(2\,A\,b^2+2\,A\,c^2+4\,B\,b^2+B\,c^2-2\,A\,a\,b-4\,B\,a\,b\right)+\frac{32\,\left(a-b\right)\,\left(B\,c^3+A\,b^2\,\sqrt{-a^2+b^2+c^2}-B\,a^2\,c+A\,c^2\,\sqrt{-a^2+b^2+c^2}+B\,b^2\,c-B\,a\,b\,\sqrt{-a^2+b^2+c^2}\right)\,\left(2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^2-4\,a^2\,b\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,c^2-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^3+a\,b^2\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b\,c^2+a\,c^3+3\,b^3\,c+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2\,c^2+3\,b\,c^3+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,c^4\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}+32\,B\,c\,\mathrm{tan}\left(\frac{x}{2}\right)\,{\left(A-B\right)}^2\,\left(a-b\right)\right)\,\left(B\,c^3+b^2\,\left(A\,\sqrt{-a^2+b^2+c^2}+B\,c\right)-B\,a^2\,c+A\,c^2\,\sqrt{-a^2+b^2+c^2}-B\,a\,b\,\sqrt{-a^2+b^2+c^2}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}-\frac{B\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)}{c+b\,1{}\mathrm{i}}-\frac{\ln\left(32\,B^3\,a^2-32\,A\,B^2\,a^2+32\,A\,B^2\,b^2-32\,A^2\,B\,b^2-32\,B^3\,a\,b+32\,A^2\,B\,a\,b-\frac{\left(B\,c^3-A\,b^2\,\sqrt{-a^2+b^2+c^2}-B\,a^2\,c-A\,c^2\,\sqrt{-a^2+b^2+c^2}+B\,b^2\,c+B\,a\,b\,\sqrt{-a^2+b^2+c^2}\right)\,\left(64\,A^2\,b^2\,c-32\,B^2\,a^2\,c+32\,B^2\,b^2\,c+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(A^2\,b^2-A^2\,c^2-2\,A\,B\,a\,b+4\,A\,B\,c^2+2\,B^2\,a^2-2\,B^2\,a\,b+B^2\,b^2-3\,B^2\,c^2\right)+64\,A\,B\,a^2\,c-64\,A\,B\,b^2\,c-64\,A^2\,a\,b\,c+\frac{\left(B\,c^3-A\,b^2\,\sqrt{-a^2+b^2+c^2}-B\,a^2\,c-A\,c^2\,\sqrt{-a^2+b^2+c^2}+B\,b^2\,c+B\,a\,b\,\sqrt{-a^2+b^2+c^2}\right)\,\left(32\,A\,a^2\,c^2-32\,B\,b^4-32\,A\,a^2\,b^2-32\,A\,b^4-32\,B\,a^2\,b^2-32\,A\,b^2\,c^2+32\,B\,a^2\,c^2+64\,B\,b^2\,c^2+64\,A\,a\,b^3+64\,B\,a\,b^3-96\,B\,a\,b\,c^2+32\,c\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(2\,A\,b^2+2\,A\,c^2+4\,B\,b^2+B\,c^2-2\,A\,a\,b-4\,B\,a\,b\right)+\frac{32\,\left(a-b\right)\,\left(B\,c^3-A\,b^2\,\sqrt{-a^2+b^2+c^2}-B\,a^2\,c-A\,c^2\,\sqrt{-a^2+b^2+c^2}+B\,b^2\,c+B\,a\,b\,\sqrt{-a^2+b^2+c^2}\right)\,\left(2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^2-4\,a^2\,b\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,c^2-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^3+a\,b^2\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b\,c^2+a\,c^3+3\,b^3\,c+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2\,c^2+3\,b\,c^3+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,c^4\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}+32\,B\,c\,\mathrm{tan}\left(\frac{x}{2}\right)\,{\left(A-B\right)}^2\,\left(a-b\right)\right)\,\left(b^2\,\left(A\,\sqrt{-a^2+b^2+c^2}-B\,c\right)-B\,c^3+B\,a^2\,c+A\,c^2\,\sqrt{-a^2+b^2+c^2}-B\,a\,b\,\sqrt{-a^2+b^2+c^2}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}-\frac{B\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,1{}\mathrm{i}}{b+c\,1{}\mathrm{i}}","Not used",1,"(log(32*B^3*a^2 - 32*A*B^2*a^2 + 32*A*B^2*b^2 - 32*A^2*B*b^2 - 32*B^3*a*b + 32*A^2*B*a*b - ((B*c^3 + A*b^2*(b^2 - a^2 + c^2)^(1/2) - B*a^2*c + A*c^2*(b^2 - a^2 + c^2)^(1/2) + B*b^2*c - B*a*b*(b^2 - a^2 + c^2)^(1/2))*(64*A^2*b^2*c - 32*B^2*a^2*c + 32*B^2*b^2*c + 32*tan(x/2)*(a - b)*(A^2*b^2 + 2*B^2*a^2 - A^2*c^2 + B^2*b^2 - 3*B^2*c^2 + 4*A*B*c^2 - 2*B^2*a*b - 2*A*B*a*b) + 64*A*B*a^2*c - 64*A*B*b^2*c - 64*A^2*a*b*c + ((B*c^3 + A*b^2*(b^2 - a^2 + c^2)^(1/2) - B*a^2*c + A*c^2*(b^2 - a^2 + c^2)^(1/2) + B*b^2*c - B*a*b*(b^2 - a^2 + c^2)^(1/2))*(32*A*a^2*c^2 - 32*B*b^4 - 32*A*a^2*b^2 - 32*A*b^4 - 32*B*a^2*b^2 - 32*A*b^2*c^2 + 32*B*a^2*c^2 + 64*B*b^2*c^2 + 64*A*a*b^3 + 64*B*a*b^3 - 96*B*a*b*c^2 + 32*c*tan(x/2)*(a - b)*(2*A*b^2 + 2*A*c^2 + 4*B*b^2 + B*c^2 - 2*A*a*b - 4*B*a*b) + (32*(a - b)*(B*c^3 + A*b^2*(b^2 - a^2 + c^2)^(1/2) - B*a^2*c + A*c^2*(b^2 - a^2 + c^2)^(1/2) + B*b^2*c - B*a*b*(b^2 - a^2 + c^2)^(1/2))*(3*c^4*tan(x/2) + a*c^3 + 3*b*c^3 + 3*b^3*c + 2*a^2*b^2*tan(x/2) - 2*a^2*c^2*tan(x/2) + 3*b^2*c^2*tan(x/2) - 2*a*b^3*tan(x/2) + a*b^2*c - 4*a^2*b*c - 2*a*b*c^2*tan(x/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2)) + 32*B*c*tan(x/2)*(A - B)^2*(a - b))*(B*c^3 + b^2*(A*(b^2 - a^2 + c^2)^(1/2) + B*c) - B*a^2*c + A*c^2*(b^2 - a^2 + c^2)^(1/2) - B*a*b*(b^2 - a^2 + c^2)^(1/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2)) - (B*log(tan(x/2) + 1i))/(b*1i + c) - (B*log(tan(x/2) - 1i)*1i)/(b + c*1i) - (log(32*B^3*a^2 - 32*A*B^2*a^2 + 32*A*B^2*b^2 - 32*A^2*B*b^2 - 32*B^3*a*b + 32*A^2*B*a*b - ((B*c^3 - A*b^2*(b^2 - a^2 + c^2)^(1/2) - B*a^2*c - A*c^2*(b^2 - a^2 + c^2)^(1/2) + B*b^2*c + B*a*b*(b^2 - a^2 + c^2)^(1/2))*(64*A^2*b^2*c - 32*B^2*a^2*c + 32*B^2*b^2*c + 32*tan(x/2)*(a - b)*(A^2*b^2 + 2*B^2*a^2 - A^2*c^2 + B^2*b^2 - 3*B^2*c^2 + 4*A*B*c^2 - 2*B^2*a*b - 2*A*B*a*b) + 64*A*B*a^2*c - 64*A*B*b^2*c - 64*A^2*a*b*c + ((B*c^3 - A*b^2*(b^2 - a^2 + c^2)^(1/2) - B*a^2*c - A*c^2*(b^2 - a^2 + c^2)^(1/2) + B*b^2*c + B*a*b*(b^2 - a^2 + c^2)^(1/2))*(32*A*a^2*c^2 - 32*B*b^4 - 32*A*a^2*b^2 - 32*A*b^4 - 32*B*a^2*b^2 - 32*A*b^2*c^2 + 32*B*a^2*c^2 + 64*B*b^2*c^2 + 64*A*a*b^3 + 64*B*a*b^3 - 96*B*a*b*c^2 + 32*c*tan(x/2)*(a - b)*(2*A*b^2 + 2*A*c^2 + 4*B*b^2 + B*c^2 - 2*A*a*b - 4*B*a*b) + (32*(a - b)*(B*c^3 - A*b^2*(b^2 - a^2 + c^2)^(1/2) - B*a^2*c - A*c^2*(b^2 - a^2 + c^2)^(1/2) + B*b^2*c + B*a*b*(b^2 - a^2 + c^2)^(1/2))*(3*c^4*tan(x/2) + a*c^3 + 3*b*c^3 + 3*b^3*c + 2*a^2*b^2*tan(x/2) - 2*a^2*c^2*tan(x/2) + 3*b^2*c^2*tan(x/2) - 2*a*b^3*tan(x/2) + a*b^2*c - 4*a^2*b*c - 2*a*b*c^2*tan(x/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2)) + 32*B*c*tan(x/2)*(A - B)^2*(a - b))*(b^2*(A*(b^2 - a^2 + c^2)^(1/2) - B*c) - B*c^3 + B*a^2*c + A*c^2*(b^2 - a^2 + c^2)^(1/2) - B*a*b*(b^2 - a^2 + c^2)^(1/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2))","B"
536,1,205,113,3.252651,"\text{Not used}","int((A + B*cos(x))/(a + b*cos(x) + c*sin(x))^2,x)","\frac{2\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a-2\,b\right)+\frac{2\,\left(-a^2\,c+b^2\,c+c^3\right)}{-a^2+b^2+c^2}}{2\,\sqrt{-a^2+b^2+c^2}}\right)\,\left(A\,a-B\,b\right)}{{\left(-a^2+b^2+c^2\right)}^{3/2}}-\frac{\frac{2\,\left(A\,a\,c-B\,b\,c\right)}{\left(a-b\right)\,\left(-a^2+b^2+c^2\right)}+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A\,b^2+B\,a^2+A\,c^2-B\,c^2-A\,a\,b-B\,a\,b\right)}{\left(a-b\right)\,\left(-a^2+b^2+c^2\right)}}{\left(a-b\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,c\,\mathrm{tan}\left(\frac{x}{2}\right)+a+b}","Not used",1,"(2*atanh((tan(x/2)*(2*a - 2*b) + (2*(b^2*c - a^2*c + c^3))/(b^2 - a^2 + c^2))/(2*(b^2 - a^2 + c^2)^(1/2)))*(A*a - B*b))/(b^2 - a^2 + c^2)^(3/2) - ((2*(A*a*c - B*b*c))/((a - b)*(b^2 - a^2 + c^2)) + (2*tan(x/2)*(A*b^2 + B*a^2 + A*c^2 - B*c^2 - A*a*b - B*a*b))/((a - b)*(b^2 - a^2 + c^2)))/(a + b + 2*c*tan(x/2) + tan(x/2)^2*(a - b))","B"
537,1,946,200,6.844869,"\text{Not used}","int((A + B*cos(x))/(a + b*cos(x) + c*sin(x))^3,x)","-\frac{\frac{-4\,A\,a^4\,c+5\,B\,a^3\,b\,c+3\,A\,a^2\,b^2\,c+A\,a^2\,c^3-5\,B\,a\,b^3\,c-2\,B\,a\,b\,c^3+A\,b^4\,c+A\,b^2\,c^3}{{\left(a-b\right)}^2\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A\,b^5+2\,B\,a^5+2\,B\,b^5+3\,A\,a^2\,b^3+5\,A\,a^3\,b^2+11\,A\,a^3\,c^2+B\,a^2\,b^3+B\,a^3\,b^2-A\,b^3\,c^2-4\,B\,a^3\,c^2+4\,B\,b^3\,c^2-5\,A\,a\,b^4-4\,A\,a^4\,b-2\,A\,a\,c^4-3\,B\,a\,b^4-3\,B\,a^4\,b-2\,A\,b\,c^4+2\,B\,a\,c^4+2\,B\,b\,c^4-7\,A\,a\,b^2\,c^2-3\,A\,a^2\,b\,c^2+8\,B\,a\,b^2\,c^2-8\,B\,a^2\,b\,c^2\right)}{{\left(a-b\right)}^2\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,B\,c^5-2\,A\,c^5+7\,A\,a^2\,c^3-A\,b^2\,c^3-4\,B\,a^2\,c^3+4\,B\,b^2\,c^3+4\,A\,a^4\,c+A\,b^4\,c+2\,B\,a^4\,c+2\,B\,b^4\,c-6\,A\,a\,b\,c^3-6\,A\,a\,b^3\,c-12\,A\,a^3\,b\,c-9\,B\,a\,b^3\,c-9\,B\,a^3\,b\,c+13\,A\,a^2\,b^2\,c+14\,B\,a^2\,b^2\,c\right)}{{\left(a-b\right)}^2\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(A\,b^4-2\,B\,a^4+2\,A\,c^4-2\,B\,b^4-2\,B\,c^4-7\,A\,a^2\,b^2-5\,A\,a^2\,c^2-2\,B\,a^2\,b^2+3\,A\,b^2\,c^2+4\,B\,a^2\,c^2-4\,B\,b^2\,c^2+2\,A\,a\,b^3+4\,A\,a^3\,b+3\,B\,a\,b^3+3\,B\,a^3\,b+2\,A\,a\,b\,c^2\right)}{\left(a-b\right)\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+2\,a\,b+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a\,c+4\,b\,c\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(4\,a\,c-4\,b\,c\right)+a^2+b^2+{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^2-2\,b^2+4\,c^2\right)}-\frac{\mathrm{atanh}\left(\frac{2\,a^4\,c-4\,a^2\,b^2\,c-4\,a^2\,c^3+2\,b^4\,c+4\,b^2\,c^3+2\,c^5}{2\,{\left(-a^2+b^2+c^2\right)}^{5/2}}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}{2\,{\left(-a^2+b^2+c^2\right)}^{5/2}}\right)\,\left(2\,A\,a^2-3\,B\,a\,b+A\,b^2+A\,c^2\right)}{{\left(-a^2+b^2+c^2\right)}^{5/2}}","Not used",1,"- ((A*a^2*c^3 + A*b^2*c^3 - 4*A*a^4*c + A*b^4*c - 2*B*a*b*c^3 - 5*B*a*b^3*c + 5*B*a^3*b*c + 3*A*a^2*b^2*c)/((a - b)^2*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)) - (tan(x/2)*(A*b^5 + 2*B*a^5 + 2*B*b^5 + 3*A*a^2*b^3 + 5*A*a^3*b^2 + 11*A*a^3*c^2 + B*a^2*b^3 + B*a^3*b^2 - A*b^3*c^2 - 4*B*a^3*c^2 + 4*B*b^3*c^2 - 5*A*a*b^4 - 4*A*a^4*b - 2*A*a*c^4 - 3*B*a*b^4 - 3*B*a^4*b - 2*A*b*c^4 + 2*B*a*c^4 + 2*B*b*c^4 - 7*A*a*b^2*c^2 - 3*A*a^2*b*c^2 + 8*B*a*b^2*c^2 - 8*B*a^2*b*c^2))/((a - b)^2*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)) - (tan(x/2)^2*(2*B*c^5 - 2*A*c^5 + 7*A*a^2*c^3 - A*b^2*c^3 - 4*B*a^2*c^3 + 4*B*b^2*c^3 + 4*A*a^4*c + A*b^4*c + 2*B*a^4*c + 2*B*b^4*c - 6*A*a*b*c^3 - 6*A*a*b^3*c - 12*A*a^3*b*c - 9*B*a*b^3*c - 9*B*a^3*b*c + 13*A*a^2*b^2*c + 14*B*a^2*b^2*c))/((a - b)^2*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)) + (tan(x/2)^3*(A*b^4 - 2*B*a^4 + 2*A*c^4 - 2*B*b^4 - 2*B*c^4 - 7*A*a^2*b^2 - 5*A*a^2*c^2 - 2*B*a^2*b^2 + 3*A*b^2*c^2 + 4*B*a^2*c^2 - 4*B*b^2*c^2 + 2*A*a*b^3 + 4*A*a^3*b + 3*B*a*b^3 + 3*B*a^3*b + 2*A*a*b*c^2))/((a - b)*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)))/(tan(x/2)^4*(a^2 - 2*a*b + b^2) + 2*a*b + tan(x/2)*(4*a*c + 4*b*c) + tan(x/2)^3*(4*a*c - 4*b*c) + a^2 + b^2 + tan(x/2)^2*(2*a^2 - 2*b^2 + 4*c^2)) - (atanh((2*a^4*c + 2*b^4*c + 2*c^5 - 4*a^2*c^3 + 4*b^2*c^3 - 4*a^2*b^2*c)/(2*(b^2 - a^2 + c^2)^(5/2)) + (tan(x/2)*(2*a - 2*b)*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2))/(2*(b^2 - a^2 + c^2)^(5/2)))*(2*A*a^2 + A*b^2 + A*c^2 - 3*B*a*b))/(b^2 - a^2 + c^2)^(5/2)","B"
538,1,99,84,4.332717,"\text{Not used}","int((A + B*cos(x))/(a + b*cos(x) + b*sin(x)*1i),x)","\frac{B}{a\,\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)}+\frac{B\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2\,b}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,\left(A\,a\,1{}\mathrm{i}-\frac{B\,b\,1{}\mathrm{i}}{2}\right)}{a^2}-\frac{\ln\left(a+b-a\,\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}+b\,\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}\right)\,\left(B\,a^2-2\,A\,a\,b+B\,b^2\right)\,1{}\mathrm{i}}{2\,a^2\,b}","Not used",1,"B/(a*(tan(x/2) - 1i)) + (B*log(tan(x/2) + 1i)*1i)/(2*b) - (log(tan(x/2) - 1i)*(A*a*1i - (B*b*1i)/2))/a^2 - (log(a + b - a*tan(x/2)*1i + b*tan(x/2)*1i)*(B*a^2 + B*b^2 - 2*A*a*b)*1i)/(2*a^2*b)","B"
539,1,584,84,8.385699,"\text{Not used}","int((A + B*cos(x))/(a + b*cos(x) - b*sin(x)*1i),x)","\left(\sum _{k=1}^3\ln\left(-{\left(a-b\right)}^2\,\left(4\,A^2\,a^2-4\,A\,B\,a\,b-B^2\,a^2+B^2\,b^2\right)\,1{}\mathrm{i}-\mathrm{root}\left(a^4\,b^2\,d^3\,64{}\mathrm{i}-A\,B\,a\,b^3\,d\,64{}\mathrm{i}-A\,B\,a^3\,b\,d\,32{}\mathrm{i}+B^2\,a^2\,b^2\,d\,16{}\mathrm{i}+A^2\,a^2\,b^2\,d\,64{}\mathrm{i}+B^2\,b^4\,d\,16{}\mathrm{i}+B^2\,a^4\,d\,16{}\mathrm{i}-32\,A^2\,B\,a^2\,b+32\,A\,B^2\,a\,b^2-8\,B^3\,a^2\,b+16\,A\,B^2\,a^3-8\,B^3\,b^3,d,k\right)\,\left(4\,A\,a^3\,{\left(a-b\right)}^2-\mathrm{root}\left(a^4\,b^2\,d^3\,64{}\mathrm{i}-A\,B\,a\,b^3\,d\,64{}\mathrm{i}-A\,B\,a^3\,b\,d\,32{}\mathrm{i}+B^2\,a^2\,b^2\,d\,16{}\mathrm{i}+A^2\,a^2\,b^2\,d\,64{}\mathrm{i}+B^2\,b^4\,d\,16{}\mathrm{i}+B^2\,a^4\,d\,16{}\mathrm{i}-32\,A^2\,B\,a^2\,b+32\,A\,B^2\,a\,b^2-8\,B^3\,a^2\,b+16\,A\,B^2\,a^3-8\,B^3\,b^3,d,k\right)\,a^2\,{\left(a-b\right)}^2\,\left(a^2\,\mathrm{tan}\left(\frac{x}{2}\right)+b^2\,\mathrm{tan}\left(\frac{x}{2}\right)-a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)-a^2\,1{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,8+4\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,{\left(a-b\right)}^2\,\left(A\,a^2\,1{}\mathrm{i}+B\,a^2\,1{}\mathrm{i}+B\,b^2\,1{}\mathrm{i}-A\,a\,b\,2{}\mathrm{i}-B\,a\,b\,1{}\mathrm{i}\right)\right)+\mathrm{tan}\left(\frac{x}{2}\right)\,{\left(a-b\right)}^2\,{\left(B\,a-2\,A\,a+B\,b\right)}^2\right)\,\mathrm{root}\left(a^4\,b^2\,d^3\,64{}\mathrm{i}-A\,B\,a\,b^3\,d\,64{}\mathrm{i}-A\,B\,a^3\,b\,d\,32{}\mathrm{i}+B^2\,a^2\,b^2\,d\,16{}\mathrm{i}+A^2\,a^2\,b^2\,d\,64{}\mathrm{i}+B^2\,b^4\,d\,16{}\mathrm{i}+B^2\,a^4\,d\,16{}\mathrm{i}-32\,A^2\,B\,a^2\,b+32\,A\,B^2\,a\,b^2-8\,B^3\,a^2\,b+16\,A\,B^2\,a^3-8\,B^3\,b^3,d,k\right)\right)+\frac{B}{a\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)}","Not used",1,"symsum(log(tan(x/2)*(a - b)^2*(B*a - 2*A*a + B*b)^2 - root(a^4*b^2*d^3*64i - A*B*a*b^3*d*64i - A*B*a^3*b*d*32i + B^2*a^2*b^2*d*16i + A^2*a^2*b^2*d*64i + B^2*b^4*d*16i + B^2*a^4*d*16i - 32*A^2*B*a^2*b + 32*A*B^2*a*b^2 - 8*B^3*a^2*b + 16*A*B^2*a^3 - 8*B^3*b^3, d, k)*(4*A*a^3*(a - b)^2 - 8*root(a^4*b^2*d^3*64i - A*B*a*b^3*d*64i - A*B*a^3*b*d*32i + B^2*a^2*b^2*d*16i + A^2*a^2*b^2*d*64i + B^2*b^4*d*16i + B^2*a^4*d*16i - 32*A^2*B*a^2*b + 32*A*B^2*a*b^2 - 8*B^3*a^2*b + 16*A*B^2*a^3 - 8*B^3*b^3, d, k)*a^2*(a - b)^2*(a^2*tan(x/2) + b^2*tan(x/2) - a^2*1i + b^2*1i - a*b*tan(x/2)) + 4*a*tan(x/2)*(a - b)^2*(A*a^2*1i + B*a^2*1i + B*b^2*1i - A*a*b*2i - B*a*b*1i)) - (a - b)^2*(4*A^2*a^2 - B^2*a^2 + B^2*b^2 - 4*A*B*a*b)*1i)*root(a^4*b^2*d^3*64i - A*B*a*b^3*d*64i - A*B*a^3*b*d*32i + B^2*a^2*b^2*d*16i + A^2*a^2*b^2*d*64i + B^2*b^4*d*16i + B^2*a^4*d*16i - 32*A^2*B*a^2*b + 32*A*B^2*a*b^2 - 8*B^3*a^2*b + 16*A*B^2*a^3 - 8*B^3*b^3, d, k), k, 1, 3) + B/(a*(tan(x/2) + 1i))","B"
540,1,1741,116,24.863183,"\text{Not used}","int((A + C*sin(x))/(a + b*cos(x) + c*sin(x)),x)","\frac{C\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)}{b-c\,1{}\mathrm{i}}-\frac{\ln\left(32\,A\,C^2\,a^2+32\,A\,C^2\,b^2-64\,A\,C^2\,a\,b-32\,A^2\,C\,a\,c+32\,A^2\,C\,b\,c+32\,C\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(A^2\,b+2\,C^2\,a-2\,C^2\,b-2\,A\,C\,c\right)+\frac{\left(C\,b^3+A\,b^2\,\sqrt{-a^2+b^2+c^2}-C\,a^2\,b+A\,c^2\,\sqrt{-a^2+b^2+c^2}+C\,b\,c^2-C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(64\,A^2\,b^2\,c+32\,C^2\,a^2\,c+32\,C^2\,b^2\,c+64\,A\,C\,b^3+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(A^2\,b^2-A^2\,c^2+2\,A\,C\,a\,c-4\,A\,C\,b\,c-2\,C^2\,a^2+2\,C^2\,a\,b+2\,C^2\,c^2\right)-128\,A\,C\,a\,b^2+64\,A\,C\,a^2\,b-64\,A^2\,a\,b\,c-64\,C^2\,a\,b\,c+\frac{\left(C\,b^3+A\,b^2\,\sqrt{-a^2+b^2+c^2}-C\,a^2\,b+A\,c^2\,\sqrt{-a^2+b^2+c^2}+C\,b\,c^2-C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(32\,A\,b^4+32\,A\,a^2\,b^2-32\,A\,a^2\,c^2+32\,A\,b^2\,c^2-32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(-2\,C\,b^3+2\,A\,b^2\,c+2\,C\,a\,b^2+C\,b\,c^2-2\,A\,a\,b\,c+2\,A\,c^3-2\,C\,a\,c^2\right)-64\,A\,a\,b^3+32\,C\,a\,c^3-32\,C\,b\,c^3+64\,C\,b^3\,c-128\,C\,a\,b^2\,c+64\,C\,a^2\,b\,c+\frac{32\,\left(a-b\right)\,\left(C\,b^3+A\,b^2\,\sqrt{-a^2+b^2+c^2}-C\,a^2\,b+A\,c^2\,\sqrt{-a^2+b^2+c^2}+C\,b\,c^2-C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^2-4\,a^2\,b\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,c^2-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^3+a\,b^2\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b\,c^2+a\,c^3+3\,b^3\,c+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2\,c^2+3\,b\,c^3+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,c^4\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)\,\left(C\,b^3-b\,\left(C\,a^2-C\,c^2\right)+A\,b^2\,\sqrt{-a^2+b^2+c^2}+A\,c^2\,\sqrt{-a^2+b^2+c^2}-C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}+\frac{\ln\left(32\,A\,C^2\,a^2+32\,A\,C^2\,b^2-64\,A\,C^2\,a\,b-32\,A^2\,C\,a\,c+32\,A^2\,C\,b\,c+32\,C\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(A^2\,b+2\,C^2\,a-2\,C^2\,b-2\,A\,C\,c\right)+\frac{\left(C\,b^3-A\,b^2\,\sqrt{-a^2+b^2+c^2}-C\,a^2\,b-A\,c^2\,\sqrt{-a^2+b^2+c^2}+C\,b\,c^2+C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(64\,A^2\,b^2\,c+32\,C^2\,a^2\,c+32\,C^2\,b^2\,c+64\,A\,C\,b^3+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(A^2\,b^2-A^2\,c^2+2\,A\,C\,a\,c-4\,A\,C\,b\,c-2\,C^2\,a^2+2\,C^2\,a\,b+2\,C^2\,c^2\right)-128\,A\,C\,a\,b^2+64\,A\,C\,a^2\,b-64\,A^2\,a\,b\,c-64\,C^2\,a\,b\,c+\frac{\left(C\,b^3-A\,b^2\,\sqrt{-a^2+b^2+c^2}-C\,a^2\,b-A\,c^2\,\sqrt{-a^2+b^2+c^2}+C\,b\,c^2+C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(32\,A\,b^4+32\,A\,a^2\,b^2-32\,A\,a^2\,c^2+32\,A\,b^2\,c^2-32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(-2\,C\,b^3+2\,A\,b^2\,c+2\,C\,a\,b^2+C\,b\,c^2-2\,A\,a\,b\,c+2\,A\,c^3-2\,C\,a\,c^2\right)-64\,A\,a\,b^3+32\,C\,a\,c^3-32\,C\,b\,c^3+64\,C\,b^3\,c-128\,C\,a\,b^2\,c+64\,C\,a^2\,b\,c+\frac{32\,\left(a-b\right)\,\left(C\,b^3-A\,b^2\,\sqrt{-a^2+b^2+c^2}-C\,a^2\,b-A\,c^2\,\sqrt{-a^2+b^2+c^2}+C\,b\,c^2+C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^2-4\,a^2\,b\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,c^2-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^3+a\,b^2\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b\,c^2+a\,c^3+3\,b^3\,c+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2\,c^2+3\,b\,c^3+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,c^4\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)\,\left(b\,\left(C\,a^2-C\,c^2\right)-C\,b^3+A\,b^2\,\sqrt{-a^2+b^2+c^2}+A\,c^2\,\sqrt{-a^2+b^2+c^2}-C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}+\frac{C\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,1{}\mathrm{i}}{-c+b\,1{}\mathrm{i}}","Not used",1,"(C*log(tan(x/2) + 1i))/(b - c*1i) + (C*log(tan(x/2) - 1i)*1i)/(b*1i - c) - (log(32*A*C^2*a^2 + 32*A*C^2*b^2 - 64*A*C^2*a*b - 32*A^2*C*a*c + 32*A^2*C*b*c + 32*C*tan(x/2)*(a - b)*(A^2*b + 2*C^2*a - 2*C^2*b - 2*A*C*c) + ((C*b^3 + A*b^2*(b^2 - a^2 + c^2)^(1/2) - C*a^2*b + A*c^2*(b^2 - a^2 + c^2)^(1/2) + C*b*c^2 - C*a*c*(b^2 - a^2 + c^2)^(1/2))*(64*A^2*b^2*c + 32*C^2*a^2*c + 32*C^2*b^2*c + 64*A*C*b^3 + 32*tan(x/2)*(a - b)*(A^2*b^2 - A^2*c^2 - 2*C^2*a^2 + 2*C^2*c^2 + 2*C^2*a*b + 2*A*C*a*c - 4*A*C*b*c) - 128*A*C*a*b^2 + 64*A*C*a^2*b - 64*A^2*a*b*c - 64*C^2*a*b*c + ((C*b^3 + A*b^2*(b^2 - a^2 + c^2)^(1/2) - C*a^2*b + A*c^2*(b^2 - a^2 + c^2)^(1/2) + C*b*c^2 - C*a*c*(b^2 - a^2 + c^2)^(1/2))*(32*A*b^4 + 32*A*a^2*b^2 - 32*A*a^2*c^2 + 32*A*b^2*c^2 - 32*tan(x/2)*(a - b)*(2*A*c^3 - 2*C*b^3 + 2*A*b^2*c + 2*C*a*b^2 - 2*C*a*c^2 + C*b*c^2 - 2*A*a*b*c) - 64*A*a*b^3 + 32*C*a*c^3 - 32*C*b*c^3 + 64*C*b^3*c - 128*C*a*b^2*c + 64*C*a^2*b*c + (32*(a - b)*(C*b^3 + A*b^2*(b^2 - a^2 + c^2)^(1/2) - C*a^2*b + A*c^2*(b^2 - a^2 + c^2)^(1/2) + C*b*c^2 - C*a*c*(b^2 - a^2 + c^2)^(1/2))*(3*c^4*tan(x/2) + a*c^3 + 3*b*c^3 + 3*b^3*c + 2*a^2*b^2*tan(x/2) - 2*a^2*c^2*tan(x/2) + 3*b^2*c^2*tan(x/2) - 2*a*b^3*tan(x/2) + a*b^2*c - 4*a^2*b*c - 2*a*b*c^2*tan(x/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2)))*(C*b^3 - b*(C*a^2 - C*c^2) + A*b^2*(b^2 - a^2 + c^2)^(1/2) + A*c^2*(b^2 - a^2 + c^2)^(1/2) - C*a*c*(b^2 - a^2 + c^2)^(1/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2)) + (log(32*A*C^2*a^2 + 32*A*C^2*b^2 - 64*A*C^2*a*b - 32*A^2*C*a*c + 32*A^2*C*b*c + 32*C*tan(x/2)*(a - b)*(A^2*b + 2*C^2*a - 2*C^2*b - 2*A*C*c) + ((C*b^3 - A*b^2*(b^2 - a^2 + c^2)^(1/2) - C*a^2*b - A*c^2*(b^2 - a^2 + c^2)^(1/2) + C*b*c^2 + C*a*c*(b^2 - a^2 + c^2)^(1/2))*(64*A^2*b^2*c + 32*C^2*a^2*c + 32*C^2*b^2*c + 64*A*C*b^3 + 32*tan(x/2)*(a - b)*(A^2*b^2 - A^2*c^2 - 2*C^2*a^2 + 2*C^2*c^2 + 2*C^2*a*b + 2*A*C*a*c - 4*A*C*b*c) - 128*A*C*a*b^2 + 64*A*C*a^2*b - 64*A^2*a*b*c - 64*C^2*a*b*c + ((C*b^3 - A*b^2*(b^2 - a^2 + c^2)^(1/2) - C*a^2*b - A*c^2*(b^2 - a^2 + c^2)^(1/2) + C*b*c^2 + C*a*c*(b^2 - a^2 + c^2)^(1/2))*(32*A*b^4 + 32*A*a^2*b^2 - 32*A*a^2*c^2 + 32*A*b^2*c^2 - 32*tan(x/2)*(a - b)*(2*A*c^3 - 2*C*b^3 + 2*A*b^2*c + 2*C*a*b^2 - 2*C*a*c^2 + C*b*c^2 - 2*A*a*b*c) - 64*A*a*b^3 + 32*C*a*c^3 - 32*C*b*c^3 + 64*C*b^3*c - 128*C*a*b^2*c + 64*C*a^2*b*c + (32*(a - b)*(C*b^3 - A*b^2*(b^2 - a^2 + c^2)^(1/2) - C*a^2*b - A*c^2*(b^2 - a^2 + c^2)^(1/2) + C*b*c^2 + C*a*c*(b^2 - a^2 + c^2)^(1/2))*(3*c^4*tan(x/2) + a*c^3 + 3*b*c^3 + 3*b^3*c + 2*a^2*b^2*tan(x/2) - 2*a^2*c^2*tan(x/2) + 3*b^2*c^2*tan(x/2) - 2*a*b^3*tan(x/2) + a*b^2*c - 4*a^2*b*c - 2*a*b*c^2*tan(x/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2)))*(b*(C*a^2 - C*c^2) - C*b^3 + A*b^2*(b^2 - a^2 + c^2)^(1/2) + A*c^2*(b^2 - a^2 + c^2)^(1/2) - C*a*c*(b^2 - a^2 + c^2)^(1/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2))","B"
541,1,204,114,3.191179,"\text{Not used}","int((A + C*sin(x))/(a + b*cos(x) + c*sin(x))^2,x)","\frac{2\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a-2\,b\right)+\frac{2\,\left(-a^2\,c+b^2\,c+c^3\right)}{-a^2+b^2+c^2}}{2\,\sqrt{-a^2+b^2+c^2}}\right)\,\left(A\,a-C\,c\right)}{{\left(-a^2+b^2+c^2\right)}^{3/2}}-\frac{\frac{2\,\left(-C\,a^2+A\,c\,a+C\,b^2\right)}{\left(a-b\right)\,\left(-a^2+b^2+c^2\right)}+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A\,b^2+C\,b\,c-A\,a\,b+A\,c^2-C\,a\,c\right)}{\left(a-b\right)\,\left(-a^2+b^2+c^2\right)}}{\left(a-b\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,c\,\mathrm{tan}\left(\frac{x}{2}\right)+a+b}","Not used",1,"(2*atanh((tan(x/2)*(2*a - 2*b) + (2*(b^2*c - a^2*c + c^3))/(b^2 - a^2 + c^2))/(2*(b^2 - a^2 + c^2)^(1/2)))*(A*a - C*c))/(b^2 - a^2 + c^2)^(3/2) - ((2*(C*b^2 - C*a^2 + A*a*c))/((a - b)*(b^2 - a^2 + c^2)) + (2*tan(x/2)*(A*b^2 + A*c^2 - A*a*b - C*a*c + C*b*c))/((a - b)*(b^2 - a^2 + c^2)))/(a + b + 2*c*tan(x/2) + tan(x/2)^2*(a - b))","B"
542,1,912,200,6.734419,"\text{Not used}","int((A + C*sin(x))/(a + b*cos(x) + c*sin(x))^3,x)","-\frac{\frac{2\,C\,a^5-4\,A\,a^4\,c-4\,C\,a^3\,b^2+C\,a^3\,c^2+3\,A\,a^2\,b^2\,c+A\,a^2\,c^3+2\,C\,a\,b^4-C\,a\,b^2\,c^2+A\,b^4\,c+A\,b^2\,c^3}{{\left(a-b\right)}^2\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,A\,a^4\,b+5\,C\,a^4\,c-5\,A\,a^3\,b^2-5\,C\,a^3\,b\,c-11\,A\,a^3\,c^2-3\,A\,a^2\,b^3-5\,C\,a^2\,b^2\,c+3\,A\,a^2\,b\,c^2+4\,C\,a^2\,c^3+5\,A\,a\,b^4+5\,C\,a\,b^3\,c+7\,A\,a\,b^2\,c^2-4\,C\,a\,b\,c^3+2\,A\,a\,c^4-A\,b^5+A\,b^3\,c^2+2\,A\,b\,c^4\right)}{{\left(a-b\right)}^2\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,C\,a^5-2\,C\,a^4\,b-4\,A\,a^4\,c-4\,C\,a^3\,b^2+12\,A\,a^3\,b\,c+5\,C\,a^3\,c^2+4\,C\,a^2\,b^3-13\,A\,a^2\,b^2\,c-14\,C\,a^2\,b\,c^2-7\,A\,a^2\,c^3+2\,C\,a\,b^4+6\,A\,a\,b^3\,c+13\,C\,a\,b^2\,c^2+6\,A\,a\,b\,c^3+2\,C\,a\,c^4-2\,C\,b^5-A\,b^4\,c-4\,C\,b^3\,c^2+A\,b^2\,c^3-2\,C\,b\,c^4+2\,A\,c^5\right)}{{\left(a-b\right)}^2\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(4\,A\,a^3\,b+3\,C\,a^3\,c-7\,A\,a^2\,b^2-6\,C\,a^2\,b\,c-5\,A\,a^2\,c^2+2\,A\,a\,b^3+3\,C\,a\,b^2\,c+2\,A\,a\,b\,c^2+A\,b^4+3\,A\,b^2\,c^2+2\,A\,c^4\right)}{\left(a-b\right)\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+2\,a\,b+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a\,c+4\,b\,c\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(4\,a\,c-4\,b\,c\right)+a^2+b^2+{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^2-2\,b^2+4\,c^2\right)}-\frac{\mathrm{atanh}\left(\frac{2\,a^4\,c-4\,a^2\,b^2\,c-4\,a^2\,c^3+2\,b^4\,c+4\,b^2\,c^3+2\,c^5}{2\,{\left(-a^2+b^2+c^2\right)}^{5/2}}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}{2\,{\left(-a^2+b^2+c^2\right)}^{5/2}}\right)\,\left(2\,A\,a^2-3\,C\,a\,c+A\,b^2+A\,c^2\right)}{{\left(-a^2+b^2+c^2\right)}^{5/2}}","Not used",1,"- ((2*C*a^5 + A*a^2*c^3 + A*b^2*c^3 - 4*C*a^3*b^2 + C*a^3*c^2 - 4*A*a^4*c + A*b^4*c + 2*C*a*b^4 + 3*A*a^2*b^2*c - C*a*b^2*c^2)/((a - b)^2*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)) + (tan(x/2)*(A*b^3*c^2 - 3*A*a^2*b^3 - 5*A*a^3*b^2 - 11*A*a^3*c^2 - A*b^5 + 4*C*a^2*c^3 + 5*A*a*b^4 + 4*A*a^4*b + 2*A*a*c^4 + 2*A*b*c^4 + 5*C*a^4*c - 4*C*a*b*c^3 + 5*C*a*b^3*c - 5*C*a^3*b*c + 7*A*a*b^2*c^2 + 3*A*a^2*b*c^2 - 5*C*a^2*b^2*c))/((a - b)^2*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)) + (tan(x/2)^2*(2*A*c^5 + 2*C*a^5 - 2*C*b^5 - 7*A*a^2*c^3 + A*b^2*c^3 + 4*C*a^2*b^3 - 4*C*a^3*b^2 + 5*C*a^3*c^2 - 4*C*b^3*c^2 - 4*A*a^4*c - A*b^4*c + 2*C*a*b^4 - 2*C*a^4*b + 2*C*a*c^4 - 2*C*b*c^4 + 6*A*a*b*c^3 + 6*A*a*b^3*c + 12*A*a^3*b*c - 13*A*a^2*b^2*c + 13*C*a*b^2*c^2 - 14*C*a^2*b*c^2))/((a - b)^2*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)) + (tan(x/2)^3*(A*b^4 + 2*A*c^4 - 7*A*a^2*b^2 - 5*A*a^2*c^2 + 3*A*b^2*c^2 + 2*A*a*b^3 + 4*A*a^3*b + 3*C*a^3*c + 2*A*a*b*c^2 + 3*C*a*b^2*c - 6*C*a^2*b*c))/((a - b)*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)))/(tan(x/2)^4*(a^2 - 2*a*b + b^2) + 2*a*b + tan(x/2)*(4*a*c + 4*b*c) + tan(x/2)^3*(4*a*c - 4*b*c) + a^2 + b^2 + tan(x/2)^2*(2*a^2 - 2*b^2 + 4*c^2)) - (atanh((2*a^4*c + 2*b^4*c + 2*c^5 - 4*a^2*c^3 + 4*b^2*c^3 - 4*a^2*b^2*c)/(2*(b^2 - a^2 + c^2)^(5/2)) + (tan(x/2)*(2*a - 2*b)*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2))/(2*(b^2 - a^2 + c^2)^(5/2)))*(2*A*a^2 + A*b^2 + A*c^2 - 3*C*a*c))/(b^2 - a^2 + c^2)^(5/2)","B"
543,1,96,85,4.354161,"\text{Not used}","int((A + C*sin(x))/(a + b*cos(x) + b*sin(x)*1i),x)","\ln\left(a+b-a\,\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}+b\,\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}\right)\,\left(\frac{C\,b}{2\,a^2}-\frac{C}{2\,b}+\frac{A\,1{}\mathrm{i}}{a}\right)+\frac{C\,1{}\mathrm{i}}{a\,\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)}+\frac{C\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)}{2\,b}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,\left(\frac{C\,b}{2}+A\,a\,1{}\mathrm{i}\right)}{a^2}","Not used",1,"log(a + b - a*tan(x/2)*1i + b*tan(x/2)*1i)*((A*1i)/a - C/(2*b) + (C*b)/(2*a^2)) + (C*1i)/(a*(tan(x/2) - 1i)) + (C*log(tan(x/2) + 1i))/(2*b) - (log(tan(x/2) - 1i)*(A*a*1i + (C*b)/2))/a^2","B"
544,1,96,85,4.343362,"\text{Not used}","int((A + C*sin(x))/(a + b*cos(x) - b*sin(x)*1i),x)","-\ln\left(a+b+a\,\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}-b\,\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}\right)\,\left(\frac{C}{2\,b}-\frac{C\,b}{2\,a^2}+\frac{A\,1{}\mathrm{i}}{a}\right)-\frac{C\,1{}\mathrm{i}}{a\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)}+\frac{C\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)}{2\,b}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)\,\left(-\frac{C\,b}{2}+A\,a\,1{}\mathrm{i}\right)}{a^2}","Not used",1,"(C*log(tan(x/2) - 1i))/(2*b) - (C*1i)/(a*(tan(x/2) + 1i)) - log(a + b + a*tan(x/2)*1i - b*tan(x/2)*1i)*((A*1i)/a + C/(2*b) - (C*b)/(2*a^2)) + (log(tan(x/2) + 1i)*(A*a*1i - (C*b)/2))/a^2","B"
