1,1,17,37,0.075000," ","int(2/(3-cos(4+6*x)),x)","\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, \tan \left(2+3 x \right)\right)}{6}"," ",0,"1/6*2^(1/2)*arctan(2^(1/2)*tan(2+3*x))","A"
2,1,17,37,0.305000," ","int(2*csc(4+6*x)/(-cot(4+6*x)+3*csc(4+6*x)),x)","\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, \tan \left(2+3 x \right)\right)}{6}"," ",0,"1/6*2^(1/2)*arctan(2^(1/2)*tan(2+3*x))","A"
3,1,17,41,0.168000," ","int(1/(1+sin(2+3*x)^2),x)","\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, \tan \left(2+3 x \right)\right)}{6}"," ",0,"1/6*2^(1/2)*arctan(2^(1/2)*tan(2+3*x))","A"
4,1,17,41,0.099000," ","int(1/(2-cos(2+3*x)^2),x)","\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, \tan \left(2+3 x \right)\right)}{6}"," ",0,"1/6*2^(1/2)*arctan(2^(1/2)*tan(2+3*x))","A"
5,1,17,41,0.227000," ","int(1/(cos(2+3*x)^2+2*sin(2+3*x)^2),x)","\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, \tan \left(2+3 x \right)\right)}{6}"," ",0,"1/6*2^(1/2)*arctan(2^(1/2)*tan(2+3*x))","A"
6,1,17,41,0.288000," ","int(sec(2+3*x)^2/(1+2*tan(2+3*x)^2),x)","\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, \tan \left(2+3 x \right)\right)}{6}"," ",0,"1/6*2^(1/2)*arctan(2^(1/2)*tan(2+3*x))","A"
7,1,17,41,0.286000," ","int(csc(2+3*x)^2/(2+cot(2+3*x)^2),x)","\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, \tan \left(2+3 x \right)\right)}{6}"," ",0,"1/6*2^(1/2)*arctan(2^(1/2)*tan(2+3*x))","A"
8,1,17,48,0.058000," ","int(2/(1-3*cos(4+6*x)),x)","-\frac{\sqrt{2}\, \arctanh \left(\sqrt{2}\, \tan \left(2+3 x \right)\right)}{6}"," ",0,"-1/6*2^(1/2)*arctanh(2^(1/2)*tan(2+3*x))","A"
9,1,17,48,0.303000," ","int(2*csc(4+6*x)/(-3*cot(4+6*x)+csc(4+6*x)),x)","-\frac{\sqrt{2}\, \arctanh \left(\sqrt{2}\, \tan \left(2+3 x \right)\right)}{6}"," ",0,"-1/6*2^(1/2)*arctanh(2^(1/2)*tan(2+3*x))","A"
10,1,17,48,0.148000," ","int(1/(-1+3*sin(2+3*x)^2),x)","-\frac{\sqrt{2}\, \arctanh \left(\sqrt{2}\, \tan \left(2+3 x \right)\right)}{6}"," ",0,"-1/6*2^(1/2)*arctanh(2^(1/2)*tan(2+3*x))","A"
11,1,17,48,0.098000," ","int(1/(2-3*cos(2+3*x)^2),x)","-\frac{\sqrt{2}\, \arctanh \left(\sqrt{2}\, \tan \left(2+3 x \right)\right)}{6}"," ",0,"-1/6*2^(1/2)*arctanh(2^(1/2)*tan(2+3*x))","A"
12,1,17,48,0.225000," ","int(1/(-cos(2+3*x)^2+2*sin(2+3*x)^2),x)","-\frac{\sqrt{2}\, \arctanh \left(\sqrt{2}\, \tan \left(2+3 x \right)\right)}{6}"," ",0,"-1/6*2^(1/2)*arctanh(2^(1/2)*tan(2+3*x))","A"
13,1,17,48,0.277000," ","int(sec(2+3*x)^2/(-1+2*tan(2+3*x)^2),x)","-\frac{\sqrt{2}\, \arctanh \left(\sqrt{2}\, \tan \left(2+3 x \right)\right)}{6}"," ",0,"-1/6*2^(1/2)*arctanh(2^(1/2)*tan(2+3*x))","A"
14,1,17,48,0.263000," ","int(csc(2+3*x)^2/(2-cot(2+3*x)^2),x)","-\frac{\sqrt{2}\, \arctanh \left(\sqrt{2}\, \tan \left(2+3 x \right)\right)}{6}"," ",0,"-1/6*2^(1/2)*arctanh(2^(1/2)*tan(2+3*x))","A"
15,1,18,35,0.060000," ","int(2/(3+cos(4+6*x)),x)","\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(2+3 x \right)}{2}\right)}{6}"," ",0,"1/6*2^(1/2)*arctan(1/2*2^(1/2)*tan(2+3*x))","A"
16,1,18,35,0.314000," ","int(2*csc(4+6*x)/(cot(4+6*x)+3*csc(4+6*x)),x)","\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(2+3 x \right)}{2}\right)}{6}"," ",0,"1/6*2^(1/2)*arctan(1/2*2^(1/2)*tan(2+3*x))","A"
17,1,18,41,0.146000," ","int(1/(2-sin(2+3*x)^2),x)","\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(2+3 x \right)}{2}\right)}{6}"," ",0,"1/6*2^(1/2)*arctan(1/2*2^(1/2)*tan(2+3*x))","A"
18,1,18,41,0.095000," ","int(1/(1+cos(2+3*x)^2),x)","\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(2+3 x \right)}{2}\right)}{6}"," ",0,"1/6*2^(1/2)*arctan(1/2*2^(1/2)*tan(2+3*x))","A"
19,1,18,41,0.228000," ","int(1/(2*cos(2+3*x)^2+sin(2+3*x)^2),x)","\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(2+3 x \right)}{2}\right)}{6}"," ",0,"1/6*2^(1/2)*arctan(1/2*2^(1/2)*tan(2+3*x))","A"
20,1,18,41,0.269000," ","int(sec(2+3*x)^2/(2+tan(2+3*x)^2),x)","\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(2+3 x \right)}{2}\right)}{6}"," ",0,"1/6*2^(1/2)*arctan(1/2*2^(1/2)*tan(2+3*x))","A"
21,1,18,41,0.276000," ","int(csc(2+3*x)^2/(1+2*cot(2+3*x)^2),x)","\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(2+3 x \right)}{2}\right)}{6}"," ",0,"1/6*2^(1/2)*arctan(1/2*2^(1/2)*tan(2+3*x))","A"
22,1,18,49,0.059000," ","int(-2/(1+3*cos(4+6*x)),x)","-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}\, \tan \left(2+3 x \right)}{2}\right)}{6}"," ",0,"-1/6*2^(1/2)*arctanh(1/2*2^(1/2)*tan(2+3*x))","A"
23,1,18,49,0.313000," ","int(-2*csc(4+6*x)/(3*cot(4+6*x)+csc(4+6*x)),x)","-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}\, \tan \left(2+3 x \right)}{2}\right)}{6}"," ",0,"-1/6*2^(1/2)*arctanh(1/2*2^(1/2)*tan(2+3*x))","A"
24,1,18,49,0.147000," ","int(1/(-2+3*sin(2+3*x)^2),x)","-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}\, \tan \left(2+3 x \right)}{2}\right)}{6}"," ",0,"-1/6*2^(1/2)*arctanh(1/2*2^(1/2)*tan(2+3*x))","A"
25,1,18,49,0.096000," ","int(1/(1-3*cos(2+3*x)^2),x)","-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}\, \tan \left(2+3 x \right)}{2}\right)}{6}"," ",0,"-1/6*2^(1/2)*arctanh(1/2*2^(1/2)*tan(2+3*x))","A"
26,1,18,49,0.229000," ","int(1/(-2*cos(2+3*x)^2+sin(2+3*x)^2),x)","-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}\, \tan \left(2+3 x \right)}{2}\right)}{6}"," ",0,"-1/6*2^(1/2)*arctanh(1/2*2^(1/2)*tan(2+3*x))","A"
27,1,18,49,0.277000," ","int(sec(2+3*x)^2/(-2+tan(2+3*x)^2),x)","-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}\, \tan \left(2+3 x \right)}{2}\right)}{6}"," ",0,"-1/6*2^(1/2)*arctanh(1/2*2^(1/2)*tan(2+3*x))","A"
28,1,18,49,0.302000," ","int(csc(2+3*x)^2/(1-2*cot(2+3*x)^2),x)","-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}\, \tan \left(2+3 x \right)}{2}\right)}{6}"," ",0,"-1/6*2^(1/2)*arctanh(1/2*2^(1/2)*tan(2+3*x))","A"
29,1,25,24,0.037000," ","int((x+sin(x))^2,x)","\frac{x}{2}+\frac{x^{3}}{3}-2 x \cos \left(x \right)+2 \sin \left(x \right)-\frac{\cos \left(x \right) \sin \left(x \right)}{2}"," ",0,"1/2*x+1/3*x^3-2*x*cos(x)+2*sin(x)-1/2*cos(x)*sin(x)","A"
30,1,57,46,0.039000," ","int((x+sin(x))^3,x)","-\frac{\left(2+\sin^{2}\left(x \right)\right) \cos \left(x \right)}{3}+3 x \left(-\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)-\frac{3 x^{2}}{4}+\frac{3 \left(\sin^{2}\left(x \right)\right)}{4}-3 x^{2} \cos \left(x \right)+6 \cos \left(x \right)+6 x \sin \left(x \right)+\frac{x^{4}}{4}"," ",0,"-1/3*(2+sin(x)^2)*cos(x)+3*x*(-1/2*cos(x)*sin(x)+1/2*x)-3/4*x^2+3/4*sin(x)^2-3*x^2*cos(x)+6*cos(x)+6*x*sin(x)+1/4*x^4","A"
31,1,229,157,0.053000," ","int(sin(b*x+a)/(d*x^2+c),x)","b \left(\frac{\Si \left(b x +a -\frac{b \sqrt{-c d}+d a}{d}\right) \cos \left(\frac{b \sqrt{-c d}+d a}{d}\right)+\Ci \left(b x +a -\frac{b \sqrt{-c d}+d a}{d}\right) \sin \left(\frac{b \sqrt{-c d}+d a}{d}\right)}{2 \left(\frac{b \sqrt{-c d}+d a}{d}-a \right) d}+\frac{\Si \left(b x +a +\frac{b \sqrt{-c d}-d a}{d}\right) \cos \left(\frac{b \sqrt{-c d}-d a}{d}\right)-\Ci \left(b x +a +\frac{b \sqrt{-c d}-d a}{d}\right) \sin \left(\frac{b \sqrt{-c d}-d a}{d}\right)}{2 \left(-\frac{b \sqrt{-c d}-d a}{d}-a \right) d}\right)"," ",0,"b*(1/2/((b*(-c*d)^(1/2)+d*a)/d-a)/d*(Si(b*x+a-(b*(-c*d)^(1/2)+d*a)/d)*cos((b*(-c*d)^(1/2)+d*a)/d)+Ci(b*x+a-(b*(-c*d)^(1/2)+d*a)/d)*sin((b*(-c*d)^(1/2)+d*a)/d))+1/2/(-(b*(-c*d)^(1/2)-d*a)/d-a)/d*(Si(b*x+a+(b*(-c*d)^(1/2)-d*a)/d)*cos((b*(-c*d)^(1/2)-d*a)/d)-Ci(b*x+a+(b*(-c*d)^(1/2)-d*a)/d)*sin((b*(-c*d)^(1/2)-d*a)/d)))","A"
32,1,320,231,0.043000," ","int(sin(b*x+a)/(e*x^2+d*x+c),x)","b \left(\frac{\Si \left(b x +a -\frac{2 a e -d b +\sqrt{-4 b^{2} c e +b^{2} d^{2}}}{2 e}\right) \cos \left(\frac{2 a e -d b +\sqrt{-4 b^{2} c e +b^{2} d^{2}}}{2 e}\right)+\Ci \left(b x +a -\frac{2 a e -d b +\sqrt{-4 b^{2} c e +b^{2} d^{2}}}{2 e}\right) \sin \left(\frac{2 a e -d b +\sqrt{-4 b^{2} c e +b^{2} d^{2}}}{2 e}\right)}{\sqrt{-4 b^{2} c e +b^{2} d^{2}}}-\frac{\Si \left(b x +a +\frac{-2 a e +d b +\sqrt{-4 b^{2} c e +b^{2} d^{2}}}{2 e}\right) \cos \left(\frac{-2 a e +d b +\sqrt{-4 b^{2} c e +b^{2} d^{2}}}{2 e}\right)-\Ci \left(b x +a +\frac{-2 a e +d b +\sqrt{-4 b^{2} c e +b^{2} d^{2}}}{2 e}\right) \sin \left(\frac{-2 a e +d b +\sqrt{-4 b^{2} c e +b^{2} d^{2}}}{2 e}\right)}{\sqrt{-4 b^{2} c e +b^{2} d^{2}}}\right)"," ",0,"b*(1/(-4*b^2*c*e+b^2*d^2)^(1/2)*(Si(b*x+a-1/2/e*(2*a*e-d*b+(-4*b^2*c*e+b^2*d^2)^(1/2)))*cos(1/2/e*(2*a*e-d*b+(-4*b^2*c*e+b^2*d^2)^(1/2)))+Ci(b*x+a-1/2/e*(2*a*e-d*b+(-4*b^2*c*e+b^2*d^2)^(1/2)))*sin(1/2/e*(2*a*e-d*b+(-4*b^2*c*e+b^2*d^2)^(1/2))))-1/(-4*b^2*c*e+b^2*d^2)^(1/2)*(Si(b*x+a+1/2*(-2*a*e+d*b+(-4*b^2*c*e+b^2*d^2)^(1/2))/e)*cos(1/2*(-2*a*e+d*b+(-4*b^2*c*e+b^2*d^2)^(1/2))/e)-Ci(b*x+a+1/2*(-2*a*e+d*b+(-4*b^2*c*e+b^2*d^2)^(1/2))/e)*sin(1/2*(-2*a*e+d*b+(-4*b^2*c*e+b^2*d^2)^(1/2))/e)))","A"
33,1,9,8,0.007000," ","int(sin((-7+x)^(1/2))/(-7+x)^(1/2),x)","-2 \cos \left(\sqrt{-7+x}\right)"," ",0,"-2*cos((-7+x)^(1/2))","A"
34,1,72,24,0.079000," ","int(sin(x)*(b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x)","-\frac{\sqrt{-\frac{-b \,x^{2}+a}{x^{2}}}\, \left(b \,x^{2}-a \right) x \sqrt{\frac{-b \,x^{2}+a}{b \,x^{2}-a}}\, \left(-i \Si \left(x \right)+\frac{i \pi  \,\mathrm{csgn}\left(x \right)}{2}\right)}{\left(-b \,x^{2}+a \right)^{\frac{3}{2}}}"," ",0,"-(-(-b*x^2+a)/x^2)^(1/2)*(b*x^2-a)/(-b*x^2+a)^(3/2)*x*(1/(b*x^2-a)*(-b*x^2+a))^(1/2)*(-I*Si(x)+1/2*I*Pi*csgn(x))","C"
35,1,12,12,0.076000," ","int(1/x/(1+sin(ln(x))),x)","-\frac{2}{\tan \left(\frac{\ln \left(x \right)}{2}\right)+1}"," ",0,"-2/(tan(1/2*ln(x))+1)","A"
36,1,142,100,0.036000," ","int(sin((b*x+a)/(d*x+c)),x)","-\left(d a -c b \right) \left(-\frac{\sin \left(\frac{b}{d}+\frac{d a -c b}{d \left(d x +c \right)}\right)}{\left(\left(\frac{b}{d}+\frac{d a -c b}{d \left(d x +c \right)}\right) d -b \right) d}+\frac{-\frac{\Si \left(\frac{d a -c b}{d \left(d x +c \right)}\right) \sin \left(\frac{b}{d}\right)}{d}+\frac{\Ci \left(\frac{d a -c b}{d \left(d x +c \right)}\right) \cos \left(\frac{b}{d}\right)}{d}}{d}\right)"," ",0,"-(a*d-b*c)*(-sin(b/d+(a*d-b*c)/d/(d*x+c))/((b/d+(a*d-b*c)/d/(d*x+c))*d-b)/d+(-Si((a*d-b*c)/d/(d*x+c))*sin(b/d)/d+Ci((a*d-b*c)/d/(d*x+c))*cos(b/d)/d)/d)","A"
37,1,195,107,0.071000," ","int(sin((b*x+a)/(d*x+c))^2,x)","-\frac{\left(d a -c b \right) \left(-\frac{d}{2 \left(\left(\frac{b}{d}+\frac{d a -c b}{d \left(d x +c \right)}\right) d -b \right)}-\frac{d^{2} \left(-\frac{2 \cos \left(\frac{2 d a -2 c b}{d \left(d x +c \right)}+\frac{2 b}{d}\right)}{\left(\left(\frac{b}{d}+\frac{d a -c b}{d \left(d x +c \right)}\right) d -b \right) d}-\frac{2 \left(\frac{2 \Si \left(\frac{2 d a -2 c b}{d \left(d x +c \right)}\right) \cos \left(\frac{2 b}{d}\right)}{d}+\frac{2 \Ci \left(\frac{2 d a -2 c b}{d \left(d x +c \right)}\right) \sin \left(\frac{2 b}{d}\right)}{d}\right)}{d}\right)}{4}\right)}{d^{2}}"," ",0,"-1/d^2*(a*d-b*c)*(-1/2*d/((b/d+(a*d-b*c)/d/(d*x+c))*d-b)-1/4*d^2*(-2*cos(2*(a*d-b*c)/d/(d*x+c)+2*b/d)/((b/d+(a*d-b*c)/d/(d*x+c))*d-b)/d-2*(2*Si(2*(a*d-b*c)/d/(d*x+c))*cos(2*b/d)/d+2*Ci(2*(a*d-b*c)/d/(d*x+c))*sin(2*b/d)/d)/d))","A"
38,1,295,186,0.070000," ","int(sin((b*x+a)/(d*x+c))^3,x)","-\frac{\left(d a -c b \right) \left(-\frac{d^{2} \left(-\frac{3 \sin \left(\frac{3 d a -3 c b}{d \left(d x +c \right)}+\frac{3 b}{d}\right)}{\left(\left(\frac{b}{d}+\frac{d a -c b}{d \left(d x +c \right)}\right) d -b \right) d}+\frac{-\frac{9 \Si \left(\frac{3 d a -3 c b}{d \left(d x +c \right)}\right) \sin \left(\frac{3 b}{d}\right)}{d}+\frac{9 \Ci \left(\frac{3 d a -3 c b}{d \left(d x +c \right)}\right) \cos \left(\frac{3 b}{d}\right)}{d}}{d}\right)}{12}+\frac{3 d^{2} \left(-\frac{\sin \left(\frac{b}{d}+\frac{d a -c b}{d \left(d x +c \right)}\right)}{\left(\left(\frac{b}{d}+\frac{d a -c b}{d \left(d x +c \right)}\right) d -b \right) d}+\frac{-\frac{\Si \left(\frac{d a -c b}{d \left(d x +c \right)}\right) \sin \left(\frac{b}{d}\right)}{d}+\frac{\Ci \left(\frac{d a -c b}{d \left(d x +c \right)}\right) \cos \left(\frac{b}{d}\right)}{d}}{d}\right)}{4}\right)}{d^{2}}"," ",0,"-1/d^2*(a*d-b*c)*(-1/12*d^2*(-3*sin(3*(a*d-b*c)/d/(d*x+c)+3*b/d)/((b/d+(a*d-b*c)/d/(d*x+c))*d-b)/d+3*(-3*Si(3*(a*d-b*c)/d/(d*x+c))*sin(3*b/d)/d+3*Ci(3*(a*d-b*c)/d/(d*x+c))*cos(3*b/d)/d)/d)+3/4*d^2*(-sin(b/d+(a*d-b*c)/d/(d*x+c))/((b/d+(a*d-b*c)/d/(d*x+c))*d-b)/d+(-Si((a*d-b*c)/d/(d*x+c))*sin(b/d)/d+Ci((a*d-b*c)/d/(d*x+c))*cos(b/d)/d)/d))","A"
39,0,0,46,0.576000," ","int(sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))^3/(-a^2*x^2+1),x)","\int \frac{\sin^{3}\left(\frac{\sqrt{-a x +1}}{\sqrt{a x +1}}\right)}{-a^{2} x^{2}+1}\, dx"," ",0,"int(sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))^3/(-a^2*x^2+1),x)","F"
40,0,0,46,0.292000," ","int(sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2/(-a^2*x^2+1),x)","\int \frac{\sin^{2}\left(\frac{\sqrt{-a x +1}}{\sqrt{a x +1}}\right)}{-a^{2} x^{2}+1}\, dx"," ",0,"int(sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2/(-a^2*x^2+1),x)","F"
41,0,0,22,0.070000," ","int(sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))/(-a^2*x^2+1),x)","\int \frac{\sin \left(\frac{\sqrt{-a x +1}}{\sqrt{a x +1}}\right)}{-a^{2} x^{2}+1}\, dx"," ",0,"int(sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))/(-a^2*x^2+1),x)","F"
42,0,0,35,0.179000," ","int(1/(-a^2*x^2+1)/sin((-a*x+1)^(1/2)/(a*x+1)^(1/2)),x)","\int \frac{1}{\left(-a^{2} x^{2}+1\right) \sin \left(\frac{\sqrt{-a x +1}}{\sqrt{a x +1}}\right)}\, dx"," ",0,"int(1/(-a^2*x^2+1)/sin((-a*x+1)^(1/2)/(a*x+1)^(1/2)),x)","F"
43,0,0,37,0.243000," ","int(1/(-a^2*x^2+1)/sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2,x)","\int \frac{1}{\left(-a^{2} x^{2}+1\right) \sin \left(\frac{\sqrt{-a x +1}}{\sqrt{a x +1}}\right)^{2}}\, dx"," ",0,"int(1/(-a^2*x^2+1)/sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2,x)","F"
44,1,25,24,0.035000," ","int((x+cos(x))^2,x)","\frac{x}{2}+\frac{x^{3}}{3}+2 \cos \left(x \right)+2 x \sin \left(x \right)+\frac{\cos \left(x \right) \sin \left(x \right)}{2}"," ",0,"1/2*x+1/3*x^3+2*cos(x)+2*x*sin(x)+1/2*cos(x)*sin(x)","A"
45,1,57,46,0.030000," ","int((x+cos(x))^3,x)","\frac{\left(2+\cos^{2}\left(x \right)\right) \sin \left(x \right)}{3}+3 x \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)-\frac{3 x^{2}}{4}-\frac{3 \left(\sin^{2}\left(x \right)\right)}{4}+3 x^{2} \sin \left(x \right)-6 \sin \left(x \right)+6 x \cos \left(x \right)+\frac{x^{4}}{4}"," ",0,"1/3*(2+cos(x)^2)*sin(x)+3*x*(1/2*cos(x)*sin(x)+1/2*x)-3/4*x^2-3/4*sin(x)^2+3*x^2*sin(x)-6*sin(x)+6*x*cos(x)+1/4*x^4","A"
46,1,229,157,0.048000," ","int(cos(b*x+a)/(d*x^2+c),x)","b \left(\frac{-\Si \left(b x +a -\frac{b \sqrt{-c d}+d a}{d}\right) \sin \left(\frac{b \sqrt{-c d}+d a}{d}\right)+\Ci \left(b x +a -\frac{b \sqrt{-c d}+d a}{d}\right) \cos \left(\frac{b \sqrt{-c d}+d a}{d}\right)}{2 d \left(\frac{b \sqrt{-c d}+d a}{d}-a \right)}+\frac{\Si \left(b x +a +\frac{b \sqrt{-c d}-d a}{d}\right) \sin \left(\frac{b \sqrt{-c d}-d a}{d}\right)+\Ci \left(b x +a +\frac{b \sqrt{-c d}-d a}{d}\right) \cos \left(\frac{b \sqrt{-c d}-d a}{d}\right)}{2 d \left(-\frac{b \sqrt{-c d}-d a}{d}-a \right)}\right)"," ",0,"b*(1/2/d/((b*(-c*d)^(1/2)+d*a)/d-a)*(-Si(b*x+a-(b*(-c*d)^(1/2)+d*a)/d)*sin((b*(-c*d)^(1/2)+d*a)/d)+Ci(b*x+a-(b*(-c*d)^(1/2)+d*a)/d)*cos((b*(-c*d)^(1/2)+d*a)/d))+1/2/d/(-(b*(-c*d)^(1/2)-d*a)/d-a)*(Si(b*x+a+(b*(-c*d)^(1/2)-d*a)/d)*sin((b*(-c*d)^(1/2)-d*a)/d)+Ci(b*x+a+(b*(-c*d)^(1/2)-d*a)/d)*cos((b*(-c*d)^(1/2)-d*a)/d)))","A"
47,1,320,231,0.050000," ","int(cos(b*x+a)/(e*x^2+d*x+c),x)","b \left(\frac{-\Si \left(b x +a -\frac{2 a e -d b +\sqrt{-4 b^{2} c e +b^{2} d^{2}}}{2 e}\right) \sin \left(\frac{2 a e -d b +\sqrt{-4 b^{2} c e +b^{2} d^{2}}}{2 e}\right)+\Ci \left(b x +a -\frac{2 a e -d b +\sqrt{-4 b^{2} c e +b^{2} d^{2}}}{2 e}\right) \cos \left(\frac{2 a e -d b +\sqrt{-4 b^{2} c e +b^{2} d^{2}}}{2 e}\right)}{\sqrt{-4 b^{2} c e +b^{2} d^{2}}}-\frac{\Si \left(b x +a +\frac{-2 a e +d b +\sqrt{-4 b^{2} c e +b^{2} d^{2}}}{2 e}\right) \sin \left(\frac{-2 a e +d b +\sqrt{-4 b^{2} c e +b^{2} d^{2}}}{2 e}\right)+\Ci \left(b x +a +\frac{-2 a e +d b +\sqrt{-4 b^{2} c e +b^{2} d^{2}}}{2 e}\right) \cos \left(\frac{-2 a e +d b +\sqrt{-4 b^{2} c e +b^{2} d^{2}}}{2 e}\right)}{\sqrt{-4 b^{2} c e +b^{2} d^{2}}}\right)"," ",0,"b*(1/(-4*b^2*c*e+b^2*d^2)^(1/2)*(-Si(b*x+a-1/2/e*(2*a*e-d*b+(-4*b^2*c*e+b^2*d^2)^(1/2)))*sin(1/2/e*(2*a*e-d*b+(-4*b^2*c*e+b^2*d^2)^(1/2)))+Ci(b*x+a-1/2/e*(2*a*e-d*b+(-4*b^2*c*e+b^2*d^2)^(1/2)))*cos(1/2/e*(2*a*e-d*b+(-4*b^2*c*e+b^2*d^2)^(1/2))))-1/(-4*b^2*c*e+b^2*d^2)^(1/2)*(Si(b*x+a+1/2*(-2*a*e+d*b+(-4*b^2*c*e+b^2*d^2)^(1/2))/e)*sin(1/2*(-2*a*e+d*b+(-4*b^2*c*e+b^2*d^2)^(1/2))/e)+Ci(b*x+a+1/2*(-2*a*e+d*b+(-4*b^2*c*e+b^2*d^2)^(1/2))/e)*cos(1/2*(-2*a*e+d*b+(-4*b^2*c*e+b^2*d^2)^(1/2))/e)))","A"
48,1,9,8,0.045000," ","int(x*cos((x^2+1)^(1/2))/(x^2+1)^(1/2),x)","\sin \left(\sqrt{x^{2}+1}\right)"," ",0,"sin((x^2+1)^(1/2))","A"
49,1,18,17,0.079000," ","int(x*cos(3^(1/2)*(x^2+2)^(1/2))/(x^2+2)^(1/2),x)","\frac{\sin \left(\sqrt{3}\, \sqrt{x^{2}+2}\right) \sqrt{3}}{3}"," ",0,"1/3*sin(3^(1/2)*(x^2+2)^(1/2))*3^(1/2)","A"
50,1,16,18,0.072000," ","int((-1+2*x)*cos((6+3*(-1+2*x)^2)^(1/2))/(6+3*(-1+2*x)^2)^(1/2),x)","\frac{\sin \left(\sqrt{12 x^{2}-12 x +9}\right)}{6}"," ",0,"1/6*sin((12*x^2-12*x+9)^(1/2))","A"
51,1,142,101,0.095000," ","int(cos((b*x+a)/(d*x+c)),x)","-\left(d a -c b \right) \left(-\frac{\cos \left(\frac{b}{d}+\frac{d a -c b}{d \left(d x +c \right)}\right)}{\left(\left(\frac{b}{d}+\frac{d a -c b}{d \left(d x +c \right)}\right) d -b \right) d}-\frac{\frac{\Si \left(\frac{d a -c b}{d \left(d x +c \right)}\right) \cos \left(\frac{b}{d}\right)}{d}+\frac{\Ci \left(\frac{d a -c b}{d \left(d x +c \right)}\right) \sin \left(\frac{b}{d}\right)}{d}}{d}\right)"," ",0,"-(a*d-b*c)*(-cos(b/d+(a*d-b*c)/d/(d*x+c))/((b/d+(a*d-b*c)/d/(d*x+c))*d-b)/d-(Si((a*d-b*c)/d/(d*x+c))*cos(b/d)/d+Ci((a*d-b*c)/d/(d*x+c))*sin(b/d)/d)/d)","A"
52,1,195,107,0.136000," ","int(cos((b*x+a)/(d*x+c))^2,x)","-\frac{\left(d a -c b \right) \left(\frac{d^{2} \left(-\frac{2 \cos \left(\frac{2 d a -2 c b}{d \left(d x +c \right)}+\frac{2 b}{d}\right)}{\left(\left(\frac{b}{d}+\frac{d a -c b}{d \left(d x +c \right)}\right) d -b \right) d}-\frac{2 \left(\frac{2 \Si \left(\frac{2 d a -2 c b}{d \left(d x +c \right)}\right) \cos \left(\frac{2 b}{d}\right)}{d}+\frac{2 \Ci \left(\frac{2 d a -2 c b}{d \left(d x +c \right)}\right) \sin \left(\frac{2 b}{d}\right)}{d}\right)}{d}\right)}{4}-\frac{d}{2 \left(\left(\frac{b}{d}+\frac{d a -c b}{d \left(d x +c \right)}\right) d -b \right)}\right)}{d^{2}}"," ",0,"-1/d^2*(a*d-b*c)*(1/4*d^2*(-2*cos(2*(a*d-b*c)/d/(d*x+c)+2*b/d)/((b/d+(a*d-b*c)/d/(d*x+c))*d-b)/d-2*(2*Si(2*(a*d-b*c)/d/(d*x+c))*cos(2*b/d)/d+2*Ci(2*(a*d-b*c)/d/(d*x+c))*sin(2*b/d)/d)/d)-1/2*d/((b/d+(a*d-b*c)/d/(d*x+c))*d-b))","A"
53,0,0,46,0.744000," ","int(cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))^3/(-a^2*x^2+1),x)","\int \frac{\cos^{3}\left(\frac{\sqrt{-a x +1}}{\sqrt{a x +1}}\right)}{-a^{2} x^{2}+1}\, dx"," ",0,"int(cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))^3/(-a^2*x^2+1),x)","F"
54,0,0,46,0.363000," ","int(cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2/(-a^2*x^2+1),x)","\int \frac{\cos^{2}\left(\frac{\sqrt{-a x +1}}{\sqrt{a x +1}}\right)}{-a^{2} x^{2}+1}\, dx"," ",0,"int(cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2/(-a^2*x^2+1),x)","F"
55,0,0,22,0.079000," ","int(cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))/(-a^2*x^2+1),x)","\int \frac{\cos \left(\frac{\sqrt{-a x +1}}{\sqrt{a x +1}}\right)}{-a^{2} x^{2}+1}\, dx"," ",0,"int(cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))/(-a^2*x^2+1),x)","F"
56,0,0,35,0.107000," ","int(1/(-a^2*x^2+1)/cos((-a*x+1)^(1/2)/(a*x+1)^(1/2)),x)","\int \frac{1}{\left(-a^{2} x^{2}+1\right) \cos \left(\frac{\sqrt{-a x +1}}{\sqrt{a x +1}}\right)}\, dx"," ",0,"int(1/(-a^2*x^2+1)/cos((-a*x+1)^(1/2)/(a*x+1)^(1/2)),x)","F"
57,0,0,37,0.250000," ","int(1/(-a^2*x^2+1)/cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2,x)","\int \frac{1}{\left(-a^{2} x^{2}+1\right) \cos \left(\frac{\sqrt{-a x +1}}{\sqrt{a x +1}}\right)^{2}}\, dx"," ",0,"int(1/(-a^2*x^2+1)/cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2,x)","F"
58,1,8,7,0.004000," ","int(tan(x^(1/2))/x^(1/2),x)","-2 \ln \left(\cos \left(\sqrt{x}\right)\right)"," ",0,"-2*ln(cos(x^(1/2)))","A"
59,1,13,12,0.008000," ","int(tan(x^(1/2))^2/x^(1/2),x)","-2 \sqrt{x}+2 \tan \left(\sqrt{x}\right)"," ",0,"-2*x^(1/2)+2*tan(x^(1/2))","A"
60,0,0,50,0.105000," ","int(x^(1/2)*tan(x^(1/2)),x)","\int \sqrt{x}\, \tan \left(\sqrt{x}\right)\, dx"," ",0,"int(x^(1/2)*tan(x^(1/2)),x)","F"
61,1,18,17,0.152000," ","int(1/2*b*tan(c*x^2+b*x+a)/c+x*tan(c*x^2+b*x+a),x)","-\frac{\ln \left(\cos \left(c \,x^{2}+b x +a \right)\right)}{2 c}"," ",0,"-1/2*ln(cos(c*x^2+b*x+a))/c","A"
62,1,14,12,0.007000," ","int(cot(x^(1/2))^2/x^(1/2),x)","-2 \cot \left(\sqrt{x}\right)+\pi -2 \sqrt{x}"," ",0,"-2*cot(x^(1/2))+Pi-2*x^(1/2)","A"
63,1,150,87,0.621000," ","int((a+b*sec(d*x+c))^(1/2)/(1+cos(d*x+c)),x)","-\frac{\EllipticE \left(\frac{\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{a \cos \left(d x +c \right)+b}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)-1\right) \sqrt{\frac{a \cos \left(d x +c \right)+b}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-a -b \right)}{d \left(a \cos \left(d x +c \right)+b \right) \sin \left(d x +c \right)^{2}}"," ",0,"-1/d*EllipticE((cos(d*x+c)-1)/sin(d*x+c),((a-b)/(a+b))^(1/2))*((a*cos(d*x+c)+b)/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)-1)*((a*cos(d*x+c)+b)/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2/(a*cos(d*x+c)+b)/sin(d*x+c)^2*(-a-b)","A"
64,1,48,31,0.169000," ","int(sec(b*x+a)*sec(2*b*x+2*a),x)","\frac{\ln \left(\sin \left(b x +a \right)-1\right)}{2 b}+\frac{\arctanh \left(\sin \left(b x +a \right) \sqrt{2}\right) \sqrt{2}}{b}-\frac{\ln \left(1+\sin \left(b x +a \right)\right)}{2 b}"," ",0,"1/2/b*ln(sin(b*x+a)-1)+arctanh(sin(b*x+a)*2^(1/2))*2^(1/2)/b-1/2/b*ln(1+sin(b*x+a))","A"
65,1,48,31,0.000000," ","int(sec(b*x+a)*sec(2*b*x+2*a),x)","\frac{\ln \left(\sin \left(b x +a \right)-1\right)}{2 b}+\frac{\arctanh \left(\sin \left(b x +a \right) \sqrt{2}\right) \sqrt{2}}{b}-\frac{\ln \left(1+\sin \left(b x +a \right)\right)}{2 b}"," ",0,"1/2/b*ln(sin(b*x+a)-1)+arctanh(sin(b*x+a)*2^(1/2))*2^(1/2)/b-1/2/b*ln(1+sin(b*x+a))","A"
66,1,7,11,0.049000," ","int(sin(x)*sin(2*x),x)","\frac{2 \left(\sin^{3}\left(x \right)\right)}{3}"," ",0,"2/3*sin(x)^3","A"
67,1,14,13,0.109000," ","int(sin(x)*sin(3*x),x)","\frac{\sin \left(2 x \right)}{4}-\frac{\sin \left(4 x \right)}{8}"," ",0,"1/4*sin(2*x)-1/8*sin(4*x)","A"
68,1,14,13,0.096000," ","int(sin(x)*sin(4*x),x)","\frac{\sin \left(3 x \right)}{6}-\frac{\sin \left(5 x \right)}{10}"," ",0,"1/6*sin(3*x)-1/10*sin(5*x)","A"
69,1,28,31,0.079000," ","int(sin(x)*sin(m*x),x)","\frac{\sin \left(\left(-1+m \right) x \right)}{-2+2 m}-\frac{\sin \left(\left(1+m \right) x \right)}{2 \left(1+m \right)}"," ",0,"1/2/(-1+m)*sin((-1+m)*x)-1/2*sin((1+m)*x)/(1+m)","A"
70,1,12,11,0.070000," ","int(cos(2*x)*sin(x),x)","\frac{\cos \left(x \right)}{2}-\frac{\cos \left(3 x \right)}{6}"," ",0,"1/2*cos(x)-1/6*cos(3*x)","A"
71,1,14,13,0.102000," ","int(cos(3*x)*sin(x),x)","\frac{\cos \left(2 x \right)}{4}-\frac{\cos \left(4 x \right)}{8}"," ",0,"1/4*cos(2*x)-1/8*cos(4*x)","A"
72,1,14,13,0.108000," ","int(cos(4*x)*sin(x),x)","\frac{\cos \left(3 x \right)}{6}-\frac{\cos \left(5 x \right)}{10}"," ",0,"1/6*cos(3*x)-1/10*cos(5*x)","A"
73,1,28,31,0.033000," ","int(cos(m*x)*sin(x),x)","\frac{\cos \left(\left(-1+m \right) x \right)}{-2+2 m}-\frac{\cos \left(\left(1+m \right) x \right)}{2 \left(1+m \right)}"," ",0,"1/2*cos((-1+m)*x)/(-1+m)-1/2*cos((1+m)*x)/(1+m)","A"
74,1,18,17,0.161000," ","int(sin(x)*tan(2*x),x)","-\sin \left(x \right)+\frac{\arctanh \left(\sin \left(x \right) \sqrt{2}\right) \sqrt{2}}{2}"," ",0,"-sin(x)+1/2*arctanh(sin(x)*2^(1/2))*2^(1/2)","A"
75,1,38,39,0.301000," ","int(sin(x)*tan(3*x),x)","-\frac{\ln \left(-1+2 \sin \left(x \right)\right)}{6}+\frac{\ln \left(1+2 \sin \left(x \right)\right)}{6}-\frac{\ln \left(\sin \left(x \right)-1\right)}{6}+\frac{\ln \left(1+\sin \left(x \right)\right)}{6}-\sin \left(x \right)"," ",0,"-1/6*ln(-1+2*sin(x))+1/6*ln(1+2*sin(x))-1/6*ln(sin(x)-1)+1/6*ln(1+sin(x))-sin(x)","A"
76,1,115,51,0.411000," ","int(sin(x)*tan(4*x),x)","\frac{\left(\sqrt{2}-2\right) \sqrt{2}\, \arctanh \left(\frac{2 \sin \left(x \right)}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2-\sqrt{2}}}+\frac{\sqrt{2+\sqrt{2}}\, \sqrt{2}\, \arctanh \left(\frac{2 \sin \left(x \right)}{\sqrt{2+\sqrt{2}}}\right)}{4}-\sin \left(x \right)+\frac{\sqrt{2}\, \arctanh \left(\frac{2 \sin \left(x \right)}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2-\sqrt{2}}}-\frac{\sqrt{2}\, \arctanh \left(\frac{2 \sin \left(x \right)}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2+\sqrt{2}}}"," ",0,"1/4*(2^(1/2)-2)*2^(1/2)/(2-2^(1/2))^(1/2)*arctanh(2*sin(x)/(2-2^(1/2))^(1/2))+1/4*(2+2^(1/2))^(1/2)*2^(1/2)*arctanh(2*sin(x)/(2+2^(1/2))^(1/2))-sin(x)+1/4*2^(1/2)/(2-2^(1/2))^(1/2)*arctanh(2*sin(x)/(2-2^(1/2))^(1/2))-1/4*2^(1/2)/(2+2^(1/2))^(1/2)*arctanh(2*sin(x)/(2+2^(1/2))^(1/2))","B"
77,1,84,86,0.411000," ","int(sin(x)*tan(5*x),x)","\frac{\ln \left(4 \left(\sin^{2}\left(x \right)\right)+2 \sin \left(x \right)-1\right)}{20}+\frac{\sqrt{5}\, \arctanh \left(\frac{\left(8 \sin \left(x \right)+2\right) \sqrt{5}}{10}\right)}{10}-\frac{\ln \left(\sin \left(x \right)-1\right)}{10}-\frac{\ln \left(4 \left(\sin^{2}\left(x \right)\right)-2 \sin \left(x \right)-1\right)}{20}+\frac{\sqrt{5}\, \arctanh \left(\frac{\left(8 \sin \left(x \right)-2\right) \sqrt{5}}{10}\right)}{10}+\frac{\ln \left(1+\sin \left(x \right)\right)}{10}-\sin \left(x \right)"," ",0,"1/20*ln(4*sin(x)^2+2*sin(x)-1)+1/10*5^(1/2)*arctanh(1/10*(8*sin(x)+2)*5^(1/2))-1/10*ln(sin(x)-1)-1/20*ln(4*sin(x)^2-2*sin(x)-1)+1/10*5^(1/2)*arctanh(1/10*(8*sin(x)-2)*5^(1/2))+1/10*ln(1+sin(x))-sin(x)","A"
78,1,256,79,0.615000," ","int(sin(x)*tan(6*x),x)","\frac{\left(-3+2 \sqrt{3}\right) \sqrt{3}\, \arctanh \left(\frac{8 \sin \left(x \right)}{2 \sqrt{6}-2 \sqrt{2}}\right)}{6 \sqrt{6}-6 \sqrt{2}}+\frac{\left(3+2 \sqrt{3}\right) \sqrt{3}\, \arctanh \left(\frac{8 \sin \left(x \right)}{2 \sqrt{6}+2 \sqrt{2}}\right)}{6 \sqrt{6}+6 \sqrt{2}}+\frac{\arctanh \left(\sin \left(x \right) \sqrt{2}\right) \sqrt{2}}{6}-\frac{4 \arctanh \left(\frac{8 \sin \left(x \right)}{2 \sqrt{6}-2 \sqrt{2}}\right)}{3 \left(2 \sqrt{6}-2 \sqrt{2}\right)}-\frac{4 \arctanh \left(\frac{8 \sin \left(x \right)}{2 \sqrt{6}+2 \sqrt{2}}\right)}{3 \left(2 \sqrt{6}+2 \sqrt{2}\right)}-\sin \left(x \right)+\frac{\left(3+2 \sqrt{3}\right) \sqrt{3}\, \arctanh \left(\frac{8 \sin \left(x \right)}{2 \sqrt{6}-2 \sqrt{2}}\right)}{18 \sqrt{6}-18 \sqrt{2}}+\frac{\left(-3+2 \sqrt{3}\right) \sqrt{3}\, \arctanh \left(\frac{8 \sin \left(x \right)}{2 \sqrt{6}+2 \sqrt{2}}\right)}{18 \sqrt{6}+18 \sqrt{2}}"," ",0,"1/3*(-3+2*3^(1/2))*3^(1/2)/(2*6^(1/2)-2*2^(1/2))*arctanh(8*sin(x)/(2*6^(1/2)-2*2^(1/2)))+1/3*(3+2*3^(1/2))*3^(1/2)/(2*6^(1/2)+2*2^(1/2))*arctanh(8*sin(x)/(2*6^(1/2)+2*2^(1/2)))+1/6*arctanh(sin(x)*2^(1/2))*2^(1/2)-4/3/(2*6^(1/2)-2*2^(1/2))*arctanh(8*sin(x)/(2*6^(1/2)-2*2^(1/2)))-4/3/(2*6^(1/2)+2*2^(1/2))*arctanh(8*sin(x)/(2*6^(1/2)+2*2^(1/2)))-sin(x)+1/9*(3+2*3^(1/2))*3^(1/2)/(2*6^(1/2)-2*2^(1/2))*arctanh(8*sin(x)/(2*6^(1/2)-2*2^(1/2)))+1/9*(-3+2*3^(1/2))*3^(1/2)/(2*6^(1/2)+2*2^(1/2))*arctanh(8*sin(x)/(2*6^(1/2)+2*2^(1/2)))","B"
79,0,0,85,0.437000," ","int(sin(x)*tan(n*x),x)","\int \sin \left(x \right) \tan \left(n x \right)\, dx"," ",0,"int(sin(x)*tan(n*x),x)","F"
80,1,12,8,0.076000," ","int(cot(2*x)*sin(x),x)","\sin \left(x \right)-\frac{\ln \left(\sec \left(x \right)+\tan \left(x \right)\right)}{2}"," ",0,"sin(x)-1/2*ln(sec(x)+tan(x))","A"
81,1,17,16,0.117000," ","int(cot(3*x)*sin(x),x)","\sin \left(x \right)-\frac{\arctanh \left(\frac{2 \sin \left(x \right) \sqrt{3}}{3}\right) \sqrt{3}}{3}"," ",0,"sin(x)-1/3*arctanh(2/3*sin(x)*3^(1/2))*3^(1/2)","A"
82,1,30,20,0.125000," ","int(cot(4*x)*sin(x),x)","\sin \left(x \right)+\frac{\ln \left(\sin \left(x \right)-1\right)}{8}-\frac{\arctanh \left(\sin \left(x \right) \sqrt{2}\right) \sqrt{2}}{4}-\frac{\ln \left(1+\sin \left(x \right)\right)}{8}"," ",0,"sin(x)+1/8*ln(sin(x)-1)-1/4*arctanh(sin(x)*2^(1/2))*2^(1/2)-1/8*ln(1+sin(x))","A"
83,1,70,54,0.209000," ","int(cot(5*x)*sin(x),x)","\sin \left(x \right)-\frac{\left(\sqrt{5}-1\right) \sqrt{5}\, \arctanh \left(\frac{4 \sin \left(x \right)}{\sqrt{10-2 \sqrt{5}}}\right)}{5 \sqrt{10-2 \sqrt{5}}}-\frac{\left(\sqrt{5}+1\right) \sqrt{5}\, \arctanh \left(\frac{4 \sin \left(x \right)}{\sqrt{10+2 \sqrt{5}}}\right)}{5 \sqrt{10+2 \sqrt{5}}}"," ",0,"sin(x)-1/5*(5^(1/2)-1)*5^(1/2)/(10-2*5^(1/2))^(1/2)*arctanh(4*sin(x)/(10-2*5^(1/2))^(1/2))-1/5*(5^(1/2)+1)*5^(1/2)/(10+2*5^(1/2))^(1/2)*arctanh(4*sin(x)/(10+2*5^(1/2))^(1/2))","A"
84,1,49,28,0.158000," ","int(cot(6*x)*sin(x),x)","\sin \left(x \right)+\frac{\ln \left(-1+2 \sin \left(x \right)\right)}{12}-\frac{\ln \left(1+2 \sin \left(x \right)\right)}{12}-\frac{\arctanh \left(\frac{2 \sin \left(x \right) \sqrt{3}}{3}\right) \sqrt{3}}{6}+\frac{\ln \left(\sin \left(x \right)-1\right)}{12}-\frac{\ln \left(1+\sin \left(x \right)\right)}{12}"," ",0,"sin(x)+1/12*ln(-1+2*sin(x))-1/12*ln(1+2*sin(x))-1/6*arctanh(2/3*sin(x)*3^(1/2))*3^(1/2)+1/12*ln(sin(x)-1)-1/12*ln(1+sin(x))","A"
85,1,13,12,0.134000," ","int(sec(2*x)*sin(x),x)","\frac{\arctanh \left(\cos \left(x \right) \sqrt{2}\right) \sqrt{2}}{2}"," ",0,"1/2*arctanh(cos(x)*2^(1/2))*2^(1/2)","A"
86,1,18,17,0.188000," ","int(sec(3*x)*sin(x),x)","-\frac{\ln \left(4 \left(\cos^{2}\left(x \right)\right)-3\right)}{6}+\frac{\ln \left(\cos \left(x \right)\right)}{3}"," ",0,"-1/6*ln(4*cos(x)^2-3)+1/3*ln(cos(x))","A"
87,1,54,49,0.206000," ","int(sec(4*x)*sin(x),x)","-\frac{\sqrt{2}\, \arctanh \left(\frac{2 \cos \left(x \right)}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2-\sqrt{2}}}+\frac{\sqrt{2}\, \arctanh \left(\frac{2 \cos \left(x \right)}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2+\sqrt{2}}}"," ",0,"-1/4*2^(1/2)/(2-2^(1/2))^(1/2)*arctanh(2*cos(x)/(2-2^(1/2))^(1/2))+1/4*2^(1/2)/(2+2^(1/2))^(1/2)*arctanh(2*cos(x)/(2+2^(1/2))^(1/2))","A"
88,1,43,48,0.228000," ","int(sec(5*x)*sin(x),x)","\frac{\ln \left(16 \left(\cos^{4}\left(x \right)\right)-20 \left(\cos^{2}\left(x \right)\right)+5\right)}{20}+\frac{\sqrt{5}\, \arctanh \left(\frac{\left(32 \left(\cos^{2}\left(x \right)\right)-20\right) \sqrt{5}}{20}\right)}{10}-\frac{\ln \left(\cos \left(x \right)\right)}{5}"," ",0,"1/20*ln(16*cos(x)^4-20*cos(x)^2+5)+1/10*5^(1/2)*arctanh(1/20*(32*cos(x)^2-20)*5^(1/2))-1/5*ln(cos(x))","A"
89,1,80,79,0.244000," ","int(sec(6*x)*sin(x),x)","\frac{2 \arctanh \left(\frac{8 \cos \left(x \right)}{2 \sqrt{6}-2 \sqrt{2}}\right)}{3 \left(2 \sqrt{6}-2 \sqrt{2}\right)}+\frac{2 \arctanh \left(\frac{8 \cos \left(x \right)}{2 \sqrt{6}+2 \sqrt{2}}\right)}{3 \left(2 \sqrt{6}+2 \sqrt{2}\right)}-\frac{\arctanh \left(\cos \left(x \right) \sqrt{2}\right) \sqrt{2}}{6}"," ",0,"2/3/(2*6^(1/2)-2*2^(1/2))*arctanh(8*cos(x)/(2*6^(1/2)-2*2^(1/2)))+2/3/(2*6^(1/2)+2*2^(1/2))*arctanh(8*cos(x)/(2*6^(1/2)+2*2^(1/2)))-1/6*arctanh(cos(x)*2^(1/2))*2^(1/2)","A"
90,1,9,5,0.080000," ","int(csc(2*x)*sin(x),x)","\frac{\ln \left(\sec \left(x \right)+\tan \left(x \right)\right)}{2}"," ",0,"1/2*ln(sec(x)+tan(x))","A"
91,1,14,33,0.205000," ","int(csc(3*x)*sin(x),x)","\frac{\sqrt{3}\, \arctanh \left(\frac{\tan \left(x \right) \sqrt{3}}{3}\right)}{3}"," ",0,"1/3*3^(1/2)*arctanh(1/3*tan(x)*3^(1/2))","A"
92,1,28,18,0.227000," ","int(csc(4*x)*sin(x),x)","\frac{\ln \left(\sin \left(x \right)-1\right)}{8}+\frac{\arctanh \left(\sin \left(x \right) \sqrt{2}\right) \sqrt{2}}{4}-\frac{\ln \left(1+\sin \left(x \right)\right)}{8}"," ",0,"1/8*ln(sin(x)-1)+1/4*arctanh(sin(x)*2^(1/2))*2^(1/2)-1/8*ln(1+sin(x))","A"
93,1,66,113,0.287000," ","int(csc(5*x)*sin(x),x)","-\frac{\left(3+\sqrt{5}\right) \sqrt{5}\, \arctanh \left(\frac{\tan \left(x \right)}{\sqrt{5+2 \sqrt{5}}}\right)}{10 \sqrt{5+2 \sqrt{5}}}-\frac{\left(\sqrt{5}-3\right) \sqrt{5}\, \arctanh \left(\frac{\tan \left(x \right)}{\sqrt{5-2 \sqrt{5}}}\right)}{10 \sqrt{5-2 \sqrt{5}}}"," ",0,"-1/10*(3+5^(1/2))*5^(1/2)/(5+2*5^(1/2))^(1/2)*arctanh(tan(x)/(5+2*5^(1/2))^(1/2))-1/10*(5^(1/2)-3)*5^(1/2)/(5-2*5^(1/2))^(1/2)*arctanh(tan(x)/(5-2*5^(1/2))^(1/2))","A"
94,1,47,26,0.263000," ","int(csc(6*x)*sin(x),x)","-\frac{\ln \left(-1+2 \sin \left(x \right)\right)}{12}+\frac{\ln \left(1+2 \sin \left(x \right)\right)}{12}-\frac{\arctanh \left(\frac{2 \sin \left(x \right) \sqrt{3}}{3}\right) \sqrt{3}}{6}-\frac{\ln \left(\sin \left(x \right)-1\right)}{12}+\frac{\ln \left(1+\sin \left(x \right)\right)}{12}"," ",0,"-1/12*ln(-1+2*sin(x))+1/12*ln(1+2*sin(x))-1/6*arctanh(2/3*sin(x)*3^(1/2))*3^(1/2)-1/12*ln(sin(x)-1)+1/12*ln(1+sin(x))","A"
95,1,9,8,0.102000," ","int(csc(x)*sin(3*x),x)","x +2 \cos \left(x \right) \sin \left(x \right)"," ",0,"x+2*cos(x)*sin(x)","A"
96,1,9,6,0.043000," ","int(csc(3*x)*sin(6*x),x)","\frac{2}{3 \csc \left(3 x \right)}"," ",0,"2/3/csc(3*x)","A"
97,1,7,11,0.043000," ","int(cos(x)*sin(2*x),x)","-\frac{2 \left(\cos^{3}\left(x \right)\right)}{3}"," ",0,"-2/3*cos(x)^3","A"
98,1,14,13,0.070000," ","int(cos(x)*sin(3*x),x)","-\left(\cos^{4}\left(x \right)\right)+\frac{\left(\cos^{2}\left(x \right)\right)}{2}"," ",0,"-cos(x)^4+1/2*cos(x)^2","A"
99,1,14,13,0.058000," ","int(cos(x)*sin(4*x),x)","-\frac{8 \left(\cos^{5}\left(x \right)\right)}{5}+\frac{4 \left(\cos^{3}\left(x \right)\right)}{3}"," ",0,"-8/5*cos(x)^5+4/3*cos(x)^3","A"
100,1,28,31,0.018000," ","int(cos(x)*sin(m*x),x)","-\frac{\cos \left(\left(-1+m \right) x \right)}{2 \left(-1+m \right)}-\frac{\cos \left(\left(1+m \right) x \right)}{2 \left(1+m \right)}"," ",0,"-1/2*cos((-1+m)*x)/(-1+m)-1/2*cos((1+m)*x)/(1+m)","A"
101,1,12,11,0.066000," ","int(cos(x)*cos(2*x),x)","\frac{\sin \left(x \right)}{2}+\frac{\sin \left(3 x \right)}{6}"," ",0,"1/2*sin(x)+1/6*sin(3*x)","A"
102,1,14,13,0.072000," ","int(cos(x)*cos(3*x),x)","\frac{\sin \left(2 x \right)}{4}+\frac{\sin \left(4 x \right)}{8}"," ",0,"1/4*sin(2*x)+1/8*sin(4*x)","A"
103,1,14,13,0.100000," ","int(cos(x)*cos(4*x),x)","\frac{\sin \left(3 x \right)}{6}+\frac{\sin \left(5 x \right)}{10}"," ",0,"1/6*sin(3*x)+1/10*sin(5*x)","A"
104,1,28,31,0.029000," ","int(cos(x)*cos(m*x),x)","\frac{\sin \left(\left(-1+m \right) x \right)}{-2+2 m}+\frac{\sin \left(\left(1+m \right) x \right)}{2+2 m}"," ",0,"1/2/(-1+m)*sin((-1+m)*x)+1/2*sin((1+m)*x)/(1+m)","A"
105,1,18,17,0.040000," ","int(cos(x)*tan(2*x),x)","-\cos \left(x \right)+\frac{\arctanh \left(\cos \left(x \right) \sqrt{2}\right) \sqrt{2}}{2}"," ",0,"-cos(x)+1/2*arctanh(cos(x)*2^(1/2))*2^(1/2)","A"
106,1,19,18,0.047000," ","int(cos(x)*tan(3*x),x)","-\cos \left(x \right)+\frac{\arctanh \left(\frac{2 \cos \left(x \right) \sqrt{3}}{3}\right) \sqrt{3}}{3}"," ",0,"-cos(x)+1/3*arctanh(2/3*cos(x)*3^(1/2))*3^(1/2)","A"
107,1,68,51,0.078000," ","int(cos(x)*tan(4*x),x)","-\cos \left(x \right)+\frac{\left(\sqrt{2}-1\right) \sqrt{2}\, \arctanh \left(\frac{2 \cos \left(x \right)}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2-\sqrt{2}}}+\frac{\left(1+\sqrt{2}\right) \sqrt{2}\, \arctanh \left(\frac{2 \cos \left(x \right)}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2+\sqrt{2}}}"," ",0,"-cos(x)+1/4*(2^(1/2)-1)*2^(1/2)/(2-2^(1/2))^(1/2)*arctanh(2*cos(x)/(2-2^(1/2))^(1/2))+1/4*(1+2^(1/2))*2^(1/2)/(2+2^(1/2))^(1/2)*arctanh(2*cos(x)/(2+2^(1/2))^(1/2))","A"
108,1,72,56,0.071000," ","int(cos(x)*tan(5*x),x)","-\cos \left(x \right)+\frac{\left(\sqrt{5}-1\right) \sqrt{5}\, \arctanh \left(\frac{4 \cos \left(x \right)}{\sqrt{10-2 \sqrt{5}}}\right)}{5 \sqrt{10-2 \sqrt{5}}}+\frac{\left(\sqrt{5}+1\right) \sqrt{5}\, \arctanh \left(\frac{4 \cos \left(x \right)}{\sqrt{10+2 \sqrt{5}}}\right)}{5 \sqrt{10+2 \sqrt{5}}}"," ",0,"-cos(x)+1/5*(5^(1/2)-1)*5^(1/2)/(10-2*5^(1/2))^(1/2)*arctanh(4*cos(x)/(10-2*5^(1/2))^(1/2))+1/5*(5^(1/2)+1)*5^(1/2)/(10+2*5^(1/2))^(1/2)*arctanh(4*cos(x)/(10+2*5^(1/2))^(1/2))","A"
109,1,104,79,0.085000," ","int(cos(x)*tan(6*x),x)","-\cos \left(x \right)+\frac{2 \left(-3+2 \sqrt{3}\right) \sqrt{3}\, \arctanh \left(\frac{8 \cos \left(x \right)}{2 \sqrt{6}-2 \sqrt{2}}\right)}{9 \left(2 \sqrt{6}-2 \sqrt{2}\right)}+\frac{2 \left(3+2 \sqrt{3}\right) \sqrt{3}\, \arctanh \left(\frac{8 \cos \left(x \right)}{2 \sqrt{6}+2 \sqrt{2}}\right)}{9 \left(2 \sqrt{6}+2 \sqrt{2}\right)}+\frac{\arctanh \left(\cos \left(x \right) \sqrt{2}\right) \sqrt{2}}{6}"," ",0,"-cos(x)+2/9*(-3+2*3^(1/2))*3^(1/2)/(2*6^(1/2)-2*2^(1/2))*arctanh(8*cos(x)/(2*6^(1/2)-2*2^(1/2)))+2/9*(3+2*3^(1/2))*3^(1/2)/(2*6^(1/2)+2*2^(1/2))*arctanh(8*cos(x)/(2*6^(1/2)+2*2^(1/2)))+1/6*arctanh(cos(x)*2^(1/2))*2^(1/2)","A"
110,1,14,8,0.086000," ","int(cos(x)*cot(2*x),x)","\cos \left(x \right)+\frac{\ln \left(\csc \left(x \right)-\cot \left(x \right)\right)}{2}"," ",0,"cos(x)+1/2*ln(csc(x)-cot(x))","A"
111,1,36,37,0.315000," ","int(cos(x)*cot(3*x),x)","\frac{\ln \left(2 \cos \left(x \right)-1\right)}{6}-\frac{\ln \left(1+2 \cos \left(x \right)\right)}{6}+\frac{\ln \left(-1+\cos \left(x \right)\right)}{6}-\frac{\ln \left(1+\cos \left(x \right)\right)}{6}+\cos \left(x \right)"," ",0,"1/6*ln(2*cos(x)-1)-1/6*ln(1+2*cos(x))+1/6*ln(-1+cos(x))-1/6*ln(1+cos(x))+cos(x)","A"
112,1,30,20,0.408000," ","int(cos(x)*cot(4*x),x)","\frac{\ln \left(-1+\cos \left(x \right)\right)}{8}-\frac{\arctanh \left(\cos \left(x \right) \sqrt{2}\right) \sqrt{2}}{4}-\frac{\ln \left(1+\cos \left(x \right)\right)}{8}+\cos \left(x \right)"," ",0,"1/8*ln(-1+cos(x))-1/4*arctanh(cos(x)*2^(1/2))*2^(1/2)-1/8*ln(1+cos(x))+cos(x)","A"
113,1,82,84,0.437000," ","int(cos(x)*cot(5*x),x)","-\frac{\ln \left(4 \left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-1\right)}{20}-\frac{\sqrt{5}\, \arctanh \left(\frac{\left(8 \cos \left(x \right)+2\right) \sqrt{5}}{10}\right)}{10}+\frac{\ln \left(-1+\cos \left(x \right)\right)}{10}+\frac{\ln \left(4 \left(\cos^{2}\left(x \right)\right)-2 \cos \left(x \right)-1\right)}{20}-\frac{\sqrt{5}\, \arctanh \left(\frac{\left(8 \cos \left(x \right)-2\right) \sqrt{5}}{10}\right)}{10}-\frac{\ln \left(1+\cos \left(x \right)\right)}{10}+\cos \left(x \right)"," ",0,"-1/20*ln(4*cos(x)^2+2*cos(x)-1)-1/10*5^(1/2)*arctanh(1/10*(8*cos(x)+2)*5^(1/2))+1/10*ln(-1+cos(x))+1/20*ln(4*cos(x)^2-2*cos(x)-1)-1/10*5^(1/2)*arctanh(1/10*(8*cos(x)-2)*5^(1/2))-1/10*ln(1+cos(x))+cos(x)","A"
114,1,49,28,0.555000," ","int(cos(x)*cot(6*x),x)","\frac{\ln \left(2 \cos \left(x \right)-1\right)}{12}-\frac{\ln \left(1+2 \cos \left(x \right)\right)}{12}-\frac{\arctanh \left(\frac{2 \cos \left(x \right) \sqrt{3}}{3}\right) \sqrt{3}}{6}+\frac{\ln \left(-1+\cos \left(x \right)\right)}{12}-\frac{\ln \left(1+\cos \left(x \right)\right)}{12}+\cos \left(x \right)"," ",0,"1/12*ln(2*cos(x)-1)-1/12*ln(1+2*cos(x))-1/6*arctanh(2/3*cos(x)*3^(1/2))*3^(1/2)+1/12*ln(-1+cos(x))-1/12*ln(1+cos(x))+cos(x)","A"
115,0,0,76,0.553000," ","int(cos(x)*cot(n*x),x)","\int \cos \left(x \right) \cot \left(n x \right)\, dx"," ",0,"int(cos(x)*cot(n*x),x)","F"
116,1,13,12,0.134000," ","int(cos(x)*sec(2*x),x)","\frac{\arctanh \left(\sin \left(x \right) \sqrt{2}\right) \sqrt{2}}{2}"," ",0,"1/2*arctanh(sin(x)*2^(1/2))*2^(1/2)","A"
117,1,13,32,0.175000," ","int(cos(x)*sec(3*x),x)","\frac{\sqrt{3}\, \arctanh \left(\tan \left(x \right) \sqrt{3}\right)}{3}"," ",0,"1/3*3^(1/2)*arctanh(tan(x)*3^(1/2))","A"
118,1,54,49,0.217000," ","int(cos(x)*sec(4*x),x)","\frac{\sqrt{2}\, \arctanh \left(\frac{2 \sin \left(x \right)}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2-\sqrt{2}}}-\frac{\sqrt{2}\, \arctanh \left(\frac{2 \sin \left(x \right)}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2+\sqrt{2}}}"," ",0,"1/4*2^(1/2)/(2-2^(1/2))^(1/2)*arctanh(2*sin(x)/(2-2^(1/2))^(1/2))-1/4*2^(1/2)/(2+2^(1/2))^(1/2)*arctanh(2*sin(x)/(2+2^(1/2))^(1/2))","A"
119,1,68,111,0.259000," ","int(cos(x)*sec(5*x),x)","-\frac{\left(5+\sqrt{5}\right) \sqrt{5}\, \arctanh \left(\frac{5 \tan \left(x \right)}{\sqrt{25+10 \sqrt{5}}}\right)}{10 \sqrt{25+10 \sqrt{5}}}-\frac{\sqrt{5}\, \left(\sqrt{5}-5\right) \arctanh \left(\frac{5 \tan \left(x \right)}{\sqrt{25-10 \sqrt{5}}}\right)}{10 \sqrt{25-10 \sqrt{5}}}"," ",0,"-1/10*(5+5^(1/2))*5^(1/2)/(25+10*5^(1/2))^(1/2)*arctanh(5*tan(x)/(25+10*5^(1/2))^(1/2))-1/10*5^(1/2)*(5^(1/2)-5)/(25-10*5^(1/2))^(1/2)*arctanh(5*tan(x)/(25-10*5^(1/2))^(1/2))","A"
