1,0,0,124,0.744000," ","int(x^5*(a+b*sec(d*x^2+c)),x)","\int x^{5} \left(a +b \sec \left(d \,x^{2}+c \right)\right)\, dx"," ",0,"int(x^5*(a+b*sec(d*x^2+c)),x)","F"
2,0,0,23,0.742000," ","int(x^4*(a+b*sec(d*x^2+c)),x)","\int x^{4} \left(a +b \sec \left(d \,x^{2}+c \right)\right)\, dx"," ",0,"int(x^4*(a+b*sec(d*x^2+c)),x)","F"
3,0,0,75,0.742000," ","int(x^3*(a+b*sec(d*x^2+c)),x)","\int x^{3} \left(a +b \sec \left(d \,x^{2}+c \right)\right)\, dx"," ",0,"int(x^3*(a+b*sec(d*x^2+c)),x)","F"
4,0,0,23,0.752000," ","int(x^2*(a+b*sec(d*x^2+c)),x)","\int x^{2} \left(a +b \sec \left(d \,x^{2}+c \right)\right)\, dx"," ",0,"int(x^2*(a+b*sec(d*x^2+c)),x)","F"
5,1,39,22,0.201000," ","int(x*(a+b*sec(d*x^2+c)),x)","\frac{a \,x^{2}}{2}+\frac{b \ln \left(\sec \left(d \,x^{2}+c \right)+\tan \left(d \,x^{2}+c \right)\right)}{2 d}+\frac{c a}{2 d}"," ",0,"1/2*a*x^2+1/2/d*b*ln(sec(d*x^2+c)+tan(d*x^2+c))+1/2/d*c*a","A"
6,0,0,21,0.758000," ","int((a+b*sec(d*x^2+c))/x,x)","\int \frac{a +b \sec \left(d \,x^{2}+c \right)}{x}\, dx"," ",0,"int((a+b*sec(d*x^2+c))/x,x)","F"
7,0,0,23,0.704000," ","int((a+b*sec(d*x^2+c))/x^2,x)","\int \frac{a +b \sec \left(d \,x^{2}+c \right)}{x^{2}}\, dx"," ",0,"int((a+b*sec(d*x^2+c))/x^2,x)","F"
8,0,0,211,1.100000," ","int(x^5*(a+b*sec(d*x^2+c))^2,x)","\int x^{5} \left(a +b \sec \left(d \,x^{2}+c \right)\right)^{2}\, dx"," ",0,"int(x^5*(a+b*sec(d*x^2+c))^2,x)","F"
9,0,0,20,1.134000," ","int(x^4*(a+b*sec(d*x^2+c))^2,x)","\int x^{4} \left(a +b \sec \left(d \,x^{2}+c \right)\right)^{2}\, dx"," ",0,"int(x^4*(a+b*sec(d*x^2+c))^2,x)","F"
10,0,0,116,1.288000," ","int(x^3*(a+b*sec(d*x^2+c))^2,x)","\int x^{3} \left(a +b \sec \left(d \,x^{2}+c \right)\right)^{2}\, dx"," ",0,"int(x^3*(a+b*sec(d*x^2+c))^2,x)","F"
11,0,0,20,0.979000," ","int(x^2*(a+b*sec(d*x^2+c))^2,x)","\int x^{2} \left(a +b \sec \left(d \,x^{2}+c \right)\right)^{2}\, dx"," ",0,"int(x^2*(a+b*sec(d*x^2+c))^2,x)","F"
12,1,59,40,0.524000," ","int(x*(a+b*sec(d*x^2+c))^2,x)","\frac{a^{2} x^{2}}{2}+\frac{b^{2} \tan \left(d \,x^{2}+c \right)}{2 d}+\frac{a b \ln \left(\sec \left(d \,x^{2}+c \right)+\tan \left(d \,x^{2}+c \right)\right)}{d}+\frac{a^{2} c}{2 d}"," ",0,"1/2*a^2*x^2+1/2*b^2*tan(d*x^2+c)/d+1/d*a*b*ln(sec(d*x^2+c)+tan(d*x^2+c))+1/2/d*a^2*c","A"
13,0,0,20,1.155000," ","int((a+b*sec(d*x^2+c))^2/x,x)","\int \frac{\left(a +b \sec \left(d \,x^{2}+c \right)\right)^{2}}{x}\, dx"," ",0,"int((a+b*sec(d*x^2+c))^2/x,x)","F"
14,0,0,20,1.122000," ","int((a+b*sec(d*x^2+c))^2/x^2,x)","\int \frac{\left(a +b \sec \left(d \,x^{2}+c \right)\right)^{2}}{x^{2}}\, dx"," ",0,"int((a+b*sec(d*x^2+c))^2/x^2,x)","F"
15,1,92,82,0.553000," ","int(x*sec(b*x^2+a)^7,x)","\frac{\left(\sec^{5}\left(b \,x^{2}+a \right)\right) \tan \left(b \,x^{2}+a \right)}{12 b}+\frac{5 \left(\sec^{3}\left(b \,x^{2}+a \right)\right) \tan \left(b \,x^{2}+a \right)}{48 b}+\frac{5 \sec \left(b \,x^{2}+a \right) \tan \left(b \,x^{2}+a \right)}{32 b}+\frac{5 \ln \left(\sec \left(b \,x^{2}+a \right)+\tan \left(b \,x^{2}+a \right)\right)}{32 b}"," ",0,"1/12*sec(b*x^2+a)^5*tan(b*x^2+a)/b+5/48*sec(b*x^2+a)^3*tan(b*x^2+a)/b+5/32*sec(b*x^2+a)*tan(b*x^2+a)/b+5/32/b*ln(sec(b*x^2+a)+tan(b*x^2+a))","A"
16,0,0,336,0.846000," ","int(x^5/(a+b*sec(d*x^2+c)),x)","\int \frac{x^{5}}{a +b \sec \left(d \,x^{2}+c \right)}\, dx"," ",0,"int(x^5/(a+b*sec(d*x^2+c)),x)","F"
17,0,0,20,0.798000," ","int(x^4/(a+b*sec(d*x^2+c)),x)","\int \frac{x^{4}}{a +b \sec \left(d \,x^{2}+c \right)}\, dx"," ",0,"int(x^4/(a+b*sec(d*x^2+c)),x)","F"
18,0,0,225,0.825000," ","int(x^3/(a+b*sec(d*x^2+c)),x)","\int \frac{x^{3}}{a +b \sec \left(d \,x^{2}+c \right)}\, dx"," ",0,"int(x^3/(a+b*sec(d*x^2+c)),x)","F"
19,0,0,20,0.831000," ","int(x^2/(a+b*sec(d*x^2+c)),x)","\int \frac{x^{2}}{a +b \sec \left(d \,x^{2}+c \right)}\, dx"," ",0,"int(x^2/(a+b*sec(d*x^2+c)),x)","F"
20,1,70,55,0.543000," ","int(x/(a+b*sec(d*x^2+c)),x)","-\frac{b \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{d \,x^{2}}{2}+\frac{c}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d a \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{\arctan \left(\tan \left(\frac{d \,x^{2}}{2}+\frac{c}{2}\right)\right)}{d a}"," ",0,"-1/d/a*b/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*d*x^2+1/2*c)/((a-b)*(a+b))^(1/2))+1/d/a*arctan(tan(1/2*d*x^2+1/2*c))","A"
21,0,0,20,0.701000," ","int(1/x/(a+b*sec(d*x^2+c)),x)","\int \frac{1}{x \left(a +b \sec \left(d \,x^{2}+c \right)\right)}\, dx"," ",0,"int(1/x/(a+b*sec(d*x^2+c)),x)","F"
22,0,0,23,0.030000," ","int((a+b*sec(d*x^2+c))/x^2,x)","\int \frac{a +b \sec \left(d \,x^{2}+c \right)}{x^{2}}\, dx"," ",0,"int((a+b*sec(d*x^2+c))/x^2,x)","F"
23,0,0,979,1.673000," ","int(x^5/(a+b*sec(d*x^2+c))^2,x)","\int \frac{x^{5}}{\left(a +b \sec \left(d \,x^{2}+c \right)\right)^{2}}\, dx"," ",0,"int(x^5/(a+b*sec(d*x^2+c))^2,x)","F"
24,0,0,20,1.413000," ","int(x^4/(a+b*sec(d*x^2+c))^2,x)","\int \frac{x^{4}}{\left(a +b \sec \left(d \,x^{2}+c \right)\right)^{2}}\, dx"," ",0,"int(x^4/(a+b*sec(d*x^2+c))^2,x)","F"
25,0,0,530,1.535000," ","int(x^3/(a+b*sec(d*x^2+c))^2,x)","\int \frac{x^{3}}{\left(a +b \sec \left(d \,x^{2}+c \right)\right)^{2}}\, dx"," ",0,"int(x^3/(a+b*sec(d*x^2+c))^2,x)","F"
26,0,0,20,1.128000," ","int(x^2/(a+b*sec(d*x^2+c))^2,x)","\int \frac{x^{2}}{\left(a +b \sec \left(d \,x^{2}+c \right)\right)^{2}}\, dx"," ",0,"int(x^2/(a+b*sec(d*x^2+c))^2,x)","F"
27,1,214,110,0.529000," ","int(x/(a+b*sec(d*x^2+c))^2,x)","-\frac{b^{2} \tan \left(\frac{d \,x^{2}}{2}+\frac{c}{2}\right)}{d a \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d \,x^{2}}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d \,x^{2}}{2}+\frac{c}{2}\right)\right) b -a -b \right)}-\frac{2 b \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{d \,x^{2}}{2}+\frac{c}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{b^{3} \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{d \,x^{2}}{2}+\frac{c}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{\arctan \left(\tan \left(\frac{d \,x^{2}}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"-1/d*b^2/a/(a^2-b^2)*tan(1/2*d*x^2+1/2*c)/(a*tan(1/2*d*x^2+1/2*c)^2-tan(1/2*d*x^2+1/2*c)^2*b-a-b)-2/d*b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*d*x^2+1/2*c)/((a-b)*(a+b))^(1/2))+1/d*b^3/a^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*d*x^2+1/2*c)/((a-b)*(a+b))^(1/2))+1/d/a^2*arctan(tan(1/2*d*x^2+1/2*c))","A"