545,1,1864,119,28.555065,"\text{Not used}","int((B*cos(x) + C*sin(x))/(a + b*cos(x) + c*sin(x)),x)","\frac{\ln\left(32\,B^3\,a^2+32\,B\,C^2\,a^2+32\,B\,C^2\,b^2+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(2\,C^3\,a+B^3\,c-2\,C^3\,b+2\,B^2\,C\,a-B^2\,C\,b+2\,B\,C^2\,c\right)-32\,B^3\,a\,b-64\,B\,C^2\,a\,b+32\,B^2\,C\,a\,c-32\,B^2\,C\,b\,c-\frac{\left(B\,c^3-C\,b^3-B\,a^2\,c+C\,a^2\,b+B\,b^2\,c-C\,b\,c^2+B\,a\,b\,\sqrt{-a^2+b^2+c^2}+C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(32\,B^2\,b^2\,c-32\,B^2\,a^2\,c+32\,C^2\,a^2\,c+32\,C^2\,b^2\,c+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(2\,B^2\,a^2-2\,B^2\,a\,b+B^2\,b^2-3\,B^2\,c^2-4\,B\,C\,a\,c+6\,B\,C\,b\,c-2\,C^2\,a^2+2\,C^2\,a\,b+2\,C^2\,c^2\right)-128\,B\,C\,a^3-64\,B\,C\,b^3+192\,B\,C\,a^2\,b+64\,B\,C\,a\,c^2-64\,B\,C\,b\,c^2-64\,C^2\,a\,b\,c+\frac{\left(B\,c^3-C\,b^3-B\,a^2\,c+C\,a^2\,b+B\,b^2\,c-C\,b\,c^2+B\,a\,b\,\sqrt{-a^2+b^2+c^2}+C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(32\,B\,a^2\,c^2-32\,B\,a^2\,b^2-32\,B\,b^4+64\,B\,b^2\,c^2+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(-2\,C\,b^3+4\,B\,b^2\,c+2\,C\,a\,b^2+C\,b\,c^2-4\,B\,a\,b\,c+B\,c^3-2\,C\,a\,c^2\right)+64\,B\,a\,b^3-32\,C\,a\,c^3+32\,C\,b\,c^3-64\,C\,b^3\,c-96\,B\,a\,b\,c^2+128\,C\,a\,b^2\,c-64\,C\,a^2\,b\,c+\frac{32\,\left(a-b\right)\,\left(B\,c^3-C\,b^3-B\,a^2\,c+C\,a^2\,b+B\,b^2\,c-C\,b\,c^2+B\,a\,b\,\sqrt{-a^2+b^2+c^2}+C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^2-4\,a^2\,b\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,c^2-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^3+a\,b^2\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b\,c^2+a\,c^3+3\,b^3\,c+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2\,c^2+3\,b\,c^3+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,c^4\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)\,\left(B\,c^3-C\,b^3-B\,a^2\,c+C\,a^2\,b+B\,b^2\,c-C\,b\,c^2+B\,a\,b\,\sqrt{-a^2+b^2+c^2}+C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,\left(B+C\,1{}\mathrm{i}\right)}{-c+b\,1{}\mathrm{i}}-\frac{\ln\left(32\,B^3\,a^2+32\,B\,C^2\,a^2+32\,B\,C^2\,b^2+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(2\,C^3\,a+B^3\,c-2\,C^3\,b+2\,B^2\,C\,a-B^2\,C\,b+2\,B\,C^2\,c\right)-32\,B^3\,a\,b-64\,B\,C^2\,a\,b+32\,B^2\,C\,a\,c-32\,B^2\,C\,b\,c+\frac{\left(C\,b^3-B\,c^3+B\,a^2\,c-C\,a^2\,b-B\,b^2\,c+C\,b\,c^2+B\,a\,b\,\sqrt{-a^2+b^2+c^2}+C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(32\,B^2\,b^2\,c-32\,B^2\,a^2\,c+32\,C^2\,a^2\,c+32\,C^2\,b^2\,c+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(2\,B^2\,a^2-2\,B^2\,a\,b+B^2\,b^2-3\,B^2\,c^2-4\,B\,C\,a\,c+6\,B\,C\,b\,c-2\,C^2\,a^2+2\,C^2\,a\,b+2\,C^2\,c^2\right)-128\,B\,C\,a^3-64\,B\,C\,b^3+192\,B\,C\,a^2\,b+64\,B\,C\,a\,c^2-64\,B\,C\,b\,c^2-64\,C^2\,a\,b\,c+\frac{\left(C\,b^3-B\,c^3+B\,a^2\,c-C\,a^2\,b-B\,b^2\,c+C\,b\,c^2+B\,a\,b\,\sqrt{-a^2+b^2+c^2}+C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(32\,B\,b^4+32\,B\,a^2\,b^2-32\,B\,a^2\,c^2-64\,B\,b^2\,c^2-32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(-2\,C\,b^3+4\,B\,b^2\,c+2\,C\,a\,b^2+C\,b\,c^2-4\,B\,a\,b\,c+B\,c^3-2\,C\,a\,c^2\right)-64\,B\,a\,b^3+32\,C\,a\,c^3-32\,C\,b\,c^3+64\,C\,b^3\,c+96\,B\,a\,b\,c^2-128\,C\,a\,b^2\,c+64\,C\,a^2\,b\,c+\frac{32\,\left(a-b\right)\,\left(C\,b^3-B\,c^3+B\,a^2\,c-C\,a^2\,b-B\,b^2\,c+C\,b\,c^2+B\,a\,b\,\sqrt{-a^2+b^2+c^2}+C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^2-4\,a^2\,b\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,c^2-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^3+a\,b^2\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b\,c^2+a\,c^3+3\,b^3\,c+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2\,c^2+3\,b\,c^3+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,c^4\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)\,\left(C\,b^3-B\,c^3+B\,a^2\,c-C\,a^2\,b-B\,b^2\,c+C\,b\,c^2+B\,a\,b\,\sqrt{-a^2+b^2+c^2}+C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)\,\left(B-C\,1{}\mathrm{i}\right)}{c+b\,1{}\mathrm{i}}","Not used",1,"(log(tan(x/2) - 1i)*(B + C*1i))/(b*1i - c) - (log(tan(x/2) + 1i)*(B - C*1i))/(b*1i + c) - (log(32*B^3*a^2 + 32*B*C^2*a^2 + 32*B*C^2*b^2 + 32*tan(x/2)*(a - b)*(2*C^3*a + B^3*c - 2*C^3*b + 2*B^2*C*a - B^2*C*b + 2*B*C^2*c) - 32*B^3*a*b - 64*B*C^2*a*b + 32*B^2*C*a*c - 32*B^2*C*b*c + ((C*b^3 - B*c^3 + B*a^2*c - C*a^2*b - B*b^2*c + C*b*c^2 + B*a*b*(b^2 - a^2 + c^2)^(1/2) + C*a*c*(b^2 - a^2 + c^2)^(1/2))*(32*B^2*b^2*c - 32*B^2*a^2*c + 32*C^2*a^2*c + 32*C^2*b^2*c + 32*tan(x/2)*(a - b)*(2*B^2*a^2 + B^2*b^2 - 2*C^2*a^2 - 3*B^2*c^2 + 2*C^2*c^2 - 2*B^2*a*b + 2*C^2*a*b - 4*B*C*a*c + 6*B*C*b*c) - 128*B*C*a^3 - 64*B*C*b^3 + 192*B*C*a^2*b + 64*B*C*a*c^2 - 64*B*C*b*c^2 - 64*C^2*a*b*c + ((C*b^3 - B*c^3 + B*a^2*c - C*a^2*b - B*b^2*c + C*b*c^2 + B*a*b*(b^2 - a^2 + c^2)^(1/2) + C*a*c*(b^2 - a^2 + c^2)^(1/2))*(32*B*b^4 + 32*B*a^2*b^2 - 32*B*a^2*c^2 - 64*B*b^2*c^2 - 32*tan(x/2)*(a - b)*(B*c^3 - 2*C*b^3 + 2*C*a*b^2 + 4*B*b^2*c - 2*C*a*c^2 + C*b*c^2 - 4*B*a*b*c) - 64*B*a*b^3 + 32*C*a*c^3 - 32*C*b*c^3 + 64*C*b^3*c + 96*B*a*b*c^2 - 128*C*a*b^2*c + 64*C*a^2*b*c + (32*(a - b)*(C*b^3 - B*c^3 + B*a^2*c - C*a^2*b - B*b^2*c + C*b*c^2 + B*a*b*(b^2 - a^2 + c^2)^(1/2) + C*a*c*(b^2 - a^2 + c^2)^(1/2))*(3*c^4*tan(x/2) + a*c^3 + 3*b*c^3 + 3*b^3*c + 2*a^2*b^2*tan(x/2) - 2*a^2*c^2*tan(x/2) + 3*b^2*c^2*tan(x/2) - 2*a*b^3*tan(x/2) + a*b^2*c - 4*a^2*b*c - 2*a*b*c^2*tan(x/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2)))*(C*b^3 - B*c^3 + B*a^2*c - C*a^2*b - B*b^2*c + C*b*c^2 + B*a*b*(b^2 - a^2 + c^2)^(1/2) + C*a*c*(b^2 - a^2 + c^2)^(1/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2)) + (log(32*B^3*a^2 + 32*B*C^2*a^2 + 32*B*C^2*b^2 + 32*tan(x/2)*(a - b)*(2*C^3*a + B^3*c - 2*C^3*b + 2*B^2*C*a - B^2*C*b + 2*B*C^2*c) - 32*B^3*a*b - 64*B*C^2*a*b + 32*B^2*C*a*c - 32*B^2*C*b*c - ((B*c^3 - C*b^3 - B*a^2*c + C*a^2*b + B*b^2*c - C*b*c^2 + B*a*b*(b^2 - a^2 + c^2)^(1/2) + C*a*c*(b^2 - a^2 + c^2)^(1/2))*(32*B^2*b^2*c - 32*B^2*a^2*c + 32*C^2*a^2*c + 32*C^2*b^2*c + 32*tan(x/2)*(a - b)*(2*B^2*a^2 + B^2*b^2 - 2*C^2*a^2 - 3*B^2*c^2 + 2*C^2*c^2 - 2*B^2*a*b + 2*C^2*a*b - 4*B*C*a*c + 6*B*C*b*c) - 128*B*C*a^3 - 64*B*C*b^3 + 192*B*C*a^2*b + 64*B*C*a*c^2 - 64*B*C*b*c^2 - 64*C^2*a*b*c + ((B*c^3 - C*b^3 - B*a^2*c + C*a^2*b + B*b^2*c - C*b*c^2 + B*a*b*(b^2 - a^2 + c^2)^(1/2) + C*a*c*(b^2 - a^2 + c^2)^(1/2))*(32*B*a^2*c^2 - 32*B*a^2*b^2 - 32*B*b^4 + 64*B*b^2*c^2 + 32*tan(x/2)*(a - b)*(B*c^3 - 2*C*b^3 + 2*C*a*b^2 + 4*B*b^2*c - 2*C*a*c^2 + C*b*c^2 - 4*B*a*b*c) + 64*B*a*b^3 - 32*C*a*c^3 + 32*C*b*c^3 - 64*C*b^3*c - 96*B*a*b*c^2 + 128*C*a*b^2*c - 64*C*a^2*b*c + (32*(a - b)*(B*c^3 - C*b^3 - B*a^2*c + C*a^2*b + B*b^2*c - C*b*c^2 + B*a*b*(b^2 - a^2 + c^2)^(1/2) + C*a*c*(b^2 - a^2 + c^2)^(1/2))*(3*c^4*tan(x/2) + a*c^3 + 3*b*c^3 + 3*b^3*c + 2*a^2*b^2*tan(x/2) - 2*a^2*c^2*tan(x/2) + 3*b^2*c^2*tan(x/2) - 2*a*b^3*tan(x/2) + a*b^2*c - 4*a^2*b*c - 2*a*b*c^2*tan(x/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2)))*(B*c^3 - C*b^3 - B*a^2*c + C*a^2*b + B*b^2*c - C*b*c^2 + B*a*b*(b^2 - a^2 + c^2)^(1/2) + C*a*c*(b^2 - a^2 + c^2)^(1/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2))","B"
546,1,202,110,3.238087,"\text{Not used}","int((B*cos(x) + C*sin(x))/(a + b*cos(x) + c*sin(x))^2,x)","\frac{\frac{2\,\left(C\,a^2-C\,b^2+B\,c\,b\right)}{\left(a-b\right)\,\left(-a^2+b^2+c^2\right)}+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-B\,a^2+C\,a\,c+B\,b\,a+B\,c^2-C\,b\,c\right)}{\left(a-b\right)\,\left(-a^2+b^2+c^2\right)}}{\left(a-b\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,c\,\mathrm{tan}\left(\frac{x}{2}\right)+a+b}-\frac{2\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a-2\,b\right)+\frac{2\,\left(-a^2\,c+b^2\,c+c^3\right)}{-a^2+b^2+c^2}}{2\,\sqrt{-a^2+b^2+c^2}}\right)\,\left(B\,b+C\,c\right)}{{\left(-a^2+b^2+c^2\right)}^{3/2}}","Not used",1,"((2*(C*a^2 - C*b^2 + B*b*c))/((a - b)*(b^2 - a^2 + c^2)) + (2*tan(x/2)*(B*c^2 - B*a^2 + B*a*b + C*a*c - C*b*c))/((a - b)*(b^2 - a^2 + c^2)))/(a + b + 2*c*tan(x/2) + tan(x/2)^2*(a - b)) - (2*atanh((tan(x/2)*(2*a - 2*b) + (2*(b^2*c - a^2*c + c^3))/(b^2 - a^2 + c^2))/(2*(b^2 - a^2 + c^2)^(1/2)))*(B*b + C*c))/(b^2 - a^2 + c^2)^(3/2)","B"
547,1,923,197,6.362194,"\text{Not used}","int((B*cos(x) + C*sin(x))/(a + b*cos(x) + c*sin(x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(2\,B\,a^4-3\,B\,a^3\,b-3\,C\,a^3\,c+2\,B\,a^2\,b^2+6\,C\,a^2\,b\,c-4\,B\,a^2\,c^2-3\,B\,a\,b^3-3\,C\,a\,b^2\,c+2\,B\,b^4+4\,B\,b^2\,c^2+2\,B\,c^4\right)}{\left(a-b\right)\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}-\frac{2\,C\,a^5-4\,C\,a^3\,b^2+5\,B\,a^3\,b\,c+C\,a^3\,c^2+2\,C\,a\,b^4-5\,B\,a\,b^3\,c-C\,a\,b^2\,c^2-2\,B\,a\,b\,c^3}{{\left(a-b\right)}^2\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(-2\,C\,a^5+2\,C\,a^4\,b+2\,B\,a^4\,c+4\,C\,a^3\,b^2-9\,B\,a^3\,b\,c-5\,C\,a^3\,c^2-4\,C\,a^2\,b^3+14\,B\,a^2\,b^2\,c+14\,C\,a^2\,b\,c^2-4\,B\,a^2\,c^3-2\,C\,a\,b^4-9\,B\,a\,b^3\,c-13\,C\,a\,b^2\,c^2-2\,C\,a\,c^4+2\,C\,b^5+2\,B\,b^4\,c+4\,C\,b^3\,c^2+4\,B\,b^2\,c^3+2\,C\,b\,c^4+2\,B\,c^5\right)}{{\left(a-b\right)}^2\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,B\,a^5-3\,B\,a^4\,b-5\,C\,a^4\,c+B\,a^3\,b^2+5\,C\,a^3\,b\,c-4\,B\,a^3\,c^2+B\,a^2\,b^3+5\,C\,a^2\,b^2\,c-8\,B\,a^2\,b\,c^2-4\,C\,a^2\,c^3-3\,B\,a\,b^4-5\,C\,a\,b^3\,c+8\,B\,a\,b^2\,c^2+4\,C\,a\,b\,c^3+2\,B\,a\,c^4+2\,B\,b^5+4\,B\,b^3\,c^2+2\,B\,b\,c^4\right)}{{\left(a-b\right)}^2\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+2\,a\,b+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a\,c+4\,b\,c\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(4\,a\,c-4\,b\,c\right)+a^2+b^2+{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^2-2\,b^2+4\,c^2\right)}+\frac{3\,a\,\mathrm{atanh}\left(\frac{3\,a\,\left(B\,b+C\,c\right)\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a-2\,b\right)+\frac{2\,a^4\,c-4\,a^2\,b^2\,c-4\,a^2\,c^3+2\,b^4\,c+4\,b^2\,c^3+2\,c^5}{a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4}\right)\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}{2\,\left(3\,B\,a\,b+3\,C\,a\,c\right)\,{\left(-a^2+b^2+c^2\right)}^{5/2}}\right)\,\left(B\,b+C\,c\right)}{{\left(-a^2+b^2+c^2\right)}^{5/2}}","Not used",1,"((tan(x/2)^3*(2*B*a^4 + 2*B*b^4 + 2*B*c^4 + 2*B*a^2*b^2 - 4*B*a^2*c^2 + 4*B*b^2*c^2 - 3*B*a*b^3 - 3*B*a^3*b - 3*C*a^3*c - 3*C*a*b^2*c + 6*C*a^2*b*c))/((a - b)*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)) - (2*C*a^5 - 4*C*a^3*b^2 + C*a^3*c^2 + 2*C*a*b^4 - 2*B*a*b*c^3 - 5*B*a*b^3*c + 5*B*a^3*b*c - C*a*b^2*c^2)/((a - b)^2*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)) + (tan(x/2)^2*(2*B*c^5 - 2*C*a^5 + 2*C*b^5 - 4*B*a^2*c^3 - 4*C*a^2*b^3 + 4*C*a^3*b^2 + 4*B*b^2*c^3 - 5*C*a^3*c^2 + 4*C*b^3*c^2 + 2*B*a^4*c - 2*C*a*b^4 + 2*C*a^4*b + 2*B*b^4*c - 2*C*a*c^4 + 2*C*b*c^4 - 9*B*a*b^3*c - 9*B*a^3*b*c + 14*B*a^2*b^2*c - 13*C*a*b^2*c^2 + 14*C*a^2*b*c^2))/((a - b)^2*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)) + (tan(x/2)*(2*B*a^5 + 2*B*b^5 + B*a^2*b^3 + B*a^3*b^2 - 4*B*a^3*c^2 + 4*B*b^3*c^2 - 4*C*a^2*c^3 - 3*B*a*b^4 - 3*B*a^4*b + 2*B*a*c^4 + 2*B*b*c^4 - 5*C*a^4*c + 4*C*a*b*c^3 - 5*C*a*b^3*c + 5*C*a^3*b*c + 8*B*a*b^2*c^2 - 8*B*a^2*b*c^2 + 5*C*a^2*b^2*c))/((a - b)^2*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)))/(tan(x/2)^4*(a^2 - 2*a*b + b^2) + 2*a*b + tan(x/2)*(4*a*c + 4*b*c) + tan(x/2)^3*(4*a*c - 4*b*c) + a^2 + b^2 + tan(x/2)^2*(2*a^2 - 2*b^2 + 4*c^2)) + (3*a*atanh((3*a*(B*b + C*c)*(tan(x/2)*(2*a - 2*b) + (2*a^4*c + 2*b^4*c + 2*c^5 - 4*a^2*c^3 + 4*b^2*c^3 - 4*a^2*b^2*c)/(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2))*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2))/(2*(3*B*a*b + 3*C*a*c)*(b^2 - a^2 + c^2)^(5/2)))*(B*b + C*c))/(b^2 - a^2 + c^2)^(5/2)","B"
548,1,118,92,5.318574,"\text{Not used}","int((B*cos(x) + C*sin(x))/(a + b*cos(x) + b*sin(x)*1i),x)","-\ln\left(a+b-a\,\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}+b\,\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}\right)\,\left(\frac{\frac{C}{2}+\frac{B\,1{}\mathrm{i}}{2}}{b}+\frac{-\frac{C\,b^2}{2}+\frac{B\,b^2\,1{}\mathrm{i}}{2}}{a^2\,b}\right)+\frac{B+C\,1{}\mathrm{i}}{a\,\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)\,\left(C+B\,1{}\mathrm{i}\right)}{2\,b}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,\left(-C\,b+B\,b\,1{}\mathrm{i}\right)}{2\,a^2}","Not used",1,"(B + C*1i)/(a*(tan(x/2) - 1i)) - log(a + b - a*tan(x/2)*1i + b*tan(x/2)*1i)*(((B*1i)/2 + C/2)/b + ((B*b^2*1i)/2 - (C*b^2)/2)/(a^2*b)) + (log(tan(x/2) + 1i)*(B*1i + C))/(2*b) + (log(tan(x/2) - 1i)*(B*b*1i - C*b))/(2*a^2)","B"
549,1,118,90,4.505866,"\text{Not used}","int((B*cos(x) + C*sin(x))/(a + b*cos(x) - b*sin(x)*1i),x)","\ln\left(a+b+a\,\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}-b\,\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}\right)\,\left(\frac{-\frac{C}{2}+\frac{B\,1{}\mathrm{i}}{2}}{b}+\frac{\frac{C\,b^2}{2}+\frac{B\,b^2\,1{}\mathrm{i}}{2}}{a^2\,b}\right)+\frac{B-C\,1{}\mathrm{i}}{a\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)\,\left(C\,b+B\,b\,1{}\mathrm{i}\right)}{2\,a^2}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,\left(-C+B\,1{}\mathrm{i}\right)}{2\,b}","Not used",1,"log(a + b + a*tan(x/2)*1i - b*tan(x/2)*1i)*(((B*1i)/2 - C/2)/b + ((B*b^2*1i)/2 + (C*b^2)/2)/(a^2*b)) + (B - C*1i)/(a*(tan(x/2) + 1i)) - (log(tan(x/2) + 1i)*(B*b*1i + C*b))/(2*a^2) - (log(tan(x/2) - 1i)*(B*1i - C))/(2*b)","B"
550,1,2711,131,55.105395,"\text{Not used}","int((A + B*cos(x) + C*sin(x))/(a + b*cos(x) + c*sin(x)),x)","\frac{\ln\left(32\,B^3\,a^2-32\,A\,B^2\,a^2+32\,A\,B^2\,b^2+32\,A\,C^2\,a^2-32\,A^2\,B\,b^2+32\,A\,C^2\,b^2+32\,B\,C^2\,a^2+32\,B\,C^2\,b^2+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(2\,C^3\,a+B^3\,c-2\,C^3\,b-2\,A\,B^2\,c+A^2\,B\,c+A^2\,C\,b+2\,B^2\,C\,a-2\,A\,C^2\,c-B^2\,C\,b+2\,B\,C^2\,c-2\,A\,B\,C\,a\right)-32\,B^3\,a\,b+32\,A^2\,B\,a\,b-64\,A\,C^2\,a\,b-64\,B\,C^2\,a\,b-32\,A^2\,C\,a\,c+32\,A^2\,C\,b\,c+32\,B^2\,C\,a\,c-32\,B^2\,C\,b\,c-\frac{\left(B\,c^3-C\,b^3-A\,b^2\,\sqrt{-a^2+b^2+c^2}-B\,a^2\,c+C\,a^2\,b-A\,c^2\,\sqrt{-a^2+b^2+c^2}+B\,b^2\,c-C\,b\,c^2+B\,a\,b\,\sqrt{-a^2+b^2+c^2}+C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(64\,A^2\,b^2\,c-32\,B^2\,a^2\,c+32\,B^2\,b^2\,c+32\,C^2\,a^2\,c+32\,C^2\,b^2\,c+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(A^2\,b^2-A^2\,c^2-2\,A\,B\,a\,b+4\,A\,B\,c^2+2\,A\,C\,a\,c-4\,A\,C\,b\,c+2\,B^2\,a^2-2\,B^2\,a\,b+B^2\,b^2-3\,B^2\,c^2-4\,B\,C\,a\,c+6\,B\,C\,b\,c-2\,C^2\,a^2+2\,C^2\,a\,b+2\,C^2\,c^2\right)+64\,A\,C\,b^3-128\,B\,C\,a^3-64\,B\,C\,b^3+64\,A\,B\,a^2\,c-128\,A\,C\,a\,b^2+64\,A\,C\,a^2\,b-64\,A\,B\,b^2\,c+192\,B\,C\,a^2\,b+64\,B\,C\,a\,c^2-64\,B\,C\,b\,c^2-64\,A^2\,a\,b\,c-64\,C^2\,a\,b\,c-\frac{\left(B\,c^3-C\,b^3-A\,b^2\,\sqrt{-a^2+b^2+c^2}-B\,a^2\,c+C\,a^2\,b-A\,c^2\,\sqrt{-a^2+b^2+c^2}+B\,b^2\,c-C\,b\,c^2+B\,a\,b\,\sqrt{-a^2+b^2+c^2}+C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(32\,A\,b^4+32\,B\,b^4-32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(2\,A\,c^3+B\,c^3-2\,C\,b^3+2\,A\,b^2\,c+2\,C\,a\,b^2+4\,B\,b^2\,c-2\,C\,a\,c^2+C\,b\,c^2-2\,A\,a\,b\,c-4\,B\,a\,b\,c\right)+32\,A\,a^2\,b^2-32\,A\,a^2\,c^2+32\,B\,a^2\,b^2+32\,A\,b^2\,c^2-32\,B\,a^2\,c^2-64\,B\,b^2\,c^2-64\,A\,a\,b^3-64\,B\,a\,b^3+32\,C\,a\,c^3-32\,C\,b\,c^3+64\,C\,b^3\,c+96\,B\,a\,b\,c^2-128\,C\,a\,b^2\,c+64\,C\,a^2\,b\,c-\frac{32\,\left(a-b\right)\,\left(B\,c^3-C\,b^3-A\,b^2\,\sqrt{-a^2+b^2+c^2}-B\,a^2\,c+C\,a^2\,b-A\,c^2\,\sqrt{-a^2+b^2+c^2}+B\,b^2\,c-C\,b\,c^2+B\,a\,b\,\sqrt{-a^2+b^2+c^2}+C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^2-4\,a^2\,b\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,c^2-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^3+a\,b^2\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b\,c^2+a\,c^3+3\,b^3\,c+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2\,c^2+3\,b\,c^3+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,c^4\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)\,\left(c\,\left(B\,b^2-B\,a^2+C\,a\,\sqrt{-a^2+b^2+c^2}\right)+B\,c^3-C\,b^3-c^2\,\left(A\,\sqrt{-a^2+b^2+c^2}+C\,b\right)-A\,b^2\,\sqrt{-a^2+b^2+c^2}+C\,a^2\,b+B\,a\,b\,\sqrt{-a^2+b^2+c^2}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,\left(B+C\,1{}\mathrm{i}\right)}{-c+b\,1{}\mathrm{i}}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)\,\left(B-C\,1{}\mathrm{i}\right)}{c+b\,1{}\mathrm{i}}+\frac{\ln\left(32\,B^3\,a^2-32\,A\,B^2\,a^2+32\,A\,B^2\,b^2+32\,A\,C^2\,a^2-32\,A^2\,B\,b^2+32\,A\,C^2\,b^2+32\,B\,C^2\,a^2+32\,B\,C^2\,b^2+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(2\,C^3\,a+B^3\,c-2\,C^3\,b-2\,A\,B^2\,c+A^2\,B\,c+A^2\,C\,b+2\,B^2\,C\,a-2\,A\,C^2\,c-B^2\,C\,b+2\,B\,C^2\,c-2\,A\,B\,C\,a\right)-32\,B^3\,a\,b+32\,A^2\,B\,a\,b-64\,A\,C^2\,a\,b-64\,B\,C^2\,a\,b-32\,A^2\,C\,a\,c+32\,A^2\,C\,b\,c+32\,B^2\,C\,a\,c-32\,B^2\,C\,b\,c-\frac{\left(B\,c^3-C\,b^3+A\,b^2\,\sqrt{-a^2+b^2+c^2}-B\,a^2\,c+C\,a^2\,b+A\,c^2\,\sqrt{-a^2+b^2+c^2}+B\,b^2\,c-C\,b\,c^2-B\,a\,b\,\sqrt{-a^2+b^2+c^2}-C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(64\,A^2\,b^2\,c-32\,B^2\,a^2\,c+32\,B^2\,b^2\,c+32\,C^2\,a^2\,c+32\,C^2\,b^2\,c+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(A^2\,b^2-A^2\,c^2-2\,A\,B\,a\,b+4\,A\,B\,c^2+2\,A\,C\,a\,c-4\,A\,C\,b\,c+2\,B^2\,a^2-2\,B^2\,a\,b+B^2\,b^2-3\,B^2\,c^2-4\,B\,C\,a\,c+6\,B\,C\,b\,c-2\,C^2\,a^2+2\,C^2\,a\,b+2\,C^2\,c^2\right)+64\,A\,C\,b^3-128\,B\,C\,a^3-64\,B\,C\,b^3+64\,A\,B\,a^2\,c-128\,A\,C\,a\,b^2+64\,A\,C\,a^2\,b-64\,A\,B\,b^2\,c+192\,B\,C\,a^2\,b+64\,B\,C\,a\,c^2-64\,B\,C\,b\,c^2-64\,A^2\,a\,b\,c-64\,C^2\,a\,b\,c-\frac{\left(B\,c^3-C\,b^3+A\,b^2\,\sqrt{-a^2+b^2+c^2}-B\,a^2\,c+C\,a^2\,b+A\,c^2\,\sqrt{-a^2+b^2+c^2}+B\,b^2\,c-C\,b\,c^2-B\,a\,b\,\sqrt{-a^2+b^2+c^2}-C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(32\,A\,b^4+32\,B\,b^4-32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(2\,A\,c^3+B\,c^3-2\,C\,b^3+2\,A\,b^2\,c+2\,C\,a\,b^2+4\,B\,b^2\,c-2\,C\,a\,c^2+C\,b\,c^2-2\,A\,a\,b\,c-4\,B\,a\,b\,c\right)+32\,A\,a^2\,b^2-32\,A\,a^2\,c^2+32\,B\,a^2\,b^2+32\,A\,b^2\,c^2-32\,B\,a^2\,c^2-64\,B\,b^2\,c^2-64\,A\,a\,b^3-64\,B\,a\,b^3+32\,C\,a\,c^3-32\,C\,b\,c^3+64\,C\,b^3\,c+96\,B\,a\,b\,c^2-128\,C\,a\,b^2\,c+64\,C\,a^2\,b\,c-\frac{32\,\left(a-b\right)\,\left(B\,c^3-C\,b^3+A\,b^2\,\sqrt{-a^2+b^2+c^2}-B\,a^2\,c+C\,a^2\,b+A\,c^2\,\sqrt{-a^2+b^2+c^2}+B\,b^2\,c-C\,b\,c^2-B\,a\,b\,\sqrt{-a^2+b^2+c^2}-C\,a\,c\,\sqrt{-a^2+b^2+c^2}\right)\,\left(2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^2-4\,a^2\,b\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,c^2-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^3+a\,b^2\,c-2\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b\,c^2+a\,c^3+3\,b^3\,c+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^2\,c^2+3\,b\,c^3+3\,\mathrm{tan}\left(\frac{x}{2}\right)\,c^4\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}\right)\,\left(B\,c^3-c\,\left(B\,a^2-B\,b^2+C\,a\,\sqrt{-a^2+b^2+c^2}\right)-C\,b^3+c^2\,\left(A\,\sqrt{-a^2+b^2+c^2}-C\,b\right)+A\,b^2\,\sqrt{-a^2+b^2+c^2}+C\,a^2\,b-B\,a\,b\,\sqrt{-a^2+b^2+c^2}\right)}{\left(b^2+c^2\right)\,\left(-a^2+b^2+c^2\right)}","Not used",1,"(log(tan(x/2) - 1i)*(B + C*1i))/(b*1i - c) - (log(tan(x/2) + 1i)*(B - C*1i))/(b*1i + c) + (log(32*B^3*a^2 - 32*A*B^2*a^2 + 32*A*B^2*b^2 + 32*A*C^2*a^2 - 32*A^2*B*b^2 + 32*A*C^2*b^2 + 32*B*C^2*a^2 + 32*B*C^2*b^2 + 32*tan(x/2)*(a - b)*(2*C^3*a + B^3*c - 2*C^3*b - 2*A*B^2*c + A^2*B*c + A^2*C*b + 2*B^2*C*a - 2*A*C^2*c - B^2*C*b + 2*B*C^2*c - 2*A*B*C*a) - 32*B^3*a*b + 32*A^2*B*a*b - 64*A*C^2*a*b - 64*B*C^2*a*b - 32*A^2*C*a*c + 32*A^2*C*b*c + 32*B^2*C*a*c - 32*B^2*C*b*c - ((B*c^3 - C*b^3 - A*b^2*(b^2 - a^2 + c^2)^(1/2) - B*a^2*c + C*a^2*b - A*c^2*(b^2 - a^2 + c^2)^(1/2) + B*b^2*c - C*b*c^2 + B*a*b*(b^2 - a^2 + c^2)^(1/2) + C*a*c*(b^2 - a^2 + c^2)^(1/2))*(64*A^2*b^2*c - 32*B^2*a^2*c + 32*B^2*b^2*c + 32*C^2*a^2*c + 32*C^2*b^2*c + 32*tan(x/2)*(a - b)*(A^2*b^2 + 2*B^2*a^2 - A^2*c^2 + B^2*b^2 - 2*C^2*a^2 - 3*B^2*c^2 + 2*C^2*c^2 + 4*A*B*c^2 - 2*B^2*a*b + 2*C^2*a*b - 2*A*B*a*b + 2*A*C*a*c - 4*A*C*b*c - 4*B*C*a*c + 6*B*C*b*c) + 64*A*C*b^3 - 128*B*C*a^3 - 64*B*C*b^3 + 64*A*B*a^2*c - 128*A*C*a*b^2 + 64*A*C*a^2*b - 64*A*B*b^2*c + 192*B*C*a^2*b + 64*B*C*a*c^2 - 64*B*C*b*c^2 - 64*A^2*a*b*c - 64*C^2*a*b*c - ((B*c^3 - C*b^3 - A*b^2*(b^2 - a^2 + c^2)^(1/2) - B*a^2*c + C*a^2*b - A*c^2*(b^2 - a^2 + c^2)^(1/2) + B*b^2*c - C*b*c^2 + B*a*b*(b^2 - a^2 + c^2)^(1/2) + C*a*c*(b^2 - a^2 + c^2)^(1/2))*(32*A*b^4 + 32*B*b^4 - 32*tan(x/2)*(a - b)*(2*A*c^3 + B*c^3 - 2*C*b^3 + 2*A*b^2*c + 2*C*a*b^2 + 4*B*b^2*c - 2*C*a*c^2 + C*b*c^2 - 2*A*a*b*c - 4*B*a*b*c) + 32*A*a^2*b^2 - 32*A*a^2*c^2 + 32*B*a^2*b^2 + 32*A*b^2*c^2 - 32*B*a^2*c^2 - 64*B*b^2*c^2 - 64*A*a*b^3 - 64*B*a*b^3 + 32*C*a*c^3 - 32*C*b*c^3 + 64*C*b^3*c + 96*B*a*b*c^2 - 128*C*a*b^2*c + 64*C*a^2*b*c - (32*(a - b)*(B*c^3 - C*b^3 - A*b^2*(b^2 - a^2 + c^2)^(1/2) - B*a^2*c + C*a^2*b - A*c^2*(b^2 - a^2 + c^2)^(1/2) + B*b^2*c - C*b*c^2 + B*a*b*(b^2 - a^2 + c^2)^(1/2) + C*a*c*(b^2 - a^2 + c^2)^(1/2))*(3*c^4*tan(x/2) + a*c^3 + 3*b*c^3 + 3*b^3*c + 2*a^2*b^2*tan(x/2) - 2*a^2*c^2*tan(x/2) + 3*b^2*c^2*tan(x/2) - 2*a*b^3*tan(x/2) + a*b^2*c - 4*a^2*b*c - 2*a*b*c^2*tan(x/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2)))*(c*(B*b^2 - B*a^2 + C*a*(b^2 - a^2 + c^2)^(1/2)) + B*c^3 - C*b^3 - c^2*(A*(b^2 - a^2 + c^2)^(1/2) + C*b) - A*b^2*(b^2 - a^2 + c^2)^(1/2) + C*a^2*b + B*a*b*(b^2 - a^2 + c^2)^(1/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2)) + (log(32*B^3*a^2 - 32*A*B^2*a^2 + 32*A*B^2*b^2 + 32*A*C^2*a^2 - 32*A^2*B*b^2 + 32*A*C^2*b^2 + 32*B*C^2*a^2 + 32*B*C^2*b^2 + 32*tan(x/2)*(a - b)*(2*C^3*a + B^3*c - 2*C^3*b - 2*A*B^2*c + A^2*B*c + A^2*C*b + 2*B^2*C*a - 2*A*C^2*c - B^2*C*b + 2*B*C^2*c - 2*A*B*C*a) - 32*B^3*a*b + 32*A^2*B*a*b - 64*A*C^2*a*b - 64*B*C^2*a*b - 32*A^2*C*a*c + 32*A^2*C*b*c + 32*B^2*C*a*c - 32*B^2*C*b*c - ((B*c^3 - C*b^3 + A*b^2*(b^2 - a^2 + c^2)^(1/2) - B*a^2*c + C*a^2*b + A*c^2*(b^2 - a^2 + c^2)^(1/2) + B*b^2*c - C*b*c^2 - B*a*b*(b^2 - a^2 + c^2)^(1/2) - C*a*c*(b^2 - a^2 + c^2)^(1/2))*(64*A^2*b^2*c - 32*B^2*a^2*c + 32*B^2*b^2*c + 32*C^2*a^2*c + 32*C^2*b^2*c + 32*tan(x/2)*(a - b)*(A^2*b^2 + 2*B^2*a^2 - A^2*c^2 + B^2*b^2 - 2*C^2*a^2 - 3*B^2*c^2 + 2*C^2*c^2 + 4*A*B*c^2 - 2*B^2*a*b + 2*C^2*a*b - 2*A*B*a*b + 2*A*C*a*c - 4*A*C*b*c - 4*B*C*a*c + 6*B*C*b*c) + 64*A*C*b^3 - 128*B*C*a^3 - 64*B*C*b^3 + 64*A*B*a^2*c - 128*A*C*a*b^2 + 64*A*C*a^2*b - 64*A*B*b^2*c + 192*B*C*a^2*b + 64*B*C*a*c^2 - 64*B*C*b*c^2 - 64*A^2*a*b*c - 64*C^2*a*b*c - ((B*c^3 - C*b^3 + A*b^2*(b^2 - a^2 + c^2)^(1/2) - B*a^2*c + C*a^2*b + A*c^2*(b^2 - a^2 + c^2)^(1/2) + B*b^2*c - C*b*c^2 - B*a*b*(b^2 - a^2 + c^2)^(1/2) - C*a*c*(b^2 - a^2 + c^2)^(1/2))*(32*A*b^4 + 32*B*b^4 - 32*tan(x/2)*(a - b)*(2*A*c^3 + B*c^3 - 2*C*b^3 + 2*A*b^2*c + 2*C*a*b^2 + 4*B*b^2*c - 2*C*a*c^2 + C*b*c^2 - 2*A*a*b*c - 4*B*a*b*c) + 32*A*a^2*b^2 - 32*A*a^2*c^2 + 32*B*a^2*b^2 + 32*A*b^2*c^2 - 32*B*a^2*c^2 - 64*B*b^2*c^2 - 64*A*a*b^3 - 64*B*a*b^3 + 32*C*a*c^3 - 32*C*b*c^3 + 64*C*b^3*c + 96*B*a*b*c^2 - 128*C*a*b^2*c + 64*C*a^2*b*c - (32*(a - b)*(B*c^3 - C*b^3 + A*b^2*(b^2 - a^2 + c^2)^(1/2) - B*a^2*c + C*a^2*b + A*c^2*(b^2 - a^2 + c^2)^(1/2) + B*b^2*c - C*b*c^2 - B*a*b*(b^2 - a^2 + c^2)^(1/2) - C*a*c*(b^2 - a^2 + c^2)^(1/2))*(3*c^4*tan(x/2) + a*c^3 + 3*b*c^3 + 3*b^3*c + 2*a^2*b^2*tan(x/2) - 2*a^2*c^2*tan(x/2) + 3*b^2*c^2*tan(x/2) - 2*a*b^3*tan(x/2) + a*b^2*c - 4*a^2*b*c - 2*a*b*c^2*tan(x/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2))))/((b^2 + c^2)*(b^2 - a^2 + c^2)))*(B*c^3 - c*(B*a^2 - B*b^2 + C*a*(b^2 - a^2 + c^2)^(1/2)) - C*b^3 + c^2*(A*(b^2 - a^2 + c^2)^(1/2) - C*b) + A*b^2*(b^2 - a^2 + c^2)^(1/2) + C*a^2*b - B*a*b*(b^2 - a^2 + c^2)^(1/2)))/((b^2 + c^2)*(b^2 - a^2 + c^2))","B"
551,1,227,127,3.487245,"\text{Not used}","int((A + B*cos(x) + C*sin(x))/(a + b*cos(x) + c*sin(x))^2,x)","\frac{\frac{2\,\left(C\,a^2-A\,c\,a-C\,b^2+B\,c\,b\right)}{\left(a-b\right)\,\left(-a^2+b^2+c^2\right)}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A\,b^2+B\,a^2+A\,c^2-B\,c^2-A\,a\,b-B\,a\,b-C\,a\,c+C\,b\,c\right)}{\left(a-b\right)\,\left(-a^2+b^2+c^2\right)}}{\left(a-b\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,c\,\mathrm{tan}\left(\frac{x}{2}\right)+a+b}-\frac{2\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a-2\,b\right)+\frac{2\,\left(-a^2\,c+b^2\,c+c^3\right)}{-a^2+b^2+c^2}}{2\,\sqrt{-a^2+b^2+c^2}}\right)\,\left(B\,b-A\,a+C\,c\right)}{{\left(-a^2+b^2+c^2\right)}^{3/2}}","Not used",1,"((2*(C*a^2 - C*b^2 - A*a*c + B*b*c))/((a - b)*(b^2 - a^2 + c^2)) - (2*tan(x/2)*(A*b^2 + B*a^2 + A*c^2 - B*c^2 - A*a*b - B*a*b - C*a*c + C*b*c))/((a - b)*(b^2 - a^2 + c^2)))/(a + b + 2*c*tan(x/2) + tan(x/2)^2*(a - b)) - (2*atanh((tan(x/2)*(2*a - 2*b) + (2*(b^2*c - a^2*c + c^3))/(b^2 - a^2 + c^2))/(2*(b^2 - a^2 + c^2)^(1/2)))*(B*b - A*a + C*c))/(b^2 - a^2 + c^2)^(3/2)","B"
552,1,1160,237,8.214805,"\text{Not used}","int((A + B*cos(x) + C*sin(x))/(a + b*cos(x) + c*sin(x))^3,x)","-\frac{\frac{2\,C\,a^5-4\,A\,a^4\,c-4\,C\,a^3\,b^2+5\,B\,a^3\,b\,c+C\,a^3\,c^2+3\,A\,a^2\,b^2\,c+A\,a^2\,c^3+2\,C\,a\,b^4-5\,B\,a\,b^3\,c-C\,a\,b^2\,c^2-2\,B\,a\,b\,c^3+A\,b^4\,c+A\,b^2\,c^3}{{\left(a-b\right)}^2\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(A\,b^4-2\,B\,a^4+2\,A\,c^4-2\,B\,b^4-2\,B\,c^4-7\,A\,a^2\,b^2-5\,A\,a^2\,c^2-2\,B\,a^2\,b^2+3\,A\,b^2\,c^2+4\,B\,a^2\,c^2-4\,B\,b^2\,c^2+2\,A\,a\,b^3+4\,A\,a^3\,b+3\,B\,a\,b^3+3\,B\,a^3\,b+3\,C\,a^3\,c+2\,A\,a\,b\,c^2+3\,C\,a\,b^2\,c-6\,C\,a^2\,b\,c\right)}{\left(a-b\right)\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,B\,c^5-2\,C\,a^5-2\,A\,c^5+2\,C\,b^5+7\,A\,a^2\,c^3-A\,b^2\,c^3-4\,B\,a^2\,c^3-4\,C\,a^2\,b^3+4\,C\,a^3\,b^2+4\,B\,b^2\,c^3-5\,C\,a^3\,c^2+4\,C\,b^3\,c^2+4\,A\,a^4\,c+A\,b^4\,c+2\,B\,a^4\,c-2\,C\,a\,b^4+2\,C\,a^4\,b+2\,B\,b^4\,c-2\,C\,a\,c^4+2\,C\,b\,c^4-6\,A\,a\,b\,c^3-6\,A\,a\,b^3\,c-12\,A\,a^3\,b\,c-9\,B\,a\,b^3\,c-9\,B\,a^3\,b\,c+13\,A\,a^2\,b^2\,c+14\,B\,a^2\,b^2\,c-13\,C\,a\,b^2\,c^2+14\,C\,a^2\,b\,c^2\right)}{{\left(a-b\right)}^2\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A\,b^5+2\,B\,a^5+2\,B\,b^5+3\,A\,a^2\,b^3+5\,A\,a^3\,b^2+11\,A\,a^3\,c^2+B\,a^2\,b^3+B\,a^3\,b^2-A\,b^3\,c^2-4\,B\,a^3\,c^2+4\,B\,b^3\,c^2-4\,C\,a^2\,c^3-5\,A\,a\,b^4-4\,A\,a^4\,b-2\,A\,a\,c^4-3\,B\,a\,b^4-3\,B\,a^4\,b-2\,A\,b\,c^4+2\,B\,a\,c^4+2\,B\,b\,c^4-5\,C\,a^4\,c+4\,C\,a\,b\,c^3-5\,C\,a\,b^3\,c+5\,C\,a^3\,b\,c-7\,A\,a\,b^2\,c^2-3\,A\,a^2\,b\,c^2+8\,B\,a\,b^2\,c^2-8\,B\,a^2\,b\,c^2+5\,C\,a^2\,b^2\,c\right)}{{\left(a-b\right)}^2\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+2\,a\,b+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a\,c+4\,b\,c\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(4\,a\,c-4\,b\,c\right)+a^2+b^2+{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^2-2\,b^2+4\,c^2\right)}-\frac{\mathrm{atanh}\left(\frac{2\,a^4\,c-4\,a^2\,b^2\,c-4\,a^2\,c^3+2\,b^4\,c+4\,b^2\,c^3+2\,c^5}{2\,{\left(-a^2+b^2+c^2\right)}^{5/2}}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^4-2\,a^2\,b^2-2\,a^2\,c^2+b^4+2\,b^2\,c^2+c^4\right)}{2\,{\left(-a^2+b^2+c^2\right)}^{5/2}}\right)\,\left(2\,A\,a^2-3\,B\,a\,b-3\,C\,a\,c+A\,b^2+A\,c^2\right)}{{\left(-a^2+b^2+c^2\right)}^{5/2}}","Not used",1,"- ((2*C*a^5 + A*a^2*c^3 + A*b^2*c^3 - 4*C*a^3*b^2 + C*a^3*c^2 - 4*A*a^4*c + A*b^4*c + 2*C*a*b^4 - 2*B*a*b*c^3 - 5*B*a*b^3*c + 5*B*a^3*b*c + 3*A*a^2*b^2*c - C*a*b^2*c^2)/((a - b)^2*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)) + (tan(x/2)^3*(A*b^4 - 2*B*a^4 + 2*A*c^4 - 2*B*b^4 - 2*B*c^4 - 7*A*a^2*b^2 - 5*A*a^2*c^2 - 2*B*a^2*b^2 + 3*A*b^2*c^2 + 4*B*a^2*c^2 - 4*B*b^2*c^2 + 2*A*a*b^3 + 4*A*a^3*b + 3*B*a*b^3 + 3*B*a^3*b + 3*C*a^3*c + 2*A*a*b*c^2 + 3*C*a*b^2*c - 6*C*a^2*b*c))/((a - b)*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)) - (tan(x/2)^2*(2*B*c^5 - 2*C*a^5 - 2*A*c^5 + 2*C*b^5 + 7*A*a^2*c^3 - A*b^2*c^3 - 4*B*a^2*c^3 - 4*C*a^2*b^3 + 4*C*a^3*b^2 + 4*B*b^2*c^3 - 5*C*a^3*c^2 + 4*C*b^3*c^2 + 4*A*a^4*c + A*b^4*c + 2*B*a^4*c - 2*C*a*b^4 + 2*C*a^4*b + 2*B*b^4*c - 2*C*a*c^4 + 2*C*b*c^4 - 6*A*a*b*c^3 - 6*A*a*b^3*c - 12*A*a^3*b*c - 9*B*a*b^3*c - 9*B*a^3*b*c + 13*A*a^2*b^2*c + 14*B*a^2*b^2*c - 13*C*a*b^2*c^2 + 14*C*a^2*b*c^2))/((a - b)^2*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)) - (tan(x/2)*(A*b^5 + 2*B*a^5 + 2*B*b^5 + 3*A*a^2*b^3 + 5*A*a^3*b^2 + 11*A*a^3*c^2 + B*a^2*b^3 + B*a^3*b^2 - A*b^3*c^2 - 4*B*a^3*c^2 + 4*B*b^3*c^2 - 4*C*a^2*c^3 - 5*A*a*b^4 - 4*A*a^4*b - 2*A*a*c^4 - 3*B*a*b^4 - 3*B*a^4*b - 2*A*b*c^4 + 2*B*a*c^4 + 2*B*b*c^4 - 5*C*a^4*c + 4*C*a*b*c^3 - 5*C*a*b^3*c + 5*C*a^3*b*c - 7*A*a*b^2*c^2 - 3*A*a^2*b*c^2 + 8*B*a*b^2*c^2 - 8*B*a^2*b*c^2 + 5*C*a^2*b^2*c))/((a - b)^2*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2)))/(tan(x/2)^4*(a^2 - 2*a*b + b^2) + 2*a*b + tan(x/2)*(4*a*c + 4*b*c) + tan(x/2)^3*(4*a*c - 4*b*c) + a^2 + b^2 + tan(x/2)^2*(2*a^2 - 2*b^2 + 4*c^2)) - (atanh((2*a^4*c + 2*b^4*c + 2*c^5 - 4*a^2*c^3 + 4*b^2*c^3 - 4*a^2*b^2*c)/(2*(b^2 - a^2 + c^2)^(5/2)) + (tan(x/2)*(2*a - 2*b)*(a^4 + b^4 + c^4 - 2*a^2*b^2 - 2*a^2*c^2 + 2*b^2*c^2))/(2*(b^2 - a^2 + c^2)^(5/2)))*(2*A*a^2 + A*b^2 + A*c^2 - 3*B*a*b - 3*C*a*c))/(b^2 - a^2 + c^2)^(5/2)","B"