120,1,80,79,0.264000," ","int(cos(x)*sec(6*x),x)","\frac{2 \arctanh \left(\frac{8 \sin \left(x \right)}{2 \sqrt{6}-2 \sqrt{2}}\right)}{3 \left(2 \sqrt{6}-2 \sqrt{2}\right)}+\frac{2 \arctanh \left(\frac{8 \sin \left(x \right)}{2 \sqrt{6}+2 \sqrt{2}}\right)}{3 \left(2 \sqrt{6}+2 \sqrt{2}\right)}-\frac{\arctanh \left(\sin \left(x \right) \sqrt{2}\right) \sqrt{2}}{6}"," ",0,"2/3/(2*6^(1/2)-2*2^(1/2))*arctanh(8*sin(x)/(2*6^(1/2)-2*2^(1/2)))+2/3/(2*6^(1/2)+2*2^(1/2))*arctanh(8*sin(x)/(2*6^(1/2)+2*2^(1/2)))-1/6*arctanh(sin(x)*2^(1/2))*2^(1/2)","A"
121,1,14,10,0.117000," ","int(cos(2*x)*sec(x),x)","2 \sin \left(x \right)-\ln \left(\sec \left(x \right)+\tan \left(x \right)\right)"," ",0,"2*sin(x)-ln(sec(x)+tan(x))","A"
122,1,18,12,0.139000," ","int(cos(4*x)*sec(2*x),x)","-\frac{\ln \left(\sec \left(2 x \right)+\tan \left(2 x \right)\right)}{2}+\sin \left(2 x \right)"," ",0,"-1/2*ln(sec(2*x)+tan(2*x))+sin(2*x)","A"
123,1,11,5,0.080000," ","int(cos(x)*csc(2*x),x)","\frac{\ln \left(\csc \left(x \right)-\cot \left(x \right)\right)}{2}"," ",0,"1/2*ln(csc(x)-cot(x))","A"
124,1,34,17,0.223000," ","int(cos(x)*csc(3*x),x)","-\frac{\ln \left(2 \cos \left(x \right)-1\right)}{6}-\frac{\ln \left(1+2 \cos \left(x \right)\right)}{6}+\frac{\ln \left(-1+\cos \left(x \right)\right)}{6}+\frac{\ln \left(1+\cos \left(x \right)\right)}{6}"," ",0,"-1/6*ln(2*cos(x)-1)-1/6*ln(1+2*cos(x))+1/6*ln(-1+cos(x))+1/6*ln(1+cos(x))","A"
125,1,28,18,0.141000," ","int(cos(x)*csc(4*x),x)","\frac{\ln \left(-1+\cos \left(x \right)\right)}{8}+\frac{\arctanh \left(\cos \left(x \right) \sqrt{2}\right) \sqrt{2}}{4}-\frac{\ln \left(1+\cos \left(x \right)\right)}{8}"," ",0,"1/8*ln(-1+cos(x))+1/4*arctanh(cos(x)*2^(1/2))*2^(1/2)-1/8*ln(1+cos(x))","A"
126,1,80,48,0.259000," ","int(cos(x)*csc(5*x),x)","-\frac{\ln \left(4 \left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-1\right)}{20}-\frac{\sqrt{5}\, \arctanh \left(\frac{\left(8 \cos \left(x \right)+2\right) \sqrt{5}}{10}\right)}{10}+\frac{\ln \left(-1+\cos \left(x \right)\right)}{10}-\frac{\ln \left(4 \left(\cos^{2}\left(x \right)\right)-2 \cos \left(x \right)-1\right)}{20}+\frac{\sqrt{5}\, \arctanh \left(\frac{\left(8 \cos \left(x \right)-2\right) \sqrt{5}}{10}\right)}{10}+\frac{\ln \left(1+\cos \left(x \right)\right)}{10}"," ",0,"-1/20*ln(4*cos(x)^2+2*cos(x)-1)-1/10*5^(1/2)*arctanh(1/10*(8*cos(x)+2)*5^(1/2))+1/10*ln(-1+cos(x))-1/20*ln(4*cos(x)^2-2*cos(x)-1)+1/10*5^(1/2)*arctanh(1/10*(8*cos(x)-2)*5^(1/2))+1/10*ln(1+cos(x))","A"
127,1,47,26,0.167000," ","int(cos(x)*csc(6*x),x)","\frac{\ln \left(2 \cos \left(x \right)-1\right)}{12}-\frac{\ln \left(1+2 \cos \left(x \right)\right)}{12}+\frac{\arctanh \left(\frac{2 \cos \left(x \right) \sqrt{3}}{3}\right) \sqrt{3}}{6}+\frac{\ln \left(-1+\cos \left(x \right)\right)}{12}-\frac{\ln \left(1+\cos \left(x \right)\right)}{12}"," ",0,"1/12*ln(2*cos(x)-1)-1/12*ln(1+2*cos(x))+1/6*arctanh(2/3*cos(x)*3^(1/2))*3^(1/2)+1/12*ln(-1+cos(x))-1/12*ln(1+cos(x))","A"
128,1,26,25,0.253000," ","int(cos(6*x)^3*sin(x),x)","\frac{3 \cos \left(5 x \right)}{40}-\frac{3 \cos \left(7 x \right)}{56}+\frac{\cos \left(17 x \right)}{136}-\frac{\cos \left(19 x \right)}{152}"," ",0,"3/40*cos(5*x)-3/56*cos(7*x)+1/136*cos(17*x)-1/152*cos(19*x)","A"
129,1,26,25,0.135000," ","int(cos(6*x)^3*sin(9*x),x)","-\frac{\cos \left(3 x \right)}{8}+\frac{\cos \left(9 x \right)}{72}-\frac{\cos \left(15 x \right)}{40}-\frac{\cos \left(27 x \right)}{216}"," ",0,"-1/8*cos(3*x)+1/72*cos(9*x)-1/40*cos(15*x)-1/216*cos(27*x)","A"
130,1,20,19,0.124000," ","int(cos(2*x)*sin(6*x)^2,x)","\frac{\sin \left(2 x \right)}{4}-\frac{\sin \left(10 x \right)}{40}-\frac{\sin \left(14 x \right)}{56}"," ",0,"1/4*sin(2*x)-1/40*sin(10*x)-1/56*sin(14*x)","A"
131,1,18,17,0.129000," ","int(cos(x)*sin(6*x)^2,x)","\frac{\sin \left(x \right)}{2}-\frac{\sin \left(11 x \right)}{44}-\frac{\sin \left(13 x \right)}{52}"," ",0,"1/2*sin(x)-1/44*sin(11*x)-1/52*sin(13*x)","A"
132,1,26,25,0.141000," ","int(cos(x)*sin(6*x)^3,x)","-\frac{3 \cos \left(5 x \right)}{40}-\frac{3 \cos \left(7 x \right)}{56}+\frac{\cos \left(17 x \right)}{136}+\frac{\cos \left(19 x \right)}{152}"," ",0,"-3/40*cos(5*x)-3/56*cos(7*x)+1/136*cos(17*x)+1/152*cos(19*x)","A"
133,1,24,23,0.450000," ","int(cos(7*x)*sin(6*x)^3,x)","\frac{3 \cos \left(x \right)}{8}+\frac{\cos \left(11 x \right)}{88}-\frac{3 \cos \left(13 x \right)}{104}+\frac{\cos \left(25 x \right)}{200}"," ",0,"3/8*cos(x)+1/88*cos(11*x)-3/104*cos(13*x)+1/200*cos(25*x)","A"
134,1,32,31,0.171000," ","int(cos(3*x)^2*sin(2*x)^3,x)","-\frac{3 \cos \left(2 x \right)}{16}+\frac{3 \cos \left(4 x \right)}{64}+\frac{\cos \left(6 x \right)}{48}-\frac{3 \cos \left(8 x \right)}{128}+\frac{\cos \left(12 x \right)}{192}"," ",0,"-3/16*cos(2*x)+3/64*cos(4*x)+1/48*cos(6*x)-3/128*cos(8*x)+1/192*cos(12*x)","A"
135,1,24,23,0.053000," ","int(sin(b*x+a)*sin(b*x+c),x)","\frac{x \cos \left(a -c \right)}{2}-\frac{\sin \left(2 b x +a +c \right)}{4 b}"," ",0,"1/2*x*cos(a-c)-1/4*sin(2*b*x+a+c)/b","A"
136,1,24,23,0.046000," ","int(-sin(b*x-c)*sin(b*x+a),x)","-\frac{x \cos \left(a +c \right)}{2}+\frac{\sin \left(2 b x +a -c \right)}{4 b}"," ",0,"-1/2*x*cos(a+c)+1/4*sin(2*b*x+a-c)/b","A"
137,1,24,23,0.045000," ","int(cos(b*x+a)*cos(b*x+c),x)","\frac{x \cos \left(a -c \right)}{2}+\frac{\sin \left(2 b x +a +c \right)}{4 b}"," ",0,"1/2*x*cos(a-c)+1/4*sin(2*b*x+a+c)/b","A"
138,1,24,23,0.046000," ","int(cos(b*x-c)*cos(b*x+a),x)","\frac{x \cos \left(a +c \right)}{2}+\frac{\sin \left(2 b x +a -c \right)}{4 b}"," ",0,"1/2*x*cos(a+c)+1/4*sin(2*b*x+a-c)/b","A"
139,1,173,39,0.136000," ","int(tan(b*x+a)*tan(b*x+c),x)","-x -\frac{i \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) {\mathrm e}^{2 i a}}{b \left({\mathrm e}^{2 i a}-{\mathrm e}^{2 i c}\right)}-\frac{i \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) {\mathrm e}^{2 i c}}{b \left({\mathrm e}^{2 i a}-{\mathrm e}^{2 i c}\right)}+\frac{i \ln \left({\mathrm e}^{2 i \left(b x +a \right)}+{\mathrm e}^{2 i \left(a -c \right)}\right) {\mathrm e}^{2 i a}}{b \left({\mathrm e}^{2 i a}-{\mathrm e}^{2 i c}\right)}+\frac{i \ln \left({\mathrm e}^{2 i \left(b x +a \right)}+{\mathrm e}^{2 i \left(a -c \right)}\right) {\mathrm e}^{2 i c}}{b \left({\mathrm e}^{2 i a}-{\mathrm e}^{2 i c}\right)}"," ",0,"-x-I/b/(exp(2*I*a)-exp(2*I*c))*ln(1+exp(2*I*(b*x+a)))*exp(2*I*a)-I/b/(exp(2*I*a)-exp(2*I*c))*ln(1+exp(2*I*(b*x+a)))*exp(2*I*c)+I/b/(exp(2*I*a)-exp(2*I*c))*ln(exp(2*I*(b*x+a))+exp(2*I*(a-c)))*exp(2*I*a)+I/b/(exp(2*I*a)-exp(2*I*c))*ln(exp(2*I*(b*x+a))+exp(2*I*(a-c)))*exp(2*I*c)","C"
140,1,145,35,0.135000," ","int(-tan(b*x-c)*tan(b*x+a),x)","x +\frac{i \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) {\mathrm e}^{2 i \left(a +c \right)}}{b \left({\mathrm e}^{2 i \left(a +c \right)}-1\right)}+\frac{i \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b \left({\mathrm e}^{2 i \left(a +c \right)}-1\right)}-\frac{i \ln \left({\mathrm e}^{2 i \left(a +c \right)}+{\mathrm e}^{2 i \left(b x +a \right)}\right) {\mathrm e}^{2 i \left(a +c \right)}}{b \left({\mathrm e}^{2 i \left(a +c \right)}-1\right)}-\frac{i \ln \left({\mathrm e}^{2 i \left(a +c \right)}+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b \left({\mathrm e}^{2 i \left(a +c \right)}-1\right)}"," ",0,"x+I/b/(exp(2*I*(a+c))-1)*ln(1+exp(2*I*(b*x+a)))*exp(2*I*(a+c))+I/b/(exp(2*I*(a+c))-1)*ln(1+exp(2*I*(b*x+a)))-I/b/(exp(2*I*(a+c))-1)*ln(exp(2*I*(a+c))+exp(2*I*(b*x+a)))*exp(2*I*(a+c))-I/b/(exp(2*I*(a+c))-1)*ln(exp(2*I*(a+c))+exp(2*I*(b*x+a)))","C"
141,1,177,39,0.189000," ","int(cot(b*x+a)*cot(b*x+c),x)","-x -\frac{i \ln \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right) {\mathrm e}^{2 i a}}{b \left({\mathrm e}^{2 i a}-{\mathrm e}^{2 i c}\right)}-\frac{i \ln \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right) {\mathrm e}^{2 i c}}{b \left({\mathrm e}^{2 i a}-{\mathrm e}^{2 i c}\right)}+\frac{i \ln \left({\mathrm e}^{2 i \left(b x +a \right)}-{\mathrm e}^{2 i \left(a -c \right)}\right) {\mathrm e}^{2 i a}}{b \left({\mathrm e}^{2 i a}-{\mathrm e}^{2 i c}\right)}+\frac{i \ln \left({\mathrm e}^{2 i \left(b x +a \right)}-{\mathrm e}^{2 i \left(a -c \right)}\right) {\mathrm e}^{2 i c}}{b \left({\mathrm e}^{2 i a}-{\mathrm e}^{2 i c}\right)}"," ",0,"-x-I/b/(exp(2*I*a)-exp(2*I*c))*ln(exp(2*I*(b*x+a))-1)*exp(2*I*a)-I/b/(exp(2*I*a)-exp(2*I*c))*ln(exp(2*I*(b*x+a))-1)*exp(2*I*c)+I/b/(exp(2*I*a)-exp(2*I*c))*ln(exp(2*I*(b*x+a))-exp(2*I*(a-c)))*exp(2*I*a)+I/b/(exp(2*I*a)-exp(2*I*c))*ln(exp(2*I*(b*x+a))-exp(2*I*(a-c)))*exp(2*I*c)","C"
142,1,149,37,0.185000," ","int(-cot(b*x-c)*cot(b*x+a),x)","x -\frac{i \ln \left(-{\mathrm e}^{2 i \left(a +c \right)}+{\mathrm e}^{2 i \left(b x +a \right)}\right) {\mathrm e}^{2 i \left(a +c \right)}}{b \left({\mathrm e}^{2 i \left(a +c \right)}-1\right)}-\frac{i \ln \left(-{\mathrm e}^{2 i \left(a +c \right)}+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b \left({\mathrm e}^{2 i \left(a +c \right)}-1\right)}+\frac{i \ln \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right) {\mathrm e}^{2 i \left(a +c \right)}}{b \left({\mathrm e}^{2 i \left(a +c \right)}-1\right)}+\frac{i \ln \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}{b \left({\mathrm e}^{2 i \left(a +c \right)}-1\right)}"," ",0,"x-I/b/(exp(2*I*(a+c))-1)*ln(-exp(2*I*(a+c))+exp(2*I*(b*x+a)))*exp(2*I*(a+c))-I/b/(exp(2*I*(a+c))-1)*ln(-exp(2*I*(a+c))+exp(2*I*(b*x+a)))+I/b/(exp(2*I*(a+c))-1)*ln(exp(2*I*(b*x+a))-1)*exp(2*I*(a+c))+I/b/(exp(2*I*(a+c))-1)*ln(exp(2*I*(b*x+a))-1)","C"
143,1,55,36,0.475000," ","int(sec(b*x+a)*sec(b*x+c),x)","-\frac{\ln \left(-\tan \left(b x +a \right) \cos \left(a \right) \sin \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \cos \left(c \right)+\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right)}{b \left(\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)}"," ",0,"-1/b/(cos(a)*sin(c)-sin(a)*cos(c))*ln(-tan(b*x+a)*cos(a)*sin(c)+tan(b*x+a)*sin(a)*cos(c)+cos(a)*cos(c)+sin(a)*sin(c))","A"
144,1,53,34,0.460000," ","int(sec(b*x-c)*sec(b*x+a),x)","\frac{\ln \left(\tan \left(b x +a \right) \cos \left(a \right) \sin \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \cos \left(c \right)+\cos \left(a \right) \cos \left(c \right)-\sin \left(a \right) \sin \left(c \right)\right)}{b \left(\sin \left(a \right) \cos \left(c \right)+\cos \left(a \right) \sin \left(c \right)\right)}"," ",0,"1/b/(sin(a)*cos(c)+cos(a)*sin(c))*ln(tan(b*x+a)*cos(a)*sin(c)+tan(b*x+a)*sin(a)*cos(c)+cos(a)*cos(c)-sin(a)*sin(c))","A"
145,1,169,36,0.490000," ","int(csc(b*x+a)*csc(b*x+c),x)","-\frac{\ln \left(\tan \left(b x +a \right) \cos \left(a \right) \cos \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \sin \left(c \right)+\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right) \cos \left(a \right) \cos \left(c \right)}{b \left(\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right) \left(\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right)}-\frac{\ln \left(\tan \left(b x +a \right) \cos \left(a \right) \cos \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \sin \left(c \right)+\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right) \sin \left(a \right) \sin \left(c \right)}{b \left(\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right) \left(\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right)}+\frac{\ln \left(\tan \left(b x +a \right)\right)}{b \left(\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)}"," ",0,"-1/b/(cos(a)*sin(c)-sin(a)*cos(c))/(cos(a)*cos(c)+sin(a)*sin(c))*ln(tan(b*x+a)*cos(a)*cos(c)+tan(b*x+a)*sin(a)*sin(c)+cos(a)*sin(c)-sin(a)*cos(c))*cos(a)*cos(c)-1/b/(cos(a)*sin(c)-sin(a)*cos(c))/(cos(a)*cos(c)+sin(a)*sin(c))*ln(tan(b*x+a)*cos(a)*cos(c)+tan(b*x+a)*sin(a)*sin(c)+cos(a)*sin(c)-sin(a)*cos(c))*sin(a)*sin(c)+1/b/(cos(a)*sin(c)-sin(a)*cos(c))*ln(tan(b*x+a))","B"
146,1,81,36,0.477000," ","int(-csc(b*x-c)*csc(b*x+a),x)","-\frac{\ln \left(\tan \left(b x +a \right) \cos \left(a \right) \cos \left(c \right)-\tan \left(b x +a \right) \sin \left(a \right) \sin \left(c \right)-\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)}{b \left(\sin \left(a \right) \cos \left(c \right)+\cos \left(a \right) \sin \left(c \right)\right)}+\frac{\ln \left(\tan \left(b x +a \right)\right)}{b \left(\sin \left(a \right) \cos \left(c \right)+\cos \left(a \right) \sin \left(c \right)\right)}"," ",0,"-1/b/(sin(a)*cos(c)+cos(a)*sin(c))*ln(tan(b*x+a)*cos(a)*cos(c)-tan(b*x+a)*sin(a)*sin(c)-cos(a)*sin(c)-sin(a)*cos(c))+1/b/(sin(a)*cos(c)+cos(a)*sin(c))*ln(tan(b*x+a))","B"
147,1,177,11,0.395000," ","int((sin(x)*tan(x))^(1/2),x)","\frac{\left(-1+\cos \left(x \right)\right) \left(4 \cos \left(x \right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}+4 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}+\ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right)-\ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)\right) \cos \left(x \right) \sqrt{-\frac{-1+\cos^{2}\left(x \right)}{\cos \left(x \right)}}\, \sqrt{4}}{4 \sin \left(x \right)^{3} \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}}"," ",0,"1/4*(-1+cos(x))*(4*cos(x)*(-cos(x)/(1+cos(x))^2)^(1/2)+4*(-cos(x)/(1+cos(x))^2)^(1/2)+ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)-ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2))*cos(x)*(-(-1+cos(x)^2)/cos(x))^(1/2)/sin(x)^3/(-cos(x)/(1+cos(x))^2)^(1/2)*4^(1/2)","B"
148,1,587,23,0.263000," ","int((sin(x)*tan(x))^(3/2),x)","-\frac{\left(-1+\cos \left(x \right)\right)^{2} \left(3 \left(\cos^{3}\left(x \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}-3 \left(\cos^{3}\left(x \right)\right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}+9 \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right) \left(\cos^{2}\left(x \right)\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}-9 \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right) \left(\cos^{2}\left(x \right)\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}+9 \cos \left(x \right) \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}-9 \cos \left(x \right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}+3 \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}-3 \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}-4 \left(\cos^{3}\left(x \right)\right)-12 \cos \left(x \right)\right) \left(1+\cos \left(x \right)\right)^{2} \left(-\frac{-1+\cos^{2}\left(x \right)}{\cos \left(x \right)}\right)^{\frac{3}{2}} \sqrt{4}}{12 \sin \left(x \right)^{7}}"," ",0,"-1/12*(-1+cos(x))^2*(3*cos(x)^3*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*(-cos(x)/(1+cos(x))^2)^(3/2)-3*cos(x)^3*ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*(-cos(x)/(1+cos(x))^2)^(3/2)+9*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(3/2)-9*ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(3/2)+9*cos(x)*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*(-cos(x)/(1+cos(x))^2)^(3/2)-9*cos(x)*ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*(-cos(x)/(1+cos(x))^2)^(3/2)+3*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*(-cos(x)/(1+cos(x))^2)^(3/2)-3*ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*(-cos(x)/(1+cos(x))^2)^(3/2)-4*cos(x)^3-12*cos(x))*(1+cos(x))^2*(-(-1+cos(x)^2)/cos(x))^(3/2)/sin(x)^7*4^(1/2)","B"
149,1,324,38,0.345000," ","int((sin(x)*tan(x))^(5/2),x)","-\frac{\left(-1+\cos \left(x \right)\right)^{2} \left(6 \left(\cos^{4}\left(x \right)\right)-15 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}\, \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)+15 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}\, \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right)-15 \cos \left(x \right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}\, \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)+15 \cos \left(x \right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}\, \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right)-60 \left(\cos^{2}\left(x \right)\right)-10\right) \cos \left(x \right) \left(1+\cos \left(x \right)\right)^{2} \left(-\frac{-1+\cos^{2}\left(x \right)}{\cos \left(x \right)}\right)^{\frac{5}{2}} \sqrt{4}}{30 \sin \left(x \right)^{9}}"," ",0,"-1/30*(-1+cos(x))^2*(6*cos(x)^4-15*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)+15*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)*ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)-15*cos(x)*(-cos(x)/(1+cos(x))^2)^(1/2)*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)+15*cos(x)*(-cos(x)/(1+cos(x))^2)^(1/2)*ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)-60*cos(x)^2-10)*cos(x)*(1+cos(x))^2*(-(-1+cos(x)^2)/cos(x))^(5/2)/sin(x)^9*4^(1/2)","B"
150,1,20,11,0.254000," ","int((cos(x)*cot(x))^(1/2),x)","\frac{2 \sin \left(x \right) \sqrt{\frac{\cos^{2}\left(x \right)}{\sin \left(x \right)}}}{\cos \left(x \right)}"," ",0,"2*sin(x)*(cos(x)^2/sin(x))^(1/2)/cos(x)","A"
151,1,26,23,0.248000," ","int((cos(x)*cot(x))^(3/2),x)","\frac{2 \left(\cos^{2}\left(x \right)-4\right) \left(\frac{\cos^{2}\left(x \right)}{\sin \left(x \right)}\right)^{\frac{3}{2}} \sin \left(x \right)}{3 \cos \left(x \right)^{3}}"," ",0,"2/3*(cos(x)^2-4)*(cos(x)^2/sin(x))^(3/2)*sin(x)/cos(x)^3","A"
152,1,34,38,0.303000," ","int((cos(x)*cot(x))^(5/2),x)","\frac{2 \left(3 \left(\cos^{4}\left(x \right)\right)+24 \left(\cos^{2}\left(x \right)\right)-32\right) \left(\frac{\cos^{2}\left(x \right)}{\sin \left(x \right)}\right)^{\frac{5}{2}} \sin \left(x \right)}{15 \cos \left(x \right)^{5}}"," ",0,"2/15*(3*cos(x)^4+24*cos(x)^2-32)*(cos(x)^2/sin(x))^(5/2)*sin(x)/cos(x)^5","A"
153,1,159,52,0.524000," ","int(x*cos(x)/(a+b*sin(x))^2,x)","-\frac{2 i x \,{\mathrm e}^{i x}}{b \left(b \,{\mathrm e}^{2 i x}-b +2 i a \,{\mathrm e}^{i x}\right)}-\frac{\ln \left({\mathrm e}^{i x}+\frac{i a \sqrt{-a^{2}+b^{2}}-a^{2}+b^{2}}{\sqrt{-a^{2}+b^{2}}\, b}\right)}{\sqrt{-a^{2}+b^{2}}\, b}+\frac{\ln \left({\mathrm e}^{i x}+\frac{i a \sqrt{-a^{2}+b^{2}}+a^{2}-b^{2}}{\sqrt{-a^{2}+b^{2}}\, b}\right)}{\sqrt{-a^{2}+b^{2}}\, b}"," ",0,"-2*I*x*exp(I*x)/b/(b*exp(2*I*x)-b+2*I*a*exp(I*x))-1/(-a^2+b^2)^(1/2)/b*ln(exp(I*x)+(I*a*(-a^2+b^2)^(1/2)-a^2+b^2)/(-a^2+b^2)^(1/2)/b)+1/(-a^2+b^2)^(1/2)/b*ln(exp(I*x)+(I*a*(-a^2+b^2)^(1/2)+a^2-b^2)/(-a^2+b^2)^(1/2)/b)","C"
154,1,257,75,0.829000," ","int(x*cos(x)/(a+b*sin(x))^3,x)","\frac{2 i a^{2} {\mathrm e}^{2 i x}+i b^{2} {\mathrm e}^{2 i x}+2 x \,a^{2} {\mathrm e}^{2 i x}+b a \,{\mathrm e}^{3 i x}-2 b^{2} x \,{\mathrm e}^{2 i x}-i b^{2}-3 a b \,{\mathrm e}^{i x}}{\left(b \,{\mathrm e}^{2 i x}-b +2 i a \,{\mathrm e}^{i x}\right)^{2} \left(a^{2}-b^{2}\right) b}-\frac{a \ln \left({\mathrm e}^{i x}+\frac{i a \sqrt{-a^{2}+b^{2}}-a^{2}+b^{2}}{\sqrt{-a^{2}+b^{2}}\, b}\right)}{2 \sqrt{-a^{2}+b^{2}}\, \left(a +b \right) \left(a -b \right) b}+\frac{a \ln \left({\mathrm e}^{i x}+\frac{i a \sqrt{-a^{2}+b^{2}}+a^{2}-b^{2}}{\sqrt{-a^{2}+b^{2}}\, b}\right)}{2 \sqrt{-a^{2}+b^{2}}\, \left(a +b \right) \left(a -b \right) b}"," ",0,"(2*I*a^2*exp(2*I*x)+I*b^2*exp(2*I*x)+2*x*a^2*exp(2*I*x)+b*a*exp(3*I*x)-2*b^2*x*exp(2*I*x)-I*b^2-3*a*b*exp(I*x))/(b*exp(2*I*x)-b+2*I*a*exp(I*x))^2/(a^2-b^2)/b-1/2/(-a^2+b^2)^(1/2)*a/(a+b)/(a-b)/b*ln(exp(I*x)+(I*a*(-a^2+b^2)^(1/2)-a^2+b^2)/(-a^2+b^2)^(1/2)/b)+1/2/(-a^2+b^2)^(1/2)*a/(a+b)/(a-b)/b*ln(exp(I*x)+(I*a*(-a^2+b^2)^(1/2)+a^2-b^2)/(-a^2+b^2)^(1/2)/b)","C"
155,1,154,49,0.264000," ","int(x*sin(x)/(a+b*cos(x))^2,x)","\frac{2 x \,{\mathrm e}^{i x}}{b \left(b \,{\mathrm e}^{2 i x}+2 a \,{\mathrm e}^{i x}+b \right)}-\frac{i \ln \left({\mathrm e}^{i x}+\frac{a \sqrt{a^{2}-b^{2}}+a^{2}-b^{2}}{\sqrt{a^{2}-b^{2}}\, b}\right)}{\sqrt{a^{2}-b^{2}}\, b}+\frac{i \ln \left({\mathrm e}^{i x}+\frac{a \sqrt{a^{2}-b^{2}}-a^{2}+b^{2}}{\sqrt{a^{2}-b^{2}}\, b}\right)}{\sqrt{a^{2}-b^{2}}\, b}"," ",0,"2*x*exp(I*x)/b/(b*exp(2*I*x)+2*a*exp(I*x)+b)-I/(a^2-b^2)^(1/2)/b*ln(exp(I*x)+(a*(a^2-b^2)^(1/2)+a^2-b^2)/(a^2-b^2)^(1/2)/b)+I/(a^2-b^2)^(1/2)/b*ln(exp(I*x)+(a*(a^2-b^2)^(1/2)-a^2+b^2)/(a^2-b^2)^(1/2)/b)","C"
156,1,250,74,0.435000," ","int(x*sin(x)/(a+b*cos(x))^3,x)","\frac{i \left(-2 i a^{2} x \,{\mathrm e}^{2 i x}+2 i b^{2} x \,{\mathrm e}^{2 i x}+b a \,{\mathrm e}^{3 i x}+2 a^{2} {\mathrm e}^{2 i x}+b^{2} {\mathrm e}^{2 i x}+3 a b \,{\mathrm e}^{i x}+b^{2}\right)}{b \left(b \,{\mathrm e}^{2 i x}+2 a \,{\mathrm e}^{i x}+b \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{i a \ln \left({\mathrm e}^{i x}+\frac{a \sqrt{a^{2}-b^{2}}+a^{2}-b^{2}}{\sqrt{a^{2}-b^{2}}\, b}\right)}{2 \sqrt{a^{2}-b^{2}}\, \left(a +b \right) \left(a -b \right) b}+\frac{i a \ln \left({\mathrm e}^{i x}+\frac{a \sqrt{a^{2}-b^{2}}-a^{2}+b^{2}}{\sqrt{a^{2}-b^{2}}\, b}\right)}{2 \sqrt{a^{2}-b^{2}}\, \left(a +b \right) \left(a -b \right) b}"," ",0,"I*(-2*I*a^2*x*exp(2*I*x)+2*I*b^2*x*exp(2*I*x)+b*a*exp(3*I*x)+2*a^2*exp(2*I*x)+b^2*exp(2*I*x)+3*a*b*exp(I*x)+b^2)/b/(b*exp(2*I*x)+2*a*exp(I*x)+b)^2/(a^2-b^2)-1/2*I/(a^2-b^2)^(1/2)*a/(a+b)/(a-b)/b*ln(exp(I*x)+(a*(a^2-b^2)^(1/2)+a^2-b^2)/(a^2-b^2)^(1/2)/b)+1/2*I/(a^2-b^2)^(1/2)*a/(a+b)/(a-b)/b*ln(exp(I*x)+(a*(a^2-b^2)^(1/2)-a^2+b^2)/(a^2-b^2)^(1/2)/b)","C"
157,1,86,50,0.318000," ","int(x*sec(x)^2/(a+b*tan(x))^2,x)","-\frac{2 i x}{a^{2}+b^{2}}+\frac{2 i x}{\left(-i b \,{\mathrm e}^{2 i x}+a \,{\mathrm e}^{2 i x}+i b +a \right) \left(-i b +a \right)}+\frac{\ln \left({\mathrm e}^{2 i x}-\frac{i b +a}{i b -a}\right)}{a^{2}+b^{2}}"," ",0,"-2*I/(a^2+b^2)*x+2*I*x/(-I*b*exp(2*I*x)+a*exp(2*I*x)+I*b+a)/(-I*b+a)+1/(a^2+b^2)*ln(exp(2*I*x)-(I*b+a)/(I*b-a))","C"
158,1,87,50,0.308000," ","int(x*csc(x)^2/(a+b*cot(x))^2,x)","-\frac{2 i x}{a^{2}+b^{2}}-\frac{2 i x}{\left(i b \,{\mathrm e}^{2 i x}+a \,{\mathrm e}^{2 i x}+i b -a \right) \left(i b +a \right)}+\frac{\ln \left({\mathrm e}^{2 i x}+\frac{i b -a}{i b +a}\right)}{a^{2}+b^{2}}"," ",0,"-2*I/(a^2+b^2)*x-2*I*x/(I*b*exp(2*I*x)+a*exp(2*I*x)+I*b-a)/(I*b+a)+1/(a^2+b^2)*ln(exp(2*I*x)+(I*b-a)/(I*b+a))","C"
159,1,24,24,0.322000," ","int(sec(d*x+c)^2/(a+b*tan(d*x+c)^2),x)","\frac{\arctan \left(\frac{\tan \left(d x +c \right) b}{\sqrt{a b}}\right)}{d \sqrt{a b}}"," ",0,"1/d/(a*b)^(1/2)*arctan(tan(d*x+c)*b/(a*b)^(1/2))","A"
160,1,1003,161,0.602000," ","int(x*sec(d*x+c)^2/(a+b*tan(d*x+c)^2),x)","-\frac{a c x}{d \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{b c x}{d \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right) a x}{2 d \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{\polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right)}{2 d^{2} \left(-2 \sqrt{a b}-a -b \right)}-\frac{\polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a b}-a -b}\right)}{4 d^{2} \sqrt{a b}}-\frac{a \,c^{2}}{2 d^{2} \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{b \,c^{2}}{2 d^{2} \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a b}-a -b}\right) c}{2 d^{2} \sqrt{a b}}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right) c}{d^{2} \left(-2 \sqrt{a b}-a -b \right)}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a b}-a -b}\right) x}{2 d \sqrt{a b}}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right) x}{d \left(-2 \sqrt{a b}-a -b \right)}-\frac{\polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right) b}{4 d^{2} \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{\polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right) a}{4 d^{2} \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{i c \arctanh \left(\frac{2 \left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}+2 a +2 b}{4 \sqrt{a b}}\right)}{d^{2} \sqrt{a b}}-\frac{c^{2}}{2 d^{2} \sqrt{a b}}-\frac{c^{2}}{d^{2} \left(-2 \sqrt{a b}-a -b \right)}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right) a c}{2 d^{2} \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{a \,x^{2}}{2 \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{b \,x^{2}}{2 \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{c x}{d \sqrt{a b}}-\frac{2 c x}{d \left(-2 \sqrt{a b}-a -b \right)}-\frac{x^{2}}{2 \sqrt{a b}}-\frac{x^{2}}{-2 \sqrt{a b}-a -b}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right) b c}{2 d^{2} \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right) b x}{2 d \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}"," ",0,"-1/d/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*a*c*x-1/d/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*b*c*x-1/2*I/d^2/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))*a*c-1/4/d^2/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*polylog(2,(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))*b-1/2/d^2/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*a*c^2-1/2/d^2/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*b*c^2-1/4/d^2/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*polylog(2,(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))*a-I/d^2*c/(a*b)^(1/2)*arctanh(1/4*(2*(a-b)*exp(2*I*(d*x+c))+2*a+2*b)/(a*b)^(1/2))-1/2*I/d^2/(a*b)^(1/2)*ln(1-(a-b)*exp(2*I*(d*x+c))/(2*(a*b)^(1/2)-a-b))*c-I/d^2/(-2*(a*b)^(1/2)-a-b)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))*c-1/2*I/d/(a*b)^(1/2)*ln(1-(a-b)*exp(2*I*(d*x+c))/(2*(a*b)^(1/2)-a-b))*x-I/d/(-2*(a*b)^(1/2)-a-b)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))*x-1/2/d^2/(a*b)^(1/2)*c^2-1/d^2/(-2*(a*b)^(1/2)-a-b)*c^2-1/2/d^2/(-2*(a*b)^(1/2)-a-b)*polylog(2,(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))-1/4/d^2/(a*b)^(1/2)*polylog(2,(a-b)*exp(2*I*(d*x+c))/(2*(a*b)^(1/2)-a-b))-1/2/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*a*x^2-1/2/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*b*x^2-1/d/(a*b)^(1/2)*c*x-2/d/(-2*(a*b)^(1/2)-a-b)*c*x-1/2*I/d/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))*b*x-1/2*I/d^2/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))*b*c-1/2*I/d/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))*a*x-1/2/(a*b)^(1/2)*x^2-1/(-2*(a*b)^(1/2)-a-b)*x^2","B"
161,1,1251,253,0.463000," ","int(x^2*sec(d*x+c)^2/(a+b*tan(d*x+c)^2),x)","\frac{2 a \,c^{3}}{3 d^{3} \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}+\frac{2 b \,c^{3}}{3 d^{3} \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right) x^{2}}{d \left(-2 \sqrt{a b}-a -b \right)}+\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right) c^{2}}{d^{3} \left(-2 \sqrt{a b}-a -b \right)}+\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a b}-a -b}\right) c^{2}}{2 d^{3} \sqrt{a b}}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a b}-a -b}\right) x^{2}}{2 d \sqrt{a b}}+\frac{i c^{2} \arctanh \left(\frac{2 \left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}+2 a +2 b}{4 \sqrt{a b}}\right)}{d^{3} \sqrt{a b}}+\frac{2 c^{3}}{3 d^{3} \sqrt{a b}}+\frac{4 c^{3}}{3 d^{3} \left(-2 \sqrt{a b}-a -b \right)}+\frac{c^{2} x}{d^{2} \sqrt{a b}}+\frac{2 c^{2} x}{d^{2} \left(-2 \sqrt{a b}-a -b \right)}-\frac{b \,x^{3}}{3 \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{a \,x^{3}}{3 \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{\polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a b}-a -b}\right) x}{2 d^{2} \sqrt{a b}}-\frac{\polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right) x}{d^{2} \left(-2 \sqrt{a b}-a -b \right)}-\frac{i \polylog \left(3, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{a b}-a -b}\right)}{4 d^{3} \sqrt{a b}}-\frac{i \polylog \left(3, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right)}{2 d^{3} \left(-2 \sqrt{a b}-a -b \right)}+\frac{i b \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right) c^{2}}{2 d^{3} \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{i a \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right) x^{2}}{2 d \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{i b \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right) x^{2}}{2 d \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}+\frac{i a \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right) c^{2}}{2 d^{3} \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{x^{3}}{3 \sqrt{a b}}-\frac{2 x^{3}}{3 \left(-2 \sqrt{a b}-a -b \right)}+\frac{a \,c^{2} x}{d^{2} \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{i a \polylog \left(3, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right)}{4 d^{3} \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{i b \polylog \left(3, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right)}{4 d^{3} \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{b \polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right) x}{2 d^{2} \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}-\frac{a \polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{a b}-a -b}\right) x}{2 d^{2} \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}+\frac{b \,c^{2} x}{d^{2} \sqrt{a b}\, \left(-2 \sqrt{a b}-a -b \right)}"," ",0,"I/d^3*c^2/(a*b)^(1/2)*arctanh(1/4*(2*(a-b)*exp(2*I*(d*x+c))+2*a+2*b)/(a*b)^(1/2))-I/d/(-2*(a*b)^(1/2)-a-b)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))*x^2+2/3/d^3/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*a*c^3+2/3/d^3/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*b*c^3+I/d^3/(-2*(a*b)^(1/2)-a-b)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))*c^2+1/2*I/d^3/(a*b)^(1/2)*ln(1-(a-b)*exp(2*I*(d*x+c))/(2*(a*b)^(1/2)-a-b))*c^2-1/2*I/d/(a*b)^(1/2)*ln(1-(a-b)*exp(2*I*(d*x+c))/(2*(a*b)^(1/2)-a-b))*x^2+2/3/d^3/(a*b)^(1/2)*c^3+4/3/d^3/(-2*(a*b)^(1/2)-a-b)*c^3+1/d^2/(a*b)^(1/2)*c^2*x+2/d^2/(-2*(a*b)^(1/2)-a-b)*c^2*x-1/2/d^2/(a*b)^(1/2)*polylog(2,(a-b)*exp(2*I*(d*x+c))/(2*(a*b)^(1/2)-a-b))*x-1/d^2/(-2*(a*b)^(1/2)-a-b)*polylog(2,(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))*x-1/3/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*b*x^3-1/3/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*a*x^3-1/4*I/d^3/(a*b)^(1/2)*polylog(3,(a-b)*exp(2*I*(d*x+c))/(2*(a*b)^(1/2)-a-b))-1/2*I/d^3/(-2*(a*b)^(1/2)-a-b)*polylog(3,(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))+1/2*I/d^3/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*b*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))*c^2-1/2*I/d/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*a*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))*x^2-1/2*I/d/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*b*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))*x^2-1/3/(a*b)^(1/2)*x^3-2/3/(-2*(a*b)^(1/2)-a-b)*x^3+1/d^2/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*a*c^2*x+1/d^2/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*b*c^2*x-1/2/d^2/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*b*polylog(2,(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))*x-1/2/d^2/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*a*polylog(2,(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))*x-1/4*I/d^3/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*a*polylog(3,(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))-1/4*I/d^3/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*b*polylog(3,(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))+1/2*I/d^3/(a*b)^(1/2)/(-2*(a*b)^(1/2)-a-b)*a*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*(a*b)^(1/2)-a-b))*c^2","B"
162,1,34,32,0.362000," ","int(sec(d*x+c)^2/(a+c*sec(d*x+c)^2+b*tan(d*x+c)^2),x)","\frac{\arctan \left(\frac{\left(b +c \right) \tan \left(d x +c \right)}{\sqrt{\left(a +c \right) \left(b +c \right)}}\right)}{d \sqrt{\left(a +c \right) \left(b +c \right)}}"," ",0,"1/d/((a+c)*(b+c))^(1/2)*arctan((b+c)*tan(d*x+c)/((a+c)*(b+c))^(1/2))","A"
163,1,1670,217,0.605000," ","int(x*sec(d*x+c)^2/(a+c*sec(d*x+c)^2+b*tan(d*x+c)^2),x)","-\frac{a c x}{d \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{b c x}{d \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) c^{2}}{d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) c}{2 d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) c}{d^{2} \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) x}{2 d \sqrt{\left(a +c \right) \left(b +c \right)}}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) x}{d \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) a x}{2 d \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) b c}{2 d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{i c \arctanh \left(\frac{2 \left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}+2 a +2 b +4 c}{4 \sqrt{a b +a c +c b +c^{2}}}\right)}{d^{2} \sqrt{a b +a c +c b +c^{2}}}-\frac{\polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) a}{4 d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{\polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) b}{4 d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{\polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) c}{2 d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{c x}{d \sqrt{\left(a +c \right) \left(b +c \right)}}-\frac{2 c x}{d \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{c^{3}}{d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{b \,x^{2}}{2 \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{c \,x^{2}}{\sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{a \,x^{2}}{2 \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{\polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right)}{4 d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}}-\frac{\polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right)}{2 d^{2} \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) c x}{d \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) a c}{2 d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{2 c^{2} x}{d \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{a \,c^{2}}{2 d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{b \,c^{2}}{2 d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{c^{2}}{2 d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}}-\frac{c^{2}}{d^{2} \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{x^{2}}{2 \sqrt{\left(a +c \right) \left(b +c \right)}}-\frac{x^{2}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) b x}{2 d \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}"," ",0,"-1/d/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*a*c*x-1/d/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*b*c*x-I/d^2/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*c^2-1/2*I/d^2/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*b*c-1/2*I/d/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*a*x-1/2*I/d/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*b*x-1/2*I/d^2/((a+c)*(b+c))^(1/2)*ln(1-(a-b)*exp(2*I*(d*x+c))/(2*((a+c)*(b+c))^(1/2)-a-b-2*c))*c-I/d^2/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*c-1/2*I/d/((a+c)*(b+c))^(1/2)*ln(1-(a-b)*exp(2*I*(d*x+c))/(2*((a+c)*(b+c))^(1/2)-a-b-2*c))*x-I/d/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*x-I/d^2*c/(a*b+a*c+b*c+c^2)^(1/2)*arctanh(1/4*(2*(a-b)*exp(2*I*(d*x+c))+2*a+2*b+4*c)/(a*b+a*c+b*c+c^2)^(1/2))-1/d/((a+c)*(b+c))^(1/2)*c*x-2/d/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*c*x-1/d^2/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*c^3-1/2/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*b*x^2-1/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*c*x^2-1/2/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*a*x^2-I/d/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*c*x-1/2*I/d^2/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*a*c-2/d/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*c^2*x-1/2/d^2/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*a*c^2-1/2/d^2/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*b*c^2-1/4/d^2/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*polylog(2,(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*a-1/4/d^2/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*polylog(2,(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*b-1/2/d^2/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*polylog(2,(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*c-1/4/d^2/((a+c)*(b+c))^(1/2)*polylog(2,(a-b)*exp(2*I*(d*x+c))/(2*((a+c)*(b+c))^(1/2)-a-b-2*c))-1/2/d^2/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*polylog(2,(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))-1/2/d^2/((a+c)*(b+c))^(1/2)*c^2-1/d^2/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*c^2-1/2/((a+c)*(b+c))^(1/2)*x^2-1/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*x^2","B"
164,1,2061,331,0.547000," ","int(x^2*sec(d*x+c)^2/(a+c*sec(d*x+c)^2+b*tan(d*x+c)^2),x)","-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) x^{2}}{d \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{i \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) x^{2}}{2 d \sqrt{\left(a +c \right) \left(b +c \right)}}+\frac{i c^{2} \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right)}{2 d^{3} \sqrt{\left(a +c \right) \left(b +c \right)}}+\frac{i c^{2} \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right)}{d^{3} \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}+\frac{i c^{2} \arctanh \left(\frac{2 \left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}+2 a +2 b +4 c}{4 \sqrt{a b +a c +c b +c^{2}}}\right)}{d^{3} \sqrt{a b +a c +c b +c^{2}}}+\frac{a \,c^{2} x}{d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}+\frac{b \,c^{2} x}{d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}+\frac{2 c^{3} x}{d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}+\frac{2 a \,c^{3}}{3 d^{3} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}+\frac{2 b \,c^{3}}{3 d^{3} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{a \,x^{3}}{3 \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{b \,x^{3}}{3 \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{2 c \,x^{3}}{3 \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}+\frac{4 c^{4}}{3 d^{3} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}+\frac{c^{2} x}{d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}}+\frac{2 c^{2} x}{d^{2} \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{\polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) x}{2 d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}}-\frac{\polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) x}{d^{2} \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{i \polylog \left(3, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right)}{4 d^{3} \sqrt{\left(a +c \right) \left(b +c \right)}}+\frac{2 c^{3}}{3 d^{3} \sqrt{\left(a +c \right) \left(b +c \right)}}+\frac{4 c^{3}}{3 d^{3} \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{i c \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) x^{2}}{d \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{i b \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) x^{2}}{2 d \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{i a \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) x^{2}}{2 d \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}+\frac{i b \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) c^{2}}{2 d^{3} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}+\frac{i a \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) c^{2}}{2 d^{3} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}+\frac{i c^{3} \ln \left(1-\frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right)}{d^{3} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{b \polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) x}{2 d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{c \polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) x}{d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{a \polylog \left(2, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right) x}{2 d^{2} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{i a \polylog \left(3, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right)}{4 d^{3} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{i b \polylog \left(3, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right)}{4 d^{3} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{i c \polylog \left(3, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right)}{2 d^{3} \sqrt{\left(a +c \right) \left(b +c \right)}\, \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{i \polylog \left(3, \frac{\left(a -b \right) {\mathrm e}^{2 i \left(d x +c \right)}}{-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c}\right)}{2 d^{3} \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}-\frac{x^{3}}{3 \sqrt{\left(a +c \right) \left(b +c \right)}}-\frac{2 x^{3}}{3 \left(-2 \sqrt{\left(a +c \right) \left(b +c \right)}-a -b -2 c \right)}"," ",0,"-I/d/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*c*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*x^2-1/2*I/d/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*b*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*x^2-1/2*I/d/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*a*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*x^2+1/2*I/d^3/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*b*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*c^2+1/2*I/d^3/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*a*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*c^2-1/2/d^2/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*b*polylog(2,(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*x-1/d^2/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*c*polylog(2,(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*x-1/2/d^2/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*a*polylog(2,(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*x+1/d^2/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*a*c^2*x+1/d^2/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*b*c^2*x-1/4*I/d^3/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*a*polylog(3,(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))-1/4*I/d^3/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*b*polylog(3,(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))+2/d^2*c^3/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*x+2/3/d^3/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*a*c^3+2/3/d^3/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*b*c^3+I/d^3*c^2/(a*b+a*c+b*c+c^2)^(1/2)*arctanh(1/4*(2*(a-b)*exp(2*I*(d*x+c))+2*a+2*b+4*c)/(a*b+a*c+b*c+c^2)^(1/2))-I/d/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*x^2-1/2*I/d/((a+c)*(b+c))^(1/2)*ln(1-(a-b)*exp(2*I*(d*x+c))/(2*((a+c)*(b+c))^(1/2)-a-b-2*c))*x^2+1/2*I/d^3*c^2/((a+c)*(b+c))^(1/2)*ln(1-(a-b)*exp(2*I*(d*x+c))/(2*((a+c)*(b+c))^(1/2)-a-b-2*c))+I/d^3*c^2/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))-1/3/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*a*x^3-1/3/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*b*x^3-2/3/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*c*x^3-1/2/d^2/((a+c)*(b+c))^(1/2)*polylog(2,(a-b)*exp(2*I*(d*x+c))/(2*((a+c)*(b+c))^(1/2)-a-b-2*c))*x-1/d^2/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*polylog(2,(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))*x+4/3/d^3*c^4/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)+1/d^2*c^2/((a+c)*(b+c))^(1/2)*x+2/d^2*c^2/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*x-1/4*I/d^3/((a+c)*(b+c))^(1/2)*polylog(3,(a-b)*exp(2*I*(d*x+c))/(2*((a+c)*(b+c))^(1/2)-a-b-2*c))-1/2*I/d^3/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*polylog(3,(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))+2/3/d^3*c^3/((a+c)*(b+c))^(1/2)+4/3/d^3*c^3/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)-1/2*I/d^3/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*c*polylog(3,(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))+I/d^3/((a+c)*(b+c))^(1/2)/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*c^3*ln(1-(a-b)*exp(2*I*(d*x+c))/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c))-1/3/((a+c)*(b+c))^(1/2)*x^3-2/3/(-2*((a+c)*(b+c))^(1/2)-a-b-2*c)*x^3","B"