28,0,0,20,1.311000," ","int(1/x/(a+b*sec(d*x^2+c))^2,x)","\int \frac{1}{x \left(a +b \sec \left(d \,x^{2}+c \right)\right)^{2}}\, dx"," ",0,"int(1/x/(a+b*sec(d*x^2+c))^2,x)","F"
29,0,0,20,1.465000," ","int(1/x^2/(a+b*sec(d*x^2+c))^2,x)","\int \frac{1}{x^{2} \left(a +b \sec \left(d \,x^{2}+c \right)\right)^{2}}\, dx"," ",0,"int(1/x^2/(a+b*sec(d*x^2+c))^2,x)","F"
30,0,0,20,1.635000," ","int(1/x^3/(a+b*sec(d*x^2+c))^2,x)","\int \frac{1}{x^{3} \left(a +b \sec \left(d \,x^{2}+c \right)\right)^{2}}\, dx"," ",0,"int(1/x^3/(a+b*sec(d*x^2+c))^2,x)","F"
31,0,0,377,1.289000," ","int(x^3*(a+b*sec(c+d*x^(1/2))),x)","\int x^{3} \left(a +b \sec \left(c +d \sqrt{x}\right)\right)\, dx"," ",0,"int(x^3*(a+b*sec(c+d*x^(1/2))),x)","F"
32,0,0,275,1.165000," ","int(x^2*(a+b*sec(c+d*x^(1/2))),x)","\int x^{2} \left(a +b \sec \left(c +d \sqrt{x}\right)\right)\, dx"," ",0,"int(x^2*(a+b*sec(c+d*x^(1/2))),x)","F"
33,0,0,173,1.151000," ","int(x*(a+b*sec(c+d*x^(1/2))),x)","\int x \left(a +b \sec \left(c +d \sqrt{x}\right)\right)\, dx"," ",0,"int(x*(a+b*sec(c+d*x^(1/2))),x)","F"
34,0,0,21,1.349000," ","int((a+b*sec(c+d*x^(1/2)))/x,x)","\int \frac{a +b \sec \left(c +d \sqrt{x}\right)}{x}\, dx"," ",0,"int((a+b*sec(c+d*x^(1/2)))/x,x)","F"
35,0,0,23,1.337000," ","int((a+b*sec(c+d*x^(1/2)))/x^2,x)","\int \frac{a +b \sec \left(c +d \sqrt{x}\right)}{x^{2}}\, dx"," ",0,"int((a+b*sec(c+d*x^(1/2)))/x^2,x)","F"
36,0,0,604,1.385000," ","int(x^3*(a+b*sec(c+d*x^(1/2)))^2,x)","\int x^{3} \left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2}\, dx"," ",0,"int(x^3*(a+b*sec(c+d*x^(1/2)))^2,x)","F"
37,0,0,445,1.384000," ","int(x^2*(a+b*sec(c+d*x^(1/2)))^2,x)","\int x^{2} \left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2}\, dx"," ",0,"int(x^2*(a+b*sec(c+d*x^(1/2)))^2,x)","F"
38,0,0,286,1.378000," ","int(x*(a+b*sec(c+d*x^(1/2)))^2,x)","\int x \left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2}\, dx"," ",0,"int(x*(a+b*sec(c+d*x^(1/2)))^2,x)","F"
39,0,0,20,1.402000," ","int((a+b*sec(c+d*x^(1/2)))^2/x,x)","\int \frac{\left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2}}{x}\, dx"," ",0,"int((a+b*sec(c+d*x^(1/2)))^2/x,x)","F"
40,0,0,20,1.398000," ","int((a+b*sec(c+d*x^(1/2)))^2/x^2,x)","\int \frac{\left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2}}{x^{2}}\, dx"," ",0,"int((a+b*sec(c+d*x^(1/2)))^2/x^2,x)","F"
41,0,0,887,1.134000," ","int(x^3/(a+b*sec(c+d*x^(1/2))),x)","\int \frac{x^{3}}{a +b \sec \left(c +d \sqrt{x}\right)}\, dx"," ",0,"int(x^3/(a+b*sec(c+d*x^(1/2))),x)","F"
42,0,0,665,1.128000," ","int(x^2/(a+b*sec(c+d*x^(1/2))),x)","\int \frac{x^{2}}{a +b \sec \left(c +d \sqrt{x}\right)}\, dx"," ",0,"int(x^2/(a+b*sec(c+d*x^(1/2))),x)","F"
43,0,0,443,1.358000," ","int(x/(a+b*sec(c+d*x^(1/2))),x)","\int \frac{x}{a +b \sec \left(c +d \sqrt{x}\right)}\, dx"," ",0,"int(x/(a+b*sec(c+d*x^(1/2))),x)","F"
44,0,0,20,1.234000," ","int(1/x/(a+b*sec(c+d*x^(1/2))),x)","\int \frac{1}{x \left(a +b \sec \left(c +d \sqrt{x}\right)\right)}\, dx"," ",0,"int(1/x/(a+b*sec(c+d*x^(1/2))),x)","F"
45,0,0,23,0.026000," ","int((a+b*sec(c+d*x^(1/2)))/x^2,x)","\int \frac{a +b \sec \left(c +d \sqrt{x}\right)}{x^{2}}\, dx"," ",0,"int((a+b*sec(c+d*x^(1/2)))/x^2,x)","F"
46,0,0,2692,1.374000," ","int(x^3/(a+b*sec(c+d*x^(1/2)))^2,x)","\int \frac{x^{3}}{\left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2}}\, dx"," ",0,"int(x^3/(a+b*sec(c+d*x^(1/2)))^2,x)","F"
47,0,0,2002,1.296000," ","int(x^2/(a+b*sec(c+d*x^(1/2)))^2,x)","\int \frac{x^{2}}{\left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2}}\, dx"," ",0,"int(x^2/(a+b*sec(c+d*x^(1/2)))^2,x)","F"
48,0,0,1312,1.306000," ","int(x/(a+b*sec(c+d*x^(1/2)))^2,x)","\int \frac{x}{\left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2}}\, dx"," ",0,"int(x/(a+b*sec(c+d*x^(1/2)))^2,x)","F"
49,0,0,20,1.303000," ","int(1/x/(a+b*sec(c+d*x^(1/2)))^2,x)","\int \frac{1}{x \left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2}}\, dx"," ",0,"int(1/x/(a+b*sec(c+d*x^(1/2)))^2,x)","F"
50,0,0,20,1.281000," ","int(1/x^2/(a+b*sec(c+d*x^(1/2)))^2,x)","\int \frac{1}{x^{2} \left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2}}\, dx"," ",0,"int(1/x^2/(a+b*sec(c+d*x^(1/2)))^2,x)","F"
51,0,0,223,1.204000," ","int(x^(3/2)*(a+b*sec(c+d*x^(1/2))),x)","\int x^{\frac{3}{2}} \left(a +b \sec \left(c +d \sqrt{x}\right)\right)\, dx"," ",0,"int(x^(3/2)*(a+b*sec(c+d*x^(1/2))),x)","F"
52,0,0,123,1.181000," ","int((a+b*sec(c+d*x^(1/2)))*x^(1/2),x)","\int \left(a +b \sec \left(c +d \sqrt{x}\right)\right) \sqrt{x}\, dx"," ",0,"int((a+b*sec(c+d*x^(1/2)))*x^(1/2),x)","F"
53,1,32,22,0.264000," ","int((a+b*sec(c+d*x^(1/2)))/x^(1/2),x)","2 a \sqrt{x}+\frac{2 b \ln \left(\sec \left(c +d \sqrt{x}\right)+\tan \left(c +d \sqrt{x}\right)\right)}{d}"," ",0,"2*a*x^(1/2)+2*b/d*ln(sec(c+d*x^(1/2))+tan(c+d*x^(1/2)))","A"
54,0,0,23,1.381000," ","int((a+b*sec(c+d*x^(1/2)))/x^(3/2),x)","\int \frac{a +b \sec \left(c +d \sqrt{x}\right)}{x^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*sec(c+d*x^(1/2)))/x^(3/2),x)","F"
55,0,0,23,1.456000," ","int((a+b*sec(c+d*x^(1/2)))/x^(5/2),x)","\int \frac{a +b \sec \left(c +d \sqrt{x}\right)}{x^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*sec(c+d*x^(1/2)))/x^(5/2),x)","F"
56,0,0,365,1.287000," ","int(x^(3/2)*(a+b*sec(c+d*x^(1/2)))^2,x)","\int x^{\frac{3}{2}} \left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2}\, dx"," ",0,"int(x^(3/2)*(a+b*sec(c+d*x^(1/2)))^2,x)","F"
57,0,0,206,1.289000," ","int((a+b*sec(c+d*x^(1/2)))^2*x^(1/2),x)","\int \left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2} \sqrt{x}\, dx"," ",0,"int((a+b*sec(c+d*x^(1/2)))^2*x^(1/2),x)","F"