553,1,132,105,6.927324,"\text{Not used}","int((A + B*cos(x) + C*sin(x))/(a + b*cos(x) + b*sin(x)*1i),x)","-\ln\left(a+b-a\,\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}+b\,\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}\right)\,\left(\frac{\frac{C}{2}+\frac{B\,1{}\mathrm{i}}{2}}{b}-\frac{\frac{C\,b^2}{2}-\frac{B\,b^2\,1{}\mathrm{i}}{2}+A\,a\,b\,1{}\mathrm{i}}{a^2\,b}\right)+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)\,\left(C+B\,1{}\mathrm{i}\right)}{2\,b}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,\left(B\,b-2\,A\,a+C\,b\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2\,a^2}+\frac{5\,B+C\,5{}\mathrm{i}}{5\,a\,\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)}","Not used",1,"(log(tan(x/2) + 1i)*(B*1i + C))/(2*b) - log(a + b - a*tan(x/2)*1i + b*tan(x/2)*1i)*(((B*1i)/2 + C/2)/b - ((C*b^2)/2 - (B*b^2*1i)/2 + A*a*b*1i)/(a^2*b)) + (log(tan(x/2) - 1i)*(B*b - 2*A*a + C*b*1i)*1i)/(2*a^2) + (5*B + C*5i)/(5*a*(tan(x/2) - 1i))","B"
554,1,133,103,6.858214,"\text{Not used}","int((A + B*cos(x) + C*sin(x))/(a + b*cos(x) - b*sin(x)*1i),x)","\ln\left(a+b+a\,\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}-b\,\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}\right)\,\left(\frac{-\frac{C}{2}+\frac{B\,1{}\mathrm{i}}{2}}{b}+\frac{\frac{B\,b^2\,1{}\mathrm{i}}{2}+\frac{C\,b^2}{2}-A\,a\,b\,1{}\mathrm{i}}{a^2\,b}\right)+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)\,\left(2\,A\,a-B\,b+C\,b\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2\,a^2}+\frac{5\,B-C\,5{}\mathrm{i}}{5\,a\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,\left(-C+B\,1{}\mathrm{i}\right)}{2\,b}","Not used",1,"log(a + b + a*tan(x/2)*1i - b*tan(x/2)*1i)*(((B*1i)/2 - C/2)/b + ((B*b^2*1i)/2 + (C*b^2)/2 - A*a*b*1i)/(a^2*b)) + (log(tan(x/2) + 1i)*(2*A*a - B*b + C*b*1i)*1i)/(2*a^2) + (5*B - C*5i)/(5*a*(tan(x/2) + 1i)) - (log(tan(x/2) - 1i)*(B*1i - C))/(2*b)","B"
555,1,62,24,3.031286,"\text{Not used}","int((b^2 + c^2 + a*c*sin(x) + a*b*cos(x))/(a + b*cos(x) + c*sin(x))^2,x)","-\frac{\frac{2\,a\,c}{a-b}+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(b^2-a\,b+c^2\right)}{a-b}}{\left(a-b\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,c\,\mathrm{tan}\left(\frac{x}{2}\right)+a+b}","Not used",1,"-((2*a*c)/(a - b) + (2*tan(x/2)*(b^2 - a*b + c^2))/(a - b))/(a + b + 2*c*tan(x/2) + tan(x/2)^2*(a - b))","B"
556,0,-1,390,0.000000,"\text{Not used}","int((a + b*cos(x) + c*sin(x))^(5/2)*(d + b*e*cos(x) + c*e*sin(x)),x)","\int {\left(a+b\,\cos\left(x\right)+c\,\sin\left(x\right)\right)}^{5/2}\,\left(d+b\,e\,\cos\left(x\right)+c\,e\,\sin\left(x\right)\right) \,d x","Not used",1,"int((a + b*cos(x) + c*sin(x))^(5/2)*(d + b*e*cos(x) + c*e*sin(x)), x)","F"
557,0,-1,294,0.000000,"\text{Not used}","int((a + b*cos(x) + c*sin(x))^(3/2)*(d + b*e*cos(x) + c*e*sin(x)),x)","\int {\left(a+b\,\cos\left(x\right)+c\,\sin\left(x\right)\right)}^{3/2}\,\left(d+b\,e\,\cos\left(x\right)+c\,e\,\sin\left(x\right)\right) \,d x","Not used",1,"int((a + b*cos(x) + c*sin(x))^(3/2)*(d + b*e*cos(x) + c*e*sin(x)), x)","F"
558,0,-1,229,0.000000,"\text{Not used}","int((a + b*cos(x) + c*sin(x))^(1/2)*(d + b*e*cos(x) + c*e*sin(x)),x)","\int \sqrt{a+b\,\cos\left(x\right)+c\,\sin\left(x\right)}\,\left(d+b\,e\,\cos\left(x\right)+c\,e\,\sin\left(x\right)\right) \,d x","Not used",1,"int((a + b*cos(x) + c*sin(x))^(1/2)*(d + b*e*cos(x) + c*e*sin(x)), x)","F"
559,0,-1,180,0.000000,"\text{Not used}","int((d + b*e*cos(x) + c*e*sin(x))/(a + b*cos(x) + c*sin(x))^(1/2),x)","\int \frac{d+b\,e\,\cos\left(x\right)+c\,e\,\sin\left(x\right)}{\sqrt{a+b\,\cos\left(x\right)+c\,\sin\left(x\right)}} \,d x","Not used",1,"int((d + b*e*cos(x) + c*e*sin(x))/(a + b*cos(x) + c*sin(x))^(1/2), x)","F"
560,0,-1,250,0.000000,"\text{Not used}","int((d + b*e*cos(x) + c*e*sin(x))/(a + b*cos(x) + c*sin(x))^(3/2),x)","\int \frac{d+b\,e\,\cos\left(x\right)+c\,e\,\sin\left(x\right)}{{\left(a+b\,\cos\left(x\right)+c\,\sin\left(x\right)\right)}^{3/2}} \,d x","Not used",1,"int((d + b*e*cos(x) + c*e*sin(x))/(a + b*cos(x) + c*sin(x))^(3/2), x)","F"
561,0,-1,378,0.000000,"\text{Not used}","int((d + b*e*cos(x) + c*e*sin(x))/(a + b*cos(x) + c*sin(x))^(5/2),x)","\int \frac{d+b\,e\,\cos\left(x\right)+c\,e\,\sin\left(x\right)}{{\left(a+b\,\cos\left(x\right)+c\,\sin\left(x\right)\right)}^{5/2}} \,d x","Not used",1,"int((d + b*e*cos(x) + c*e*sin(x))/(a + b*cos(x) + c*sin(x))^(5/2), x)","F"
562,1,1143,84,9.625335,"\text{Not used}","int((A + B*cos(d + e*x) + C*sin(d + e*x))/(a + c*sin(d + e*x)),x)","\frac{\ln\left(32\,B^3\,a^2-32\,A\,B^2\,a^2+32\,A\,C^2\,a^2+32\,B\,C^2\,a^2+32\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(c\,A^2\,B-2\,c\,A\,B^2-2\,a\,A\,B\,C-2\,c\,A\,C^2+c\,B^3+2\,a\,B^2\,C+2\,c\,B\,C^2+2\,a\,C^3\right)-32\,A^2\,C\,a\,c+32\,B^2\,C\,a\,c-\frac{\left(B\,a^2-B\,c^2+A\,c\,\sqrt{c^2-a^2}-C\,a\,\sqrt{c^2-a^2}\right)\,\left(32\,C^2\,a^2\,c-32\,B^2\,a^2\,c-128\,B\,C\,a^3+32\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-A^2\,c^2+4\,A\,B\,c^2+2\,A\,C\,a\,c+2\,B^2\,a^2-3\,B^2\,c^2-4\,B\,C\,a\,c-2\,C^2\,a^2+2\,C^2\,c^2\right)+64\,A\,B\,a^2\,c+64\,B\,C\,a\,c^2+\frac{\left(B\,a^2-B\,c^2+A\,c\,\sqrt{c^2-a^2}-C\,a\,\sqrt{c^2-a^2}\right)\,\left(32\,A\,a^2\,c^2+32\,B\,a^2\,c^2-32\,C\,a\,c^3+32\,a\,c^2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,A\,c-2\,C\,a+B\,c\right)+\frac{32\,a\,c\,\left(-2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,a^2+a\,c+3\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,c^2\right)\,\left(B\,a^2-B\,c^2+A\,c\,\sqrt{c^2-a^2}-C\,a\,\sqrt{c^2-a^2}\right)}{a^2-c^2}\right)}{c\,\left(a^2-c^2\right)}\right)}{c\,\left(a^2-c^2\right)}\right)\,\left(B\,a^2-B\,c^2+A\,c\,\sqrt{c^2-a^2}-C\,a\,\sqrt{c^2-a^2}\right)}{c\,e\,\left(a^2-c^2\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(B-C\,1{}\mathrm{i}\right)}{c\,e}-\frac{\ln\left(\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)-\mathrm{i}\right)\,\left(B+C\,1{}\mathrm{i}\right)}{c\,e}+\frac{\ln\left(32\,B^3\,a^2-32\,A\,B^2\,a^2+32\,A\,C^2\,a^2+32\,B\,C^2\,a^2+32\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(c\,A^2\,B-2\,c\,A\,B^2-2\,a\,A\,B\,C-2\,c\,A\,C^2+c\,B^3+2\,a\,B^2\,C+2\,c\,B\,C^2+2\,a\,C^3\right)-32\,A^2\,C\,a\,c+32\,B^2\,C\,a\,c-\frac{\left(B\,a^2-B\,c^2-A\,c\,\sqrt{c^2-a^2}+C\,a\,\sqrt{c^2-a^2}\right)\,\left(32\,C^2\,a^2\,c-32\,B^2\,a^2\,c-128\,B\,C\,a^3+32\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(-A^2\,c^2+4\,A\,B\,c^2+2\,A\,C\,a\,c+2\,B^2\,a^2-3\,B^2\,c^2-4\,B\,C\,a\,c-2\,C^2\,a^2+2\,C^2\,c^2\right)+64\,A\,B\,a^2\,c+64\,B\,C\,a\,c^2+\frac{\left(B\,a^2-B\,c^2-A\,c\,\sqrt{c^2-a^2}+C\,a\,\sqrt{c^2-a^2}\right)\,\left(32\,A\,a^2\,c^2+32\,B\,a^2\,c^2-32\,C\,a\,c^3+32\,a\,c^2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,A\,c-2\,C\,a+B\,c\right)+\frac{32\,a\,c\,\left(-2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,a^2+a\,c+3\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,c^2\right)\,\left(B\,a^2-B\,c^2-A\,c\,\sqrt{c^2-a^2}+C\,a\,\sqrt{c^2-a^2}\right)}{a^2-c^2}\right)}{c\,\left(a^2-c^2\right)}\right)}{c\,\left(a^2-c^2\right)}\right)\,\left(B\,a^2-B\,c^2-A\,c\,\sqrt{c^2-a^2}+C\,a\,\sqrt{c^2-a^2}\right)}{c\,e\,\left(a^2-c^2\right)}","Not used",1,"(log(32*B^3*a^2 - 32*A*B^2*a^2 + 32*A*C^2*a^2 + 32*B*C^2*a^2 + 32*a*tan(d/2 + (e*x)/2)*(2*C^3*a + B^3*c - 2*A*B^2*c + A^2*B*c + 2*B^2*C*a - 2*A*C^2*c + 2*B*C^2*c - 2*A*B*C*a) - 32*A^2*C*a*c + 32*B^2*C*a*c - ((B*a^2 - B*c^2 + A*c*(c^2 - a^2)^(1/2) - C*a*(c^2 - a^2)^(1/2))*(32*C^2*a^2*c - 32*B^2*a^2*c - 128*B*C*a^3 + 32*a*tan(d/2 + (e*x)/2)*(2*B^2*a^2 - A^2*c^2 - 2*C^2*a^2 - 3*B^2*c^2 + 2*C^2*c^2 + 4*A*B*c^2 + 2*A*C*a*c - 4*B*C*a*c) + 64*A*B*a^2*c + 64*B*C*a*c^2 + ((B*a^2 - B*c^2 + A*c*(c^2 - a^2)^(1/2) - C*a*(c^2 - a^2)^(1/2))*(32*A*a^2*c^2 + 32*B*a^2*c^2 - 32*C*a*c^3 + 32*a*c^2*tan(d/2 + (e*x)/2)*(2*A*c - 2*C*a + B*c) + (32*a*c*(a*c - 2*a^2*tan(d/2 + (e*x)/2) + 3*c^2*tan(d/2 + (e*x)/2))*(B*a^2 - B*c^2 + A*c*(c^2 - a^2)^(1/2) - C*a*(c^2 - a^2)^(1/2)))/(a^2 - c^2)))/(c*(a^2 - c^2))))/(c*(a^2 - c^2)))*(B*a^2 - B*c^2 + A*c*(c^2 - a^2)^(1/2) - C*a*(c^2 - a^2)^(1/2)))/(c*e*(a^2 - c^2)) - (log(tan(d/2 + (e*x)/2) + 1i)*(B - C*1i))/(c*e) - (log(tan(d/2 + (e*x)/2) - 1i)*(B + C*1i))/(c*e) + (log(32*B^3*a^2 - 32*A*B^2*a^2 + 32*A*C^2*a^2 + 32*B*C^2*a^2 + 32*a*tan(d/2 + (e*x)/2)*(2*C^3*a + B^3*c - 2*A*B^2*c + A^2*B*c + 2*B^2*C*a - 2*A*C^2*c + 2*B*C^2*c - 2*A*B*C*a) - 32*A^2*C*a*c + 32*B^2*C*a*c - ((B*a^2 - B*c^2 - A*c*(c^2 - a^2)^(1/2) + C*a*(c^2 - a^2)^(1/2))*(32*C^2*a^2*c - 32*B^2*a^2*c - 128*B*C*a^3 + 32*a*tan(d/2 + (e*x)/2)*(2*B^2*a^2 - A^2*c^2 - 2*C^2*a^2 - 3*B^2*c^2 + 2*C^2*c^2 + 4*A*B*c^2 + 2*A*C*a*c - 4*B*C*a*c) + 64*A*B*a^2*c + 64*B*C*a*c^2 + ((B*a^2 - B*c^2 - A*c*(c^2 - a^2)^(1/2) + C*a*(c^2 - a^2)^(1/2))*(32*A*a^2*c^2 + 32*B*a^2*c^2 - 32*C*a*c^3 + 32*a*c^2*tan(d/2 + (e*x)/2)*(2*A*c - 2*C*a + B*c) + (32*a*c*(a*c - 2*a^2*tan(d/2 + (e*x)/2) + 3*c^2*tan(d/2 + (e*x)/2))*(B*a^2 - B*c^2 - A*c*(c^2 - a^2)^(1/2) + C*a*(c^2 - a^2)^(1/2)))/(a^2 - c^2)))/(c*(a^2 - c^2))))/(c*(a^2 - c^2)))*(B*a^2 - B*c^2 - A*c*(c^2 - a^2)^(1/2) + C*a*(c^2 - a^2)^(1/2)))/(c*e*(a^2 - c^2))","B"
563,1,227,118,3.327459,"\text{Not used}","int((A + B*cos(d + e*x) + C*sin(d + e*x))/(a + c*sin(d + e*x))^2,x)","\frac{\frac{2\,\left(A\,c-C\,a\right)}{a^2-c^2}+\frac{2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(B\,a^2+A\,c^2-B\,c^2-C\,a\,c\right)}{a\,\left(a^2-c^2\right)}}{e\,\left(a\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+2\,c\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+a\right)}+\frac{2\,\mathrm{atan}\left(\frac{\left(a^2-c^2\right)\,\left(\frac{2\,a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(A\,a-C\,c\right)}{{\left(a+c\right)}^{3/2}\,{\left(a-c\right)}^{3/2}}+\frac{2\,\left(a^2\,c-c^3\right)\,\left(A\,a-C\,c\right)}{{\left(a+c\right)}^{3/2}\,\left(a^2-c^2\right)\,{\left(a-c\right)}^{3/2}}\right)}{2\,\left(A\,a-C\,c\right)}\right)\,\left(A\,a-C\,c\right)}{e\,{\left(a+c\right)}^{3/2}\,{\left(a-c\right)}^{3/2}}","Not used",1,"((2*(A*c - C*a))/(a^2 - c^2) + (2*tan(d/2 + (e*x)/2)*(B*a^2 + A*c^2 - B*c^2 - C*a*c))/(a*(a^2 - c^2)))/(e*(a + 2*c*tan(d/2 + (e*x)/2) + a*tan(d/2 + (e*x)/2)^2)) + (2*atan(((a^2 - c^2)*((2*a*tan(d/2 + (e*x)/2)*(A*a - C*c))/((a + c)^(3/2)*(a - c)^(3/2)) + (2*(a^2*c - c^3)*(A*a - C*c))/((a + c)^(3/2)*(a^2 - c^2)*(a - c)^(3/2))))/(2*(A*a - C*c)))*(A*a - C*c))/(e*(a + c)^(3/2)*(a - c)^(3/2))","B"
564,1,557,185,5.272164,"\text{Not used}","int((A + B*cos(d + e*x) + C*sin(d + e*x))/(a + c*sin(d + e*x))^3,x)","\frac{\mathrm{atan}\left(\frac{\left(\frac{\left(2\,A\,a^2-3\,C\,a\,c+A\,c^2\right)\,\left(2\,a^4\,c-4\,a^2\,c^3+2\,c^5\right)}{2\,{\left(a+c\right)}^{5/2}\,{\left(a-c\right)}^{5/2}\,\left(a^4-2\,a^2\,c^2+c^4\right)}+\frac{a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,A\,a^2-3\,C\,a\,c+A\,c^2\right)}{{\left(a+c\right)}^{5/2}\,{\left(a-c\right)}^{5/2}}\right)\,\left(a^4-2\,a^2\,c^2+c^4\right)}{2\,A\,a^2-3\,C\,a\,c+A\,c^2}\right)\,\left(2\,A\,a^2-3\,C\,a\,c+A\,c^2\right)}{e\,{\left(a+c\right)}^{5/2}\,{\left(a-c\right)}^{5/2}}-\frac{\frac{2\,C\,a^3-4\,A\,a^2\,c+C\,a\,c^2+A\,c^3}{a^4-2\,a^2\,c^2+c^4}-\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(2\,B\,a^4-2\,A\,c^4+2\,B\,c^4+5\,A\,a^2\,c^2-4\,B\,a^2\,c^2-3\,C\,a^3\,c\right)}{a\,\left(a^4-2\,a^2\,c^2+c^4\right)}+\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,A\,c^4-2\,B\,a^4-2\,B\,c^4-11\,A\,a^2\,c^2+4\,B\,a^2\,c^2+4\,C\,a\,c^3+5\,C\,a^3\,c\right)}{a\,\left(a^4-2\,a^2\,c^2+c^4\right)}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(2\,A\,c^5+2\,C\,a^5-2\,B\,c^5-7\,A\,a^2\,c^3+4\,B\,a^2\,c^3+5\,C\,a^3\,c^2-4\,A\,a^4\,c-2\,B\,a^4\,c+2\,C\,a\,c^4\right)}{a^2\,\left(a^4-2\,a^2\,c^2+c^4\right)}}{e\,\left({\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(2\,a^2+4\,c^2\right)+a^2\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4+a^2+4\,a\,c\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3+4\,a\,c\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\right)}","Not used",1,"(atan(((((2*A*a^2 + A*c^2 - 3*C*a*c)*(2*a^4*c + 2*c^5 - 4*a^2*c^3))/(2*(a + c)^(5/2)*(a - c)^(5/2)*(a^4 + c^4 - 2*a^2*c^2)) + (a*tan(d/2 + (e*x)/2)*(2*A*a^2 + A*c^2 - 3*C*a*c))/((a + c)^(5/2)*(a - c)^(5/2)))*(a^4 + c^4 - 2*a^2*c^2))/(2*A*a^2 + A*c^2 - 3*C*a*c))*(2*A*a^2 + A*c^2 - 3*C*a*c))/(e*(a + c)^(5/2)*(a - c)^(5/2)) - ((A*c^3 + 2*C*a^3 - 4*A*a^2*c + C*a*c^2)/(a^4 + c^4 - 2*a^2*c^2) - (tan(d/2 + (e*x)/2)^3*(2*B*a^4 - 2*A*c^4 + 2*B*c^4 + 5*A*a^2*c^2 - 4*B*a^2*c^2 - 3*C*a^3*c))/(a*(a^4 + c^4 - 2*a^2*c^2)) + (tan(d/2 + (e*x)/2)*(2*A*c^4 - 2*B*a^4 - 2*B*c^4 - 11*A*a^2*c^2 + 4*B*a^2*c^2 + 4*C*a*c^3 + 5*C*a^3*c))/(a*(a^4 + c^4 - 2*a^2*c^2)) + (tan(d/2 + (e*x)/2)^2*(2*A*c^5 + 2*C*a^5 - 2*B*c^5 - 7*A*a^2*c^3 + 4*B*a^2*c^3 + 5*C*a^3*c^2 - 4*A*a^4*c - 2*B*a^4*c + 2*C*a*c^4))/(a^2*(a^4 + c^4 - 2*a^2*c^2)))/(e*(tan(d/2 + (e*x)/2)^2*(2*a^2 + 4*c^2) + a^2*tan(d/2 + (e*x)/2)^4 + a^2 + 4*a*c*tan(d/2 + (e*x)/2)^3 + 4*a*c*tan(d/2 + (e*x)/2)))","B"
565,1,1085,258,6.218104,"\text{Not used}","int((A + B*cos(d + e*x) + C*sin(d + e*x))/(a + c*sin(d + e*x))^4,x)","\frac{\frac{-6\,C\,a^5+18\,A\,a^4\,c-10\,C\,a^3\,c^2-5\,A\,a^2\,c^3+C\,a\,c^4+2\,A\,c^5}{3\,\left(a^6-3\,a^4\,c^2+3\,a^2\,c^4-c^6\right)}+\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,B\,a^6+2\,A\,c^6-2\,B\,c^6-4\,A\,a^2\,c^4+27\,A\,a^4\,c^2+6\,B\,a^2\,c^4-6\,B\,a^4\,c^2-19\,C\,a^3\,c^3+2\,C\,a\,c^5-8\,C\,a^5\,c\right)}{a\,\left(a^6-3\,a^4\,c^2+3\,a^2\,c^4-c^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(2\,A\,c^7-2\,C\,a^7-2\,B\,c^7-3\,A\,a^2\,c^5+20\,A\,a^4\,c^3+6\,B\,a^2\,c^5-6\,B\,a^4\,c^3-14\,C\,a^3\,c^4-10\,C\,a^5\,c^2+6\,A\,a^6\,c+2\,B\,a^6\,c+C\,a\,c^6\right)}{a^2\,\left(a^6-3\,a^4\,c^2+3\,a^2\,c^4-c^6\right)}+\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(4\,A\,c^7-2\,C\,a^7-4\,B\,c^7-12\,A\,a^2\,c^5+27\,A\,a^4\,c^3+12\,B\,a^2\,c^5-12\,B\,a^4\,c^3-11\,C\,a^3\,c^4-14\,C\,a^5\,c^2+6\,A\,a^6\,c+4\,B\,a^6\,c+2\,C\,a\,c^6\right)}{a^2\,\left(a^6-3\,a^4\,c^2+3\,a^2\,c^4-c^6\right)}-\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(2\,B\,c^6-2\,A\,c^6-2\,B\,a^6+6\,A\,a^2\,c^4-9\,A\,a^4\,c^2-6\,B\,a^2\,c^4+6\,B\,a^4\,c^2+C\,a^3\,c^3+4\,C\,a^5\,c\right)}{a\,\left(a^6-3\,a^4\,c^2+3\,a^2\,c^4-c^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(3\,a^2+2\,c^2\right)\,\left(2\,B\,a^6+2\,A\,c^6-2\,B\,c^6-5\,A\,a^2\,c^4+18\,A\,a^4\,c^2+6\,B\,a^2\,c^4-6\,B\,a^4\,c^2-10\,C\,a^3\,c^3+C\,a\,c^5-6\,C\,a^5\,c\right)}{3\,a^3\,\left(a^6-3\,a^4\,c^2+3\,a^2\,c^4-c^6\right)}}{e\,\left(a^3\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(3\,a^3+12\,a\,c^2\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(3\,a^3+12\,a\,c^2\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(12\,a^2\,c+8\,c^3\right)+a^3+6\,a^2\,c\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+6\,a^2\,c\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\right)}+\frac{\mathrm{atan}\left(\frac{\left(\frac{\left(2\,A\,a^3-4\,C\,a^2\,c+3\,A\,a\,c^2-C\,c^3\right)\,\left(2\,a^6\,c-6\,a^4\,c^3+6\,a^2\,c^5-2\,c^7\right)}{2\,{\left(a+c\right)}^{7/2}\,{\left(a-c\right)}^{7/2}\,\left(a^6-3\,a^4\,c^2+3\,a^2\,c^4-c^6\right)}+\frac{a\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,A\,a^3-4\,C\,a^2\,c+3\,A\,a\,c^2-C\,c^3\right)}{{\left(a+c\right)}^{7/2}\,{\left(a-c\right)}^{7/2}}\right)\,\left(a^6-3\,a^4\,c^2+3\,a^2\,c^4-c^6\right)}{2\,A\,a^3-4\,C\,a^2\,c+3\,A\,a\,c^2-C\,c^3}\right)\,\left(2\,A\,a^3-4\,C\,a^2\,c+3\,A\,a\,c^2-C\,c^3\right)}{e\,{\left(a+c\right)}^{7/2}\,{\left(a-c\right)}^{7/2}}","Not used",1,"((2*A*c^5 - 6*C*a^5 - 5*A*a^2*c^3 - 10*C*a^3*c^2 + 18*A*a^4*c + C*a*c^4)/(3*(a^6 - c^6 + 3*a^2*c^4 - 3*a^4*c^2)) + (tan(d/2 + (e*x)/2)*(2*B*a^6 + 2*A*c^6 - 2*B*c^6 - 4*A*a^2*c^4 + 27*A*a^4*c^2 + 6*B*a^2*c^4 - 6*B*a^4*c^2 - 19*C*a^3*c^3 + 2*C*a*c^5 - 8*C*a^5*c))/(a*(a^6 - c^6 + 3*a^2*c^4 - 3*a^4*c^2)) + (2*tan(d/2 + (e*x)/2)^2*(2*A*c^7 - 2*C*a^7 - 2*B*c^7 - 3*A*a^2*c^5 + 20*A*a^4*c^3 + 6*B*a^2*c^5 - 6*B*a^4*c^3 - 14*C*a^3*c^4 - 10*C*a^5*c^2 + 6*A*a^6*c + 2*B*a^6*c + C*a*c^6))/(a^2*(a^6 - c^6 + 3*a^2*c^4 - 3*a^4*c^2)) + (tan(d/2 + (e*x)/2)^4*(4*A*c^7 - 2*C*a^7 - 4*B*c^7 - 12*A*a^2*c^5 + 27*A*a^4*c^3 + 12*B*a^2*c^5 - 12*B*a^4*c^3 - 11*C*a^3*c^4 - 14*C*a^5*c^2 + 6*A*a^6*c + 4*B*a^6*c + 2*C*a*c^6))/(a^2*(a^6 - c^6 + 3*a^2*c^4 - 3*a^4*c^2)) - (tan(d/2 + (e*x)/2)^5*(2*B*c^6 - 2*A*c^6 - 2*B*a^6 + 6*A*a^2*c^4 - 9*A*a^4*c^2 - 6*B*a^2*c^4 + 6*B*a^4*c^2 + C*a^3*c^3 + 4*C*a^5*c))/(a*(a^6 - c^6 + 3*a^2*c^4 - 3*a^4*c^2)) + (2*tan(d/2 + (e*x)/2)^3*(3*a^2 + 2*c^2)*(2*B*a^6 + 2*A*c^6 - 2*B*c^6 - 5*A*a^2*c^4 + 18*A*a^4*c^2 + 6*B*a^2*c^4 - 6*B*a^4*c^2 - 10*C*a^3*c^3 + C*a*c^5 - 6*C*a^5*c))/(3*a^3*(a^6 - c^6 + 3*a^2*c^4 - 3*a^4*c^2)))/(e*(a^3*tan(d/2 + (e*x)/2)^6 + tan(d/2 + (e*x)/2)^2*(12*a*c^2 + 3*a^3) + tan(d/2 + (e*x)/2)^4*(12*a*c^2 + 3*a^3) + tan(d/2 + (e*x)/2)^3*(12*a^2*c + 8*c^3) + a^3 + 6*a^2*c*tan(d/2 + (e*x)/2) + 6*a^2*c*tan(d/2 + (e*x)/2)^5)) + (atan(((((2*A*a^3 - C*c^3 + 3*A*a*c^2 - 4*C*a^2*c)*(2*a^6*c - 2*c^7 + 6*a^2*c^5 - 6*a^4*c^3))/(2*(a + c)^(7/2)*(a - c)^(7/2)*(a^6 - c^6 + 3*a^2*c^4 - 3*a^4*c^2)) + (a*tan(d/2 + (e*x)/2)*(2*A*a^3 - C*c^3 + 3*A*a*c^2 - 4*C*a^2*c))/((a + c)^(7/2)*(a - c)^(7/2)))*(a^6 - c^6 + 3*a^2*c^4 - 3*a^4*c^2))/(2*A*a^3 - C*c^3 + 3*A*a*c^2 - 4*C*a^2*c))*(2*A*a^3 - C*c^3 + 3*A*a*c^2 - 4*C*a^2*c))/(e*(a + c)^(7/2)*(a - c)^(7/2))","B"
566,0,-1,131,0.000000,"\text{Not used}","int((a + b*cos(c + d*x)*sin(c + d*x))^m,x)","\int {\left(a+b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int((a + b*cos(c + d*x)*sin(c + d*x))^m, x)","F"
567,1,125,107,3.437350,"\text{Not used}","int((a + b*cos(c + d*x)*sin(c + d*x))^3,x)","a^3\,x-\frac{{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(72\,a^2\,b+6\,b^3\right)+36\,a^2\,b+2\,b^3+36\,a^2\,b\,{\mathrm{tan}\left(c+d\,x\right)}^4-9\,a\,b^2\,{\mathrm{tan}\left(c+d\,x\right)}^5+9\,a\,b^2\,\mathrm{tan}\left(c+d\,x\right)}{d\,\left(24\,{\mathrm{tan}\left(c+d\,x\right)}^6+72\,{\mathrm{tan}\left(c+d\,x\right)}^4+72\,{\mathrm{tan}\left(c+d\,x\right)}^2+24\right)}+\frac{3\,a\,b^2\,x}{8}","Not used",1,"a^3*x - (tan(c + d*x)^2*(72*a^2*b + 6*b^3) + 36*a^2*b + 2*b^3 + 36*a^2*b*tan(c + d*x)^4 - 9*a*b^2*tan(c + d*x)^5 + 9*a*b^2*tan(c + d*x))/(d*(72*tan(c + d*x)^2 + 72*tan(c + d*x)^4 + 24*tan(c + d*x)^6 + 24)) + (3*a*b^2*x)/8","B"
568,1,78,61,3.034221,"\text{Not used}","int((a + b*cos(c + d*x)*sin(c + d*x))^2,x)","x\,\left(a^2+\frac{b^2}{8}\right)-\frac{-\frac{b^2\,{\mathrm{tan}\left(c+d\,x\right)}^3}{8}+\frac{b^2\,\mathrm{tan}\left(c+d\,x\right)}{8}+a\,b\,{\mathrm{tan}\left(c+d\,x\right)}^2+a\,b}{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 + b^2/8) - (a*b + (b^2*tan(c + d*x))/8 - (b^2*tan(c + d*x)^3)/8 + a*b*tan(c + d*x)^2)/(d*(2*tan(c + d*x)^2 + tan(c + d*x)^4 + 1))","B"
569,1,22,20,2.942029,"\text{Not used}","int(a + b*cos(c + d*x)*sin(c + d*x),x)","-\frac{\frac{b\,{\cos\left(c+d\,x\right)}^2}{2}-a\,d\,x}{d}","Not used",1,"-((b*cos(c + d*x)^2)/2 - a*d*x)/d","B"
570,1,44,48,3.113760,"\text{Not used}","int(1/(a + b*cos(c + d*x)*sin(c + d*x)),x)","\frac{2\,\mathrm{atan}\left(\frac{b+2\,a\,\mathrm{tan}\left(c+d\,x\right)}{\sqrt{4\,a^2-b^2}}\right)}{d\,\sqrt{4\,a^2-b^2}}","Not used",1,"(2*atan((b + 2*a*tan(c + d*x))/(4*a^2 - b^2)^(1/2)))/(d*(4*a^2 - b^2)^(1/2))","B"
571,1,181,95,3.049734,"\text{Not used}","int(1/(a + b*cos(c + d*x)*sin(c + d*x))^2,x)","\frac{\frac{2\,b}{4\,a^2-b^2}+\frac{b^2\,\mathrm{tan}\left(c+d\,x\right)}{a\,\left(4\,a^2-b^2\right)}}{d\,\left(a\,{\mathrm{tan}\left(c+d\,x\right)}^2+b\,\mathrm{tan}\left(c+d\,x\right)+a\right)}+\frac{8\,a\,\mathrm{atan}\left(\frac{\left(4\,a^2-b^2\right)\,\left(\frac{8\,a^2\,\mathrm{tan}\left(c+d\,x\right)}{{\left(2\,a+b\right)}^{3/2}\,{\left(2\,a-b\right)}^{3/2}}+\frac{4\,a\,\left(4\,a^2\,b-b^3\right)}{{\left(2\,a+b\right)}^{3/2}\,\left(4\,a^2-b^2\right)\,{\left(2\,a-b\right)}^{3/2}}\right)}{4\,a}\right)}{d\,{\left(2\,a+b\right)}^{3/2}\,{\left(2\,a-b\right)}^{3/2}}","Not used",1,"((2*b)/(4*a^2 - b^2) + (b^2*tan(c + d*x))/(a*(4*a^2 - b^2)))/(d*(a + b*tan(c + d*x) + a*tan(c + d*x)^2)) + (8*a*atan(((4*a^2 - b^2)*((8*a^2*tan(c + d*x))/((2*a + b)^(3/2)*(2*a - b)^(3/2)) + (4*a*(4*a^2*b - b^3))/((2*a + b)^(3/2)*(4*a^2 - b^2)*(2*a - b)^(3/2))))/(4*a)))/(d*(2*a + b)^(3/2)*(2*a - b)^(3/2))","B"
572,1,396,149,3.874096,"\text{Not used}","int(1/(a + b*cos(c + d*x)*sin(c + d*x))^3,x)","\frac{\frac{16\,a^2\,b-b^3}{16\,a^4-8\,a^2\,b^2+b^4}+\frac{b\,\mathrm{tan}\left(c+d\,x\right)\,\left(22\,a^2\,b-b^3\right)}{a\,\left(16\,a^4-8\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(16\,a^2\,b-b^3\right)\,\left(2\,a^2+b^2\right)}{2\,a^2\,\left(16\,a^4-8\,a^2\,b^2+b^4\right)}+\frac{b\,{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(10\,a^2\,b-b^3\right)}{a\,\left(16\,a^4-8\,a^2\,b^2+b^4\right)}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^2\,\left(2\,a^2+b^2\right)+a^2+a^2\,{\mathrm{tan}\left(c+d\,x\right)}^4+2\,a\,b\,\mathrm{tan}\left(c+d\,x\right)+2\,a\,b\,{\mathrm{tan}\left(c+d\,x\right)}^3\right)}+\frac{4\,\mathrm{atan}\left(\frac{\left(\frac{4\,a\,\mathrm{tan}\left(c+d\,x\right)\,\left(8\,a^2+b^2\right)}{{\left(2\,a+b\right)}^{5/2}\,{\left(2\,a-b\right)}^{5/2}}+\frac{2\,\left(8\,a^2+b^2\right)\,\left(16\,a^4\,b-8\,a^2\,b^3+b^5\right)}{{\left(2\,a+b\right)}^{5/2}\,{\left(2\,a-b\right)}^{5/2}\,\left(16\,a^4-8\,a^2\,b^2+b^4\right)}\right)\,\left(16\,a^4-8\,a^2\,b^2+b^4\right)}{16\,a^2+2\,b^2}\right)\,\left(8\,a^2+b^2\right)}{d\,{\left(2\,a+b\right)}^{5/2}\,{\left(2\,a-b\right)}^{5/2}}","Not used",1,"((16*a^2*b - b^3)/(16*a^4 + b^4 - 8*a^2*b^2) + (b*tan(c + d*x)*(22*a^2*b - b^3))/(a*(16*a^4 + b^4 - 8*a^2*b^2)) + (tan(c + d*x)^2*(16*a^2*b - b^3)*(2*a^2 + b^2))/(2*a^2*(16*a^4 + b^4 - 8*a^2*b^2)) + (b*tan(c + d*x)^3*(10*a^2*b - b^3))/(a*(16*a^4 + b^4 - 8*a^2*b^2)))/(d*(tan(c + d*x)^2*(2*a^2 + b^2) + a^2 + a^2*tan(c + d*x)^4 + 2*a*b*tan(c + d*x) + 2*a*b*tan(c + d*x)^3)) + (4*atan((((4*a*tan(c + d*x)*(8*a^2 + b^2))/((2*a + b)^(5/2)*(2*a - b)^(5/2)) + (2*(8*a^2 + b^2)*(16*a^4*b + b^5 - 8*a^2*b^3))/((2*a + b)^(5/2)*(2*a - b)^(5/2)*(16*a^4 + b^4 - 8*a^2*b^2)))*(16*a^4 + b^4 - 8*a^2*b^2))/(16*a^2 + 2*b^2))*(8*a^2 + b^2))/(d*(2*a + b)^(5/2)*(2*a - b)^(5/2))","B"
573,0,-1,265,0.000000,"\text{Not used}","int((a + b*cos(c + d*x)*sin(c + d*x))^(5/2),x)","\int {\left(a+b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + b*cos(c + d*x)*sin(c + d*x))^(5/2), x)","F"
574,0,-1,212,0.000000,"\text{Not used}","int((a + b*cos(c + d*x)*sin(c + d*x))^(3/2),x)","\int {\left(a+b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + b*cos(c + d*x)*sin(c + d*x))^(3/2), x)","F"
575,0,-1,76,0.000000,"\text{Not used}","int((a + b*cos(c + d*x)*sin(c + d*x))^(1/2),x)","\int \sqrt{a+b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((a + b*cos(c + d*x)*sin(c + d*x))^(1/2), x)","F"
576,0,-1,76,0.000000,"\text{Not used}","int(1/(a + b*cos(c + d*x)*sin(c + d*x))^(1/2),x)","\int \frac{1}{\sqrt{a+b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(a + b*cos(c + d*x)*sin(c + d*x))^(1/2), x)","F"
577,0,-1,143,0.000000,"\text{Not used}","int(1/(a + b*cos(c + d*x)*sin(c + d*x))^(3/2),x)","\int \frac{1}{{\left(a+b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(a + b*cos(c + d*x)*sin(c + d*x))^(3/2), x)","F"
578,0,-1,295,0.000000,"\text{Not used}","int(1/(a + b*cos(c + d*x)*sin(c + d*x))^(5/2),x)","\int \frac{1}{{\left(a+b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(a + b*cos(c + d*x)*sin(c + d*x))^(5/2), x)","F"
579,0,-1,461,0.000000,"\text{Not used}","int(x^3/(a + b*cos(x)*sin(x)),x)","\int \frac{x^3}{a+b\,\cos\left(x\right)\,\sin\left(x\right)} \,d x","Not used",1,"int(x^3/(a + b*cos(x)*sin(x)), x)","F"
580,0,-1,340,0.000000,"\text{Not used}","int(x^2/(a + b*cos(x)*sin(x)),x)","\int \frac{x^2}{a+b\,\cos\left(x\right)\,\sin\left(x\right)} \,d x","Not used",1,"int(x^2/(a + b*cos(x)*sin(x)), x)","F"
581,0,-1,225,0.000000,"\text{Not used}","int(x/(a + b*cos(x)*sin(x)),x)","\int \frac{x}{a+b\,\cos\left(x\right)\,\sin\left(x\right)} \,d x","Not used",1,"int(x/(a + b*cos(x)*sin(x)), x)","F"
582,0,-1,20,0.000000,"\text{Not used}","int(1/(x*(a + b*cos(x)*sin(x))),x)","\int \frac{1}{x\,\left(a+b\,\cos\left(x\right)\,\sin\left(x\right)\right)} \,d x","Not used",0,"int(1/(x*(a + b*cos(x)*sin(x))), x)","F"
583,0,-1,79,0.000000,"\text{Not used}","int((sin(a*x)^n*(b*x)^(2 - n))/(c*sin(a*x) - a*c*x*cos(a*x))^2,x)","\int \frac{{\sin\left(a\,x\right)}^n\,{\left(b\,x\right)}^{2-n}}{{\left(c\,\sin\left(a\,x\right)-a\,c\,x\,\cos\left(a\,x\right)\right)}^2} \,d x","Not used",0,"int((sin(a*x)^n*(b*x)^(2 - n))/(c*sin(a*x) - a*c*x*cos(a*x))^2, x)","F"
584,0,-1,79,0.000000,"\text{Not used}","int((cos(a*x)^n*(b*x)^(2 - n))/(c*cos(a*x) + a*c*x*sin(a*x))^2,x)","\int \frac{{\cos\left(a\,x\right)}^n\,{\left(b\,x\right)}^{2-n}}{{\left(c\,\cos\left(a\,x\right)+a\,c\,x\,\sin\left(a\,x\right)\right)}^2} \,d x","Not used",0,"int((cos(a*x)^n*(b*x)^(2 - n))/(c*cos(a*x) + a*c*x*sin(a*x))^2, x)","F"