165,0,0,139,0.402000," ","int(x^3*(a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2),x)","\int x^{3} \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{c +c \sin \left(f x +e \right)}\, dx"," ",0,"int(x^3*(a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2),x)","F"
166,0,0,106,0.176000," ","int(x^2*(a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2),x)","\int x^{2} \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{c +c \sin \left(f x +e \right)}\, dx"," ",0,"int(x^2*(a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2),x)","F"
167,0,0,66,0.169000," ","int(x*(a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2),x)","\int x \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{c +c \sin \left(f x +e \right)}\, dx"," ",0,"int(x*(a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2),x)","F"
168,0,0,78,0.174000," ","int((a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2)/x,x)","\int \frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{c +c \sin \left(f x +e \right)}}{x}\, dx"," ",0,"int((a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2)/x,x)","F"
169,0,0,111,0.183000," ","int((a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2)/x^2,x)","\int \frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{c +c \sin \left(f x +e \right)}}{x^{2}}\, dx"," ",0,"int((a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2)/x^2,x)","F"
170,0,0,152,0.184000," ","int((a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2)/x^3,x)","\int \frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{c +c \sin \left(f x +e \right)}}{x^{3}}\, dx"," ",0,"int((a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2)/x^3,x)","F"
171,0,0,345,0.177000," ","int(x^3*(c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2),x)","\int x^{3} \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}\, dx"," ",0,"int(x^3*(c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2),x)","F"
172,0,0,233,0.170000," ","int(x^2*(c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2),x)","\int x^{2} \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}\, dx"," ",0,"int(x^2*(c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2),x)","F"
173,0,0,146,0.168000," ","int(x*(c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2),x)","\int x \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}\, dx"," ",0,"int(x*(c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2),x)","F"
174,0,0,166,0.171000," ","int((c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2)/x,x)","\int \frac{\left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}}{x}\, dx"," ",0,"int((c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2)/x,x)","F"
175,0,0,247,0.171000," ","int((c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2)/x^2,x)","\int \frac{\left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}}{x^{2}}\, dx"," ",0,"int((c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2)/x^2,x)","F"
176,0,0,341,0.168000," ","int((c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2)/x^3,x)","\int \frac{\left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}}{x^{3}}\, dx"," ",0,"int((c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2)/x^3,x)","F"
177,0,0,675,0.208000," ","int((h*x+g)^3*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(1/2),x)","\int \frac{\left(h x +g \right)^{3} \sqrt{a -a \sin \left(f x +e \right)}}{\sqrt{c +c \sin \left(f x +e \right)}}\, dx"," ",0,"int((h*x+g)^3*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(1/2),x)","F"
178,0,0,490,0.187000," ","int((h*x+g)^2*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(1/2),x)","\int \frac{\left(h x +g \right)^{2} \sqrt{a -a \sin \left(f x +e \right)}}{\sqrt{c +c \sin \left(f x +e \right)}}\, dx"," ",0,"int((h*x+g)^2*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(1/2),x)","F"
179,0,0,310,0.354000," ","int((h*x+g)*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(1/2),x)","\int \frac{\left(h x +g \right) \sqrt{a -a \sin \left(f x +e \right)}}{\sqrt{c +c \sin \left(f x +e \right)}}\, dx"," ",0,"int((h*x+g)*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(1/2),x)","F"
180,0,0,100,0.188000," ","int((a-a*sin(f*x+e))^(1/2)/(h*x+g)/(c+c*sin(f*x+e))^(1/2),x)","\int \frac{\sqrt{a -a \sin \left(f x +e \right)}}{\left(h x +g \right) \sqrt{c +c \sin \left(f x +e \right)}}\, dx"," ",0,"int((a-a*sin(f*x+e))^(1/2)/(h*x+g)/(c+c*sin(f*x+e))^(1/2),x)","F"
181,0,0,479,0.144000," ","int(x^3*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(3/2),x)","\int \frac{x^{3} \sqrt{a -a \sin \left(f x +e \right)}}{\left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(3/2),x)","F"
182,0,0,256,0.150000," ","int(x^2*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(3/2),x)","\int \frac{x^{2} \sqrt{a -a \sin \left(f x +e \right)}}{\left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(3/2),x)","F"
183,0,0,155,0.146000," ","int(x*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(3/2),x)","\int \frac{x \sqrt{a -a \sin \left(f x +e \right)}}{\left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(3/2),x)","F"
184,1,154,240,0.145000," ","int(z^2*(1+cos(z))^(1/2)/(1-cos(z))^(1/2),z)","\frac{\left({\mathrm e}^{i z}-1\right) \sqrt{\left({\mathrm e}^{i z}+1\right)^{2} {\mathrm e}^{-i z}}\, z^{3}}{3 \sqrt{-\left({\mathrm e}^{i z}-1\right)^{2} {\mathrm e}^{-i z}}\, \left({\mathrm e}^{i z}+1\right)}+\frac{2 i \left({\mathrm e}^{i z}-1\right) \sqrt{\left({\mathrm e}^{i z}+1\right)^{2} {\mathrm e}^{-i z}}\, \left(\frac{i z^{3}}{3}-z^{2} \ln \left(1-{\mathrm e}^{i z}\right)+2 i z \polylog \left(2, {\mathrm e}^{i z}\right)-2 \polylog \left(3, {\mathrm e}^{i z}\right)\right)}{\sqrt{-\left({\mathrm e}^{i z}-1\right)^{2} {\mathrm e}^{-i z}}\, \left({\mathrm e}^{i z}+1\right)}"," ",0,"1/3/(-(exp(I*z)-1)^2*exp(-I*z))^(1/2)*(exp(I*z)-1)*((exp(I*z)+1)^2*exp(-I*z))^(1/2)/(exp(I*z)+1)*z^3+2*I/(-(exp(I*z)-1)^2*exp(-I*z))^(1/2)*(exp(I*z)-1)*((exp(I*z)+1)^2*exp(-I*z))^(1/2)/(exp(I*z)+1)*(1/3*I*z^3-z^2*ln(1-exp(I*z))+2*I*z*polylog(2,exp(I*z))-2*polylog(3,exp(I*z)))","A"
185,1,24,18,0.099000," ","int((a+a*cos(x))*(A+B*sec(x)),x)","a A \sin \left(x \right)+B a x +a A x +B a \ln \left(\sec \left(x \right)+\tan \left(x \right)\right)"," ",0,"a*A*sin(x)+B*a*x+a*A*x+B*a*ln(sec(x)+tan(x))","A"
186,1,52,51,0.100000," ","int((a+a*cos(x))^2*(A+B*sec(x)),x)","\frac{a^{2} A \sin \left(x \right) \cos \left(x \right)}{2}+\frac{3 a^{2} A x}{2}+a^{2} B \sin \left(x \right)+2 a^{2} A \sin \left(x \right)+2 a^{2} B x +a^{2} B \ln \left(\sec \left(x \right)+\tan \left(x \right)\right)"," ",0,"1/2*a^2*A*sin(x)*cos(x)+3/2*a^2*A*x+a^2*B*sin(x)+2*a^2*A*sin(x)+2*a^2*B*x+a^2*B*ln(sec(x)+tan(x))","A"
187,1,77,67,0.106000," ","int((a+a*cos(x))^3*(A+B*sec(x)),x)","\frac{A \,a^{3} \left(2+\cos^{2}\left(x \right)\right) \sin \left(x \right)}{3}+\frac{B \,a^{3} \sin \left(x \right) \cos \left(x \right)}{2}+\frac{7 B \,a^{3} x}{2}+\frac{3 A \,a^{3} \sin \left(x \right) \cos \left(x \right)}{2}+\frac{5 A \,a^{3} x}{2}+3 B \,a^{3} \sin \left(x \right)+3 A \,a^{3} \sin \left(x \right)+B \,a^{3} \ln \left(\sec \left(x \right)+\tan \left(x \right)\right)"," ",0,"1/3*A*a^3*(2+cos(x)^2)*sin(x)+1/2*B*a^3*sin(x)*cos(x)+7/2*B*a^3*x+3/2*A*a^3*sin(x)*cos(x)+5/2*A*a^3*x+3*B*a^3*sin(x)+3*A*a^3*sin(x)+B*a^3*ln(sec(x)+tan(x))","A"
188,1,103,94,0.115000," ","int((a+a*cos(x))^4*(A+B*sec(x)),x)","\frac{A \,a^{4} \sin \left(x \right) \left(\cos^{3}\left(x \right)\right)}{4}+\frac{27 A \,a^{4} \sin \left(x \right) \cos \left(x \right)}{8}+\frac{35 A \,a^{4} x}{8}+\frac{B \,a^{4} \left(2+\cos^{2}\left(x \right)\right) \sin \left(x \right)}{3}+\frac{4 A \,a^{4} \left(2+\cos^{2}\left(x \right)\right) \sin \left(x \right)}{3}+2 B \,a^{4} \sin \left(x \right) \cos \left(x \right)+6 B \,a^{4} x +6 B \,a^{4} \sin \left(x \right)+4 A \,a^{4} \sin \left(x \right)+B \,a^{4} \ln \left(\sec \left(x \right)+\tan \left(x \right)\right)"," ",0,"1/4*A*a^4*sin(x)*cos(x)^3+27/8*A*a^4*sin(x)*cos(x)+35/8*A*a^4*x+1/3*B*a^4*(2+cos(x)^2)*sin(x)+4/3*A*a^4*(2+cos(x)^2)*sin(x)+2*B*a^4*sin(x)*cos(x)+6*B*a^4*x+6*B*a^4*sin(x)+4*A*a^4*sin(x)+B*a^4*ln(sec(x)+tan(x))","A"
189,1,46,25,0.088000," ","int((A+B*sec(x))/(a+a*cos(x)),x)","\frac{A \tan \left(\frac{x}{2}\right)}{a}-\frac{B \tan \left(\frac{x}{2}\right)}{a}-\frac{B \ln \left(\tan \left(\frac{x}{2}\right)-1\right)}{a}+\frac{B \ln \left(1+\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"1/a*A*tan(1/2*x)-1/a*B*tan(1/2*x)-1/a*B*ln(tan(1/2*x)-1)+1/a*B*ln(1+tan(1/2*x))","A"
190,1,71,44,0.087000," ","int((A+B*sec(x))/(a+a*cos(x))^2,x)","\frac{\left(\tan^{3}\left(\frac{x}{2}\right)\right) A}{6 a^{2}}-\frac{\left(\tan^{3}\left(\frac{x}{2}\right)\right) B}{6 a^{2}}+\frac{A \tan \left(\frac{x}{2}\right)}{2 a^{2}}-\frac{3 B \tan \left(\frac{x}{2}\right)}{2 a^{2}}-\frac{B \ln \left(\tan \left(\frac{x}{2}\right)-1\right)}{a^{2}}+\frac{B \ln \left(1+\tan \left(\frac{x}{2}\right)\right)}{a^{2}}"," ",0,"1/6/a^2*tan(1/2*x)^3*A-1/6/a^2*tan(1/2*x)^3*B+1/2/a^2*A*tan(1/2*x)-3/2/a^2*B*tan(1/2*x)-1/a^2*B*ln(tan(1/2*x)-1)+1/a^2*B*ln(1+tan(1/2*x))","A"
191,1,95,69,0.096000," ","int((A+B*sec(x))/(a+a*cos(x))^3,x)","\frac{\left(\tan^{3}\left(\frac{x}{2}\right)\right) A}{6 a^{3}}-\frac{\left(\tan^{3}\left(\frac{x}{2}\right)\right) B}{3 a^{3}}-\frac{B \ln \left(\tan \left(\frac{x}{2}\right)-1\right)}{a^{3}}+\frac{A \tan \left(\frac{x}{2}\right)}{4 a^{3}}-\frac{7 B \tan \left(\frac{x}{2}\right)}{4 a^{3}}+\frac{B \ln \left(1+\tan \left(\frac{x}{2}\right)\right)}{a^{3}}+\frac{\left(\tan^{5}\left(\frac{x}{2}\right)\right) A}{20 a^{3}}-\frac{\left(\tan^{5}\left(\frac{x}{2}\right)\right) B}{20 a^{3}}"," ",0,"1/6/a^3*tan(1/2*x)^3*A-1/3/a^3*tan(1/2*x)^3*B-1/a^3*B*ln(tan(1/2*x)-1)+1/4/a^3*A*tan(1/2*x)-7/4/a^3*B*tan(1/2*x)+1/a^3*B*ln(1+tan(1/2*x))+1/20/a^3*tan(1/2*x)^5*A-1/20/a^3*tan(1/2*x)^5*B","A"
192,1,119,88,0.096000," ","int((A+B*sec(x))/(a+a*cos(x))^4,x)","\frac{\left(\tan^{7}\left(\frac{x}{2}\right)\right) A}{56 a^{4}}-\frac{\left(\tan^{7}\left(\frac{x}{2}\right)\right) B}{56 a^{4}}+\frac{\left(\tan^{3}\left(\frac{x}{2}\right)\right) A}{8 a^{4}}-\frac{11 \left(\tan^{3}\left(\frac{x}{2}\right)\right) B}{24 a^{4}}-\frac{B \ln \left(\tan \left(\frac{x}{2}\right)-1\right)}{a^{4}}+\frac{A \tan \left(\frac{x}{2}\right)}{8 a^{4}}-\frac{15 B \tan \left(\frac{x}{2}\right)}{8 a^{4}}+\frac{B \ln \left(1+\tan \left(\frac{x}{2}\right)\right)}{a^{4}}+\frac{3 \left(\tan^{5}\left(\frac{x}{2}\right)\right) A}{40 a^{4}}-\frac{\left(\tan^{5}\left(\frac{x}{2}\right)\right) B}{8 a^{4}}"," ",0,"1/56/a^4*tan(1/2*x)^7*A-1/56/a^4*tan(1/2*x)^7*B+1/8/a^4*tan(1/2*x)^3*A-11/24/a^4*tan(1/2*x)^3*B-1/a^4*B*ln(tan(1/2*x)-1)+1/8/a^4*A*tan(1/2*x)-15/8/a^4*B*tan(1/2*x)+1/a^4*B*ln(1+tan(1/2*x))+3/40/a^4*tan(1/2*x)^5*A-1/8/a^4*tan(1/2*x)^5*B","A"
193,1,228,80,0.382000," ","int((a+a*cos(x))^(5/2)*(A+B*sec(x)),x)","\frac{a^{\frac{3}{2}} \cos \left(\frac{x}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \left(24 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \sqrt{a}\, \left(\sin^{4}\left(\frac{x}{2}\right)\right)-20 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \sqrt{a}\, \left(4 A +B \right) \left(\sin^{2}\left(\frac{x}{2}\right)\right)+120 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \sqrt{a}+90 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \sqrt{a}+15 B \ln \left(\frac{4 a \sqrt{2}\, \cos \left(\frac{x}{2}\right)+4 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}+8 a}{2 \cos \left(\frac{x}{2}\right)+\sqrt{2}}\right) a +15 B \ln \left(-\frac{4 \left(\sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}-a \sqrt{2}\, \cos \left(\frac{x}{2}\right)+2 a \right)}{-2 \cos \left(\frac{x}{2}\right)+\sqrt{2}}\right) a \right)}{15 \sin \left(\frac{x}{2}\right) \sqrt{\left(\cos^{2}\left(\frac{x}{2}\right)\right) a}}"," ",0,"1/15*a^(3/2)*cos(1/2*x)*(a*sin(1/2*x)^2)^(1/2)*(24*A*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)*a^(1/2)*sin(1/2*x)^4-20*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)*a^(1/2)*(4*A+B)*sin(1/2*x)^2+120*A*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)*a^(1/2)+90*B*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)*a^(1/2)+15*B*ln(4/(2*cos(1/2*x)+2^(1/2))*(a*2^(1/2)*cos(1/2*x)+a^(1/2)*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)+2*a))*a+15*B*ln(-4/(-2*cos(1/2*x)+2^(1/2))*(a^(1/2)*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)-a*2^(1/2)*cos(1/2*x)+2*a))*a)/sin(1/2*x)/(cos(1/2*x)^2*a)^(1/2)","B"
194,1,199,58,0.310000," ","int((a+a*cos(x))^(3/2)*(A+B*sec(x)),x)","\frac{\sqrt{a}\, \cos \left(\frac{x}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \left(-4 A \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \left(\sin^{2}\left(\frac{x}{2}\right)\right)+12 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \sqrt{a}+6 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \sqrt{a}+3 B \ln \left(\frac{4 a \sqrt{2}\, \cos \left(\frac{x}{2}\right)+4 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}+8 a}{2 \cos \left(\frac{x}{2}\right)+\sqrt{2}}\right) a +3 B \ln \left(-\frac{4 \left(\sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}-a \sqrt{2}\, \cos \left(\frac{x}{2}\right)+2 a \right)}{-2 \cos \left(\frac{x}{2}\right)+\sqrt{2}}\right) a \right)}{3 \sin \left(\frac{x}{2}\right) \sqrt{\left(\cos^{2}\left(\frac{x}{2}\right)\right) a}}"," ",0,"1/3*a^(1/2)*cos(1/2*x)*(a*sin(1/2*x)^2)^(1/2)*(-4*A*a^(1/2)*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)*sin(1/2*x)^2+12*A*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)*a^(1/2)+6*B*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)*a^(1/2)+3*B*ln(4/(2*cos(1/2*x)+2^(1/2))*(a*2^(1/2)*cos(1/2*x)+a^(1/2)*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)+2*a))*a+3*B*ln(-4/(-2*cos(1/2*x)+2^(1/2))*(a^(1/2)*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)-a*2^(1/2)*cos(1/2*x)+2*a))*a)/sin(1/2*x)/(cos(1/2*x)^2*a)^(1/2)","B"
195,1,152,36,0.303000," ","int((a+a*cos(x))^(1/2)*(A+B*sec(x)),x)","\frac{\cos \left(\frac{x}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \left(2 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \sqrt{a}+B \ln \left(\frac{4 a \sqrt{2}\, \cos \left(\frac{x}{2}\right)+4 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}+8 a}{2 \cos \left(\frac{x}{2}\right)+\sqrt{2}}\right) a +B \ln \left(-\frac{4 \left(\sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}-a \sqrt{2}\, \cos \left(\frac{x}{2}\right)+2 a \right)}{-2 \cos \left(\frac{x}{2}\right)+\sqrt{2}}\right) a \right)}{\sqrt{a}\, \sin \left(\frac{x}{2}\right) \sqrt{\left(\cos^{2}\left(\frac{x}{2}\right)\right) a}}"," ",0,"1/a^(1/2)*cos(1/2*x)*(a*sin(1/2*x)^2)^(1/2)*(2*A*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)*a^(1/2)+B*ln(4/(2*cos(1/2*x)+2^(1/2))*(a*2^(1/2)*cos(1/2*x)+a^(1/2)*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)+2*a))*a+B*ln(-4/(-2*cos(1/2*x)+2^(1/2))*(a^(1/2)*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)-a*2^(1/2)*cos(1/2*x)+2*a))*a)/sin(1/2*x)/(cos(1/2*x)^2*a)^(1/2)","B"
196,1,192,53,0.348000," ","int((A+B*sec(x))/(a+a*cos(x))^(1/2),x)","\frac{\cos \left(\frac{x}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \left(\sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}+4 a}{\cos \left(\frac{x}{2}\right)}\right) A -\sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}+4 a}{\cos \left(\frac{x}{2}\right)}\right) B +B \ln \left(\frac{4 a \sqrt{2}\, \cos \left(\frac{x}{2}\right)+4 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}+8 a}{2 \cos \left(\frac{x}{2}\right)+\sqrt{2}}\right)+B \ln \left(-\frac{4 \left(\sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}-a \sqrt{2}\, \cos \left(\frac{x}{2}\right)+2 a \right)}{-2 \cos \left(\frac{x}{2}\right)+\sqrt{2}}\right)\right)}{\sqrt{a}\, \sin \left(\frac{x}{2}\right) \sqrt{\left(\cos^{2}\left(\frac{x}{2}\right)\right) a}}"," ",0,"cos(1/2*x)*(a*sin(1/2*x)^2)^(1/2)*(2^(1/2)*ln(4/cos(1/2*x)*(a^(1/2)*(a*sin(1/2*x)^2)^(1/2)+a))*A-2^(1/2)*ln(4/cos(1/2*x)*(a^(1/2)*(a*sin(1/2*x)^2)^(1/2)+a))*B+B*ln(4/(2*cos(1/2*x)+2^(1/2))*(a*2^(1/2)*cos(1/2*x)+a^(1/2)*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)+2*a))+B*ln(-4/(-2*cos(1/2*x)+2^(1/2))*(a^(1/2)*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)-a*2^(1/2)*cos(1/2*x)+2*a)))/a^(1/2)/sin(1/2*x)/(cos(1/2*x)^2*a)^(1/2)","B"
197,1,270,71,0.345000," ","int((A+B*sec(x))/(a+a*cos(x))^(3/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \left(A \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}+4 a}{\cos \left(\frac{x}{2}\right)}\right) \left(\cos^{2}\left(\frac{x}{2}\right)\right) a -5 B \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}+4 a}{\cos \left(\frac{x}{2}\right)}\right) \left(\cos^{2}\left(\frac{x}{2}\right)\right) a +4 B \ln \left(\frac{4 a \sqrt{2}\, \cos \left(\frac{x}{2}\right)+4 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}+8 a}{2 \cos \left(\frac{x}{2}\right)+\sqrt{2}}\right) \left(\cos^{2}\left(\frac{x}{2}\right)\right) a +4 B \ln \left(-\frac{4 \left(a \sqrt{2}\, \cos \left(\frac{x}{2}\right)-\sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}-2 a \right)}{2 \cos \left(\frac{x}{2}\right)-\sqrt{2}}\right) \left(\cos^{2}\left(\frac{x}{2}\right)\right) a +A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \sqrt{a}-B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \sqrt{a}\right)}{4 a^{\frac{5}{2}} \cos \left(\frac{x}{2}\right) \sin \left(\frac{x}{2}\right) \sqrt{\left(\cos^{2}\left(\frac{x}{2}\right)\right) a}}"," ",0,"1/4/a^(5/2)/cos(1/2*x)*(a*sin(1/2*x)^2)^(1/2)*(A*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*x)^2)^(1/2)+2*a)/cos(1/2*x))*cos(1/2*x)^2*a-5*B*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*x)^2)^(1/2)+2*a)/cos(1/2*x))*cos(1/2*x)^2*a+4*B*ln(4/(2*cos(1/2*x)+2^(1/2))*(a*2^(1/2)*cos(1/2*x)+a^(1/2)*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)+2*a))*cos(1/2*x)^2*a+4*B*ln(-4*(a*2^(1/2)*cos(1/2*x)-a^(1/2)*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)-2*a)/(2*cos(1/2*x)-2^(1/2)))*cos(1/2*x)^2*a+A*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)*a^(1/2)-B*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)*a^(1/2))/sin(1/2*x)/(cos(1/2*x)^2*a)^(1/2)","B"
198,1,322,95,0.355000," ","int((A+B*sec(x))/(a+a*cos(x))^(5/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \left(3 A \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}+4 a}{\cos \left(\frac{x}{2}\right)}\right) \left(\cos^{4}\left(\frac{x}{2}\right)\right) a -43 B \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}+4 a}{\cos \left(\frac{x}{2}\right)}\right) a \left(\cos^{4}\left(\frac{x}{2}\right)\right)+32 B \ln \left(\frac{4 a \sqrt{2}\, \cos \left(\frac{x}{2}\right)+4 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}+8 a}{2 \cos \left(\frac{x}{2}\right)+\sqrt{2}}\right) a \left(\cos^{4}\left(\frac{x}{2}\right)\right)+32 B \ln \left(-\frac{4 \left(a \sqrt{2}\, \cos \left(\frac{x}{2}\right)-\sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}-2 a \right)}{2 \cos \left(\frac{x}{2}\right)-\sqrt{2}}\right) a \left(\cos^{4}\left(\frac{x}{2}\right)\right)+3 A \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \left(\cos^{2}\left(\frac{x}{2}\right)\right)-11 B \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \left(\cos^{2}\left(\frac{x}{2}\right)\right)+2 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \sqrt{a}-2 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}\, \sqrt{a}\right)}{32 a^{\frac{7}{2}} \cos \left(\frac{x}{2}\right)^{3} \sin \left(\frac{x}{2}\right) \sqrt{\left(\cos^{2}\left(\frac{x}{2}\right)\right) a}}"," ",0,"1/32/a^(7/2)/cos(1/2*x)^3*(a*sin(1/2*x)^2)^(1/2)*(3*A*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*x)^2)^(1/2)+2*a)/cos(1/2*x))*cos(1/2*x)^4*a-43*B*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*x)^2)^(1/2)+2*a)/cos(1/2*x))*a*cos(1/2*x)^4+32*B*ln(4/(2*cos(1/2*x)+2^(1/2))*(a*2^(1/2)*cos(1/2*x)+a^(1/2)*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)+2*a))*a*cos(1/2*x)^4+32*B*ln(-4*(a*2^(1/2)*cos(1/2*x)-a^(1/2)*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)-2*a)/(2*cos(1/2*x)-2^(1/2)))*a*cos(1/2*x)^4+3*A*a^(1/2)*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)*cos(1/2*x)^2-11*B*a^(1/2)*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)*cos(1/2*x)^2+2*A*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)*a^(1/2)-2*B*2^(1/2)*(a*sin(1/2*x)^2)^(1/2)*a^(1/2))/sin(1/2*x)/(cos(1/2*x)^2*a)^(1/2)","B"
199,1,80,25,0.702000," ","int(x*(b+a*sin(x))/(a+b*sin(x))^2,x)","\frac{x \left(\tan^{4}\left(\frac{x}{2}\right)\right)-x}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right) \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)}+\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)}{b}-\frac{\ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{b}"," ",0,"(x*tan(1/2*x)^4-x)/(1+tan(1/2*x)^2)/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)+1/b*ln(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)-1/b*ln(1+tan(1/2*x)^2)","B"
200,1,91,24,0.408000," ","int(x*(b+a*cos(x))/(a+b*cos(x))^2,x)","\frac{2 x \tan \left(\frac{x}{2}\right)+2 x \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right) \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+a +b \right)}+\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+a +b \right)}{b}-\frac{\ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{b}"," ",0,"(2*x*tan(1/2*x)+2*x*tan(1/2*x)^3)/(1+tan(1/2*x)^2)/(a*tan(1/2*x)^2-b*tan(1/2*x)^2+a+b)+1/b*ln(a*tan(1/2*x)^2-b*tan(1/2*x)^2+a+b)-1/b*ln(1+tan(1/2*x)^2)","B"
201,1,9,8,0.081000," ","int((1+sin(x)^2)/(1-sin(x)^2),x)","-x +2 \tan \left(x \right)"," ",0,"-x+2*tan(x)","A"
202,1,16,30,0.083000," ","int((1-sin(x)^2)/(1+sin(x)^2),x)","\sqrt{2}\, \arctan \left(\sqrt{2}\, \tan \left(x \right)\right)-x"," ",0,"2^(1/2)*arctan(2^(1/2)*tan(x))-x","A"
203,1,11,8,0.078000," ","int((1+cos(x)^2)/(1-cos(x)^2),x)","-\frac{2}{\tan \left(x \right)}-x"," ",0,"-2/tan(x)-x","A"
204,1,17,31,0.075000," ","int((1-cos(x)^2)/(1+cos(x)^2),x)","\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(x \right)}{2}\right)-x"," ",0,"2^(1/2)*arctan(1/2*2^(1/2)*tan(x))-x","A"
205,1,32,14,0.098000," ","int((-1+c^2/d^2+sin(x)^2)/(c+d*cos(x)),x)","-\frac{2 \tan \left(\frac{x}{2}\right)}{d \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}+\frac{2 c \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{d^{2}}"," ",0,"-2/d*tan(1/2*x)/(1+tan(1/2*x)^2)+2/d^2*c*arctan(tan(1/2*x))","B"
206,1,148,85,0.108000," ","int((a+b*sin(x)^2)/(c+d*cos(x)),x)","\frac{2 \arctan \left(\frac{\left(c -d \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a}{\sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{2 \arctan \left(\frac{\left(c -d \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) c^{2} b}{d^{2} \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 \arctan \left(\frac{\left(c -d \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) b}{\sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{2 b \tan \left(\frac{x}{2}\right)}{d \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}+\frac{2 b c \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{d^{2}}"," ",0,"2/((c+d)*(c-d))^(1/2)*arctan((c-d)*tan(1/2*x)/((c+d)*(c-d))^(1/2))*a-2/d^2/((c+d)*(c-d))^(1/2)*arctan((c-d)*tan(1/2*x)/((c+d)*(c-d))^(1/2))*c^2*b+2/((c+d)*(c-d))^(1/2)*arctan((c-d)*tan(1/2*x)/((c+d)*(c-d))^(1/2))*b-2*b/d*tan(1/2*x)/(1+tan(1/2*x)^2)+2*b/d^2*c*arctan(tan(1/2*x))","A"
207,1,44,52,0.128000," ","int((a+b*sin(x)^2)/(c+c*cos(x)^2),x)","\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(x \right)}{2}\right) a}{2 c}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(x \right)}{2}\right) b}{c}-\frac{b \arctan \left(\tan \left(x \right)\right)}{c}"," ",0,"1/2/c*2^(1/2)*arctan(1/2*2^(1/2)*tan(x))*a+1/c*2^(1/2)*arctan(1/2*2^(1/2)*tan(x))*b-1/c*b*arctan(tan(x))","A"
208,1,20,15,0.109000," ","int((a+b*sin(x)^2)/(c-c*cos(x)^2),x)","-\frac{a}{c \tan \left(x \right)}+\frac{b \arctan \left(\tan \left(x \right)\right)}{c}"," ",0,"-1/c*a/tan(x)+1/c*b*arctan(tan(x))","A"
209,1,78,41,0.118000," ","int((a+b*sin(x)^2)/(c+d*cos(x)^2),x)","\frac{\arctan \left(\frac{c \tan \left(x \right)}{\sqrt{\left(c +d \right) c}}\right) a}{\sqrt{\left(c +d \right) c}}+\frac{\arctan \left(\frac{c \tan \left(x \right)}{\sqrt{\left(c +d \right) c}}\right) c b}{d \sqrt{\left(c +d \right) c}}+\frac{\arctan \left(\frac{c \tan \left(x \right)}{\sqrt{\left(c +d \right) c}}\right) b}{\sqrt{\left(c +d \right) c}}-\frac{b \arctan \left(\tan \left(x \right)\right)}{d}"," ",0,"1/((c+d)*c)^(1/2)*arctan(c*tan(x)/((c+d)*c)^(1/2))*a+1/d/((c+d)*c)^(1/2)*arctan(c*tan(x)/((c+d)*c)^(1/2))*c*b+1/((c+d)*c)^(1/2)*arctan(c*tan(x)/((c+d)*c)^(1/2))*b-b/d*arctan(tan(x))","A"
210,1,28,13,0.115000," ","int((-1+c^2/d^2+cos(x)^2)/(c+d*sin(x)),x)","\frac{2}{d \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}+\frac{2 c \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{d^{2}}"," ",0,"2/d/(1+tan(1/2*x)^2)+2/d^2*c*arctan(tan(1/2*x))","B"
211,1,153,88,0.080000," ","int((a+b*cos(x)^2)/(c+d*sin(x)),x)","\frac{2 \arctan \left(\frac{2 c \tan \left(\frac{x}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) a}{\sqrt{c^{2}-d^{2}}}-\frac{2 \arctan \left(\frac{2 c \tan \left(\frac{x}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) c^{2} b}{d^{2} \sqrt{c^{2}-d^{2}}}+\frac{2 \arctan \left(\frac{2 c \tan \left(\frac{x}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) b}{\sqrt{c^{2}-d^{2}}}+\frac{2 b}{d \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}+\frac{2 b c \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{d^{2}}"," ",0,"2/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*x)+2*d)/(c^2-d^2)^(1/2))*a-2/d^2/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*x)+2*d)/(c^2-d^2)^(1/2))*c^2*b+2/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*x)+2*d)/(c^2-d^2)^(1/2))*b+2*b/d/(1+tan(1/2*x)^2)+2*b/d^2*c*arctan(tan(1/2*x))","A"
212,1,42,52,0.121000," ","int((a+b*cos(x)^2)/(c+c*sin(x)^2),x)","\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, \tan \left(x \right)\right) a}{2 c}+\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, \tan \left(x \right)\right) b}{c}-\frac{b \arctan \left(\tan \left(x \right)\right)}{c}"," ",0,"1/2/c*2^(1/2)*arctan(2^(1/2)*tan(x))*a+1/c*2^(1/2)*arctan(2^(1/2)*tan(x))*b-1/c*b*arctan(tan(x))","A"
213,1,17,14,0.109000," ","int((a+b*cos(x)^2)/(c-c*sin(x)^2),x)","\frac{a \tan \left(x \right)}{c}+\frac{b \arctan \left(\tan \left(x \right)\right)}{c}"," ",0,"a*tan(x)/c+1/c*b*arctan(tan(x))","A"
214,1,84,41,0.125000," ","int((a+b*cos(x)^2)/(c+d*sin(x)^2),x)","\frac{\arctan \left(\frac{\left(c +d \right) \tan \left(x \right)}{\sqrt{\left(c +d \right) c}}\right) a}{\sqrt{\left(c +d \right) c}}+\frac{\arctan \left(\frac{\left(c +d \right) \tan \left(x \right)}{\sqrt{\left(c +d \right) c}}\right) c b}{d \sqrt{\left(c +d \right) c}}+\frac{\arctan \left(\frac{\left(c +d \right) \tan \left(x \right)}{\sqrt{\left(c +d \right) c}}\right) b}{\sqrt{\left(c +d \right) c}}-\frac{b \arctan \left(\tan \left(x \right)\right)}{d}"," ",0,"1/((c+d)*c)^(1/2)*arctan((c+d)*tan(x)/((c+d)*c)^(1/2))*a+1/d/((c+d)*c)^(1/2)*arctan((c+d)*tan(x)/((c+d)*c)^(1/2))*c*b+1/((c+d)*c)^(1/2)*arctan((c+d)*tan(x)/((c+d)*c)^(1/2))*b-b/d*arctan(tan(x))","B"
215,1,135,64,0.100000," ","int((a+b*sec(x)^2)/(c+d*cos(x)),x)","\frac{2 \arctan \left(\frac{\left(c -d \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a}{\sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 \arctan \left(\frac{\left(c -d \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) b \,d^{2}}{c^{2} \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{b}{c \left(\tan \left(\frac{x}{2}\right)-1\right)}+\frac{d b \ln \left(\tan \left(\frac{x}{2}\right)-1\right)}{c^{2}}-\frac{b}{c \left(1+\tan \left(\frac{x}{2}\right)\right)}-\frac{d b \ln \left(1+\tan \left(\frac{x}{2}\right)\right)}{c^{2}}"," ",0,"2/((c+d)*(c-d))^(1/2)*arctan((c-d)*tan(1/2*x)/((c+d)*(c-d))^(1/2))*a+2/c^2/((c+d)*(c-d))^(1/2)*arctan((c-d)*tan(1/2*x)/((c+d)*(c-d))^(1/2))*b*d^2-b/c/(tan(1/2*x)-1)+d*b/c^2*ln(tan(1/2*x)-1)-b/c/(1+tan(1/2*x))-d*b/c^2*ln(1+tan(1/2*x))","B"
216,1,120,66,0.106000," ","int((a+b*csc(x)^2)/(c+d*sin(x)),x)","\frac{b \tan \left(\frac{x}{2}\right)}{2 c}-\frac{b}{2 c \tan \left(\frac{x}{2}\right)}-\frac{d b \ln \left(\tan \left(\frac{x}{2}\right)\right)}{c^{2}}+\frac{2 \arctan \left(\frac{2 c \tan \left(\frac{x}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) a}{\sqrt{c^{2}-d^{2}}}+\frac{2 \arctan \left(\frac{2 c \tan \left(\frac{x}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) b \,d^{2}}{c^{2} \sqrt{c^{2}-d^{2}}}"," ",0,"1/2*b/c*tan(1/2*x)-1/2*b/c/tan(1/2*x)-1/c^2*d*b*ln(tan(1/2*x))+2/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*x)+2*d)/(c^2-d^2)^(1/2))*a+2/c^2/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*x)+2*d)/(c^2-d^2)^(1/2))*b*d^2","A"
217,0,0,128,1.001000," ","int((a*cos(d*x+c)+b*sin(d*x+c))^n,x)","\int \left(a \cos \left(d x +c \right)+b \sin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((a*cos(d*x+c)+b*sin(d*x+c))^n,x)","F"
218,0,0,79,1.055000," ","int((2*cos(d*x+c)+3*sin(d*x+c))^n,x)","\int \left(2 \cos \left(d x +c \right)+3 \sin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((2*cos(d*x+c)+3*sin(d*x+c))^n,x)","F"
219,1,321,123,0.414000," ","int((a*cos(d*x+c)+b*sin(d*x+c))^7,x)","\frac{-\frac{b^{7} \left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)}{7}+a \,b^{6} \left(\sin^{7}\left(d x +c \right)\right)+21 a^{2} b^{5} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{7}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{35}-\frac{8 \left(\cos^{3}\left(d x +c \right)\right)}{105}\right)+35 a^{3} b^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{7}-\frac{3 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{35}\right)+35 a^{4} b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+21 a^{5} b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-a^{6} b \left(\cos^{7}\left(d x +c \right)\right)+\frac{a^{7} \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}}{d}"," ",0,"1/d*(-1/7*b^7*(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c)+a*b^6*sin(d*x+c)^7+21*a^2*b^5*(-1/7*sin(d*x+c)^4*cos(d*x+c)^3-4/35*sin(d*x+c)^2*cos(d*x+c)^3-8/105*cos(d*x+c)^3)+35*a^3*b^4*(-1/7*sin(d*x+c)^3*cos(d*x+c)^4-3/35*sin(d*x+c)*cos(d*x+c)^4+1/35*(2+cos(d*x+c)^2)*sin(d*x+c))+35*a^4*b^3*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+21*a^5*b^2*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-a^6*b*cos(d*x+c)^7+1/7*a^7*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))","B"
220,1,285,153,0.335000," ","int((a*cos(d*x+c)+b*sin(d*x+c))^6,x)","\frac{b^{6} \left(-\frac{\left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)+a \,b^{5} \left(\sin^{6}\left(d x +c \right)\right)+15 a^{2} b^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{8}+\frac{\sin \left(d x +c \right) \cos \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)+20 a^{3} b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)+15 a^{4} b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)-a^{5} b \left(\cos^{6}\left(d x +c \right)\right)+a^{6} \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)}{d}"," ",0,"1/d*(b^6*(-1/6*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/16*d*x+5/16*c)+a*b^5*sin(d*x+c)^6+15*a^2*b^4*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*sin(d*x+c)*cos(d*x+c)^3+1/16*sin(d*x+c)*cos(d*x+c)+1/16*d*x+1/16*c)+20*a^3*b^3*(-1/6*sin(d*x+c)^2*cos(d*x+c)^4-1/12*cos(d*x+c)^4)+15*a^4*b^2*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)-a^5*b*cos(d*x+c)^6+a^6*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c))","A"
221,1,175,90,0.267000," ","int((a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{-\frac{b^{5} \left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)}{5}+a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)+10 a^{2} b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+10 a^{3} b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-a^{4} b \left(\cos^{5}\left(d x +c \right)\right)+\frac{a^{5} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(-1/5*b^5*(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c)+a*b^4*sin(d*x+c)^5+10*a^2*b^3*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+10*a^3*b^2*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-a^4*b*cos(d*x+c)^5+1/5*a^5*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
222,1,153,102,0.253000," ","int((a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{b^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)+6 a^{2} b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\sin \left(d x +c \right) \cos \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\left(\cos^{4}\left(d x +c \right)\right) a^{3} b +a^{4} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(b^4*(-1/4*(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)+3/8*d*x+3/8*c)+a*b^3*sin(d*x+c)^4+6*a^2*b^2*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*sin(d*x+c)*cos(d*x+c)+1/8*d*x+1/8*c)-cos(d*x+c)^4*a^3*b+a^4*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
223,1,75,56,0.242000," ","int((a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{-\frac{b^{3} \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}+a \,b^{2} \left(\sin^{3}\left(d x +c \right)\right)-a^{2} b \left(\cos^{3}\left(d x +c \right)\right)+\frac{a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(-1/3*b^3*(2+sin(d*x+c)^2)*cos(d*x+c)+a*b^2*sin(d*x+c)^3-a^2*b*cos(d*x+c)^3+1/3*a^3*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
224,1,70,51,0.239000," ","int((a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{b^{2} \left(-\frac{\sin \left(d x +c \right) \cos \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-\left(\cos^{2}\left(d x +c \right)\right) a b +a^{2} \left(\frac{\sin \left(d x +c \right) \cos \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(b^2*(-1/2*sin(d*x+c)*cos(d*x+c)+1/2*d*x+1/2*c)-cos(d*x+c)^2*a*b+a^2*(1/2*sin(d*x+c)*cos(d*x+c)+1/2*d*x+1/2*c))","A"
225,1,25,24,0.044000," ","int(a*cos(d*x+c)+b*sin(d*x+c),x)","-\frac{b \cos \left(d x +c \right)}{d}+\frac{a \sin \left(d x +c \right)}{d}"," ",0,"-b*cos(d*x+c)/d+a*sin(d*x+c)/d","A"
226,1,43,43,0.404000," ","int(1/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{2 \arctanh \left(\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a -2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{d \sqrt{a^{2}+b^{2}}}"," ",0,"2/d/(a^2+b^2)^(1/2)*arctanh(1/2*(2*tan(1/2*d*x+1/2*c)*a-2*b)/(a^2+b^2)^(1/2))","A"
227,1,21,32,0.490000," ","int(1/(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","-\frac{1}{d b \left(a +b \tan \left(d x +c \right)\right)}"," ",0,"-1/d/b/(a+b*tan(d*x+c))","A"
228,1,191,95,0.534000," ","int(1/(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{-\frac{2 \left(-\frac{\left(a^{2}+2 b^{2}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 \left(a^{2}+b^{2}\right) a}-\frac{b \left(a^{2}-2 b^{2}\right) \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 \left(a^{2}+b^{2}\right) a^{2}}-\frac{\left(a^{2}-2 b^{2}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a \left(a^{2}+b^{2}\right)}+\frac{b}{2 a^{2}+2 b^{2}}\right)}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-a \right)^{2}}+\frac{\arctanh \left(\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a -2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(a^{2}+b^{2}\right)^{\frac{3}{2}}}}{d}"," ",0,"1/d*(-2*(-1/2*(a^2+2*b^2)/(a^2+b^2)/a*tan(1/2*d*x+1/2*c)^3-1/2*b*(a^2-2*b^2)/(a^2+b^2)/a^2*tan(1/2*d*x+1/2*c)^2-1/2*(a^2-2*b^2)/a/(a^2+b^2)*tan(1/2*d*x+1/2*c)+1/2*b/(a^2+b^2))/(a*tan(1/2*d*x+1/2*c)^2-2*b*tan(1/2*d*x+1/2*c)-a)^2+1/(a^2+b^2)^(3/2)*arctanh(1/2*(2*tan(1/2*d*x+1/2*c)*a-2*b)/(a^2+b^2)^(1/2)))","A"
229,1,64,94,0.559000," ","int(1/(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{\frac{a}{b^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{a^{2}+b^{2}}{3 b^{3} \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{1}{b^{3} \left(a +b \tan \left(d x +c \right)\right)}}{d}"," ",0,"1/d*(a/b^3/(a+b*tan(d*x+c))^2-1/3*(a^2+b^2)/b^3/(a+b*tan(d*x+c))^3-1/b^3/(a+b*tan(d*x+c)))","A"