58,1,60,41,0.758000," ","int((a+b*sec(c+d*x^(1/2)))^2/x^(1/2),x)","2 a^{2} \sqrt{x}+\frac{2 b^{2} \tan \left(c +d \sqrt{x}\right)}{d}+\frac{4 a b \ln \left(\sec \left(c +d \sqrt{x}\right)+\tan \left(c +d \sqrt{x}\right)\right)}{d}+\frac{2 a^{2} c}{d}"," ",0,"2*a^2*x^(1/2)+2*b^2*tan(c+d*x^(1/2))/d+4/d*a*b*ln(sec(c+d*x^(1/2))+tan(c+d*x^(1/2)))+2/d*a^2*c","A"
59,0,0,20,1.290000," ","int((a+b*sec(c+d*x^(1/2)))^2/x^(3/2),x)","\int \frac{\left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2}}{x^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*sec(c+d*x^(1/2)))^2/x^(3/2),x)","F"
60,0,0,20,1.315000," ","int((a+b*sec(c+d*x^(1/2)))^2/x^(5/2),x)","\int \frac{\left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2}}{x^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*sec(c+d*x^(1/2)))^2/x^(5/2),x)","F"
61,0,0,555,1.071000," ","int(x^(3/2)/(a+b*sec(c+d*x^(1/2))),x)","\int \frac{x^{\frac{3}{2}}}{a +b \sec \left(c +d \sqrt{x}\right)}\, dx"," ",0,"int(x^(3/2)/(a+b*sec(c+d*x^(1/2))),x)","F"
62,0,0,333,1.011000," ","int(x^(1/2)/(a+b*sec(c+d*x^(1/2))),x)","\int \frac{\sqrt{x}}{a +b \sec \left(c +d \sqrt{x}\right)}\, dx"," ",0,"int(x^(1/2)/(a+b*sec(c+d*x^(1/2))),x)","F"
63,1,71,55,0.706000," ","int(1/(a+b*sec(c+d*x^(1/2)))/x^(1/2),x)","-\frac{4 b \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{c}{2}+\frac{d \sqrt{x}}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d a \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{4 \arctan \left(\tan \left(\frac{c}{2}+\frac{d \sqrt{x}}{2}\right)\right)}{d a}"," ",0,"-4/d/a*b/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*c+1/2*d*x^(1/2))/((a-b)*(a+b))^(1/2))+4/d/a*arctan(tan(1/2*c+1/2*d*x^(1/2)))","A"
64,0,0,20,1.000000," ","int(1/x^(3/2)/(a+b*sec(c+d*x^(1/2))),x)","\int \frac{1}{x^{\frac{3}{2}} \left(a +b \sec \left(c +d \sqrt{x}\right)\right)}\, dx"," ",0,"int(1/x^(3/2)/(a+b*sec(c+d*x^(1/2))),x)","F"
65,0,0,20,0.987000," ","int(1/x^(5/2)/(a+b*sec(c+d*x^(1/2))),x)","\int \frac{1}{x^{\frac{5}{2}} \left(a +b \sec \left(c +d \sqrt{x}\right)\right)}\, dx"," ",0,"int(1/x^(5/2)/(a+b*sec(c+d*x^(1/2))),x)","F"
66,0,0,1660,1.332000," ","int(x^(3/2)/(a+b*sec(c+d*x^(1/2)))^2,x)","\int \frac{x^{\frac{3}{2}}}{\left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2}}\, dx"," ",0,"int(x^(3/2)/(a+b*sec(c+d*x^(1/2)))^2,x)","F"
67,0,0,970,1.159000," ","int(x^(1/2)/(a+b*sec(c+d*x^(1/2)))^2,x)","\int \frac{\sqrt{x}}{\left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2}}\, dx"," ",0,"int(x^(1/2)/(a+b*sec(c+d*x^(1/2)))^2,x)","F"
68,1,216,110,0.852000," ","int(1/(a+b*sec(c+d*x^(1/2)))^2/x^(1/2),x)","-\frac{4 b^{2} \tan \left(\frac{c}{2}+\frac{d \sqrt{x}}{2}\right)}{d a \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{c}{2}+\frac{d \sqrt{x}}{2}\right)\right)-\left(\tan^{2}\left(\frac{c}{2}+\frac{d \sqrt{x}}{2}\right)\right) b -a -b \right)}-\frac{8 b \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{c}{2}+\frac{d \sqrt{x}}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{4 b^{3} \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{c}{2}+\frac{d \sqrt{x}}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{4 \arctan \left(\tan \left(\frac{c}{2}+\frac{d \sqrt{x}}{2}\right)\right)}{d \,a^{2}}"," ",0,"-4/d*b^2/a/(a^2-b^2)*tan(1/2*c+1/2*d*x^(1/2))/(a*tan(1/2*c+1/2*d*x^(1/2))^2-tan(1/2*c+1/2*d*x^(1/2))^2*b-a-b)-8/d*b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*c+1/2*d*x^(1/2))/((a-b)*(a+b))^(1/2))+4/d*b^3/a^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*c+1/2*d*x^(1/2))/((a-b)*(a+b))^(1/2))+4/d/a^2*arctan(tan(1/2*c+1/2*d*x^(1/2)))","A"
69,0,0,20,1.308000," ","int(1/x^(3/2)/(a+b*sec(c+d*x^(1/2)))^2,x)","\int \frac{1}{x^{\frac{3}{2}} \left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2}}\, dx"," ",0,"int(1/x^(3/2)/(a+b*sec(c+d*x^(1/2)))^2,x)","F"
70,0,0,20,1.237000," ","int(1/x^(5/2)/(a+b*sec(c+d*x^(1/2)))^2,x)","\int \frac{1}{x^{\frac{5}{2}} \left(a +b \sec \left(c +d \sqrt{x}\right)\right)^{2}}\, dx"," ",0,"int(1/x^(5/2)/(a+b*sec(c+d*x^(1/2)))^2,x)","F"
71,0,0,31,1.509000," ","int((e*x)^m*(a+b*sec(c+d*x^n))^p,x)","\int \left(e x \right)^{m} \left(a +b \sec \left(c +d \,x^{n}\right)\right)^{p}\, dx"," ",0,"int((e*x)^m*(a+b*sec(c+d*x^n))^p,x)","F"
72,1,159,44,1.584000," ","int((e*x)^(-1+n)*(a+b*sec(c+d*x^n)),x)","\frac{a x \,{\mathrm e}^{\frac{\left(-1+n \right) \left(-i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)+i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}+i \pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}-i \pi  \mathrm{csgn}\left(i e x \right)^{3}+2 \ln \left(x \right)+2 \ln \left(e \right)\right)}{2}}}{n}-\frac{2 i \arctan \left({\mathrm e}^{i \left(c +d \,x^{n}\right)}\right) e^{n} b \,{\mathrm e}^{\frac{i \pi  \,\mathrm{csgn}\left(i e x \right) \left(-1+n \right) \left(\mathrm{csgn}\left(i e x \right)-\mathrm{csgn}\left(i x \right)\right) \left(-\mathrm{csgn}\left(i e x \right)+\mathrm{csgn}\left(i e \right)\right)}{2}}}{d e n}"," ",0,"a/n*x*exp(1/2*(-1+n)*(-I*Pi*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+I*Pi*csgn(I*e)*csgn(I*e*x)^2+I*Pi*csgn(I*x)*csgn(I*e*x)^2-I*Pi*csgn(I*e*x)^3+2*ln(x)+2*ln(e)))-2*I*arctan(exp(I*(c+d*x^n)))/d/e*e^n/n*b*exp(1/2*I*Pi*csgn(I*e*x)*(-1+n)*(csgn(I*e*x)-csgn(I*x))*(-csgn(I*e*x)+csgn(I*e)))","C"