585,0,-1,175,0.000000,"\text{Not used}","int(sin(a*x)^6/(x^4*(sin(a*x) - a*x*cos(a*x))^2),x)","\int \frac{{\sin\left(a\,x\right)}^6}{x^4\,{\left(\sin\left(a\,x\right)-a\,x\,\cos\left(a\,x\right)\right)}^2} \,d x","Not used",1,"int(sin(a*x)^6/(x^4*(sin(a*x) - a*x*cos(a*x))^2), x)","F"
586,0,-1,131,0.000000,"\text{Not used}","int(sin(a*x)^5/(x^3*(sin(a*x) - a*x*cos(a*x))^2),x)","\int \frac{{\sin\left(a\,x\right)}^5}{x^3\,{\left(\sin\left(a\,x\right)-a\,x\,\cos\left(a\,x\right)\right)}^2} \,d x","Not used",1,"int(sin(a*x)^5/(x^3*(sin(a*x) - a*x*cos(a*x))^2), x)","F"
587,0,-1,80,0.000000,"\text{Not used}","int(sin(a*x)^4/(x^2*(sin(a*x) - a*x*cos(a*x))^2),x)","\int \frac{{\sin\left(a\,x\right)}^4}{x^2\,{\left(\sin\left(a\,x\right)-a\,x\,\cos\left(a\,x\right)\right)}^2} \,d x","Not used",1,"int(sin(a*x)^4/(x^2*(sin(a*x) - a*x*cos(a*x))^2), x)","F"
588,0,-1,56,0.000000,"\text{Not used}","int(sin(a*x)^3/(x*(sin(a*x) - a*x*cos(a*x))^2),x)","\int \frac{{\sin\left(a\,x\right)}^3}{x\,{\left(\sin\left(a\,x\right)-a\,x\,\cos\left(a\,x\right)\right)}^2} \,d x","Not used",1,"int(sin(a*x)^3/(x*(sin(a*x) - a*x*cos(a*x))^2), x)","F"
589,1,24,35,3.027722,"\text{Not used}","int(sin(a*x)^2/(sin(a*x) - a*x*cos(a*x))^2,x)","-\frac{\cos\left(a\,x\right)}{a\,\left(\sin\left(a\,x\right)-a\,x\,\cos\left(a\,x\right)\right)}","Not used",1,"-cos(a*x)/(a*(sin(a*x) - a*x*cos(a*x)))","B"
590,1,23,20,0.118038,"\text{Not used}","int((x*sin(a*x))/(sin(a*x) - a*x*cos(a*x))^2,x)","-\frac{1}{a^2\,\sin\left(a\,x\right)-a^3\,x\,\cos\left(a\,x\right)}","Not used",1,"-1/(a^2*sin(a*x) - a^3*x*cos(a*x))","B"
591,0,-1,35,0.000000,"\text{Not used}","int(x^2/(sin(a*x) - a*x*cos(a*x))^2,x)","\int \frac{x^2}{{\left(\sin\left(a\,x\right)-a\,x\,\cos\left(a\,x\right)\right)}^2} \,d x","Not used",1,"int(x^2/(sin(a*x) - a*x*cos(a*x))^2, x)","F"
592,0,-1,104,0.000000,"\text{Not used}","int(x^3/(sin(a*x)*(sin(a*x) - a*x*cos(a*x))^2),x)","\int \frac{x^3}{\sin\left(a\,x\right)\,{\left(\sin\left(a\,x\right)-a\,x\,\cos\left(a\,x\right)\right)}^2} \,d x","Not used",1,"int(x^3/(sin(a*x)*(sin(a*x) - a*x*cos(a*x))^2), x)","F"
593,0,-1,127,0.000000,"\text{Not used}","int(x^4/(sin(a*x)^2*(sin(a*x) - a*x*cos(a*x))^2),x)","\int \frac{x^4}{{\sin\left(a\,x\right)}^2\,{\left(\sin\left(a\,x\right)-a\,x\,\cos\left(a\,x\right)\right)}^2} \,d x","Not used",1,"int(x^4/(sin(a*x)^2*(sin(a*x) - a*x*cos(a*x))^2), x)","F"
594,0,-1,176,0.000000,"\text{Not used}","int(cos(a*x)^6/(x^4*(cos(a*x) + a*x*sin(a*x))^2),x)","\int \frac{{\cos\left(a\,x\right)}^6}{x^4\,{\left(\cos\left(a\,x\right)+a\,x\,\sin\left(a\,x\right)\right)}^2} \,d x","Not used",1,"int(cos(a*x)^6/(x^4*(cos(a*x) + a*x*sin(a*x))^2), x)","F"
595,0,-1,132,0.000000,"\text{Not used}","int(cos(a*x)^5/(x^3*(cos(a*x) + a*x*sin(a*x))^2),x)","\int \frac{{\cos\left(a\,x\right)}^5}{x^3\,{\left(\cos\left(a\,x\right)+a\,x\,\sin\left(a\,x\right)\right)}^2} \,d x","Not used",1,"int(cos(a*x)^5/(x^3*(cos(a*x) + a*x*sin(a*x))^2), x)","F"
596,0,-1,80,0.000000,"\text{Not used}","int(cos(a*x)^4/(x^2*(cos(a*x) + a*x*sin(a*x))^2),x)","\int \frac{{\cos\left(a\,x\right)}^4}{x^2\,{\left(\cos\left(a\,x\right)+a\,x\,\sin\left(a\,x\right)\right)}^2} \,d x","Not used",1,"int(cos(a*x)^4/(x^2*(cos(a*x) + a*x*sin(a*x))^2), x)","F"
597,0,-1,56,0.000000,"\text{Not used}","int(cos(a*x)^3/(x*(cos(a*x) + a*x*sin(a*x))^2),x)","\int \frac{{\cos\left(a\,x\right)}^3}{x\,{\left(\cos\left(a\,x\right)+a\,x\,\sin\left(a\,x\right)\right)}^2} \,d x","Not used",1,"int(cos(a*x)^3/(x*(cos(a*x) + a*x*sin(a*x))^2), x)","F"
598,1,22,34,0.163388,"\text{Not used}","int(cos(a*x)^2/(cos(a*x) + a*x*sin(a*x))^2,x)","\frac{\sin\left(a\,x\right)}{a\,\left(\cos\left(a\,x\right)+a\,x\,\sin\left(a\,x\right)\right)}","Not used",1,"sin(a*x)/(a*(cos(a*x) + a*x*sin(a*x)))","B"
599,1,22,19,0.092675,"\text{Not used}","int((x*cos(a*x))/(cos(a*x) + a*x*sin(a*x))^2,x)","-\frac{1}{a^2\,\cos\left(a\,x\right)+a^3\,x\,\sin\left(a\,x\right)}","Not used",1,"-1/(a^2*cos(a*x) + a^3*x*sin(a*x))","B"
600,0,-1,33,0.000000,"\text{Not used}","int(x^2/(cos(a*x) + a*x*sin(a*x))^2,x)","\int \frac{x^2}{{\left(\cos\left(a\,x\right)+a\,x\,\sin\left(a\,x\right)\right)}^2} \,d x","Not used",1,"int(x^2/(cos(a*x) + a*x*sin(a*x))^2, x)","F"
601,0,-1,110,0.000000,"\text{Not used}","int(x^3/(cos(a*x)*(cos(a*x) + a*x*sin(a*x))^2),x)","\int \frac{x^3}{\cos\left(a\,x\right)\,{\left(\cos\left(a\,x\right)+a\,x\,\sin\left(a\,x\right)\right)}^2} \,d x","Not used",1,"int(x^3/(cos(a*x)*(cos(a*x) + a*x*sin(a*x))^2), x)","F"
602,0,-1,124,0.000000,"\text{Not used}","int(x^4/(cos(a*x)^2*(cos(a*x) + a*x*sin(a*x))^2),x)","\int \frac{x^4}{{\cos\left(a\,x\right)}^2\,{\left(\cos\left(a\,x\right)+a\,x\,\sin\left(a\,x\right)\right)}^2} \,d x","Not used",1,"int(x^4/(cos(a*x)^2*(cos(a*x) + a*x*sin(a*x))^2), x)","F"
603,1,463,157,8.883561,"\text{Not used}","int((c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2)/cos(2*a + 2*b*x)^4,x)","-\frac{{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,\sqrt{\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}}\,16{}\mathrm{i}}{35\,b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)}+\frac{\left(\frac{8{}\mathrm{i}}{7\,b}-\frac{{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,8{}\mathrm{i}}{7\,b}\right)\,\sqrt{\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}}}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)\,{\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}^3}-\frac{\left(\frac{8{}\mathrm{i}}{5\,b}-\frac{{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,64{}\mathrm{i}}{35\,b}\right)\,\sqrt{\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}}}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)\,{\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}^2}-\frac{{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,\sqrt{\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}}\,8{}\mathrm{i}}{35\,b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}","Not used",1,"((8i/(7*b) - (exp(a*2i + b*x*2i)*8i)/(7*b))*((c*(exp(a*2i + b*x*2i)*1i - 1i)*(exp(a*4i + b*x*4i)*1i - 1i))/((exp(a*2i + b*x*2i) + 1)*(exp(a*4i + b*x*4i) + 1)))^(1/2))/((exp(a*2i + b*x*2i) - 1)*(exp(a*4i + b*x*4i) + 1)^3) - (exp(a*2i + b*x*2i)*((c*(exp(a*2i + b*x*2i)*1i - 1i)*(exp(a*4i + b*x*4i)*1i - 1i))/((exp(a*2i + b*x*2i) + 1)*(exp(a*4i + b*x*4i) + 1)))^(1/2)*16i)/(35*b*(exp(a*2i + b*x*2i) - 1)) - ((8i/(5*b) - (exp(a*2i + b*x*2i)*64i)/(35*b))*((c*(exp(a*2i + b*x*2i)*1i - 1i)*(exp(a*4i + b*x*4i)*1i - 1i))/((exp(a*2i + b*x*2i) + 1)*(exp(a*4i + b*x*4i) + 1)))^(1/2))/((exp(a*2i + b*x*2i) - 1)*(exp(a*4i + b*x*4i) + 1)^2) - (exp(a*2i + b*x*2i)*((c*(exp(a*2i + b*x*2i)*1i - 1i)*(exp(a*4i + b*x*4i)*1i - 1i))/((exp(a*2i + b*x*2i) + 1)*(exp(a*4i + b*x*4i) + 1)))^(1/2)*8i)/(35*b*(exp(a*2i + b*x*2i) - 1)*(exp(a*4i + b*x*4i) + 1))","B"
604,1,148,110,11.027446,"\text{Not used}","int((c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2)/cos(2*a + 2*b*x)^3,x)","\frac{4\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,5{}\mathrm{i}+{\mathrm{e}}^{a\,6{}\mathrm{i}+b\,x\,6{}\mathrm{i}}\,5{}\mathrm{i}+{\mathrm{e}}^{a\,10{}\mathrm{i}+b\,x\,10{}\mathrm{i}}\,2{}\mathrm{i}+2{}\mathrm{i}\right)\,\sqrt{\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}}}{15\,b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)\,{\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}^2}","Not used",1,"(4*(exp(a*4i + b*x*4i)*5i + exp(a*6i + b*x*6i)*5i + exp(a*10i + b*x*10i)*2i + 2i)*((c*(exp(a*2i + b*x*2i)*1i - 1i)*(exp(a*4i + b*x*4i)*1i - 1i))/((exp(a*2i + b*x*2i) + 1)*(exp(a*4i + b*x*4i) + 1)))^(1/2))/(15*b*(exp(a*2i + b*x*2i) - 1)*(exp(a*4i + b*x*4i) + 1)^2)","B"
605,1,129,72,7.342667,"\text{Not used}","int((c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2)/cos(2*a + 2*b*x)^2,x)","-\frac{2\,\left({\mathrm{e}}^{a\,6{}\mathrm{i}+b\,x\,6{}\mathrm{i}}\,1{}\mathrm{i}+1{}\mathrm{i}\right)\,\sqrt{\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}}}{3\,b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-{\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+{\mathrm{e}}^{a\,6{}\mathrm{i}+b\,x\,6{}\mathrm{i}}-1\right)}","Not used",1,"-(2*(exp(a*6i + b*x*6i)*1i + 1i)*((c*(exp(a*2i + b*x*2i)*1i - 1i)*(exp(a*4i + b*x*4i)*1i - 1i))/((exp(a*2i + b*x*2i) + 1)*(exp(a*4i + b*x*4i) + 1)))^(1/2))/(3*b*(exp(a*2i + b*x*2i) - exp(a*4i + b*x*4i) + exp(a*6i + b*x*6i) - 1))","B"
606,1,87,33,3.677132,"\text{Not used}","int((c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2)/cos(2*a + 2*b*x),x)","-\frac{\sin\left(2\,a+2\,b\,x\right)\,\sqrt{\frac{c\,\left(\cos\left(2\,a+2\,b\,x\right)-\cos\left(6\,a+6\,b\,x\right)\right)}{3\,\cos\left(2\,a+2\,b\,x\right)+2\,\cos\left(4\,a+4\,b\,x\right)+\cos\left(6\,a+6\,b\,x\right)+2}}}{b\,\left(\cos\left(2\,a+2\,b\,x\right)-1\right)}","Not used",1,"-(sin(2*a + 2*b*x)*((c*(cos(2*a + 2*b*x) - cos(6*a + 6*b*x)))/(3*cos(2*a + 2*b*x) + 2*cos(4*a + 4*b*x) + cos(6*a + 6*b*x) + 2))^(1/2))/(b*(cos(2*a + 2*b*x) - 1))","B"
607,0,-1,45,0.000000,"\text{Not used}","int((c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2),x)","\int \sqrt{c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)} \,d x","Not used",1,"int((c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2), x)","F"
608,0,-1,84,0.000000,"\text{Not used}","int(cos(2*a + 2*b*x)*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2),x)","\int \cos\left(2\,a+2\,b\,x\right)\,\sqrt{c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)} \,d x","Not used",1,"int(cos(2*a + 2*b*x)*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2), x)","F"
609,0,-1,129,0.000000,"\text{Not used}","int(cos(2*a + 2*b*x)^2*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2),x)","\int {\cos\left(2\,a+2\,b\,x\right)}^2\,\sqrt{c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)} \,d x","Not used",1,"int(cos(2*a + 2*b*x)^2*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2), x)","F"
610,0,-1,176,0.000000,"\text{Not used}","int(cos(2*a + 2*b*x)^3*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2),x)","\int {\cos\left(2\,a+2\,b\,x\right)}^3\,\sqrt{c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)} \,d x","Not used",1,"int(cos(2*a + 2*b*x)^3*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2), x)","F"
611,1,594,208,10.183021,"\text{Not used}","int((c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2)/cos(2*a + 2*b*x)^4,x)","\frac{\left(\frac{c\,16{}\mathrm{i}}{9\,b}+\frac{c\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,16{}\mathrm{i}}{9\,b}\right)\,\sqrt{\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}}}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)\,{\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}^4}-\frac{\left(\frac{c\,40{}\mathrm{i}}{7\,b}+\frac{c\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,88{}\mathrm{i}}{63\,b}\right)\,\sqrt{\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}}}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)\,{\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}^3}+\frac{\left(\frac{c\,24{}\mathrm{i}}{5\,b}-\frac{c\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,176{}\mathrm{i}}{105\,b}\right)\,\sqrt{\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}}}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)\,{\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}^2}+\frac{c\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,\sqrt{\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}}\,272{}\mathrm{i}}{315\,b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)}+\frac{c\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,\sqrt{\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}}\,136{}\mathrm{i}}{315\,b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}","Not used",1,"(((c*16i)/(9*b) + (c*exp(a*2i + b*x*2i)*16i)/(9*b))*((c*(exp(a*2i + b*x*2i)*1i - 1i)*(exp(a*4i + b*x*4i)*1i - 1i))/((exp(a*2i + b*x*2i) + 1)*(exp(a*4i + b*x*4i) + 1)))^(1/2))/((exp(a*2i + b*x*2i) - 1)*(exp(a*4i + b*x*4i) + 1)^4) - (((c*40i)/(7*b) + (c*exp(a*2i + b*x*2i)*88i)/(63*b))*((c*(exp(a*2i + b*x*2i)*1i - 1i)*(exp(a*4i + b*x*4i)*1i - 1i))/((exp(a*2i + b*x*2i) + 1)*(exp(a*4i + b*x*4i) + 1)))^(1/2))/((exp(a*2i + b*x*2i) - 1)*(exp(a*4i + b*x*4i) + 1)^3) + (((c*24i)/(5*b) - (c*exp(a*2i + b*x*2i)*176i)/(105*b))*((c*(exp(a*2i + b*x*2i)*1i - 1i)*(exp(a*4i + b*x*4i)*1i - 1i))/((exp(a*2i + b*x*2i) + 1)*(exp(a*4i + b*x*4i) + 1)))^(1/2))/((exp(a*2i + b*x*2i) - 1)*(exp(a*4i + b*x*4i) + 1)^2) + (c*exp(a*2i + b*x*2i)*((c*(exp(a*2i + b*x*2i)*1i - 1i)*(exp(a*4i + b*x*4i)*1i - 1i))/((exp(a*2i + b*x*2i) + 1)*(exp(a*4i + b*x*4i) + 1)))^(1/2)*272i)/(315*b*(exp(a*2i + b*x*2i) - 1)) + (c*exp(a*2i + b*x*2i)*((c*(exp(a*2i + b*x*2i)*1i - 1i)*(exp(a*4i + b*x*4i)*1i - 1i))/((exp(a*2i + b*x*2i) + 1)*(exp(a*4i + b*x*4i) + 1)))^(1/2)*136i)/(315*b*(exp(a*2i + b*x*2i) - 1)*(exp(a*4i + b*x*4i) + 1))","B"
612,1,479,148,9.262437,"\text{Not used}","int((c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2)/cos(2*a + 2*b*x)^3,x)","\frac{\left(\frac{c\,8{}\mathrm{i}}{7\,b}-\frac{c\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,8{}\mathrm{i}}{7\,b}\right)\,\sqrt{\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}}}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)\,{\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}^3}-\frac{\left(\frac{c\,4{}\mathrm{i}}{5\,b}-\frac{c\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,92{}\mathrm{i}}{35\,b}\right)\,\sqrt{\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}}}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)\,{\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}^2}-\frac{\left(\frac{c\,4{}\mathrm{i}}{3\,b}+\frac{c\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,52{}\mathrm{i}}{105\,b}\right)\,\sqrt{\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}}}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}-\frac{c\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,\sqrt{\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}}\,104{}\mathrm{i}}{105\,b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)}","Not used",1,"(((c*8i)/(7*b) - (c*exp(a*2i + b*x*2i)*8i)/(7*b))*((c*(exp(a*2i + b*x*2i)*1i - 1i)*(exp(a*4i + b*x*4i)*1i - 1i))/((exp(a*2i + b*x*2i) + 1)*(exp(a*4i + b*x*4i) + 1)))^(1/2))/((exp(a*2i + b*x*2i) - 1)*(exp(a*4i + b*x*4i) + 1)^3) - (((c*4i)/(5*b) - (c*exp(a*2i + b*x*2i)*92i)/(35*b))*((c*(exp(a*2i + b*x*2i)*1i - 1i)*(exp(a*4i + b*x*4i)*1i - 1i))/((exp(a*2i + b*x*2i) + 1)*(exp(a*4i + b*x*4i) + 1)))^(1/2))/((exp(a*2i + b*x*2i) - 1)*(exp(a*4i + b*x*4i) + 1)^2) - (((c*4i)/(3*b) + (c*exp(a*2i + b*x*2i)*52i)/(105*b))*((c*(exp(a*2i + b*x*2i)*1i - 1i)*(exp(a*4i + b*x*4i)*1i - 1i))/((exp(a*2i + b*x*2i) + 1)*(exp(a*4i + b*x*4i) + 1)))^(1/2))/((exp(a*2i + b*x*2i) - 1)*(exp(a*4i + b*x*4i) + 1)) - (c*exp(a*2i + b*x*2i)*((c*(exp(a*2i + b*x*2i)*1i - 1i)*(exp(a*4i + b*x*4i)*1i - 1i))/((exp(a*2i + b*x*2i) + 1)*(exp(a*4i + b*x*4i) + 1)))^(1/2)*104i)/(105*b*(exp(a*2i + b*x*2i) - 1))","B"
613,1,149,110,11.036744,"\text{Not used}","int((c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2)/cos(2*a + 2*b*x)^2,x)","\frac{2\,c\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,5{}\mathrm{i}+{\mathrm{e}}^{a\,6{}\mathrm{i}+b\,x\,6{}\mathrm{i}}\,5{}\mathrm{i}+{\mathrm{e}}^{a\,10{}\mathrm{i}+b\,x\,10{}\mathrm{i}}\,3{}\mathrm{i}+3{}\mathrm{i}\right)\,\sqrt{\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}}}{5\,b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)\,{\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}^2}","Not used",1,"(2*c*(exp(a*4i + b*x*4i)*5i + exp(a*6i + b*x*6i)*5i + exp(a*10i + b*x*10i)*3i + 3i)*((c*(exp(a*2i + b*x*2i)*1i - 1i)*(exp(a*4i + b*x*4i)*1i - 1i))/((exp(a*2i + b*x*2i) + 1)*(exp(a*4i + b*x*4i) + 1)))^(1/2))/(5*b*(exp(a*2i + b*x*2i) - 1)*(exp(a*4i + b*x*4i) + 1)^2)","B"
614,1,158,75,7.865895,"\text{Not used}","int((c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2)/cos(2*a + 2*b*x),x)","-\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,3{}\mathrm{i}+{\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,3{}\mathrm{i}+{\mathrm{e}}^{a\,6{}\mathrm{i}+b\,x\,6{}\mathrm{i}}\,5{}\mathrm{i}+5{}\mathrm{i}\right)\,\sqrt{\frac{c\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+1\right)}}}{3\,b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-{\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+{\mathrm{e}}^{a\,6{}\mathrm{i}+b\,x\,6{}\mathrm{i}}-1\right)}","Not used",1,"-(c*(exp(a*2i + b*x*2i)*3i + exp(a*4i + b*x*4i)*3i + exp(a*6i + b*x*6i)*5i + 5i)*((c*(exp(a*2i + b*x*2i)*1i - 1i)*(exp(a*4i + b*x*4i)*1i - 1i))/((exp(a*2i + b*x*2i) + 1)*(exp(a*4i + b*x*4i) + 1)))^(1/2))/(3*b*(exp(a*2i + b*x*2i) - exp(a*4i + b*x*4i) + exp(a*6i + b*x*6i) - 1))","B"
615,0,-1,80,0.000000,"\text{Not used}","int((c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2),x)","\int {\left(c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2), x)","F"
616,0,-1,86,0.000000,"\text{Not used}","int(cos(2*a + 2*b*x)*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2),x)","\int \cos\left(2\,a+2\,b\,x\right)\,{\left(c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(2*a + 2*b*x)*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2), x)","F"
617,0,-1,133,0.000000,"\text{Not used}","int(cos(2*a + 2*b*x)^2*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2),x)","\int {\cos\left(2\,a+2\,b\,x\right)}^2\,{\left(c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(2*a + 2*b*x)^2*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2), x)","F"
618,0,-1,182,0.000000,"\text{Not used}","int(cos(2*a + 2*b*x)^3*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2),x)","\int {\cos\left(2\,a+2\,b\,x\right)}^3\,{\left(c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(2*a + 2*b*x)^3*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2), x)","F"
619,0,-1,175,0.000000,"\text{Not used}","int(1/(cos(2*a + 2*b*x)^4*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2)),x)","\int \frac{1}{{\cos\left(2\,a+2\,b\,x\right)}^4\,\sqrt{c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)}} \,d x","Not used",1,"int(1/(cos(2*a + 2*b*x)^4*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2)), x)","F"
620,0,-1,129,0.000000,"\text{Not used}","int(1/(cos(2*a + 2*b*x)^3*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2)),x)","\int \frac{1}{{\cos\left(2\,a+2\,b\,x\right)}^3\,\sqrt{c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)}} \,d x","Not used",1,"int(1/(cos(2*a + 2*b*x)^3*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2)), x)","F"
621,0,-1,88,0.000000,"\text{Not used}","int(1/(cos(2*a + 2*b*x)^2*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2)),x)","\int \frac{1}{{\cos\left(2\,a+2\,b\,x\right)}^2\,\sqrt{c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)}} \,d x","Not used",1,"int(1/(cos(2*a + 2*b*x)^2*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2)), x)","F"
622,0,-1,55,0.000000,"\text{Not used}","int(1/(cos(2*a + 2*b*x)*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2)),x)","\int \frac{1}{\cos\left(2\,a+2\,b\,x\right)\,\sqrt{c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)}} \,d x","Not used",1,"int(1/(cos(2*a + 2*b*x)*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2)), x)","F"
623,0,-1,100,0.000000,"\text{Not used}","int(1/(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2),x)","\int \frac{1}{\sqrt{c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)}} \,d x","Not used",1,"int(1/(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2), x)","F"
624,0,-1,138,0.000000,"\text{Not used}","int(cos(2*a + 2*b*x)/(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2),x)","\int \frac{\cos\left(2\,a+2\,b\,x\right)}{\sqrt{c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)}} \,d x","Not used",1,"int(cos(2*a + 2*b*x)/(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2), x)","F"
625,0,-1,182,0.000000,"\text{Not used}","int(cos(2*a + 2*b*x)^2/(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2),x)","\int \frac{{\cos\left(2\,a+2\,b\,x\right)}^2}{\sqrt{c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)}} \,d x","Not used",1,"int(cos(2*a + 2*b*x)^2/(c*tan(a + b*x)*tan(2*a + 2*b*x))^(1/2), x)","F"
626,0,-1,180,0.000000,"\text{Not used}","int(1/(cos(2*a + 2*b*x)^4*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2)),x)","\int \frac{1}{{\cos\left(2\,a+2\,b\,x\right)}^4\,{\left(c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(2*a + 2*b*x)^4*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2)), x)","F"
627,0,-1,128,0.000000,"\text{Not used}","int(1/(cos(2*a + 2*b*x)^3*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2)),x)","\int \frac{1}{{\cos\left(2\,a+2\,b\,x\right)}^3\,{\left(c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(2*a + 2*b*x)^3*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2)), x)","F"
628,0,-1,93,0.000000,"\text{Not used}","int(1/(cos(2*a + 2*b*x)^2*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2)),x)","\int \frac{1}{{\cos\left(2\,a+2\,b\,x\right)}^2\,{\left(c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(2*a + 2*b*x)^2*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2)), x)","F"
629,0,-1,93,0.000000,"\text{Not used}","int(1/(cos(2*a + 2*b*x)*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2)),x)","\int \frac{1}{\cos\left(2\,a+2\,b\,x\right)\,{\left(c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(2*a + 2*b*x)*(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2)), x)","F"
630,0,-1,138,0.000000,"\text{Not used}","int(1/(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2),x)","\int \frac{1}{{\left(c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2), x)","F"
631,0,-1,178,0.000000,"\text{Not used}","int(cos(2*a + 2*b*x)/(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2),x)","\int \frac{\cos\left(2\,a+2\,b\,x\right)}{{\left(c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(2*a + 2*b*x)/(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2), x)","F"
632,0,-1,234,0.000000,"\text{Not used}","int(cos(2*a + 2*b*x)^2/(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2),x)","\int \frac{{\cos\left(2\,a+2\,b\,x\right)}^2}{{\left(c\,\mathrm{tan}\left(a+b\,x\right)\,\mathrm{tan}\left(2\,a+2\,b\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(2*a + 2*b*x)^2/(c*tan(a + b*x)*tan(2*a + 2*b*x))^(3/2), x)","F"
633,1,14,16,3.098644,"\text{Not used}","int(cot(x)/(sin(2*x)^(1/2)*sin(x)),x)","-\frac{\sqrt{\sin\left(2\,x\right)}\,\cos\left(x\right)}{3\,{\sin\left(x\right)}^2}","Not used",1,"-(sin(2*x)^(1/2)*cos(x))/(3*sin(x)^2)","B"
634,0,-1,69,0.000000,"\text{Not used}","int(1/(sin(2*x)^(1/2)*cos(x)*sin(x)^2*(tan(x) - 2)),x)","\int \frac{1}{\sqrt{\sin\left(2\,x\right)}\,\cos\left(x\right)\,{\sin\left(x\right)}^2\,\left(\mathrm{tan}\left(x\right)-2\right)} \,d x","Not used",1,"int(1/(sin(2*x)^(1/2)*cos(x)*sin(x)^2*(tan(x) - 2)), x)","F"
635,0,-1,79,0.000000,"\text{Not used}","int(-(cos(x)^2*sin(x))/(sin(2*x)^(5/2)*(sin(2*x) - sin(x)^2)),x)","-\int \frac{{\cos\left(x\right)}^2\,\sin\left(x\right)}{{\sin\left(2\,x\right)}^{5/2}\,\left(\sin\left(2\,x\right)-{\sin\left(x\right)}^2\right)} \,d x","Not used",1,"-int((cos(x)^2*sin(x))/(sin(2*x)^(5/2)*(sin(2*x) - sin(x)^2)), x)","F"
636,0,-1,95,0.000000,"\text{Not used}","int(-(cos(2*x)*cos(x)^3)/(sin(2*x)^(5/2)*(sin(2*x) - sin(x)^2)),x)","\int -\frac{\cos\left(2\,x\right)\,{\cos\left(x\right)}^3}{{\sin\left(2\,x\right)}^{5/2}\,\left(\sin\left(2\,x\right)-{\sin\left(x\right)}^2\right)} \,d x","Not used",1,"int(-(cos(2*x)*cos(x)^3)/(sin(2*x)^(5/2)*(sin(2*x) - sin(x)^2)), x)","F"
637,1,63,30,5.539676,"\text{Not used}","int((a*sin(c + d*x) + b/cos(c + d*x))^n*(a*cos(c + d*x) + (b*tan(c + d*x))/cos(c + d*x)),x)","\left\{\begin{array}{cl} \frac{\ln\left(a\,\sin\left(c+d\,x\right)+\frac{b}{\cos\left(c+d\,x\right)}\right)}{d} & \text{\ if\ \ }n=-1\\ \frac{{\left(a\,\sin\left(c+d\,x\right)+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{n+1}}{d\,\left(n+1\right)} & \text{\ if\ \ }n\neq -1 \end{array}\right.","Not used",1,"piecewise(n == -1, log(a*sin(c + d*x) + b/cos(c + d*x))/d, n ~= -1, (a*sin(c + d*x) + b/cos(c + d*x))^(n + 1)/(d*(n + 1)))","B"
638,1,185,26,3.566007,"\text{Not used}","int((a*sin(c + d*x) + b/cos(c + d*x))^3*(a*cos(c + d*x) + (b*tan(c + d*x))/cos(c + d*x)),x)","\frac{a^4\,{\cos\left(2\,c+2\,d\,x\right)}^4-2\,a^4\,{\cos\left(2\,c+2\,d\,x\right)}^2+a^4-8\,\sin\left(2\,c+2\,d\,x\right)\,a^3\,b\,{\cos\left(2\,c+2\,d\,x\right)}^2+8\,\sin\left(2\,c+2\,d\,x\right)\,a^3\,b-24\,a^2\,b^2\,{\cos\left(2\,c+2\,d\,x\right)}^2+24\,a^2\,b^2+32\,\sin\left(2\,c+2\,d\,x\right)\,a\,b^3-4\,b^4\,{\cos\left(2\,c+2\,d\,x\right)}^2-8\,b^4\,\cos\left(2\,c+2\,d\,x\right)+12\,b^4}{d\,\left(16\,{\cos\left(2\,c+2\,d\,x\right)}^2+32\,\cos\left(2\,c+2\,d\,x\right)+16\right)}","Not used",1,"(a^4*cos(2*c + 2*d*x)^4 - 2*a^4*cos(2*c + 2*d*x)^2 - 4*b^4*cos(2*c + 2*d*x)^2 + a^4 + 12*b^4 + 24*a^2*b^2 - 8*b^4*cos(2*c + 2*d*x) - 24*a^2*b^2*cos(2*c + 2*d*x)^2 + 32*a*b^3*sin(2*c + 2*d*x) + 8*a^3*b*sin(2*c + 2*d*x) - 8*a^3*b*cos(2*c + 2*d*x)^2*sin(2*c + 2*d*x))/(d*(32*cos(2*c + 2*d*x) + 16*cos(2*c + 2*d*x)^2 + 16))","B"
639,1,100,26,3.222607,"\text{Not used}","int((a*sin(c + d*x) + b/cos(c + d*x))^2*(a*cos(c + d*x) + (b*tan(c + d*x))/cos(c + d*x)),x)","\frac{a^3\,\sin\left(c+d\,x\right)}{3\,d}+\frac{a^2\,b\,{\cos\left(c+d\,x\right)}^2+\sin\left(c+d\,x\right)\,a\,b^2\,\cos\left(c+d\,x\right)+\frac{b^3}{3}}{d\,{\cos\left(c+d\,x\right)}^3}-\frac{a^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}-\frac{a^2\,b\,\cos\left(c+d\,x\right)}{d}","Not used",1,"(a^3*sin(c + d*x))/(3*d) + (b^3/3 + a^2*b*cos(c + d*x)^2 + a*b^2*cos(c + d*x)*sin(c + d*x))/(d*cos(c + d*x)^3) - (a^3*cos(c + d*x)^2*sin(c + d*x))/(3*d) - (a^2*b*cos(c + d*x))/d","B"
640,1,61,26,3.177074,"\text{Not used}","int((a*sin(c + d*x) + b/cos(c + d*x))*(a*cos(c + d*x) + (b*tan(c + d*x))/cos(c + d*x)),x)","-\frac{\frac{a^2\,\left(2\,{\sin\left(2\,c+2\,d\,x\right)}^2-1\right)}{16}+\frac{a^2}{16}+\frac{b^2}{2}+\frac{a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2}}{d\,\left({\sin\left(c+d\,x\right)}^2-1\right)}","Not used",1,"-((a^2*(2*sin(2*c + 2*d*x)^2 - 1))/16 + a^2/16 + b^2/2 + (a*b*sin(2*c + 2*d*x))/2)/(d*(sin(c + d*x)^2 - 1))","B"
641,1,133,22,4.858534,"\text{Not used}","int((a*cos(c + d*x) + (b*tan(c + d*x))/cos(c + d*x))/(a*sin(c + d*x) + b/cos(c + d*x)),x)","\frac{\mathrm{atan}\left(\frac{-\cos\left(c+d\,x\right)\,a^6+8\,\cos\left(c+d\,x\right)\,a^4\,b^2-16\,\cos\left(c+d\,x\right)\,a^2\,b^4+\frac{\sin\left(2\,c+2\,d\,x\right)\,a\,b^5}{2}+b^6}{1{}\mathrm{i}\,\cos\left(c+d\,x\right)\,a^6-8{}\mathrm{i}\,\cos\left(c+d\,x\right)\,a^4\,b^2+16{}\mathrm{i}\,\cos\left(c+d\,x\right)\,a^2\,b^4+\frac{1{}\mathrm{i}\,\sin\left(2\,c+2\,d\,x\right)\,a\,b^5}{2}+b^6\,1{}\mathrm{i}}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(atan((b^6 - a^6*cos(c + d*x) - 16*a^2*b^4*cos(c + d*x) + 8*a^4*b^2*cos(c + d*x) + (a*b^5*sin(2*c + 2*d*x))/2)/(a^6*cos(c + d*x)*1i + b^6*1i + a^2*b^4*cos(c + d*x)*16i - a^4*b^2*cos(c + d*x)*8i + (a*b^5*sin(2*c + 2*d*x)*1i)/2))*2i)/d","B"