230,1,514,146,0.604000," ","int(1/(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{-\frac{2 \left(-\frac{\left(5 a^{4}+16 a^{2} b^{2}+8 b^{4}\right) \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}+\frac{3 b \left(a^{4}+16 a^{2} b^{2}+8 b^{4}\right) \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{2} \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}-\frac{\left(3 a^{6}-36 a^{4} b^{2}+56 a^{2} b^{4}+32 b^{6}\right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{3} \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}+\frac{b \left(15 a^{6}-114 a^{4} b^{2}-8 a^{2} b^{4}+16 b^{6}\right) \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{4} \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}-\frac{\left(3 a^{6}+84 a^{4} b^{2}-56 a^{2} b^{4}-32 b^{6}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{3} \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}-\frac{b \left(23 a^{4}-64 a^{2} b^{2}-24 b^{4}\right) \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{2} \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}-\frac{\left(5 a^{4}-24 a^{2} b^{2}-8 b^{4}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}+\frac{b \left(5 a^{2}+2 b^{2}\right)}{8 a^{4}+16 a^{2} b^{2}+8 b^{4}}\right)}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-a \right)^{4}}+\frac{3 \arctanh \left(\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a -2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{4 \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}+b^{2}}}}{d}"," ",0,"1/d*(-2*(-1/8*(5*a^4+16*a^2*b^2+8*b^4)/a/(a^4+2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)^7+3/8*b*(a^4+16*a^2*b^2+8*b^4)/a^2/(a^4+2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)^6-1/8/a^3*(3*a^6-36*a^4*b^2+56*a^2*b^4+32*b^6)/(a^4+2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)^5+1/8/a^4*b*(15*a^6-114*a^4*b^2-8*a^2*b^4+16*b^6)/(a^4+2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)^4-1/8/a^3*(3*a^6+84*a^4*b^2-56*a^2*b^4-32*b^6)/(a^4+2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)^3-1/8*b*(23*a^4-64*a^2*b^2-24*b^4)/a^2/(a^4+2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)^2-1/8*(5*a^4-24*a^2*b^2-8*b^4)/a/(a^4+2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)+1/8*b*(5*a^2+2*b^2)/(a^4+2*a^2*b^2+b^4))/(a*tan(1/2*d*x+1/2*c)^2-2*b*tan(1/2*d*x+1/2*c)-a)^4+3/4/(a^4+2*a^2*b^2+b^4)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*tan(1/2*d*x+1/2*c)*a-2*b)/(a^2+b^2)^(1/2)))","B"
231,1,125,145,0.644000," ","int(1/(a*cos(d*x+c)+b*sin(d*x+c))^6,x)","\frac{-\frac{a^{4}+2 a^{2} b^{2}+b^{4}}{5 b^{5} \left(a +b \tan \left(d x +c \right)\right)^{5}}+\frac{a \left(a^{2}+b^{2}\right)}{b^{5} \left(a +b \tan \left(d x +c \right)\right)^{4}}-\frac{6 a^{2}+2 b^{2}}{3 b^{5} \left(a +b \tan \left(d x +c \right)\right)^{3}}+\frac{2 a}{b^{5} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{1}{b^{5} \left(a +b \tan \left(d x +c \right)\right)}}{d}"," ",0,"1/d*(-1/5*(a^4+2*a^2*b^2+b^4)/b^5/(a+b*tan(d*x+c))^5+a*(a^2+b^2)/b^5/(a+b*tan(d*x+c))^4-1/3*(6*a^2+2*b^2)/b^5/(a+b*tan(d*x+c))^3+2*a/b^5/(a+b*tan(d*x+c))^2-1/b^5/(a+b*tan(d*x+c)))","A"
232,1,183,206,0.444000," ","int((a*cos(d*x+c)+b*sin(d*x+c))^(7/2),x)","\frac{\left(a^{2}+b^{2}\right)^{2} \left(6 \left(\sin^{5}\left(d x +c -\arctan \left(-a , b\right)\right)\right)+5 \sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \sqrt{-2 \sin \left(d x +c -\arctan \left(-a , b\right)\right)+2}\, \sqrt{-\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \EllipticF \left(\sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}, \frac{\sqrt{2}}{2}\right)+4 \left(\sin^{3}\left(d x +c -\arctan \left(-a , b\right)\right)\right)-10 \sin \left(d x +c -\arctan \left(-a , b\right)\right)\right)}{21 \cos \left(d x +c -\arctan \left(-a , b\right)\right) \sqrt{\sin \left(d x +c -\arctan \left(-a , b\right)\right) \sqrt{a^{2}+b^{2}}}\, d}"," ",0,"1/21*(a^2+b^2)^2*(6*sin(d*x+c-arctan(-a,b))^5+5*(1+sin(d*x+c-arctan(-a,b)))^(1/2)*(-2*sin(d*x+c-arctan(-a,b))+2)^(1/2)*(-sin(d*x+c-arctan(-a,b)))^(1/2)*EllipticF((1+sin(d*x+c-arctan(-a,b)))^(1/2),1/2*2^(1/2))+4*sin(d*x+c-arctan(-a,b))^3-10*sin(d*x+c-arctan(-a,b)))/cos(d*x+c-arctan(-a,b))/(sin(d*x+c-arctan(-a,b))*(a^2+b^2)^(1/2))^(1/2)/d","A"
233,1,246,155,0.372000," ","int((a*cos(d*x+c)+b*sin(d*x+c))^(5/2),x)","-\frac{\left(a^{2}+b^{2}\right)^{\frac{3}{2}} \left(6 \sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \sqrt{-2 \sin \left(d x +c -\arctan \left(-a , b\right)\right)+2}\, \sqrt{-\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \EllipticE \left(\sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \sqrt{-2 \sin \left(d x +c -\arctan \left(-a , b\right)\right)+2}\, \sqrt{-\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \EllipticF \left(\sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}, \frac{\sqrt{2}}{2}\right)-2 \left(\sin^{4}\left(d x +c -\arctan \left(-a , b\right)\right)\right)+2 \left(\sin^{2}\left(d x +c -\arctan \left(-a , b\right)\right)\right)\right)}{5 \cos \left(d x +c -\arctan \left(-a , b\right)\right) \sqrt{\sin \left(d x +c -\arctan \left(-a , b\right)\right) \sqrt{a^{2}+b^{2}}}\, d}"," ",0,"-1/5*(a^2+b^2)^(3/2)*(6*(1+sin(d*x+c-arctan(-a,b)))^(1/2)*(-2*sin(d*x+c-arctan(-a,b))+2)^(1/2)*(-sin(d*x+c-arctan(-a,b)))^(1/2)*EllipticE((1+sin(d*x+c-arctan(-a,b)))^(1/2),1/2*2^(1/2))-3*(1+sin(d*x+c-arctan(-a,b)))^(1/2)*(-2*sin(d*x+c-arctan(-a,b))+2)^(1/2)*(-sin(d*x+c-arctan(-a,b)))^(1/2)*EllipticF((1+sin(d*x+c-arctan(-a,b)))^(1/2),1/2*2^(1/2))-2*sin(d*x+c-arctan(-a,b))^4+2*sin(d*x+c-arctan(-a,b))^2)/cos(d*x+c-arctan(-a,b))/(sin(d*x+c-arctan(-a,b))*(a^2+b^2)^(1/2))^(1/2)/d","A"
234,1,163,155,0.372000," ","int((a*cos(d*x+c)+b*sin(d*x+c))^(3/2),x)","\frac{\left(a^{2}+b^{2}\right) \left(\sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \sqrt{-2 \sin \left(d x +c -\arctan \left(-a , b\right)\right)+2}\, \sqrt{-\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \EllipticF \left(\sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}, \frac{\sqrt{2}}{2}\right)+2 \left(\sin^{3}\left(d x +c -\arctan \left(-a , b\right)\right)\right)-2 \sin \left(d x +c -\arctan \left(-a , b\right)\right)\right)}{3 \cos \left(d x +c -\arctan \left(-a , b\right)\right) \sqrt{\sin \left(d x +c -\arctan \left(-a , b\right)\right) \sqrt{a^{2}+b^{2}}}\, d}"," ",0,"1/3*(a^2+b^2)*((1+sin(d*x+c-arctan(-a,b)))^(1/2)*(-2*sin(d*x+c-arctan(-a,b))+2)^(1/2)*(-sin(d*x+c-arctan(-a,b)))^(1/2)*EllipticF((1+sin(d*x+c-arctan(-a,b)))^(1/2),1/2*2^(1/2))+2*sin(d*x+c-arctan(-a,b))^3-2*sin(d*x+c-arctan(-a,b)))/cos(d*x+c-arctan(-a,b))/(sin(d*x+c-arctan(-a,b))*(a^2+b^2)^(1/2))^(1/2)/d","A"
235,1,159,105,0.355000," ","int((a*cos(d*x+c)+b*sin(d*x+c))^(1/2),x)","-\frac{\sqrt{a^{2}+b^{2}}\, \sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \sqrt{-2 \sin \left(d x +c -\arctan \left(-a , b\right)\right)+2}\, \sqrt{-\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \left(2 \EllipticE \left(\sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}, \frac{\sqrt{2}}{2}\right)-\EllipticF \left(\sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}, \frac{\sqrt{2}}{2}\right)\right)}{\cos \left(d x +c -\arctan \left(-a , b\right)\right) \sqrt{\sin \left(d x +c -\arctan \left(-a , b\right)\right) \sqrt{a^{2}+b^{2}}}\, d}"," ",0,"-(a^2+b^2)^(1/2)*(1+sin(d*x+c-arctan(-a,b)))^(1/2)*(-2*sin(d*x+c-arctan(-a,b))+2)^(1/2)*(-sin(d*x+c-arctan(-a,b)))^(1/2)*(2*EllipticE((1+sin(d*x+c-arctan(-a,b)))^(1/2),1/2*2^(1/2))-EllipticF((1+sin(d*x+c-arctan(-a,b)))^(1/2),1/2*2^(1/2)))/cos(d*x+c-arctan(-a,b))/(sin(d*x+c-arctan(-a,b))*(a^2+b^2)^(1/2))^(1/2)/d","A"
236,1,121,105,0.251000," ","int(1/(a*cos(d*x+c)+b*sin(d*x+c))^(1/2),x)","\frac{\sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \sqrt{-2 \sin \left(d x +c -\arctan \left(-a , b\right)\right)+2}\, \sqrt{-\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \EllipticF \left(\sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}, \frac{\sqrt{2}}{2}\right)}{\cos \left(d x +c -\arctan \left(-a , b\right)\right) \sqrt{\sin \left(d x +c -\arctan \left(-a , b\right)\right) \sqrt{a^{2}+b^{2}}}\, d}"," ",0,"(1+sin(d*x+c-arctan(-a,b)))^(1/2)*(-2*sin(d*x+c-arctan(-a,b))+2)^(1/2)*(-sin(d*x+c-arctan(-a,b)))^(1/2)*EllipticF((1+sin(d*x+c-arctan(-a,b)))^(1/2),1/2*2^(1/2))/cos(d*x+c-arctan(-a,b))/(sin(d*x+c-arctan(-a,b))*(a^2+b^2)^(1/2))^(1/2)/d","A"
237,1,228,166,0.346000," ","int(1/(a*cos(d*x+c)+b*sin(d*x+c))^(3/2),x)","\frac{2 \sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \sqrt{-2 \sin \left(d x +c -\arctan \left(-a , b\right)\right)+2}\, \sqrt{-\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \EllipticE \left(\sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}, \frac{\sqrt{2}}{2}\right)-\sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \sqrt{-2 \sin \left(d x +c -\arctan \left(-a , b\right)\right)+2}\, \sqrt{-\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \EllipticF \left(\sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{2}\left(d x +c -\arctan \left(-a , b\right)\right)\right)}{\sqrt{a^{2}+b^{2}}\, \cos \left(d x +c -\arctan \left(-a , b\right)\right) \sqrt{\sin \left(d x +c -\arctan \left(-a , b\right)\right) \sqrt{a^{2}+b^{2}}}\, d}"," ",0,"(2*(1+sin(d*x+c-arctan(-a,b)))^(1/2)*(-2*sin(d*x+c-arctan(-a,b))+2)^(1/2)*(-sin(d*x+c-arctan(-a,b)))^(1/2)*EllipticE((1+sin(d*x+c-arctan(-a,b)))^(1/2),1/2*2^(1/2))-(1+sin(d*x+c-arctan(-a,b)))^(1/2)*(-2*sin(d*x+c-arctan(-a,b))+2)^(1/2)*(-sin(d*x+c-arctan(-a,b)))^(1/2)*EllipticF((1+sin(d*x+c-arctan(-a,b)))^(1/2),1/2*2^(1/2))-2*cos(d*x+c-arctan(-a,b))^2)/(a^2+b^2)^(1/2)/cos(d*x+c-arctan(-a,b))/(sin(d*x+c-arctan(-a,b))*(a^2+b^2)^(1/2))^(1/2)/d","A"
238,1,178,166,0.335000," ","int(1/(a*cos(d*x+c)+b*sin(d*x+c))^(5/2),x)","\frac{\sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \sqrt{-2 \sin \left(d x +c -\arctan \left(-a , b\right)\right)+2}\, \sqrt{-\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \EllipticF \left(\sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c -\arctan \left(-a , b\right)\right)-2 \left(\cos^{2}\left(d x +c -\arctan \left(-a , b\right)\right)\right)}{3 \sin \left(d x +c -\arctan \left(-a , b\right)\right) \left(a^{2}+b^{2}\right) \cos \left(d x +c -\arctan \left(-a , b\right)\right) \sqrt{\sin \left(d x +c -\arctan \left(-a , b\right)\right) \sqrt{a^{2}+b^{2}}}\, d}"," ",0,"1/3/sin(d*x+c-arctan(-a,b))/(a^2+b^2)*((1+sin(d*x+c-arctan(-a,b)))^(1/2)*(-2*sin(d*x+c-arctan(-a,b))+2)^(1/2)*(-sin(d*x+c-arctan(-a,b)))^(1/2)*EllipticF((1+sin(d*x+c-arctan(-a,b)))^(1/2),1/2*2^(1/2))*sin(d*x+c-arctan(-a,b))-2*cos(d*x+c-arctan(-a,b))^2)/cos(d*x+c-arctan(-a,b))/(sin(d*x+c-arctan(-a,b))*(a^2+b^2)^(1/2))^(1/2)/d","A"
239,1,309,217,0.379000," ","int(1/(a*cos(d*x+c)+b*sin(d*x+c))^(7/2),x)","\frac{\sqrt{a^{2}+b^{2}}\, \left(6 \sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \sqrt{-2 \sin \left(d x +c -\arctan \left(-a , b\right)\right)+2}\, \sqrt{-\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \left(\sin^{2}\left(d x +c -\arctan \left(-a , b\right)\right)\right) \EllipticE \left(\sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \sqrt{-2 \sin \left(d x +c -\arctan \left(-a , b\right)\right)+2}\, \sqrt{-\sin \left(d x +c -\arctan \left(-a , b\right)\right)}\, \left(\sin^{2}\left(d x +c -\arctan \left(-a , b\right)\right)\right) \EllipticF \left(\sqrt{1+\sin \left(d x +c -\arctan \left(-a , b\right)\right)}, \frac{\sqrt{2}}{2}\right)+6 \left(\sin^{4}\left(d x +c -\arctan \left(-a , b\right)\right)\right)-4 \left(\sin^{2}\left(d x +c -\arctan \left(-a , b\right)\right)\right)-2\right)}{5 \sin \left(d x +c -\arctan \left(-a , b\right)\right)^{2} \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \cos \left(d x +c -\arctan \left(-a , b\right)\right) \sqrt{\sin \left(d x +c -\arctan \left(-a , b\right)\right) \sqrt{a^{2}+b^{2}}}\, d}"," ",0,"1/5/sin(d*x+c-arctan(-a,b))^2*(a^2+b^2)^(1/2)*(6*(1+sin(d*x+c-arctan(-a,b)))^(1/2)*(-2*sin(d*x+c-arctan(-a,b))+2)^(1/2)*(-sin(d*x+c-arctan(-a,b)))^(1/2)*sin(d*x+c-arctan(-a,b))^2*EllipticE((1+sin(d*x+c-arctan(-a,b)))^(1/2),1/2*2^(1/2))-3*(1+sin(d*x+c-arctan(-a,b)))^(1/2)*(-2*sin(d*x+c-arctan(-a,b))+2)^(1/2)*(-sin(d*x+c-arctan(-a,b)))^(1/2)*sin(d*x+c-arctan(-a,b))^2*EllipticF((1+sin(d*x+c-arctan(-a,b)))^(1/2),1/2*2^(1/2))+6*sin(d*x+c-arctan(-a,b))^4-4*sin(d*x+c-arctan(-a,b))^2-2)/(a^4+2*a^2*b^2+b^4)/cos(d*x+c-arctan(-a,b))/(sin(d*x+c-arctan(-a,b))*(a^2+b^2)^(1/2))^(1/2)/d","A"
240,1,128,140,0.346000," ","int((2*cos(d*x+c)+3*sin(d*x+c))^(7/2),x)","\frac{\frac{338 \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right) \left(\cos^{4}\left(d x +c +\arctan \left(\frac{2}{3}\right)\right)\right)}{7}+\frac{845 \sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \sqrt{-2 \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)+2}\, \sqrt{-\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \EllipticF \left(\sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}, \frac{\sqrt{2}}{2}\right)}{21}-\frac{2704 \left(\cos^{2}\left(d x +c +\arctan \left(\frac{2}{3}\right)\right)\right) \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}{21}}{\cos \left(d x +c +\arctan \left(\frac{2}{3}\right)\right) \sqrt{\sqrt{13}\, \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, d}"," ",0,"(338/7*sin(d*x+c+arctan(2/3))*cos(d*x+c+arctan(2/3))^4+845/21*(1+sin(d*x+c+arctan(2/3)))^(1/2)*(-2*sin(d*x+c+arctan(2/3))+2)^(1/2)*(-sin(d*x+c+arctan(2/3)))^(1/2)*EllipticF((1+sin(d*x+c+arctan(2/3)))^(1/2),1/2*2^(1/2))-2704/21*cos(d*x+c+arctan(2/3))^2*sin(d*x+c+arctan(2/3)))/cos(d*x+c+arctan(2/3))/(13^(1/2)*sin(d*x+c+arctan(2/3)))^(1/2)/d","A"
241,1,174,99,0.372000," ","int((2*cos(d*x+c)+3*sin(d*x+c))^(5/2),x)","-\frac{13 \sqrt{13}\, \left(6 \sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \sqrt{-2 \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)+2}\, \sqrt{-\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \EllipticE \left(\sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \sqrt{-2 \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)+2}\, \sqrt{-\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \EllipticF \left(\sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}, \frac{\sqrt{2}}{2}\right)-2 \left(\sin^{4}\left(d x +c +\arctan \left(\frac{2}{3}\right)\right)\right)+2 \left(\sin^{2}\left(d x +c +\arctan \left(\frac{2}{3}\right)\right)\right)\right)}{5 \cos \left(d x +c +\arctan \left(\frac{2}{3}\right)\right) \sqrt{\sqrt{13}\, \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, d}"," ",0,"-13/5*13^(1/2)*(6*(1+sin(d*x+c+arctan(2/3)))^(1/2)*(-2*sin(d*x+c+arctan(2/3))+2)^(1/2)*(-sin(d*x+c+arctan(2/3)))^(1/2)*EllipticE((1+sin(d*x+c+arctan(2/3)))^(1/2),1/2*2^(1/2))-3*(1+sin(d*x+c+arctan(2/3)))^(1/2)*(-2*sin(d*x+c+arctan(2/3))+2)^(1/2)*(-sin(d*x+c+arctan(2/3)))^(1/2)*EllipticF((1+sin(d*x+c+arctan(2/3)))^(1/2),1/2*2^(1/2))-2*sin(d*x+c+arctan(2/3))^4+2*sin(d*x+c+arctan(2/3))^2)/cos(d*x+c+arctan(2/3))/(13^(1/2)*sin(d*x+c+arctan(2/3)))^(1/2)/d","A"
242,1,108,99,0.336000," ","int((2*cos(d*x+c)+3*sin(d*x+c))^(3/2),x)","\frac{\frac{13 \sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \sqrt{-2 \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)+2}\, \sqrt{-\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \EllipticF \left(\sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}, \frac{\sqrt{2}}{2}\right)}{3}-\frac{26 \left(\cos^{2}\left(d x +c +\arctan \left(\frac{2}{3}\right)\right)\right) \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}{3}}{\cos \left(d x +c +\arctan \left(\frac{2}{3}\right)\right) \sqrt{\sqrt{13}\, \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, d}"," ",0,"(13/3*(1+sin(d*x+c+arctan(2/3)))^(1/2)*(-2*sin(d*x+c+arctan(2/3))+2)^(1/2)*(-sin(d*x+c+arctan(2/3)))^(1/2)*EllipticF((1+sin(d*x+c+arctan(2/3)))^(1/2),1/2*2^(1/2))-26/3*cos(d*x+c+arctan(2/3))^2*sin(d*x+c+arctan(2/3)))/cos(d*x+c+arctan(2/3))/(13^(1/2)*sin(d*x+c+arctan(2/3)))^(1/2)/d","A"
243,1,112,57,0.333000," ","int((2*cos(d*x+c)+3*sin(d*x+c))^(1/2),x)","-\frac{\sqrt{13}\, \sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \sqrt{-2 \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)+2}\, \sqrt{-\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \left(2 \EllipticE \left(\sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}, \frac{\sqrt{2}}{2}\right)-\EllipticF \left(\sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}, \frac{\sqrt{2}}{2}\right)\right)}{\cos \left(d x +c +\arctan \left(\frac{2}{3}\right)\right) \sqrt{\sqrt{13}\, \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, d}"," ",0,"-13^(1/2)*(1+sin(d*x+c+arctan(2/3)))^(1/2)*(-2*sin(d*x+c+arctan(2/3))+2)^(1/2)*(-sin(d*x+c+arctan(2/3)))^(1/2)*(2*EllipticE((1+sin(d*x+c+arctan(2/3)))^(1/2),1/2*2^(1/2))-EllipticF((1+sin(d*x+c+arctan(2/3)))^(1/2),1/2*2^(1/2)))/cos(d*x+c+arctan(2/3))/(13^(1/2)*sin(d*x+c+arctan(2/3)))^(1/2)/d","A"
244,1,85,57,0.243000," ","int(1/(2*cos(d*x+c)+3*sin(d*x+c))^(1/2),x)","\frac{\sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \sqrt{-2 \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)+2}\, \sqrt{-\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \EllipticF \left(\sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}, \frac{\sqrt{2}}{2}\right)}{\cos \left(d x +c +\arctan \left(\frac{2}{3}\right)\right) \sqrt{\sqrt{13}\, \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, d}"," ",0,"(1+sin(d*x+c+arctan(2/3)))^(1/2)*(-2*sin(d*x+c+arctan(2/3))+2)^(1/2)*(-sin(d*x+c+arctan(2/3)))^(1/2)*EllipticF((1+sin(d*x+c+arctan(2/3)))^(1/2),1/2*2^(1/2))/cos(d*x+c+arctan(2/3))/(13^(1/2)*sin(d*x+c+arctan(2/3)))^(1/2)/d","A"
245,1,162,99,0.336000," ","int(1/(2*cos(d*x+c)+3*sin(d*x+c))^(3/2),x)","\frac{\sqrt{13}\, \left(2 \sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \sqrt{-2 \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)+2}\, \sqrt{-\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \EllipticE \left(\sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}, \frac{\sqrt{2}}{2}\right)-\sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \sqrt{-2 \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)+2}\, \sqrt{-\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \EllipticF \left(\sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{2}\left(d x +c +\arctan \left(\frac{2}{3}\right)\right)\right)\right)}{13 \cos \left(d x +c +\arctan \left(\frac{2}{3}\right)\right) \sqrt{\sqrt{13}\, \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, d}"," ",0,"1/13*13^(1/2)*(2*(1+sin(d*x+c+arctan(2/3)))^(1/2)*(-2*sin(d*x+c+arctan(2/3))+2)^(1/2)*(-sin(d*x+c+arctan(2/3)))^(1/2)*EllipticE((1+sin(d*x+c+arctan(2/3)))^(1/2),1/2*2^(1/2))-(1+sin(d*x+c+arctan(2/3)))^(1/2)*(-2*sin(d*x+c+arctan(2/3))+2)^(1/2)*(-sin(d*x+c+arctan(2/3)))^(1/2)*EllipticF((1+sin(d*x+c+arctan(2/3)))^(1/2),1/2*2^(1/2))-2*cos(d*x+c+arctan(2/3))^2)/cos(d*x+c+arctan(2/3))/(13^(1/2)*sin(d*x+c+arctan(2/3)))^(1/2)/d","A"
246,1,118,99,0.332000," ","int(1/(2*cos(d*x+c)+3*sin(d*x+c))^(5/2),x)","\frac{\sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \sqrt{-2 \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)+2}\, \sqrt{-\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \EllipticF \left(\sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)-2 \left(\cos^{2}\left(d x +c +\arctan \left(\frac{2}{3}\right)\right)\right)}{39 \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right) \cos \left(d x +c +\arctan \left(\frac{2}{3}\right)\right) \sqrt{\sqrt{13}\, \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, d}"," ",0,"1/39/sin(d*x+c+arctan(2/3))*((1+sin(d*x+c+arctan(2/3)))^(1/2)*(-2*sin(d*x+c+arctan(2/3))+2)^(1/2)*(-sin(d*x+c+arctan(2/3)))^(1/2)*EllipticF((1+sin(d*x+c+arctan(2/3)))^(1/2),1/2*2^(1/2))*sin(d*x+c+arctan(2/3))-2*cos(d*x+c+arctan(2/3))^2)/cos(d*x+c+arctan(2/3))/(13^(1/2)*sin(d*x+c+arctan(2/3)))^(1/2)/d","A"
247,1,205,140,0.349000," ","int(1/(2*cos(d*x+c)+3*sin(d*x+c))^(7/2),x)","\frac{\sqrt{13}\, \left(6 \sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \sqrt{-2 \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)+2}\, \sqrt{-\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \left(\sin^{2}\left(d x +c +\arctan \left(\frac{2}{3}\right)\right)\right) \EllipticE \left(\sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \sqrt{-2 \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)+2}\, \sqrt{-\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, \left(\sin^{2}\left(d x +c +\arctan \left(\frac{2}{3}\right)\right)\right) \EllipticF \left(\sqrt{1+\sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}, \frac{\sqrt{2}}{2}\right)+6 \left(\sin^{4}\left(d x +c +\arctan \left(\frac{2}{3}\right)\right)\right)-4 \left(\sin^{2}\left(d x +c +\arctan \left(\frac{2}{3}\right)\right)\right)-2\right)}{845 \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)^{2} \cos \left(d x +c +\arctan \left(\frac{2}{3}\right)\right) \sqrt{\sqrt{13}\, \sin \left(d x +c +\arctan \left(\frac{2}{3}\right)\right)}\, d}"," ",0,"1/845*13^(1/2)/sin(d*x+c+arctan(2/3))^2*(6*(1+sin(d*x+c+arctan(2/3)))^(1/2)*(-2*sin(d*x+c+arctan(2/3))+2)^(1/2)*(-sin(d*x+c+arctan(2/3)))^(1/2)*sin(d*x+c+arctan(2/3))^2*EllipticE((1+sin(d*x+c+arctan(2/3)))^(1/2),1/2*2^(1/2))-3*(1+sin(d*x+c+arctan(2/3)))^(1/2)*(-2*sin(d*x+c+arctan(2/3))+2)^(1/2)*(-sin(d*x+c+arctan(2/3)))^(1/2)*sin(d*x+c+arctan(2/3))^2*EllipticF((1+sin(d*x+c+arctan(2/3)))^(1/2),1/2*2^(1/2))+6*sin(d*x+c+arctan(2/3))^4-4*sin(d*x+c+arctan(2/3))^2-2)/cos(d*x+c+arctan(2/3))/(13^(1/2)*sin(d*x+c+arctan(2/3)))^(1/2)/d","A"
248,1,31,30,0.259000," ","int((a*cos(d*x+c)+I*a*sin(d*x+c))^n,x)","-\frac{i \left(a \cos \left(d x +c \right)+i a \sin \left(d x +c \right)\right)^{n}}{d n}"," ",0,"-I*(a*cos(d*x+c)+I*a*sin(d*x+c))^n/d/n","A"
249,1,151,27,0.292000," ","int((a*cos(d*x+c)+I*a*sin(d*x+c))^4,x)","\frac{a^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)-i a^{4} \left(\sin^{4}\left(d x +c \right)\right)-6 a^{4} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\sin \left(d x +c \right) \cos \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-i a^{4} \left(\cos^{4}\left(d x +c \right)\right)+a^{4} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(a^4*(-1/4*(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)+3/8*d*x+3/8*c)-I*a^4*sin(d*x+c)^4-6*a^4*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*sin(d*x+c)*cos(d*x+c)+1/8*d*x+1/8*c)-I*a^4*cos(d*x+c)^4+a^4*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","B"
250,1,76,27,0.276000," ","int((a*cos(d*x+c)+I*a*sin(d*x+c))^3,x)","\frac{\frac{i a^{3} \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}-a^{3} \left(\sin^{3}\left(d x +c \right)\right)-i a^{3} \left(\cos^{3}\left(d x +c \right)\right)+\frac{a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(1/3*I*a^3*(2+sin(d*x+c)^2)*cos(d*x+c)-a^3*sin(d*x+c)^3-I*a^3*cos(d*x+c)^3+1/3*a^3*(2+cos(d*x+c)^2)*sin(d*x+c))","B"
251,1,73,27,0.261000," ","int((a*cos(d*x+c)+I*a*sin(d*x+c))^2,x)","\frac{-a^{2} \left(-\frac{\sin \left(d x +c \right) \cos \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-i a^{2} \left(\cos^{2}\left(d x +c \right)\right)+a^{2} \left(\frac{\sin \left(d x +c \right) \cos \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(-a^2*(-1/2*sin(d*x+c)*cos(d*x+c)+1/2*d*x+1/2*c)-I*a^2*cos(d*x+c)^2+a^2*(1/2*sin(d*x+c)*cos(d*x+c)+1/2*d*x+1/2*c))","B"
252,1,26,25,0.002000," ","int(a*cos(d*x+c)+I*a*sin(d*x+c),x)","-\frac{i a \cos \left(d x +c \right)}{d}+\frac{a \sin \left(d x +c \right)}{d}"," ",0,"-I*a*cos(d*x+c)/d+a*sin(d*x+c)/d","A"
253,1,23,27,0.402000," ","int(1/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{2}{d a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}"," ",0,"2/d/a/(tan(1/2*d*x+1/2*c)-I)","A"
254,1,23,27,0.398000," ","int(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x)","\frac{i}{d \,a^{2} \left(1+i \tan \left(d x +c \right)\right)}"," ",0,"I/d/a^2/(1+I*tan(d*x+c))","A"
255,1,57,27,0.429000," ","int(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x)","\frac{\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i}-\frac{8}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{4 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}}{d \,a^{3}}"," ",0,"2/d/a^3*(1/(tan(1/2*d*x+1/2*c)-I)-4/3/(tan(1/2*d*x+1/2*c)-I)^3+2*I/(tan(1/2*d*x+1/2*c)-I)^2)","B"
256,1,36,27,0.420000," ","int(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^4,x)","\frac{-\frac{i}{\left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{1}{\tan \left(d x +c \right)-i}}{d \,a^{4}}"," ",0,"1/d/a^4*(-I/(tan(d*x+c)-I)^2-1/(tan(d*x+c)-I))","A"
257,1,28,27,0.363000," ","int((a*cos(d*x+c)+I*a*sin(d*x+c))^(5/2),x)","-\frac{2 i \left(a \cos \left(d x +c \right)+i a \sin \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d}"," ",0,"-2/5*I*(a*cos(d*x+c)+I*a*sin(d*x+c))^(5/2)/d","A"
258,1,28,27,0.220000," ","int((a*cos(d*x+c)+I*a*sin(d*x+c))^(3/2),x)","-\frac{2 i \left(a \cos \left(d x +c \right)+i a \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}"," ",0,"-2/3*I*(a*cos(d*x+c)+I*a*sin(d*x+c))^(3/2)/d","A"
259,1,28,27,0.219000," ","int((a*cos(d*x+c)+I*a*sin(d*x+c))^(1/2),x)","-\frac{2 i \sqrt{a \cos \left(d x +c \right)+i a \sin \left(d x +c \right)}}{d}"," ",0,"-2*I*(a*cos(d*x+c)+I*a*sin(d*x+c))^(1/2)/d","A"
260,1,28,27,0.221000," ","int(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^(1/2),x)","\frac{2 i}{d \sqrt{a \cos \left(d x +c \right)+i a \sin \left(d x +c \right)}}"," ",0,"2*I/d/(a*cos(d*x+c)+I*a*sin(d*x+c))^(1/2)","A"
261,1,28,27,0.214000," ","int(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^(3/2),x)","\frac{2 i}{3 d \left(a \cos \left(d x +c \right)+i a \sin \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"2/3*I/d/(a*cos(d*x+c)+I*a*sin(d*x+c))^(3/2)","A"
262,1,28,27,0.211000," ","int(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^(5/2),x)","\frac{2 i}{5 d \left(a \cos \left(d x +c \right)+i a \sin \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"2/5*I/d/(a*cos(d*x+c)+I*a*sin(d*x+c))^(5/2)","A"
263,1,199,139,0.184000," ","int((a*sec(x)+b*tan(x))^5,x)","\frac{a^{5} \tan \left(x \right) \left(\sec^{3}\left(x \right)\right)}{4}+\frac{3 a^{5} \sec \left(x \right) \tan \left(x \right)}{8}+\frac{3 a^{5} \ln \left(\sec \left(x \right)+\tan \left(x \right)\right)}{8}+\frac{5 a^{4} b}{4 \cos \left(x \right)^{4}}+\frac{5 a^{3} b^{2} \left(\sin^{3}\left(x \right)\right)}{2 \cos \left(x \right)^{4}}+\frac{5 a^{3} b^{2} \left(\sin^{3}\left(x \right)\right)}{4 \cos \left(x \right)^{2}}+\frac{5 a^{3} b^{2} \sin \left(x \right)}{4}-\frac{5 a^{3} b^{2} \ln \left(\sec \left(x \right)+\tan \left(x \right)\right)}{4}+\frac{5 a^{2} b^{3} \left(\sin^{4}\left(x \right)\right)}{2 \cos \left(x \right)^{4}}+\frac{5 a \,b^{4} \left(\sin^{5}\left(x \right)\right)}{4 \cos \left(x \right)^{4}}-\frac{5 a \,b^{4} \left(\sin^{5}\left(x \right)\right)}{8 \cos \left(x \right)^{2}}-\frac{5 a \,b^{4} \left(\sin^{3}\left(x \right)\right)}{8}-\frac{15 a \,b^{4} \sin \left(x \right)}{8}+\frac{15 a \,b^{4} \ln \left(\sec \left(x \right)+\tan \left(x \right)\right)}{8}+\frac{b^{5} \left(\tan^{4}\left(x \right)\right)}{4}-\frac{b^{5} \left(\tan^{2}\left(x \right)\right)}{2}-b^{5} \ln \left(\cos \left(x \right)\right)"," ",0,"1/4*a^5*tan(x)*sec(x)^3+3/8*a^5*sec(x)*tan(x)+3/8*a^5*ln(sec(x)+tan(x))+5/4*a^4*b/cos(x)^4+5/2*a^3*b^2*sin(x)^3/cos(x)^4+5/4*a^3*b^2*sin(x)^3/cos(x)^2+5/4*a^3*b^2*sin(x)-5/4*a^3*b^2*ln(sec(x)+tan(x))+5/2*a^2*b^3*sin(x)^4/cos(x)^4+5/4*a*b^4*sin(x)^5/cos(x)^4-5/8*a*b^4*sin(x)^5/cos(x)^2-5/8*a*b^4*sin(x)^3-15/8*a*b^4*sin(x)+15/8*a*b^4*ln(sec(x)+tan(x))+1/4*b^5*tan(x)^4-1/2*b^5*tan(x)^2-b^5*ln(cos(x))","A"
264,1,96,92,0.089000," ","int((a*sec(x)+b*tan(x))^4,x)","-a^{4} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(x \right)\right)}{3}\right) \tan \left(x \right)+\frac{4 a^{3} b}{3 \cos \left(x \right)^{3}}+\frac{2 a^{2} b^{2} \left(\sin^{3}\left(x \right)\right)}{\cos \left(x \right)^{3}}+4 a \,b^{3} \left(\frac{\sin^{4}\left(x \right)}{3 \cos \left(x \right)^{3}}-\frac{\sin^{4}\left(x \right)}{3 \cos \left(x \right)}-\frac{\left(2+\sin^{2}\left(x \right)\right) \cos \left(x \right)}{3}\right)+b^{4} \left(\frac{\left(\tan^{3}\left(x \right)\right)}{3}-\tan \left(x \right)+x \right)"," ",0,"-a^4*(-2/3-1/3*sec(x)^2)*tan(x)+4/3*a^3*b/cos(x)^3+2*a^2*b^2*sin(x)^3/cos(x)^3+4*a*b^3*(1/3*sin(x)^4/cos(x)^3-1/3*sin(x)^4/cos(x)-1/3*(2+sin(x)^2)*cos(x))+b^4*(1/3*tan(x)^3-tan(x)+x)","A"
265,1,82,67,0.082000," ","int((a*sec(x)+b*tan(x))^3,x)","\frac{a^{3} \sec \left(x \right) \tan \left(x \right)}{2}+\frac{a^{3} \ln \left(\sec \left(x \right)+\tan \left(x \right)\right)}{2}+\frac{3 a^{2} b}{2 \cos \left(x \right)^{2}}+\frac{3 a \,b^{2} \left(\sin^{3}\left(x \right)\right)}{2 \cos \left(x \right)^{2}}+\frac{3 a \,b^{2} \sin \left(x \right)}{2}-\frac{3 a \,b^{2} \ln \left(\sec \left(x \right)+\tan \left(x \right)\right)}{2}+\frac{b^{3} \left(\tan^{2}\left(x \right)\right)}{2}+b^{3} \ln \left(\cos \left(x \right)\right)"," ",0,"1/2*a^3*sec(x)*tan(x)+1/2*a^3*ln(sec(x)+tan(x))+3/2*a^2*b/cos(x)^2+3/2*a*b^2*sin(x)^3/cos(x)^2+3/2*a*b^2*sin(x)-3/2*a*b^2*ln(sec(x)+tan(x))+1/2*b^3*tan(x)^2+b^3*ln(cos(x))","A"
266,1,26,27,0.049000," ","int((a*sec(x)+b*tan(x))^2,x)","a^{2} \tan \left(x \right)+\frac{2 a b}{\cos \left(x \right)}+b^{2} \left(\tan \left(x \right)-x \right)"," ",0,"a^2*tan(x)+2*a*b/cos(x)+b^2*(tan(x)-x)","A"
267,1,16,12,0.003000," ","int(a*sec(x)+b*tan(x),x)","a \ln \left(\sec \left(x \right)+\tan \left(x \right)\right)-b \ln \left(\cos \left(x \right)\right)"," ",0,"a*ln(sec(x)+tan(x))-b*ln(cos(x))","A"
268,1,12,11,0.118000," ","int(1/(a*sec(x)+b*tan(x)),x)","\frac{\ln \left(a +b \sin \left(x \right)\right)}{b}"," ",0,"ln(a+b*sin(x))/b","A"
269,1,106,60,0.163000," ","int(1/(a*sec(x)+b*tan(x))^2,x)","-\frac{2 \tan \left(\frac{x}{2}\right)}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right) a}-\frac{2}{b \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)}+\frac{2 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b^{2} \sqrt{a^{2}-b^{2}}}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b^{2}}"," ",0,"-2/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)/a*tan(1/2*x)-2/b/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)+2/b^2*a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))-2/b^2*arctan(tan(1/2*x))","A"
270,1,57,49,0.174000," ","int(1/(a*sec(x)+b*tan(x))^3,x)","-\frac{2 a}{b^{3} \left(a +b \sin \left(x \right)\right)}-\frac{\ln \left(a +b \sin \left(x \right)\right)}{b^{3}}+\frac{a^{2}}{2 b^{3} \left(a +b \sin \left(x \right)\right)^{2}}-\frac{1}{2 b \left(a +b \sin \left(x \right)\right)^{2}}"," ",0,"-2*a/b^3/(a+b*sin(x))-ln(a+b*sin(x))/b^3+1/2/b^3/(a+b*sin(x))^2*a^2-1/2/b/(a+b*sin(x))^2","A"
271,1,967,143,0.208000," ","int(1/(a*sec(x)+b*tan(x))^4,x)","\frac{a^{3} \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{b^{2} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} \left(a^{2}-b^{2}\right)}-\frac{2 a \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} \left(a^{2}-b^{2}\right)}+\frac{2 b^{2} \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} a \left(a^{2}-b^{2}\right)}+\frac{2 a^{4} \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{b^{3} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} \left(a^{2}-b^{2}\right)}+\frac{3 a^{2} \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{b \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} \left(a^{2}-b^{2}\right)}-\frac{4 b \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} \left(a^{2}-b^{2}\right)}+\frac{4 b^{3} \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} \left(a^{2}-b^{2}\right) a^{2}}+\frac{12 a^{3} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{b^{2} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} \left(a^{2}-b^{2}\right)}-\frac{2 a \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} \left(a^{2}-b^{2}\right)}-\frac{8 b^{2} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{3 \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} a \left(a^{2}-b^{2}\right)}+\frac{8 b^{4} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{3 \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} a^{3} \left(a^{2}-b^{2}\right)}+\frac{4 a^{4} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{b^{3} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} \left(a^{2}-b^{2}\right)}+\frac{16 a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{b \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} \left(a^{2}-b^{2}\right)}-\frac{14 b \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} \left(a^{2}-b^{2}\right)}+\frac{4 b^{3} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} \left(a^{2}-b^{2}\right) a^{2}}+\frac{11 a^{3} \tan \left(\frac{x}{2}\right)}{b^{2} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} \left(a^{2}-b^{2}\right)}-\frac{8 a \tan \left(\frac{x}{2}\right)}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} \left(a^{2}-b^{2}\right)}+\frac{2 b^{2} \tan \left(\frac{x}{2}\right)}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} a \left(a^{2}-b^{2}\right)}+\frac{2 a^{4}}{b^{3} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} \left(a^{2}-b^{2}\right)}-\frac{5 a^{2}}{3 b \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} \left(a^{2}-b^{2}\right)}+\frac{2 b}{3 \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)^{3} \left(a^{2}-b^{2}\right)}-\frac{2 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b^{4} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{3 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b^{4}}"," ",0,"1/b^2/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3*a^3/(a^2-b^2)*tan(1/2*x)^5-2/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3*a/(a^2-b^2)*tan(1/2*x)^5+2*b^2/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3/a/(a^2-b^2)*tan(1/2*x)^5+2/b^3/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3/(a^2-b^2)*a^4*tan(1/2*x)^4+3/b/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3/(a^2-b^2)*a^2*tan(1/2*x)^4-4*b/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3/(a^2-b^2)*tan(1/2*x)^4+4*b^3/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3/(a^2-b^2)/a^2*tan(1/2*x)^4+12/b^2/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3*a^3/(a^2-b^2)*tan(1/2*x)^3-2/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3*a/(a^2-b^2)*tan(1/2*x)^3-8/3*b^2/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3/a/(a^2-b^2)*tan(1/2*x)^3+8/3*b^4/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3/a^3/(a^2-b^2)*tan(1/2*x)^3+4/b^3/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3/(a^2-b^2)*a^4*tan(1/2*x)^2+16/b/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3/(a^2-b^2)*a^2*tan(1/2*x)^2-14*b/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3/(a^2-b^2)*tan(1/2*x)^2+4*b^3/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3/(a^2-b^2)/a^2*tan(1/2*x)^2+11/b^2/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3*a^3/(a^2-b^2)*tan(1/2*x)-8/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3*a/(a^2-b^2)*tan(1/2*x)+2*b^2/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3/a/(a^2-b^2)*tan(1/2*x)+2/b^3/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3/(a^2-b^2)*a^4-5/3/b/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3/(a^2-b^2)*a^2+2/3*b/(a*tan(1/2*x)^2+2*b*tan(1/2*x)+a)^3/(a^2-b^2)-2/b^4*a^3/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+3/b^2*a/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+2/b^4*arctan(tan(1/2*x))","B"
272,1,130,94,0.211000," ","int(1/(a*sec(x)+b*tan(x))^5,x)","\frac{4 a}{b^{5} \left(a +b \sin \left(x \right)\right)}-\frac{a^{4}}{4 b^{5} \left(a +b \sin \left(x \right)\right)^{4}}+\frac{a^{2}}{2 b^{3} \left(a +b \sin \left(x \right)\right)^{4}}-\frac{1}{4 b \left(a +b \sin \left(x \right)\right)^{4}}+\frac{4 a^{3}}{3 b^{5} \left(a +b \sin \left(x \right)\right)^{3}}-\frac{4 a}{3 b^{3} \left(a +b \sin \left(x \right)\right)^{3}}+\frac{\ln \left(a +b \sin \left(x \right)\right)}{b^{5}}-\frac{3 a^{2}}{b^{5} \left(a +b \sin \left(x \right)\right)^{2}}+\frac{1}{b^{3} \left(a +b \sin \left(x \right)\right)^{2}}"," ",0,"4*a/b^5/(a+b*sin(x))-1/4/b^5/(a+b*sin(x))^4*a^4+1/2/b^3/(a+b*sin(x))^4*a^2-1/4/b/(a+b*sin(x))^4+4/3*a^3/b^5/(a+b*sin(x))^3-4/3*a/b^3/(a+b*sin(x))^3+ln(a+b*sin(x))/b^5-3/b^5/(a+b*sin(x))^2*a^2+1/b^3/(a+b*sin(x))^2","A"
273,1,106,30,0.118000," ","int((sec(x)+tan(x))^5,x)","-\left(-\frac{\left(\sec^{3}\left(x \right)\right)}{4}-\frac{3 \sec \left(x \right)}{8}\right) \tan \left(x \right)+\ln \left(\sec \left(x \right)+\tan \left(x \right)\right)+\frac{5}{4 \cos \left(x \right)^{4}}+\frac{5 \left(\sin^{3}\left(x \right)\right)}{2 \cos \left(x \right)^{4}}+\frac{5 \left(\sin^{3}\left(x \right)\right)}{4 \cos \left(x \right)^{2}}-\frac{5 \sin \left(x \right)}{8}+\frac{5 \left(\sin^{4}\left(x \right)\right)}{2 \cos \left(x \right)^{4}}+\frac{5 \left(\sin^{5}\left(x \right)\right)}{4 \cos \left(x \right)^{4}}-\frac{5 \left(\sin^{5}\left(x \right)\right)}{8 \cos \left(x \right)^{2}}-\frac{5 \left(\sin^{3}\left(x \right)\right)}{8}+\frac{\left(\tan^{4}\left(x \right)\right)}{4}-\frac{\left(\tan^{2}\left(x \right)\right)}{2}-\ln \left(\cos \left(x \right)\right)"," ",0,"-(-1/4*sec(x)^3-3/8*sec(x))*tan(x)+ln(sec(x)+tan(x))+5/4/cos(x)^4+5/2*sin(x)^3/cos(x)^4+5/4*sin(x)^3/cos(x)^2-5/8*sin(x)+5/2*sin(x)^4/cos(x)^4+5/4*sin(x)^5/cos(x)^4-5/8*sin(x)^5/cos(x)^2-5/8*sin(x)^3+1/4*tan(x)^4-1/2*tan(x)^2-ln(cos(x))","B"
274,1,71,28,0.095000," ","int((sec(x)+tan(x))^4,x)","-\left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(x \right)\right)}{3}\right) \tan \left(x \right)+\frac{4}{3 \cos \left(x \right)^{3}}+\frac{2 \left(\sin^{3}\left(x \right)\right)}{\cos \left(x \right)^{3}}+\frac{4 \left(\sin^{4}\left(x \right)\right)}{3 \cos \left(x \right)^{3}}-\frac{4 \left(\sin^{4}\left(x \right)\right)}{3 \cos \left(x \right)}-\frac{4 \left(2+\sin^{2}\left(x \right)\right) \cos \left(x \right)}{3}+\frac{\left(\tan^{3}\left(x \right)\right)}{3}-\tan \left(x \right)+x"," ",0,"-(-2/3-1/3*sec(x)^2)*tan(x)+4/3/cos(x)^3+2*sin(x)^3/cos(x)^3+4/3*sin(x)^4/cos(x)^3-4/3*sin(x)^4/cos(x)-4/3*(2+sin(x)^2)*cos(x)+1/3*tan(x)^3-tan(x)+x","B"
275,1,45,18,0.096000," ","int((sec(x)+tan(x))^3,x)","\frac{\sec \left(x \right) \tan \left(x \right)}{2}-\ln \left(\sec \left(x \right)+\tan \left(x \right)\right)+\frac{3}{2 \cos \left(x \right)^{2}}+\frac{3 \left(\sin^{3}\left(x \right)\right)}{2 \cos \left(x \right)^{2}}+\frac{3 \sin \left(x \right)}{2}+\frac{\left(\tan^{2}\left(x \right)\right)}{2}+\ln \left(\cos \left(x \right)\right)"," ",0,"1/2*sec(x)*tan(x)-ln(sec(x)+tan(x))+3/2/cos(x)^2+3/2*sin(x)^3/cos(x)^2+3/2*sin(x)+1/2*tan(x)^2+ln(cos(x))","B"
276,1,15,16,0.046000," ","int((sec(x)+tan(x))^2,x)","2 \tan \left(x \right)+\frac{2}{\cos \left(x \right)}-x"," ",0,"2*tan(x)+2/cos(x)-x","A"
277,1,13,11,0.001000," ","int(sec(x)+tan(x),x)","\ln \left(\sec \left(x \right)+\tan \left(x \right)\right)-\ln \left(\cos \left(x \right)\right)"," ",0,"ln(sec(x)+tan(x))-ln(cos(x))","A"
278,1,6,5,0.116000," ","int(1/(sec(x)+tan(x)),x)","\ln \left(1+\sin \left(x \right)\right)"," ",0,"ln(1+sin(x))","A"
279,1,15,14,0.118000," ","int(1/(sec(x)+tan(x))^2,x)","-\frac{4}{1+\tan \left(\frac{x}{2}\right)}-x"," ",0,"-4/(1+tan(1/2*x))-x","A"
280,1,17,16,0.158000," ","int(1/(sec(x)+tan(x))^3,x)","-\ln \left(1+\sin \left(x \right)\right)-\frac{2}{1+\sin \left(x \right)}"," ",0,"-ln(1+sin(x))-2/(1+sin(x))","A"
281,1,23,24,0.151000," ","int(1/(sec(x)+tan(x))^4,x)","-\frac{16}{3 \left(1+\tan \left(\frac{x}{2}\right)\right)^{3}}+\frac{8}{\left(1+\tan \left(\frac{x}{2}\right)\right)^{2}}+x"," ",0,"-16/3/(1+tan(1/2*x))^3+8/(1+tan(1/2*x))^2+x","A"
282,1,23,22,0.184000," ","int(1/(sec(x)+tan(x))^5,x)","\ln \left(1+\sin \left(x \right)\right)-\frac{2}{\left(1+\sin \left(x \right)\right)^{2}}+\frac{4}{1+\sin \left(x \right)}"," ",0,"ln(1+sin(x))-2/(1+sin(x))^2+4/(1+sin(x))","A"
283,1,204,142,0.136000," ","int((a*cot(x)+b*csc(x))^5,x)","-\frac{a^{5} \left(\cot^{4}\left(x \right)\right)}{4}+\frac{a^{5} \left(\cot^{2}\left(x \right)\right)}{2}+a^{5} \ln \left(\sin \left(x \right)\right)-\frac{5 a^{4} b \left(\cos^{5}\left(x \right)\right)}{4 \sin \left(x \right)^{4}}+\frac{5 a^{4} b \left(\cos^{5}\left(x \right)\right)}{8 \sin \left(x \right)^{2}}+\frac{5 \left(\cos^{3}\left(x \right)\right) a^{4} b}{8}+\frac{15 a^{4} b \cos \left(x \right)}{8}+\frac{15 a^{4} b \ln \left(\csc \left(x \right)-\cot \left(x \right)\right)}{8}-\frac{5 a^{3} b^{2} \left(\cos^{4}\left(x \right)\right)}{2 \sin \left(x \right)^{4}}-\frac{5 a^{2} b^{3} \left(\cos^{3}\left(x \right)\right)}{2 \sin \left(x \right)^{4}}-\frac{5 a^{2} b^{3} \left(\cos^{3}\left(x \right)\right)}{4 \sin \left(x \right)^{2}}-\frac{5 \cos \left(x \right) a^{2} b^{3}}{4}-\frac{5 a^{2} b^{3} \ln \left(\csc \left(x \right)-\cot \left(x \right)\right)}{4}-\frac{5 a \,b^{4}}{4 \sin \left(x \right)^{4}}-\frac{b^{5} \cot \left(x \right) \left(\csc^{3}\left(x \right)\right)}{4}-\frac{3 b^{5} \csc \left(x \right) \cot \left(x \right)}{8}+\frac{3 b^{5} \ln \left(\csc \left(x \right)-\cot \left(x \right)\right)}{8}"," ",0,"-1/4*a^5*cot(x)^4+1/2*a^5*cot(x)^2+a^5*ln(sin(x))-5/4*a^4*b/sin(x)^4*cos(x)^5+5/8*a^4*b/sin(x)^2*cos(x)^5+5/8*cos(x)^3*a^4*b+15/8*a^4*b*cos(x)+15/8*a^4*b*ln(csc(x)-cot(x))-5/2*a^3*b^2/sin(x)^4*cos(x)^4-5/2*a^2*b^3/sin(x)^4*cos(x)^3-5/4*a^2*b^3/sin(x)^2*cos(x)^3-5/4*cos(x)*a^2*b^3-5/4*a^2*b^3*ln(csc(x)-cot(x))-5/4*a*b^4/sin(x)^4-1/4*b^5*cot(x)*csc(x)^3-3/8*b^5*csc(x)*cot(x)+3/8*b^5*ln(csc(x)-cot(x))","A"