73,1,873,140,1.867000," ","int((e*x)^(-1+2*n)*(a+b*sec(c+d*x^n)),x)","\frac{a x \,{\mathrm e}^{\frac{\left(-1+2 n \right) \left(-i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)+i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}+i \pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}-i \pi  \mathrm{csgn}\left(i e x \right)^{3}+2 \ln \left(x \right)+2 \ln \left(e \right)\right)}{2}}}{2 n}+\frac{i e^{2 n} b \ln \left(1+{\mathrm e}^{i x^{n} d} \sqrt{-{\mathrm e}^{2 i c}}\right) x^{n} \sqrt{-{\mathrm e}^{2 i c}}\, \left(-1\right)^{\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} {\mathrm e}^{-i \pi  n \mathrm{csgn}\left(i e x \right)^{3}} {\mathrm e}^{i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}} {\mathrm e}^{i \pi  n \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}} {\mathrm e}^{-i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(i e x \right)^{3}}{2}} {\mathrm e}^{-i c}}{d n e}-\frac{i e^{2 n} b \ln \left(1-{\mathrm e}^{i x^{n} d} \sqrt{-{\mathrm e}^{2 i c}}\right) x^{n} \sqrt{-{\mathrm e}^{2 i c}}\, \left(-1\right)^{\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} {\mathrm e}^{-i \pi  n \mathrm{csgn}\left(i e x \right)^{3}} {\mathrm e}^{i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}} {\mathrm e}^{i \pi  n \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}} {\mathrm e}^{-i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(i e x \right)^{3}}{2}} {\mathrm e}^{-i c}}{d n e}+\frac{e^{2 n} b \dilog \left(1+{\mathrm e}^{i x^{n} d} \sqrt{-{\mathrm e}^{2 i c}}\right) \sqrt{-{\mathrm e}^{2 i c}}\, \left(-1\right)^{\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} {\mathrm e}^{-i \pi  n \mathrm{csgn}\left(i e x \right)^{3}} {\mathrm e}^{i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}} {\mathrm e}^{i \pi  n \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}} {\mathrm e}^{-i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(i e x \right)^{3}}{2}} {\mathrm e}^{-i c}}{d^{2} n e}-\frac{e^{2 n} b \dilog \left(1-{\mathrm e}^{i x^{n} d} \sqrt{-{\mathrm e}^{2 i c}}\right) \sqrt{-{\mathrm e}^{2 i c}}\, \left(-1\right)^{\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} {\mathrm e}^{-i \pi  n \mathrm{csgn}\left(i e x \right)^{3}} {\mathrm e}^{i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}} {\mathrm e}^{i \pi  n \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}} {\mathrm e}^{-i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(i e x \right)^{3}}{2}} {\mathrm e}^{-i c}}{d^{2} n e}"," ",0,"1/2*a/n*x*exp(1/2*(-1+2*n)*(-I*Pi*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+I*Pi*csgn(I*e)*csgn(I*e*x)^2+I*Pi*csgn(I*x)*csgn(I*e*x)^2-I*Pi*csgn(I*e*x)^3+2*ln(x)+2*ln(e)))+I/d/n/e*(e^n)^2*b*ln(1+exp(I*x^n*d)*(-exp(2*I*c))^(1/2))*x^n*(-exp(2*I*c))^(1/2)*(-1)^(1/2*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*(-1)^(-1/2*csgn(I*x)*csgn(I*e*x)^2)*(-1)^(-1/2*csgn(I*e)*csgn(I*e*x)^2)*exp(-I*Pi*n*csgn(I*e*x)^3)*exp(I*Pi*n*csgn(I*e)*csgn(I*e*x)^2)*exp(I*Pi*n*csgn(I*x)*csgn(I*e*x)^2)*exp(-I*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*exp(1/2*I*Pi*csgn(I*e*x)^3)*exp(-I*c)-I/d/n/e*(e^n)^2*b*ln(1-exp(I*x^n*d)*(-exp(2*I*c))^(1/2))*x^n*(-exp(2*I*c))^(1/2)*(-1)^(1/2*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*(-1)^(-1/2*csgn(I*x)*csgn(I*e*x)^2)*(-1)^(-1/2*csgn(I*e)*csgn(I*e*x)^2)*exp(-I*Pi*n*csgn(I*e*x)^3)*exp(I*Pi*n*csgn(I*e)*csgn(I*e*x)^2)*exp(I*Pi*n*csgn(I*x)*csgn(I*e*x)^2)*exp(-I*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*exp(1/2*I*Pi*csgn(I*e*x)^3)*exp(-I*c)+1/d^2/n/e*(e^n)^2*b*dilog(1+exp(I*x^n*d)*(-exp(2*I*c))^(1/2))*(-exp(2*I*c))^(1/2)*(-1)^(1/2*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*(-1)^(-1/2*csgn(I*x)*csgn(I*e*x)^2)*(-1)^(-1/2*csgn(I*e)*csgn(I*e*x)^2)*exp(-I*Pi*n*csgn(I*e*x)^3)*exp(I*Pi*n*csgn(I*e)*csgn(I*e*x)^2)*exp(I*Pi*n*csgn(I*x)*csgn(I*e*x)^2)*exp(-I*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*exp(1/2*I*Pi*csgn(I*e*x)^3)*exp(-I*c)-1/d^2/n/e*(e^n)^2*b*dilog(1-exp(I*x^n*d)*(-exp(2*I*c))^(1/2))*(-exp(2*I*c))^(1/2)*(-1)^(1/2*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*(-1)^(-1/2*csgn(I*x)*csgn(I*e*x)^2)*(-1)^(-1/2*csgn(I*e)*csgn(I*e*x)^2)*exp(-I*Pi*n*csgn(I*e*x)^3)*exp(I*Pi*n*csgn(I*e)*csgn(I*e*x)^2)*exp(I*Pi*n*csgn(I*x)*csgn(I*e*x)^2)*exp(-I*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*exp(1/2*I*Pi*csgn(I*e*x)^3)*exp(-I*c)","C"
74,0,0,224,2.273000," ","int((e*x)^(-1+3*n)*(a+b*sec(c+d*x^n)),x)","\int \left(e x \right)^{-1+3 n} \left(a +b \sec \left(c +d \,x^{n}\right)\right)\, dx"," ",0,"int((e*x)^(-1+3*n)*(a+b*sec(c+d*x^n)),x)","F"
75,1,276,79,1.191000," ","int((e*x)^(-1+n)*(a+b*sec(c+d*x^n))^2,x)","\frac{a^{2} x \,{\mathrm e}^{\frac{\left(-1+n \right) \left(-i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)+i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}+i \pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}-i \pi  \mathrm{csgn}\left(i e x \right)^{3}+2 \ln \left(x \right)+2 \ln \left(e \right)\right)}{2}}}{n}+\frac{2 i x \,b^{2} {\mathrm e}^{\frac{\left(-1+n \right) \left(-i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)+i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}+i \pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}-i \pi  \mathrm{csgn}\left(i e x \right)^{3}+2 \ln \left(x \right)+2 \ln \left(e \right)\right)}{2}} x^{-n}}{d n \left(1+{\mathrm e}^{2 i \left(c +d \,x^{n}\right)}\right)}-\frac{4 i \arctan \left({\mathrm e}^{i \left(c +d \,x^{n}\right)}\right) e^{n} a b \,{\mathrm e}^{\frac{i \pi  \,\mathrm{csgn}\left(i e x \right) \left(-1+n \right) \left(\mathrm{csgn}\left(i e x \right)-\mathrm{csgn}\left(i x \right)\right) \left(-\mathrm{csgn}\left(i e x \right)+\mathrm{csgn}\left(i e \right)\right)}{2}}}{d e n}"," ",0,"a^2/n*x*exp(1/2*(-1+n)*(-I*Pi*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+I*Pi*csgn(I*e)*csgn(I*e*x)^2+I*Pi*csgn(I*x)*csgn(I*e*x)^2-I*Pi*csgn(I*e*x)^3+2*ln(x)+2*ln(e)))+2*I*x*b^2*exp(1/2*(-1+n)*(-I*Pi*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+I*Pi*csgn(I*e)*csgn(I*e*x)^2+I*Pi*csgn(I*x)*csgn(I*e*x)^2-I*Pi*csgn(I*e*x)^3+2*ln(x)+2*ln(e)))/d/n/(x^n)/(1+exp(2*I*(c+d*x^n)))-4*I*arctan(exp(I*(c+d*x^n)))/d/e*e^n/n*a*b*exp(1/2*I*Pi*csgn(I*e*x)*(-1+n)*(csgn(I*e*x)-csgn(I*x))*(-csgn(I*e*x)+csgn(I*e)))","C"