642,1,47,24,3.236037,"\text{Not used}","int((a*cos(c + d*x) + (b*tan(c + d*x))/cos(c + d*x))/(a*sin(c + d*x) + b/cos(c + d*x))^2,x)","-\frac{b\,\left(\cos\left(c+d\,x\right)+1\right)+\frac{a\,\sin\left(2\,c+2\,d\,x\right)}{2}}{b\,d\,\left(b+\frac{a\,\sin\left(2\,c+2\,d\,x\right)}{2}\right)}","Not used",1,"-(b*(cos(c + d*x) + 1) + (a*sin(2*c + 2*d*x))/2)/(b*d*(b + (a*sin(2*c + 2*d*x))/2))","B"
643,1,291,26,6.313016,"\text{Not used}","int((a*cos(c + d*x) + (b*tan(c + d*x))/cos(c + d*x))/(a*sin(c + d*x) + b/cos(c + d*x))^3,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2+b^2\right)}{b^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^2+b^2\right)}{b^2}+\frac{2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-b^2\right)}{b^2}+\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{b}-\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{b}-\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{b}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^2+4\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(8\,a^2-6\,b^2\right)+b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+b^2+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^2*(a^2 + b^2))/b^2 + (2*tan(c/2 + (d*x)/2)^6*(a^2 + b^2))/b^2 + (2*a*tan(c/2 + (d*x)/2))/b - (4*tan(c/2 + (d*x)/2)^4*(a^2 - b^2))/b^2 + (2*a*tan(c/2 + (d*x)/2)^3)/b - (2*a*tan(c/2 + (d*x)/2)^5)/b - (2*a*tan(c/2 + (d*x)/2)^7)/b)/(d*(tan(c/2 + (d*x)/2)^2*(4*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^6*(4*a^2 + 4*b^2) - tan(c/2 + (d*x)/2)^4*(8*a^2 - 6*b^2) + b^2*tan(c/2 + (d*x)/2)^8 + b^2 + 4*a*b*tan(c/2 + (d*x)/2)^3 - 4*a*b*tan(c/2 + (d*x)/2)^5 - 4*a*b*tan(c/2 + (d*x)/2)^7 + 4*a*b*tan(c/2 + (d*x)/2)))","B"
644,0,-1,21,0.000000,"\text{Not used}","int(sin(a + b*x)*F(c, d, cos(a + b*x), r, s),x)","\int \sin\left(a+b\,x\right)\,F\left(c,d,\cos\left(a+b\,x\right),r,s\right) \,d x","Not used",0,"int(sin(a + b*x)*F(c, d, cos(a + b*x), r, s), x)","F"
645,0,-1,21,0.000000,"\text{Not used}","int(cos(a + b*x)*F(c, d, sin(a + b*x), r, s),x)","\int \cos\left(a+b\,x\right)\,F\left(c,d,\sin\left(a+b\,x\right),r,s\right) \,d x","Not used",0,"int(cos(a + b*x)*F(c, d, sin(a + b*x), r, s), x)","F"
646,0,-1,23,0.000000,"\text{Not used}","int(F(c, d, tan(a + b*x), r, s)/cos(a + b*x)^2,x)","\int \frac{F\left(c,d,\mathrm{tan}\left(a+b\,x\right),r,s\right)}{{\cos\left(a+b\,x\right)}^2} \,d x","Not used",0,"int(F(c, d, tan(a + b*x), r, s)/cos(a + b*x)^2, x)","F"
647,0,-1,23,0.000000,"\text{Not used}","int(F(c, d, cot(a + b*x), r, s)/sin(a + b*x)^2,x)","\int \frac{F\left(c,d,\mathrm{cot}\left(a+b\,x\right),r,s\right)}{{\sin\left(a+b\,x\right)}^2} \,d x","Not used",0,"int(F(c, d, cot(a + b*x), r, s)/sin(a + b*x)^2, x)","F"
648,1,12,12,0.057327,"\text{Not used}","int(sin(x)/(a + b*cos(x)),x)","-\frac{\ln\left(a+b\,\cos\left(x\right)\right)}{b}","Not used",1,"-log(a + b*cos(x))/b","B"
649,1,20,20,3.150181,"\text{Not used}","int(sin(x)*(a + b*cos(x))^n,x)","-\frac{{\left(a+b\,\cos\left(x\right)\right)}^{n+1}}{b\,\left(n+1\right)}","Not used",1,"-(a + b*cos(x))^(n + 1)/(b*(n + 1))","B"
650,1,5,5,3.077942,"\text{Not used}","int(sin(x)/(cos(x)^2 + 1)^(1/2),x)","-\mathrm{asinh}\left(\cos\left(x\right)\right)","Not used",1,"-asinh(cos(x))","B"
651,1,5,5,0.087988,"\text{Not used}","int(cos(cos(x))*sin(x),x)","-\sin\left(\cos\left(x\right)\right)","Not used",1,"-sin(cos(x))","B"
652,1,22,28,3.046032,"\text{Not used}","int(cos(cos(x))*sin(cos(x))*cos(x)*sin(x),x)","\frac{\cos\left(x\right)\,{\cos\left(\cos\left(x\right)\right)}^2}{2}-\frac{\sin\left(\cos\left(x\right)\right)\,\cos\left(\cos\left(x\right)\right)}{4}-\frac{\cos\left(x\right)}{4}","Not used",1,"(cos(cos(x))^2*cos(x))/2 - cos(x)/4 - (cos(cos(x))*sin(cos(x)))/4","B"
653,1,20,26,3.133857,"\text{Not used}","int(cos(cos(x))*sin(6*cos(x))^2*sin(x),x)","\frac{\sin\left(11\,\cos\left(x\right)\right)}{44}-\frac{\sin\left(\cos\left(x\right)\right)}{2}+\frac{\sin\left(13\,\cos\left(x\right)\right)}{52}","Not used",1,"sin(11*cos(x))/44 - sin(cos(x))/2 + sin(13*cos(x))/52","B"
654,1,39,36,0.089639,"\text{Not used}","int(cos(x)^3*sin(x)*(a + b*cos(x)^2)^3,x)","-\frac{a^3\,{\cos\left(x\right)}^4}{4}-\frac{a^2\,b\,{\cos\left(x\right)}^6}{2}-\frac{3\,a\,b^2\,{\cos\left(x\right)}^8}{8}-\frac{b^3\,{\cos\left(x\right)}^{10}}{10}","Not used",1,"- (a^3*cos(x)^4)/4 - (b^3*cos(x)^10)/10 - (a^2*b*cos(x)^6)/2 - (3*a*b^2*cos(x)^8)/8","B"
655,1,7,9,3.009597,"\text{Not used}","int(sin(3*x)*sin(cos(3*x)),x)","\frac{\cos\left(\cos\left(3\,x\right)\right)}{3}","Not used",1,"cos(cos(3*x))/3","B"
656,1,17,31,0.116213,"\text{Not used}","int(exp(cos(3*x + 1))*cos(3*x + 1)*sin(3*x + 1),x)","-\frac{{\mathrm{e}}^{\cos\left(3\,x+1\right)}\,\left(\cos\left(3\,x+1\right)-1\right)}{3}","Not used",1,"-(exp(cos(3*x + 1))*(cos(3*x + 1) - 1))/3","B"
657,0,-1,9,0.000000,"\text{Not used}","int((cos(x)^2*sin(x))/(1 - cos(x)^6)^(1/2),x)","\int \frac{{\cos\left(x\right)}^2\,\sin\left(x\right)}{\sqrt{1-{\cos\left(x\right)}^6}} \,d x","Not used",1,"int((cos(x)^2*sin(x))/(1 - cos(x)^6)^(1/2), x)","F"
658,0,-1,71,0.000000,"\text{Not used}","int(sin(x)^5/(1 - 5*cos(x))^(1/2),x)","\int \frac{{\sin\left(x\right)}^5}{\sqrt{1-5\,\cos\left(x\right)}} \,d x","Not used",1,"int(sin(x)^5/(1 - 5*cos(x))^(1/2), x)","F"
659,1,17,18,0.100907,"\text{Not used}","int(exp(n*cos(a + b*x))*sin(a + b*x),x)","-\frac{{\mathrm{e}}^{n\,\cos\left(a+b\,x\right)}}{b\,n}","Not used",1,"-exp(n*cos(a + b*x))/(b*n)","B"
660,1,23,23,3.160390,"\text{Not used}","int(sin(c*(a + b*x))*exp(n*cos(a*c + b*c*x)),x)","-\frac{{\mathrm{e}}^{n\,\cos\left(a\,c+b\,c\,x\right)}}{b\,c\,n}","Not used",1,"-exp(n*cos(a*c + b*c*x))/(b*c*n)","B"
661,1,23,24,3.022831,"\text{Not used}","int(exp(n*cos(c*(a + b*x)))*sin(a*c + b*c*x),x)","-\frac{{\mathrm{e}}^{n\,\cos\left(a\,c+b\,c\,x\right)}}{b\,c\,n}","Not used",1,"-exp(n*cos(a*c + b*c*x))/(b*c*n)","B"
662,0,-1,14,0.000000,"\text{Not used}","int(exp(n*cos(a + b*x))*tan(a + b*x),x)","\int {\mathrm{e}}^{n\,\cos\left(a+b\,x\right)}\,\mathrm{tan}\left(a+b\,x\right) \,d x","Not used",1,"int(exp(n*cos(a + b*x))*tan(a + b*x), x)","F"
663,0,-1,19,0.000000,"\text{Not used}","int(tan(c*(a + b*x))*exp(n*cos(a*c + b*c*x)),x)","\int \mathrm{tan}\left(c\,\left(a+b\,x\right)\right)\,{\mathrm{e}}^{n\,\cos\left(a\,c+b\,c\,x\right)} \,d x","Not used",1,"int(tan(c*(a + b*x))*exp(n*cos(a*c + b*c*x)), x)","F"
664,0,-1,20,0.000000,"\text{Not used}","int(exp(n*cos(c*(a + b*x)))*tan(a*c + b*c*x),x)","\int {\mathrm{e}}^{n\,\cos\left(c\,\left(a+b\,x\right)\right)}\,\mathrm{tan}\left(a\,c+b\,c\,x\right) \,d x","Not used",1,"int(exp(n*cos(c*(a + b*x)))*tan(a*c + b*c*x), x)","F"
665,1,11,11,0.034242,"\text{Not used}","int(cos(x)/(a + b*sin(x)),x)","\frac{\ln\left(a+b\,\sin\left(x\right)\right)}{b}","Not used",1,"log(a + b*sin(x))/b","B"
666,1,19,19,3.134862,"\text{Not used}","int(cos(x)*(a + b*sin(x))^n,x)","\frac{{\left(a+b\,\sin\left(x\right)\right)}^{n+1}}{b\,\left(n+1\right)}","Not used",1,"(a + b*sin(x))^(n + 1)/(b*(n + 1))","B"
667,1,9,3,0.021429,"\text{Not used}","int(cos(x)/(sin(x)^2 + 1)^(1/2),x)","-\mathrm{asin}\left(\sin\left(x\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}","Not used",1,"-asin(sin(x)*1i)*1i","B"
668,1,5,7,2.978665,"\text{Not used}","int(cos(x)/(4 - sin(x)^2)^(1/2),x)","\mathrm{asin}\left(\frac{\sin\left(x\right)}{2}\right)","Not used",1,"asin(sin(x)/2)","B"
669,1,9,13,2.983620,"\text{Not used}","int(cos(3*x)/(4 - sin(3*x)^2)^(1/2),x)","\frac{\mathrm{asin}\left(\frac{\sin\left(3\,x\right)}{2}\right)}{3}","Not used",1,"asin(sin(3*x)/2)/3","B"
670,1,47,21,3.095338,"\text{Not used}","int(cos(x)*(1/sin(x) + 1)^(1/2),x)","\sin\left(x\right)\,\sqrt{\frac{1}{\sin\left(x\right)}+1}+\frac{\ln\left(\sin\left(x\right)+\sqrt{{\sin\left(x\right)}^2+\sin\left(x\right)}+\frac{1}{2}\right)\,\sin\left(x\right)\,\sqrt{\frac{1}{\sin\left(x\right)}+1}}{2\,\sqrt{{\sin\left(x\right)}^2+\sin\left(x\right)}}","Not used",1,"sin(x)*(1/sin(x) + 1)^(1/2) + (log(sin(x) + (sin(x) + sin(x)^2)^(1/2) + 1/2)*sin(x)*(1/sin(x) + 1)^(1/2))/(2*(sin(x) + sin(x)^2)^(1/2))","B"
671,1,20,28,2.965120,"\text{Not used}","int(cos(x)*(4 - sin(x)^2)^(1/2),x)","2\,\mathrm{asin}\left(\frac{\sin\left(x\right)}{2}\right)+\frac{\sin\left(x\right)\,\sqrt{{\cos\left(x\right)}^2+3}}{2}","Not used",1,"2*asin(sin(x)/2) + (sin(x)*(cos(x)^2 + 3)^(1/2))/2","B"
672,1,10,14,0.100333,"\text{Not used}","int(cos(x)*sin(x)*(sin(x)^2 + 1)^(1/2),x)","\frac{{\left({\sin\left(x\right)}^2+1\right)}^{3/2}}{3}","Not used",1,"(sin(x)^2 + 1)^(3/2)/3","B"
673,1,14,19,3.169505,"\text{Not used}","int(cos(x)/(2*sin(x) + sin(x)^2)^(1/2),x)","\ln\left(\sin\left(x\right)+\sqrt{\sin\left(x\right)\,\left(\sin\left(x\right)+2\right)}+1\right)","Not used",1,"log(sin(x) + (sin(x)*(sin(x) + 2))^(1/2) + 1)","B"
674,1,3,3,2.952889,"\text{Not used}","int(cos(sin(x))*cos(x),x)","\sin\left(\sin\left(x\right)\right)","Not used",1,"sin(sin(x))","B"
675,1,4,4,3.002410,"\text{Not used}","int(cos(sin(x))*cos(sin(sin(x)))*cos(x),x)","\sin\left(\sin\left(\sin\left(x\right)\right)\right)","Not used",1,"sin(sin(sin(x)))","B"
676,1,21,4,3.239673,"\text{Not used}","int(cos(x)/cos(sin(x)),x)","-\mathrm{atan}\left({\mathrm{e}}^{-\frac{{\mathrm{e}}^{-x\,1{}\mathrm{i}}}{2}}\,{\mathrm{e}}^{\frac{{\mathrm{e}}^{x\,1{}\mathrm{i}}}{2}}\right)\,2{}\mathrm{i}","Not used",1,"-atan(exp(-exp(-x*1i)/2)*exp(exp(x*1i)/2))*2i","B"
677,1,73,36,0.071641,"\text{Not used}","int(cos(x)*sin(x)^3*(a + b*sin(x)^2)^3,x)","\frac{b^2\,{\cos\left(x\right)}^8\,\left(3\,a+4\,b\right)}{8}-\frac{b^3\,{\cos\left(x\right)}^{10}}{10}-\frac{{\cos\left(x\right)}^2\,{\left(a+b\right)}^3}{2}-\frac{b\,{\cos\left(x\right)}^6\,\left(a^2+3\,a\,b+2\,b^2\right)}{2}+\frac{{\cos\left(x\right)}^4\,{\left(a+b\right)}^2\,\left(a+4\,b\right)}{4}","Not used",1,"(b^2*cos(x)^8*(3*a + 4*b))/8 - (b^3*cos(x)^10)/10 - (cos(x)^2*(a + b)^3)/2 - (b*cos(x)^6*(3*a*b + a^2 + 2*b^2))/2 + (cos(x)^4*(a + b)^2*(a + 4*b))/4","B"
678,1,8,14,2.914575,"\text{Not used}","int(exp(sin(x))*cos(x)*sin(x),x)","{\mathrm{e}}^{\sin\left(x\right)}\,\left(\sin\left(x\right)-1\right)","Not used",1,"exp(sin(x))*(sin(x) - 1)","B"
679,0,-1,25,0.000000,"\text{Not used}","int(cos(x)^3/(sin(x)^3)^(1/2),x)","\int \frac{{\cos\left(x\right)}^3}{\sqrt{{\sin\left(x\right)}^3}} \,d x","Not used",1,"int(cos(x)^3/(sin(x)^3)^(1/2), x)","F"
680,1,7,10,3.001941,"\text{Not used}","int((exp(sin(x)^(1/2))*cos(x))/sin(x)^(1/2),x)","2\,{\mathrm{e}}^{\sqrt{\sin\left(x\right)}}","Not used",1,"2*exp(sin(x)^(1/2))","B"
681,1,6,6,2.908158,"\text{Not used}","int(exp(sin(x) + 4)*cos(x),x)","{\mathrm{e}}^{\sin\left(x\right)}\,{\mathrm{e}}^4","Not used",1,"exp(sin(x))*exp(4)","B"
682,1,7,10,2.993495,"\text{Not used}","int(cos(2*x)*exp(cos(x)*sin(x)),x)","{\mathrm{e}}^{\frac{\sin\left(2\,x\right)}{2}}","Not used",1,"exp(sin(2*x)/2)","B"
683,1,7,10,2.952240,"\text{Not used}","int(exp(cos(x/2)*sin(x/2))*cos(x),x)","2\,{\mathrm{e}}^{\frac{\sin\left(x\right)}{2}}","Not used",1,"2*exp(sin(x)/2)","B"
684,1,16,17,0.106650,"\text{Not used}","int(cos(a + b*x)*exp(n*sin(a + b*x)),x)","\frac{{\mathrm{e}}^{n\,\sin\left(a+b\,x\right)}}{b\,n}","Not used",1,"exp(n*sin(a + b*x))/(b*n)","B"
685,1,22,22,3.079962,"\text{Not used}","int(cos(c*(a + b*x))*exp(n*sin(a*c + b*c*x)),x)","\frac{{\mathrm{e}}^{n\,\sin\left(a\,c+b\,c\,x\right)}}{b\,c\,n}","Not used",1,"exp(n*sin(a*c + b*c*x))/(b*c*n)","B"
686,1,22,23,2.985484,"\text{Not used}","int(exp(n*sin(c*(a + b*x)))*cos(a*c + b*c*x),x)","\frac{{\mathrm{e}}^{n\,\sin\left(a\,c+b\,c\,x\right)}}{b\,c\,n}","Not used",1,"exp(n*sin(a*c + b*c*x))/(b*c*n)","B"
687,0,-1,13,0.000000,"\text{Not used}","int(cot(a + b*x)*exp(n*sin(a + b*x)),x)","\int \mathrm{cot}\left(a+b\,x\right)\,{\mathrm{e}}^{n\,\sin\left(a+b\,x\right)} \,d x","Not used",1,"int(cot(a + b*x)*exp(n*sin(a + b*x)), x)","F"
688,0,-1,18,0.000000,"\text{Not used}","int(cot(c*(a + b*x))*exp(n*sin(a*c + b*c*x)),x)","\int \mathrm{cot}\left(c\,\left(a+b\,x\right)\right)\,{\mathrm{e}}^{n\,\sin\left(a\,c+b\,c\,x\right)} \,d x","Not used",1,"int(cot(c*(a + b*x))*exp(n*sin(a*c + b*c*x)), x)","F"
689,0,-1,19,0.000000,"\text{Not used}","int(exp(n*sin(c*(a + b*x)))*cot(a*c + b*c*x),x)","\int {\mathrm{e}}^{n\,\sin\left(c\,\left(a+b\,x\right)\right)}\,\mathrm{cot}\left(a\,c+b\,c\,x\right) \,d x","Not used",1,"int(exp(n*sin(c*(a + b*x)))*cot(a*c + b*c*x), x)","F"
690,1,11,11,3.026006,"\text{Not used}","int(1/(cos(x)^2*(a + b*tan(x))),x)","\frac{\ln\left(a+b\,\mathrm{tan}\left(x\right)\right)}{b}","Not used",1,"log(a + b*tan(x))/b","B"
691,1,3,11,3.082121,"\text{Not used}","int(-1/(cos(x)^2*(tan(x)^2 - 1)),x)","\mathrm{atanh}\left(\mathrm{tan}\left(x\right)\right)","Not used",1,"atanh(tan(x))","B"
692,1,7,27,2.882332,"\text{Not used}","int(1/(cos(x)^2*(tan(x)^2 + 9)),x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(x\right)}{3}\right)}{3}","Not used",1,"atan(tan(x)/3)/3","B"
693,1,37,19,3.562807,"\text{Not used}","int((a + b*tan(x))^n/cos(x)^2,x)","\left\{\begin{array}{cl} \frac{\ln\left(a+b\,\mathrm{tan}\left(x\right)\right)}{b} & \text{\ if\ \ }n=-1\\ \frac{{\left(a+b\,\mathrm{tan}\left(x\right)\right)}^{n+1}}{b\,\left(n+1\right)} & \text{\ if\ \ }n\neq -1 \end{array}\right.","Not used",1,"piecewise(n == -1, log(a + b*tan(x))/b, n ~= -1, (a + b*tan(x))^(n + 1)/(b*(n + 1)))","B"
694,1,4,4,2.936754,"\text{Not used}","int((1/(tan(x)^2 + 1) + 1)/cos(x)^2,x)","x+\mathrm{tan}\left(x\right)","Not used",1,"x + tan(x)","B"
695,1,4,4,2.996625,"\text{Not used}","int((tan(x)^2 + 2)/(cos(x)^2*(tan(x)^2 + 1)),x)","x+\mathrm{tan}\left(x\right)","Not used",1,"x + tan(x)","B"
696,1,5,33,3.122496,"\text{Not used}","int(1/(cos(x)^2*(2*tan(x) + tan(x)^2 + 2)),x)","\mathrm{atan}\left(\mathrm{tan}\left(x\right)+1\right)","Not used",1,"atan(tan(x) + 1)","B"
697,1,16,10,3.097730,"\text{Not used}","int(1/(cos(x)^2*(tan(x)^2 + tan(x)^3)),x)","2\,\mathrm{atanh}\left(2\,\mathrm{tan}\left(x\right)+1\right)-\frac{1}{\mathrm{tan}\left(x\right)}","Not used",1,"2*atanh(2*tan(x) + 1) - 1/tan(x)","B"
698,1,14,10,2.984032,"\text{Not used}","int(-1/(cos(x)^2*(tan(x)^2 - tan(x)^3)),x)","\frac{1}{\mathrm{tan}\left(x\right)}-2\,\mathrm{atanh}\left(2\,\mathrm{tan}\left(x\right)-1\right)","Not used",1,"1/tan(x) - 2*atanh(2*tan(x) - 1)","B"
699,1,75,176,3.308335,"\text{Not used}","int(-1/(cos(x)^2*(4*tan(x)^3 - 3)),x)","-\frac{6^{1/3}\,\ln\left(\mathrm{tan}\left(x\right)-\frac{6^{1/3}}{2}\right)}{18}-\frac{6^{1/3}\,\ln\left(\mathrm{tan}\left(x\right)-\frac{6^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{4}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{36}+\frac{6^{1/3}\,\ln\left(\mathrm{tan}\left(x\right)+\frac{6^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{4}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{36}","Not used",1,"(6^(1/3)*log(tan(x) + (6^(1/3)*(3^(1/2)*1i + 1))/4)*(3^(1/2)*1i + 1))/36 - (6^(1/3)*log(tan(x) - (6^(1/3)*(3^(1/2)*1i - 1))/4)*(3^(1/2)*1i - 1))/36 - (6^(1/3)*log(tan(x) - 6^(1/3)/2))/18","B"
700,1,17,53,3.114534,"\text{Not used}","int(1/(cos(x)^2*(5*tan(x)^2 - 5*tan(x) + 11)),x)","\frac{2\,\sqrt{195}\,\mathrm{atan}\left(\frac{\sqrt{195}\,\left(2\,\mathrm{tan}\left(x\right)-1\right)}{39}\right)}{195}","Not used",1,"(2*195^(1/2)*atan((195^(1/2)*(2*tan(x) - 1))/39))/195","B"
701,1,27,28,3.093042,"\text{Not used}","int((a + b*tan(x))/(cos(x)^2*(c + d*tan(x))),x)","\frac{b\,\mathrm{tan}\left(x\right)}{d}+\frac{\ln\left(c+d\,\mathrm{tan}\left(x\right)\right)\,\left(a\,d-b\,c\right)}{d^2}","Not used",1,"(b*tan(x))/d + (log(c + d*tan(x))*(a*d - b*c))/d^2","B"
702,1,65,53,2.983718,"\text{Not used}","int((a + b*tan(x))^2/(cos(x)^2*(c + d*tan(x))),x)","\frac{\ln\left(c+d\,\mathrm{tan}\left(x\right)\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{d^3}-\mathrm{tan}\left(x\right)\,\left(\frac{b^2\,c}{d^2}-\frac{2\,a\,b}{d}\right)+\frac{b^2\,{\mathrm{tan}\left(x\right)}^2}{2\,d}","Not used",1,"(log(c + d*tan(x))*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/d^3 - tan(x)*((b^2*c)/d^2 - (2*a*b)/d) + (b^2*tan(x)^2)/(2*d)","B"
703,1,122,78,2.955453,"\text{Not used}","int((a + b*tan(x))^3/(cos(x)^2*(c + d*tan(x))),x)","\mathrm{tan}\left(x\right)\,\left(\frac{3\,a^2\,b}{d}-\frac{c\,\left(\frac{3\,a\,b^2}{d}-\frac{b^3\,c}{d^2}\right)}{d}\right)+{\mathrm{tan}\left(x\right)}^2\,\left(\frac{3\,a\,b^2}{2\,d}-\frac{b^3\,c}{2\,d^2}\right)+\frac{b^3\,{\mathrm{tan}\left(x\right)}^3}{3\,d}+\frac{\ln\left(c+d\,\mathrm{tan}\left(x\right)\right)\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{d^4}","Not used",1,"tan(x)*((3*a^2*b)/d - (c*((3*a*b^2)/d - (b^3*c)/d^2))/d) + tan(x)^2*((3*a*b^2)/(2*d) - (b^3*c)/(2*d^2)) + (b^3*tan(x)^3)/(3*d) + (log(c + d*tan(x))*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/d^4","B"
704,1,12,12,2.930358,"\text{Not used}","int(tan(x)^2/(cos(x)^2*(tan(x)^3 + 2)^2),x)","-\frac{1}{3\,\left({\mathrm{tan}\left(x\right)}^3+2\right)}","Not used",1,"-1/(3*(tan(x)^3 + 2))","B"
705,1,25,33,2.921529,"\text{Not used}","int((tan(x)^6*(tan(x)^2 + 1)^3)/cos(x)^2,x)","\frac{{\mathrm{tan}\left(x\right)}^{13}}{13}+\frac{3\,{\mathrm{tan}\left(x\right)}^{11}}{11}+\frac{{\mathrm{tan}\left(x\right)}^9}{3}+\frac{{\mathrm{tan}\left(x\right)}^7}{7}","Not used",1,"tan(x)^7/7 + tan(x)^9/3 + (3*tan(x)^11)/11 + tan(x)^13/13","B"
706,1,30,46,2.965187,"\text{Not used}","int((tan(x)^2 + 2)/(cos(x)^2*(tan(x)^3 + 1)),x)","\ln\left(\mathrm{tan}\left(x\right)+1\right)-\frac{2\,\sqrt{3}\,\mathrm{atan}\left(\frac{\sqrt{3}-\sqrt{3}\,\mathrm{tan}\left(x\right)}{\mathrm{tan}\left(x\right)+1}\right)}{3}","Not used",1,"log(tan(x) + 1) - (2*3^(1/2)*atan((3^(1/2) - 3^(1/2)*tan(x))/(tan(x) + 1)))/3","B"
707,1,4,4,2.881997,"\text{Not used}","int((cos(x)^2 + 1)/cos(x)^2,x)","x+\mathrm{tan}\left(x\right)","Not used",1,"x + tan(x)","B"
708,1,9,21,3.507713,"\text{Not used}","int(1/(cos(x)^2*(1/cos(x)^2 - 3*tan(x) + 1)),x)","-2\,\mathrm{atanh}\left(2\,\mathrm{tan}\left(x\right)-3\right)","Not used",1,"-2*atanh(2*tan(x) - 3)","B"
709,0,-1,9,0.000000,"\text{Not used}","int(1/(cos(x)^2*(4 - 1/cos(x)^2)^(1/2)),x)","\int \frac{1}{{\cos\left(x\right)}^2\,\sqrt{4-\frac{1}{{\cos\left(x\right)}^2}}} \,d x","Not used",1,"int(1/(cos(x)^2*(4 - 1/cos(x)^2)^(1/2)), x)","F"
710,0,-1,9,0.000000,"\text{Not used}","int(1/(cos(x)^2*(1 - 4*tan(x)^2)^(1/2)),x)","\int \frac{1}{{\cos\left(x\right)}^2\,\sqrt{1-4\,{\mathrm{tan}\left(x\right)}^2}} \,d x","Not used",1,"int(1/(cos(x)^2*(1 - 4*tan(x)^2)^(1/2)), x)","F"
711,0,-1,14,0.000000,"\text{Not used}","int(1/(cos(x)^2*(tan(x)^2 - 4)^(1/2)),x)","\int \frac{1}{{\cos\left(x\right)}^2\,\sqrt{{\mathrm{tan}\left(x\right)}^2-4}} \,d x","Not used",1,"int(1/(cos(x)^2*(tan(x)^2 - 4)^(1/2)), x)","F"
712,1,19,19,3.060840,"\text{Not used}","int((1 - cot(x)^2)^(1/2)/cos(x)^2,x)","\mathrm{asin}\left(\mathrm{cot}\left(x\right)\right)+\frac{\sqrt{1-{\mathrm{cot}\left(x\right)}^2}}{\mathrm{cot}\left(x\right)}","Not used",1,"asin(cot(x)) + (1 - cot(x)^2)^(1/2)/cot(x)","B"
713,0,-1,26,0.000000,"\text{Not used}","int((1 - tan(x)^2)^(1/2)/cos(x)^2,x)","\int \frac{\sqrt{1-{\mathrm{tan}\left(x\right)}^2}}{{\cos\left(x\right)}^2} \,d x","Not used",1,"int((1 - tan(x)^2)^(1/2)/cos(x)^2, x)","F"
714,1,3,4,3.102262,"\text{Not used}","int(exp(tan(x))/cos(x)^2,x)","{\mathrm{e}}^{\mathrm{tan}\left(x\right)}","Not used",1,"exp(tan(x))","B"
715,1,14,17,2.922782,"\text{Not used}","int((tan(x)*(1/cos(x)^2 - 1)^2)/cos(x)^4,x)","\frac{{\mathrm{tan}\left(x\right)}^6\,\left(3\,{\mathrm{tan}\left(x\right)}^2+4\right)}{24}","Not used",1,"(tan(x)^6*(3*tan(x)^2 + 4))/24","B"
716,1,16,12,3.012273,"\text{Not used}","int(1/(sin(x)^2*(a + b*cot(x))),x)","-\frac{2\,\mathrm{atanh}\left(\frac{2\,a\,\mathrm{tan}\left(x\right)}{b}+1\right)}{b}","Not used",1,"-(2*atanh((2*a*tan(x))/b + 1))/b","B"
717,1,43,20,3.186430,"\text{Not used}","int((a + b*cot(x))^n/sin(x)^2,x)","\left\{\begin{array}{cl} -\frac{\ln\left(a+\frac{b}{\mathrm{tan}\left(x\right)}\right)}{b} & \text{\ if\ \ }n=-1\\ -\frac{{\left(a+\frac{b}{\mathrm{tan}\left(x\right)}\right)}^{n+1}}{b\,\left(n+1\right)} & \text{\ if\ \ }n\neq -1 \end{array}\right.","Not used",1,"piecewise(n == -1, -log(a + b/tan(x))/b, n ~= -1, -(a + b/tan(x))^(n + 1)/(b*(n + 1)))","B"
718,1,6,6,2.934714,"\text{Not used}","int((sin(x)^2 + 1)/sin(x)^2,x)","x-\mathrm{cot}\left(x\right)","Not used",1,"x - cot(x)","B"
719,1,6,6,2.941844,"\text{Not used}","int((1/(cot(x)^2 + 1) + 1)/sin(x)^2,x)","x-\mathrm{cot}\left(x\right)","Not used",1,"x - cot(x)","B"
720,1,35,28,3.069462,"\text{Not used}","int((a + b*cot(x))/(sin(x)^2*(c + d*cot(x))),x)","-\frac{b}{d\,\mathrm{tan}\left(x\right)}-\frac{2\,\mathrm{atanh}\left(\frac{2\,c\,\mathrm{tan}\left(x\right)}{d}+1\right)\,\left(a\,d-b\,c\right)}{d^2}","Not used",1,"- b/(d*tan(x)) - (2*atanh((2*c*tan(x))/d + 1)*(a*d - b*c))/d^2","B"
721,1,92,53,3.072444,"\text{Not used}","int((a + b*cot(x))^2/(sin(x)^2*(c + d*cot(x))),x)","-\frac{\frac{b^2}{2\,d}+\frac{b\,\mathrm{tan}\left(x\right)\,\left(2\,a\,d-b\,c\right)}{d^2}}{{\mathrm{tan}\left(x\right)}^2}-\frac{2\,\mathrm{atanh}\left(\frac{\left(d+2\,c\,\mathrm{tan}\left(x\right)\right)\,{\left(a\,d-b\,c\right)}^2}{d\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}\right)\,{\left(a\,d-b\,c\right)}^2}{d^3}","Not used",1,"- (b^2/(2*d) + (b*tan(x)*(2*a*d - b*c))/d^2)/tan(x)^2 - (2*atanh(((d + 2*c*tan(x))*(a*d - b*c)^2)/(d*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))*(a*d - b*c)^2)/d^3","B"
722,1,141,78,3.080473,"\text{Not used}","int((a + b*cot(x))^3/(sin(x)^2*(c + d*cot(x))),x)","-\frac{\frac{b^3}{3\,d}+\frac{b^2\,\mathrm{tan}\left(x\right)\,\left(3\,a\,d-b\,c\right)}{2\,d^2}+\frac{b\,{\mathrm{tan}\left(x\right)}^2\,\left(3\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)}{d^3}}{{\mathrm{tan}\left(x\right)}^3}-\frac{2\,\mathrm{atanh}\left(\frac{\left(d+2\,c\,\mathrm{tan}\left(x\right)\right)\,{\left(a\,d-b\,c\right)}^3}{d\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}\right)\,{\left(a\,d-b\,c\right)}^3}{d^4}","Not used",1,"- (b^3/(3*d) + (b^2*tan(x)*(3*a*d - b*c))/(2*d^2) + (b*tan(x)^2*(3*a^2*d^2 + b^2*c^2 - 3*a*b*c*d))/d^3)/tan(x)^3 - (2*atanh(((d + 2*c*tan(x))*(a*d - b*c)^3)/(d*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)))*(a*d - b*c)^3)/d^4","B"
723,1,7,6,2.937891,"\text{Not used}","int(exp(-cot(x))/sin(x)^2,x)","{\mathrm{e}}^{-\frac{1}{\mathrm{tan}\left(x\right)}}","Not used",1,"exp(-1/tan(x))","B"
724,1,48,11,3.245894,"\text{Not used}","int(tan(x)/(cos(x)*(a + b/cos(x))),x)","\frac{\mathrm{atan}\left(\frac{b\,{\sin\left(\frac{x}{2}\right)}^2}{a\,{\cos\left(\frac{x}{2}\right)}^2\,1{}\mathrm{i}+b\,{\cos\left(\frac{x}{2}\right)}^2\,1{}\mathrm{i}-a\,{\sin\left(\frac{x}{2}\right)}^2\,1{}\mathrm{i}}\right)\,2{}\mathrm{i}}{b}","Not used",1,"(atan((b*sin(x/2)^2)/(a*cos(x/2)^2*1i + b*cos(x/2)^2*1i - a*sin(x/2)^2*1i))*2i)/b","B"
725,1,7,5,2.949753,"\text{Not used}","int(tan(x)/(cos(x)*(1/cos(x)^2 + 1)),x)","\mathrm{atan}\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2\right)","Not used",1,"atan(tan(x/2)^2)","B"
726,1,13,11,3.043544,"\text{Not used}","int(tan(x)/(cos(x)*(4/cos(x)^2 + 9)),x)","\frac{\mathrm{atan}\left(\frac{13\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{12}-\frac{5}{12}\right)}{6}","Not used",1,"atan((13*tan(x/2)^2)/12 - 5/12)/6","B"
727,1,9,7,3.072174,"\text{Not used}","int(tan(x)/(cos(x)*(1/cos(x) + 1/cos(x)^2)),x)","\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)","Not used",1,"log(tan(x/2)^2 + 1)","B"
728,1,7,5,3.102186,"\text{Not used}","int(tan(x)/(cos(x)*(1/cos(x)^2 + 4)^(1/2)),x)","\mathrm{asinh}\left(\frac{1}{2\,\cos\left(x\right)}\right)","Not used",1,"asinh(1/(2*cos(x)))","B"
729,1,13,13,0.105622,"\text{Not used}","int(tan(x)/(cos(x)*(cos(x)^2 + 1)^(1/2)),x)","\frac{\sqrt{{\cos\left(x\right)}^2+1}}{\cos\left(x\right)}","Not used",1,"(cos(x)^2 + 1)^(1/2)/cos(x)","B"
730,1,5,4,3.093137,"\text{Not used}","int((exp(1/cos(x))*tan(x))/cos(x),x)","{\mathrm{e}}^{\frac{1}{\cos\left(x\right)}}","Not used",1,"exp(1/cos(x))","B"
731,1,11,9,3.122793,"\text{Not used}","int((2^(1/cos(x))*tan(x))/cos(x),x)","\frac{2^{\frac{1}{\cos\left(x\right)}}}{\ln\left(2\right)}","Not used",1,"2^(1/cos(x))/log(2)","B"
732,1,18,12,3.114307,"\text{Not used}","int(tan(2*x)/(cos(2*x)*(1/cos(2*x) + 1)^(3/2)),x)","-\frac{1}{\sqrt{\cos\left(2\,x\right)+1}\,\sqrt{\frac{1}{\cos\left(2\,x\right)}}}","Not used",1,"-1/((cos(2*x) + 1)^(1/2)*(1/cos(2*x))^(1/2))","B"
733,1,36,43,3.256719,"\text{Not used}","int((tan(3*x)*(5*cos(3*x)^2 + 1)^(1/2))/cos(3*x),x)","\frac{\sqrt{\frac{5\,\cos\left(6\,x\right)}{2}+\frac{7}{2}}}{3\,\cos\left(3\,x\right)}+\frac{\sqrt{5}\,\mathrm{asin}\left(\sqrt{5}\,\cos\left(3\,x\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{3}","Not used",1,"(5^(1/2)*asin(5^(1/2)*cos(3*x)*1i)*1i)/3 + ((5*cos(6*x))/2 + 7/2)^(1/2)/(3*cos(3*x))","B"
734,1,18,22,3.025758,"\text{Not used}","int(tan(3*x)/(cos(3*x)*(5*cos(3*x)^2 + 1)^(1/2)),x)","\frac{\sqrt{\frac{5\,\cos\left(6\,x\right)}{2}+\frac{7}{2}}}{3\,\cos\left(3\,x\right)}","Not used",1,"((5*cos(6*x))/2 + 7/2)^(1/2)/(3*cos(3*x))","B"
735,1,31,12,3.179544,"\text{Not used}","int(cot(x)/(sin(x)*(a + b/sin(x))),x)","-\frac{\ln\left(b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)+b\right)-\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{b}","Not used",1,"-(log(b + 2*a*tan(x/2) + b*tan(x/2)^2) - log(tan(x/2)))/b","B"
736,1,14,14,2.968417,"\text{Not used}","int((5^(1/sin(3*x))*cot(3*x))/sin(3*x),x)","-\frac{5^{\frac{1}{\sin\left(3\,x\right)}}}{3\,\ln\left(5\right)}","Not used",1,"-5^(1/sin(3*x))/(3*log(5))","B"
737,1,26,3,3.215083,"\text{Not used}","int(cot(x)/(sin(x)*(1/sin(x)^2 + 1)),x)","\mathrm{atan}\left(\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{2}+\frac{5\,\mathrm{tan}\left(\frac{x}{2}\right)}{2}\right)-\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2}\right)","Not used",1,"atan((5*tan(x/2))/2 + tan(x/2)^3/2) - atan(tan(x/2)/2)","B"
738,1,57,43,3.148018,"\text{Not used}","int(cot(6*x)/(sin(6*x)*(11/sin(6*x)^2 - 5)^2),x)","-\frac{55\,\sin\left(6\,x\right)-11\,\sqrt{55}\,\mathrm{atanh}\left(\frac{\sqrt{55}\,\sin\left(6\,x\right)}{11}\right)+5\,\sqrt{55}\,{\sin\left(6\,x\right)}^2\,\mathrm{atanh}\left(\frac{\sqrt{55}\,\sin\left(6\,x\right)}{11}\right)}{16500\,{\sin\left(6\,x\right)}^2-36300}","Not used",1,"-(55*sin(6*x) - 11*55^(1/2)*atanh((55^(1/2)*sin(6*x))/11) + 5*55^(1/2)*sin(6*x)^2*atanh((55^(1/2)*sin(6*x))/11))/(16500*sin(6*x)^2 - 36300)","B"