284,1,93,93,0.067000," ","int((a*cot(x)+b*csc(x))^4,x)","a^{4} \left(-\frac{\left(\cot^{3}\left(x \right)\right)}{3}+\cot \left(x \right)+x \right)+4 a^{3} b \left(-\frac{\cos^{4}\left(x \right)}{3 \sin \left(x \right)^{3}}+\frac{\cos^{4}\left(x \right)}{3 \sin \left(x \right)}+\frac{\left(2+\cos^{2}\left(x \right)\right) \sin \left(x \right)}{3}\right)-\frac{2 a^{2} b^{2} \left(\cos^{3}\left(x \right)\right)}{\sin \left(x \right)^{3}}-\frac{4 a \,b^{3}}{3 \sin \left(x \right)^{3}}+b^{4} \left(-\frac{2}{3}-\frac{\left(\csc^{2}\left(x \right)\right)}{3}\right) \cot \left(x \right)"," ",0,"a^4*(-1/3*cot(x)^3+cot(x)+x)+4*a^3*b*(-1/3/sin(x)^3*cos(x)^4+1/3/sin(x)*cos(x)^4+1/3*(2+cos(x)^2)*sin(x))-2*a^2*b^2/sin(x)^3*cos(x)^3-4/3*a*b^3/sin(x)^3+b^4*(-2/3-1/3*csc(x)^2)*cot(x)","A"
285,1,87,69,0.068000," ","int((a*cot(x)+b*csc(x))^3,x)","-\frac{a^{3} \left(\cot^{2}\left(x \right)\right)}{2}-a^{3} \ln \left(\sin \left(x \right)\right)-\frac{3 a^{2} b \left(\cos^{3}\left(x \right)\right)}{2 \sin \left(x \right)^{2}}-\frac{3 a^{2} b \cos \left(x \right)}{2}-\frac{3 a^{2} b \ln \left(\csc \left(x \right)-\cot \left(x \right)\right)}{2}-\frac{3 a \,b^{2}}{2 \sin \left(x \right)^{2}}-\frac{b^{3} \csc \left(x \right) \cot \left(x \right)}{2}+\frac{b^{3} \ln \left(\csc \left(x \right)-\cot \left(x \right)\right)}{2}"," ",0,"-1/2*a^3*cot(x)^2-a^3*ln(sin(x))-3/2*a^2*b/sin(x)^2*cos(x)^3-3/2*a^2*b*cos(x)-3/2*a^2*b*ln(csc(x)-cot(x))-3/2*a*b^2/sin(x)^2-1/2*b^3*csc(x)*cot(x)+1/2*b^3*ln(csc(x)-cot(x))","A"
286,1,29,29,0.042000," ","int((a*cot(x)+b*csc(x))^2,x)","a^{2} \left(-\cot \left(x \right)-x \right)-\frac{2 a b}{\sin \left(x \right)}-b^{2} \cot \left(x \right)"," ",0,"a^2*(-cot(x)-x)-2*a*b/sin(x)-b^2*cot(x)","A"
287,1,16,12,0.003000," ","int(a*cot(x)+b*csc(x),x)","a \ln \left(\sin \left(x \right)\right)-b \ln \left(\cot \left(x \right)+\csc \left(x \right)\right)"," ",0,"a*ln(sin(x))-b*ln(cot(x)+csc(x))","A"
288,1,13,12,0.108000," ","int(1/(a*cot(x)+b*csc(x)),x)","-\frac{\ln \left(b +a \cos \left(x \right)\right)}{a}"," ",0,"-ln(b+a*cos(x))/a","A"
289,1,86,57,0.122000," ","int(1/(a*cot(x)+b*csc(x))^2,x)","-\frac{2 \tan \left(\frac{x}{2}\right)}{a \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-a -b \right)}+\frac{2 b \arctanh \left(\frac{\tan \left(\frac{x}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{a^{2} \sqrt{\left(a +b \right) \left(a -b \right)}}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a^{2}}"," ",0,"-2/a*tan(1/2*x)/(a*tan(1/2*x)^2-b*tan(1/2*x)^2-a-b)+2/a^2*b/((a+b)*(a-b))^(1/2)*arctanh(tan(1/2*x)*(a-b)/((a+b)*(a-b))^(1/2))-2/a^2*arctan(tan(1/2*x))","A"
290,1,56,48,0.119000," ","int(1/(a*cot(x)+b*csc(x))^3,x)","\frac{\ln \left(b +a \cos \left(x \right)\right)}{a^{3}}+\frac{1}{2 a \left(b +a \cos \left(x \right)\right)^{2}}-\frac{b^{2}}{2 a^{3} \left(b +a \cos \left(x \right)\right)^{2}}+\frac{2 b}{a^{3} \left(b +a \cos \left(x \right)\right)}"," ",0,"ln(b+a*cos(x))/a^3+1/2/a/(b+a*cos(x))^2-1/2/a^3/(b+a*cos(x))^2*b^2+2*b/a^3/(b+a*cos(x))","A"
291,1,534,142,0.143000," ","int(1/(a*cot(x)+b*csc(x))^4,x)","\frac{2 \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-a -b \right)^{3} \left(a +b \right)}-\frac{\left(\tan^{5}\left(\frac{x}{2}\right)\right) b}{a \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-a -b \right)^{3} \left(a +b \right)}-\frac{3 \left(\tan^{5}\left(\frac{x}{2}\right)\right) b^{2}}{a^{2} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-a -b \right)^{3} \left(a +b \right)}+\frac{2 \left(\tan^{5}\left(\frac{x}{2}\right)\right) b^{3}}{a^{3} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-a -b \right)^{3} \left(a +b \right)}-\frac{20 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{3 a \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-a -b \right)^{3}}+\frac{4 \left(\tan^{3}\left(\frac{x}{2}\right)\right) b^{2}}{a^{3} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-a -b \right)^{3}}+\frac{2 \tan \left(\frac{x}{2}\right)}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-a -b \right)^{3} \left(a -b \right)}+\frac{\tan \left(\frac{x}{2}\right) b}{a \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-a -b \right)^{3} \left(a -b \right)}-\frac{3 \tan \left(\frac{x}{2}\right) b^{2}}{a^{2} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-a -b \right)^{3} \left(a -b \right)}-\frac{2 \tan \left(\frac{x}{2}\right) b^{3}}{a^{3} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-a -b \right)^{3} \left(a -b \right)}-\frac{3 b \arctanh \left(\frac{\tan \left(\frac{x}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{a^{2} \left(a^{2}-b^{2}\right) \sqrt{\left(a +b \right) \left(a -b \right)}}+\frac{2 b^{3} \arctanh \left(\frac{\tan \left(\frac{x}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{a^{4} \left(a^{2}-b^{2}\right) \sqrt{\left(a +b \right) \left(a -b \right)}}+\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a^{4}}"," ",0,"2/(a*tan(1/2*x)^2-b*tan(1/2*x)^2-a-b)^3/(a+b)*tan(1/2*x)^5-1/a/(a*tan(1/2*x)^2-b*tan(1/2*x)^2-a-b)^3/(a+b)*tan(1/2*x)^5*b-3/a^2/(a*tan(1/2*x)^2-b*tan(1/2*x)^2-a-b)^3/(a+b)*tan(1/2*x)^5*b^2+2/a^3/(a*tan(1/2*x)^2-b*tan(1/2*x)^2-a-b)^3/(a+b)*tan(1/2*x)^5*b^3-20/3/a/(a*tan(1/2*x)^2-b*tan(1/2*x)^2-a-b)^3*tan(1/2*x)^3+4/a^3/(a*tan(1/2*x)^2-b*tan(1/2*x)^2-a-b)^3*tan(1/2*x)^3*b^2+2/(a*tan(1/2*x)^2-b*tan(1/2*x)^2-a-b)^3/(a-b)*tan(1/2*x)+1/a/(a*tan(1/2*x)^2-b*tan(1/2*x)^2-a-b)^3/(a-b)*tan(1/2*x)*b-3/a^2/(a*tan(1/2*x)^2-b*tan(1/2*x)^2-a-b)^3/(a-b)*tan(1/2*x)*b^2-2/a^3/(a*tan(1/2*x)^2-b*tan(1/2*x)^2-a-b)^3/(a-b)*tan(1/2*x)*b^3-3/a^2*b/(a^2-b^2)/((a+b)*(a-b))^(1/2)*arctanh(tan(1/2*x)*(a-b)/((a+b)*(a-b))^(1/2))+2/a^4*b^3/(a^2-b^2)/((a+b)*(a-b))^(1/2)*arctanh(tan(1/2*x)*(a-b)/((a+b)*(a-b))^(1/2))+2/a^4*arctan(tan(1/2*x))","B"
292,1,132,97,0.128000," ","int(1/(a*cot(x)+b*csc(x))^5,x)","\frac{4 b}{3 a^{3} \left(b +a \cos \left(x \right)\right)^{3}}-\frac{4 b^{3}}{3 a^{5} \left(b +a \cos \left(x \right)\right)^{3}}-\frac{4 b}{a^{5} \left(b +a \cos \left(x \right)\right)}-\frac{\ln \left(b +a \cos \left(x \right)\right)}{a^{5}}-\frac{1}{a^{3} \left(b +a \cos \left(x \right)\right)^{2}}+\frac{3 b^{2}}{a^{5} \left(b +a \cos \left(x \right)\right)^{2}}+\frac{1}{4 a \left(b +a \cos \left(x \right)\right)^{4}}-\frac{b^{2}}{2 a^{3} \left(b +a \cos \left(x \right)\right)^{4}}+\frac{b^{4}}{4 a^{5} \left(b +a \cos \left(x \right)\right)^{4}}"," ",0,"4/3*b/a^3/(b+a*cos(x))^3-4/3*b^3/a^5/(b+a*cos(x))^3-4*b/a^5/(b+a*cos(x))-ln(b+a*cos(x))/a^5-1/a^3/(b+a*cos(x))^2+3/a^5/(b+a*cos(x))^2*b^2+1/4/a/(b+a*cos(x))^4-1/2/a^3/(b+a*cos(x))^4*b^2+1/4/a^5/(b+a*cos(x))^4*b^4","A"
293,1,105,28,0.108000," ","int((cot(x)+csc(x))^5,x)","-\frac{\left(\cot^{4}\left(x \right)\right)}{4}+\frac{\left(\cot^{2}\left(x \right)\right)}{2}+\ln \left(\sin \left(x \right)\right)-\frac{5 \left(\cos^{5}\left(x \right)\right)}{4 \sin \left(x \right)^{4}}+\frac{5 \left(\cos^{5}\left(x \right)\right)}{8 \sin \left(x \right)^{2}}+\frac{5 \left(\cos^{3}\left(x \right)\right)}{8}+\frac{5 \cos \left(x \right)}{8}+\ln \left(\csc \left(x \right)-\cot \left(x \right)\right)-\frac{5 \left(\cos^{4}\left(x \right)\right)}{2 \sin \left(x \right)^{4}}-\frac{5 \left(\cos^{3}\left(x \right)\right)}{2 \sin \left(x \right)^{4}}-\frac{5 \left(\cos^{3}\left(x \right)\right)}{4 \sin \left(x \right)^{2}}-\frac{5}{4 \sin \left(x \right)^{4}}+\left(-\frac{\left(\csc^{3}\left(x \right)\right)}{4}-\frac{3 \csc \left(x \right)}{8}\right) \cot \left(x \right)"," ",0,"-1/4*cot(x)^4+1/2*cot(x)^2+ln(sin(x))-5/4/sin(x)^4*cos(x)^5+5/8/sin(x)^2*cos(x)^5+5/8*cos(x)^3+5/8*cos(x)+ln(csc(x)-cot(x))-5/2/sin(x)^4*cos(x)^4-5/2/sin(x)^4*cos(x)^3-5/4/sin(x)^2*cos(x)^3-5/4/sin(x)^4+(-1/4*csc(x)^3-3/8*csc(x))*cot(x)","B"
294,1,68,28,0.088000," ","int((cot(x)+csc(x))^4,x)","-\frac{\left(\cot^{3}\left(x \right)\right)}{3}+\cot \left(x \right)+x -\frac{4 \left(\cos^{4}\left(x \right)\right)}{3 \sin \left(x \right)^{3}}+\frac{4 \left(\cos^{4}\left(x \right)\right)}{3 \sin \left(x \right)}+\frac{4 \left(2+\cos^{2}\left(x \right)\right) \sin \left(x \right)}{3}-\frac{2 \left(\cos^{3}\left(x \right)\right)}{\sin \left(x \right)^{3}}-\frac{4}{3 \sin \left(x \right)^{3}}+\left(-\frac{2}{3}-\frac{\left(\csc^{2}\left(x \right)\right)}{3}\right) \cot \left(x \right)"," ",0,"-1/3*cot(x)^3+cot(x)+x-4/3/sin(x)^3*cos(x)^4+4/3/sin(x)*cos(x)^4+4/3*(2+cos(x)^2)*sin(x)-2/sin(x)^3*cos(x)^3-4/3/sin(x)^3+(-2/3-1/3*csc(x)^2)*cot(x)","B"
295,1,49,20,0.081000," ","int((cot(x)+csc(x))^3,x)","-\frac{\left(\cot^{2}\left(x \right)\right)}{2}-\ln \left(\sin \left(x \right)\right)-\frac{3 \left(\cos^{3}\left(x \right)\right)}{2 \sin \left(x \right)^{2}}-\frac{3 \cos \left(x \right)}{2}-\ln \left(\csc \left(x \right)-\cot \left(x \right)\right)-\frac{3}{2 \sin \left(x \right)^{2}}-\frac{\cot \left(x \right) \csc \left(x \right)}{2}"," ",0,"-1/2*cot(x)^2-ln(sin(x))-3/2/sin(x)^2*cos(x)^3-3/2*cos(x)-ln(csc(x)-cot(x))-3/2/sin(x)^2-1/2*cot(x)*csc(x)","B"
296,1,15,16,0.043000," ","int((cot(x)+csc(x))^2,x)","-2 \cot \left(x \right)-x -\frac{2}{\sin \left(x \right)}"," ",0,"-2*cot(x)-x-2/sin(x)","A"
297,1,13,9,0.001000," ","int(cot(x)+csc(x),x)","\ln \left(\sin \left(x \right)\right)-\ln \left(\cot \left(x \right)+\csc \left(x \right)\right)"," ",0,"ln(sin(x))-ln(cot(x)+csc(x))","A"
298,1,8,7,0.108000," ","int(1/(cot(x)+csc(x)),x)","-\ln \left(1+\cos \left(x \right)\right)"," ",0,"-ln(1+cos(x))","A"
299,1,11,14,0.109000," ","int(1/(cot(x)+csc(x))^2,x)","2 \tan \left(\frac{x}{2}\right)-x"," ",0,"2*tan(1/2*x)-x","A"
300,1,15,14,0.151000," ","int(1/(cot(x)+csc(x))^3,x)","\frac{2}{1+\cos \left(x \right)}+\ln \left(1+\cos \left(x \right)\right)"," ",0,"2/(1+cos(x))+ln(1+cos(x))","A"
301,1,17,24,0.142000," ","int(1/(cot(x)+csc(x))^4,x)","\frac{2 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{3}-2 \tan \left(\frac{x}{2}\right)+x"," ",0,"2/3*tan(1/2*x)^3-2*tan(1/2*x)+x","A"
302,1,25,24,0.158000," ","int(1/(cot(x)+csc(x))^5,x)","\frac{2}{\left(1+\cos \left(x \right)\right)^{2}}-\frac{4}{1+\cos \left(x \right)}-\ln \left(1+\cos \left(x \right)\right)"," ",0,"2/(1+cos(x))^2-4/(1+cos(x))-ln(1+cos(x))","A"
303,1,39,34,0.060000," ","int((csc(x)-sin(x))^4,x)","-\frac{\left(\sin^{3}\left(x \right)+\frac{3 \sin \left(x \right)}{2}\right) \cos \left(x \right)}{4}+\frac{35 x}{8}+2 \cos \left(x \right) \sin \left(x \right)+4 \cot \left(x \right)+\left(-\frac{2}{3}-\frac{\left(\csc^{2}\left(x \right)\right)}{3}\right) \cot \left(x \right)"," ",0,"-1/4*(sin(x)^3+3/2*sin(x))*cos(x)+35/8*x+2*cos(x)*sin(x)+4*cot(x)+(-2/3-1/3*csc(x)^2)*cot(x)","A"
304,1,32,26,0.058000," ","int((csc(x)-sin(x))^3,x)","\frac{\left(2+\sin^{2}\left(x \right)\right) \cos \left(x \right)}{3}-3 \cos \left(x \right)-\frac{5 \ln \left(\csc \left(x \right)-\cot \left(x \right)\right)}{2}-\frac{\cot \left(x \right) \csc \left(x \right)}{2}"," ",0,"1/3*(2+sin(x)^2)*cos(x)-3*cos(x)-5/2*ln(csc(x)-cot(x))-1/2*cot(x)*csc(x)","A"
305,1,15,16,0.049000," ","int((csc(x)-sin(x))^2,x)","-\frac{\cos \left(x \right) \sin \left(x \right)}{2}-\frac{3 x}{2}-\cot \left(x \right)"," ",0,"-1/2*cos(x)*sin(x)-3/2*x-cot(x)","A"
306,1,12,8,0.001000," ","int(csc(x)-sin(x),x)","\cos \left(x \right)-\ln \left(\cot \left(x \right)+\csc \left(x \right)\right)"," ",0,"cos(x)-ln(cot(x)+csc(x))","A"
307,1,5,2,0.099000," ","int(1/(csc(x)-sin(x)),x)","\frac{1}{\cos \left(x \right)}"," ",0,"1/cos(x)","A"
308,1,7,6,0.106000," ","int(1/(csc(x)-sin(x))^2,x)","\frac{\left(\tan^{3}\left(x \right)\right)}{3}"," ",0,"1/3*tan(x)^3","A"
309,1,14,13,0.116000," ","int(1/(csc(x)-sin(x))^3,x)","-\frac{1}{3 \cos \left(x \right)^{3}}+\frac{1}{5 \cos \left(x \right)^{5}}"," ",0,"-1/3/cos(x)^3+1/5/cos(x)^5","A"
310,1,14,13,0.113000," ","int(1/(csc(x)-sin(x))^4,x)","\frac{\left(\tan^{5}\left(x \right)\right)}{5}+\frac{\left(\tan^{7}\left(x \right)\right)}{7}"," ",0,"1/5*tan(x)^5+1/7*tan(x)^7","A"
311,1,20,19,0.122000," ","int(1/(csc(x)-sin(x))^5,x)","-\frac{2}{7 \cos \left(x \right)^{7}}+\frac{1}{9 \cos \left(x \right)^{9}}+\frac{1}{5 \cos \left(x \right)^{5}}"," ",0,"-2/7/cos(x)^7+1/9/cos(x)^9+1/5/cos(x)^5","A"
312,1,20,19,0.125000," ","int(1/(csc(x)-sin(x))^6,x)","\frac{\left(\tan^{7}\left(x \right)\right)}{7}+\frac{2 \left(\tan^{9}\left(x \right)\right)}{9}+\frac{\left(\tan^{11}\left(x \right)\right)}{11}"," ",0,"1/7*tan(x)^7+2/9*tan(x)^9+1/11*tan(x)^11","A"
313,1,26,25,0.135000," ","int(1/(csc(x)-sin(x))^7,x)","\frac{1}{13 \cos \left(x \right)^{13}}-\frac{1}{7 \cos \left(x \right)^{7}}+\frac{1}{3 \cos \left(x \right)^{9}}-\frac{3}{11 \cos \left(x \right)^{11}}"," ",0,"1/13/cos(x)^13-1/7/cos(x)^7+1/3/cos(x)^9-3/11/cos(x)^11","A"
314,1,40,57,0.313000," ","int((csc(x)-sin(x))^(7/2),x)","\frac{2 \left(5 \left(\cos^{6}\left(x \right)\right)+20 \left(\cos^{4}\left(x \right)\right)-160 \left(\cos^{2}\left(x \right)\right)+128\right) \sin \left(x \right) \left(\frac{\cos^{2}\left(x \right)}{\sin \left(x \right)}\right)^{\frac{7}{2}}}{35 \cos \left(x \right)^{7}}"," ",0,"2/35*(5*cos(x)^6+20*cos(x)^4-160*cos(x)^2+128)*sin(x)*(cos(x)^2/sin(x))^(7/2)/cos(x)^7","A"
315,1,34,38,0.282000," ","int((csc(x)-sin(x))^(5/2),x)","\frac{2 \left(3 \left(\cos^{4}\left(x \right)\right)+24 \left(\cos^{2}\left(x \right)\right)-32\right) \left(\frac{\cos^{2}\left(x \right)}{\sin \left(x \right)}\right)^{\frac{5}{2}} \sin \left(x \right)}{15 \cos \left(x \right)^{5}}"," ",0,"2/15*(3*cos(x)^4+24*cos(x)^2-32)*(cos(x)^2/sin(x))^(5/2)*sin(x)/cos(x)^5","A"
316,1,26,23,0.238000," ","int((csc(x)-sin(x))^(3/2),x)","\frac{2 \left(\cos^{2}\left(x \right)-4\right) \left(\frac{\cos^{2}\left(x \right)}{\sin \left(x \right)}\right)^{\frac{3}{2}} \sin \left(x \right)}{3 \cos \left(x \right)^{3}}"," ",0,"2/3*(cos(x)^2-4)*(cos(x)^2/sin(x))^(3/2)*sin(x)/cos(x)^3","A"
317,1,20,11,0.234000," ","int((csc(x)-sin(x))^(1/2),x)","\frac{2 \sin \left(x \right) \sqrt{\frac{\cos^{2}\left(x \right)}{\sin \left(x \right)}}}{\cos \left(x \right)}"," ",0,"2*sin(x)*(cos(x)^2/sin(x))^(1/2)/cos(x)","A"
318,0,0,48,0.257000," ","int(1/(csc(x)-sin(x))^(1/2),x)","\int \frac{1}{\sqrt{\csc \left(x \right)-\sin \left(x \right)}}\, dx"," ",0,"int(1/(csc(x)-sin(x))^(1/2),x)","F"
319,1,450,60,0.549000," ","int(1/(csc(x)-sin(x))^(3/2),x)","\frac{\left(-1+\cos \left(x \right)\right) \left(i \sin \left(x \right) \left(\cos^{2}\left(x \right)\right) \EllipticPi \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}+i \sin \left(x \right) \left(\cos^{2}\left(x \right)\right) \EllipticPi \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}-2 i \sin \left(x \right) \left(\cos^{2}\left(x \right)\right) \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}-\sin \left(x \right) \left(\cos^{2}\left(x \right)\right) \EllipticPi \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}+\sin \left(x \right) \left(\cos^{2}\left(x \right)\right) \EllipticPi \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}+2 \cos \left(x \right) \sqrt{2}-2 \sqrt{2}\right) \cos \left(x \right) \left(1+\cos \left(x \right)\right)^{2} \sqrt{2}}{8 \left(\frac{\cos^{2}\left(x \right)}{\sin \left(x \right)}\right)^{\frac{3}{2}} \sin \left(x \right)^{5}}"," ",0,"1/8*(-1+cos(x))*(I*sin(x)*cos(x)^2*EllipticPi(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)+I*sin(x)*cos(x)^2*EllipticPi(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)-2*I*sin(x)*cos(x)^2*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)-sin(x)*cos(x)^2*EllipticPi(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)+sin(x)*cos(x)^2*EllipticPi(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)+2*cos(x)*2^(1/2)-2*2^(1/2))*cos(x)*(1+cos(x))^2/(cos(x)^2/sin(x))^(3/2)/sin(x)^5*2^(1/2)","C"
320,1,382,75,0.353000," ","int(1/(csc(x)-sin(x))^(5/2),x)","-\frac{\left(-1+\cos \left(x \right)\right) \left(3 i \left(\cos^{4}\left(x \right)\right) \EllipticPi \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}-3 i \left(\cos^{4}\left(x \right)\right) \EllipticPi \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}-3 \left(\cos^{4}\left(x \right)\right) \EllipticPi \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}-3 \left(\cos^{4}\left(x \right)\right) \EllipticPi \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}+6 \left(\cos^{3}\left(x \right)\right) \sqrt{2}-6 \left(\cos^{2}\left(x \right)\right) \sqrt{2}-8 \cos \left(x \right) \sqrt{2}+8 \sqrt{2}\right) \cos \left(x \right) \left(1+\cos \left(x \right)\right)^{2} \sqrt{2}}{64 \sin \left(x \right)^{5} \left(\frac{\cos^{2}\left(x \right)}{\sin \left(x \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/64*(-1+cos(x))*(3*I*cos(x)^4*EllipticPi(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)-3*I*cos(x)^4*EllipticPi(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)-3*cos(x)^4*EllipticPi(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)-3*cos(x)^4*EllipticPi(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)+6*cos(x)^3*2^(1/2)-6*cos(x)^2*2^(1/2)-8*cos(x)*2^(1/2)+8*2^(1/2))*cos(x)*(1+cos(x))^2/sin(x)^5/(cos(x)^2/sin(x))^(5/2)*2^(1/2)","C"
321,1,487,90,0.387000," ","int(1/(csc(x)-sin(x))^(7/2),x)","\frac{\left(-1+\cos \left(x \right)\right) \left(-15 i \sin \left(x \right) \left(\cos^{6}\left(x \right)\right) \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-15 i \sin \left(x \right) \left(\cos^{6}\left(x \right)\right) \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+30 i \sin \left(x \right) \left(\cos^{6}\left(x \right)\right) \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right)+15 \sin \left(x \right) \left(\cos^{6}\left(x \right)\right) \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-15 \sin \left(x \right) \left(\cos^{6}\left(x \right)\right) \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+10 \sqrt{2}\, \left(\cos^{5}\left(x \right)\right)-10 \sqrt{2}\, \left(\cos^{4}\left(x \right)\right)-104 \left(\cos^{3}\left(x \right)\right) \sqrt{2}+104 \left(\cos^{2}\left(x \right)\right) \sqrt{2}+64 \cos \left(x \right) \sqrt{2}-64 \sqrt{2}\right) \cos \left(x \right) \left(1+\cos \left(x \right)\right)^{2} \sqrt{2}}{768 \left(\frac{\cos^{2}\left(x \right)}{\sin \left(x \right)}\right)^{\frac{7}{2}} \sin \left(x \right)^{7}}"," ",0,"1/768*(-1+cos(x))*(-15*I*sin(x)*cos(x)^6*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*EllipticPi(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))-15*I*sin(x)*cos(x)^6*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*EllipticPi(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))+30*I*sin(x)*cos(x)^6*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))+15*sin(x)*cos(x)^6*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*EllipticPi(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))-15*sin(x)*cos(x)^6*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*EllipticPi(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))+10*2^(1/2)*cos(x)^5-10*2^(1/2)*cos(x)^4-104*cos(x)^3*2^(1/2)+104*cos(x)^2*2^(1/2)+64*cos(x)*2^(1/2)-64*2^(1/2))*cos(x)*(1+cos(x))^2/(cos(x)^2/sin(x))^(7/2)/sin(x)^7*2^(1/2)","C"
322,1,40,34,0.059000," ","int((-cos(x)+sec(x))^4,x)","-\left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(x \right)\right)}{3}\right) \tan \left(x \right)-4 \tan \left(x \right)+\frac{35 x}{8}-2 \cos \left(x \right) \sin \left(x \right)+\frac{\left(\cos^{3}\left(x \right)+\frac{3 \cos \left(x \right)}{2}\right) \sin \left(x \right)}{4}"," ",0,"-(-2/3-1/3*sec(x)^2)*tan(x)-4*tan(x)+35/8*x-2*cos(x)*sin(x)+1/4*(cos(x)^3+3/2*cos(x))*sin(x)","A"
323,1,30,26,0.059000," ","int((-cos(x)+sec(x))^3,x)","\frac{\sec \left(x \right) \tan \left(x \right)}{2}-\frac{5 \ln \left(\sec \left(x \right)+\tan \left(x \right)\right)}{2}+3 \sin \left(x \right)-\frac{\left(2+\cos^{2}\left(x \right)\right) \sin \left(x \right)}{3}"," ",0,"1/2*sec(x)*tan(x)-5/2*ln(sec(x)+tan(x))+3*sin(x)-1/3*(2+cos(x)^2)*sin(x)","A"
324,1,13,16,0.046000," ","int((-cos(x)+sec(x))^2,x)","\tan \left(x \right)-\frac{3 x}{2}+\frac{\cos \left(x \right) \sin \left(x \right)}{2}"," ",0,"tan(x)-3/2*x+1/2*cos(x)*sin(x)","A"
325,1,12,8,0.002000," ","int(-cos(x)+sec(x),x)","-\sin \left(x \right)+\ln \left(\sec \left(x \right)+\tan \left(x \right)\right)"," ",0,"-sin(x)+ln(sec(x)+tan(x))","A"
326,1,7,4,0.096000," ","int(1/(-cos(x)+sec(x)),x)","-\frac{1}{\sin \left(x \right)}"," ",0,"-1/sin(x)","A"
327,1,7,6,0.098000," ","int(1/(-cos(x)+sec(x))^2,x)","-\frac{1}{3 \tan \left(x \right)^{3}}"," ",0,"-1/3/tan(x)^3","A"
328,1,14,13,0.105000," ","int(1/(-cos(x)+sec(x))^3,x)","\frac{1}{3 \sin \left(x \right)^{3}}-\frac{1}{5 \sin \left(x \right)^{5}}"," ",0,"1/3/sin(x)^3-1/5/sin(x)^5","A"
329,1,14,13,0.106000," ","int(1/(-cos(x)+sec(x))^4,x)","-\frac{1}{7 \tan \left(x \right)^{7}}-\frac{1}{5 \tan \left(x \right)^{5}}"," ",0,"-1/7/tan(x)^7-1/5/tan(x)^5","A"
330,1,20,19,0.109000," ","int(1/(-cos(x)+sec(x))^5,x)","-\frac{1}{9 \sin \left(x \right)^{9}}+\frac{2}{7 \sin \left(x \right)^{7}}-\frac{1}{5 \sin \left(x \right)^{5}}"," ",0,"-1/9/sin(x)^9+2/7/sin(x)^7-1/5/sin(x)^5","A"
331,1,20,19,0.110000," ","int(1/(-cos(x)+sec(x))^6,x)","-\frac{2}{9 \tan \left(x \right)^{9}}-\frac{1}{7 \tan \left(x \right)^{7}}-\frac{1}{11 \tan \left(x \right)^{11}}"," ",0,"-2/9/tan(x)^9-1/7/tan(x)^7-1/11/tan(x)^11","A"
332,1,26,25,0.113000," ","int(1/(-cos(x)+sec(x))^7,x)","-\frac{1}{13 \sin \left(x \right)^{13}}-\frac{1}{3 \sin \left(x \right)^{9}}+\frac{1}{7 \sin \left(x \right)^{7}}+\frac{3}{11 \sin \left(x \right)^{11}}"," ",0,"-1/13/sin(x)^13-1/3/sin(x)^9+1/7/sin(x)^7+3/11/sin(x)^11","A"
333,1,603,57,0.408000," ","int((-cos(x)+sec(x))^(7/2),x)","\frac{\left(-1+\cos \left(x \right)\right)^{2} \left(-105 \left(\cos^{4}\left(x \right)\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right)+105 \left(\cos^{4}\left(x \right)\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)-315 \left(\cos^{3}\left(x \right)\right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}+315 \left(\cos^{3}\left(x \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}+20 \left(\cos^{6}\left(x \right)\right)-315 \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right) \left(\cos^{2}\left(x \right)\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}+315 \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right) \left(\cos^{2}\left(x \right)\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}-105 \cos \left(x \right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}+105 \cos \left(x \right) \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}-140 \left(\cos^{4}\left(x \right)\right)-420 \left(\cos^{2}\left(x \right)\right)+28\right) \cos \left(x \right) \left(1+\cos \left(x \right)\right)^{2} \left(-\frac{-1+\cos^{2}\left(x \right)}{\cos \left(x \right)}\right)^{\frac{7}{2}}}{70 \sin \left(x \right)^{11}}"," ",0,"1/70*(-1+cos(x))^2*(-105*cos(x)^4*(-cos(x)/(1+cos(x))^2)^(3/2)*ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)+105*cos(x)^4*(-cos(x)/(1+cos(x))^2)^(3/2)*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)-315*cos(x)^3*ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*(-cos(x)/(1+cos(x))^2)^(3/2)+315*cos(x)^3*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*(-cos(x)/(1+cos(x))^2)^(3/2)+20*cos(x)^6-315*ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(3/2)+315*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(3/2)-105*cos(x)*ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*(-cos(x)/(1+cos(x))^2)^(3/2)+105*cos(x)*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*(-cos(x)/(1+cos(x))^2)^(3/2)-140*cos(x)^4-420*cos(x)^2+28)*cos(x)*(1+cos(x))^2*(-(-1+cos(x)^2)/cos(x))^(7/2)/sin(x)^11","B"
334,1,321,38,0.330000," ","int((-cos(x)+sec(x))^(5/2),x)","-\frac{\left(-1+\cos \left(x \right)\right)^{2} \left(6 \left(\cos^{4}\left(x \right)\right)-15 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}\, \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)+15 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}\, \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right)-15 \cos \left(x \right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}\, \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)+15 \cos \left(x \right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}\, \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right)-60 \left(\cos^{2}\left(x \right)\right)-10\right) \cos \left(x \right) \left(1+\cos \left(x \right)\right)^{2} \left(-\frac{-1+\cos^{2}\left(x \right)}{\cos \left(x \right)}\right)^{\frac{5}{2}}}{15 \sin \left(x \right)^{9}}"," ",0,"-1/15*(-1+cos(x))^2*(6*cos(x)^4-15*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)+15*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)*ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)-15*cos(x)*(-cos(x)/(1+cos(x))^2)^(1/2)*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)+15*cos(x)*(-cos(x)/(1+cos(x))^2)^(1/2)*ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)-60*cos(x)^2-10)*cos(x)*(1+cos(x))^2*(-(-1+cos(x)^2)/cos(x))^(5/2)/sin(x)^9","B"
335,1,584,23,0.266000," ","int((-cos(x)+sec(x))^(3/2),x)","\frac{\left(-1+\cos \left(x \right)\right)^{2} \left(3 \left(\cos^{3}\left(x \right)\right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}-3 \left(\cos^{3}\left(x \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}+9 \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right) \left(\cos^{2}\left(x \right)\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}-9 \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right) \left(\cos^{2}\left(x \right)\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}+9 \cos \left(x \right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}-9 \cos \left(x \right) \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}+3 \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}-3 \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}+4 \left(\cos^{3}\left(x \right)\right)+12 \cos \left(x \right)\right) \left(1+\cos \left(x \right)\right)^{2} \left(-\frac{-1+\cos^{2}\left(x \right)}{\cos \left(x \right)}\right)^{\frac{3}{2}}}{6 \sin \left(x \right)^{7}}"," ",0,"1/6*(-1+cos(x))^2*(3*cos(x)^3*ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*(-cos(x)/(1+cos(x))^2)^(3/2)-3*cos(x)^3*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*(-cos(x)/(1+cos(x))^2)^(3/2)+9*ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(3/2)-9*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(3/2)+9*cos(x)*ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*(-cos(x)/(1+cos(x))^2)^(3/2)-9*cos(x)*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*(-cos(x)/(1+cos(x))^2)^(3/2)+3*ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*(-cos(x)/(1+cos(x))^2)^(3/2)-3*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)*(-cos(x)/(1+cos(x))^2)^(3/2)+4*cos(x)^3+12*cos(x))*(1+cos(x))^2*(-(-1+cos(x)^2)/cos(x))^(3/2)/sin(x)^7","B"
336,1,174,11,0.313000," ","int((-cos(x)+sec(x))^(1/2),x)","\frac{\left(-1+\cos \left(x \right)\right) \left(4 \cos \left(x \right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}+4 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}+\ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1\right)}{\sin \left(x \right)^{2}}\right)-\ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)\right) \cos \left(x \right) \sqrt{-\frac{-1+\cos^{2}\left(x \right)}{\cos \left(x \right)}}}{2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}\, \sin \left(x \right)^{3}}"," ",0,"1/2*(-1+cos(x))*(4*cos(x)*(-cos(x)/(1+cos(x))^2)^(1/2)+4*(-cos(x)/(1+cos(x))^2)^(1/2)+ln(-2*(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)-ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2))*cos(x)*(-(-1+cos(x)^2)/cos(x))^(1/2)/(-cos(x)/(1+cos(x))^2)^(1/2)/sin(x)^3","B"
337,1,105,40,0.281000," ","int(1/(-cos(x)+sec(x))^(1/2),x)","-\frac{\left(\arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}}\right)+\ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)\right) \left(1+\cos \left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}\, \sqrt{\frac{1-\left(\cos^{2}\left(x \right)\right)}{\cos \left(x \right)}}}{2 \sin \left(x \right)}"," ",0,"-1/2*(arctan(1/2/(-cos(x)/(1+cos(x))^2)^(1/2))+ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2))*(1+cos(x))*(-cos(x)/(1+cos(x))^2)^(1/2)*((1-cos(x)^2)/cos(x))^(1/2)/sin(x)","B"
338,1,265,52,0.314000," ","int(1/(-cos(x)+sec(x))^(3/2),x)","-\frac{\left(-1+\cos \left(x \right)\right) \left(8 \left(\cos^{2}\left(x \right)\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}+16 \cos \left(x \right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}-\left(\cos^{2}\left(x \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)+\left(\cos^{2}\left(x \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}}\right)+8 \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}+4 \cos \left(x \right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-4 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}+\ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)-\arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}}\right)\right)}{8 \left(-\frac{-1+\cos^{2}\left(x \right)}{\cos \left(x \right)}\right)^{\frac{3}{2}} \cos \left(x \right) \sin \left(x \right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}}"," ",0,"-1/8*(-1+cos(x))*(8*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(3/2)+16*cos(x)*(-cos(x)/(1+cos(x))^2)^(3/2)-cos(x)^2*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)+cos(x)^2*arctan(1/2/(-cos(x)/(1+cos(x))^2)^(1/2))+8*(-cos(x)/(1+cos(x))^2)^(3/2)+4*cos(x)*(-cos(x)/(1+cos(x))^2)^(1/2)-4*(-cos(x)/(1+cos(x))^2)^(1/2)+ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)-arctan(1/2/(-cos(x)/(1+cos(x))^2)^(1/2)))/(-(-1+cos(x)^2)/cos(x))^(3/2)/cos(x)/sin(x)/(-cos(x)/(1+cos(x))^2)^(1/2)","B"
339,1,454,67,0.320000," ","int(1/(-cos(x)+sec(x))^(5/2),x)","\frac{\left(24 \left(\cos^{3}\left(x \right)\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}+40 \left(\cos^{2}\left(x \right)\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}-12 \left(\cos^{3}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-3 \left(\cos^{3}\left(x \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)-3 \left(\cos^{3}\left(x \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}}\right)+8 \cos \left(x \right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}+24 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}+3 \left(\cos^{2}\left(x \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)+3 \left(\cos^{2}\left(x \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}}\right)-8 \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}-12 \cos \left(x \right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}+3 \cos \left(x \right) \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)+3 \cos \left(x \right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}}\right)-3 \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)-3 \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}}\right)\right) \sin \left(x \right)}{64 \left(-\frac{-1+\cos^{2}\left(x \right)}{\cos \left(x \right)}\right)^{\frac{5}{2}} \cos \left(x \right)^{2} \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}}"," ",0,"1/64*(24*cos(x)^3*(-cos(x)/(1+cos(x))^2)^(3/2)+40*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(3/2)-12*cos(x)^3*(-cos(x)/(1+cos(x))^2)^(1/2)-3*cos(x)^3*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)-3*cos(x)^3*arctan(1/2/(-cos(x)/(1+cos(x))^2)^(1/2))+8*cos(x)*(-cos(x)/(1+cos(x))^2)^(3/2)+24*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)+3*cos(x)^2*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)+3*cos(x)^2*arctan(1/2/(-cos(x)/(1+cos(x))^2)^(1/2))-8*(-cos(x)/(1+cos(x))^2)^(3/2)-12*cos(x)*(-cos(x)/(1+cos(x))^2)^(1/2)+3*cos(x)*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)+3*cos(x)*arctan(1/2/(-cos(x)/(1+cos(x))^2)^(1/2))-3*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)-3*arctan(1/2/(-cos(x)/(1+cos(x))^2)^(1/2)))*sin(x)/(-(-1+cos(x)^2)/cos(x))^(5/2)/cos(x)^2/(-cos(x)/(1+cos(x))^2)^(1/2)","B"
340,1,494,82,0.358000," ","int(1/(-cos(x)+sec(x))^(7/2),x)","\frac{\left(56 \left(\cos^{4}\left(x \right)\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}-16 \left(\cos^{3}\left(x \right)\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}-15 \left(\cos^{4}\left(x \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)+15 \left(\cos^{4}\left(x \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}}\right)-192 \left(\cos^{2}\left(x \right)\right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}+76 \left(\cos^{3}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}+30 \left(\cos^{3}\left(x \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)-30 \left(\cos^{3}\left(x \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}}\right)+16 \cos \left(x \right) \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}-148 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}+136 \left(-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}}+196 \cos \left(x \right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-30 \cos \left(x \right) \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)+30 \cos \left(x \right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}}\right)-60 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}+15 \ln \left(-\frac{2 \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-\left(\cos^{2}\left(x \right)\right)+2 \cos \left(x \right)-2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}-1}{\sin \left(x \right)^{2}}\right)-15 \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}}\right)\right) \left(\sin^{3}\left(x \right)\right)}{768 \left(-1+\cos \left(x \right)\right) \left(-\frac{-1+\cos^{2}\left(x \right)}{\cos \left(x \right)}\right)^{\frac{7}{2}} \cos \left(x \right)^{3} \sqrt{-\frac{\cos \left(x \right)}{\left(1+\cos \left(x \right)\right)^{2}}}}"," ",0,"1/768*(56*cos(x)^4*(-cos(x)/(1+cos(x))^2)^(3/2)-16*cos(x)^3*(-cos(x)/(1+cos(x))^2)^(3/2)-15*cos(x)^4*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)+15*cos(x)^4*arctan(1/2/(-cos(x)/(1+cos(x))^2)^(1/2))-192*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(3/2)+76*cos(x)^3*(-cos(x)/(1+cos(x))^2)^(1/2)+30*cos(x)^3*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)-30*cos(x)^3*arctan(1/2/(-cos(x)/(1+cos(x))^2)^(1/2))+16*cos(x)*(-cos(x)/(1+cos(x))^2)^(3/2)-148*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)+136*(-cos(x)/(1+cos(x))^2)^(3/2)+196*cos(x)*(-cos(x)/(1+cos(x))^2)^(1/2)-30*cos(x)*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)+30*cos(x)*arctan(1/2/(-cos(x)/(1+cos(x))^2)^(1/2))-60*(-cos(x)/(1+cos(x))^2)^(1/2)+15*ln(-(2*cos(x)^2*(-cos(x)/(1+cos(x))^2)^(1/2)-cos(x)^2+2*cos(x)-2*(-cos(x)/(1+cos(x))^2)^(1/2)-1)/sin(x)^2)-15*arctan(1/2/(-cos(x)/(1+cos(x))^2)^(1/2)))*sin(x)^3/(-1+cos(x))/(-(-1+cos(x)^2)/cos(x))^(7/2)/cos(x)^3/(-cos(x)/(1+cos(x))^2)^(1/2)","B"
341,1,66,45,0.066000," ","int((sin(x)+tan(x))^4,x)","\frac{23 \left(\sin^{3}\left(x \right)+\frac{3 \sin \left(x \right)}{2}\right) \cos \left(x \right)}{4}-\frac{61 x}{8}+\frac{2 \left(\sin^{3}\left(x \right)\right)}{3}+2 \sin \left(x \right)-2 \ln \left(\sec \left(x \right)+\tan \left(x \right)\right)+\frac{6 \left(\sin^{5}\left(x \right)\right)}{\cos \left(x \right)}+\frac{2 \left(\sin^{5}\left(x \right)\right)}{\cos \left(x \right)^{2}}+\frac{\left(\tan^{3}\left(x \right)\right)}{3}-\tan \left(x \right)"," ",0,"23/4*(sin(x)^3+3/2*sin(x))*cos(x)-61/8*x+2/3*sin(x)^3+2*sin(x)-2*ln(sec(x)+tan(x))+6*sin(x)^5/cos(x)+2*sin(x)^5/cos(x)^2+1/3*tan(x)^3-tan(x)","A"
342,1,39,32,0.069000," ","int((sin(x)+tan(x))^3,x)","\frac{8 \left(2+\sin^{2}\left(x \right)\right) \cos \left(x \right)}{3}-\frac{3 \left(\sin^{2}\left(x \right)\right)}{2}-2 \ln \left(\cos \left(x \right)\right)+\frac{3 \left(\sin^{4}\left(x \right)\right)}{\cos \left(x \right)}+\frac{\left(\tan^{2}\left(x \right)\right)}{2}"," ",0,"8/3*(2+sin(x)^2)*cos(x)-3/2*sin(x)^2-2*ln(cos(x))+3*sin(x)^4/cos(x)+1/2*tan(x)^2","A"
343,1,25,21,0.046000," ","int((sin(x)+tan(x))^2,x)","-\frac{\cos \left(x \right) \sin \left(x \right)}{2}-\frac{x}{2}-2 \sin \left(x \right)+2 \ln \left(\sec \left(x \right)+\tan \left(x \right)\right)+\tan \left(x \right)"," ",0,"-1/2*cos(x)*sin(x)-1/2*x-2*sin(x)+2*ln(sec(x)+tan(x))+tan(x)","A"
344,1,11,10,0.003000," ","int(sin(x)+tan(x),x)","-\cos \left(x \right)-\ln \left(\cos \left(x \right)\right)"," ",0,"-cos(x)-ln(cos(x))","A"
345,1,24,18,0.106000," ","int(1/(sin(x)+tan(x)),x)","\frac{\ln \left(-1+\cos \left(x \right)\right)}{4}-\frac{1}{2 \left(1+\cos \left(x \right)\right)}-\frac{\ln \left(1+\cos \left(x \right)\right)}{4}"," ",0,"1/4*ln(-1+cos(x))-1/2/(1+cos(x))-1/4*ln(1+cos(x))","A"
346,1,32,25,0.115000," ","int(1/(sin(x)+tan(x))^2,x)","\frac{\left(\tan^{5}\left(\frac{x}{2}\right)\right)}{40}-\frac{\left(\tan^{3}\left(\frac{x}{2}\right)\right)}{24}-\frac{\tan \left(\frac{x}{2}\right)}{8}-\frac{1}{8 \tan \left(\frac{x}{2}\right)}"," ",0,"1/40*tan(1/2*x)^5-1/24*tan(1/2*x)^3-1/8*tan(1/2*x)-1/8/tan(1/2*x)","A"
347,1,56,48,0.126000," ","int(1/(sin(x)+tan(x))^3,x)","\frac{1}{-32+32 \cos \left(x \right)}-\frac{\ln \left(-1+\cos \left(x \right)\right)}{64}-\frac{1}{16 \left(1+\cos \left(x \right)\right)^{4}}+\frac{1}{6 \left(1+\cos \left(x \right)\right)^{3}}-\frac{3}{32 \left(1+\cos \left(x \right)\right)^{2}}-\frac{1}{16 \left(1+\cos \left(x \right)\right)}+\frac{\ln \left(1+\cos \left(x \right)\right)}{64}"," ",0,"1/32/(-1+cos(x))-1/64*ln(-1+cos(x))-1/16/(1+cos(x))^4+1/6/(1+cos(x))^3-3/32/(1+cos(x))^2-1/16/(1+cos(x))+1/64*ln(1+cos(x))","A"
348,1,64,49,0.127000," ","int(1/(sin(x)+tan(x))^4,x)","\frac{\left(\tan^{11}\left(\frac{x}{2}\right)\right)}{1408}-\frac{\left(\tan^{9}\left(\frac{x}{2}\right)\right)}{1152}-\frac{3 \left(\tan^{7}\left(\frac{x}{2}\right)\right)}{896}+\frac{3 \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{640}+\frac{\left(\tan^{3}\left(\frac{x}{2}\right)\right)}{128}-\frac{3 \tan \left(\frac{x}{2}\right)}{128}+\frac{1}{128 \tan \left(\frac{x}{2}\right)}-\frac{1}{384 \tan \left(\frac{x}{2}\right)^{3}}"," ",0,"1/1408*tan(1/2*x)^11-1/1152*tan(1/2*x)^9-3/896*tan(1/2*x)^7+3/640*tan(1/2*x)^5+1/128*tan(1/2*x)^3-3/128*tan(1/2*x)+1/128/tan(1/2*x)-1/384/tan(1/2*x)^3","A"
349,1,150,70,0.144000," ","int((A+C*sin(x))/(b*cos(x)+c*sin(x)),x)","-\frac{b C \ln \left(b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 c \tan \left(\frac{x}{2}\right)-b \right)}{b^{2}+c^{2}}+\frac{2 \arctanh \left(\frac{2 b \tan \left(\frac{x}{2}\right)-2 c}{2 \sqrt{b^{2}+c^{2}}}\right) A \,b^{2}}{\left(b^{2}+c^{2}\right)^{\frac{3}{2}}}+\frac{2 \arctanh \left(\frac{2 b \tan \left(\frac{x}{2}\right)-2 c}{2 \sqrt{b^{2}+c^{2}}}\right) A \,c^{2}}{\left(b^{2}+c^{2}\right)^{\frac{3}{2}}}+\frac{C b \ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}+\frac{2 C c \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}"," ",0,"-1/(b^2+c^2)*b*C*ln(b*tan(1/2*x)^2-2*c*tan(1/2*x)-b)+2/(b^2+c^2)^(3/2)*arctanh(1/2*(2*b*tan(1/2*x)-2*c)/(b^2+c^2)^(1/2))*A*b^2+2/(b^2+c^2)^(3/2)*arctanh(1/2*(2*b*tan(1/2*x)-2*c)/(b^2+c^2)^(1/2))*A*c^2+C/(b^2+c^2)*b*ln(1+tan(1/2*x)^2)+2*C/(b^2+c^2)*c*arctan(tan(1/2*x))","B"
350,1,108,71,0.168000," ","int((A+C*sin(x))/(b*cos(x)+c*sin(x))^2,x)","\frac{-\frac{2 \left(A \,b^{2}+A \,c^{2}+C b c \right) \tan \left(\frac{x}{2}\right)}{b \left(b^{2}+c^{2}\right)}-\frac{2 C b}{b^{2}+c^{2}}}{b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 c \tan \left(\frac{x}{2}\right)-b}+\frac{2 C c \arctanh \left(\frac{2 b \tan \left(\frac{x}{2}\right)-2 c}{2 \sqrt{b^{2}+c^{2}}}\right)}{\left(b^{2}+c^{2}\right)^{\frac{3}{2}}}"," ",0,"2*(-(A*b^2+A*c^2+C*b*c)/b/(b^2+c^2)*tan(1/2*x)-C*b/(b^2+c^2))/(b*tan(1/2*x)^2-2*c*tan(1/2*x)-b)+2*C*c/(b^2+c^2)^(3/2)*arctanh(1/2*(2*b*tan(1/2*x)-2*c)/(b^2+c^2)^(1/2))","A"