76,1,1096,214,1.202000," ","int((e*x)^(-1+2*n)*(a+b*sec(c+d*x^n))^2,x)","\frac{a^{2} x \,{\mathrm e}^{\frac{\left(-1+2 n \right) \left(-i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)+i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}+i \pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}-i \pi  \mathrm{csgn}\left(i e x \right)^{3}+2 \ln \left(x \right)+2 \ln \left(e \right)\right)}{2}}}{2 n}+\frac{2 i x \,b^{2} {\mathrm e}^{\frac{\left(-1+2 n \right) \left(-i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)+i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}+i \pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}-i \pi  \mathrm{csgn}\left(i e x \right)^{3}+2 \ln \left(x \right)+2 \ln \left(e \right)\right)}{2}} x^{-n}}{d n \left(1+{\mathrm e}^{2 i \left(c +d \,x^{n}\right)}\right)}+\frac{b^{2} \ln \left(1+{\mathrm e}^{2 i \left(c +d \,x^{n}\right)}\right) e^{2 n} {\mathrm e}^{\frac{i \mathrm{csgn}\left(i e x \right) \pi  \left(-1+2 n \right) \left(\mathrm{csgn}\left(i e x \right)-\mathrm{csgn}\left(i x \right)\right) \left(-\mathrm{csgn}\left(i e x \right)+\mathrm{csgn}\left(i e \right)\right)}{2}}}{d^{2} n e}-\frac{2 b^{2} \ln \left({\mathrm e}^{i x^{n} d}\right) e^{2 n} {\mathrm e}^{\frac{i \mathrm{csgn}\left(i e x \right) \pi  \left(-1+2 n \right) \left(\mathrm{csgn}\left(i e x \right)-\mathrm{csgn}\left(i x \right)\right) \left(-\mathrm{csgn}\left(i e x \right)+\mathrm{csgn}\left(i e \right)\right)}{2}}}{d^{2} n e}+\frac{2 i b \ln \left(1+{\mathrm e}^{i x^{n} d} \sqrt{-{\mathrm e}^{2 i c}}\right) x^{n} \sqrt{-{\mathrm e}^{2 i c}}\, a \,e^{2 n} {\mathrm e}^{-\frac{i \left(2 \pi  n \mathrm{csgn}\left(i e x \right)^{3}-2 \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}-2 \pi  n \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}+2 \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)-\pi  \mathrm{csgn}\left(i e x \right)^{3}+\pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}+\pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}-\pi  \,\mathrm{csgn}\left(i e x \right) \mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right)+2 c \right)}{2}}}{d n e}-\frac{2 i b \ln \left(1-{\mathrm e}^{i x^{n} d} \sqrt{-{\mathrm e}^{2 i c}}\right) x^{n} \sqrt{-{\mathrm e}^{2 i c}}\, a \,e^{2 n} {\mathrm e}^{-\frac{i \left(2 \pi  n \mathrm{csgn}\left(i e x \right)^{3}-2 \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}-2 \pi  n \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}+2 \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)-\pi  \mathrm{csgn}\left(i e x \right)^{3}+\pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}+\pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}-\pi  \,\mathrm{csgn}\left(i e x \right) \mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right)+2 c \right)}{2}}}{d n e}+\frac{2 b \dilog \left(1+{\mathrm e}^{i x^{n} d} \sqrt{-{\mathrm e}^{2 i c}}\right) \sqrt{-{\mathrm e}^{2 i c}}\, a \,e^{2 n} {\mathrm e}^{-\frac{i \left(2 \pi  n \mathrm{csgn}\left(i e x \right)^{3}-2 \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}-2 \pi  n \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}+2 \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)-\pi  \mathrm{csgn}\left(i e x \right)^{3}+\pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}+\pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}-\pi  \,\mathrm{csgn}\left(i e x \right) \mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right)+2 c \right)}{2}}}{d^{2} n e}-\frac{2 b \dilog \left(1-{\mathrm e}^{i x^{n} d} \sqrt{-{\mathrm e}^{2 i c}}\right) \sqrt{-{\mathrm e}^{2 i c}}\, a \,e^{2 n} {\mathrm e}^{-\frac{i \left(2 \pi  n \mathrm{csgn}\left(i e x \right)^{3}-2 \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}-2 \pi  n \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}+2 \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)-\pi  \mathrm{csgn}\left(i e x \right)^{3}+\pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}+\pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}-\pi  \,\mathrm{csgn}\left(i e x \right) \mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right)+2 c \right)}{2}}}{d^{2} n e}"," ",0,"1/2*a^2/n*x*exp(1/2*(-1+2*n)*(-I*Pi*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+I*Pi*csgn(I*e)*csgn(I*e*x)^2+I*Pi*csgn(I*x)*csgn(I*e*x)^2-I*Pi*csgn(I*e*x)^3+2*ln(x)+2*ln(e)))+2*I*x*b^2*exp(1/2*(-1+2*n)*(-I*Pi*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+I*Pi*csgn(I*e)*csgn(I*e*x)^2+I*Pi*csgn(I*x)*csgn(I*e*x)^2-I*Pi*csgn(I*e*x)^3+2*ln(x)+2*ln(e)))/d/n/(x^n)/(1+exp(2*I*(c+d*x^n)))+1/d^2*b^2*ln(1+exp(2*I*(c+d*x^n)))/n/e*(e^n)^2*exp(1/2*I*csgn(I*e*x)*Pi*(-1+2*n)*(csgn(I*e*x)-csgn(I*x))*(-csgn(I*e*x)+csgn(I*e)))-2/d^2*b^2*ln(exp(I*x^n*d))/n/e*(e^n)^2*exp(1/2*I*csgn(I*e*x)*Pi*(-1+2*n)*(csgn(I*e*x)-csgn(I*x))*(-csgn(I*e*x)+csgn(I*e)))+2*I/d*b*ln(1+exp(I*x^n*d)*(-exp(2*I*c))^(1/2))*x^n*(-exp(2*I*c))^(1/2)/n*a/e*(e^n)^2*exp(-1/2*I*(2*Pi*n*csgn(I*e*x)^3-2*Pi*n*csgn(I*e)*csgn(I*e*x)^2-2*Pi*n*csgn(I*x)*csgn(I*e*x)^2+2*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x)-Pi*csgn(I*e*x)^3+Pi*csgn(I*e)*csgn(I*e*x)^2+Pi*csgn(I*x)*csgn(I*e*x)^2-Pi*csgn(I*e*x)*csgn(I*e)*csgn(I*x)+2*c))-2*I/d*b*ln(1-exp(I*x^n*d)*(-exp(2*I*c))^(1/2))*x^n*(-exp(2*I*c))^(1/2)/n*a/e*(e^n)^2*exp(-1/2*I*(2*Pi*n*csgn(I*e*x)^3-2*Pi*n*csgn(I*e)*csgn(I*e*x)^2-2*Pi*n*csgn(I*x)*csgn(I*e*x)^2+2*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x)-Pi*csgn(I*e*x)^3+Pi*csgn(I*e)*csgn(I*e*x)^2+Pi*csgn(I*x)*csgn(I*e*x)^2-Pi*csgn(I*e*x)*csgn(I*e)*csgn(I*x)+2*c))+2/d^2*b*dilog(1+exp(I*x^n*d)*(-exp(2*I*c))^(1/2))*(-exp(2*I*c))^(1/2)/n*a/e*(e^n)^2*exp(-1/2*I*(2*Pi*n*csgn(I*e*x)^3-2*Pi*n*csgn(I*e)*csgn(I*e*x)^2-2*Pi*n*csgn(I*x)*csgn(I*e*x)^2+2*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x)-Pi*csgn(I*e*x)^3+Pi*csgn(I*e)*csgn(I*e*x)^2+Pi*csgn(I*x)*csgn(I*e*x)^2-Pi*csgn(I*e*x)*csgn(I*e)*csgn(I*x)+2*c))-2/d^2*b*dilog(1-exp(I*x^n*d)*(-exp(2*I*c))^(1/2))*(-exp(2*I*c))^(1/2)/n*a/e*(e^n)^2*exp(-1/2*I*(2*Pi*n*csgn(I*e*x)^3-2*Pi*n*csgn(I*e)*csgn(I*e*x)^2-2*Pi*n*csgn(I*x)*csgn(I*e*x)^2+2*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x)-Pi*csgn(I*e*x)^3+Pi*csgn(I*e)*csgn(I*e*x)^2+Pi*csgn(I*x)*csgn(I*e*x)^2-Pi*csgn(I*e*x)*csgn(I*e)*csgn(I*x)+2*c))","C"
77,0,0,377,3.020000," ","int((e*x)^(-1+3*n)*(a+b*sec(c+d*x^n))^2,x)","\int \left(e x \right)^{-1+3 n} \left(a +b \sec \left(c +d \,x^{n}\right)\right)^{2}\, dx"," ",0,"int((e*x)^(-1+3*n)*(a+b*sec(c+d*x^n))^2,x)","F"