739,1,34,14,3.113801,"\text{Not used}","int(cot(x)/(sin(x)*(sin(x)^2 + 1)^(1/2)),x)","-\frac{\sqrt{\frac{1}{{\sin\left(x\right)}^2}+1}}{\sin\left(x\right)\,\left(\sqrt{\frac{1}{{\sin\left(x\right)}^2}+1}+1\right)\,\sqrt{{\sin\left(x\right)}^2+1}}","Not used",1,"-(1/sin(x)^2 + 1)^(1/2)/(sin(x)*((1/sin(x)^2 + 1)^(1/2) + 1)*(sin(x)^2 + 1)^(1/2))","B"
740,1,28,43,3.144048,"\text{Not used}","int(cot(5*x)/(sin(5*x)^3*(sin(5*x)^2 + 1)^(1/2)),x)","\frac{\sqrt{{\sin\left(5\,x\right)}^2+1}\,\left(2\,{\sin\left(5\,x\right)}^2-1\right)}{15\,{\sin\left(5\,x\right)}^3}","Not used",1,"((sin(5*x)^2 + 1)^(1/2)*(2*sin(5*x)^2 - 1))/(15*sin(5*x)^3)","B"
741,1,27,43,3.178176,"\text{Not used}","int(exp(n*sin(a + b*x))*sin(2*a + 2*b*x),x)","\frac{2\,{\mathrm{e}}^{n\,\sin\left(a+b\,x\right)}\,\left(n\,\sin\left(a+b\,x\right)-1\right)}{b\,n^2}","Not used",1,"(2*exp(n*sin(a + b*x))*(n*sin(a + b*x) - 1))/(b*n^2)","B"
742,1,27,43,0.001958,"\text{Not used}","int(exp(n*sin(a + b*x))*sin(2*a + 2*b*x),x)","\frac{2\,{\mathrm{e}}^{n\,\sin\left(a+b\,x\right)}\,\left(n\,\sin\left(a+b\,x\right)-1\right)}{b\,n^2}","Not used",1,"(2*exp(n*sin(a + b*x))*(n*sin(a + b*x) - 1))/(b*n^2)","B"
743,1,33,64,3.177034,"\text{Not used}","int(exp(n*sin(a/2 + (b*x)/2))*sin(a + b*x),x)","\frac{4\,{\mathrm{e}}^{n\,\sin\left(\frac{a}{2}+\frac{b\,x}{2}\right)}\,\left(n\,\sin\left(\frac{a}{2}+\frac{b\,x}{2}\right)-1\right)}{b\,n^2}","Not used",1,"(4*exp(n*sin(a/2 + (b*x)/2))*(n*sin(a/2 + (b*x)/2) - 1))/(b*n^2)","B"
744,1,33,64,0.002033,"\text{Not used}","int(exp(n*sin(a/2 + (b*x)/2))*sin(a + b*x),x)","\frac{4\,{\mathrm{e}}^{n\,\sin\left(\frac{a}{2}+\frac{b\,x}{2}\right)}\,\left(n\,\sin\left(\frac{a}{2}+\frac{b\,x}{2}\right)-1\right)}{b\,n^2}","Not used",1,"(4*exp(n*sin(a/2 + (b*x)/2))*(n*sin(a/2 + (b*x)/2) - 1))/(b*n^2)","B"
745,1,27,43,3.213522,"\text{Not used}","int(exp(n*cos(a + b*x))*sin(2*a + 2*b*x),x)","-\frac{2\,{\mathrm{e}}^{n\,\cos\left(a+b\,x\right)}\,\left(n\,\cos\left(a+b\,x\right)-1\right)}{b\,n^2}","Not used",1,"-(2*exp(n*cos(a + b*x))*(n*cos(a + b*x) - 1))/(b*n^2)","B"
746,1,27,43,0.001954,"\text{Not used}","int(exp(n*cos(a + b*x))*sin(2*a + 2*b*x),x)","-\frac{2\,{\mathrm{e}}^{n\,\cos\left(a+b\,x\right)}\,\left(n\,\cos\left(a+b\,x\right)-1\right)}{b\,n^2}","Not used",1,"-(2*exp(n*cos(a + b*x))*(n*cos(a + b*x) - 1))/(b*n^2)","B"
747,1,33,64,3.173701,"\text{Not used}","int(exp(n*cos(a/2 + (b*x)/2))*sin(a + b*x),x)","-\frac{4\,{\mathrm{e}}^{n\,\cos\left(\frac{a}{2}+\frac{b\,x}{2}\right)}\,\left(n\,\cos\left(\frac{a}{2}+\frac{b\,x}{2}\right)-1\right)}{b\,n^2}","Not used",1,"-(4*exp(n*cos(a/2 + (b*x)/2))*(n*cos(a/2 + (b*x)/2) - 1))/(b*n^2)","B"
748,1,33,64,0.002156,"\text{Not used}","int(exp(n*cos(a/2 + (b*x)/2))*sin(a + b*x),x)","-\frac{4\,{\mathrm{e}}^{n\,\cos\left(\frac{a}{2}+\frac{b\,x}{2}\right)}\,\left(n\,\cos\left(\frac{a}{2}+\frac{b\,x}{2}\right)-1\right)}{b\,n^2}","Not used",1,"-(4*exp(n*cos(a/2 + (b*x)/2))*(n*cos(a/2 + (b*x)/2) - 1))/(b*n^2)","B"
749,1,27,9,5.267587,"\text{Not used}","int(log(tan(x))/(cos(x)*sin(x)),x)","\frac{{\ln\left(-\frac{{\mathrm{e}}^{x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}}{{\mathrm{e}}^{x\,2{}\mathrm{i}}+1}\right)}^2}{2}","Not used",1,"log(-(exp(x*2i)*1i - 1i)/(exp(x*2i) + 1))^2/2","B"
750,1,27,9,3.527293,"\text{Not used}","int(log(tan(x))/sin(2*x),x)","\frac{{\ln\left(-\frac{{\mathrm{e}}^{x\,2{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}}{{\mathrm{e}}^{x\,2{}\mathrm{i}}+1}\right)}^2}{4}","Not used",1,"log(-(exp(x*2i)*1i - 1i)/(exp(x*2i) + 1))^2/4","B"
751,1,4,3,0.026033,"\text{Not used}","int(exp(cos(x)^2 + sin(x)^2),x)","x\,\mathrm{e}","Not used",1,"x*exp(1)","B"
752,1,8,8,0.023667,"\text{Not used}","int(x/cos(x)^2,x)","\ln\left(\cos\left(x\right)\right)+x\,\mathrm{tan}\left(x\right)","Not used",1,"log(cos(x)) + x*tan(x)","B"
753,1,22,34,2.972881,"\text{Not used}","int(x*cos(x^2)^4,x)","\frac{\sin\left(2\,x^2\right)}{8}+\frac{\sin\left(4\,x^2\right)}{64}+\frac{3\,x^2}{16}","Not used",1,"sin(2*x^2)/8 + sin(4*x^2)/64 + (3*x^2)/16","B"
754,1,6,10,0.067332,"\text{Not used}","int(cos(x)^(1/2)*sin(x),x)","-\frac{2\,{\cos\left(x\right)}^{3/2}}{3}","Not used",1,"-(2*cos(x)^(3/2))/3","B"
755,1,12,11,3.536339,"\text{Not used}","int(exp(-2*x)*tan(exp(-2*x)),x)","-\frac{\ln\left({\mathrm{tan}\left({\mathrm{e}}^{-2\,x}\right)}^2+1\right)}{4}","Not used",1,"-log(tan(exp(-2*x))^2 + 1)/4","B"
756,1,7,7,2.923568,"\text{Not used}","int(sin(2*x)/(cos(x)*(cos(x) + 1)),x)","-2\,\ln\left(\cos\left(x\right)+1\right)","Not used",1,"-2*log(cos(x) + 1)","B"
757,1,15,19,2.896901,"\text{Not used}","int(x/cos(3*x)^2,x)","\frac{\ln\left(\cos\left(3\,x\right)\right)}{9}+\frac{x\,\mathrm{tan}\left(3\,x\right)}{3}","Not used",1,"log(cos(3*x))/9 + (x*tan(3*x))/3","B"
758,1,25,37,2.900590,"\text{Not used}","int(exp(-2*Pi*x)*cos(2*Pi*x),x)","-\frac{{\mathrm{e}}^{-2\,\Pi \,x}\,\left(2\,\cos\left(2\,\Pi \,x\right)-2\,\sin\left(2\,\Pi \,x\right)\right)}{8\,\Pi }","Not used",1,"-(exp(-2*Pi*x)*(2*cos(2*Pi*x) - 2*sin(2*Pi*x)))/(8*Pi)","B"
759,1,49,12,2.986439,"\text{Not used}","int(cos(x)^12*sin(x)^10 - cos(x)^10*sin(x)^12,x)","-\frac{\sin\left(x\right)\,{\cos\left(x\right)}^{21}}{11}+\frac{5\,\sin\left(x\right)\,{\cos\left(x\right)}^{19}}{11}-\frac{10\,\sin\left(x\right)\,{\cos\left(x\right)}^{17}}{11}+\frac{10\,\sin\left(x\right)\,{\cos\left(x\right)}^{15}}{11}-\frac{5\,\sin\left(x\right)\,{\cos\left(x\right)}^{13}}{11}+\frac{\sin\left(x\right)\,{\cos\left(x\right)}^{11}}{11}","Not used",1,"(cos(x)^11*sin(x))/11 - (5*cos(x)^13*sin(x))/11 + (10*cos(x)^15*sin(x))/11 - (10*cos(x)^17*sin(x))/11 + (5*cos(x)^19*sin(x))/11 - (cos(x)^21*sin(x))/11","B"
760,1,19,9,0.116908,"\text{Not used}","int(x*cot(x^2),x)","\frac{\ln\left({\mathrm{e}}^{x^2\,2{}\mathrm{i}}-1\right)}{2}-\frac{x^2\,1{}\mathrm{i}}{2}","Not used",1,"log(exp(x^2*2i) - 1)/2 - (x^2*1i)/2","B"
761,1,14,8,0.099097,"\text{Not used}","int(x/cos(x^2)^2,x)","\frac{1{}\mathrm{i}}{{\mathrm{e}}^{x^2\,2{}\mathrm{i}}+1}","Not used",1,"1i/(exp(x^2*2i) + 1)","B"
762,1,13,15,2.964832,"\text{Not used}","int(sin(8*x)/(sin(4*x)^4 + 9),x)","\frac{\mathrm{atan}\left(\frac{10\,{\mathrm{tan}\left(4\,x\right)}^2}{3}+3\right)}{12}","Not used",1,"atan((10*tan(4*x)^2)/3 + 3)/12","B"
763,1,15,23,0.074140,"\text{Not used}","int(cos(2*x)/(sin(2*x)^2 + 8),x)","\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sin\left(2\,x\right)}{4}\right)}{8}","Not used",1,"(2^(1/2)*atan((2^(1/2)*sin(2*x))/4))/8","B"
764,1,33,37,2.972584,"\text{Not used}","int(x*(cos(x^2)^3 - sin(x^2)^3),x)","-\frac{{\cos\left(x^2\right)}^3}{6}+\frac{\sin\left(x^2\right)\,{\cos\left(x^2\right)}^2}{6}+\frac{\cos\left(x^2\right)}{2}+\frac{\sin\left(x^2\right)}{3}","Not used",1,"cos(x^2)/2 + sin(x^2)/3 + (cos(x^2)^2*sin(x^2))/6 - cos(x^2)^3/6","B"
765,1,8,10,2.918158,"\text{Not used}","int(-(cos(x)*sin(x))/(cos(x) - 1),x)","\ln\left(\cos\left(x\right)-1\right)+\cos\left(x\right)","Not used",1,"log(cos(x) - 1) + cos(x)","B"
766,1,6,8,0.056390,"\text{Not used}","int(x*cos(x^2),x)","\frac{\sin\left(x^2\right)}{2}","Not used",1,"sin(x^2)/2","B"
767,1,8,10,0.058694,"\text{Not used}","int(x^2*cos(4*x^3),x)","\frac{\sin\left(4\,x^3\right)}{12}","Not used",1,"sin(4*x^3)/12","B"
768,1,6,8,0.066971,"\text{Not used}","int(x^3*cos(x^4),x)","\frac{\sin\left(x^4\right)}{4}","Not used",1,"sin(x^4)/4","B"
769,1,8,10,2.923848,"\text{Not used}","int(x*sin(x^2/2),x)","-\cos\left(\frac{x^2}{2}\right)","Not used",1,"-cos(x^2/2)","B"
770,1,8,8,0.074721,"\text{Not used}","int((x*tan(x^2))/cos(x^2),x)","\frac{1}{2\,\cos\left(x^2\right)}","Not used",1,"1/(2*cos(x^2))","B"
771,1,10,10,2.915605,"\text{Not used}","int(tan(1/x)^2/x^2,x)","\frac{1}{x}-\mathrm{tan}\left(\frac{1}{x}\right)","Not used",1,"1/x - tan(1/x)","B"
772,1,13,11,0.282749,"\text{Not used}","int(x*tan(x^2 + 1),x)","\frac{\ln\left({\mathrm{tan}\left(x^2+1\right)}^2+1\right)}{4}","Not used",1,"log(tan(x^2 + 1)^2 + 1)/4","B"
773,1,13,12,2.923378,"\text{Not used}","int(sin(Pi*(2*x + 1)),x)","-\frac{\cos\left(\Pi \,\left(2\,x+1\right)\right)}{2\,\Pi }","Not used",1,"-cos(Pi*(2*x + 1))/(2*Pi)","B"
774,1,16,21,3.000950,"\text{Not used}","int(-(cot(x) + 1/sin(x)^2)/(cos(x)^2 - 1),x)","-\frac{\mathrm{cot}\left(x\right)\,\left(2\,{\mathrm{cot}\left(x\right)}^2+3\,\mathrm{cot}\left(x\right)+6\right)}{6}","Not used",1,"-(cot(x)*(3*cot(x) + 2*cot(x)^2 + 6))/6","B"
775,1,15,19,3.027060,"\text{Not used}","int(x^2*cos(4*x^3)*cos(5*x^3),x)","\frac{\sin\left(x^3\right)}{6}+\frac{\sin\left(9\,x^3\right)}{54}","Not used",1,"sin(x^3)/6 + sin(9*x^3)/54","B"
776,1,43,47,3.004170,"\text{Not used}","int(x^14*sin(x^3),x)","4\,x^6\,\cos\left(x^3\right)-8\,\cos\left(x^3\right)-\frac{x^{12}\,\cos\left(x^3\right)}{3}-8\,x^3\,\sin\left(x^3\right)+\frac{4\,x^9\,\sin\left(x^3\right)}{3}","Not used",1,"4*x^6*cos(x^3) - 8*cos(x^3) - (x^12*cos(x^3))/3 - 8*x^3*sin(x^3) + (4*x^9*sin(x^3))/3","B"
777,1,25,35,2.965622,"\text{Not used}","int(x^2*exp(-3*x^3)*sin(2*x^3),x)","-\frac{{\mathrm{e}}^{-3\,x^3}\,\left(2\,\cos\left(2\,x^3\right)+3\,\sin\left(2\,x^3\right)\right)}{39}","Not used",1,"-(exp(-3*x^3)*(2*cos(2*x^3) + 3*sin(2*x^3)))/39","B"
778,1,4,4,2.923815,"\text{Not used}","int(2*x*cos(x^2),x)","\sin\left(x^2\right)","Not used",1,"sin(x^2)","B"
779,1,6,6,0.057439,"\text{Not used}","int(3*x^2*cos(x^3 + 7),x)","\sin\left(x^3+7\right)","Not used",1,"sin(x^3 + 7)","B"
780,1,7,7,0.054678,"\text{Not used}","int(sin(x) + 1/(x^2 + 1),x)","\mathrm{atan}\left(x\right)-\cos\left(x\right)","Not used",1,"atan(x) - cos(x)","B"
781,1,8,10,0.041878,"\text{Not used}","int(x*sin(x^2 + 1),x)","-\frac{\cos\left(x^2+1\right)}{2}","Not used",1,"-cos(x^2 + 1)/2","B"
782,1,8,10,2.981054,"\text{Not used}","int(x*cos(x^2 + 1),x)","\frac{\sin\left(x^2+1\right)}{2}","Not used",1,"sin(x^2 + 1)/2","B"
783,1,8,10,0.045652,"\text{Not used}","int(x^2*cos(x^3) + 1,x)","x+\frac{\sin\left(x^3\right)}{3}","Not used",1,"x + sin(x^3)/3","B"
784,1,8,10,0.047325,"\text{Not used}","int(x^2*sin(x^3 + 1),x)","-\frac{\cos\left(x^3+1\right)}{3}","Not used",1,"-cos(x^3 + 1)/3","B"
785,1,6,6,0.050665,"\text{Not used}","int(12*x^2*cos(x^3),x)","4\,\sin\left(x^3\right)","Not used",1,"4*sin(x^3)","B"
786,1,14,14,2.945005,"\text{Not used}","int(sin(x + 1)*(x + 1),x)","\sin\left(x+1\right)-\cos\left(x+1\right)\,\left(x+1\right)","Not used",1,"sin(x + 1) - cos(x + 1)*(x + 1)","B"
787,1,16,20,2.964950,"\text{Not used}","int(x^5*cos(x^3),x)","\frac{\cos\left(x^3\right)}{3}+\frac{x^3\,\sin\left(x^3\right)}{3}","Not used",1,"cos(x^3)/3 + (x^3*sin(x^3))/3","B"
788,1,15,23,0.021277,"\text{Not used}","int(exp(-3*x)*cos(x),x)","-\frac{{\mathrm{e}}^{-3\,x}\,\left(3\,\cos\left(x\right)-\sin\left(x\right)\right)}{10}","Not used",1,"-(exp(-3*x)*(3*cos(x) - sin(x)))/10","B"
789,1,16,20,2.958972,"\text{Not used}","int(x^3*sin(x^2),x)","\frac{\sin\left(x^2\right)}{2}-\frac{x^2\,\cos\left(x^2\right)}{2}","Not used",1,"sin(x^2)/2 - (x^2*cos(x^2))/2","B"
790,1,16,20,0.049824,"\text{Not used}","int(x^3*cos(x^2),x)","\frac{\cos\left(x^2\right)}{2}+\frac{x^2\,\sin\left(x^2\right)}{2}","Not used",1,"cos(x^2)/2 + (x^2*sin(x^2))/2","B"
791,1,7,9,0.072150,"\text{Not used}","int(cos(2*sin(x))*cos(x),x)","\frac{\sin\left(2\,\sin\left(x\right)\right)}{2}","Not used",1,"sin(2*sin(x))/2","B"
792,1,17,11,3.007902,"\text{Not used}","int((cos(x)*sin(x))/(cos(x)^2 + 1),x)","-\mathrm{atanh}\left(\frac{16}{3\,\left(12\,{\mathrm{tan}\left(x\right)}^2+16\right)}-\frac{1}{3}\right)","Not used",1,"-atanh(16/(3*(12*tan(x)^2 + 16)) - 1/3)","B"
793,1,8,10,3.152677,"\text{Not used}","int((cos(x) + 1)*(x + sin(x))^3,x)","\frac{{\left(x+\sin\left(x\right)\right)}^4}{4}","Not used",1,"(x + sin(x))^4/4","B"
794,1,6,9,2.925651,"\text{Not used}","int((cos(x) + 1)/sin(x)^2,x)","-\mathrm{cot}\left(\frac{x}{2}\right)","Not used",1,"-cot(x/2)","B"
795,1,7,5,3.001119,"\text{Not used}","int(sin(x)*tan(x)^2,x)","\cos\left(x\right)+\frac{1}{\cos\left(x\right)}","Not used",1,"cos(x) + 1/cos(x)","B"
796,1,14,13,3.121284,"\text{Not used}","int(-(exp(sin(x))*(sin(x) - x*cos(x)^3))/cos(x)^2,x)","\frac{{\mathrm{e}}^{\sin\left(x\right)}\,\left(x\,\cos\left(x\right)-1\right)}{\cos\left(x\right)}","Not used",1,"(exp(sin(x))*(x*cos(x) - 1))/cos(x)","B"
797,1,9,9,0.028297,"\text{Not used}","int(x/sin(x)^2,x)","\ln\left(\sin\left(x\right)\right)-x\,\mathrm{cot}\left(x\right)","Not used",1,"log(sin(x)) - x*cot(x)","B"
798,1,18,20,0.028390,"\text{Not used}","int(cos(x)*sin(Pi/6 + x),x)","\frac{x\,\sin\left(\frac{\Pi }{6}\right)}{2}-\frac{\cos\left(\frac{\Pi }{6}+2\,x\right)}{4}","Not used",1,"(x*sin(Pi/6))/2 - cos(Pi/6 + 2*x)/4","B"
799,1,14,19,2.952409,"\text{Not used}","int(x*sin(x^2)^3,x)","\frac{\cos\left(x^2\right)\,\left({\cos\left(x^2\right)}^2-3\right)}{6}","Not used",1,"(cos(x^2)*(cos(x^2)^2 - 3))/6","B"
800,1,16,14,2.950251,"\text{Not used}","int(sin(x)^2*tan(x),x)","\frac{{\cos\left(x\right)}^2}{2}+\frac{\ln\left({\mathrm{tan}\left(x\right)}^2+1\right)}{2}","Not used",1,"log(tan(x)^2 + 1)/2 + cos(x)^2/2","B"
801,1,32,22,2.971273,"\text{Not used}","int(cos(x)^2*cot(x)^3,x)","\ln\left({\mathrm{tan}\left(x\right)}^2+1\right)-2\,\ln\left(\mathrm{tan}\left(x\right)\right)-\frac{{\mathrm{tan}\left(x\right)}^2+\frac{1}{2}}{{\mathrm{tan}\left(x\right)}^4+{\mathrm{tan}\left(x\right)}^2}","Not used",1,"log(tan(x)^2 + 1) - 2*log(tan(x)) - (tan(x)^2 + 1/2)/(tan(x)^2 + tan(x)^4)","B"
802,1,5,5,2.938256,"\text{Not used}","int(-(sin(x) - 1)/cos(x),x)","\ln\left(\sin\left(x\right)+1\right)","Not used",1,"log(sin(x) + 1)","B"
803,1,5,7,2.907123,"\text{Not used}","int((cos(x) + 1)/sin(x),x)","\ln\left(\cos\left(x\right)-1\right)","Not used",1,"log(cos(x) - 1)","B"
804,1,6,5,2.888105,"\text{Not used}","int(-cos(x)^2*(tan(x)^2 - 1),x)","\frac{\sin\left(2\,x\right)}{2}","Not used",1,"sin(2*x)/2","B"
805,1,24,15,3.110209,"\text{Not used}","int((cos(x) + sin(x))/sin(2*x),x)","\frac{\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+\mathrm{tan}\left(\frac{x}{2}\right)\right)}{2}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)}{2}","Not used",1,"log(tan(x/2) + tan(x/2)^2)/2 - log(tan(x/2) - 1)/2","B"
806,1,11,11,0.084800,"\text{Not used}","int((cos(x)*(2*sin(x) - 3))/(sin(x)^2 - 3*sin(x) + 2),x)","\ln\left({\sin\left(x\right)}^2-3\,\sin\left(x\right)+2\right)","Not used",1,"log(sin(x)^2 - 3*sin(x) + 2)","B"
807,1,17,20,2.904672,"\text{Not used}","int((cos(x)^2*sin(x))/(cos(x)^2 + 5),x)","\sqrt{5}\,\mathrm{atan}\left(\frac{\sqrt{5}\,\cos\left(x\right)}{5}\right)-\cos\left(x\right)","Not used",1,"5^(1/2)*atan((5^(1/2)*cos(x))/5) - cos(x)","B"
808,1,9,11,2.979155,"\text{Not used}","int(cos(x)/(sin(x) + sin(x)^2),x)","-2\,\mathrm{atanh}\left(2\,\sin\left(x\right)+1\right)","Not used",1,"-2*atanh(2*sin(x) + 1)","B"
809,1,29,26,3.075236,"\text{Not used}","int(cos(x)/(sin(x) + sin(x)^(2^(1/2))),x)","\ln\left(\sin\left(x\right)\right)\,\left(\sqrt{2}+2\right)-\frac{\ln\left(\sin\left(x\right)+{\sin\left(x\right)}^{\sqrt{2}}\right)}{\sqrt{2}-1}","Not used",1,"log(sin(x))*(2^(1/2) + 2) - log(sin(x) + sin(x)^(2^(1/2)))/(2^(1/2) - 1)","B"
810,1,16,24,3.073355,"\text{Not used}","int(1/(sin(2*x) + 2*sin(x)),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{4}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8}","Not used",1,"log(tan(x/2))/4 + tan(x/2)^2/8","B"
811,1,34,40,2.900219,"\text{Not used}","int(sin(2*x)*(4*x + x^2 - 3),x)","\frac{7\,\cos\left(2\,x\right)}{4}+\sin\left(2\,x\right)-2\,x\,\cos\left(2\,x\right)+\frac{x\,\sin\left(2\,x\right)}{2}-\frac{x^2\,\cos\left(2\,x\right)}{2}","Not used",1,"(7*cos(2*x))/4 + sin(2*x) - 2*x*cos(2*x) + (x*sin(2*x))/2 - (x^2*cos(2*x))/2","B"
812,1,19,27,0.030578,"\text{Not used}","int(cos(4*x)*exp(-3*x),x)","-\frac{{\mathrm{e}}^{-3\,x}\,\left(3\,\cos\left(4\,x\right)-4\,\sin\left(4\,x\right)\right)}{25}","Not used",1,"-(exp(-3*x)*(3*cos(4*x) - 4*sin(4*x)))/25","B"
813,1,12,23,0.102045,"\text{Not used}","int((cos(x)*sin(x))/(sin(x) + 1)^(1/2),x)","\frac{2\,\sqrt{\sin\left(x\right)+1}\,\left(\sin\left(x\right)-2\right)}{3}","Not used",1,"(2*(sin(x) + 1)^(1/2)*(sin(x) - 2))/3","B"
814,1,24,30,2.998108,"\text{Not used}","int(x + 60*cos(x)^5*sin(x)^4,x)","\frac{x^2}{2}+\frac{20\,{\sin\left(x\right)}^9}{3}-\frac{120\,{\sin\left(x\right)}^7}{7}+12\,{\sin\left(x\right)}^5","Not used",1,"12*sin(x)^5 - (120*sin(x)^7)/7 + (20*sin(x)^9)/3 + x^2/2","B"
815,1,6,6,2.945106,"\text{Not used}","int(cos(x)*(tan(x) + 1/cos(x)),x)","x-\cos\left(x\right)","Not used",1,"x - cos(x)","B"
816,1,12,7,2.967292,"\text{Not used}","int(cos(x)*(tan(x) + 1/cos(x)^3),x)","\frac{\sin\left(x\right)}{\cos\left(x\right)}-\cos\left(x\right)","Not used",1,"sin(x)/cos(x) - cos(x)","B"
817,1,6,13,2.930059,"\text{Not used}","int(1/(2*sin(x)^2) - cot(x)/(2*sin(x)),x)","\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2}","Not used",1,"tan(x/2)/2","B"
818,1,14,11,2.918283,"\text{Not used}","int(sin(2*x) - 1/sin(x)^2,x)","\frac{\cos\left(x\right)}{\sin\left(x\right)}-{\cos\left(x\right)}^2","Not used",1,"cos(x)/sin(x) - cos(x)^2","B"
819,1,24,10,3.083315,"\text{Not used}","int(2*cot(2*x) - 3*sin(3*x),x)","\cos\left(3\,x\right)+\ln\left(\cos\left(\frac{x}{2}\right)\,\left(\sin\left(\frac{x}{2}\right)-2\,{\sin\left(\frac{x}{2}\right)}^3\right)\right)","Not used",1,"cos(3*x) + log(cos(x/2)*(sin(x/2) - 2*sin(x/2)^3))","B"
820,1,8,10,0.049736,"\text{Not used}","int(x*sin(2*x^2),x)","\frac{{\sin\left(x^2\right)}^2}{2}","Not used",1,"sin(x^2)^2/2","B"
821,1,12,18,2.993060,"\text{Not used}","int(cos(x - 1)*sin(x - 1)*(sin(x - 1)^2 + 1)^(1/2),x)","\frac{{\left({\sin\left(x-1\right)}^2+1\right)}^{3/2}}{3}","Not used",1,"(sin(x - 1)^2 + 1)^(3/2)/3","B"
822,1,8,10,2.918858,"\text{Not used}","int((cos(1/x)*sin(1/x))/x^2,x)","\frac{{\cos\left(\frac{1}{x}\right)}^2}{2}","Not used",1,"cos(1/x)^2/2","B"
823,1,14,16,0.078799,"\text{Not used}","int(cos((3*x)/2 + 1/2)*sin((3*x)/2 + 1/2)^3,x)","\frac{{\left(\frac{\cos\left(3\,x+1\right)}{2}-\frac{1}{2}\right)}^2}{6}","Not used",1,"(cos(3*x + 1)/2 - 1/2)^2/6","B"
824,1,9,7,0.074387,"\text{Not used}","int(4*x*tan(x^2),x)","\ln\left({\mathrm{tan}\left(x^2\right)}^2+1\right)","Not used",1,"log(tan(x^2)^2 + 1)","B"
825,1,15,13,3.526488,"\text{Not used}","int(x/cos(x^2 - 5),x)","-\mathrm{atan}\left({\mathrm{e}}^{-5{}\mathrm{i}}\,{\mathrm{e}}^{x^2\,1{}\mathrm{i}}\right)\,1{}\mathrm{i}","Not used",1,"-atan(exp(-5i)*exp(x^2*1i))*1i","B"
826,1,31,5,3.680599,"\text{Not used}","int(1/(x^2*sin(1/x)),x)","\ln\left(-{\mathrm{e}}^{1{}\mathrm{i}/x}\,2{}\mathrm{i}-2{}\mathrm{i}\right)-\ln\left(-{\mathrm{e}}^{1{}\mathrm{i}/x}\,2{}\mathrm{i}+2{}\mathrm{i}\right)","Not used",1,"log(- exp(1i/x)*2i - 2i) - log(2i - exp(1i/x)*2i)","B"
827,1,26,7,3.254306,"\text{Not used}","int(-(cos(x) + sin(x))*(1/cos(x) - 1/sin(x)),x)","\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^3-\mathrm{tan}\left(\frac{x}{2}\right)\right)-2\,\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)","Not used",1,"log(tan(x/2)^3 - tan(x/2)) - 2*log(tan(x/2)^2 + 1)","B"
828,1,4,4,3.074320,"\text{Not used}","int(cos(2*x)*sin(3*x) - cos(3*x)*sin(2*x),x)","-\cos\left(x\right)","Not used",1,"-cos(x)","B"
829,1,13,13,2.993652,"\text{Not used}","int((4*x)/cos(2*x)^2,x)","\ln\left(\cos\left(2\,x\right)\right)+2\,x\,\mathrm{tan}\left(2\,x\right)","Not used",1,"log(cos(2*x)) + 2*x*tan(2*x)","B"
830,1,18,16,2.960980,"\text{Not used}","int(4*sin(x)^2*tan(x)^2,x)","2\,\cos\left(x\right)\,\sin\left(x\right)-6\,x+\frac{4\,\sin\left(x\right)}{\cos\left(x\right)}","Not used",1,"2*cos(x)*sin(x) - 6*x + (4*sin(x))/cos(x)","B"
831,1,26,32,2.995153,"\text{Not used}","int(cos(x)^4*cot(x)^2,x)","\frac{\frac{{\cos\left(x\right)}^5}{4}+\frac{5\,{\cos\left(x\right)}^3}{8}-\frac{15\,\cos\left(x\right)}{8}}{\sin\left(x\right)}-\frac{15\,x}{8}","Not used",1,"((5*cos(x)^3)/8 - (15*cos(x))/8 + cos(x)^5/4)/sin(x) - (15*x)/8","B"
832,1,18,18,0.047463,"\text{Not used}","int(16*cos(x)^2*sin(x)^2,x)","4\,\cos\left(x\right)\,{\sin\left(x\right)}^3-2\,\cos\left(x\right)\,\sin\left(x\right)+2\,x","Not used",1,"2*x - 2*cos(x)*sin(x) + 4*cos(x)*sin(x)^3","B"
833,1,24,34,0.050067,"\text{Not used}","int(8*cos(x)^2*sin(x)^4,x)","\frac{4\,\cos\left(x\right)\,{\sin\left(x\right)}^5}{3}+\frac{x}{2}-\frac{\sin\left(2\,x\right)}{3}+\frac{\sin\left(4\,x\right)}{24}","Not used",1,"x/2 - sin(2*x)/3 + sin(4*x)/24 + (4*cos(x)*sin(x)^5)/3","B"
834,1,13,13,0.039119,"\text{Not used}","int(35*cos(x)^3*sin(x)^4,x)","7\,{\sin\left(x\right)}^5-5\,{\sin\left(x\right)}^7","Not used",1,"7*sin(x)^5 - 5*sin(x)^7","B"
835,1,33,46,0.040539,"\text{Not used}","int(4*cos(x)^4*sin(x)^4,x)","\frac{3\,x}{32}-\frac{\sin\left(2\,x\right)}{16}+\frac{\sin\left(4\,x\right)}{128}+4\,{\sin\left(x\right)}^5\,\left(\frac{{\cos\left(x\right)}^3}{8}+\frac{\cos\left(x\right)}{16}\right)","Not used",1,"(3*x)/32 - sin(2*x)/16 + sin(4*x)/128 + 4*sin(x)^5*(cos(x)/16 + cos(x)^3/8)","B"
836,1,13,9,3.008353,"\text{Not used}","int(-cos(x)/(sin(x) - sin(x)^3),x)","\frac{\ln\left({\cos\left(x\right)}^2\right)}{2}-\ln\left(\sin\left(x\right)\right)","Not used",1,"log(cos(x)^2)/2 - log(sin(x))","B"
837,1,11,14,2.969988,"\text{Not used}","int(cos(x)*sin(x) + 2*cos(x)^2 - 1,x)","-\frac{\cos\left(x\right)\,\left(\cos\left(x\right)-2\,\sin\left(x\right)\right)}{2}","Not used",1,"-(cos(x)*(cos(x) - 2*sin(x)))/2","B"
838,1,1,1,2.933664,"\text{Not used}","int(cos(x)^2 + sin(x)^2,x)","x","Not used",1,"x","B"
839,1,6,6,2.936286,"\text{Not used}","int(sin(x)^2 - cos(x)^2,x)","-\frac{\sin\left(2\,x\right)}{2}","Not used",1,"-sin(2*x)/2","B"
840,1,9,9,0.072330,"\text{Not used}","int(2^sin(x)*cos(x),x)","\frac{2^{\sin\left(x\right)}}{\ln\left(2\right)}","Not used",1,"2^sin(x)/log(2)","B"
841,1,6,8,2.945262,"\text{Not used}","int(tan(x)^3 + tan(x)^5,x)","\frac{{\mathrm{tan}\left(x\right)}^4}{4}","Not used",1,"tan(x)^4/4","B"
842,1,8,6,0.084917,"\text{Not used}","int((x*(x*tan(x) + 2))/cos(x),x)","\frac{x^2}{\cos\left(x\right)}","Not used",1,"x^2/cos(x)","B"
843,1,8,8,3.069122,"\text{Not used}","int(cot(x^(1/2))/(x^(1/2)*sin(x^(1/2))),x)","-\frac{2}{\sin\left(\sqrt{x}\right)}","Not used",1,"-2/sin(x^(1/2))","B"
844,1,8,8,3.051130,"\text{Not used}","int((cos(x^(1/2))*sin(x^(1/2)))/x^(1/2),x)","-{\cos\left(\sqrt{x}\right)}^2","Not used",1,"-cos(x^(1/2))^2","B"
845,1,8,8,3.004919,"\text{Not used}","int(tan(x^(1/2))/(x^(1/2)*cos(x^(1/2))),x)","\frac{2}{\cos\left(\sqrt{x}\right)}","Not used",1,"2/cos(x^(1/2))","B"
846,1,1108,55,4.178093,"\text{Not used}","int(sin(x)^2/(a + b*sin(2*x)),x)","\frac{\ln\left({\mathrm{tan}\left(x\right)}^2+1\right)}{4\,b}+\frac{\mathrm{atan}\left(\frac{2\,\mathrm{tan}\left(x\right)\,{\left(a^2-b^2\right)}^{3/2}\,\left(\frac{\left(4\,a^2\,b-2\,b^3\right)\,\left(2\,a\,b-\frac{\frac{8\,a\,b^3+\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}}{4\,\sqrt{a^2-b^2}}+\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{8\,\sqrt{a^2-b^2}\,\left(16\,b^4-16\,a^2\,b^2\right)}}{4\,\sqrt{a^2-b^2}}+\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(4\,a^3-16\,a\,b^2+\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(8\,a\,b^3+\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}-\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{32\,\left(a^2-b^2\right)\,\left(16\,b^4-16\,a^2\,b^2\right)}\right)}{a^3\,{\left(4\,a^2-3\,b^2\right)}^2}-\frac{\left(4\,a^4-5\,a^2\,b^2+2\,b^4\right)\,\left(\frac{4\,a^3-16\,a\,b^2+\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(8\,a\,b^3+\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}}{4\,\sqrt{a^2-b^2}}-\frac{96\,a\,b^4-64\,a^3\,b^2}{64\,{\left(a^2-b^2\right)}^{3/2}}+\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(\frac{8\,a\,b^3+\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}}{4\,\sqrt{a^2-b^2}}+\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{8\,\sqrt{a^2-b^2}\,\left(16\,b^4-16\,a^2\,b^2\right)}\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}\right)}{a^3\,\sqrt{a^2-b^2}\,{\left(4\,a^2-3\,b^2\right)}^2}\right)}{a}+\frac{2\,\left(a^2-b^2\right)\,\left(\frac{6\,a^2\,b-\frac{8\,a^2\,b^3\,{\left(8\,a^2\,b-8\,b^3\right)}^2}{{\left(16\,b^4-16\,a^2\,b^2\right)}^2}}{4\,\sqrt{a^2-b^2}}+\frac{a^2\,b^3}{2\,{\left(a^2-b^2\right)}^{3/2}}-\frac{4\,a^2\,b^3\,{\left(8\,a^2\,b-8\,b^3\right)}^2}{\sqrt{a^2-b^2}\,{\left(16\,b^4-16\,a^2\,b^2\right)}^2}\right)\,\left(4\,a^4-5\,a^2\,b^2+2\,b^4\right)}{a^4\,{\left(4\,a^2-3\,b^2\right)}^2}-\frac{2\,\left(4\,a^2\,b-2\,b^3\right)\,{\left(a^2-b^2\right)}^{3/2}\,\left(\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(6\,a^2\,b-\frac{8\,a^2\,b^3\,{\left(8\,a^2\,b-8\,b^3\right)}^2}{{\left(16\,b^4-16\,a^2\,b^2\right)}^2}\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}-a^2+\frac{3\,a^2\,b^3\,\left(8\,a^2\,b-8\,b^3\right)}{\left(a^2-b^2\right)\,\left(16\,b^4-16\,a^2\,b^2\right)}\right)}{a^4\,{\left(4\,a^2-3\,b^2\right)}^2}\right)}{2\,\sqrt{a^2-b^2}}+\frac{\ln\left(a\,{\mathrm{tan}\left(x\right)}^2+2\,b\,\mathrm{tan}\left(x\right)+a\right)\,\left(8\,a^2\,b-8\,b^3\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}","Not used",1,"log(tan(x)^2 + 1)/(4*b) + atan((2*tan(x)*(a^2 - b^2)^(3/2)*(((4*a^2*b - 2*b^3)*(2*a*b - ((8*a*b^3 + ((8*a^2*b - 8*b^3)*(96*a*b^4 - 64*a^3*b^2))/(2*(16*b^4 - 16*a^2*b^2)))/(4*(a^2 - b^2)^(1/2)) + ((8*a^2*b - 8*b^3)*(96*a*b^4 - 64*a^3*b^2))/(8*(a^2 - b^2)^(1/2)*(16*b^4 - 16*a^2*b^2)))/(4*(a^2 - b^2)^(1/2)) + ((8*a^2*b - 8*b^3)*(4*a^3 - 16*a*b^2 + ((8*a^2*b - 8*b^3)*(8*a*b^3 + ((8*a^2*b - 8*b^3)*(96*a*b^4 - 64*a^3*b^2))/(2*(16*b^4 - 16*a^2*b^2))))/(2*(16*b^4 - 16*a^2*b^2))))/(2*(16*b^4 - 16*a^2*b^2)) - ((8*a^2*b - 8*b^3)*(96*a*b^4 - 64*a^3*b^2))/(32*(a^2 - b^2)*(16*b^4 - 16*a^2*b^2))))/(a^3*(4*a^2 - 3*b^2)^2) - ((4*a^4 + 2*b^4 - 5*a^2*b^2)*((4*a^3 - 16*a*b^2 + ((8*a^2*b - 8*b^3)*(8*a*b^3 + ((8*a^2*b - 8*b^3)*(96*a*b^4 - 64*a^3*b^2))/(2*(16*b^4 - 16*a^2*b^2))))/(2*(16*b^4 - 16*a^2*b^2)))/(4*(a^2 - b^2)^(1/2)) - (96*a*b^4 - 64*a^3*b^2)/(64*(a^2 - b^2)^(3/2)) + ((8*a^2*b - 8*b^3)*((8*a*b^3 + ((8*a^2*b - 8*b^3)*(96*a*b^4 - 64*a^3*b^2))/(2*(16*b^4 - 16*a^2*b^2)))/(4*(a^2 - b^2)^(1/2)) + ((8*a^2*b - 8*b^3)*(96*a*b^4 - 64*a^3*b^2))/(8*(a^2 - b^2)^(1/2)*(16*b^4 - 16*a^2*b^2))))/(2*(16*b^4 - 16*a^2*b^2))))/(a^3*(a^2 - b^2)^(1/2)*(4*a^2 - 3*b^2)^2)))/a + (2*(a^2 - b^2)*((6*a^2*b - (8*a^2*b^3*(8*a^2*b - 8*b^3)^2)/(16*b^4 - 16*a^2*b^2)^2)/(4*(a^2 - b^2)^(1/2)) + (a^2*b^3)/(2*(a^2 - b^2)^(3/2)) - (4*a^2*b^3*(8*a^2*b - 8*b^3)^2)/((a^2 - b^2)^(1/2)*(16*b^4 - 16*a^2*b^2)^2))*(4*a^4 + 2*b^4 - 5*a^2*b^2))/(a^4*(4*a^2 - 3*b^2)^2) - (2*(4*a^2*b - 2*b^3)*(a^2 - b^2)^(3/2)*(((8*a^2*b - 8*b^3)*(6*a^2*b - (8*a^2*b^3*(8*a^2*b - 8*b^3)^2)/(16*b^4 - 16*a^2*b^2)^2))/(2*(16*b^4 - 16*a^2*b^2)) - a^2 + (3*a^2*b^3*(8*a^2*b - 8*b^3))/((a^2 - b^2)*(16*b^4 - 16*a^2*b^2))))/(a^4*(4*a^2 - 3*b^2)^2))/(2*(a^2 - b^2)^(1/2)) + (log(a + a*tan(x)^2 + 2*b*tan(x))*(8*a^2*b - 8*b^3))/(2*(16*b^4 - 16*a^2*b^2))","B"