351,1,177,107,0.193000," ","int((A+C*sin(x))/(b*cos(x)+c*sin(x))^3,x)","-\frac{2 \left(-\frac{A \left(b^{2}+2 c^{2}\right) \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{2 \left(b^{2}+c^{2}\right) b}-\frac{\left(A \,b^{2} c -2 A \,c^{3}+2 C \,b^{3}+2 C b \,c^{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{2 \left(b^{2}+c^{2}\right) b^{2}}-\frac{A \left(b^{2}-2 c^{2}\right) \tan \left(\frac{x}{2}\right)}{2 \left(b^{2}+c^{2}\right) b}+\frac{A c}{2 b^{2}+2 c^{2}}\right)}{\left(b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 c \tan \left(\frac{x}{2}\right)-b \right)^{2}}+\frac{A \arctanh \left(\frac{2 b \tan \left(\frac{x}{2}\right)-2 c}{2 \sqrt{b^{2}+c^{2}}}\right)}{\left(b^{2}+c^{2}\right)^{\frac{3}{2}}}"," ",0,"-2*(-1/2*A*(b^2+2*c^2)/(b^2+c^2)/b*tan(1/2*x)^3-1/2*(A*b^2*c-2*A*c^3+2*C*b^3+2*C*b*c^2)/(b^2+c^2)/b^2*tan(1/2*x)^2-1/2*A*(b^2-2*c^2)/(b^2+c^2)/b*tan(1/2*x)+1/2*A*c/(b^2+c^2))/(b*tan(1/2*x)^2-2*c*tan(1/2*x)-b)^2+A/(b^2+c^2)^(3/2)*arctanh(1/2*(2*b*tan(1/2*x)-2*c)/(b^2+c^2)^(1/2))","A"
352,1,150,69,0.131000," ","int((A+B*cos(x))/(b*cos(x)+c*sin(x)),x)","\frac{B c \ln \left(b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 c \tan \left(\frac{x}{2}\right)-b \right)}{b^{2}+c^{2}}+\frac{2 \arctanh \left(\frac{2 b \tan \left(\frac{x}{2}\right)-2 c}{2 \sqrt{b^{2}+c^{2}}}\right) A \,b^{2}}{\left(b^{2}+c^{2}\right)^{\frac{3}{2}}}+\frac{2 \arctanh \left(\frac{2 b \tan \left(\frac{x}{2}\right)-2 c}{2 \sqrt{b^{2}+c^{2}}}\right) A \,c^{2}}{\left(b^{2}+c^{2}\right)^{\frac{3}{2}}}-\frac{B c \ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}+\frac{2 B b \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}"," ",0,"1/(b^2+c^2)*B*c*ln(b*tan(1/2*x)^2-2*c*tan(1/2*x)-b)+2/(b^2+c^2)^(3/2)*arctanh(1/2*(2*b*tan(1/2*x)-2*c)/(b^2+c^2)^(1/2))*A*b^2+2/(b^2+c^2)^(3/2)*arctanh(1/2*(2*b*tan(1/2*x)-2*c)/(b^2+c^2)^(1/2))*A*c^2-B/(b^2+c^2)*c*ln(1+tan(1/2*x)^2)+2*B/(b^2+c^2)*b*arctan(tan(1/2*x))","B"
353,1,109,72,0.158000," ","int((A+B*cos(x))/(b*cos(x)+c*sin(x))^2,x)","\frac{-\frac{2 \left(A \,b^{2}+A \,c^{2}-B \,c^{2}\right) \tan \left(\frac{x}{2}\right)}{b \left(b^{2}+c^{2}\right)}+\frac{2 B c}{b^{2}+c^{2}}}{b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 c \tan \left(\frac{x}{2}\right)-b}+\frac{2 b B \arctanh \left(\frac{2 b \tan \left(\frac{x}{2}\right)-2 c}{2 \sqrt{b^{2}+c^{2}}}\right)}{\left(b^{2}+c^{2}\right)^{\frac{3}{2}}}"," ",0,"2*(-(A*b^2+A*c^2-B*c^2)/b/(b^2+c^2)*tan(1/2*x)+B*c/(b^2+c^2))/(b*tan(1/2*x)^2-2*c*tan(1/2*x)-b)+2*b*B/(b^2+c^2)^(3/2)*arctanh(1/2*(2*b*tan(1/2*x)-2*c)/(b^2+c^2)^(1/2))","A"
354,1,204,108,0.181000," ","int((A+B*cos(x))/(b*cos(x)+c*sin(x))^3,x)","-\frac{2 \left(-\frac{\left(A \,b^{2}+2 A \,c^{2}-2 B \,b^{2}-2 B \,c^{2}\right) \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{2 \left(b^{2}+c^{2}\right) b}-\frac{c \left(A \,b^{2}-2 A \,c^{2}+2 B \,b^{2}+2 B \,c^{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{2 \left(b^{2}+c^{2}\right) b^{2}}-\frac{\left(A \,b^{2}-2 A \,c^{2}+2 B \,b^{2}+2 B \,c^{2}\right) \tan \left(\frac{x}{2}\right)}{2 \left(b^{2}+c^{2}\right) b}+\frac{A c}{2 b^{2}+2 c^{2}}\right)}{\left(b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 c \tan \left(\frac{x}{2}\right)-b \right)^{2}}+\frac{A \arctanh \left(\frac{2 b \tan \left(\frac{x}{2}\right)-2 c}{2 \sqrt{b^{2}+c^{2}}}\right)}{\left(b^{2}+c^{2}\right)^{\frac{3}{2}}}"," ",0,"-2*(-1/2*(A*b^2+2*A*c^2-2*B*b^2-2*B*c^2)/(b^2+c^2)/b*tan(1/2*x)^3-1/2*c*(A*b^2-2*A*c^2+2*B*b^2+2*B*c^2)/(b^2+c^2)/b^2*tan(1/2*x)^2-1/2*(A*b^2-2*A*c^2+2*B*b^2+2*B*c^2)/(b^2+c^2)/b*tan(1/2*x)+1/2*A*c/(b^2+c^2))/(b*tan(1/2*x)^2-2*c*tan(1/2*x)-b)^2+A/(b^2+c^2)^(3/2)*arctanh(1/2*(2*b*tan(1/2*x)-2*c)/(b^2+c^2)^(1/2))","A"
355,1,514,222,0.302000," ","int((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^4,x)","\frac{b^{4} \left(e x +d \right)+2 b^{2} c^{2} \left(e x +d \right)+c^{4} \left(e x +d \right)+b^{4} \left(\frac{\left(\cos^{3}\left(e x +d \right)+\frac{3 \cos \left(e x +d \right)}{2}\right) \sin \left(e x +d \right)}{4}+\frac{3 e x}{8}+\frac{3 d}{8}\right)+6 b^{4} \left(\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)+c^{4} \left(-\frac{\left(\sin^{3}\left(e x +d \right)+\frac{3 \sin \left(e x +d \right)}{2}\right) \cos \left(e x +d \right)}{4}+\frac{3 e x}{8}+\frac{3 d}{8}\right)+6 c^{4} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)-4 \sqrt{b^{2}+c^{2}}\, b^{2} c \left(\cos^{3}\left(e x +d \right)\right)+4 \sqrt{b^{2}+c^{2}}\, b \,c^{2} \left(\sin^{3}\left(e x +d \right)\right)+\frac{4 \sqrt{b^{2}+c^{2}}\, b^{3} \left(2+\cos^{2}\left(e x +d \right)\right) \sin \left(e x +d \right)}{3}+6 b^{2} c^{2} \left(\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)+4 \sqrt{b^{2}+c^{2}}\, b^{3} \sin \left(e x +d \right)-\frac{4 \sqrt{b^{2}+c^{2}}\, c^{3} \left(2+\sin^{2}\left(e x +d \right)\right) \cos \left(e x +d \right)}{3}+6 b^{2} c^{2} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)-4 \sqrt{b^{2}+c^{2}}\, c^{3} \cos \left(e x +d \right)-\left(\cos^{4}\left(e x +d \right)\right) b^{3} c +6 b^{2} c^{2} \left(-\frac{\sin \left(e x +d \right) \left(\cos^{3}\left(e x +d \right)\right)}{4}+\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{8}+\frac{e x}{8}+\frac{d}{8}\right)+c^{3} b \left(\sin^{4}\left(e x +d \right)\right)-6 \left(\cos^{2}\left(e x +d \right)\right) b^{3} c -6 \left(\cos^{2}\left(e x +d \right)\right) b \,c^{3}+4 \sqrt{b^{2}+c^{2}}\, b \,c^{2} \sin \left(e x +d \right)-4 \sqrt{b^{2}+c^{2}}\, b^{2} c \cos \left(e x +d \right)}{e}"," ",0,"1/e*(b^4*(e*x+d)+2*b^2*c^2*(e*x+d)+c^4*(e*x+d)+b^4*(1/4*(cos(e*x+d)^3+3/2*cos(e*x+d))*sin(e*x+d)+3/8*e*x+3/8*d)+6*b^4*(1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)+c^4*(-1/4*(sin(e*x+d)^3+3/2*sin(e*x+d))*cos(e*x+d)+3/8*e*x+3/8*d)+6*c^4*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)-4*(b^2+c^2)^(1/2)*b^2*c*cos(e*x+d)^3+4*(b^2+c^2)^(1/2)*b*c^2*sin(e*x+d)^3+4/3*(b^2+c^2)^(1/2)*b^3*(2+cos(e*x+d)^2)*sin(e*x+d)+6*b^2*c^2*(1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)+4*(b^2+c^2)^(1/2)*b^3*sin(e*x+d)-4/3*(b^2+c^2)^(1/2)*c^3*(2+sin(e*x+d)^2)*cos(e*x+d)+6*b^2*c^2*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)-4*(b^2+c^2)^(1/2)*c^3*cos(e*x+d)-cos(e*x+d)^4*b^3*c+6*b^2*c^2*(-1/4*sin(e*x+d)*cos(e*x+d)^3+1/8*sin(e*x+d)*cos(e*x+d)+1/8*e*x+1/8*d)+c^3*b*sin(e*x+d)^4-6*cos(e*x+d)^2*b^3*c-6*cos(e*x+d)^2*b*c^3+4*(b^2+c^2)^(1/2)*b*c^2*sin(e*x+d)-4*(b^2+c^2)^(1/2)*b^2*c*cos(e*x+d))","B"
356,1,250,160,0.251000," ","int((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^3,x)","\frac{\frac{b^{3} \left(2+\cos^{2}\left(e x +d \right)\right) \sin \left(e x +d \right)}{3}-\left(\cos^{3}\left(e x +d \right)\right) b^{2} c +3 \sqrt{b^{2}+c^{2}}\, b^{2} \left(\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)+c^{2} b \left(\sin^{3}\left(e x +d \right)\right)-3 \sqrt{b^{2}+c^{2}}\, b c \left(\cos^{2}\left(e x +d \right)\right)+3 \sin \left(e x +d \right) b^{3}+3 c^{2} b \sin \left(e x +d \right)-\frac{c^{3} \left(2+\sin^{2}\left(e x +d \right)\right) \cos \left(e x +d \right)}{3}+3 \sqrt{b^{2}+c^{2}}\, c^{2} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)-3 \cos \left(e x +d \right) b^{2} c -3 \cos \left(e x +d \right) c^{3}+\sqrt{b^{2}+c^{2}}\, b^{2} \left(e x +d \right)+\sqrt{b^{2}+c^{2}}\, c^{2} \left(e x +d \right)}{e}"," ",0,"1/e*(1/3*b^3*(2+cos(e*x+d)^2)*sin(e*x+d)-cos(e*x+d)^3*b^2*c+3*(b^2+c^2)^(1/2)*b^2*(1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)+c^2*b*sin(e*x+d)^3-3*(b^2+c^2)^(1/2)*b*c*cos(e*x+d)^2+3*sin(e*x+d)*b^3+3*c^2*b*sin(e*x+d)-1/3*c^3*(2+sin(e*x+d)^2)*cos(e*x+d)+3*(b^2+c^2)^(1/2)*c^2*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)-3*cos(e*x+d)*b^2*c-3*cos(e*x+d)*c^3+(b^2+c^2)^(1/2)*b^2*(e*x+d)+(b^2+c^2)^(1/2)*c^2*(e*x+d))","A"
357,1,124,102,0.220000," ","int((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^2,x)","\frac{b^{2} \left(\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)-\left(\cos^{2}\left(e x +d \right)\right) b c +c^{2} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)+2 \sqrt{b^{2}+c^{2}}\, b \sin \left(e x +d \right)-2 \sqrt{b^{2}+c^{2}}\, c \cos \left(e x +d \right)+b^{2} \left(e x +d \right)+c^{2} \left(e x +d \right)}{e}"," ",0,"1/e*(b^2*(1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)-cos(e*x+d)^2*b*c+c^2*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)+2*(b^2+c^2)^(1/2)*b*sin(e*x+d)-2*(b^2+c^2)^(1/2)*c*cos(e*x+d)+b^2*(e*x+d)+c^2*(e*x+d))","A"
358,1,36,35,0.039000," ","int(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2),x)","-\frac{c \cos \left(e x +d \right)}{e}+\frac{b \sin \left(e x +d \right)}{e}+x \sqrt{b^{2}+c^{2}}"," ",0,"-c*cos(e*x+d)/e+b*sin(e*x+d)/e+x*(b^2+c^2)^(1/2)","A"
359,1,50,47,0.289000," ","int(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2)),x)","-\frac{2 \left(\sqrt{b^{2}+c^{2}}+b \right)}{e \,c^{2} \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)+\frac{\sqrt{b^{2}+c^{2}}}{c}+\frac{b}{c}\right)}"," ",0,"-2/e*((b^2+c^2)^(1/2)+b)/c^2/(tan(1/2*d+1/2*e*x)+1/c*(b^2+c^2)^(1/2)+b/c)","A"
360,1,233,118,0.395000," ","int(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^2,x)","\frac{2 \left(\sqrt{b^{2}+c^{2}}+b \right) \left(-\frac{\left(\sqrt{b^{2}+c^{2}}+b \right) \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{c^{2}}-\frac{\left(2 b^{2}+c^{2}+2 \sqrt{b^{2}+c^{2}}\, b \right) \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{c^{3}}-\frac{2 \left(2 \sqrt{b^{2}+c^{2}}\, b^{2}+\sqrt{b^{2}+c^{2}}\, c^{2}+2 b^{3}+2 c^{2} b \right)}{3 c^{4}}\right)}{e \,c^{2} \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)+\frac{2 \sqrt{b^{2}+c^{2}}\, \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{c}+\frac{2 b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{c}+\frac{2 \sqrt{b^{2}+c^{2}}\, b}{c^{2}}+\frac{2 b^{2}}{c^{2}}+1\right) \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)+\frac{\sqrt{b^{2}+c^{2}}}{c}+\frac{b}{c}\right)}"," ",0,"2/e*((b^2+c^2)^(1/2)+b)/c^2*(-((b^2+c^2)^(1/2)+b)/c^2*tan(1/2*d+1/2*e*x)^2-1/c^3*(2*b^2+c^2+2*(b^2+c^2)^(1/2)*b)*tan(1/2*d+1/2*e*x)-2/3*(2*(b^2+c^2)^(1/2)*b^2+(b^2+c^2)^(1/2)*c^2+2*b^3+2*c^2*b)/c^4)/(tan(1/2*d+1/2*e*x)^2+2/c*(b^2+c^2)^(1/2)*tan(1/2*d+1/2*e*x)+2*b/c*tan(1/2*d+1/2*e*x)+2/c^2*(b^2+c^2)^(1/2)*b+2/c^2*b^2+1)/(tan(1/2*d+1/2*e*x)+1/c*(b^2+c^2)^(1/2)+b/c)","A"
361,1,496,177,0.522000," ","int(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^3,x)","\frac{-\frac{2 \left(4 \sqrt{b^{2}+c^{2}}\, b^{2}+\sqrt{b^{2}+c^{2}}\, c^{2}+4 b^{3}+3 c^{2} b \right) \left(\tan^{4}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{c^{2}}-\frac{4 \left(8 b^{4}+8 b^{2} c^{2}+c^{4}+8 \sqrt{b^{2}+c^{2}}\, b^{3}+4 \sqrt{b^{2}+c^{2}}\, b \,c^{2}\right) \left(\tan^{3}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{c^{3}}-\frac{8 \left(24 \sqrt{b^{2}+c^{2}}\, b^{4}+20 \sqrt{b^{2}+c^{2}}\, b^{2} c^{2}+2 \sqrt{b^{2}+c^{2}}\, c^{4}+24 b^{5}+32 b^{3} c^{2}+9 c^{4} b \right) \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{3 c^{4}}-\frac{4 \left(48 b^{6}+76 b^{4} c^{2}+31 b^{2} c^{4}+2 c^{6}+48 \sqrt{b^{2}+c^{2}}\, b^{5}+52 \sqrt{b^{2}+c^{2}}\, b^{3} c^{2}+11 \sqrt{b^{2}+c^{2}}\, b \,c^{4}\right) \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{3 c^{5}}-\frac{2 \left(192 \sqrt{b^{2}+c^{2}}\, b^{6}+256 \sqrt{b^{2}+c^{2}}\, b^{4} c^{2}+96 \sqrt{b^{2}+c^{2}}\, b^{2} c^{4}+7 \sqrt{b^{2}+c^{2}}\, c^{6}+192 b^{7}+352 b^{5} c^{2}+200 b^{3} c^{4}+35 c^{6} b \right)}{15 c^{6}}}{e \,c^{4} \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)+\frac{2 \sqrt{b^{2}+c^{2}}\, \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{c}+\frac{2 b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{c}+\frac{2 \sqrt{b^{2}+c^{2}}\, b}{c^{2}}+\frac{2 b^{2}}{c^{2}}+1\right)^{2} \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)+\frac{\sqrt{b^{2}+c^{2}}}{c}+\frac{b}{c}\right)}"," ",0,"2/e/c^4*(-(4*(b^2+c^2)^(1/2)*b^2+(b^2+c^2)^(1/2)*c^2+4*b^3+3*c^2*b)/c^2*tan(1/2*d+1/2*e*x)^4-2*(8*b^4+8*b^2*c^2+c^4+8*(b^2+c^2)^(1/2)*b^3+4*(b^2+c^2)^(1/2)*b*c^2)/c^3*tan(1/2*d+1/2*e*x)^3-4/3*(24*(b^2+c^2)^(1/2)*b^4+20*(b^2+c^2)^(1/2)*b^2*c^2+2*(b^2+c^2)^(1/2)*c^4+24*b^5+32*b^3*c^2+9*c^4*b)/c^4*tan(1/2*d+1/2*e*x)^2-2/3*(48*b^6+76*b^4*c^2+31*b^2*c^4+2*c^6+48*(b^2+c^2)^(1/2)*b^5+52*(b^2+c^2)^(1/2)*b^3*c^2+11*(b^2+c^2)^(1/2)*b*c^4)/c^5*tan(1/2*d+1/2*e*x)-1/15/c^6*(192*(b^2+c^2)^(1/2)*b^6+256*(b^2+c^2)^(1/2)*b^4*c^2+96*(b^2+c^2)^(1/2)*b^2*c^4+7*(b^2+c^2)^(1/2)*c^6+192*b^7+352*b^5*c^2+200*b^3*c^4+35*c^6*b))/(tan(1/2*d+1/2*e*x)^2+2/c*(b^2+c^2)^(1/2)*tan(1/2*d+1/2*e*x)+2*b/c*tan(1/2*d+1/2*e*x)+2/c^2*(b^2+c^2)^(1/2)*b+2/c^2*b^2+1)^2/(tan(1/2*d+1/2*e*x)+1/c*(b^2+c^2)^(1/2)+b/c)","B"
362,1,823,237,0.710000," ","int(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^4,x)","-\frac{2 \left(\frac{\left(8 b^{4}+8 b^{2} c^{2}+c^{4}+8 \sqrt{b^{2}+c^{2}}\, b^{3}+4 \sqrt{b^{2}+c^{2}}\, b \,c^{2}\right) \left(\tan^{6}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{c^{2}}+\frac{3 \left(16 \sqrt{b^{2}+c^{2}}\, b^{4}+12 \sqrt{b^{2}+c^{2}}\, b^{2} c^{2}+\sqrt{b^{2}+c^{2}}\, c^{4}+16 b^{5}+20 b^{3} c^{2}+5 c^{4} b \right) \left(\tan^{5}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{c^{3}}+\frac{2 \left(80 \sqrt{b^{2}+c^{2}}\, b^{5}+84 \sqrt{b^{2}+c^{2}}\, b^{3} c^{2}+17 \sqrt{b^{2}+c^{2}}\, b \,c^{4}+80 b^{6}+124 b^{4} c^{2}+49 b^{2} c^{4}+3 c^{6}\right) \left(\tan^{4}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{c^{4}}+\frac{2 \left(160 b^{7}+288 b^{5} c^{2}+150 b^{3} c^{4}+20 c^{6} b +160 \sqrt{b^{2}+c^{2}}\, b^{6}+208 \sqrt{b^{2}+c^{2}}\, b^{4} c^{2}+66 \sqrt{b^{2}+c^{2}}\, b^{2} c^{4}+3 \sqrt{b^{2}+c^{2}}\, c^{6}\right) \left(\tan^{3}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{c^{5}}+\frac{3 \left(640 b^{7} \sqrt{b^{2}+c^{2}}+992 \sqrt{b^{2}+c^{2}}\, b^{5} c^{2}+440 \sqrt{b^{2}+c^{2}}\, b^{3} c^{4}+50 \sqrt{b^{2}+c^{2}}\, b \,c^{6}+640 b^{8}+1312 b^{6} c^{2}+856 b^{4} c^{4}+186 b^{2} c^{6}+7 c^{8}\right) \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{5 c^{6}}+\frac{\left(1280 b^{9}+2944 b^{7} c^{2}+2288 b^{5} c^{4}+676 b^{3} c^{6}+57 b \,c^{8}+1280 \sqrt{b^{2}+c^{2}}\, b^{8}+2304 \sqrt{b^{2}+c^{2}}\, b^{6} c^{2}+1296 \sqrt{b^{2}+c^{2}}\, b^{4} c^{4}+236 \sqrt{b^{2}+c^{2}}\, b^{2} c^{6}+7 \sqrt{b^{2}+c^{2}}\, c^{8}\right) \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{5 c^{7}}+\frac{\frac{512 \sqrt{b^{2}+c^{2}}\, b^{9}}{7}+\frac{5248 \sqrt{b^{2}+c^{2}}\, b^{7} c^{2}}{35}+\frac{512 \sqrt{b^{2}+c^{2}}\, b^{5} c^{4}}{5}+\frac{136 \sqrt{b^{2}+c^{2}}\, b^{3} c^{6}}{5}+\frac{12 \sqrt{b^{2}+c^{2}}\, b \,c^{8}}{5}+\frac{512 b^{10}}{7}+\frac{6528 b^{8} c^{2}}{35}+\frac{5888 b^{6} c^{4}}{35}+\frac{2248 b^{4} c^{6}}{35}+\frac{68 b^{2} c^{8}}{7}+\frac{12 c^{10}}{35}}{c^{8}}\right)}{e \,c^{6} \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)+\frac{2 \sqrt{b^{2}+c^{2}}\, \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{c}+\frac{2 b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{c}+\frac{2 \sqrt{b^{2}+c^{2}}\, b}{c^{2}}+\frac{2 b^{2}}{c^{2}}+1\right)^{3} \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)+\frac{\sqrt{b^{2}+c^{2}}}{c}+\frac{b}{c}\right)}"," ",0,"-2/e/c^6*((8*b^4+8*b^2*c^2+c^4+8*(b^2+c^2)^(1/2)*b^3+4*(b^2+c^2)^(1/2)*b*c^2)/c^2*tan(1/2*d+1/2*e*x)^6+3*(16*(b^2+c^2)^(1/2)*b^4+12*(b^2+c^2)^(1/2)*b^2*c^2+(b^2+c^2)^(1/2)*c^4+16*b^5+20*b^3*c^2+5*c^4*b)/c^3*tan(1/2*d+1/2*e*x)^5+2*(80*(b^2+c^2)^(1/2)*b^5+84*(b^2+c^2)^(1/2)*b^3*c^2+17*(b^2+c^2)^(1/2)*b*c^4+80*b^6+124*b^4*c^2+49*b^2*c^4+3*c^6)/c^4*tan(1/2*d+1/2*e*x)^4+2*(160*b^7+288*b^5*c^2+150*b^3*c^4+20*c^6*b+160*(b^2+c^2)^(1/2)*b^6+208*(b^2+c^2)^(1/2)*b^4*c^2+66*(b^2+c^2)^(1/2)*b^2*c^4+3*(b^2+c^2)^(1/2)*c^6)/c^5*tan(1/2*d+1/2*e*x)^3+3/5*(640*b^7*(b^2+c^2)^(1/2)+992*(b^2+c^2)^(1/2)*b^5*c^2+440*(b^2+c^2)^(1/2)*b^3*c^4+50*(b^2+c^2)^(1/2)*b*c^6+640*b^8+1312*b^6*c^2+856*b^4*c^4+186*b^2*c^6+7*c^8)/c^6*tan(1/2*d+1/2*e*x)^2+1/5*(1280*b^9+2944*b^7*c^2+2288*b^5*c^4+676*b^3*c^6+57*b*c^8+1280*(b^2+c^2)^(1/2)*b^8+2304*(b^2+c^2)^(1/2)*b^6*c^2+1296*(b^2+c^2)^(1/2)*b^4*c^4+236*(b^2+c^2)^(1/2)*b^2*c^6+7*(b^2+c^2)^(1/2)*c^8)/c^7*tan(1/2*d+1/2*e*x)+4/35*(640*(b^2+c^2)^(1/2)*b^9+1312*(b^2+c^2)^(1/2)*b^7*c^2+896*(b^2+c^2)^(1/2)*b^5*c^4+238*(b^2+c^2)^(1/2)*b^3*c^6+21*(b^2+c^2)^(1/2)*b*c^8+640*b^10+1632*b^8*c^2+1472*b^6*c^4+562*b^4*c^6+85*b^2*c^8+3*c^10)/c^8)/(tan(1/2*d+1/2*e*x)^2+2/c*(b^2+c^2)^(1/2)*tan(1/2*d+1/2*e*x)+2*b/c*tan(1/2*d+1/2*e*x)+2/c^2*(b^2+c^2)^(1/2)*b+2/c^2*b^2+1)^3/(tan(1/2*d+1/2*e*x)+1/c*(b^2+c^2)^(1/2)+b/c)","B"
363,1,177,149,0.256000," ","int((2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^3,x)","\frac{8 a^{3} \left(e x +d \right)+24 a^{3} \sin \left(e x +d \right)-24 a^{2} c \cos \left(e x +d \right)+24 a^{3} \left(\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)-24 a^{2} c \left(\cos^{2}\left(e x +d \right)\right)+24 a \,c^{2} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)+\frac{8 a^{3} \left(2+\cos^{2}\left(e x +d \right)\right) \sin \left(e x +d \right)}{3}-8 a^{2} c \left(\cos^{3}\left(e x +d \right)\right)+8 a \,c^{2} \left(\sin^{3}\left(e x +d \right)\right)-\frac{8 c^{3} \left(2+\sin^{2}\left(e x +d \right)\right) \cos \left(e x +d \right)}{3}}{e}"," ",0,"8/e*(a^3*(e*x+d)+3*a^3*sin(e*x+d)-3*a^2*c*cos(e*x+d)+3*a^3*(1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)-3*a^2*c*cos(e*x+d)^2+3*a*c^2*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)+1/3*a^3*(2+cos(e*x+d)^2)*sin(e*x+d)-a^2*c*cos(e*x+d)^3+a*c^2*sin(e*x+d)^3-1/3*c^3*(2+sin(e*x+d)^2)*cos(e*x+d))","A"
364,1,101,81,0.219000," ","int((2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^2,x)","\frac{4 a^{2} \left(e x +d \right)+8 a^{2} \sin \left(e x +d \right)-8 a c \cos \left(e x +d \right)+4 a^{2} \left(\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)-4 a c \left(\cos^{2}\left(e x +d \right)\right)+4 c^{2} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)}{e}"," ",0,"4/e*(a^2*(e*x+d)+2*a^2*sin(e*x+d)-2*a*c*cos(e*x+d)+a^2*(1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)-a*c*cos(e*x+d)^2+c^2*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d))","A"
365,1,30,29,0.001000," ","int(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d),x)","2 a x -\frac{2 c \cos \left(e x +d \right)}{e}+\frac{2 a \sin \left(e x +d \right)}{e}"," ",0,"2*a*x-2*c*cos(e*x+d)/e+2*a*sin(e*x+d)/e","A"
366,1,23,22,0.385000," ","int(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d)),x)","\frac{\ln \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{2 c e}"," ",0,"1/2*ln(a+c*tan(1/2*d+1/2*e*x))/c/e","A"
367,1,91,70,0.490000," ","int(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^2,x)","\frac{\tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{8 e \,c^{2}}-\frac{a^{2}}{8 e \,c^{3} \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}-\frac{1}{8 e c \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}-\frac{a \ln \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{4 c^{3} e}"," ",0,"1/8/e/c^2*tan(1/2*d+1/2*e*x)-1/8/e/c^3/(a+c*tan(1/2*d+1/2*e*x))*a^2-1/8/e/c/(a+c*tan(1/2*d+1/2*e*x))-1/4*a*ln(a+c*tan(1/2*d+1/2*e*x))/c^3/e","A"
368,1,211,127,0.560000," ","int(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^3,x)","\frac{\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)}{64 e \,c^{3}}-\frac{3 \tan \left(\frac{d}{2}+\frac{e x}{2}\right) a}{32 e \,c^{4}}-\frac{a^{4}}{64 e \,c^{5} \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{2}}-\frac{a^{2}}{32 e \,c^{3} \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{2}}-\frac{1}{64 e c \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{2}}+\frac{a^{3}}{8 e \,c^{5} \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}+\frac{a}{8 e \,c^{3} \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}+\frac{3 \ln \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right) a^{2}}{16 e \,c^{5}}+\frac{\ln \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{16 e \,c^{3}}"," ",0,"1/64/e/c^3*tan(1/2*d+1/2*e*x)^2-3/32/e/c^4*tan(1/2*d+1/2*e*x)*a-1/64/e/c^5/(a+c*tan(1/2*d+1/2*e*x))^2*a^4-1/32/e/c^3/(a+c*tan(1/2*d+1/2*e*x))^2*a^2-1/64/e/c/(a+c*tan(1/2*d+1/2*e*x))^2+1/8/e*a^3/c^5/(a+c*tan(1/2*d+1/2*e*x))+1/8/e*a/c^3/(a+c*tan(1/2*d+1/2*e*x))+3/16/e/c^5*ln(a+c*tan(1/2*d+1/2*e*x))*a^2+1/16/e/c^3*ln(a+c*tan(1/2*d+1/2*e*x))","A"
369,1,378,198,0.599000," ","int(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^4,x)","\frac{\tan^{3}\left(\frac{d}{2}+\frac{e x}{2}\right)}{384 e \,c^{4}}-\frac{\left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) a}{64 e \,c^{5}}+\frac{5 a^{2} \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{64 e \,c^{6}}+\frac{3 \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{128 e \,c^{4}}+\frac{3 a^{5}}{128 e \,c^{7} \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{2}}+\frac{3 a^{3}}{64 e \,c^{5} \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{2}}+\frac{3 a}{128 e \,c^{3} \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{2}}-\frac{a^{6}}{384 e \,c^{7} \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{3}}-\frac{a^{4}}{128 e \,c^{5} \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{3}}-\frac{a^{2}}{128 e \,c^{3} \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{3}}-\frac{1}{384 e c \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{3}}-\frac{15 a^{4}}{128 e \,c^{7} \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}-\frac{9 a^{2}}{64 e \,c^{5} \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}-\frac{3}{128 e \,c^{3} \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}-\frac{5 a^{3} \ln \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{32 e \,c^{7}}-\frac{3 a \ln \left(a +c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{32 e \,c^{5}}"," ",0,"1/384/e/c^4*tan(1/2*d+1/2*e*x)^3-1/64/e/c^5*tan(1/2*d+1/2*e*x)^2*a+5/64/e/c^6*a^2*tan(1/2*d+1/2*e*x)+3/128/e/c^4*tan(1/2*d+1/2*e*x)+3/128/e*a^5/c^7/(a+c*tan(1/2*d+1/2*e*x))^2+3/64/e*a^3/c^5/(a+c*tan(1/2*d+1/2*e*x))^2+3/128/e*a/c^3/(a+c*tan(1/2*d+1/2*e*x))^2-1/384/e/c^7/(a+c*tan(1/2*d+1/2*e*x))^3*a^6-1/128/e/c^5/(a+c*tan(1/2*d+1/2*e*x))^3*a^4-1/128/e/c^3/(a+c*tan(1/2*d+1/2*e*x))^3*a^2-1/384/e/c/(a+c*tan(1/2*d+1/2*e*x))^3-15/128/e/c^7/(a+c*tan(1/2*d+1/2*e*x))*a^4-9/64/e/c^5/(a+c*tan(1/2*d+1/2*e*x))*a^2-3/128/e/c^3/(a+c*tan(1/2*d+1/2*e*x))-5/32/e*a^3/c^7*ln(a+c*tan(1/2*d+1/2*e*x))-3/32/e*a/c^5*ln(a+c*tan(1/2*d+1/2*e*x))","A"
370,1,21,20,0.396000," ","int(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d)),x)","\frac{\ln \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{2 a e}"," ",0,"1/2*ln(1+tan(1/2*d+1/2*e*x))/a/e","A"
371,1,60,70,0.408000," ","int(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d))^2,x)","\frac{\tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{8 e \,a^{2}}-\frac{1}{4 e \,a^{2} \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}-\frac{\ln \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{4 a^{2} e}"," ",0,"1/8/e/a^2*tan(1/2*d+1/2*e*x)-1/4/e/a^2/(1+tan(1/2*d+1/2*e*x))-1/4*ln(1+tan(1/2*d+1/2*e*x))/a^2/e","A"
372,1,100,116,0.447000," ","int(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d))^3,x)","\frac{\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)}{64 a^{3} e}-\frac{3 \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{32 a^{3} e}-\frac{1}{16 a^{3} e \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{2}}+\frac{1}{4 a^{3} e \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}+\frac{\ln \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{4 a^{3} e}"," ",0,"1/64/a^3/e*tan(1/2*d+1/2*e*x)^2-3/32/a^3/e*tan(1/2*d+1/2*e*x)-1/16/a^3/e/(1+tan(1/2*d+1/2*e*x))^2+1/4/a^3/e/(1+tan(1/2*d+1/2*e*x))+1/4*ln(1+tan(1/2*d+1/2*e*x))/a^3/e","A"
373,1,140,159,0.456000," ","int(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d))^4,x)","\frac{\tan^{3}\left(\frac{d}{2}+\frac{e x}{2}\right)}{384 a^{4} e}-\frac{\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)}{64 a^{4} e}+\frac{13 \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{128 a^{4} e}-\frac{1}{48 a^{4} e \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{3}}+\frac{3}{32 a^{4} e \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{2}}-\frac{9}{32 a^{4} e \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}-\frac{\ln \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{4 a^{4} e}"," ",0,"1/384/a^4/e*tan(1/2*d+1/2*e*x)^3-1/64/a^4/e*tan(1/2*d+1/2*e*x)^2+13/128/a^4/e*tan(1/2*d+1/2*e*x)-1/48/a^4/e/(1+tan(1/2*d+1/2*e*x))^3+3/32/a^4/e/(1+tan(1/2*d+1/2*e*x))^2-9/32/a^4/e/(1+tan(1/2*d+1/2*e*x))-1/4*ln(1+tan(1/2*d+1/2*e*x))/a^4/e","A"
374,1,178,149,0.250000," ","int((2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^3,x)","\frac{-\frac{8 a^{3} \left(2+\cos^{2}\left(e x +d \right)\right) \sin \left(e x +d \right)}{3}-8 a^{2} c \left(\cos^{3}\left(e x +d \right)\right)+24 a^{3} \left(\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)-8 a \,c^{2} \left(\sin^{3}\left(e x +d \right)\right)+24 a^{2} c \left(\cos^{2}\left(e x +d \right)\right)-24 a^{3} \sin \left(e x +d \right)-\frac{8 c^{3} \left(2+\sin^{2}\left(e x +d \right)\right) \cos \left(e x +d \right)}{3}+24 a \,c^{2} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)-24 a^{2} c \cos \left(e x +d \right)+8 a^{3} \left(e x +d \right)}{e}"," ",0,"8/e*(-1/3*a^3*(2+cos(e*x+d)^2)*sin(e*x+d)-a^2*c*cos(e*x+d)^3+3*a^3*(1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)-a*c^2*sin(e*x+d)^3+3*a^2*c*cos(e*x+d)^2-3*a^3*sin(e*x+d)-1/3*c^3*(2+sin(e*x+d)^2)*cos(e*x+d)+3*a*c^2*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)-3*a^2*c*cos(e*x+d)+a^3*(e*x+d))","A"
375,1,100,81,0.223000," ","int((2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^2,x)","\frac{4 a^{2} \left(e x +d \right)-8 a^{2} \sin \left(e x +d \right)-8 a c \cos \left(e x +d \right)+4 a^{2} \left(\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)+4 a c \left(\cos^{2}\left(e x +d \right)\right)+4 c^{2} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)}{e}"," ",0,"4/e*(a^2*(e*x+d)-2*a^2*sin(e*x+d)-2*a*c*cos(e*x+d)+a^2*(1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)+a*c*cos(e*x+d)^2+c^2*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d))","A"
376,1,30,29,0.001000," ","int(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d),x)","2 a x -\frac{2 c \cos \left(e x +d \right)}{e}-\frac{2 a \sin \left(e x +d \right)}{e}"," ",0,"2*a*x-2*c*cos(e*x+d)/e-2*a*sin(e*x+d)/e","A"
377,1,42,22,0.421000," ","int(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d)),x)","-\frac{\ln \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{2 e c}+\frac{\ln \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{2 e c}"," ",0,"-1/2/e/c*ln(c+a*tan(1/2*d+1/2*e*x))+1/2/e/c*ln(tan(1/2*d+1/2*e*x))","A"
378,1,110,72,0.470000," ","int(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^2,x)","-\frac{a}{8 e \,c^{2} \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}-\frac{1}{8 e a \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}+\frac{a \ln \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{4 e \,c^{3}}-\frac{1}{8 e \,c^{2} \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}-\frac{a \ln \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{4 e \,c^{3}}"," ",0,"-1/8/e/c^2*a/(c+a*tan(1/2*d+1/2*e*x))-1/8/e/a/(c+a*tan(1/2*d+1/2*e*x))+1/4/e/c^3*a*ln(c+a*tan(1/2*d+1/2*e*x))-1/8/e/c^2/tan(1/2*d+1/2*e*x)-1/4/e/c^3*a*ln(tan(1/2*d+1/2*e*x))","A"
379,1,272,129,0.566000," ","int(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^3,x)","\frac{3 a^{2}}{32 e \,c^{4} \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}+\frac{1}{16 e \,c^{2} \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}-\frac{1}{32 e \,a^{2} \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}+\frac{a^{2}}{64 e \,c^{3} \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{2}}+\frac{1}{32 e c \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{2}}+\frac{c}{64 e \,a^{2} \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{2}}-\frac{3 \ln \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right) a^{2}}{16 e \,c^{5}}-\frac{\ln \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{16 e \,c^{3}}-\frac{1}{64 e \,c^{3} \tan \left(\frac{d}{2}+\frac{e x}{2}\right)^{2}}+\frac{3 \ln \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right) a^{2}}{16 e \,c^{5}}+\frac{\ln \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{16 e \,c^{3}}+\frac{3 a}{32 e \,c^{4} \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}"," ",0,"3/32/e*a^2/c^4/(c+a*tan(1/2*d+1/2*e*x))+1/16/e/c^2/(c+a*tan(1/2*d+1/2*e*x))-1/32/e/a^2/(c+a*tan(1/2*d+1/2*e*x))+1/64/e*a^2/c^3/(c+a*tan(1/2*d+1/2*e*x))^2+1/32/e/c/(c+a*tan(1/2*d+1/2*e*x))^2+1/64/e/a^2*c/(c+a*tan(1/2*d+1/2*e*x))^2-3/16/e/c^5*ln(c+a*tan(1/2*d+1/2*e*x))*a^2-1/16/e/c^3*ln(c+a*tan(1/2*d+1/2*e*x))-1/64/e/c^3/tan(1/2*d+1/2*e*x)^2+3/16/e/c^5*ln(tan(1/2*d+1/2*e*x))*a^2+1/16/e/c^3*ln(tan(1/2*d+1/2*e*x))+3/32/e/c^4*a/tan(1/2*d+1/2*e*x)","B"
380,1,416,202,0.593000," ","int(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^4,x)","-\frac{a^{3}}{64 e \,c^{5} \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{2}}-\frac{3 a}{128 e \,c^{3} \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{2}}+\frac{c}{128 e \,a^{3} \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{2}}-\frac{5 a^{3}}{64 e \,c^{6} \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}-\frac{9 a}{128 e \,c^{4} \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}-\frac{1}{128 e \,a^{3} \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}-\frac{a^{3}}{384 e \,c^{4} \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{3}}-\frac{a}{128 e \,c^{2} \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{3}}-\frac{1}{128 e a \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{3}}-\frac{c^{2}}{384 e \,a^{3} \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{3}}+\frac{5 a^{3} \ln \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{32 e \,c^{7}}+\frac{3 a \ln \left(c +a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{32 e \,c^{5}}-\frac{1}{384 e \,c^{4} \tan \left(\frac{d}{2}+\frac{e x}{2}\right)^{3}}-\frac{5 a^{2}}{64 e \,c^{6} \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}-\frac{3}{128 e \,c^{4} \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}+\frac{a}{64 e \,c^{5} \tan \left(\frac{d}{2}+\frac{e x}{2}\right)^{2}}-\frac{5 a^{3} \ln \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{32 e \,c^{7}}-\frac{3 a \ln \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{32 e \,c^{5}}"," ",0,"-1/64/e*a^3/c^5/(c+a*tan(1/2*d+1/2*e*x))^2-3/128/e*a/c^3/(c+a*tan(1/2*d+1/2*e*x))^2+1/128/e/a^3*c/(c+a*tan(1/2*d+1/2*e*x))^2-5/64/e/c^6*a^3/(c+a*tan(1/2*d+1/2*e*x))-9/128/e/c^4*a/(c+a*tan(1/2*d+1/2*e*x))-1/128/e/a^3/(c+a*tan(1/2*d+1/2*e*x))-1/384/e*a^3/c^4/(c+a*tan(1/2*d+1/2*e*x))^3-1/128/e*a/c^2/(c+a*tan(1/2*d+1/2*e*x))^3-1/128/e/a/(c+a*tan(1/2*d+1/2*e*x))^3-1/384/e/a^3*c^2/(c+a*tan(1/2*d+1/2*e*x))^3+5/32/e*a^3/c^7*ln(c+a*tan(1/2*d+1/2*e*x))+3/32/e*a/c^5*ln(c+a*tan(1/2*d+1/2*e*x))-1/384/e/c^4/tan(1/2*d+1/2*e*x)^3-5/64/e/c^6/tan(1/2*d+1/2*e*x)*a^2-3/128/e/c^4/tan(1/2*d+1/2*e*x)+1/64/e/c^5*a/tan(1/2*d+1/2*e*x)^2-5/32/e*a^3/c^7*ln(tan(1/2*d+1/2*e*x))-3/32/e*a/c^5*ln(tan(1/2*d+1/2*e*x))","B"
381,1,177,149,0.246000," ","int((2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^3,x)","\frac{8 a^{3} \left(e x +d \right)+24 \sin \left(e x +d \right) a^{2} b -24 a^{3} \cos \left(e x +d \right)+24 a \,b^{2} \left(\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)-24 \left(\cos^{2}\left(e x +d \right)\right) a^{2} b +24 a^{3} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)+\frac{8 b^{3} \left(2+\cos^{2}\left(e x +d \right)\right) \sin \left(e x +d \right)}{3}-8 a \,b^{2} \left(\cos^{3}\left(e x +d \right)\right)+8 a^{2} b \left(\sin^{3}\left(e x +d \right)\right)-\frac{8 a^{3} \left(2+\sin^{2}\left(e x +d \right)\right) \cos \left(e x +d \right)}{3}}{e}"," ",0,"8/e*(a^3*(e*x+d)+3*sin(e*x+d)*a^2*b-3*a^3*cos(e*x+d)+3*a*b^2*(1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)-3*cos(e*x+d)^2*a^2*b+3*a^3*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)+1/3*b^3*(2+cos(e*x+d)^2)*sin(e*x+d)-a*b^2*cos(e*x+d)^3+a^2*b*sin(e*x+d)^3-1/3*a^3*(2+sin(e*x+d)^2)*cos(e*x+d))","A"
382,1,101,81,0.227000," ","int((2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^2,x)","\frac{4 a^{2} \left(e x +d \right)+8 a b \sin \left(e x +d \right)-8 a^{2} \cos \left(e x +d \right)+4 b^{2} \left(\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)-4 \left(\cos^{2}\left(e x +d \right)\right) a b +4 a^{2} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)}{e}"," ",0,"4/e*(a^2*(e*x+d)+2*a*b*sin(e*x+d)-2*a^2*cos(e*x+d)+b^2*(1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)-cos(e*x+d)^2*a*b+a^2*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d))","A"
383,1,30,29,0.002000," ","int(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d),x)","2 a x -\frac{2 a \cos \left(e x +d \right)}{e}+\frac{2 b \sin \left(e x +d \right)}{e}"," ",0,"2*a*x-2*a*cos(e*x+d)/e+2*b*sin(e*x+d)/e","A"
384,1,104,25,0.413000," ","int(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d)),x)","-\frac{\ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right) a}{2 e b \left(a -b \right)}+\frac{\ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}{2 e \left(a -b \right)}+\frac{\ln \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{2 e b}"," ",0,"-1/2/e/b/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)*a+1/2/e/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)+1/2/e/b*ln(1+tan(1/2*d+1/2*e*x))","B"
385,1,166,73,0.534000," ","int(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^2,x)","-\frac{a^{2}}{4 e \,b^{2} \left(a -b \right) \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}-\frac{1}{4 e \left(a -b \right) \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}+\frac{a \ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}{4 e \,b^{3}}-\frac{1}{4 e \,b^{2} \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}-\frac{a \ln \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{4 e \,b^{3}}"," ",0,"-1/4/e/b^2/(a-b)/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)*a^2-1/4/e/(a-b)/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)+1/4/e*a/b^3*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)-1/4/e/b^2/(1+tan(1/2*d+1/2*e*x))-1/4/e*a/b^3*ln(1+tan(1/2*d+1/2*e*x))","B"
386,1,639,130,0.572000," ","int(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^3,x)","-\frac{3 \ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right) a^{3}}{16 e \,b^{5} \left(a -b \right)}+\frac{3 \ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right) a^{2}}{16 e \,b^{4} \left(a -b \right)}-\frac{\ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right) a}{16 e \,b^{3} \left(a -b \right)}+\frac{\ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}{16 e \,b^{2} \left(a -b \right)}+\frac{a^{4}}{16 e \,b^{3} \left(a -b \right)^{2} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)^{2}}+\frac{a^{2}}{8 e b \left(a -b \right)^{2} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)^{2}}+\frac{b}{16 e \left(a -b \right)^{2} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)^{2}}+\frac{3 a^{4}}{16 e \,b^{4} \left(a -b \right)^{2} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}-\frac{a^{3}}{4 e \,b^{3} \left(a -b \right)^{2} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}+\frac{a^{2}}{8 e \,b^{2} \left(a -b \right)^{2} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}-\frac{a}{4 e b \left(a -b \right)^{2} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}-\frac{1}{16 e \left(a -b \right)^{2} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}-\frac{1}{16 e \,b^{3} \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{2}}+\frac{3 a}{16 e \,b^{4} \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}+\frac{1}{16 e \,b^{3} \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}+\frac{3 \ln \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right) a^{2}}{16 e \,b^{5}}+\frac{\ln \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{16 e \,b^{3}}"," ",0,"-3/16/e/b^5/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)*a^3+3/16/e/b^4/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)*a^2-1/16/e/b^3/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)*a+1/16/e/b^2/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)+1/16/e/b^3/(a-b)^2/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)^2*a^4+1/8/e/b/(a-b)^2/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)^2*a^2+1/16/e*b/(a-b)^2/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)^2+3/16/e/b^4/(a-b)^2/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)*a^4-1/4/e/b^3/(a-b)^2/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)*a^3+1/8/e/b^2/(a-b)^2/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)*a^2-1/4/e/b/(a-b)^2/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)*a-1/16/e/(a-b)^2/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)-1/16/e/b^3/(1+tan(1/2*d+1/2*e*x))^2+3/16/e/b^4/(1+tan(1/2*d+1/2*e*x))*a+1/16/e/b^3/(1+tan(1/2*d+1/2*e*x))+3/16/e/b^5*ln(1+tan(1/2*d+1/2*e*x))*a^2+1/16/e/b^3*ln(1+tan(1/2*d+1/2*e*x))","B"
387,1,1069,201,0.586000," ","int(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^4,x)","-\frac{5 a^{3} \ln \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{32 e \,b^{7}}-\frac{3 a \ln \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{32 e \,b^{5}}-\frac{a^{2}}{16 e \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)^{3}}+\frac{3 a}{32 e \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)^{2}}-\frac{b^{2}}{48 e \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)^{3}}+\frac{b}{32 e \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)^{2}}+\frac{a}{16 e \,b^{5} \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{2}}-\frac{5 a^{2}}{32 e \,b^{6} \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}-\frac{a}{16 e \,b^{5} \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}+\frac{5 a^{4} \ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}{32 e \,b^{7} \left(a -b \right)}-\frac{1}{48 e \,b^{4} \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{3}}+\frac{1}{32 e \,b^{4} \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)^{2}}-\frac{1}{16 e \,b^{4} \left(1+\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}-\frac{1}{16 e \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}-\frac{5 a^{3} \ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}{32 e \,b^{6} \left(a -b \right)}+\frac{3 a^{2} \ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}{32 e \,b^{5} \left(a -b \right)}-\frac{3 a \ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}{32 e \,b^{4} \left(a -b \right)}-\frac{a^{6}}{48 e \,b^{4} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)^{3}}-\frac{a^{4}}{16 e \,b^{2} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)^{3}}-\frac{a^{6}}{16 e \,b^{5} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)^{2}}+\frac{3 a^{5}}{32 e \,b^{4} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)^{2}}-\frac{3 a^{4}}{32 e \,b^{3} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)^{2}}+\frac{3 a^{3}}{16 e \,b^{2} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)^{2}}-\frac{5 a^{6}}{32 e \,b^{6} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}+\frac{3 a^{5}}{8 e \,b^{5} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}-\frac{3 a^{4}}{8 e \,b^{4} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}+\frac{3 a^{3}}{8 e \,b^{3} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}-\frac{9 a^{2}}{32 e \,b^{2} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right)}"," ",0,"-5/32/e*a^3/b^7*ln(1+tan(1/2*d+1/2*e*x))-3/32/e*a/b^5*ln(1+tan(1/2*d+1/2*e*x))-1/16/e/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)^3*a^2+3/32/e/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)^2*a-1/48/e*b^2/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)^3+1/32/e*b/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)^2+1/16/e/b^5/(1+tan(1/2*d+1/2*e*x))^2*a-5/32/e/b^6/(1+tan(1/2*d+1/2*e*x))*a^2-1/16/e/b^5/(1+tan(1/2*d+1/2*e*x))*a+5/32/e*a^4/b^7/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)-1/48/e/b^4/(1+tan(1/2*d+1/2*e*x))^3+1/32/e/b^4/(1+tan(1/2*d+1/2*e*x))^2-1/16/e/b^4/(1+tan(1/2*d+1/2*e*x))-1/16/e/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)-5/32/e*a^3/b^6/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)+3/32/e*a^2/b^5/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)-3/32/e*a/b^4/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)-1/48/e/b^4/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)^3*a^6-1/16/e/b^2/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)^3*a^4-1/16/e/b^5/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)^2*a^6+3/32/e/b^4/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)^2*a^5-3/32/e/b^3/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)^2*a^4+3/16/e/b^2/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)^2*a^3-5/32/e/b^6/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)*a^6+3/8/e/b^5/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)*a^5-3/8/e/b^4/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)*a^4+3/8/e/b^3/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)*a^3-9/32/e/b^2/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)+a+b)*a^2","B"