78,1,314,78,1.071000," ","int((e*x)^(-1+n)/(a+b*sec(c+d*x^n)),x)","\frac{x \,{\mathrm e}^{\frac{\left(-1+n \right) \left(-i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)+i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}+i \pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}-i \pi  \mathrm{csgn}\left(i e x \right)^{3}+2 \ln \left(x \right)+2 \ln \left(e \right)\right)}{2}}}{a n}+\frac{2 i \arctan \left(\frac{2 a \,{\mathrm e}^{i \left(d \,x^{n}+2 c \right)}+2 \,{\mathrm e}^{i c} b}{2 \sqrt{a^{2} {\mathrm e}^{2 i c}-{\mathrm e}^{2 i c} b^{2}}}\right) e^{n} b \,{\mathrm e}^{\frac{i \left(-\pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)+\pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}+\pi  n \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}-\pi  n \mathrm{csgn}\left(i e x \right)^{3}+\pi  \,\mathrm{csgn}\left(i e x \right) \mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right)-\pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}-\pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}+\pi  \mathrm{csgn}\left(i e x \right)^{3}+2 c \right)}{2}}}{\sqrt{a^{2} {\mathrm e}^{2 i c}-{\mathrm e}^{2 i c} b^{2}}\, d e n a}"," ",0,"1/a/n*x*exp(1/2*(-1+n)*(-I*Pi*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+I*Pi*csgn(I*e)*csgn(I*e*x)^2+I*Pi*csgn(I*x)*csgn(I*e*x)^2-I*Pi*csgn(I*e*x)^3+2*ln(x)+2*ln(e)))+2*I*arctan(1/2*(2*a*exp(I*(d*x^n+2*c))+2*exp(I*c)*b)/(a^2*exp(2*I*c)-exp(2*I*c)*b^2)^(1/2))/(a^2*exp(2*I*c)-exp(2*I*c)*b^2)^(1/2)/d/e*e^n/n*b/a*exp(1/2*I*(-Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+Pi*n*csgn(I*e)*csgn(I*e*x)^2+Pi*n*csgn(I*x)*csgn(I*e*x)^2-Pi*n*csgn(I*e*x)^3+Pi*csgn(I*e*x)*csgn(I*e)*csgn(I*x)-Pi*csgn(I*e)*csgn(I*e*x)^2-Pi*csgn(I*x)*csgn(I*e*x)^2+Pi*csgn(I*e*x)^3+2*c))","C"
79,1,1308,304,1.522000," ","int((e*x)^(-1+2*n)/(a+b*sec(c+d*x^n)),x)","\frac{x \,{\mathrm e}^{\frac{\left(-1+2 n \right) \left(-i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)+i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}+i \pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}-i \pi  \mathrm{csgn}\left(i e x \right)^{3}+2 \ln \left(x \right)+2 \ln \left(e \right)\right)}{2}}}{2 a n}+\frac{i e^{2 n} b \ln \left(\frac{a \,{\mathrm e}^{i \left(d \,x^{n}+2 c \right)}+{\mathrm e}^{i c} b -\sqrt{{\mathrm e}^{2 i c} b^{2}-a^{2} {\mathrm e}^{2 i c}}}{{\mathrm e}^{i c} b -\sqrt{{\mathrm e}^{2 i c} b^{2}-a^{2} {\mathrm e}^{2 i c}}}\right) x^{n} \left(-1\right)^{\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} {\mathrm e}^{-i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)} {\mathrm e}^{i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}} {\mathrm e}^{i \pi  n \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}} {\mathrm e}^{-i \pi  n \mathrm{csgn}\left(i e x \right)^{3}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(i e x \right)^{3}}{2}} {\mathrm e}^{i c}}{d n e a \sqrt{{\mathrm e}^{2 i c} b^{2}-a^{2} {\mathrm e}^{2 i c}}}-\frac{i e^{2 n} b \ln \left(\frac{a \,{\mathrm e}^{i \left(d \,x^{n}+2 c \right)}+{\mathrm e}^{i c} b +\sqrt{{\mathrm e}^{2 i c} b^{2}-a^{2} {\mathrm e}^{2 i c}}}{{\mathrm e}^{i c} b +\sqrt{{\mathrm e}^{2 i c} b^{2}-a^{2} {\mathrm e}^{2 i c}}}\right) x^{n} \left(-1\right)^{\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} {\mathrm e}^{-i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)} {\mathrm e}^{i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}} {\mathrm e}^{i \pi  n \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}} {\mathrm e}^{-i \pi  n \mathrm{csgn}\left(i e x \right)^{3}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(i e x \right)^{3}}{2}} {\mathrm e}^{i c}}{d n e a \sqrt{{\mathrm e}^{2 i c} b^{2}-a^{2} {\mathrm e}^{2 i c}}}+\frac{e^{2 n} b \dilog \left(\frac{a \,{\mathrm e}^{i \left(d \,x^{n}+2 c \right)}}{{\mathrm e}^{i c} b -\sqrt{{\mathrm e}^{2 i c} b^{2}-a^{2} {\mathrm e}^{2 i c}}}+\frac{{\mathrm e}^{i c} b}{{\mathrm e}^{i c} b -\sqrt{{\mathrm e}^{2 i c} b^{2}-a^{2} {\mathrm e}^{2 i c}}}-\frac{\sqrt{{\mathrm e}^{2 i c} b^{2}-a^{2} {\mathrm e}^{2 i c}}}{{\mathrm e}^{i c} b -\sqrt{{\mathrm e}^{2 i c} b^{2}-a^{2} {\mathrm e}^{2 i c}}}\right) \left(-1\right)^{\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} {\mathrm e}^{-i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)} {\mathrm e}^{i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}} {\mathrm e}^{i \pi  n \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}} {\mathrm e}^{-i \pi  n \mathrm{csgn}\left(i e x \right)^{3}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(i e x \right)^{3}}{2}} {\mathrm e}^{i c}}{d^{2} n e a \sqrt{{\mathrm e}^{2 i c} b^{2}-a^{2} {\mathrm e}^{2 i c}}}-\frac{e^{2 n} b \dilog \left(\frac{a \,{\mathrm e}^{i \left(d \,x^{n}+2 c \right)}}{{\mathrm e}^{i c} b +\sqrt{{\mathrm e}^{2 i c} b^{2}-a^{2} {\mathrm e}^{2 i c}}}+\frac{{\mathrm e}^{i c} b}{{\mathrm e}^{i c} b +\sqrt{{\mathrm e}^{2 i c} b^{2}-a^{2} {\mathrm e}^{2 i c}}}+\frac{\sqrt{{\mathrm e}^{2 i c} b^{2}-a^{2} {\mathrm e}^{2 i c}}}{{\mathrm e}^{i c} b +\sqrt{{\mathrm e}^{2 i c} b^{2}-a^{2} {\mathrm e}^{2 i c}}}\right) \left(-1\right)^{\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} {\mathrm e}^{-i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)} {\mathrm e}^{i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}} {\mathrm e}^{i \pi  n \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}} {\mathrm e}^{-i \pi  n \mathrm{csgn}\left(i e x \right)^{3}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(i e x \right)^{3}}{2}} {\mathrm e}^{i c}}{d^{2} n e a \sqrt{{\mathrm e}^{2 i c} b^{2}-a^{2} {\mathrm e}^{2 i