847,1,1374,55,3.438290,"\text{Not used}","int(cos(x)^2/(a + b*sin(2*x)),x)","-\frac{\ln\left({\mathrm{tan}\left(x\right)}^2+1\right)}{4\,b}-\frac{\mathrm{atan}\left(\frac{2\,\mathrm{tan}\left(x\right)\,\left(\frac{6\,b\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{\frac{24\,a\,b^3-\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}}{4\,\sqrt{a^2-b^2}}-\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{8\,\sqrt{a^2-b^2}\,\left(16\,b^4-16\,a^2\,b^2\right)}}{4\,\sqrt{a^2-b^2}}+\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(4\,a^3-\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(24\,a\,b^3-\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}-\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{32\,\left(a^2-b^2\right)\,\left(16\,b^4-16\,a^2\,b^2\right)}\right)}{a^3\,{\left(4\,a^2-3\,b^2\right)}^2}-\frac{\left(\frac{96\,a\,b^4-64\,a^3\,b^2}{64\,{\left(a^2-b^2\right)}^{3/2}}-\frac{4\,a^3-\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(24\,a\,b^3-\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}}{4\,\sqrt{a^2-b^2}}+\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(\frac{24\,a\,b^3-\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}}{4\,\sqrt{a^2-b^2}}-\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{8\,\sqrt{a^2-b^2}\,\left(16\,b^4-16\,a^2\,b^2\right)}\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}\right)\,\left(4\,a^4-21\,a^2\,b^2+18\,b^4\right)}{a^3\,\sqrt{a^2-b^2}\,{\left(4\,a^2-3\,b^2\right)}^2}\right)\,{\left(a^2-b^2\right)}^{3/2}}{a}-\frac{2\,\left(a^2-b^2\right)\,\left(\frac{a^2\,b^3}{2\,{\left(a^2-b^2\right)}^{3/2}}-\frac{2\,a^2\,b-\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(16\,a^2\,b^2-\frac{16\,a^2\,b^3\,\left(8\,a^2\,b-8\,b^3\right)}{16\,b^4-16\,a^2\,b^2}\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}}{4\,\sqrt{a^2-b^2}}+\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(\frac{16\,a^2\,b^2-\frac{16\,a^2\,b^3\,\left(8\,a^2\,b-8\,b^3\right)}{16\,b^4-16\,a^2\,b^2}}{4\,\sqrt{a^2-b^2}}-\frac{4\,a^2\,b^3\,\left(8\,a^2\,b-8\,b^3\right)}{\sqrt{a^2-b^2}\,\left(16\,b^4-16\,a^2\,b^2\right)}\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}\right)\,\left(4\,a^4-21\,a^2\,b^2+18\,b^4\right)}{a^4\,{\left(4\,a^2-3\,b^2\right)}^2}+\frac{12\,b\,{\left(a^2-b^2\right)}^{3/2}\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{\frac{16\,a^2\,b^2-\frac{16\,a^2\,b^3\,\left(8\,a^2\,b-8\,b^3\right)}{16\,b^4-16\,a^2\,b^2}}{4\,\sqrt{a^2-b^2}}-\frac{4\,a^2\,b^3\,\left(8\,a^2\,b-8\,b^3\right)}{\sqrt{a^2-b^2}\,\left(16\,b^4-16\,a^2\,b^2\right)}}{4\,\sqrt{a^2-b^2}}+\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(2\,a^2\,b-\frac{\left(8\,a^2\,b-8\,b^3\right)\,\left(16\,a^2\,b^2-\frac{16\,a^2\,b^3\,\left(8\,a^2\,b-8\,b^3\right)}{16\,b^4-16\,a^2\,b^2}\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}-\frac{a^2\,b^3\,\left(8\,a^2\,b-8\,b^3\right)}{\left(a^2-b^2\right)\,\left(16\,b^4-16\,a^2\,b^2\right)}\right)}{a^4\,{\left(4\,a^2-3\,b^2\right)}^2}\right)}{2\,\sqrt{a^2-b^2}}-\frac{\ln\left(a\,{\mathrm{tan}\left(x\right)}^2+2\,b\,\mathrm{tan}\left(x\right)+a\right)\,\left(8\,a^2\,b-8\,b^3\right)}{2\,\left(16\,b^4-16\,a^2\,b^2\right)}","Not used",1,"- log(tan(x)^2 + 1)/(4*b) - atan((2*tan(x)*((6*b*(2*a^2 - 3*b^2)*(((24*a*b^3 - ((8*a^2*b - 8*b^3)*(96*a*b^4 - 64*a^3*b^2))/(2*(16*b^4 - 16*a^2*b^2)))/(4*(a^2 - b^2)^(1/2)) - ((8*a^2*b - 8*b^3)*(96*a*b^4 - 64*a^3*b^2))/(8*(a^2 - b^2)^(1/2)*(16*b^4 - 16*a^2*b^2)))/(4*(a^2 - b^2)^(1/2)) + ((8*a^2*b - 8*b^3)*(4*a^3 - ((8*a^2*b - 8*b^3)*(24*a*b^3 - ((8*a^2*b - 8*b^3)*(96*a*b^4 - 64*a^3*b^2))/(2*(16*b^4 - 16*a^2*b^2))))/(2*(16*b^4 - 16*a^2*b^2))))/(2*(16*b^4 - 16*a^2*b^2)) - ((8*a^2*b - 8*b^3)*(96*a*b^4 - 64*a^3*b^2))/(32*(a^2 - b^2)*(16*b^4 - 16*a^2*b^2))))/(a^3*(4*a^2 - 3*b^2)^2) - (((96*a*b^4 - 64*a^3*b^2)/(64*(a^2 - b^2)^(3/2)) - (4*a^3 - ((8*a^2*b - 8*b^3)*(24*a*b^3 - ((8*a^2*b - 8*b^3)*(96*a*b^4 - 64*a^3*b^2))/(2*(16*b^4 - 16*a^2*b^2))))/(2*(16*b^4 - 16*a^2*b^2)))/(4*(a^2 - b^2)^(1/2)) + ((8*a^2*b - 8*b^3)*((24*a*b^3 - ((8*a^2*b - 8*b^3)*(96*a*b^4 - 64*a^3*b^2))/(2*(16*b^4 - 16*a^2*b^2)))/(4*(a^2 - b^2)^(1/2)) - ((8*a^2*b - 8*b^3)*(96*a*b^4 - 64*a^3*b^2))/(8*(a^2 - b^2)^(1/2)*(16*b^4 - 16*a^2*b^2))))/(2*(16*b^4 - 16*a^2*b^2)))*(4*a^4 + 18*b^4 - 21*a^2*b^2))/(a^3*(a^2 - b^2)^(1/2)*(4*a^2 - 3*b^2)^2))*(a^2 - b^2)^(3/2))/a - (2*(a^2 - b^2)*((a^2*b^3)/(2*(a^2 - b^2)^(3/2)) - (2*a^2*b - ((8*a^2*b - 8*b^3)*(16*a^2*b^2 - (16*a^2*b^3*(8*a^2*b - 8*b^3))/(16*b^4 - 16*a^2*b^2)))/(2*(16*b^4 - 16*a^2*b^2)))/(4*(a^2 - b^2)^(1/2)) + ((8*a^2*b - 8*b^3)*((16*a^2*b^2 - (16*a^2*b^3*(8*a^2*b - 8*b^3))/(16*b^4 - 16*a^2*b^2))/(4*(a^2 - b^2)^(1/2)) - (4*a^2*b^3*(8*a^2*b - 8*b^3))/((a^2 - b^2)^(1/2)*(16*b^4 - 16*a^2*b^2))))/(2*(16*b^4 - 16*a^2*b^2)))*(4*a^4 + 18*b^4 - 21*a^2*b^2))/(a^4*(4*a^2 - 3*b^2)^2) + (12*b*(a^2 - b^2)^(3/2)*(2*a^2 - 3*b^2)*(((16*a^2*b^2 - (16*a^2*b^3*(8*a^2*b - 8*b^3))/(16*b^4 - 16*a^2*b^2))/(4*(a^2 - b^2)^(1/2)) - (4*a^2*b^3*(8*a^2*b - 8*b^3))/((a^2 - b^2)^(1/2)*(16*b^4 - 16*a^2*b^2)))/(4*(a^2 - b^2)^(1/2)) + ((8*a^2*b - 8*b^3)*(2*a^2*b - ((8*a^2*b - 8*b^3)*(16*a^2*b^2 - (16*a^2*b^3*(8*a^2*b - 8*b^3))/(16*b^4 - 16*a^2*b^2)))/(2*(16*b^4 - 16*a^2*b^2))))/(2*(16*b^4 - 16*a^2*b^2)) - (a^2*b^3*(8*a^2*b - 8*b^3))/((a^2 - b^2)*(16*b^4 - 16*a^2*b^2))))/(a^4*(4*a^2 - 3*b^2)^2))/(2*(a^2 - b^2)^(1/2)) - (log(a + a*tan(x)^2 + 2*b*tan(x))*(8*a^2*b - 8*b^3))/(2*(16*b^4 - 16*a^2*b^2))","B"
848,1,108,52,3.433552,"\text{Not used}","int(sin(x)^2/(a + b*cos(2*x)),x)","\frac{\mathrm{atan}\left(\frac{2\,b^3\,\mathrm{tan}\left(x\right)}{2\,a^2\,b-2\,b^3}-\frac{2\,a^2\,b\,\mathrm{tan}\left(x\right)}{2\,a^2\,b-2\,b^3}\right)}{2\,b}+\frac{\mathrm{atanh}\left(\frac{a\,\mathrm{tan}\left(x\right)}{\sqrt{b^2-a^2}}-\frac{b\,\mathrm{tan}\left(x\right)}{\sqrt{b^2-a^2}}\right)\,\sqrt{b^2-a^2}}{2\,\left(a\,b-b^2\right)}","Not used",1,"atan((2*b^3*tan(x))/(2*a^2*b - 2*b^3) - (2*a^2*b*tan(x))/(2*a^2*b - 2*b^3))/(2*b) + (atanh((a*tan(x))/(b^2 - a^2)^(1/2) - (b*tan(x))/(b^2 - a^2)^(1/2))*(b^2 - a^2)^(1/2))/(2*(a*b - b^2))","B"
849,1,684,52,3.319062,"\text{Not used}","int(cos(x)^2/(a + b*cos(2*x)),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)}{2\,b}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\mathrm{tan}\left(x\right)\,\left(4\,a^3-12\,a^2\,b+12\,a\,b^2-4\,b^3\right)}{4}+\frac{\sqrt{b^2-a^2}\,\left(4\,b^4-8\,a\,b^3+4\,a^2\,b^2+\frac{\mathrm{tan}\left(x\right)\,\sqrt{b^2-a^2}\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\right)}{16\,\left(b^2+a\,b\right)}\right)}{4\,\left(b^2+a\,b\right)}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}}{b^2+a\,b}+\frac{\left(\frac{\mathrm{tan}\left(x\right)\,\left(4\,a^3-12\,a^2\,b+12\,a\,b^2-4\,b^3\right)}{4}+\frac{\sqrt{b^2-a^2}\,\left(8\,a\,b^3-4\,b^4-4\,a^2\,b^2+\frac{\mathrm{tan}\left(x\right)\,\sqrt{b^2-a^2}\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\right)}{16\,\left(b^2+a\,b\right)}\right)}{4\,\left(b^2+a\,b\right)}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}}{b^2+a\,b}}{\frac{\left(\frac{\mathrm{tan}\left(x\right)\,\left(4\,a^3-12\,a^2\,b+12\,a\,b^2-4\,b^3\right)}{4}+\frac{\sqrt{b^2-a^2}\,\left(4\,b^4-8\,a\,b^3+4\,a^2\,b^2+\frac{\mathrm{tan}\left(x\right)\,\sqrt{b^2-a^2}\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\right)}{16\,\left(b^2+a\,b\right)}\right)}{4\,\left(b^2+a\,b\right)}\right)\,\sqrt{b^2-a^2}}{b^2+a\,b}-\frac{\left(\frac{\mathrm{tan}\left(x\right)\,\left(4\,a^3-12\,a^2\,b+12\,a\,b^2-4\,b^3\right)}{4}+\frac{\sqrt{b^2-a^2}\,\left(8\,a\,b^3-4\,b^4-4\,a^2\,b^2+\frac{\mathrm{tan}\left(x\right)\,\sqrt{b^2-a^2}\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\right)}{16\,\left(b^2+a\,b\right)}\right)}{4\,\left(b^2+a\,b\right)}\right)\,\sqrt{b^2-a^2}}{b^2+a\,b}}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}}{2\,\left(b^2+a\,b\right)}","Not used",1,"atan((2*a^2*tan(x))/(2*a^2 - 4*a*b + 2*b^2) + (2*b^2*tan(x))/(2*a^2 - 4*a*b + 2*b^2) - (4*a*b*tan(x))/(2*a^2 - 4*a*b + 2*b^2))/(2*b) + (atan(((((tan(x)*(12*a*b^2 - 12*a^2*b + 4*a^3 - 4*b^3))/4 + ((b^2 - a^2)^(1/2)*(4*b^4 - 8*a*b^3 + 4*a^2*b^2 + (tan(x)*(b^2 - a^2)^(1/2)*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(16*(a*b + b^2))))/(4*(a*b + b^2)))*(b^2 - a^2)^(1/2)*1i)/(a*b + b^2) + (((tan(x)*(12*a*b^2 - 12*a^2*b + 4*a^3 - 4*b^3))/4 + ((b^2 - a^2)^(1/2)*(8*a*b^3 - 4*b^4 - 4*a^2*b^2 + (tan(x)*(b^2 - a^2)^(1/2)*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(16*(a*b + b^2))))/(4*(a*b + b^2)))*(b^2 - a^2)^(1/2)*1i)/(a*b + b^2))/((((tan(x)*(12*a*b^2 - 12*a^2*b + 4*a^3 - 4*b^3))/4 + ((b^2 - a^2)^(1/2)*(4*b^4 - 8*a*b^3 + 4*a^2*b^2 + (tan(x)*(b^2 - a^2)^(1/2)*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(16*(a*b + b^2))))/(4*(a*b + b^2)))*(b^2 - a^2)^(1/2))/(a*b + b^2) - (((tan(x)*(12*a*b^2 - 12*a^2*b + 4*a^3 - 4*b^3))/4 + ((b^2 - a^2)^(1/2)*(8*a*b^3 - 4*b^4 - 4*a^2*b^2 + (tan(x)*(b^2 - a^2)^(1/2)*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(16*(a*b + b^2))))/(4*(a*b + b^2)))*(b^2 - a^2)^(1/2))/(a*b + b^2)))*(b^2 - a^2)^(1/2)*1i)/(2*(a*b + b^2))","B"
850,0,-1,30,0.000000,"\text{Not used}","int(tan(c + d*x)/(a*sin(c + d*x)^2)^(1/2),x)","\int \frac{\mathrm{tan}\left(c+d\,x\right)}{\sqrt{a\,{\sin\left(c+d\,x\right)}^2}} \,d x","Not used",1,"int(tan(c + d*x)/(a*sin(c + d*x)^2)^(1/2), x)","F"
851,0,-1,31,0.000000,"\text{Not used}","int(cot(c + d*x)/(a*cos(c + d*x)^2)^(1/2),x)","\int \frac{\mathrm{cot}\left(c+d\,x\right)}{\sqrt{a\,{\cos\left(c+d\,x\right)}^2}} \,d x","Not used",1,"int(cot(c + d*x)/(a*cos(c + d*x)^2)^(1/2), x)","F"
852,1,6,8,3.185217,"\text{Not used}","int((x*cos(x^2))/sin(x^2)^(1/2),x)","\sqrt{\sin\left(x^2\right)}","Not used",1,"sin(x^2)^(1/2)","B"
853,0,-1,19,0.000000,"\text{Not used}","int(cos(x)/(1 - cos(2*x))^(1/2),x)","\int \frac{\cos\left(x\right)}{\sqrt{1-\cos\left(2\,x\right)}} \,d x","Not used",1,"int(cos(x)/(1 - cos(2*x))^(1/2), x)","F"
854,1,12,29,3.200877,"\text{Not used}","int((cos(log(x))^2*sin(log(x))^2)/x,x)","\frac{\ln\left(x\right)}{8}-\frac{\sin\left(4\,\ln\left(x\right)\right)}{32}","Not used",1,"log(x)/8 - sin(4*log(x))/32","B"
855,1,45,29,3.308801,"\text{Not used}","int(sin(x)^3/(cos(x)^3 + sin(x)^3),x)","\frac{x}{2}-\frac{\ln\left(\frac{1}{{\cos\left(\frac{x}{2}\right)}^2}\right)}{2}+\frac{\ln\left(\frac{\sin\left(2\,x\right)-2}{{\cos\left(\frac{x}{2}\right)}^4}\right)}{3}-\frac{\ln\left(\frac{\sin\left(x+\frac{\pi }{4}\right)}{{\cos\left(\frac{x}{2}\right)}^2}\right)}{6}","Not used",1,"x/2 - log(1/cos(x/2)^2)/2 + log((sin(2*x) - 2)/cos(x/2)^4)/3 - log(sin(x + pi/4)/cos(x/2)^2)/6","B"
856,1,45,29,3.192110,"\text{Not used}","int(cos(x)^3/(cos(x)^3 + sin(x)^3),x)","\frac{x}{2}+\frac{\ln\left(\frac{1}{{\cos\left(\frac{x}{2}\right)}^2}\right)}{2}-\frac{\ln\left(\frac{\sin\left(2\,x\right)-2}{{\cos\left(\frac{x}{2}\right)}^4}\right)}{3}+\frac{\ln\left(\frac{\sin\left(x+\frac{\pi }{4}\right)}{{\cos\left(\frac{x}{2}\right)}^2}\right)}{6}","Not used",1,"x/2 + log(1/cos(x/2)^2)/2 - log((sin(2*x) - 2)/cos(x/2)^4)/3 + log(sin(x + pi/4)/cos(x/2)^2)/6","B"
857,1,32,44,0.066048,"\text{Not used}","int(1/(cos(x)*(4*sin(x) + cos(x)^2 - 5)),x)","\frac{\ln\left(\sin\left(x\right)-1\right)}{2}-\frac{\ln\left(\sin\left(x\right)+1\right)}{18}-\frac{4\,\ln\left(\sin\left(x\right)-2\right)}{9}-\frac{1}{3\,\left(\sin\left(x\right)-2\right)}","Not used",1,"log(sin(x) - 1)/2 - log(sin(x) + 1)/18 - (4*log(sin(x) - 2))/9 - 1/(3*(sin(x) - 2))","B"
858,1,15,19,3.785747,"\text{Not used}","int(1/(cos(x)^(3/2)*(3*cos(x) + sin(x))^(1/2)),x)","\frac{2\,\sqrt{3\,\cos\left(x\right)+\sin\left(x\right)}}{\sqrt{\cos\left(x\right)}}","Not used",1,"(2*(3*cos(x) + sin(x))^(1/2))/cos(x)^(1/2)","B"
859,0,-1,44,0.000000,"\text{Not used}","int((cos(x) + sin(x))^(1/2)/(cos(x)^(3/2)*sin(x)),x)","\int \frac{\sqrt{\cos\left(x\right)+\sin\left(x\right)}}{{\cos\left(x\right)}^{3/2}\,\sin\left(x\right)} \,d x","Not used",1,"int((cos(x) + sin(x))^(1/2)/(cos(x)^(3/2)*sin(x)), x)","F"
860,0,-1,19,0.000000,"\text{Not used}","int((cos(x) + sin(x))/(sin(2*x) + 1)^(1/2),x)","\int \frac{\cos\left(x\right)+\sin\left(x\right)}{\sqrt{\sin\left(2\,x\right)+1}} \,d x","Not used",1,"int((cos(x) + sin(x))/(sin(2*x) + 1)^(1/2), x)","F"
861,1,14,13,0.291919,"\text{Not used}","int((tan(x) + 1/cos(x))^(1/2)/cos(x),x)","2\,\sqrt{\frac{1}{\cos\left(x\right)}}\,\sqrt{\sin\left(x\right)+1}","Not used",1,"2*(1/cos(x))^(1/2)*(sin(x) + 1)^(1/2)","B"
862,1,29,14,3.231112,"\text{Not used}","int((tan(x)*(3/cos(x) + 4)^(1/2))/cos(x),x)","\frac{8\,\sqrt{\frac{3}{\cos\left(x\right)}+4}}{9}+\frac{2\,\sqrt{\frac{3}{\cos\left(x\right)}+4}}{3\,\cos\left(x\right)}","Not used",1,"(8*(3/cos(x) + 4)^(1/2))/9 + (2*(3/cos(x) + 4)^(1/2))/(3*cos(x))","B"
863,1,24,25,3.334386,"\text{Not used}","int((tan(x)^3*(1/cos(x) + 1)^(1/2))/cos(x),x)","-\frac{2\,{\left(\cos\left(x\right)+1\right)}^{5/2}\,\sqrt{\frac{1}{\cos\left(x\right)}}\,\left(9\,\cos\left(x\right)-5\right)}{35\,{\cos\left(x\right)}^3}","Not used",1,"-(2*(cos(x) + 1)^(5/2)*(1/cos(x))^(1/2)*(9*cos(x) - 5))/(35*cos(x)^3)","B"
864,1,24,25,3.417760,"\text{Not used}","int((cot(x)^3*(1/sin(x) + 1)^(1/2))/sin(x),x)","\frac{2\,{\left(\sin\left(x\right)+1\right)}^{5/2}\,\sqrt{\frac{1}{\sin\left(x\right)}}\,\left(9\,\sin\left(x\right)-5\right)}{35\,{\sin\left(x\right)}^3}","Not used",1,"(2*(sin(x) + 1)^(5/2)*(1/sin(x))^(1/2)*(9*sin(x) - 5))/(35*sin(x)^3)","B"
865,1,77,20,3.459887,"\text{Not used}","int(-(1/sin(x))^(1/2)*((4*tan(x))/cos(x) - x*cos(x)),x)","\frac{\left(4\,{\cos\left(x\right)}^3-4\,\cos\left(x\right)+2\,x\,{\cos\left(x\right)}^2\,\sin\left(x\right)-\sin\left(x\right)\,4{}\mathrm{i}-x\,{\cos\left(x\right)}^3\,2{}\mathrm{i}+{\cos\left(x\right)}^2\,\sin\left(x\right)\,4{}\mathrm{i}+x\,\cos\left(x\right)\,2{}\mathrm{i}\right)\,1{}\mathrm{i}}{\cos\left(x\right)\,\sin\left(x\right)\,\sqrt{\frac{1}{\sin\left(x\right)}}\,\left(-\sin\left(x\right)+\cos\left(x\right)\,1{}\mathrm{i}\right)}","Not used",1,"((4*cos(x)^3 - sin(x)*4i - x*cos(x)^3*2i - 4*cos(x) + cos(x)^2*sin(x)*4i + x*cos(x)*2i + 2*x*cos(x)^2*sin(x))*1i)/(cos(x)*sin(x)*(1/sin(x))^(1/2)*(cos(x)*1i - sin(x)))","B"
866,0,-1,76,0.000000,"\text{Not used}","int(-cot(x)*(1/sin(x)^2 - 1)^(1/2)*(sin(x)^2 - 1)^3,x)","\int -\mathrm{cot}\left(x\right)\,\sqrt{\frac{1}{{\sin\left(x\right)}^2}-1}\,{\left({\sin\left(x\right)}^2-1\right)}^3 \,d x","Not used",1,"int(-cot(x)*(1/sin(x)^2 - 1)^(1/2)*(sin(x)^2 - 1)^3, x)","F"
867,0,-1,81,0.000000,"\text{Not used}","int(-cos(x)*(1/sin(x)^2 - 1)^(1/2)*(sin(x)^2 - 1)^3,x)","-\int \cos\left(x\right)\,\sqrt{\frac{1}{{\sin\left(x\right)}^2}-1}\,{\left({\sin\left(x\right)}^2-1\right)}^3 \,d x","Not used",1,"-int(cos(x)*(1/sin(x)^2 - 1)^(1/2)*(sin(x)^2 - 1)^3, x)","F"
868,0,-1,76,0.000000,"\text{Not used}","int(x/(cos(x)*sin(x)*(a/cos(x)^2)^(1/2)),x)","\int \frac{x}{\cos\left(x\right)\,\sin\left(x\right)\,\sqrt{\frac{a}{{\cos\left(x\right)}^2}}} \,d x","Not used",1,"int(x/(cos(x)*sin(x)*(a/cos(x)^2)^(1/2)), x)","F"
869,0,-1,128,0.000000,"\text{Not used}","int(x^2/(cos(x)*sin(x)*(a/cos(x)^2)^(1/2)),x)","\int \frac{x^2}{\cos\left(x\right)\,\sin\left(x\right)\,\sqrt{\frac{a}{{\cos\left(x\right)}^2}}} \,d x","Not used",1,"int(x^2/(cos(x)*sin(x)*(a/cos(x)^2)^(1/2)), x)","F"
870,0,-1,186,0.000000,"\text{Not used}","int(x^3/(cos(x)*sin(x)*(a/cos(x)^2)^(1/2)),x)","\int \frac{x^3}{\cos\left(x\right)\,\sin\left(x\right)\,\sqrt{\frac{a}{{\cos\left(x\right)}^2}}} \,d x","Not used",1,"int(x^3/(cos(x)*sin(x)*(a/cos(x)^2)^(1/2)), x)","F"
871,0,-1,81,0.000000,"\text{Not used}","int(x/(cos(x)*sin(x)*(a/cos(x)^4)^(1/2)),x)","\int \frac{x}{\cos\left(x\right)\,\sin\left(x\right)\,\sqrt{\frac{a}{{\cos\left(x\right)}^4}}} \,d x","Not used",1,"int(x/(cos(x)*sin(x)*(a/cos(x)^4)^(1/2)), x)","F"
872,0,-1,109,0.000000,"\text{Not used}","int(x^2/(cos(x)*sin(x)*(a/cos(x)^4)^(1/2)),x)","\int \frac{x^2}{\cos\left(x\right)\,\sin\left(x\right)\,\sqrt{\frac{a}{{\cos\left(x\right)}^4}}} \,d x","Not used",1,"int(x^2/(cos(x)*sin(x)*(a/cos(x)^4)^(1/2)), x)","F"
873,0,-1,143,0.000000,"\text{Not used}","int(x^3/(cos(x)*sin(x)*(a/cos(x)^4)^(1/2)),x)","\int \frac{x^3}{\cos\left(x\right)\,\sin\left(x\right)\,\sqrt{\frac{a}{{\cos\left(x\right)}^4}}} \,d x","Not used",1,"int(x^3/(cos(x)*sin(x)*(a/cos(x)^4)^(1/2)), x)","F"
874,0,-1,105,0.000000,"\text{Not used}","int((x*(a/cos(x)^2)^(1/2))/(cos(x)*sin(x)),x)","\int \frac{x\,\sqrt{\frac{a}{{\cos\left(x\right)}^2}}}{\cos\left(x\right)\,\sin\left(x\right)} \,d x","Not used",1,"int((x*(a/cos(x)^2)^(1/2))/(cos(x)*sin(x)), x)","F"
875,0,-1,225,0.000000,"\text{Not used}","int((x^2*(a/cos(x)^2)^(1/2))/(cos(x)*sin(x)),x)","\int \frac{x^2\,\sqrt{\frac{a}{{\cos\left(x\right)}^2}}}{\cos\left(x\right)\,\sin\left(x\right)} \,d x","Not used",1,"int((x^2*(a/cos(x)^2)^(1/2))/(cos(x)*sin(x)), x)","F"
876,0,-1,341,0.000000,"\text{Not used}","int((x^3*(a/cos(x)^2)^(1/2))/(cos(x)*sin(x)),x)","\int \frac{x^3\,\sqrt{\frac{a}{{\cos\left(x\right)}^2}}}{\cos\left(x\right)\,\sin\left(x\right)} \,d x","Not used",1,"int((x^3*(a/cos(x)^2)^(1/2))/(cos(x)*sin(x)), x)","F"
877,0,-1,142,0.000000,"\text{Not used}","int((x*(a/cos(x)^4)^(1/2))/(cos(x)*sin(x)),x)","\int \frac{x\,\sqrt{\frac{a}{{\cos\left(x\right)}^4}}}{\cos\left(x\right)\,\sin\left(x\right)} \,d x","Not used",1,"int((x*(a/cos(x)^4)^(1/2))/(cos(x)*sin(x)), x)","F"
878,0,-1,220,0.000000,"\text{Not used}","int((x^2*(a/cos(x)^4)^(1/2))/(cos(x)*sin(x)),x)","\int \frac{x^2\,\sqrt{\frac{a}{{\cos\left(x\right)}^4}}}{\cos\left(x\right)\,\sin\left(x\right)} \,d x","Not used",1,"int((x^2*(a/cos(x)^4)^(1/2))/(cos(x)*sin(x)), x)","F"
879,0,-1,356,0.000000,"\text{Not used}","int((x^3*(a/cos(x)^4)^(1/2))/(cos(x)*sin(x)),x)","\int \frac{x^3\,\sqrt{\frac{a}{{\cos\left(x\right)}^4}}}{\cos\left(x\right)\,\sin\left(x\right)} \,d x","Not used",1,"int((x^3*(a/cos(x)^4)^(1/2))/(cos(x)*sin(x)), x)","F"
880,1,14,25,2.936474,"\text{Not used}","int(sin(2*x)*sin(3*x)*sin(x),x)","-\frac{{\sin\left(x\right)}^4\,\left(8\,{\sin\left(x\right)}^2-9\right)}{6}","Not used",1,"-(sin(x)^4*(8*sin(x)^2 - 9))/6","B"
881,1,22,30,3.037037,"\text{Not used}","int(cos(2*x)*cos(3*x)*cos(x),x)","\frac{x}{4}+\frac{\sin\left(2\,x\right)}{8}+\frac{\sin\left(4\,x\right)}{16}+\frac{\sin\left(6\,x\right)}{24}","Not used",1,"x/4 + sin(2*x)/8 + sin(4*x)/16 + sin(6*x)/24","B"
882,1,22,30,3.008059,"\text{Not used}","int(sin(2*x)*sin(3*x)*cos(x),x)","\frac{x}{4}+\frac{\sin\left(2\,x\right)}{8}-\frac{\sin\left(4\,x\right)}{16}-\frac{\sin\left(6\,x\right)}{24}","Not used",1,"x/4 + sin(2*x)/8 - sin(4*x)/16 - sin(6*x)/24","B"
883,1,19,25,3.178012,"\text{Not used}","int(cos(2*x)*cos(3*x)*sin(x),x)","\frac{4\,{\sin\left(x\right)}^6}{3}-\frac{3\,{\sin\left(x\right)}^4}{2}+\frac{{\sin\left(x\right)}^2}{2}","Not used",1,"sin(x)^2/2 - (3*sin(x)^4)/2 + (4*sin(x)^6)/3","B"
884,1,6,8,0.046211,"\text{Not used}","int(x*sin(x^2),x)","-\frac{\cos\left(x^2\right)}{2}","Not used",1,"-cos(x^2)/2","B"
885,1,20,11,3.189930,"\text{Not used}","int(-(cos(x) + sin(x))^5*(cos(x) - sin(x)),x)","-\frac{\sin\left(2\,x\right)\,\left({\sin\left(2\,x\right)}^2+3\,\sin\left(2\,x\right)+3\right)}{6}","Not used",1,"-(sin(2*x)*(3*sin(2*x) + sin(2*x)^2 + 3))/6","B"
886,1,16,11,3.088679,"\text{Not used}","int((2*x*tan(x))/cos(x)^2,x)","\frac{2\,x-\sin\left(2\,x\right)}{2\,{\cos\left(x\right)}^2}","Not used",1,"(2*x - sin(2*x))/(2*cos(x)^2)","B"
887,1,8,12,2.927546,"\text{Not used}","int((cos(x)^2 + 1)/(cos(2*x) + 1),x)","\frac{x}{2}+\frac{\mathrm{tan}\left(x\right)}{2}","Not used",1,"x/2 + tan(x)/2","B"
888,1,19,12,0.086889,"\text{Not used}","int(sin(x)/(cos(x)^3 - cos(x)^5),x)","\frac{\ln\left({\sin\left(x\right)}^2\right)}{2}-\ln\left(\cos\left(x\right)\right)+\frac{1}{2\,{\cos\left(x\right)}^2}","Not used",1,"log(sin(x)^2)/2 - log(cos(x)) + 1/(2*cos(x)^2)","B"
889,1,19,19,3.672251,"\text{Not used}","int((tan(x)*(11/cos(x)^5 - 5)^2)/cos(x),x)","\frac{25\,{\cos\left(x\right)}^{10}-\frac{55\,{\cos\left(x\right)}^5}{3}+11}{{\cos\left(x\right)}^{11}}","Not used",1,"(25*cos(x)^10 - (55*cos(x)^5)/3 + 11)/cos(x)^11","B"
890,1,69,44,3.112329,"\text{Not used}","int(sin(5*x)^3*tan(5*x)^3,x)","\frac{5\,{\mathrm{tan}\left(\frac{5\,x}{2}\right)}^9+\frac{20\,{\mathrm{tan}\left(\frac{5\,x}{2}\right)}^7}{3}-\frac{22\,{\mathrm{tan}\left(\frac{5\,x}{2}\right)}^5}{3}+\frac{20\,{\mathrm{tan}\left(\frac{5\,x}{2}\right)}^3}{3}+5\,\mathrm{tan}\left(\frac{5\,x}{2}\right)}{5\,{\left({\mathrm{tan}\left(\frac{5\,x}{2}\right)}^2-1\right)}^2\,{\left({\mathrm{tan}\left(\frac{5\,x}{2}\right)}^2+1\right)}^3}-\mathrm{atanh}\left(\mathrm{tan}\left(\frac{5\,x}{2}\right)\right)","Not used",1,"(5*tan((5*x)/2) + (20*tan((5*x)/2)^3)/3 - (22*tan((5*x)/2)^5)/3 + (20*tan((5*x)/2)^7)/3 + 5*tan((5*x)/2)^9)/(5*(tan((5*x)/2)^2 - 1)^2*(tan((5*x)/2)^2 + 1)^3) - atanh(tan((5*x)/2))","B"
891,1,30,37,3.099000,"\text{Not used}","int(sin(5*x)^3*tan(5*x)^4,x)","\frac{{\left(\cos\left(5\,x\right)+1\right)}^4\,\left({\cos\left(5\,x\right)}^2-4\,\cos\left(5\,x\right)+1\right)}{15\,{\cos\left(5\,x\right)}^3}","Not used",1,"((cos(5*x) + 1)^4*(cos(5*x)^2 - 4*cos(5*x) + 1))/(15*cos(5*x)^3)","B"
892,1,85,54,7.213535,"\text{Not used}","int(sin(6*x)^5*tan(6*x)^3,x)","\frac{7\,{\mathrm{tan}\left(3\,x\right)}^{13}+\frac{70\,{\mathrm{tan}\left(3\,x\right)}^{11}}{3}+\frac{77\,{\mathrm{tan}\left(3\,x\right)}^9}{5}-\frac{412\,{\mathrm{tan}\left(3\,x\right)}^7}{15}+\frac{77\,{\mathrm{tan}\left(3\,x\right)}^5}{5}+\frac{70\,{\mathrm{tan}\left(3\,x\right)}^3}{3}+7\,\mathrm{tan}\left(3\,x\right)}{6\,{\left({\mathrm{tan}\left(3\,x\right)}^2-1\right)}^2\,{\left({\mathrm{tan}\left(3\,x\right)}^2+1\right)}^5}-\frac{7\,\mathrm{atanh}\left(\mathrm{tan}\left(3\,x\right)\right)}{6}","Not used",1,"(7*tan(3*x) + (70*tan(3*x)^3)/3 + (77*tan(3*x)^5)/5 - (412*tan(3*x)^7)/15 + (77*tan(3*x)^9)/5 + (70*tan(3*x)^11)/3 + 7*tan(3*x)^13)/(6*(tan(3*x)^2 - 1)^2*(tan(3*x)^2 + 1)^5) - (7*atanh(tan(3*x)))/6","B"
893,1,33,37,2.944034,"\text{Not used}","int(sin(2*x)*(1/cos(2*x)^2 - 1)^3,x)","\frac{\cos\left(2\,x\right)}{2}+\frac{3\,{\cos\left(2\,x\right)}^4-{\cos\left(2\,x\right)}^2+\frac{1}{5}}{2\,{\cos\left(2\,x\right)}^5}","Not used",1,"cos(2*x)/2 + (3*cos(2*x)^4 - cos(2*x)^2 + 1/5)/(2*cos(2*x)^5)","B"
894,1,69,34,3.037695,"\text{Not used}","int(sin(x)*tan(x)^5,x)","\frac{15\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{4}-\frac{\frac{15\,{\mathrm{tan}\left(\frac{x}{2}\right)}^9}{4}-10\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7+\frac{9\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{2}-10\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+\frac{15\,\mathrm{tan}\left(\frac{x}{2}\right)}{4}}{{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2-1\right)}^4\,\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}","Not used",1,"(15*atanh(tan(x/2)))/4 - ((15*tan(x/2))/4 - 10*tan(x/2)^3 + (9*tan(x/2)^5)/2 - 10*tan(x/2)^7 + (15*tan(x/2)^9)/4)/((tan(x/2)^2 - 1)^4*(tan(x/2)^2 + 1))","B"
895,1,42,43,3.056398,"\text{Not used}","int(cos(2*x)^5*cot(2*x)^4,x)","\frac{3\,{\sin\left(2\,x\right)}^8-20\,{\sin\left(2\,x\right)}^6+90\,{\sin\left(2\,x\right)}^4+60\,{\sin\left(2\,x\right)}^2-5}{30\,{\sin\left(2\,x\right)}^3}","Not used",1,"(60*sin(2*x)^2 + 90*sin(2*x)^4 - 20*sin(2*x)^6 + 3*sin(2*x)^8 - 5)/(30*sin(2*x)^3)","B"
896,1,74,87,2.970320,"\text{Not used}","int(-cos(3*x)*(1/sin(3*x)^2 - 1)^3*(sin(3*x)^2 - 1)^5,x)","-\frac{-45\,{\sin\left(3\,x\right)}^{16}+440\,{\sin\left(3\,x\right)}^{14}-1980\,{\sin\left(3\,x\right)}^{12}+5544\,{\sin\left(3\,x\right)}^{10}-11550\,{\sin\left(3\,x\right)}^8+27720\,{\sin\left(3\,x\right)}^6+13860\,{\sin\left(3\,x\right)}^4-1320\,{\sin\left(3\,x\right)}^2+99}{1485\,{\sin\left(3\,x\right)}^5}","Not used",1,"-(13860*sin(3*x)^4 - 1320*sin(3*x)^2 + 27720*sin(3*x)^6 - 11550*sin(3*x)^8 + 5544*sin(3*x)^10 - 1980*sin(3*x)^12 + 440*sin(3*x)^14 - 45*sin(3*x)^16 + 99)/(1485*sin(3*x)^5)","B"
897,1,71,42,3.160709,"\text{Not used}","int(cot(2*x)*(1/sin(2*x)^2 - 1)^2*(sin(2*x)^2 - 1)^2,x)","3\,\ln\left(\mathrm{tan}\left(2\,x\right)\right)-\frac{3\,\ln\left({\mathrm{tan}\left(2\,x\right)}^2+1\right)}{2}+\frac{3\,{\mathrm{tan}\left(2\,x\right)}^6+\frac{9\,{\mathrm{tan}\left(2\,x\right)}^4}{2}+{\mathrm{tan}\left(2\,x\right)}^2-\frac{1}{4}}{2\,\left({\mathrm{tan}\left(2\,x\right)}^8+2\,{\mathrm{tan}\left(2\,x\right)}^6+{\mathrm{tan}\left(2\,x\right)}^4\right)}","Not used",1,"3*log(tan(2*x)) - (3*log(tan(2*x)^2 + 1))/2 + (tan(2*x)^2 + (9*tan(2*x)^4)/2 + 3*tan(2*x)^6 - 1/4)/(2*(tan(2*x)^4 + 2*tan(2*x)^6 + tan(2*x)^8))","B"
898,1,57,63,2.966807,"\text{Not used}","int(cos(2*x)*(1/sin(2*x)^2 - 1)^4*(sin(2*x)^2 - 1)^2,x)","\frac{\frac{{\sin\left(2\,x\right)}^{12}}{10}-{\sin\left(2\,x\right)}^{10}+\frac{15\,{\sin\left(2\,x\right)}^8}{2}+10\,{\sin\left(2\,x\right)}^6-\frac{5\,{\sin\left(2\,x\right)}^4}{2}+\frac{3\,{\sin\left(2\,x\right)}^2}{5}-\frac{1}{14}}{{\sin\left(2\,x\right)}^7}","Not used",1,"((3*sin(2*x)^2)/5 - (5*sin(2*x)^4)/2 + 10*sin(2*x)^6 + (15*sin(2*x)^8)/2 - sin(2*x)^10 + sin(2*x)^12/10 - 1/14)/sin(2*x)^7","B"
899,1,84,60,4.673845,"\text{Not used}","int(cot(3*x)*(1/sin(3*x)^2 - 1)^3*(sin(3*x)^2 - 1)^2,x)","\frac{\ln\left({\left({\mathrm{tan}\left(3\,x\right)}^2+1\right)}^5\right)}{3}-\frac{10\,\ln\left(\mathrm{tan}\left(3\,x\right)\right)}{3}-\frac{5\,{\mathrm{tan}\left(3\,x\right)}^8+\frac{15\,{\mathrm{tan}\left(3\,x\right)}^6}{2}+\frac{5\,{\mathrm{tan}\left(3\,x\right)}^4}{3}-\frac{5\,{\mathrm{tan}\left(3\,x\right)}^2}{12}+\frac{1}{6}}{3\,\left({\mathrm{tan}\left(3\,x\right)}^{10}+2\,{\mathrm{tan}\left(3\,x\right)}^8+{\mathrm{tan}\left(3\,x\right)}^6\right)}","Not used",1,"log((tan(3*x)^2 + 1)^5)/3 - (10*log(tan(3*x)))/3 - ((5*tan(3*x)^4)/3 - (5*tan(3*x)^2)/12 + (15*tan(3*x)^6)/2 + 5*tan(3*x)^8 + 1/6)/(3*(tan(3*x)^6 + 2*tan(3*x)^8 + tan(3*x)^10))","B"
900,1,42,47,5.377532,"\text{Not used}","int((tan(9*x)^2 + 1)^3*(cot(9*x)^2 + 1)^2,x)","\frac{3\,{\mathrm{tan}\left(9\,x\right)}^8+20\,{\mathrm{tan}\left(9\,x\right)}^6+90\,{\mathrm{tan}\left(9\,x\right)}^4-60\,{\mathrm{tan}\left(9\,x\right)}^2-5}{135\,{\mathrm{tan}\left(9\,x\right)}^3}","Not used",1,"(90*tan(9*x)^4 - 60*tan(9*x)^2 + 20*tan(9*x)^6 + 3*tan(9*x)^8 - 5)/(135*tan(9*x)^3)","B"
901,1,37,43,0.076599,"\text{Not used}","int(-(cos(x)*(7*sin(x)^3 - 9)^2)/(sin(x)^2 - 1),x)","128\,\ln\left(\sin\left(x\right)+1\right)-2\,\ln\left(\sin\left(x\right)-1\right)-49\,\sin\left(x\right)+63\,{\sin\left(x\right)}^2-\frac{49\,{\sin\left(x\right)}^3}{3}-\frac{49\,{\sin\left(x\right)}^5}{5}","Not used",1,"128*log(sin(x) + 1) - 2*log(sin(x) - 1) - 49*sin(x) + 63*sin(x)^2 - (49*sin(x)^3)/3 - (49*sin(x)^5)/5","B"
902,1,71,42,3.050591,"\text{Not used}","int(cos(2*x)^4*cot(2*x)^5,x)","3\,\ln\left(\mathrm{tan}\left(2\,x\right)\right)-\frac{3\,\ln\left({\mathrm{tan}\left(2\,x\right)}^2+1\right)}{2}+\frac{3\,{\mathrm{tan}\left(2\,x\right)}^6+\frac{9\,{\mathrm{tan}\left(2\,x\right)}^4}{2}+{\mathrm{tan}\left(2\,x\right)}^2-\frac{1}{4}}{2\,\left({\mathrm{tan}\left(2\,x\right)}^8+2\,{\mathrm{tan}\left(2\,x\right)}^6+{\mathrm{tan}\left(2\,x\right)}^4\right)}","Not used",1,"3*log(tan(2*x)) - (3*log(tan(2*x)^2 + 1))/2 + (tan(2*x)^2 + (9*tan(2*x)^4)/2 + 3*tan(2*x)^6 - 1/4)/(2*(tan(2*x)^4 + 2*tan(2*x)^6 + tan(2*x)^8))","B"