388,1,176,149,0.253000," ","int((2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^3,x)","\frac{8 a^{3} \left(e x +d \right)+24 \sin \left(e x +d \right) a^{2} b +24 a^{3} \cos \left(e x +d \right)+24 a \,b^{2} \left(\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)+24 \left(\cos^{2}\left(e x +d \right)\right) a^{2} b +24 a^{3} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)+\frac{8 b^{3} \left(2+\cos^{2}\left(e x +d \right)\right) \sin \left(e x +d \right)}{3}+8 a \,b^{2} \left(\cos^{3}\left(e x +d \right)\right)+8 a^{2} b \left(\sin^{3}\left(e x +d \right)\right)+\frac{8 a^{3} \left(2+\sin^{2}\left(e x +d \right)\right) \cos \left(e x +d \right)}{3}}{e}"," ",0,"8/e*(a^3*(e*x+d)+3*sin(e*x+d)*a^2*b+3*a^3*cos(e*x+d)+3*a*b^2*(1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)+3*cos(e*x+d)^2*a^2*b+3*a^3*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)+1/3*b^3*(2+cos(e*x+d)^2)*sin(e*x+d)+a*b^2*cos(e*x+d)^3+a^2*b*sin(e*x+d)^3+1/3*a^3*(2+sin(e*x+d)^2)*cos(e*x+d))","A"
389,1,100,81,0.233000," ","int((2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^2,x)","\frac{4 a^{2} \left(e x +d \right)+8 a b \sin \left(e x +d \right)+8 a^{2} \cos \left(e x +d \right)+4 b^{2} \left(\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)+4 \left(\cos^{2}\left(e x +d \right)\right) a b +4 a^{2} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)}{e}"," ",0,"4/e*(a^2*(e*x+d)+2*a*b*sin(e*x+d)+2*a^2*cos(e*x+d)+b^2*(1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)+cos(e*x+d)^2*a*b+a^2*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d))","A"
390,1,30,29,0.001000," ","int(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d),x)","2 a x +\frac{2 a \cos \left(e x +d \right)}{e}+\frac{2 b \sin \left(e x +d \right)}{e}"," ",0,"2*a*x+2*a*cos(e*x+d)/e+2*b*sin(e*x+d)/e","A"
391,1,61,25,0.417000," ","int(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d)),x)","\frac{\ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}{2 e b}-\frac{\ln \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)-1\right)}{2 e b}"," ",0,"1/2/e/b*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)-1/2/e/b*ln(tan(1/2*d+1/2*e*x)-1)","B"
392,1,178,73,0.507000," ","int(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^2,x)","-\frac{a^{2}}{4 e \,b^{2} \left(a -b \right) \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}-\frac{1}{4 e \left(a -b \right) \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}-\frac{a \ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}{4 e \,b^{3}}-\frac{1}{4 e \,b^{2} \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)-1\right)}+\frac{a \ln \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)-1\right)}{4 e \,b^{3}}"," ",0,"-1/4/e/b^2/(a-b)/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)*a^2-1/4/e/(a-b)/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)-1/4/e*a/b^3*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)-1/4/e/b^2/(tan(1/2*d+1/2*e*x)-1)+1/4/e*a/b^3*ln(tan(1/2*d+1/2*e*x)-1)","B"
393,1,687,130,0.532000," ","int(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^3,x)","\frac{3 \ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right) a^{3}}{16 e \,b^{5} \left(a -b \right)}-\frac{3 \ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right) a^{2}}{16 e \,b^{4} \left(a -b \right)}+\frac{\ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right) a}{16 e \,b^{3} \left(a -b \right)}-\frac{\ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}{16 e \,b^{2} \left(a -b \right)}-\frac{a^{4}}{16 e \,b^{3} \left(a -b \right)^{2} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)^{2}}-\frac{a^{2}}{8 e b \left(a -b \right)^{2} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)^{2}}-\frac{b}{16 e \left(a -b \right)^{2} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)^{2}}+\frac{3 a^{4}}{16 e \,b^{4} \left(a -b \right)^{2} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}-\frac{a^{3}}{4 e \,b^{3} \left(a -b \right)^{2} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}+\frac{a^{2}}{8 e \,b^{2} \left(a -b \right)^{2} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}-\frac{a}{4 e b \left(a -b \right)^{2} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}-\frac{1}{16 e \left(a -b \right)^{2} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}+\frac{1}{16 e \,b^{3} \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)-1\right)^{2}}+\frac{3 a}{16 e \,b^{4} \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)-1\right)}+\frac{1}{16 e \,b^{3} \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)-1\right)}-\frac{3 \ln \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)-1\right) a^{2}}{16 e \,b^{5}}-\frac{\ln \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)-1\right)}{16 e \,b^{3}}"," ",0,"3/16/e/b^5/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)*a^3-3/16/e/b^4/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)*a^2+1/16/e/b^3/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)*a-1/16/e/b^2/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)-1/16/e/b^3/(a-b)^2/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)^2*a^4-1/8/e/b/(a-b)^2/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)^2*a^2-1/16/e*b/(a-b)^2/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)^2+3/16/e/b^4/(a-b)^2/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)*a^4-1/4/e/b^3/(a-b)^2/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)*a^3+1/8/e/b^2/(a-b)^2/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)*a^2-1/4/e/b/(a-b)^2/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)*a-1/16/e/(a-b)^2/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)+1/16/e/b^3/(tan(1/2*d+1/2*e*x)-1)^2+3/16/e/b^4/(tan(1/2*d+1/2*e*x)-1)*a+1/16/e/b^3/(tan(1/2*d+1/2*e*x)-1)-3/16/e/b^5*ln(tan(1/2*d+1/2*e*x)-1)*a^2-1/16/e/b^3*ln(tan(1/2*d+1/2*e*x)-1)","B"
394,1,1149,201,0.614000," ","int(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^4,x)","\frac{a^{6}}{16 e \,b^{5} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)^{2}}-\frac{3 a^{5}}{32 e \,b^{4} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)^{2}}+\frac{3 a^{4}}{32 e \,b^{3} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)^{2}}-\frac{3 a^{3}}{16 e \,b^{2} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)^{2}}-\frac{5 a^{6}}{32 e \,b^{6} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}+\frac{3 a^{5}}{8 e \,b^{5} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}-\frac{3 a^{4}}{8 e \,b^{4} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}+\frac{3 a^{3}}{8 e \,b^{3} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}-\frac{9 a^{2}}{32 e \,b^{2} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}-\frac{5 a^{4} \ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}{32 e \,b^{7} \left(a -b \right)}+\frac{5 a^{3} \ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}{32 e \,b^{6} \left(a -b \right)}-\frac{3 a^{2} \ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}{32 e \,b^{5} \left(a -b \right)}+\frac{3 a \ln \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}{32 e \,b^{4} \left(a -b \right)}-\frac{1}{16 e \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)}-\frac{1}{48 e \,b^{4} \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)-1\right)^{3}}-\frac{1}{32 e \,b^{4} \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)-1\right)^{2}}-\frac{1}{16 e \,b^{4} \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)-1\right)}-\frac{3 a}{32 e \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)^{2}}-\frac{b^{2}}{48 e \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)^{3}}-\frac{b}{32 e \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)^{2}}-\frac{a}{16 e \,b^{5} \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)-1\right)^{2}}-\frac{5 a^{2}}{32 e \,b^{6} \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)-1\right)}-\frac{a}{16 e \,b^{5} \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)-1\right)}+\frac{5 a^{3} \ln \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)-1\right)}{32 e \,b^{7}}+\frac{3 a \ln \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)-1\right)}{32 e \,b^{5}}-\frac{a^{2}}{16 e \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)^{3}}-\frac{a^{6}}{48 e \,b^{4} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)^{3}}-\frac{a^{4}}{16 e \,b^{2} \left(a -b \right)^{3} \left(a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)-a -b \right)^{3}}"," ",0,"1/16/e/b^5/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)^2*a^6-3/32/e/b^4/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)^2*a^5+3/32/e/b^3/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)^2*a^4-3/16/e/b^2/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)^2*a^3-5/32/e/b^6/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)*a^6+3/8/e/b^5/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)*a^5-3/8/e/b^4/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)*a^4+3/8/e/b^3/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)*a^3-9/32/e/b^2/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)*a^2-5/32/e*a^4/b^7/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)+5/32/e*a^3/b^6/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)-3/32/e*a^2/b^5/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)+3/32/e*a/b^4/(a-b)*ln(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)-1/16/e/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)-1/48/e/b^4/(tan(1/2*d+1/2*e*x)-1)^3-1/32/e/b^4/(tan(1/2*d+1/2*e*x)-1)^2-1/16/e/b^4/(tan(1/2*d+1/2*e*x)-1)-3/32/e/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)^2*a-1/48/e*b^2/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)^3-1/32/e*b/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)^2-1/16/e/b^5/(tan(1/2*d+1/2*e*x)-1)^2*a-5/32/e/b^6/(tan(1/2*d+1/2*e*x)-1)*a^2-1/16/e/b^5/(tan(1/2*d+1/2*e*x)-1)*a+5/32/e*a^3/b^7*ln(tan(1/2*d+1/2*e*x)-1)+3/32/e*a/b^5*ln(tan(1/2*d+1/2*e*x)-1)-1/16/e/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)^3*a^2-1/48/e/b^4/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)^3*a^6-1/16/e/b^2/(a-b)^3/(a*tan(1/2*d+1/2*e*x)-b*tan(1/2*d+1/2*e*x)-a-b)^3*a^4","B"
395,1,335,252,0.268000," ","int((a+b*cos(e*x+d)+c*sin(e*x+d))^4,x)","\frac{b^{4} \left(\frac{\left(\cos^{3}\left(e x +d \right)+\frac{3 \cos \left(e x +d \right)}{2}\right) \sin \left(e x +d \right)}{4}+\frac{3 e x}{8}+\frac{3 d}{8}\right)+c^{4} \left(-\frac{\left(\sin^{3}\left(e x +d \right)+\frac{3 \sin \left(e x +d \right)}{2}\right) \cos \left(e x +d \right)}{4}+\frac{3 e x}{8}+\frac{3 d}{8}\right)-6 a^{2} b c \left(\cos^{2}\left(e x +d \right)\right)-4 a \,b^{2} c \left(\cos^{3}\left(e x +d \right)\right)+4 a b \,c^{2} \left(\sin^{3}\left(e x +d \right)\right)+4 a^{3} b \sin \left(e x +d \right)-4 \cos \left(e x +d \right) a^{3} c +6 a^{2} b^{2} \left(\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)+6 a^{2} c^{2} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)+\frac{4 a \,b^{3} \left(2+\cos^{2}\left(e x +d \right)\right) \sin \left(e x +d \right)}{3}-\frac{4 a \,c^{3} \left(2+\sin^{2}\left(e x +d \right)\right) \cos \left(e x +d \right)}{3}+a^{4} \left(e x +d \right)-\left(\cos^{4}\left(e x +d \right)\right) b^{3} c +6 b^{2} c^{2} \left(-\frac{\sin \left(e x +d \right) \left(\cos^{3}\left(e x +d \right)\right)}{4}+\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{8}+\frac{e x}{8}+\frac{d}{8}\right)+c^{3} b \left(\sin^{4}\left(e x +d \right)\right)}{e}"," ",0,"1/e*(b^4*(1/4*(cos(e*x+d)^3+3/2*cos(e*x+d))*sin(e*x+d)+3/8*e*x+3/8*d)+c^4*(-1/4*(sin(e*x+d)^3+3/2*sin(e*x+d))*cos(e*x+d)+3/8*e*x+3/8*d)-6*a^2*b*c*cos(e*x+d)^2-4*a*b^2*c*cos(e*x+d)^3+4*a*b*c^2*sin(e*x+d)^3+4*a^3*b*sin(e*x+d)-4*cos(e*x+d)*a^3*c+6*a^2*b^2*(1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)+6*a^2*c^2*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)+4/3*a*b^3*(2+cos(e*x+d)^2)*sin(e*x+d)-4/3*a*c^3*(2+sin(e*x+d)^2)*cos(e*x+d)+a^4*(e*x+d)-cos(e*x+d)^4*b^3*c+6*b^2*c^2*(-1/4*sin(e*x+d)*cos(e*x+d)^3+1/8*sin(e*x+d)*cos(e*x+d)+1/8*e*x+1/8*d)+c^3*b*sin(e*x+d)^4)","A"
396,1,177,163,0.243000," ","int((a+b*cos(e*x+d)+c*sin(e*x+d))^3,x)","\frac{a^{3} \left(e x +d \right)+3 \sin \left(e x +d \right) a^{2} b -3 a^{2} c \cos \left(e x +d \right)+3 a \,b^{2} \left(\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)-3 a b c \left(\cos^{2}\left(e x +d \right)\right)+3 a \,c^{2} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)+\frac{b^{3} \left(2+\cos^{2}\left(e x +d \right)\right) \sin \left(e x +d \right)}{3}-\left(\cos^{3}\left(e x +d \right)\right) b^{2} c +c^{2} b \left(\sin^{3}\left(e x +d \right)\right)-\frac{c^{3} \left(2+\sin^{2}\left(e x +d \right)\right) \cos \left(e x +d \right)}{3}}{e}"," ",0,"1/e*(a^3*(e*x+d)+3*sin(e*x+d)*a^2*b-3*a^2*c*cos(e*x+d)+3*a*b^2*(1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)-3*a*b*c*cos(e*x+d)^2+3*a*c^2*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)+1/3*b^3*(2+cos(e*x+d)^2)*sin(e*x+d)-cos(e*x+d)^3*b^2*c+c^2*b*sin(e*x+d)^3-1/3*c^3*(2+sin(e*x+d)^2)*cos(e*x+d))","A"
397,1,99,83,0.224000," ","int((a+b*cos(e*x+d)+c*sin(e*x+d))^2,x)","\frac{a^{2} \left(e x +d \right)+2 a b \sin \left(e x +d \right)-2 a c \cos \left(e x +d \right)+b^{2} \left(\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)-\left(\cos^{2}\left(e x +d \right)\right) b c +c^{2} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)}{e}"," ",0,"1/e*(a^2*(e*x+d)+2*a*b*sin(e*x+d)-2*a*c*cos(e*x+d)+b^2*(1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)-cos(e*x+d)^2*b*c+c^2*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d))","A"
398,1,28,27,0.001000," ","int(a+b*cos(e*x+d)+c*sin(e*x+d),x)","a x -\frac{c \cos \left(e x +d \right)}{e}+\frac{b \sin \left(e x +d \right)}{e}"," ",0,"a*x-c*cos(e*x+d)/e+b*sin(e*x+d)/e","A"
399,1,61,56,0.378000," ","int(1/(a+b*cos(e*x+d)+c*sin(e*x+d)),x)","\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right)}{e \sqrt{a^{2}-b^{2}-c^{2}}}"," ",0,"2/e/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*d+1/2*e*x)+2*c)/(a^2-b^2-c^2)^(1/2))","A"
400,1,424,116,0.499000," ","int(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^2,x)","-\frac{2 \tan \left(\frac{d}{2}+\frac{e x}{2}\right) a b}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right) \left(a^{3}-a^{2} b -a \,b^{2}-a \,c^{2}+b^{3}+c^{2} b \right)}+\frac{2 \tan \left(\frac{d}{2}+\frac{e x}{2}\right) b^{2}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right) \left(a^{3}-a^{2} b -a \,b^{2}-a \,c^{2}+b^{3}+c^{2} b \right)}+\frac{2 \tan \left(\frac{d}{2}+\frac{e x}{2}\right) c^{2}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right) \left(a^{3}-a^{2} b -a \,b^{2}-a \,c^{2}+b^{3}+c^{2} b \right)}+\frac{2 a c}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a +b \right) \left(a^{3}-a^{2} b -a \,b^{2}-a \,c^{2}+b^{3}+c^{2} b \right)}+\frac{2 a \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right)}{e \left(a^{2}-b^{2}-c^{2}\right)^{\frac{3}{2}}}"," ",0,"-2/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)/(a^3-a^2*b-a*b^2-a*c^2+b^3+b*c^2)*tan(1/2*d+1/2*e*x)*a*b+2/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)/(a^3-a^2*b-a*b^2-a*c^2+b^3+b*c^2)*tan(1/2*d+1/2*e*x)*b^2+2/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)/(a^3-a^2*b-a*b^2-a*c^2+b^3+b*c^2)*tan(1/2*d+1/2*e*x)*c^2+2/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)*a*c/(a^3-a^2*b-a*b^2-a*c^2+b^3+b*c^2)+2/e*a/(a^2-b^2-c^2)^(3/2)*arctan(1/2*(2*(a-b)*tan(1/2*d+1/2*e*x)+2*c)/(a^2-b^2-c^2)^(1/2))","B"
401,1,3933,188,0.563000," ","int(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^3,x)","\text{output too large to display}"," ",0,"3/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)*a^2*b^3-5/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)*a*b^4-2/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)*a*c^4-1/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)*b^3*c^2-2/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)*c^4*b-3/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2*c/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*a^2*b^2-4/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a-b)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)*tan(1/2*d+1/2*e*x)^3*a^3*b+7/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a-b)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)*tan(1/2*d+1/2*e*x)^3*a^2*b^2+5/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a-b)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)*tan(1/2*d+1/2*e*x)^3*a^2*c^2-2/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a-b)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)*tan(1/2*d+1/2*e*x)^3*a*b^3-3/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a-b)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)*tan(1/2*d+1/2*e*x)^3*b^2*c^2+4/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2*c/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)^2*a^4+7/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2*c^3/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)^2*a^2+1/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2*c/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)^2*b^4-1/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2*c^3/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)^2*b^2-4/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)*a^4*b+5/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)*a^3*b^2+11/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)*a^3*c^2+2/e/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*d+1/2*e*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a^2+1/e/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*d+1/2*e*x)+2*c)/(a^2-b^2-c^2)^(1/2))*b^2+1/e/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*d+1/2*e*x)+2*c)/(a^2-b^2-c^2)^(1/2))*c^2-1/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2*c^3/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*a^2-1/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2*c/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*b^4-1/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2*c^3/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*b^2-1/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a-b)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)*tan(1/2*d+1/2*e*x)^3*b^4-2/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a-b)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)*tan(1/2*d+1/2*e*x)^3*c^4-2/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2*c^5/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)^2+1/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)*b^5+4/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2*c/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*a^4+13/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2*c/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)^2*a^2*b^2-12/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2*c/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)^2*a^3*b-2/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a-b)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)*tan(1/2*d+1/2*e*x)^3*a*b*c^2-6/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2*c/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)^2*a*b^3-6/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2*c^3/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)^2*a*b-3/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)*a^2*b*c^2-7/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a+b)^2/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)*a*b^2*c^2","B"
402,1,16909,284,0.658000," ","int(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^4,x)","\text{output too large to display}"," ",0,"result too large to display","B"
403,1,701,223,0.661000," ","int((2+3*cos(e*x+d)+5*sin(e*x+d))^(5/2),x)","\frac{\frac{16 \sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}\, \sqrt{17}\, \sqrt{\frac{1+\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)}{-\sqrt{34}+17}}\, \sqrt{-\frac{17 \left(\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-1\right)}{\sqrt{34}+17}}\, \EllipticF \left(\sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}, i \sqrt{\frac{\sqrt{34}+17}{-\sqrt{34}+17}}\right) \sqrt{34}}{17}+16 \sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}\, \sqrt{17}\, \sqrt{\frac{1+\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)}{-\sqrt{34}+17}}\, \sqrt{-\frac{17 \left(\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-1\right)}{\sqrt{34}+17}}\, \EllipticF \left(\sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}, i \sqrt{\frac{\sqrt{34}+17}{-\sqrt{34}+17}}\right)-44 \sqrt{17}\, \sqrt{\frac{1+\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)}{-\sqrt{34}+17}}\, \sqrt{-\frac{17 \left(\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-1\right)}{\sqrt{34}+17}}\, \sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}\, \EllipticF \left(\sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}, i \sqrt{\frac{-\sqrt{34}+17}{\sqrt{34}+17}}\right) \sqrt{34}+\frac{796 \sqrt{17}\, \sqrt{\frac{1+\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)}{-\sqrt{34}+17}}\, \sqrt{-\frac{17 \left(\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-1\right)}{\sqrt{34}+17}}\, \sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}\, \EllipticE \left(\sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}, i \sqrt{\frac{-\sqrt{34}+17}{\sqrt{34}+17}}\right) \sqrt{34}}{17}-48 \sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}\, \sqrt{-\frac{17 \left(\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-1\right)}{\sqrt{34}+17}}\, \sqrt{17}\, \sqrt{\frac{1+\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)}{-\sqrt{34}+17}}\, \EllipticF \left(\sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}, i \sqrt{\frac{-\sqrt{34}+17}{\sqrt{34}+17}}\right)+\frac{68 \sqrt{34}\, \left(\sin^{4}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}{5}-\frac{116 \sqrt{34}\, \left(\sin^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}{15}+\frac{1904 \left(\sin^{3}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}{15}-\frac{1904 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)}{15}-\frac{88 \sqrt{34}}{15}}{\cos \left(e x +d +\arctan \left(\frac{3}{5}\right)\right) \sqrt{\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+2}\, e}"," ",0,"(16/17*((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2)*17^(1/2)*((1+sin(e*x+d+arctan(3/5)))/(-34^(1/2)+17))^(1/2)*(-17*(sin(e*x+d+arctan(3/5))-1)/(34^(1/2)+17))^(1/2)*EllipticF(((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2),I*(1/(-34^(1/2)+17)*(34^(1/2)+17))^(1/2))*34^(1/2)+16*((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2)*17^(1/2)*((1+sin(e*x+d+arctan(3/5)))/(-34^(1/2)+17))^(1/2)*(-17*(sin(e*x+d+arctan(3/5))-1)/(34^(1/2)+17))^(1/2)*EllipticF(((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2),I*(1/(-34^(1/2)+17)*(34^(1/2)+17))^(1/2))-44*17^(1/2)*((1+sin(e*x+d+arctan(3/5)))/(-34^(1/2)+17))^(1/2)*(-17*(sin(e*x+d+arctan(3/5))-1)/(34^(1/2)+17))^(1/2)*(-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2)*EllipticF((-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2),I*((-34^(1/2)+17)/(34^(1/2)+17))^(1/2))*34^(1/2)+796/17*17^(1/2)*((1+sin(e*x+d+arctan(3/5)))/(-34^(1/2)+17))^(1/2)*(-17*(sin(e*x+d+arctan(3/5))-1)/(34^(1/2)+17))^(1/2)*(-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2)*EllipticE((-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2),I*((-34^(1/2)+17)/(34^(1/2)+17))^(1/2))*34^(1/2)-48*(-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2)*(-17*(sin(e*x+d+arctan(3/5))-1)/(34^(1/2)+17))^(1/2)*17^(1/2)*((1+sin(e*x+d+arctan(3/5)))/(-34^(1/2)+17))^(1/2)*EllipticF((-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2),I*((-34^(1/2)+17)/(34^(1/2)+17))^(1/2))+68/5*34^(1/2)*sin(e*x+d+arctan(3/5))^4-116/15*34^(1/2)*sin(e*x+d+arctan(3/5))^2+1904/15*sin(e*x+d+arctan(3/5))^3-1904/15*sin(e*x+d+arctan(3/5))-88/15*34^(1/2))/cos(e*x+d+arctan(3/5))/(34^(1/2)*sin(e*x+d+arctan(3/5))+2)^(1/2)/e","C"
404,1,686,181,0.458000," ","int((2+3*cos(e*x+d)+5*sin(e*x+d))^(3/2),x)","\frac{\frac{8 \sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}\, \sqrt{17}\, \sqrt{\frac{1+\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)}{-\sqrt{34}+17}}\, \sqrt{-\frac{17 \left(\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-1\right)}{\sqrt{34}+17}}\, \EllipticF \left(\sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}, i \sqrt{\frac{\sqrt{34}+17}{-\sqrt{34}+17}}\right) \sqrt{34}}{17}+8 \sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}\, \sqrt{17}\, \sqrt{\frac{1+\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)}{-\sqrt{34}+17}}\, \sqrt{-\frac{17 \left(\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-1\right)}{\sqrt{34}+17}}\, \EllipticF \left(\sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}, i \sqrt{\frac{\sqrt{34}+17}{-\sqrt{34}+17}}\right)+\frac{68 \left(\sin^{3}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}{3}-\frac{68 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)}{3}+\frac{4 \sqrt{34}\, \left(\sin^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}{3}-\frac{4 \sqrt{34}}{3}-4 \sqrt{17}\, \sqrt{\frac{1+\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)}{-\sqrt{34}+17}}\, \sqrt{-\frac{17 \left(\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-1\right)}{\sqrt{34}+17}}\, \sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}\, \EllipticF \left(\sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}, i \sqrt{\frac{-\sqrt{34}+17}{\sqrt{34}+17}}\right) \sqrt{34}-12 \sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}\, \sqrt{-\frac{17 \left(\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-1\right)}{\sqrt{34}+17}}\, \sqrt{17}\, \sqrt{\frac{1+\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)}{-\sqrt{34}+17}}\, \EllipticF \left(\sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}, i \sqrt{\frac{-\sqrt{34}+17}{\sqrt{34}+17}}\right)+\frac{80 \sqrt{17}\, \sqrt{\frac{1+\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)}{-\sqrt{34}+17}}\, \sqrt{-\frac{17 \left(\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-1\right)}{\sqrt{34}+17}}\, \sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}\, \EllipticE \left(\sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}, i \sqrt{\frac{-\sqrt{34}+17}{\sqrt{34}+17}}\right) \sqrt{34}}{17}}{\cos \left(e x +d +\arctan \left(\frac{3}{5}\right)\right) \sqrt{\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+2}\, e}"," ",0,"(8/17*((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2)*17^(1/2)*((1+sin(e*x+d+arctan(3/5)))/(-34^(1/2)+17))^(1/2)*(-17*(sin(e*x+d+arctan(3/5))-1)/(34^(1/2)+17))^(1/2)*EllipticF(((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2),I*(1/(-34^(1/2)+17)*(34^(1/2)+17))^(1/2))*34^(1/2)+8*((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2)*17^(1/2)*((1+sin(e*x+d+arctan(3/5)))/(-34^(1/2)+17))^(1/2)*(-17*(sin(e*x+d+arctan(3/5))-1)/(34^(1/2)+17))^(1/2)*EllipticF(((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2),I*(1/(-34^(1/2)+17)*(34^(1/2)+17))^(1/2))+68/3*sin(e*x+d+arctan(3/5))^3-68/3*sin(e*x+d+arctan(3/5))+4/3*34^(1/2)*sin(e*x+d+arctan(3/5))^2-4/3*34^(1/2)-4*17^(1/2)*((1+sin(e*x+d+arctan(3/5)))/(-34^(1/2)+17))^(1/2)*(-17*(sin(e*x+d+arctan(3/5))-1)/(34^(1/2)+17))^(1/2)*(-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2)*EllipticF((-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2),I*((-34^(1/2)+17)/(34^(1/2)+17))^(1/2))*34^(1/2)-12*(-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2)*(-17*(sin(e*x+d+arctan(3/5))-1)/(34^(1/2)+17))^(1/2)*17^(1/2)*((1+sin(e*x+d+arctan(3/5)))/(-34^(1/2)+17))^(1/2)*EllipticF((-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2),I*((-34^(1/2)+17)/(34^(1/2)+17))^(1/2))+80/17*17^(1/2)*((1+sin(e*x+d+arctan(3/5)))/(-34^(1/2)+17))^(1/2)*(-17*(sin(e*x+d+arctan(3/5))-1)/(34^(1/2)+17))^(1/2)*(-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2)*EllipticE((-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2),I*((-34^(1/2)+17)/(34^(1/2)+17))^(1/2))*34^(1/2))/cos(e*x+d+arctan(3/5))/(34^(1/2)*sin(e*x+d+arctan(3/5))+2)^(1/2)/e","C"
405,1,461,69,0.405000," ","int((2+3*cos(e*x+d)+5*sin(e*x+d))^(1/2),x)","\frac{2 \sqrt{-\frac{17 \left(\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-1\right)}{\sqrt{34}+17}}\, \sqrt{17}\, \sqrt{\frac{1+\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)}{-\sqrt{34}+17}}\, \left(15 \sqrt{34}\, \sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}\, \EllipticE \left(\sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}, i \sqrt{\frac{-\sqrt{34}+17}{\sqrt{34}+17}}\right)-17 \sqrt{34}\, \sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}\, \EllipticF \left(\sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}, i \sqrt{\frac{-\sqrt{34}+17}{\sqrt{34}+17}}\right)+2 \sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}\, \EllipticF \left(\sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}, i \sqrt{\frac{\sqrt{34}+17}{-\sqrt{34}+17}}\right) \sqrt{34}+34 \sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}\, \EllipticF \left(\sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}, i \sqrt{\frac{-\sqrt{34}+17}{\sqrt{34}+17}}\right)+34 \sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}\, \EllipticF \left(\sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}, i \sqrt{\frac{\sqrt{34}+17}{-\sqrt{34}+17}}\right)\right)}{17 \cos \left(e x +d +\arctan \left(\frac{3}{5}\right)\right) \sqrt{\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+2}\, e}"," ",0,"2/17*(-17*(sin(e*x+d+arctan(3/5))-1)/(34^(1/2)+17))^(1/2)*17^(1/2)*((1+sin(e*x+d+arctan(3/5)))/(-34^(1/2)+17))^(1/2)*(15*34^(1/2)*(-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2)*EllipticE((-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2),I*((-34^(1/2)+17)/(34^(1/2)+17))^(1/2))-17*34^(1/2)*(-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2)*EllipticF((-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2),I*((-34^(1/2)+17)/(34^(1/2)+17))^(1/2))+2*((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2)*EllipticF(((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2),I*(1/(-34^(1/2)+17)*(34^(1/2)+17))^(1/2))*34^(1/2)+34*(-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2)*EllipticF((-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2),I*((-34^(1/2)+17)/(34^(1/2)+17))^(1/2))+34*((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2)*EllipticF(((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2),I*(1/(-34^(1/2)+17)*(34^(1/2)+17))^(1/2)))/cos(e*x+d+arctan(3/5))/(34^(1/2)*sin(e*x+d+arctan(3/5))+2)^(1/2)/e","C"
406,1,152,69,0.314000," ","int(1/(2+3*cos(e*x+d)+5*sin(e*x+d))^(1/2),x)","\frac{2 \left(\sqrt{34}+17\right) \sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}\, \sqrt{17}\, \sqrt{\frac{1+\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)}{-\sqrt{34}+17}}\, \sqrt{-\frac{17 \left(\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-1\right)}{\sqrt{34}+17}}\, \EllipticF \left(\sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}, i \sqrt{\frac{\sqrt{34}+17}{-\sqrt{34}+17}}\right)}{17 \cos \left(e x +d +\arctan \left(\frac{3}{5}\right)\right) \sqrt{\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+2}\, e}"," ",0,"2/17*(34^(1/2)+17)*((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2)*17^(1/2)*((1+sin(e*x+d+arctan(3/5)))/(-34^(1/2)+17))^(1/2)*(-17*(sin(e*x+d+arctan(3/5))-1)/(34^(1/2)+17))^(1/2)*EllipticF(((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2),I*(1/(-34^(1/2)+17)*(34^(1/2)+17))^(1/2))/cos(e*x+d+arctan(3/5))/(34^(1/2)*sin(e*x+d+arctan(3/5))+2)^(1/2)/e","C"
407,1,437,112,0.490000," ","int(1/(2+3*cos(e*x+d)+5*sin(e*x+d))^(3/2),x)","\frac{\sqrt{34}\, \left(255 \sqrt{\left(17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}\right) \sqrt{34}\, \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}\, \sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}\, \sqrt{-\frac{17 \left(\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-1\right)}{\sqrt{34}+17}}\, \sqrt{\frac{1+\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)}{-\sqrt{34}+17}}\, \EllipticF \left(\sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}, i \sqrt{\frac{-\sqrt{34}+17}{\sqrt{34}+17}}\right)-255 \sqrt{\left(17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}\right) \sqrt{34}\, \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}\, \sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}\, \sqrt{-\frac{17 \left(\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-1\right)}{\sqrt{34}+17}}\, \sqrt{\frac{1+\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)}{-\sqrt{34}+17}}\, \EllipticE \left(\sqrt{-\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{-\sqrt{34}+17}}, i \sqrt{\frac{-\sqrt{34}+17}{\sqrt{34}+17}}\right)+289 \sqrt{\left(\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+2\right) \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}\, \left(\sin^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)-289 \sqrt{\left(\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+2\right) \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}\right) \sqrt{17}}{4335 \sqrt{\left(17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}\right) \sqrt{34}\, \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}\, \cos \left(e x +d +\arctan \left(\frac{3}{5}\right)\right) \sqrt{\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+2}\, e}"," ",0,"1/4335*34^(1/2)*(255*((17*sin(e*x+d+arctan(3/5))+34^(1/2))*34^(1/2)*cos(e*x+d+arctan(3/5))^2)^(1/2)*(-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2)*(-17*(sin(e*x+d+arctan(3/5))-1)/(34^(1/2)+17))^(1/2)*((1+sin(e*x+d+arctan(3/5)))/(-34^(1/2)+17))^(1/2)*EllipticF((-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2),I*((-34^(1/2)+17)/(34^(1/2)+17))^(1/2))-255*((17*sin(e*x+d+arctan(3/5))+34^(1/2))*34^(1/2)*cos(e*x+d+arctan(3/5))^2)^(1/2)*(-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2)*(-17*(sin(e*x+d+arctan(3/5))-1)/(34^(1/2)+17))^(1/2)*((1+sin(e*x+d+arctan(3/5)))/(-34^(1/2)+17))^(1/2)*EllipticE((-(17*sin(e*x+d+arctan(3/5))+34^(1/2))/(-34^(1/2)+17))^(1/2),I*((-34^(1/2)+17)/(34^(1/2)+17))^(1/2))+289*((34^(1/2)*sin(e*x+d+arctan(3/5))+2)*cos(e*x+d+arctan(3/5))^2)^(1/2)*sin(e*x+d+arctan(3/5))^2-289*((34^(1/2)*sin(e*x+d+arctan(3/5))+2)*cos(e*x+d+arctan(3/5))^2)^(1/2))*17^(1/2)/((17*sin(e*x+d+arctan(3/5))+34^(1/2))*34^(1/2)*cos(e*x+d+arctan(3/5))^2)^(1/2)/cos(e*x+d+arctan(3/5))/(34^(1/2)*sin(e*x+d+arctan(3/5))+2)^(1/2)/e","C"
408,1,542,223,0.606000," ","int(1/(2+3*cos(e*x+d)+5*sin(e*x+d))^(5/2),x)","\frac{\sqrt{-\left(-\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-2\right) \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}\, \left(-\frac{\sqrt{34}\, \sqrt{-\left(-\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-2\right) \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}}{1530 \left(\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\frac{\sqrt{34}}{17}\right)^{2}}+\frac{68 \sqrt{34}\, \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}{675 \sqrt{-\left(-289 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-17 \sqrt{34}\right) \sqrt{34}\, \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}}+\frac{23 \left(-1+\frac{\sqrt{34}}{17}\right) \sqrt{\frac{-17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-\sqrt{34}}{-\sqrt{34}+17}}\, \sqrt{\frac{-17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+17}{\sqrt{34}+17}}\, \sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+17}{-\sqrt{34}+17}}\, \EllipticF \left(\sqrt{\frac{-17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-\sqrt{34}}{-\sqrt{34}+17}}, i \sqrt{\frac{-\sqrt{34}+17}{\sqrt{34}+17}}\right)}{675 \sqrt{-\left(-\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-2\right) \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}}+\frac{4 \sqrt{34}\, \left(-1+\frac{\sqrt{34}}{17}\right) \sqrt{\frac{-17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-\sqrt{34}}{-\sqrt{34}+17}}\, \sqrt{\frac{-17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+17}{\sqrt{34}+17}}\, \sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+17}{-\sqrt{34}+17}}\, \left(\left(-\frac{\sqrt{34}}{17}-1\right) \EllipticE \left(\sqrt{\frac{-17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-\sqrt{34}}{-\sqrt{34}+17}}, i \sqrt{\frac{-\sqrt{34}+17}{\sqrt{34}+17}}\right)+\EllipticF \left(\sqrt{\frac{-17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-\sqrt{34}}{-\sqrt{34}+17}}, i \sqrt{\frac{-\sqrt{34}+17}{\sqrt{34}+17}}\right)\right)}{675 \sqrt{-\left(-\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-2\right) \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}}\right)}{\cos \left(e x +d +\arctan \left(\frac{3}{5}\right)\right) \sqrt{\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+2}\, e}"," ",0,"(-(-34^(1/2)*sin(e*x+d+arctan(3/5))-2)*cos(e*x+d+arctan(3/5))^2)^(1/2)*(-1/1530*34^(1/2)*(-(-34^(1/2)*sin(e*x+d+arctan(3/5))-2)*cos(e*x+d+arctan(3/5))^2)^(1/2)/(sin(e*x+d+arctan(3/5))+1/17*34^(1/2))^2+68/675*34^(1/2)*cos(e*x+d+arctan(3/5))^2/(-(-289*sin(e*x+d+arctan(3/5))-17*34^(1/2))*34^(1/2)*cos(e*x+d+arctan(3/5))^2)^(1/2)+23/675*(-1+1/17*34^(1/2))*((-17*sin(e*x+d+arctan(3/5))-34^(1/2))/(-34^(1/2)+17))^(1/2)*((-17*sin(e*x+d+arctan(3/5))+17)/(34^(1/2)+17))^(1/2)*((17*sin(e*x+d+arctan(3/5))+17)/(-34^(1/2)+17))^(1/2)/(-(-34^(1/2)*sin(e*x+d+arctan(3/5))-2)*cos(e*x+d+arctan(3/5))^2)^(1/2)*EllipticF(((-17*sin(e*x+d+arctan(3/5))-34^(1/2))/(-34^(1/2)+17))^(1/2),I*((-34^(1/2)+17)/(34^(1/2)+17))^(1/2))+4/675*34^(1/2)*(-1+1/17*34^(1/2))*((-17*sin(e*x+d+arctan(3/5))-34^(1/2))/(-34^(1/2)+17))^(1/2)*((-17*sin(e*x+d+arctan(3/5))+17)/(34^(1/2)+17))^(1/2)*((17*sin(e*x+d+arctan(3/5))+17)/(-34^(1/2)+17))^(1/2)/(-(-34^(1/2)*sin(e*x+d+arctan(3/5))-2)*cos(e*x+d+arctan(3/5))^2)^(1/2)*((-1/17*34^(1/2)-1)*EllipticE(((-17*sin(e*x+d+arctan(3/5))-34^(1/2))/(-34^(1/2)+17))^(1/2),I*((-34^(1/2)+17)/(34^(1/2)+17))^(1/2))+EllipticF(((-17*sin(e*x+d+arctan(3/5))-34^(1/2))/(-34^(1/2)+17))^(1/2),I*((-34^(1/2)+17)/(34^(1/2)+17))^(1/2))))/cos(e*x+d+arctan(3/5))/(34^(1/2)*sin(e*x+d+arctan(3/5))+2)^(1/2)/e","C"