c}}}"," ",0,"1/2/a/n*x*exp(1/2*(-1+2*n)*(-I*Pi*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+I*Pi*csgn(I*e)*csgn(I*e*x)^2+I*Pi*csgn(I*x)*csgn(I*e*x)^2-I*Pi*csgn(I*e*x)^3+2*ln(x)+2*ln(e)))+I/d/n/e*(e^n)^2/a*b*ln((a*exp(I*(d*x^n+2*c))+exp(I*c)*b-(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))/(exp(I*c)*b-(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)))/(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)*x^n*(-1)^(1/2*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*(-1)^(-1/2*csgn(I*x)*csgn(I*e*x)^2)*(-1)^(-1/2*csgn(I*e)*csgn(I*e*x)^2)*exp(-I*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*exp(I*Pi*n*csgn(I*e)*csgn(I*e*x)^2)*exp(I*Pi*n*csgn(I*x)*csgn(I*e*x)^2)*exp(-I*Pi*n*csgn(I*e*x)^3)*exp(1/2*I*Pi*csgn(I*e*x)^3)*exp(I*c)-I/d/n/e*(e^n)^2/a*b*ln((a*exp(I*(d*x^n+2*c))+exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))/(exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)))/(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)*x^n*(-1)^(1/2*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*(-1)^(-1/2*csgn(I*x)*csgn(I*e*x)^2)*(-1)^(-1/2*csgn(I*e)*csgn(I*e*x)^2)*exp(-I*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*exp(I*Pi*n*csgn(I*e)*csgn(I*e*x)^2)*exp(I*Pi*n*csgn(I*x)*csgn(I*e*x)^2)*exp(-I*Pi*n*csgn(I*e*x)^3)*exp(1/2*I*Pi*csgn(I*e*x)^3)*exp(I*c)+1/d^2/n/e*(e^n)^2/a*b*dilog(a/(exp(I*c)*b-(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))*exp(I*(d*x^n+2*c))+1/(exp(I*c)*b-(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))*exp(I*c)*b-1/(exp(I*c)*b-(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))*(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))/(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)*(-1)^(1/2*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*(-1)^(-1/2*csgn(I*x)*csgn(I*e*x)^2)*(-1)^(-1/2*csgn(I*e)*csgn(I*e*x)^2)*exp(-I*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*exp(I*Pi*n*csgn(I*e)*csgn(I*e*x)^2)*exp(I*Pi*n*csgn(I*x)*csgn(I*e*x)^2)*exp(-I*Pi*n*csgn(I*e*x)^3)*exp(1/2*I*Pi*csgn(I*e*x)^3)*exp(I*c)-1/d^2/n/e*(e^n)^2/a*b*dilog(a/(exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))*exp(I*(d*x^n+2*c))+1/(exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))*exp(I*c)*b+1/(exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))*(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))/(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)*(-1)^(1/2*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*(-1)^(-1/2*csgn(I*x)*csgn(I*e*x)^2)*(-1)^(-1/2*csgn(I*e)*csgn(I*e*x)^2)*exp(-I*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*exp(I*Pi*n*csgn(I*e)*csgn(I*e*x)^2)*exp(I*Pi*n*csgn(I*x)*csgn(I*e*x)^2)*exp(-I*Pi*n*csgn(I*e*x)^3)*exp(1/2*I*Pi*csgn(I*e*x)^3)*exp(I*c)","C"
80,0,0,451,1.951000," ","int((e*x)^(-1+3*n)/(a+b*sec(c+d*x^n)),x)","\int \frac{\left(e x \right)^{-1+3 n}}{a +b \sec \left(c +d \,x^{n}\right)}\, dx"," ",0,"int((e*x)^(-1+3*n)/(a+b*sec(c+d*x^n)),x)","F"
81,1,704,148,1.330000," ","int((e*x)^(-1+n)/(a+b*sec(c+d*x^n))^2,x)","\frac{x \,{\mathrm e}^{\frac{\left(-1+n \right) \left(-i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)+i \pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}+i \pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}-i \pi  \mathrm{csgn}\left(i e x \right)^{3}+2 \ln \left(x \right)+2 \ln \left(e \right)\right)}{2}}}{a^{2} n}+\frac{2 i b^{2} x \,x^{-n} \left(\frac{b \,e^{n} x^{n} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} \left(-1\right)^{\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(i e x \right)^{3}}{2}} {\mathrm e}^{-\frac{i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)}{2}} {\mathrm e}^{\frac{i \pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} {\mathrm e}^{\frac{i \pi  n \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} {\mathrm e}^{-\frac{i \pi  n \mathrm{csgn}\left(i e x \right)^{3}}{2}} {\mathrm e}^{i x^{n} d} {\mathrm e}^{i c}}{e x}+\frac{a \,e^{n} x^{n} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} \left(-1\right)^{-\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}}{2}} \left(-1\right)^{\frac{\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)}{2}} {\mathrm e}^{\frac{i \pi  \,\mathrm{csgn}\left(i e x \right) \left(-n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right)+n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)+n \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)-n \mathrm{csgn}\left(i e x \right)^{2}+\mathrm{csgn}\left(i e x \right)^{2}\right)}{2}}}{e x}\right)}{a^{2} \left(a^{2}-b^{2}\right) d n \left({\mathrm e}^{2 i \left(c +d \,x^{n}\right)} a +2 b \,{\mathrm e}^{i \left(c +d \,x^{n}\right)}+a \right)}+\frac{2 i \arctan \left(\frac{2 a \,{\mathrm e}^{i \left(d \,x^{n}+2 c \right)}+2 \,{\mathrm e}^{i c} b}{2 \sqrt{a^{2} {\mathrm e}^{2 i c}-{\mathrm e}^{2 i c} b^{2}}}\right) e^{n} \left(-2 a^{2}+b^{2}\right) b \,{\mathrm e}^{\frac{i \left(-\pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)+\pi  n \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}+\pi  n \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}-\pi  n \mathrm{csgn}\left(i e x \right)^{3}+\pi  \,\mathrm{csgn}\left(i e x \right) \mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i x \right)-\pi  \,\mathrm{csgn}\left(i e \right) \mathrm{csgn}\left(i e x \right)^{2}-\pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i e x \right)^{2}+\pi  \mathrm{csgn}\left(i e x \right)^{3}+2 c \right)}{2}}}{\sqrt{a^{2} {\mathrm e}^{2 i c}-{\mathrm e}^{2 i c} b^{2}}\, d e n \left(-a^{2}+b^{2}\right) a^{2}}"," ",0,"1/a^2/n*x*exp(1/2*(-1+n)*(-I*Pi*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+I*Pi*csgn(I*e)*csgn(I*e*x)^2+I*Pi*csgn(I*x)*csgn(I*e*x)^2-I*Pi*csgn(I*e*x)^3+2*ln(x)+2*ln(e)))+2*I*b^2*x/a^2/(a^2-b^2)/d/n/(x^n)/(exp(2*I*(c+d*x^n))*a+2*b*exp(I*(c+d*x^n))+a)*(b*e^n*x^n/e/x*(-1)^(-1/2*csgn(I*x)*csgn(I*e*x)^2)*(-1)^(-1/2*csgn(I*e)*csgn(I*e*x)^2)*(-1)^(1/2*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*exp(1/2*I*Pi*csgn(I*e*x)^3)*exp(-1/2*I*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*exp(1/2*I*Pi*n*csgn(I*e)*csgn(I*e*x)^2)*exp(1/2*I*Pi*n*csgn(I*x)*csgn(I*e*x)^2)*exp(-1/2*I*Pi*n*csgn(I*e*x)^3)*exp(I*x^n*d)*exp(I*c)+a*e^n*x^n/e/x*(-1)^(-1/2*csgn(I*x)*csgn(I*e*x)^2)*(-1)^(-1/2*csgn(I*e)*csgn(I*e*x)^2)*(-1)^(1/2*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*exp(1/2*I*Pi*csgn(I*e*x)*(-n*csgn(I*e)*csgn(I*x)+n*csgn(I*e)*csgn(I*e*x)+n*csgn(I*x)*csgn(I*e*x)-n*csgn(I*e*x)^2+csgn(I*e*x)^2)))+2*I*arctan(1/2*(2*a*exp(I*(d*x^n+2*c))+2*exp(I*c)*b)/(a^2*exp(2*I*c)-exp(2*I*c)*b^2)^(1/2))/(a^2*exp(2*I*c)-exp(2*I*c)*b^2)^(1/2)/d/e*e^n/n/(-a^2+b^2)*(-2*a^2+b^2)/a^2*b*exp(1/2*I*(-Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+Pi*n*csgn(I*e)*csgn(I*e*x)^2+Pi*n*csgn(I*x)*csgn(I*e*x)^2-Pi*n*csgn(I*e*x)^3+Pi*csgn(I*e*x)*csgn(I*e)*csgn(I*x)-Pi*csgn(I*e)*csgn(I*e*x)^2-Pi*csgn(I*x)*csgn(I*e*x)^2+Pi*csgn(I*e*x)^3+2*c))","C"