903,1,41,74,3.136968,"\text{Not used}","int(tan(x)^2/(cos(x)*(3/cos(x) + 4)),x)","\frac{2\,\sqrt{7}\,\mathrm{atanh}\left(\frac{\sqrt{7}\,\mathrm{tan}\left(\frac{x}{2}\right)}{7}\right)}{9}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)}{3\,\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2-1\right)}-\frac{8\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{9}","Not used",1,"(2*7^(1/2)*atanh((7^(1/2)*tan(x/2))/7))/9 - (2*tan(x/2))/(3*(tan(x/2)^2 - 1)) - (8*atanh(tan(x/2)))/9","B"
904,1,34,14,3.172559,"\text{Not used}","int((x*tan(x + 1))/cos(x + 1),x)","\frac{2\,x\,\cos\left(x+1\right)}{\cos\left(2\,x+2\right)+1}+\mathrm{atan}\left(\cos\left(x+1\right)+\sin\left(x+1\right)\,1{}\mathrm{i}\right)\,2{}\mathrm{i}","Not used",1,"atan(cos(x + 1) + sin(x + 1)*1i)*2i + (2*x*cos(x + 1))/(cos(2*x + 2) + 1)","B"
905,1,10,14,0.165629,"\text{Not used}","int(sin(2*x)/(9 - sin(x)^2)^(1/2),x)","-2\,\sqrt{{\cos\left(x\right)}^2+8}","Not used",1,"-2*(cos(x)^2 + 8)^(1/2)","B"
906,1,18,11,3.141666,"\text{Not used}","int(sin(2*x)/(9 - cos(x)^4)^(1/2),x)","-\mathrm{atan}\left(\frac{{\cos\left(x\right)}^2}{\sqrt{9-{\cos\left(x\right)}^4}}\right)","Not used",1,"-atan(cos(x)^2/(9 - cos(x)^4)^(1/2))","B"
907,1,33,34,2.997865,"\text{Not used}","int(cos(1/x)/x^5,x)","6\,\cos\left(\frac{1}{x}\right)-\frac{\sin\left(\frac{1}{x}\right)+3\,x\,\cos\left(\frac{1}{x}\right)-6\,x^2\,\sin\left(\frac{1}{x}\right)}{x^3}","Not used",1,"6*cos(1/x) - (sin(1/x) + 3*x*cos(1/x) - 6*x^2*sin(1/x))/x^3","B"
908,1,18,21,0.068586,"\text{Not used}","int(cos(x + 1)^3*sin(x + 1)^3,x)","-\frac{{\sin\left(x+1\right)}^4\,\left(2\,{\sin\left(x+1\right)}^2-3\right)}{12}","Not used",1,"-(sin(x + 1)^4*(2*sin(x + 1)^2 - 3))/12","B"
909,1,69,99,3.062997,"\text{Not used}","int(sin(2*x + 1)^2*(2*x + 1)^3,x)","\frac{3\,\sin\left(4\,x+2\right)\,\left(2\,x+1\right)}{16}-\frac{3\,{\sin\left(2\,x+1\right)}^2}{16}+\frac{{\left(2\,x+1\right)}^4}{16}-\frac{\sin\left(4\,x+2\right)\,{\left(2\,x+1\right)}^3}{8}+\frac{3\,{\left(2\,x+1\right)}^2\,\left(2\,{\sin\left(2\,x+1\right)}^2-1\right)}{16}","Not used",1,"(3*sin(4*x + 2)*(2*x + 1))/16 - (3*sin(2*x + 1)^2)/16 + (2*x + 1)^4/16 - (sin(4*x + 2)*(2*x + 1)^3)/8 + (3*(2*x + 1)^2*(2*sin(2*x + 1)^2 - 1))/16","B"
910,1,64,37,3.127943,"\text{Not used}","int(-(1/cos(x) - 1)/(tan(x) - 1),x)","\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+\sqrt{2}+1\right)\,\left(\frac{\sqrt{2}}{2}+\frac{1}{2}\right)-\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\sqrt{2}+1\right)\,\left(\frac{\sqrt{2}}{2}-\frac{1}{2}\right)+\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)+\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)\,\left(-\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)","Not used",1,"log(tan(x/2) + 2^(1/2) + 1)*(2^(1/2)/2 + 1/2) - log(tan(x/2) + 1i)*(1/2 + 1i/2) - log(tan(x/2) - 2^(1/2) + 1)*(2^(1/2)/2 - 1/2) - log(tan(x/2) - 1i)*(1/2 - 1i/2)","B"
911,1,45,57,3.047650,"\text{Not used}","int(x^2*cos(3*x)*cos(5*x),x)","\frac{x\,\cos\left(2\,x\right)}{4}-\frac{\sin\left(8\,x\right)}{512}-\frac{\sin\left(2\,x\right)}{8}+\frac{x\,\cos\left(8\,x\right)}{64}+\frac{x^2\,\sin\left(2\,x\right)}{4}+\frac{x^2\,\sin\left(8\,x\right)}{16}","Not used",1,"(x*cos(2*x))/4 - sin(8*x)/512 - sin(2*x)/8 + (x*cos(8*x))/64 + (x^2*sin(2*x))/4 + (x^2*sin(8*x))/16","B"
912,1,51,57,4.618881,"\text{Not used}","int((cos(x) + sin(x))/(cos(x)^(1/2)*sin(x)^(1/2)),x)","-\frac{2\,\sqrt{\cos\left(x\right)}\,{\sin\left(x\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{4},\frac{1}{4};\ \frac{5}{4};\ {\cos\left(x\right)}^2\right)}{{\left({\sin\left(x\right)}^2\right)}^{3/4}}-\frac{2\,{\cos\left(x\right)}^{3/2}\,\sqrt{\sin\left(x\right)}\,{{}}_2{\mathrm{F}}_1\left(\frac{3}{4},\frac{3}{4};\ \frac{7}{4};\ {\cos\left(x\right)}^2\right)}{3\,{\left({\sin\left(x\right)}^2\right)}^{1/4}}","Not used",1,"- (2*cos(x)^(1/2)*sin(x)^(3/2)*hypergeom([1/4, 1/4], 5/4, cos(x)^2))/(sin(x)^2)^(3/4) - (2*cos(x)^(3/2)*sin(x)^(1/2)*hypergeom([3/4, 3/4], 7/4, cos(x)^2))/(3*(sin(x)^2)^(1/4))","B"
913,1,10,5,2.965900,"\text{Not used}","int((sin(x) + 1)/cos(x)^2,x)","-\frac{2}{\mathrm{tan}\left(\frac{x}{2}\right)-1}","Not used",1,"-2/(tan(x/2) - 1)","B"
914,1,11,11,3.157759,"\text{Not used}","int(10*x^9*cos(x^5*log(x)) - x^10*sin(x^5*log(x))*(5*x^4*log(x) + x^4),x)","x^{10}\,\cos\left(x^5\,\ln\left(x\right)\right)","Not used",1,"x^10*cos(x^5*log(x))","B"
915,1,38,27,0.481821,"\text{Not used}","int(cos(x/2)^2*tan(Pi/4 + x/2),x)","-2\,\ln\left({\mathrm{e}}^{\frac{\Pi \,1{}\mathrm{i}}{2}}\,{\mathrm{e}}^{x\,1{}\mathrm{i}}+1\right)\,{\sin\left(\frac{\Pi }{4}\right)}^2+x\,{\mathrm{e}}^{\frac{\Pi \,1{}\mathrm{i}}{4}}\,\sin\left(\frac{\Pi }{4}\right)-\frac{\cos\left(x\right)}{2}","Not used",1,"x*sin(Pi/4)*exp((Pi*1i)/4) - 2*sin(Pi/4)^2*log(exp((Pi*1i)/2)*exp(x*1i) + 1) - cos(x)/2","B"
916,1,65,65,3.029112,"\text{Not used}","int(sin(x)^3*(3*x + 2)^2,x)","10\,\cos\left(x\right)+\frac{28\,\sin\left(x\right)}{3}-9\,x^2\,\cos\left(x\right)+4\,x\,{\cos\left(x\right)}^3+\frac{2\,{\cos\left(x\right)}^3}{3}+3\,x^2\,{\cos\left(x\right)}^3-\frac{4\,{\cos\left(x\right)}^2\,\sin\left(x\right)}{3}-12\,x\,\cos\left(x\right)+14\,x\,\sin\left(x\right)-2\,x\,{\cos\left(x\right)}^2\,\sin\left(x\right)","Not used",1,"10*cos(x) + (28*sin(x))/3 - 9*x^2*cos(x) + 4*x*cos(x)^3 + (2*cos(x)^3)/3 + 3*x^2*cos(x)^3 - (4*cos(x)^2*sin(x))/3 - 12*x*cos(x) + 14*x*sin(x) - 2*x*cos(x)^2*sin(x)","B"
917,1,10,8,0.144861,"\text{Not used}","int(sin(x)*(1/cos(x))^(m + 1),x)","\frac{{\left(\frac{1}{\cos\left(x\right)}\right)}^m}{m}","Not used",1,"(1/cos(x))^m/m","B"
918,1,45,32,3.430378,"\text{Not used}","int(cos(a + b*x)^n/sin(a + b*x)^(n + 2),x)","-\frac{{\cos\left(a+b\,x\right)}^n\,\sin\left(2\,a+2\,b\,x\right)}{2\,b\,{\sin\left(a+b\,x\right)}^n\,{\sin\left(a+b\,x\right)}^2\,\left(n+1\right)}","Not used",1,"-(cos(a + b*x)^n*sin(2*a + 2*b*x))/(2*b*sin(a + b*x)^n*sin(a + b*x)^2*(n + 1))","B"
919,1,26,3,3.189722,"\text{Not used}","int(1/(sin(x)*tan(x) + 1/cos(x)),x)","\mathrm{atan}\left(\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{2}+\frac{5\,\mathrm{tan}\left(\frac{x}{2}\right)}{2}\right)-\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2}\right)","Not used",1,"atan((5*tan(x/2))/2 + tan(x/2)^3/2) - atan(tan(x/2)/2)","B"
920,1,34,35,0.060970,"\text{Not used}","int(sin(x)*(a + b*x + c*x^2),x)","b\,\sin\left(x\right)-\cos\left(x\right)\,\left(a-2\,c\right)-b\,x\,\cos\left(x\right)+2\,c\,x\,\sin\left(x\right)-c\,x^2\,\cos\left(x\right)","Not used",1,"b*sin(x) - cos(x)*(a - 2*c) - b*x*cos(x) + 2*c*x*sin(x) - c*x^2*cos(x)","B"
921,0,-1,8,0.000000,"\text{Not used}","int(sin(x^5)/x,x)","\frac{\mathrm{sinint}\left(x^5\right)}{5}","Not used",1,"sinint(x^5)/5","F"
922,0,-1,37,0.000000,"\text{Not used}","int(sin(2^x)/(2^x + 1),x)","\int \frac{\sin\left(2^x\right)}{2^x+1} \,d x","Not used",1,"int(sin(2^x)/(2^x + 1), x)","F"
923,1,41,14,3.142583,"\text{Not used}","int(x*cos(2*x^2)*sin(2*x^2)^(3/4),x)","-\frac{{\cos\left(2\,x^2\right)}^2\,{\sin\left(2\,x^2\right)}^{7/4}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{8},1;\ 2;\ {\cos\left(2\,x^2\right)}^2\right)}{8\,{\left({\sin\left(2\,x^2\right)}^2\right)}^{7/8}}","Not used",1,"-(cos(2*x^2)^2*sin(2*x^2)^(7/4)*hypergeom([1/8, 1], 2, cos(2*x^2)^2))/(8*(sin(2*x^2)^2)^(7/8))","B"
924,1,19,10,3.094322,"\text{Not used}","int((x*tan(x^2)^2)/cos(x^2)^2,x)","\frac{\mathrm{tan}\left(x^2\right)}{6\,{\cos\left(x^2\right)}^2}-\frac{\mathrm{tan}\left(x^2\right)}{6}","Not used",1,"tan(x^2)/(6*cos(x^2)^2) - tan(x^2)/6","B"
925,1,56,17,3.260548,"\text{Not used}","int(x^2*cos(a + b*x^3)^7*sin(a + b*x^3),x)","-\frac{56\,\cos\left(2\,b\,x^3+2\,a\right)+28\,\cos\left(4\,b\,x^3+4\,a\right)+8\,\cos\left(6\,b\,x^3+6\,a\right)+\cos\left(8\,b\,x^3+8\,a\right)}{3072\,b}","Not used",1,"-(56*cos(2*a + 2*b*x^3) + 28*cos(4*a + 4*b*x^3) + 8*cos(6*a + 6*b*x^3) + cos(8*a + 8*b*x^3))/(3072*b)","B"
926,1,147,129,3.454843,"\text{Not used}","int(x^5*cos(a + b*x^3)^7*sin(a + b*x^3),x)","\frac{168\,\sin\left(2\,b\,x^3+2\,a\right)+42\,\sin\left(4\,b\,x^3+4\,a\right)+8\,\sin\left(6\,b\,x^3+6\,a\right)+\frac{3\,\sin\left(8\,b\,x^3+8\,a\right)}{4}+336\,b\,x^3\,\left(2\,{\sin\left(b\,x^3+a\right)}^2-1\right)+168\,b\,x^3\,\left(2\,{\sin\left(2\,b\,x^3+2\,a\right)}^2-1\right)+48\,b\,x^3\,\left(2\,{\sin\left(3\,b\,x^3+3\,a\right)}^2-1\right)+6\,b\,x^3\,\left(2\,{\sin\left(4\,b\,x^3+4\,a\right)}^2-1\right)}{18432\,b^2}","Not used",1,"(168*sin(2*a + 2*b*x^3) + 42*sin(4*a + 4*b*x^3) + 8*sin(6*a + 6*b*x^3) + (3*sin(8*a + 8*b*x^3))/4 + 336*b*x^3*(2*sin(a + b*x^3)^2 - 1) + 168*b*x^3*(2*sin(2*a + 2*b*x^3)^2 - 1) + 48*b*x^3*(2*sin(3*a + 3*b*x^3)^2 - 1) + 6*b*x^3*(2*sin(4*a + 4*b*x^3)^2 - 1))/(18432*b^2)","B"
927,1,730,110,13.421051,"\text{Not used}","int((x^5*tan(a + b*x^3))/cos(a + b*x^3)^7,x)","-\frac{\frac{8\,{\mathrm{e}}^{1{}\mathrm{i}\,b\,x^3+a\,1{}\mathrm{i}}\,\left(15\,b\,x^3-8{}\mathrm{i}\right)}{315\,b^2}-\frac{8\,{\mathrm{e}}^{3{}\mathrm{i}\,b\,x^3+a\,3{}\mathrm{i}}\,\left(35\,b\,x^3-12{}\mathrm{i}\right)}{315\,b^2}}{5\,{\mathrm{e}}^{2{}\mathrm{i}\,b\,x^3+a\,2{}\mathrm{i}}+10\,{\mathrm{e}}^{4{}\mathrm{i}\,b\,x^3+a\,4{}\mathrm{i}}+10\,{\mathrm{e}}^{6{}\mathrm{i}\,b\,x^3+a\,6{}\mathrm{i}}+5\,{\mathrm{e}}^{8{}\mathrm{i}\,b\,x^3+a\,8{}\mathrm{i}}+{\mathrm{e}}^{10{}\mathrm{i}\,b\,x^3+a\,10{}\mathrm{i}}+1}+\frac{5\,\ln\left(x^2\,\left({\mathrm{e}}^{1{}\mathrm{i}\,b\,x^3+a\,1{}\mathrm{i}}-\mathrm{i}\right)\right)}{336\,b^2}-\frac{5\,\ln\left(x^2\,\left({\mathrm{e}}^{1{}\mathrm{i}\,b\,x^3+a\,1{}\mathrm{i}}+1{}\mathrm{i}\right)\right)}{336\,b^2}-\frac{\frac{16\,{\mathrm{e}}^{3{}\mathrm{i}\,b\,x^3+a\,3{}\mathrm{i}}\,\left(5\,b\,x^3-\mathrm{i}\right)}{63\,b^2}-\frac{16\,{\mathrm{e}}^{5{}\mathrm{i}\,b\,x^3+a\,5{}\mathrm{i}}\,\left(7\,b\,x^3-\mathrm{i}\right)}{63\,b^2}}{6\,{\mathrm{e}}^{2{}\mathrm{i}\,b\,x^3+a\,2{}\mathrm{i}}+15\,{\mathrm{e}}^{4{}\mathrm{i}\,b\,x^3+a\,4{}\mathrm{i}}+20\,{\mathrm{e}}^{6{}\mathrm{i}\,b\,x^3+a\,6{}\mathrm{i}}+15\,{\mathrm{e}}^{8{}\mathrm{i}\,b\,x^3+a\,8{}\mathrm{i}}+6\,{\mathrm{e}}^{10{}\mathrm{i}\,b\,x^3+a\,10{}\mathrm{i}}+{\mathrm{e}}^{12{}\mathrm{i}\,b\,x^3+a\,12{}\mathrm{i}}+1}-\frac{\frac{64\,x^3\,{\mathrm{e}}^{5{}\mathrm{i}\,b\,x^3+a\,5{}\mathrm{i}}}{21\,b}-\frac{64\,x^3\,{\mathrm{e}}^{7{}\mathrm{i}\,b\,x^3+a\,7{}\mathrm{i}}}{21\,b}}{7\,{\mathrm{e}}^{2{}\mathrm{i}\,b\,x^3+a\,2{}\mathrm{i}}+21\,{\mathrm{e}}^{4{}\mathrm{i}\,b\,x^3+a\,4{}\mathrm{i}}+35\,{\mathrm{e}}^{6{}\mathrm{i}\,b\,x^3+a\,6{}\mathrm{i}}+35\,{\mathrm{e}}^{8{}\mathrm{i}\,b\,x^3+a\,8{}\mathrm{i}}+21\,{\mathrm{e}}^{10{}\mathrm{i}\,b\,x^3+a\,10{}\mathrm{i}}+7\,{\mathrm{e}}^{12{}\mathrm{i}\,b\,x^3+a\,12{}\mathrm{i}}+{\mathrm{e}}^{14{}\mathrm{i}\,b\,x^3+a\,14{}\mathrm{i}}+1}+\frac{{\mathrm{e}}^{1{}\mathrm{i}\,b\,x^3+a\,1{}\mathrm{i}}\,1{}\mathrm{i}}{63\,b^2\,\left(3\,{\mathrm{e}}^{2{}\mathrm{i}\,b\,x^3+a\,2{}\mathrm{i}}+3\,{\mathrm{e}}^{4{}\mathrm{i}\,b\,x^3+a\,4{}\mathrm{i}}+{\mathrm{e}}^{6{}\mathrm{i}\,b\,x^3+a\,6{}\mathrm{i}}+1\right)}+\frac{{\mathrm{e}}^{1{}\mathrm{i}\,b\,x^3+a\,1{}\mathrm{i}}\,5{}\mathrm{i}}{168\,b^2\,\left({\mathrm{e}}^{2{}\mathrm{i}\,b\,x^3+a\,2{}\mathrm{i}}+1\right)}+\frac{{\mathrm{e}}^{1{}\mathrm{i}\,b\,x^3+a\,1{}\mathrm{i}}\,5{}\mathrm{i}}{252\,b^2\,\left(2\,{\mathrm{e}}^{2{}\mathrm{i}\,b\,x^3+a\,2{}\mathrm{i}}+{\mathrm{e}}^{4{}\mathrm{i}\,b\,x^3+a\,4{}\mathrm{i}}+1\right)}+\frac{2\,{\mathrm{e}}^{1{}\mathrm{i}\,b\,x^3+a\,1{}\mathrm{i}}\,\left(60\,b\,x^3-47{}\mathrm{i}\right)}{315\,b^2\,\left(4\,{\mathrm{e}}^{2{}\mathrm{i}\,b\,x^3+a\,2{}\mathrm{i}}+6\,{\mathrm{e}}^{4{}\mathrm{i}\,b\,x^3+a\,4{}\mathrm{i}}+4\,{\mathrm{e}}^{6{}\mathrm{i}\,b\,x^3+a\,6{}\mathrm{i}}+{\mathrm{e}}^{8{}\mathrm{i}\,b\,x^3+a\,8{}\mathrm{i}}+1\right)}","Not used",1,"(5*log(x^2*(exp(a*1i + b*x^3*1i) - 1i)))/(336*b^2) - ((8*exp(a*1i + b*x^3*1i)*(15*b*x^3 - 8i))/(315*b^2) - (8*exp(a*3i + b*x^3*3i)*(35*b*x^3 - 12i))/(315*b^2))/(5*exp(a*2i + b*x^3*2i) + 10*exp(a*4i + b*x^3*4i) + 10*exp(a*6i + b*x^3*6i) + 5*exp(a*8i + b*x^3*8i) + exp(a*10i + b*x^3*10i) + 1) - (5*log(x^2*(exp(a*1i + b*x^3*1i) + 1i)))/(336*b^2) - ((16*exp(a*3i + b*x^3*3i)*(5*b*x^3 - 1i))/(63*b^2) - (16*exp(a*5i + b*x^3*5i)*(7*b*x^3 - 1i))/(63*b^2))/(6*exp(a*2i + b*x^3*2i) + 15*exp(a*4i + b*x^3*4i) + 20*exp(a*6i + b*x^3*6i) + 15*exp(a*8i + b*x^3*8i) + 6*exp(a*10i + b*x^3*10i) + exp(a*12i + b*x^3*12i) + 1) - ((64*x^3*exp(a*5i + b*x^3*5i))/(21*b) - (64*x^3*exp(a*7i + b*x^3*7i))/(21*b))/(7*exp(a*2i + b*x^3*2i) + 21*exp(a*4i + b*x^3*4i) + 35*exp(a*6i + b*x^3*6i) + 35*exp(a*8i + b*x^3*8i) + 21*exp(a*10i + b*x^3*10i) + 7*exp(a*12i + b*x^3*12i) + exp(a*14i + b*x^3*14i) + 1) + (exp(a*1i + b*x^3*1i)*1i)/(63*b^2*(3*exp(a*2i + b*x^3*2i) + 3*exp(a*4i + b*x^3*4i) + exp(a*6i + b*x^3*6i) + 1)) + (exp(a*1i + b*x^3*1i)*5i)/(168*b^2*(exp(a*2i + b*x^3*2i) + 1)) + (exp(a*1i + b*x^3*1i)*5i)/(252*b^2*(2*exp(a*2i + b*x^3*2i) + exp(a*4i + b*x^3*4i) + 1)) + (2*exp(a*1i + b*x^3*1i)*(60*b*x^3 - 47i))/(315*b^2*(4*exp(a*2i + b*x^3*2i) + 6*exp(a*4i + b*x^3*4i) + 4*exp(a*6i + b*x^3*6i) + exp(a*8i + b*x^3*8i) + 1))","B"
928,1,14,6,3.028431,"\text{Not used}","int(1/(x^2*cos(1/x)^2),x)","-\frac{2{}\mathrm{i}}{{\mathrm{e}}^{\frac{2{}\mathrm{i}}{x}}+1}","Not used",1,"-2i/(exp(2i/x) + 1)","B"
929,1,4,4,2.951683,"\text{Not used}","int(3*x^2*cos(x^3),x)","\sin\left(x^3\right)","Not used",1,"sin(x^3)","B"
930,1,23,27,0.095420,"\text{Not used}","int((2*x + 1)/cos(2*x + 1)^2,x)","\frac{\ln\left(\cos\left(2\,x+1\right)\right)}{2}+\frac{\mathrm{tan}\left(2\,x+1\right)\,\left(2\,x+1\right)}{2}","Not used",1,"log(cos(2*x + 1))/2 + (tan(2*x + 1)*(2*x + 1))/2","B"
931,1,22,26,3.474591,"\text{Not used}","int(x^4/(b*(3*sin(a + b*x) + x^3)^(1/2)) + (x^2*cos(a + b*x))/(3*sin(a + b*x) + x^3)^(1/2) + (4*x*(3*sin(a + b*x) + x^3)^(1/2))/(3*b),x)","\frac{2\,x^2\,\sqrt{3\,\sin\left(a+b\,x\right)+x^3}}{3\,b}","Not used",1,"(2*x^2*(3*sin(a + b*x) + x^3)^(1/2))/(3*b)","B"
932,0,-1,29,0.000000,"\text{Not used}","int((x^2*cos(a + b*x))/(3*sin(a + b*x) + x^3)^(1/2),x)","\int \frac{x^2\,\cos\left(a+b\,x\right)}{\sqrt{3\,\sin\left(a+b\,x\right)+x^3}} \,d x","Not used",0,"int((x^2*cos(a + b*x))/(3*sin(a + b*x) + x^3)^(1/2), x)","F"
933,1,10,9,2.954803,"\text{Not used}","int((cos(x) + sin(x))/(exp(-x) + sin(x)),x)","x+\ln\left({\mathrm{e}}^{-x}+\sin\left(x\right)\right)","Not used",1,"x + log(exp(-x) + sin(x))","B"
934,1,111,77,6.559231,"\text{Not used}","int(sin(c + d*x)*(a*sin(c + d*x)^2 + b*sin(c + d*x)^3),x)","\frac{3\,b\,x}{8}-\frac{-\frac{3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}-\frac{11\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{11\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{4\,a}{3}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(3*b*x)/8 - ((4*a)/3 + (3*b*tan(c/2 + (d*x)/2))/4 + (16*a*tan(c/2 + (d*x)/2)^2)/3 + 4*a*tan(c/2 + (d*x)/2)^4 + (11*b*tan(c/2 + (d*x)/2)^3)/4 - (11*b*tan(c/2 + (d*x)/2)^5)/4 - (3*b*tan(c/2 + (d*x)/2)^7)/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
935,1,210,161,6.744406,"\text{Not used}","int(sin(c + d*x)*(a*sin(c + d*x)^2 + b*sin(c + d*x)^3)^2,x)","\frac{5\,a\,b\,x}{8}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{80\,a^2}{3}+32\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{112\,a^2}{15}+\frac{32\,b^2}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{112\,a^2}{5}+\frac{96\,b^2}{5}\right)+\frac{32\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+\frac{16\,a^2}{15}+\frac{32\,b^2}{35}+\frac{25\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{283\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}-\frac{283\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{12}-\frac{25\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{3}-\frac{5\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{4}+\frac{5\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^7}","Not used",1,"(5*a*b*x)/8 - (tan(c/2 + (d*x)/2)^6*((80*a^2)/3 + 32*b^2) + tan(c/2 + (d*x)/2)^2*((112*a^2)/15 + (32*b^2)/5) + tan(c/2 + (d*x)/2)^4*((112*a^2)/5 + (96*b^2)/5) + (32*a^2*tan(c/2 + (d*x)/2)^8)/3 + (16*a^2)/15 + (32*b^2)/35 + (25*a*b*tan(c/2 + (d*x)/2)^3)/3 + (283*a*b*tan(c/2 + (d*x)/2)^5)/12 - (283*a*b*tan(c/2 + (d*x)/2)^9)/12 - (25*a*b*tan(c/2 + (d*x)/2)^11)/3 - (5*a*b*tan(c/2 + (d*x)/2)^13)/4 + (5*a*b*tan(c/2 + (d*x)/2))/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
936,1,73,89,3.182789,"\text{Not used}","int(sin(c + d*x)*(a*sin(c + d*x) + b*sin(c + d*x)^2 + c*sin(c + d*x)^3),x)","\frac{2\,b\,\cos\left(3\,c+3\,d\,x\right)-18\,b\,\cos\left(c+d\,x\right)-6\,a\,\sin\left(2\,c+2\,d\,x\right)-6\,c\,\sin\left(2\,c+2\,d\,x\right)+\frac{3\,c\,\sin\left(4\,c+4\,d\,x\right)}{4}+12\,a\,d\,x+9\,c\,d\,x}{24\,d}","Not used",1,"(2*b*cos(3*c + 3*d*x) - 18*b*cos(c + d*x) - 6*a*sin(2*c + 2*d*x) - 6*c*sin(2*c + 2*d*x) + (3*c*sin(4*c + 4*d*x))/4 + 12*a*d*x + 9*c*d*x)/(24*d)","B"
937,1,456,288,4.516920,"\text{Not used}","int(sin(c + d*x)*(a*sin(c + d*x) + b*sin(c + d*x)^2 + c*sin(c + d*x)^3)^2,x)","\frac{b\,\mathrm{atan}\left(\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a+5\,c\right)}{4\,\left(\frac{3\,a\,b}{2}+\frac{5\,b\,c}{4}\right)}\right)\,\left(6\,a+5\,c\right)}{4\,d}-\frac{b\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(6\,a+5\,c\right)}{4\,d}-\frac{\frac{32\,a\,c}{15}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{3\,a\,b}{2}+\frac{5\,b\,c}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(10\,a\,b+\frac{25\,b\,c}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(10\,a\,b+\frac{25\,b\,c}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{31\,a\,b}{2}+\frac{283\,b\,c}{12}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{31\,a\,b}{2}+\frac{283\,b\,c}{12}\right)+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{52\,a^2}{3}+\frac{64\,c\,a}{3}+\frac{32\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{88\,a^2}{3}+\frac{160\,a\,c}{3}+\frac{80\,b^2}{3}+32\,c^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{28\,a^2}{3}+\frac{224\,a\,c}{15}+\frac{112\,b^2}{15}+\frac{32\,c^2}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(24\,a^2+\frac{224\,a\,c}{5}+\frac{112\,b^2}{5}+\frac{96\,c^2}{5}\right)+\frac{4\,a^2}{3}+\frac{16\,b^2}{15}+\frac{32\,c^2}{35}+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,a\,b}{2}+\frac{5\,b\,c}{4}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(b*atan((b*tan(c/2 + (d*x)/2)*(6*a + 5*c))/(4*((3*a*b)/2 + (5*b*c)/4)))*(6*a + 5*c))/(4*d) - (b*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(6*a + 5*c))/(4*d) - ((32*a*c)/15 - tan(c/2 + (d*x)/2)^13*((3*a*b)/2 + (5*b*c)/4) + tan(c/2 + (d*x)/2)^3*(10*a*b + (25*b*c)/3) - tan(c/2 + (d*x)/2)^11*(10*a*b + (25*b*c)/3) + tan(c/2 + (d*x)/2)^5*((31*a*b)/2 + (283*b*c)/12) - tan(c/2 + (d*x)/2)^9*((31*a*b)/2 + (283*b*c)/12) + 4*a^2*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^8*((64*a*c)/3 + (52*a^2)/3 + (32*b^2)/3) + tan(c/2 + (d*x)/2)^6*((160*a*c)/3 + (88*a^2)/3 + (80*b^2)/3 + 32*c^2) + tan(c/2 + (d*x)/2)^2*((224*a*c)/15 + (28*a^2)/3 + (112*b^2)/15 + (32*c^2)/5) + tan(c/2 + (d*x)/2)^4*((224*a*c)/5 + 24*a^2 + (112*b^2)/5 + (96*c^2)/5) + (4*a^2)/3 + (16*b^2)/15 + (32*c^2)/35 + tan(c/2 + (d*x)/2)*((3*a*b)/2 + (5*b*c)/4))/(d*(7*tan(c/2 + (d*x)/2)^2 + 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 + 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 + 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 + 1))","B"
938,1,51,61,3.246654,"\text{Not used}","int(sin(c + d*x)*(a + c*sin(c + d*x) + b/sin(c + d*x)^(1/2)),x)","\frac{c\,x}{2}-\frac{c\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}-\frac{a\,\cos\left(c+d\,x\right)}{d}+\frac{2\,b\,\mathrm{E}\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\middle|2\right)}{d}","Not used",1,"(c*x)/2 - (c*sin(2*c + 2*d*x))/(4*d) - (a*cos(c + d*x))/d + (2*b*ellipticE(c/2 - pi/4 + (d*x)/2, 2))/d","B"
939,1,129,148,6.684454,"\text{Not used}","int(sin(c + d*x)*(a + c*sin(c + d*x) + b/sin(c + d*x)^(1/2))^2,x)","b^2\,x-\frac{a^2\,\cos\left(c+d\,x\right)}{d}-\frac{a\,c\,\left(\sin\left(2\,c+2\,d\,x\right)-2\,d\,x\right)}{2\,d}+\frac{4\,a\,b\,\mathrm{E}\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{c^2\,\cos\left(c+d\,x\right)\,\left({\cos\left(c+d\,x\right)}^2-3\right)}{3\,d}-\frac{2\,b\,c\,\cos\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^{5/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{2};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\left({\sin\left(c+d\,x\right)}^2\right)}^{5/4}}","Not used",1,"b^2*x - (a^2*cos(c + d*x))/d - (a*c*(sin(2*c + 2*d*x) - 2*d*x))/(2*d) + (4*a*b*ellipticE(c/2 - pi/4 + (d*x)/2, 2))/d + (c^2*cos(c + d*x)*(cos(c + d*x)^2 - 3))/(3*d) - (2*b*c*cos(c + d*x)*sin(c + d*x)^(5/2)*hypergeom([-1/4, 1/2], 3/2, cos(c + d*x)^2))/(d*(sin(c + d*x)^2)^(5/4))","B"
940,1,35,34,3.455537,"\text{Not used}","int(f^(a + b*x)*(cos(c + d*x) + sin(c + d*x)*1i)^n,x)","-\frac{f^{a+b\,x}\,{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\right)}^n\,1{}\mathrm{i}}{d\,n-b\,\ln\left(f\right)\,1{}\mathrm{i}}","Not used",1,"-(f^(a + b*x)*exp(c*1i + d*x*1i)^n*1i)/(d*n - b*log(f)*1i)","B"
941,1,35,36,3.350930,"\text{Not used}","int(f^(a + b*x)*(cos(c + d*x) - sin(c + d*x)*1i)^n,x)","-\frac{f^{a+b\,x}\,{\left({\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}\right)}^n}{-b\,\ln\left(f\right)+d\,n\,1{}\mathrm{i}}","Not used",1,"-(f^(a + b*x)*exp(- c*1i - d*x*1i)^n)/(d*n*1i - b*log(f))","B"
942,1,226,120,4.215978,"\text{Not used}","int((cos(a + b*x)^5 - sin(a + b*x)^5)/(cos(a + b*x)^5 + sin(a + b*x)^5),x)","\frac{\ln\left({\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^2-2\,\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)-1\right)}{5\,b}-\frac{\ln\left({\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^2+1\right)}{b}+\frac{\ln\left(2\,{\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^2-\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)+{\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^3+{\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^4+\sqrt{5}\,\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)-\sqrt{5}\,{\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^3+1\right)\,\left(\sqrt{5}+1\right)}{5\,b}-\frac{\ln\left(2\,{\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^2-\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)+{\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^3+{\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^4-\sqrt{5}\,\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)+\sqrt{5}\,{\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^3+1\right)\,\left(\sqrt{5}-1\right)}{5\,b}","Not used",1,"log(tan(a/2 + (b*x)/2)^2 - 2*tan(a/2 + (b*x)/2) - 1)/(5*b) - log(tan(a/2 + (b*x)/2)^2 + 1)/b + (log(2*tan(a/2 + (b*x)/2)^2 - tan(a/2 + (b*x)/2) + tan(a/2 + (b*x)/2)^3 + tan(a/2 + (b*x)/2)^4 + 5^(1/2)*tan(a/2 + (b*x)/2) - 5^(1/2)*tan(a/2 + (b*x)/2)^3 + 1)*(5^(1/2) + 1))/(5*b) - (log(2*tan(a/2 + (b*x)/2)^2 - tan(a/2 + (b*x)/2) + tan(a/2 + (b*x)/2)^3 + tan(a/2 + (b*x)/2)^4 - 5^(1/2)*tan(a/2 + (b*x)/2) + 5^(1/2)*tan(a/2 + (b*x)/2)^3 + 1)*(5^(1/2) - 1))/(5*b)","B"
943,1,23,72,3.166456,"\text{Not used}","int((cos(a + b*x)^4 - sin(a + b*x)^4)/(cos(a + b*x)^4 + sin(a + b*x)^4),x)","\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{\sqrt{2}\,\sin\left(2\,a+2\,b\,x\right)}{2}\right)}{2\,b}","Not used",1,"(2^(1/2)*atanh((2^(1/2)*sin(2*a + 2*b*x))/2))/(2*b)","B"
944,1,105,55,3.304541,"\text{Not used}","int((cos(a + b*x)^3 - sin(a + b*x)^3)/(cos(a + b*x)^3 + sin(a + b*x)^3),x)","\frac{\ln\left({\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^2+1\right)}{b}+\frac{\ln\left({\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^2-2\,\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)-1\right)}{3\,b}-\frac{2\,\ln\left({\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^3+2\,{\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^2-2\,\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)+1\right)}{3\,b}","Not used",1,"log(tan(a/2 + (b*x)/2)^2 + 1)/b + log(tan(a/2 + (b*x)/2)^2 - 2*tan(a/2 + (b*x)/2) - 1)/(3*b) - (2*log(2*tan(a/2 + (b*x)/2)^2 - 2*tan(a/2 + (b*x)/2) + 2*tan(a/2 + (b*x)/2)^3 + tan(a/2 + (b*x)/2)^4 + 1))/(3*b)","B"
945,1,14,16,3.033523,"\text{Not used}","int((cos(a + b*x)^2 - sin(a + b*x)^2)/(cos(a + b*x)^2 + sin(a + b*x)^2),x)","\frac{\sin\left(2\,a+2\,b\,x\right)}{2\,b}","Not used",1,"sin(2*a + 2*b*x)/(2*b)","B"
946,1,50,18,3.135922,"\text{Not used}","int((cos(a + b*x) - sin(a + b*x))/(cos(a + b*x) + sin(a + b*x)),x)","\frac{2\,\mathrm{atanh}\left(\frac{128\,\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)+128}{16\,{\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^2+32\,\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)+48}-3\right)}{b}","Not used",1,"(2*atanh((128*tan(a/2 + (b*x)/2) + 128)/(32*tan(a/2 + (b*x)/2) + 16*tan(a/2 + (b*x)/2)^2 + 48) - 3))/b","B"
947,1,50,19,3.370962,"\text{Not used}","int((1/cos(a + b*x) - 1/sin(a + b*x))/(1/cos(a + b*x) + 1/sin(a + b*x)),x)","-\frac{2\,\mathrm{atanh}\left(\frac{128\,\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)+128}{16\,{\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^2+32\,\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)+48}-3\right)}{b}","Not used",1,"-(2*atanh((128*tan(a/2 + (b*x)/2) + 128)/(32*tan(a/2 + (b*x)/2) + 16*tan(a/2 + (b*x)/2)^2 + 48) - 3))/b","B"
948,1,14,17,3.054194,"\text{Not used}","int((1/cos(a + b*x)^2 - 1/sin(a + b*x)^2)/(1/cos(a + b*x)^2 + 1/sin(a + b*x)^2),x)","-\frac{\sin\left(2\,a+2\,b\,x\right)}{2\,b}","Not used",1,"-sin(2*a + 2*b*x)/(2*b)","B"
949,1,106,54,3.233456,"\text{Not used}","int((1/cos(a + b*x)^3 - 1/sin(a + b*x)^3)/(1/cos(a + b*x)^3 + 1/sin(a + b*x)^3),x)","\frac{2\,\ln\left({\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^3+2\,{\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^2-2\,\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)+1\right)}{3\,b}-\frac{\ln\left({\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^2-2\,\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)-1\right)}{3\,b}-\frac{\ln\left({\mathrm{tan}\left(\frac{a}{2}+\frac{b\,x}{2}\right)}^2+1\right)}{b}","Not used",1,"(2*log(2*tan(a/2 + (b*x)/2)^2 - 2*tan(a/2 + (b*x)/2) + 2*tan(a/2 + (b*x)/2)^3 + tan(a/2 + (b*x)/2)^4 + 1))/(3*b) - log(tan(a/2 + (b*x)/2)^2 - 2*tan(a/2 + (b*x)/2) - 1)/(3*b) - log(tan(a/2 + (b*x)/2)^2 + 1)/b","B"
950,1,23,72,3.088618,"\text{Not used}","int((1/cos(a + b*x)^4 - 1/sin(a + b*x)^4)/(1/cos(a + b*x)^4 + 1/sin(a + b*x)^4),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{\sqrt{2}\,\sin\left(2\,a+2\,b\,x\right)}{2}\right)}{2\,b}","Not used",1,"-(2^(1/2)*atanh((2^(1/2)*sin(2*a + 2*b*x))/2))/(2*b)","B"