82,1,2817,713,1.142000," ","int((e*x)^(-1+2*n)/(a+b*sec(c+d*x^n))^2,x)","\text{output too large to display}"," ",0,"1/2/a^2/n*x*exp(1/2*(-1+2*n)*(-I*Pi*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+I*Pi*csgn(I*e)*csgn(I*e*x)^2+I*Pi*csgn(I*x)*csgn(I*e*x)^2-I*Pi*csgn(I*e*x)^3+2*ln(x)+2*ln(e)))+2*I*b^2*x/a^2/(a^2-b^2)/d/n/(x^n)/(exp(2*I*(c+d*x^n))*a+2*b*exp(I*(c+d*x^n))+a)*(b*(e^n)^2*(x^n)^2/e/x*(-1)^(-1/2*csgn(I*x)*csgn(I*e*x)^2)*(-1)^(-1/2*csgn(I*e)*csgn(I*e*x)^2)*(-1)^(1/2*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*exp(1/2*I*Pi*csgn(I*e*x)^3)*exp(-I*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*exp(I*Pi*n*csgn(I*e)*csgn(I*e*x)^2)*exp(I*Pi*n*csgn(I*x)*csgn(I*e*x)^2)*exp(-I*Pi*n*csgn(I*e*x)^3)*exp(I*x^n*d)*exp(I*c)+a*(e^n)^2*(x^n)^2/e/x*(-1)^(-1/2*csgn(I*x)*csgn(I*e*x)^2)*(-1)^(-1/2*csgn(I*e)*csgn(I*e*x)^2)*(-1)^(1/2*csgn(I*e)*csgn(I*x)*csgn(I*e*x))*exp(1/2*I*Pi*csgn(I*e*x)*(-2*n*csgn(I*e)*csgn(I*x)+2*n*csgn(I*e)*csgn(I*e*x)+2*n*csgn(I*x)*csgn(I*e*x)-2*n*csgn(I*e*x)^2+csgn(I*e*x)^2)))-I*b^3/a^2/(a^2-b^2)/d*ln((-a*exp(I*(d*x^n+2*c))-exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))/(-exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)))/(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)*x^n/n/e*(e^n)^2*exp(1/2*I*(-2*Pi*n*csgn(I*e*x)^3+2*Pi*n*csgn(I*e)*csgn(I*e*x)^2+2*Pi*n*csgn(I*x)*csgn(I*e*x)^2-2*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+Pi*csgn(I*e*x)^3-Pi*csgn(I*e)*csgn(I*e*x)^2-Pi*csgn(I*x)*csgn(I*e*x)^2+Pi*csgn(I*e*x)*csgn(I*e)*csgn(I*x)+2*c))-2*I*b/(a^2-b^2)/d*ln((a*exp(I*(d*x^n+2*c))+exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))/(exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)))/(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)*x^n/n/e*(e^n)^2*exp(1/2*I*(-2*Pi*n*csgn(I*e*x)^3+2*Pi*n*csgn(I*e)*csgn(I*e*x)^2+2*Pi*n*csgn(I*x)*csgn(I*e*x)^2-2*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+Pi*csgn(I*e*x)^3-Pi*csgn(I*e)*csgn(I*e*x)^2-Pi*csgn(I*x)*csgn(I*e*x)^2+Pi*csgn(I*e*x)*csgn(I*e)*csgn(I*x)+2*c))+I*b^3/a^2/(a^2-b^2)/d*ln((a*exp(I*(d*x^n+2*c))+exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))/(exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)))/(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)*x^n/n/e*(e^n)^2*exp(1/2*I*(-2*Pi*n*csgn(I*e*x)^3+2*Pi*n*csgn(I*e)*csgn(I*e*x)^2+2*Pi*n*csgn(I*x)*csgn(I*e*x)^2-2*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+Pi*csgn(I*e*x)^3-Pi*csgn(I*e)*csgn(I*e*x)^2-Pi*csgn(I*x)*csgn(I*e*x)^2+Pi*csgn(I*e*x)*csgn(I*e)*csgn(I*x)+2*c))+2*I*b/(a^2-b^2)/d*ln((-a*exp(I*(d*x^n+2*c))-exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))/(-exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)))/(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)*x^n/n/e*(e^n)^2*exp(1/2*I*(-2*Pi*n*csgn(I*e*x)^3+2*Pi*n*csgn(I*e)*csgn(I*e*x)^2+2*Pi*n*csgn(I*x)*csgn(I*e*x)^2-2*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+Pi*csgn(I*e*x)^3-Pi*csgn(I*e)*csgn(I*e*x)^2-Pi*csgn(I*x)*csgn(I*e*x)^2+Pi*csgn(I*e*x)*csgn(I*e)*csgn(I*x)+2*c))-2*b^2/a^2/(a^2-b^2)/d^2*ln(exp(I*x^n*d))/n/e*(e^n)^2*exp(1/2*I*csgn(I*e*x)*Pi*(-1+2*n)*(csgn(I*e*x)-csgn(I*x))*(-csgn(I*e*x)+csgn(I*e)))+b^2/a^2/(a^2-b^2)/d^2*ln(exp(2*I*(c+d*x^n))*a+2*b*exp(I*(c+d*x^n))+a)/n/e*(e^n)^2*exp(1/2*I*csgn(I*e*x)*Pi*(-1+2*n)*(csgn(I*e*x)-csgn(I*x))*(-csgn(I*e*x)+csgn(I*e)))+b^3/a^2/(a^2-b^2)/d^2*dilog((a*exp(I*(d*x^n+2*c))+exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))/(exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)))/(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)/n/e*(e^n)^2*exp(1/2*I*(-2*Pi*n*csgn(I*e*x)^3+2*Pi*n*csgn(I*e)*csgn(I*e*x)^2+2*Pi*n*csgn(I*x)*csgn(I*e*x)^2-2*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+Pi*csgn(I*e*x)^3-Pi*csgn(I*e)*csgn(I*e*x)^2-Pi*csgn(I*x)*csgn(I*e*x)^2+Pi*csgn(I*e*x)*csgn(I*e)*csgn(I*x)+2*c))+2*b/(a^2-b^2)/d^2*dilog((-a*exp(I*(d*x^n+2*c))-exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))/(-exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)))/(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)/n/e*(e^n)^2*exp(1/2*I*(-2*Pi*n*csgn(I*e*x)^3+2*Pi*n*csgn(I*e)*csgn(I*e*x)^2+2*Pi*n*csgn(I*x)*csgn(I*e*x)^2-2*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+Pi*csgn(I*e*x)^3-Pi*csgn(I*e)*csgn(I*e*x)^2-Pi*csgn(I*x)*csgn(I*e*x)^2+Pi*csgn(I*e*x)*csgn(I*e)*csgn(I*x)+2*c))-b^3/a^2/(a^2-b^2)/d^2*dilog((-a*exp(I*(d*x^n+2*c))-exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))/(-exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)))/(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)/n/e*(e^n)^2*exp(1/2*I*(-2*Pi*n*csgn(I*e*x)^3+2*Pi*n*csgn(I*e)*csgn(I*e*x)^2+2*Pi*n*csgn(I*x)*csgn(I*e*x)^2-2*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+Pi*csgn(I*e*x)^3-Pi*csgn(I*e)*csgn(I*e*x)^2-Pi*csgn(I*x)*csgn(I*e*x)^2+Pi*csgn(I*e*x)*csgn(I*e)*csgn(I*x)+2*c))-2*b/(a^2-b^2)/d^2*dilog((a*exp(I*(d*x^n+2*c))+exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2))/(exp(I*c)*b+(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)))/(exp(2*I*c)*b^2-a^2*exp(2*I*c))^(1/2)/n/e*(e^n)^2*exp(1/2*I*(-2*Pi*n*csgn(I*e*x)^3+2*Pi*n*csgn(I*e)*csgn(I*e*x)^2+2*Pi*n*csgn(I*x)*csgn(I*e*x)^2-2*Pi*n*csgn(I*e)*csgn(I*x)*csgn(I*e*x)+Pi*csgn(I*e*x)^3-Pi*csgn(I*e)*csgn(I*e*x)^2-Pi*csgn(I*x)*csgn(I*e*x)^2+Pi*csgn(I*e*x)*csgn(I*e)*csgn(I*x)+2*c))","C"
83,0,0,1303,2.933000," ","int((e*x)^(-1+3*n)/(a+b*sec(c+d*x^n))^2,x)","\int \frac{\left(e x \right)^{-1+3 n}}{\left(a +b \sec \left(c +d \,x^{n}\right)\right)^{2}}\, dx"," ",0,"int((e*x)^(-1+3*n)/(a+b*sec(c+d*x^n))^2,x)","F"