409,1,571,265,0.626000," ","int(1/(2+3*cos(e*x+d)+5*sin(e*x+d))^(7/2),x)","\frac{\sqrt{-\left(-\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-2\right) \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}\, \left(-\frac{\sqrt{-\left(-\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-2\right) \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}}{2550 \left(\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\frac{\sqrt{34}}{17}\right)^{3}}+\frac{4 \sqrt{34}\, \sqrt{-\left(-\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-2\right) \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}}{57375 \left(\sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\frac{\sqrt{34}}{17}\right)^{2}}-\frac{3383 \sqrt{34}\, \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}{101250 \sqrt{-\left(-289 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-17 \sqrt{34}\right) \sqrt{34}\, \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}}-\frac{319 \left(\frac{\sqrt{34}}{17}+1\right) \sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}\, \sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+17}{-\sqrt{34}+17}}\, \sqrt{\frac{-17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+17}{\sqrt{34}+17}}\, \EllipticF \left(\sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}, i \sqrt{\frac{\sqrt{34}+17}{-\sqrt{34}+17}}\right)}{50625 \sqrt{-\left(-\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-2\right) \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}}-\frac{199 \sqrt{34}\, \left(\frac{\sqrt{34}}{17}+1\right) \sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}\, \sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+17}{-\sqrt{34}+17}}\, \sqrt{\frac{-17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+17}{\sqrt{34}+17}}\, \left(\left(-\frac{\sqrt{34}}{17}+1\right) \EllipticE \left(\sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}, i \sqrt{\frac{\sqrt{34}+17}{-\sqrt{34}+17}}\right)-\EllipticF \left(\sqrt{\frac{17 \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+\sqrt{34}}{\sqrt{34}+17}}, i \sqrt{\frac{\sqrt{34}+17}{-\sqrt{34}+17}}\right)\right)}{101250 \sqrt{-\left(-\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)-2\right) \left(\cos^{2}\left(e x +d +\arctan \left(\frac{3}{5}\right)\right)\right)}}\right)}{\cos \left(e x +d +\arctan \left(\frac{3}{5}\right)\right) \sqrt{\sqrt{34}\, \sin \left(e x +d +\arctan \left(\frac{3}{5}\right)\right)+2}\, e}"," ",0,"(-(-34^(1/2)*sin(e*x+d+arctan(3/5))-2)*cos(e*x+d+arctan(3/5))^2)^(1/2)*(-1/2550*(-(-34^(1/2)*sin(e*x+d+arctan(3/5))-2)*cos(e*x+d+arctan(3/5))^2)^(1/2)/(sin(e*x+d+arctan(3/5))+1/17*34^(1/2))^3+4/57375*34^(1/2)*(-(-34^(1/2)*sin(e*x+d+arctan(3/5))-2)*cos(e*x+d+arctan(3/5))^2)^(1/2)/(sin(e*x+d+arctan(3/5))+1/17*34^(1/2))^2-3383/101250*34^(1/2)*cos(e*x+d+arctan(3/5))^2/(-(-289*sin(e*x+d+arctan(3/5))-17*34^(1/2))*34^(1/2)*cos(e*x+d+arctan(3/5))^2)^(1/2)-319/50625*(1/17*34^(1/2)+1)*((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2)*((17*sin(e*x+d+arctan(3/5))+17)/(-34^(1/2)+17))^(1/2)*((-17*sin(e*x+d+arctan(3/5))+17)/(34^(1/2)+17))^(1/2)/(-(-34^(1/2)*sin(e*x+d+arctan(3/5))-2)*cos(e*x+d+arctan(3/5))^2)^(1/2)*EllipticF(((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2),I*(1/(-34^(1/2)+17)*(34^(1/2)+17))^(1/2))-199/101250*34^(1/2)*(1/17*34^(1/2)+1)*((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2)*((17*sin(e*x+d+arctan(3/5))+17)/(-34^(1/2)+17))^(1/2)*((-17*sin(e*x+d+arctan(3/5))+17)/(34^(1/2)+17))^(1/2)/(-(-34^(1/2)*sin(e*x+d+arctan(3/5))-2)*cos(e*x+d+arctan(3/5))^2)^(1/2)*((-1/17*34^(1/2)+1)*EllipticE(((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2),I*(1/(-34^(1/2)+17)*(34^(1/2)+17))^(1/2))-EllipticF(((17*sin(e*x+d+arctan(3/5))+34^(1/2))/(34^(1/2)+17))^(1/2),I*(1/(-34^(1/2)+17)*(34^(1/2)+17))^(1/2))))/cos(e*x+d+arctan(3/5))/(34^(1/2)*sin(e*x+d+arctan(3/5))+2)^(1/2)/e","C"
410,1,2303,394,1.003000," ","int((a+b*cos(e*x+d)+c*sin(e*x+d))^(5/2),x)","\frac{\sqrt{-\frac{\left(-b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)-c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a \sqrt{b^{2}+c^{2}}\right) \left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)}{\sqrt{b^{2}+c^{2}}}}\, \left(\left(b^{2}+c^{2}\right)^{\frac{3}{2}} \left(-\frac{2 \sin \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \right)}}{5 \sqrt{b^{2}+c^{2}}}+\frac{8 a \sqrt{\left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \right)}}{15 \left(b^{2}+c^{2}\right)}+\frac{4 a \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)}{15 \sqrt{b^{2}+c^{2}}\, \sqrt{\left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \right)}}+\frac{2 \left(\frac{3}{5}+\frac{8 a^{2}}{15 \left(b^{2}+c^{2}\right)}\right) \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \left(\left(-\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \EllipticE \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)+\EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)\right)}{\sqrt{\left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \right)}}\right)+\left(3 a \,b^{2}+3 a \,c^{2}\right) \left(-\frac{2 \sqrt{\left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \right)}}{3 \sqrt{b^{2}+c^{2}}}+\frac{2 \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)}{3 \sqrt{\left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \right)}}-\frac{4 a \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \left(\left(-\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \EllipticE \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)+\EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)\right)}{3 \sqrt{b^{2}+c^{2}}\, \sqrt{\left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \right)}}\right)+\frac{6 a^{2} \sqrt{b^{2}+c^{2}}\, \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \left(\left(-\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \EllipticE \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)+\EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)\right)}{\sqrt{\left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \right)}}+\frac{2 a^{3} \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)}{\sqrt{-\frac{\left(-b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)-c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a \sqrt{b^{2}+c^{2}}\right) \left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)}{\sqrt{b^{2}+c^{2}}}}}\right)}{\cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \sqrt{b^{2}+c^{2}}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"(-(-b^2*sin(e*x+d-arctan(-b,c))-c^2*sin(e*x+d-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(e*x+d-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)*((b^2+c^2)^(3/2)*(-2/5/(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))*(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)+8/15/(b^2+c^2)*a*(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)+4/15/(b^2+c^2)^(1/2)*a*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+2*(3/5+8/15/(b^2+c^2)*a^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))))+(3*a*b^2+3*a*c^2)*(-2/3/(b^2+c^2)^(1/2)*(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)+2/3*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))-4/3/(b^2+c^2)^(1/2)*a*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))))+6*a^2*(b^2+c^2)^(1/2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))+2*a^3*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-b^2*sin(e*x+d-arctan(-b,c))-c^2*sin(e*x+d-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(e*x+d-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))+a*(b^2+c^2)^(1/2))/(b^2+c^2)^(1/2))^(1/2)/e","B"
411,1,1516,333,0.708000," ","int((a+b*cos(e*x+d)+c*sin(e*x+d))^(3/2),x)","\frac{\sqrt{-\frac{\left(-b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)-c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a \sqrt{b^{2}+c^{2}}\right) \left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)}{\sqrt{b^{2}+c^{2}}}}\, \left(\left(b^{2}+c^{2}\right) \left(-\frac{2 \sqrt{\left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \right)}}{3 \sqrt{b^{2}+c^{2}}}+\frac{2 \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)}{3 \sqrt{\left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \right)}}-\frac{4 a \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \left(\left(-\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \EllipticE \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)+\EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)\right)}{3 \sqrt{b^{2}+c^{2}}\, \sqrt{\left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \right)}}\right)+\frac{4 a \sqrt{b^{2}+c^{2}}\, \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \left(\left(-\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \EllipticE \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)+\EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)\right)}{\sqrt{\left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \right)}}+\frac{2 a^{2} \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)}{\sqrt{-\frac{\left(-b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)-c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a \sqrt{b^{2}+c^{2}}\right) \left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)}{\sqrt{b^{2}+c^{2}}}}}\right)}{\cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \sqrt{b^{2}+c^{2}}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"(-(-b^2*sin(e*x+d-arctan(-b,c))-c^2*sin(e*x+d-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(e*x+d-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)*((b^2+c^2)*(-2/3/(b^2+c^2)^(1/2)*(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)+2/3*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))-4/3/(b^2+c^2)^(1/2)*a*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))))+4*a*(b^2+c^2)^(1/2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))+2*a^2*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-b^2*sin(e*x+d-arctan(-b,c))-c^2*sin(e*x+d-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(e*x+d-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))+a*(b^2+c^2)^(1/2))/(b^2+c^2)^(1/2))^(1/2)/e","B"
412,1,720,137,0.460000," ","int((a+b*cos(e*x+d)+c*sin(e*x+d))^(1/2),x)","\frac{2 \left(-a +\sqrt{b^{2}+c^{2}}\right) \sqrt{-\frac{\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{-\frac{\left(\sin \left(e x +d -\arctan \left(-b , c\right)\right)-1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right) \left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)+\left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) a}\, \left(\sqrt{b^{2}+c^{2}}\, \EllipticE \left(\sqrt{-\frac{\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)}{-a +\sqrt{b^{2}+c^{2}}}-\frac{a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{-\frac{-a +\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)-\sqrt{b^{2}+c^{2}}\, \EllipticF \left(\sqrt{-\frac{\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)}{-a +\sqrt{b^{2}+c^{2}}}-\frac{a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{-\frac{-a +\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)+\EllipticE \left(\sqrt{-\frac{\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)}{-a +\sqrt{b^{2}+c^{2}}}-\frac{a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{-\frac{-a +\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right) a -\EllipticF \left(\sqrt{-\frac{\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)}{-a +\sqrt{b^{2}+c^{2}}}-\frac{a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{-\frac{-a +\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right) a \right)}{\sqrt{b^{2}+c^{2}}\, \sqrt{\left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \right)}\, \cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \sqrt{b^{2}+c^{2}}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"2/(b^2+c^2)^(1/2)*(-a+(b^2+c^2)^(1/2))*(-((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*(-(sin(e*x+d-arctan(-b,c))-1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))*cos(e*x+d-arctan(-b,c))^2+cos(e*x+d-arctan(-b,c))^2*a)^(1/2)*((b^2+c^2)^(1/2)*EllipticE((-(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2))*sin(e*x+d-arctan(-b,c))-a/(-a+(b^2+c^2)^(1/2)))^(1/2),(-(-a+(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))-(b^2+c^2)^(1/2)*EllipticF((-(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2))*sin(e*x+d-arctan(-b,c))-a/(-a+(b^2+c^2)^(1/2)))^(1/2),(-(-a+(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticE((-(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2))*sin(e*x+d-arctan(-b,c))-a/(-a+(b^2+c^2)^(1/2)))^(1/2),(-(-a+(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))*a-EllipticF((-(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2))*sin(e*x+d-arctan(-b,c))-a/(-a+(b^2+c^2)^(1/2)))^(1/2),(-(-a+(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))*a)/(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))+a*(b^2+c^2)^(1/2))/(b^2+c^2)^(1/2))^(1/2)/e","B"
413,1,303,137,0.366000," ","int(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^(1/2),x)","-\frac{2 \left(-a +\sqrt{b^{2}+c^{2}}\right) \sqrt{-\frac{\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{-\frac{\left(\sin \left(e x +d -\arctan \left(-b , c\right)\right)-1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \EllipticF \left(\sqrt{-\frac{\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{-\frac{-a +\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)}{\sqrt{b^{2}+c^{2}}\, \cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \sqrt{b^{2}+c^{2}}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"-2*(-a+(b^2+c^2)^(1/2))*(-((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*(-(sin(e*x+d-arctan(-b,c))-1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)*EllipticF((-((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a)/(-a+(b^2+c^2)^(1/2)))^(1/2),(-(-a+(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))/(b^2+c^2)^(1/2)/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))+a*(b^2+c^2)^(1/2))/(b^2+c^2)^(1/2))^(1/2)/e","B"
414,1,2388,213,0.773000," ","int(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^(3/2),x)","\frac{\sqrt{-\frac{\left(-b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)-c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a \sqrt{b^{2}+c^{2}}\right) \left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)}{\sqrt{b^{2}+c^{2}}}}\, \left(-\frac{\sqrt{b^{2}+c^{2}}\, \left(-b^{2}-c^{2}\right) \left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)}{\left(a^{2}-b^{2}-c^{2}\right) \sqrt{-\left(-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a \right) \left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(b^{2}+c^{2}\right)}}+\frac{a \left(b^{2}+c^{2}\right) \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)}{\left(a^{2}-b^{2}-c^{2}\right) \sqrt{-\left(-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a \right) \left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(b^{2}+c^{2}\right)}}+\frac{2 \left(-\left(b^{2}+c^{2}\right)^{\frac{3}{2}}+2 \sqrt{b^{2}+c^{2}}\, b^{2}+2 \sqrt{b^{2}+c^{2}}\, c^{2}\right) \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \left(\left(-\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \EllipticE \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)+\EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)\right)}{\left(2 a^{2}-2 b^{2}-2 c^{2}\right) \sqrt{-\left(-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a \right) \left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(b^{2}+c^{2}\right)}}+\frac{\left(b^{2}+c^{2}\right) \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \EllipticPi \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, -\frac{\left(-\frac{a}{\sqrt{b^{2}+c^{2}}}+1\right) \sqrt{b^{2}+c^{2}}}{2 a}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)}{2 \sqrt{-\left(-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a \right) \left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(b^{2}+c^{2}\right)}\, a}+\frac{\left(b^{2}+c^{2}\right) \left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)}{\left(a^{2}-b^{2}-c^{2}\right) \sqrt{-\left(-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a \right) \left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)}}+\frac{\sqrt{b^{2}+c^{2}}\, a \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)}{\left(a^{2}-b^{2}-c^{2}\right) \sqrt{-\left(-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a \right) \left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)}}+\frac{\left(b^{2}+c^{2}\right) \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \left(\left(-\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \EllipticE \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)+\EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)\right)}{\left(a^{2}-b^{2}-c^{2}\right) \sqrt{-\left(-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a \right) \left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)}}-\frac{\left(\frac{b^{2}}{2}+\frac{c^{2}}{2}\right) \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \EllipticPi \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, -\frac{\left(-\frac{a}{\sqrt{b^{2}+c^{2}}}+1\right) \sqrt{b^{2}+c^{2}}}{2 a}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)}{\sqrt{b^{2}+c^{2}}\, \sqrt{-\left(-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-a \right) \left(\cos^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)}\, a}\right)}{\sqrt{b^{2}+c^{2}}\, \cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+a \sqrt{b^{2}+c^{2}}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"(-(-b^2*sin(e*x+d-arctan(-b,c))-c^2*sin(e*x+d-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(e*x+d-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)/(b^2+c^2)^(1/2)*(-(b^2+c^2)^(1/2)*(-b^2-c^2)*cos(e*x+d-arctan(-b,c))^2/(a^2-b^2-c^2)/(-(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)*cos(e*x+d-arctan(-b,c))^2*(b^2+c^2))^(1/2)+a*(b^2+c^2)/(a^2-b^2-c^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)*cos(e*x+d-arctan(-b,c))^2*(b^2+c^2))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+2*(-(b^2+c^2)^(3/2)+2*(b^2+c^2)^(1/2)*b^2+2*(b^2+c^2)^(1/2)*c^2)/(2*a^2-2*b^2-2*c^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)*cos(e*x+d-arctan(-b,c))^2*(b^2+c^2))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))+1/2*(b^2+c^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)*cos(e*x+d-arctan(-b,c))^2*(b^2+c^2))^(1/2)/a*EllipticPi(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),-1/2*(-1/(b^2+c^2)^(1/2)*a+1)*(b^2+c^2)^(1/2)/a,((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+(b^2+c^2)*cos(e*x+d-arctan(-b,c))^2/(a^2-b^2-c^2)/(-(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)*cos(e*x+d-arctan(-b,c))^2)^(1/2)+1/(a^2-b^2-c^2)*(b^2+c^2)^(1/2)*a*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)*cos(e*x+d-arctan(-b,c))^2)^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+1/(a^2-b^2-c^2)*(b^2+c^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)*cos(e*x+d-arctan(-b,c))^2)^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))-(1/2*b^2+1/2*c^2)/(b^2+c^2)^(1/2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)*cos(e*x+d-arctan(-b,c))^2)^(1/2)/a*EllipticPi(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),-1/2*(-1/(b^2+c^2)^(1/2)*a+1)*(b^2+c^2)^(1/2)/a,((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))+a*(b^2+c^2)^(1/2))/(b^2+c^2)^(1/2))^(1/2)/e","B"
415,1,2967,428,2.135000," ","int(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^(5/2),x)","\text{output too large to display}"," ",0,"(-(-b^2*sin(e*x+d-arctan(-b,c))-c^2*sin(e*x+d-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(e*x+d-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)*(-1/4/a/(a^2-b^2-c^2)*(b^2+c^2)^(1/2)*(cos(e*x+d-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)/(b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))-a*(b^2+c^2)^(1/2))+1/3/(a^2-b^2-c^2)/(b^2+c^2)*(cos(e*x+d-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)/(sin(e*x+d-arctan(-b,c))+1/(b^2+c^2)^(1/2)*a)^2-4/3*(-b^2-c^2)*cos(e*x+d-arctan(-b,c))^2/(a^2-b^2-c^2)^2*a/(cos(e*x+d-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)+2*(-1/24*(b^2+c^2)^(1/2)/(a^2-b^2-c^2)+2/3*a^2*(b^2+c^2)^(1/2)/(a^2-b^2-c^2)^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+2*(13*a^2*b^2+13*a^2*c^2+3*b^4+6*b^2*c^2+3*c^4)/(24*a^5-48*a^3*b^2-48*a^3*c^2+24*a*b^4+48*a*b^2*c^2+24*a*c^4)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))-1/8*(5*a^2*b^2+5*a^2*c^2-b^4-2*b^2*c^2-c^4)/a^2/(a^2-b^2-c^2)/(b^2+c^2)^(1/2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*EllipticPi(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),-1/2*(-1/(b^2+c^2)^(1/2)*a+1)*(b^2+c^2)^(1/2)/a,((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+1/4*(b^2+c^2)/a/(a^2-b^2-c^2)*(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)/(b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))-a*(b^2+c^2)^(1/2))+1/3/(a^2-b^2-c^2)/(b^2+c^2)^(1/2)*(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)/(sin(e*x+d-arctan(-b,c))+1/(b^2+c^2)^(1/2)*a)^2+4/3*(b^2+c^2)^(1/2)*cos(e*x+d-arctan(-b,c))^2/(a^2-b^2-c^2)^2*a/(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)+2*(-7/24/(a^2-b^2-c^2)+2/3*a^2/(a^2-b^2-c^2)^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+2*(1/8/a/(a^2-b^2-c^2)*(b^2+c^2)^(1/2)+2/3*a*(b^2+c^2)^(1/2)/(a^2-b^2-c^2)^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))+1/8*(5*a^2-b^2-c^2)/a^2/(a^2-b^2-c^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*EllipticPi(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),-1/2*(-1/(b^2+c^2)^(1/2)*a+1)*(b^2+c^2)^(1/2)/a,((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))+a*(b^2+c^2)^(1/2))/(b^2+c^2)^(1/2))^(1/2)/e","B"
416,1,3876,535,6.686000," ","int(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^(7/2),x)","\text{output too large to display}"," ",0,"(-(-b^2*sin(e*x+d-arctan(-b,c))-c^2*sin(e*x+d-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(e*x+d-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)/(b^2+c^2)^(1/2)*(-1/8/a/(a^2-b^2-c^2)*(b^2+c^2)^(3/2)*(cos(e*x+d-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)/(b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))-a*(b^2+c^2)^(1/2))^2+1/5/(a^2-b^2-c^2)/(b^2+c^2)*(cos(e*x+d-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)/(sin(e*x+d-arctan(-b,c))+1/(b^2+c^2)^(1/2)*a)^3+3/32*(5*a^2*b^2+5*a^2*c^2-b^4-2*b^2*c^2-c^4)/(a^2-b^2-c^2)^2/a^2*(cos(e*x+d-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)/(b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))-a*(b^2+c^2)^(1/2))+8/15/(a^2-b^2-c^2)^2*a/(b^2+c^2)^(1/2)*(cos(e*x+d-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)/(sin(e*x+d-arctan(-b,c))+1/(b^2+c^2)^(1/2)*a)^2-1/15*(b^2+c^2)^(1/2)*(-b^2-c^2)*cos(e*x+d-arctan(-b,c))^2/(a^2-b^2-c^2)^3*(23*a^2+9*b^2+9*c^2)/(cos(e*x+d-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)+2*(-1/64*(11*a^2*b^2+11*a^2*c^2+b^4+2*b^2*c^2+c^4)/a/(a^2-b^2-c^2)^2-4/15*a*(b^2+c^2)/(a^2-b^2-c^2)^2+1/30*a*(b^2+c^2)*(23*a^2+9*b^2+9*c^2)/(a^2-b^2-c^2)^3)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+2*(3/64*(5*a^2*b^2+5*a^2*c^2-b^4-2*b^2*c^2-c^4)*(b^2+c^2)^(1/2)/(a^2-b^2-c^2)^2/a^2-1/30*(b^2+c^2)^(3/2)*(23*a^2+9*b^2+9*c^2)/(a^2-b^2-c^2)^3+1/30*(b^2+c^2)^(1/2)*(2*b^2+2*c^2)/(a^2-b^2-c^2)^3*(23*a^2+9*b^2+9*c^2))*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))+1/64*(43*a^4*b^2+43*a^4*c^2+2*a^2*b^4+4*a^2*b^2*c^2+2*a^2*c^4+3*b^6+9*b^4*c^2+9*b^2*c^4+3*c^6)/(a^2-b^2-c^2)^2/a^3*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*EllipticPi(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),-1/2*(-1/(b^2+c^2)^(1/2)*a+1)*(b^2+c^2)^(1/2)/a,((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+1/8/a*(b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)*(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)/(b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))-a*(b^2+c^2)^(1/2))^2+1/5/(a^2-b^2-c^2)/(b^2+c^2)^(1/2)*(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)/(sin(e*x+d-arctan(-b,c))+1/(b^2+c^2)^(1/2)*a)^3-3/32*(5*a^2*b^2+5*a^2*c^2-b^4-2*b^2*c^2-c^4)*(b^2+c^2)^(1/2)/(a^2-b^2-c^2)^2/a^2*(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)/(b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))-a*(b^2+c^2)^(1/2))+8/15/(a^2-b^2-c^2)^2*a*(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)/(sin(e*x+d-arctan(-b,c))+1/(b^2+c^2)^(1/2)*a)^2+1/15*(b^2+c^2)*cos(e*x+d-arctan(-b,c))^2/(a^2-b^2-c^2)^3*(23*a^2+9*b^2+9*c^2)/(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)+2*(1/64*(11*a^2+b^2+c^2)*(b^2+c^2)^(1/2)/a/(a^2-b^2-c^2)^2-4/15*a*(b^2+c^2)^(1/2)/(a^2-b^2-c^2)^2+1/30*a*(b^2+c^2)^(1/2)*(23*a^2+9*b^2+9*c^2)/(a^2-b^2-c^2)^3)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+2*(-3/64*(5*a^2*b^2+5*a^2*c^2-b^4-2*b^2*c^2-c^4)/(a^2-b^2-c^2)^2/a^2+1/30*(b^2+c^2)*(23*a^2+9*b^2+9*c^2)/(a^2-b^2-c^2)^3)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))-1/64*(43*a^4*b^2+43*a^4*c^2+2*a^2*b^4+4*a^2*b^2*c^2+2*a^2*c^4+3*b^6+9*b^4*c^2+9*b^2*c^4+3*c^6)/(a^2-b^2-c^2)^2/a^3/(b^2+c^2)^(1/2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(e*x+d-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(e*x+d-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+a))^(1/2)*EllipticPi(((-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),-1/2*(-1/(b^2+c^2)^(1/2)*a+1)*(b^2+c^2)^(1/2)/a,((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))+a*(b^2+c^2)^(1/2))/(b^2+c^2)^(1/2))^(1/2)/e","B"
417,1,74,127,0.367000," ","int((5+4*cos(e*x+d)+3*sin(e*x+d))^(5/2),x)","\frac{50 \left(1+\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)\right) \left(\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-1\right) \left(3 \left(\sin^{2}\left(e x +d +\arctan \left(\frac{4}{3}\right)\right)\right)+14 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+43\right)}{3 \cos \left(e x +d +\arctan \left(\frac{4}{3}\right)\right) \sqrt{5+5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)}\, e}"," ",0,"50/3*(1+sin(e*x+d+arctan(4/3)))*(sin(e*x+d+arctan(4/3))-1)*(3*sin(e*x+d+arctan(4/3))^2+14*sin(e*x+d+arctan(4/3))+43)/cos(e*x+d+arctan(4/3))/(5+5*sin(e*x+d+arctan(4/3)))^(1/2)/e","A"
418,1,60,85,0.346000," ","int((5+4*cos(e*x+d)+3*sin(e*x+d))^(3/2),x)","\frac{50 \left(1+\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)\right) \left(\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-1\right) \left(\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+5\right)}{3 \cos \left(e x +d +\arctan \left(\frac{4}{3}\right)\right) \sqrt{5+5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)}\, e}"," ",0,"50/3*(1+sin(e*x+d+arctan(4/3)))*(sin(e*x+d+arctan(4/3))-1)*(sin(e*x+d+arctan(4/3))+5)/cos(e*x+d+arctan(4/3))/(5+5*sin(e*x+d+arctan(4/3)))^(1/2)/e","A"
419,1,50,42,0.297000," ","int((5+4*cos(e*x+d)+3*sin(e*x+d))^(1/2),x)","\frac{10 \left(\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-1\right) \left(1+\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)\right)}{\cos \left(e x +d +\arctan \left(\frac{4}{3}\right)\right) \sqrt{5+5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)}\, e}"," ",0,"10*(sin(e*x+d+arctan(4/3))-1)*(1+sin(e*x+d+arctan(4/3)))/cos(e*x+d+arctan(4/3))/(5+5*sin(e*x+d+arctan(4/3)))^(1/2)/e","A"
420,1,77,38,0.254000," ","int(1/(5+4*cos(e*x+d)+3*sin(e*x+d))^(1/2),x)","-\frac{\left(1+\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)\right) \sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+5}\, \sqrt{10}\, \arctanh \left(\frac{\sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+5}\, \sqrt{10}}{10}\right)}{5 \cos \left(e x +d +\arctan \left(\frac{4}{3}\right)\right) \sqrt{5+5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)}\, e}"," ",0,"-1/5*(1+sin(e*x+d+arctan(4/3)))*(-5*sin(e*x+d+arctan(4/3))+5)^(1/2)*10^(1/2)*arctanh(1/10*(-5*sin(e*x+d+arctan(4/3))+5)^(1/2)*10^(1/2))/cos(e*x+d+arctan(4/3))/(5+5*sin(e*x+d+arctan(4/3)))^(1/2)/e","A"
421,1,117,81,0.313000," ","int(1/(5+4*cos(e*x+d)+3*sin(e*x+d))^(3/2),x)","-\frac{\left(\sqrt{10}\, \arctanh \left(\frac{\sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+5}\, \sqrt{10}}{10}\right) \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+\sqrt{10}\, \arctanh \left(\frac{\sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+5}\, \sqrt{10}}{10}\right)+2 \sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+5}\right) \sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+5}}{100 \cos \left(e x +d +\arctan \left(\frac{4}{3}\right)\right) \sqrt{5+5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)}\, e}"," ",0,"-1/100*(10^(1/2)*arctanh(1/10*(-5*sin(e*x+d+arctan(4/3))+5)^(1/2)*10^(1/2))*sin(e*x+d+arctan(4/3))+10^(1/2)*arctanh(1/10*(-5*sin(e*x+d+arctan(4/3))+5)^(1/2)*10^(1/2))+2*(-5*sin(e*x+d+arctan(4/3))+5)^(1/2))*(-5*sin(e*x+d+arctan(4/3))+5)^(1/2)/cos(e*x+d+arctan(4/3))/(5+5*sin(e*x+d+arctan(4/3)))^(1/2)/e","A"
422,1,190,123,0.316000," ","int(1/(5+4*cos(e*x+d)+3*sin(e*x+d))^(5/2),x)","-\frac{\left(3 \sqrt{10}\, \arctanh \left(\frac{\sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+5}\, \sqrt{10}}{10}\right) \left(\sin^{2}\left(e x +d +\arctan \left(\frac{4}{3}\right)\right)\right)+6 \sqrt{10}\, \arctanh \left(\frac{\sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+5}\, \sqrt{10}}{10}\right) \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+6 \sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+5}\, \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+3 \sqrt{10}\, \arctanh \left(\frac{\sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+5}\, \sqrt{10}}{10}\right)+14 \sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+5}\right) \sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+5}}{4000 \left(1+\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)\right) \cos \left(e x +d +\arctan \left(\frac{4}{3}\right)\right) \sqrt{5+5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)}\, e}"," ",0,"-1/4000*(3*10^(1/2)*arctanh(1/10*(-5*sin(e*x+d+arctan(4/3))+5)^(1/2)*10^(1/2))*sin(e*x+d+arctan(4/3))^2+6*10^(1/2)*arctanh(1/10*(-5*sin(e*x+d+arctan(4/3))+5)^(1/2)*10^(1/2))*sin(e*x+d+arctan(4/3))+6*(-5*sin(e*x+d+arctan(4/3))+5)^(1/2)*sin(e*x+d+arctan(4/3))+3*10^(1/2)*arctanh(1/10*(-5*sin(e*x+d+arctan(4/3))+5)^(1/2)*10^(1/2))+14*(-5*sin(e*x+d+arctan(4/3))+5)^(1/2))*(-5*sin(e*x+d+arctan(4/3))+5)^(1/2)/(1+sin(e*x+d+arctan(4/3)))/cos(e*x+d+arctan(4/3))/(5+5*sin(e*x+d+arctan(4/3)))^(1/2)/e","A"
423,1,86,169,0.283000," ","int((-5+4*cos(e*x+d)+3*sin(e*x+d))^(7/2),x)","\frac{250 \left(\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-1\right) \left(1+\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)\right) \left(5 \left(\sin^{3}\left(e x +d +\arctan \left(\frac{4}{3}\right)\right)\right)-27 \left(\sin^{2}\left(e x +d +\arctan \left(\frac{4}{3}\right)\right)\right)+71 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-177\right)}{7 \cos \left(e x +d +\arctan \left(\frac{4}{3}\right)\right) \sqrt{-5+5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)}\, e}"," ",0,"250/7*(sin(e*x+d+arctan(4/3))-1)*(1+sin(e*x+d+arctan(4/3)))*(5*sin(e*x+d+arctan(4/3))^3-27*sin(e*x+d+arctan(4/3))^2+71*sin(e*x+d+arctan(4/3))-177)/cos(e*x+d+arctan(4/3))/(-5+5*sin(e*x+d+arctan(4/3)))^(1/2)/e","A"
424,1,74,127,0.306000," ","int((-5+4*cos(e*x+d)+3*sin(e*x+d))^(5/2),x)","\frac{50 \left(\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-1\right) \left(1+\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)\right) \left(3 \left(\sin^{2}\left(e x +d +\arctan \left(\frac{4}{3}\right)\right)\right)-14 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+43\right)}{3 \cos \left(e x +d +\arctan \left(\frac{4}{3}\right)\right) \sqrt{-5+5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)}\, e}"," ",0,"50/3*(sin(e*x+d+arctan(4/3))-1)*(1+sin(e*x+d+arctan(4/3)))*(3*sin(e*x+d+arctan(4/3))^2-14*sin(e*x+d+arctan(4/3))+43)/cos(e*x+d+arctan(4/3))/(-5+5*sin(e*x+d+arctan(4/3)))^(1/2)/e","A"
425,1,60,85,0.306000," ","int((-5+4*cos(e*x+d)+3*sin(e*x+d))^(3/2),x)","\frac{50 \left(\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-1\right) \left(1+\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)\right) \left(\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-5\right)}{3 \cos \left(e x +d +\arctan \left(\frac{4}{3}\right)\right) \sqrt{-5+5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)}\, e}"," ",0,"50/3*(sin(e*x+d+arctan(4/3))-1)*(1+sin(e*x+d+arctan(4/3)))*(sin(e*x+d+arctan(4/3))-5)/cos(e*x+d+arctan(4/3))/(-5+5*sin(e*x+d+arctan(4/3)))^(1/2)/e","A"
426,1,50,42,0.296000," ","int((-5+4*cos(e*x+d)+3*sin(e*x+d))^(1/2),x)","\frac{10 \left(\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-1\right) \left(1+\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)\right)}{\cos \left(e x +d +\arctan \left(\frac{4}{3}\right)\right) \sqrt{-5+5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)}\, e}"," ",0,"10*(sin(e*x+d+arctan(4/3))-1)*(1+sin(e*x+d+arctan(4/3)))/cos(e*x+d+arctan(4/3))/(-5+5*sin(e*x+d+arctan(4/3)))^(1/2)/e","A"
427,1,77,38,0.329000," ","int(1/(-5+4*cos(e*x+d)+3*sin(e*x+d))^(1/2),x)","\frac{\left(\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-1\right) \sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-5}\, \sqrt{10}\, \arctan \left(\frac{\sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-5}\, \sqrt{10}}{10}\right)}{5 \cos \left(e x +d +\arctan \left(\frac{4}{3}\right)\right) \sqrt{-5+5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)}\, e}"," ",0,"1/5*(sin(e*x+d+arctan(4/3))-1)*(-5*sin(e*x+d+arctan(4/3))-5)^(1/2)*10^(1/2)*arctan(1/10*(-5*sin(e*x+d+arctan(4/3))-5)^(1/2)*10^(1/2))/cos(e*x+d+arctan(4/3))/(-5+5*sin(e*x+d+arctan(4/3)))^(1/2)/e","A"
428,1,118,81,0.369000," ","int(1/(-5+4*cos(e*x+d)+3*sin(e*x+d))^(3/2),x)","\frac{\left(-\sqrt{10}\, \arctan \left(\frac{\sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-5}\, \sqrt{10}}{10}\right) \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+\sqrt{10}\, \arctan \left(\frac{\sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-5}\, \sqrt{10}}{10}\right)+2 \sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-5}\right) \sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-5}}{100 \cos \left(e x +d +\arctan \left(\frac{4}{3}\right)\right) \sqrt{-5+5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)}\, e}"," ",0,"1/100*(-10^(1/2)*arctan(1/10*(-5*sin(e*x+d+arctan(4/3))-5)^(1/2)*10^(1/2))*sin(e*x+d+arctan(4/3))+10^(1/2)*arctan(1/10*(-5*sin(e*x+d+arctan(4/3))-5)^(1/2)*10^(1/2))+2*(-5*sin(e*x+d+arctan(4/3))-5)^(1/2))*(-5*sin(e*x+d+arctan(4/3))-5)^(1/2)/cos(e*x+d+arctan(4/3))/(-5+5*sin(e*x+d+arctan(4/3)))^(1/2)/e","A"
429,1,190,123,0.338000," ","int(1/(-5+4*cos(e*x+d)+3*sin(e*x+d))^(5/2),x)","\frac{\left(3 \sqrt{10}\, \arctan \left(\frac{\sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-5}\, \sqrt{10}}{10}\right) \left(\sin^{2}\left(e x +d +\arctan \left(\frac{4}{3}\right)\right)\right)-6 \sqrt{10}\, \arctan \left(\frac{\sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-5}\, \sqrt{10}}{10}\right) \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+3 \sqrt{10}\, \arctan \left(\frac{\sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-5}\, \sqrt{10}}{10}\right)-6 \sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-5}\, \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)+14 \sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-5}\right) \sqrt{-5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-5}}{4000 \left(\sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)-1\right) \cos \left(e x +d +\arctan \left(\frac{4}{3}\right)\right) \sqrt{-5+5 \sin \left(e x +d +\arctan \left(\frac{4}{3}\right)\right)}\, e}"," ",0,"1/4000*(3*10^(1/2)*arctan(1/10*(-5*sin(e*x+d+arctan(4/3))-5)^(1/2)*10^(1/2))*sin(e*x+d+arctan(4/3))^2-6*10^(1/2)*arctan(1/10*(-5*sin(e*x+d+arctan(4/3))-5)^(1/2)*10^(1/2))*sin(e*x+d+arctan(4/3))+3*10^(1/2)*arctan(1/10*(-5*sin(e*x+d+arctan(4/3))-5)^(1/2)*10^(1/2))-6*(-5*sin(e*x+d+arctan(4/3))-5)^(1/2)*sin(e*x+d+arctan(4/3))+14*(-5*sin(e*x+d+arctan(4/3))-5)^(1/2))*(-5*sin(e*x+d+arctan(4/3))-5)^(1/2)/(sin(e*x+d+arctan(4/3))-1)/cos(e*x+d+arctan(4/3))/(-5+5*sin(e*x+d+arctan(4/3)))^(1/2)/e","A"
430,1,306,230,0.362000," ","int((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(7/2),x)","\frac{2 \left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(\sin \left(e x +d -\arctan \left(-b , c\right)\right)-1\right) \left(5 b^{4} \left(\sin^{3}\left(e x +d -\arctan \left(-b , c\right)\right)\right)+10 b^{2} c^{2} \left(\sin^{3}\left(e x +d -\arctan \left(-b , c\right)\right)\right)+5 c^{4} \left(\sin^{3}\left(e x +d -\arctan \left(-b , c\right)\right)\right)+27 b^{4} \left(\sin^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)+54 b^{2} c^{2} \left(\sin^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)+27 c^{4} \left(\sin^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)+71 b^{4} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+142 b^{2} c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+71 c^{4} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+177 b^{4}+354 b^{2} c^{2}+177 c^{4}\right)}{35 \cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+b^{2}+c^{2}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"2/35*(1+sin(e*x+d-arctan(-b,c)))*(sin(e*x+d-arctan(-b,c))-1)*(5*b^4*sin(e*x+d-arctan(-b,c))^3+10*b^2*c^2*sin(e*x+d-arctan(-b,c))^3+5*c^4*sin(e*x+d-arctan(-b,c))^3+27*b^4*sin(e*x+d-arctan(-b,c))^2+54*b^2*c^2*sin(e*x+d-arctan(-b,c))^2+27*c^4*sin(e*x+d-arctan(-b,c))^2+71*b^4*sin(e*x+d-arctan(-b,c))+142*b^2*c^2*sin(e*x+d-arctan(-b,c))+71*c^4*sin(e*x+d-arctan(-b,c))+177*b^4+354*b^2*c^2+177*c^4)/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))+b^2+c^2)/(b^2+c^2)^(1/2))^(1/2)/e","A"
431,1,200,170,0.368000," ","int((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(5/2),x)","\frac{2 \left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}\, \left(\sin \left(e x +d -\arctan \left(-b , c\right)\right)-1\right) \left(3 b^{2} \left(\sin^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)+3 c^{2} \left(\sin^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)+14 b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+14 c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+43 b^{2}+43 c^{2}\right)}{15 \cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+b^{2}+c^{2}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"2/15*(1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)*(sin(e*x+d-arctan(-b,c))-1)*(3*b^2*sin(e*x+d-arctan(-b,c))^2+3*c^2*sin(e*x+d-arctan(-b,c))^2+14*b^2*sin(e*x+d-arctan(-b,c))+14*c^2*sin(e*x+d-arctan(-b,c))+43*b^2+43*c^2)/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))+b^2+c^2)/(b^2+c^2)^(1/2))^(1/2)/e","A"
432,1,126,112,0.369000," ","int((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(3/2),x)","\frac{2 \left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(b^{2}+c^{2}\right) \left(\sin \left(e x +d -\arctan \left(-b , c\right)\right)-1\right) \left(\sin \left(e x +d -\arctan \left(-b , c\right)\right)+5\right)}{3 \cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+b^{2}+c^{2}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"2/3*(1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)*(sin(e*x+d-arctan(-b,c))-1)*(sin(e*x+d-arctan(-b,c))+5)/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))+b^2+c^2)/(b^2+c^2)^(1/2))^(1/2)/e","A"
433,1,113,51,0.355000," ","int((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(1/2),x)","\frac{2 \left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}\, \left(\sin \left(e x +d -\arctan \left(-b , c\right)\right)-1\right)}{\cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+b^{2}+c^{2}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"2*(1+sin(e*x+d-arctan(-b,c)))*(b^2+c^2)^(1/2)*(sin(e*x+d-arctan(-b,c))-1)/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))+b^2+c^2)/(b^2+c^2)^(1/2))^(1/2)/e","B"
434,1,172,75,0.378000," ","int(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(1/2),x)","-\frac{\left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \sqrt{-\sqrt{b^{2}+c^{2}}\, \left(\sin \left(e x +d -\arctan \left(-b , c\right)\right)-1\right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\sqrt{b^{2}+c^{2}}\, \left(\sin \left(e x +d -\arctan \left(-b , c\right)\right)-1\right)}\, \sqrt{2}}{2 \left(b^{2}+c^{2}\right)^{\frac{1}{4}}}\right)}{\left(b^{2}+c^{2}\right)^{\frac{1}{4}} \cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+b^{2}+c^{2}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"-(1+sin(e*x+d-arctan(-b,c)))*(-(b^2+c^2)^(1/2)*(sin(e*x+d-arctan(-b,c))-1))^(1/2)*2^(1/2)/(b^2+c^2)^(1/4)*arctanh(1/2*(-(b^2+c^2)^(1/2)*(sin(e*x+d-arctan(-b,c))-1))^(1/2)*2^(1/2)/(b^2+c^2)^(1/4))/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))+b^2+c^2)/(b^2+c^2)^(1/2))^(1/2)/e","B"
435,1,350,137,0.410000," ","int(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(3/2),x)","-\frac{\left(\sin \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+\sqrt{b^{2}+c^{2}}}\, \sqrt{2}}{2 \left(b^{2}+c^{2}\right)^{\frac{1}{4}}}\right) \left(b^{2}+c^{2}\right)+2 \sqrt{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+\sqrt{b^{2}+c^{2}}}\, \left(b^{2}+c^{2}\right)^{\frac{3}{4}}+\sqrt{2}\, \arctanh \left(\frac{\sqrt{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+\sqrt{b^{2}+c^{2}}}\, \sqrt{2}}{2 \left(b^{2}+c^{2}\right)^{\frac{1}{4}}}\right) b^{2}+\sqrt{2}\, \arctanh \left(\frac{\sqrt{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+\sqrt{b^{2}+c^{2}}}\, \sqrt{2}}{2 \left(b^{2}+c^{2}\right)^{\frac{1}{4}}}\right) c^{2}\right) \sqrt{-\sqrt{b^{2}+c^{2}}\, \left(\sin \left(e x +d -\arctan \left(-b , c\right)\right)-1\right)}}{4 \left(b^{2}+c^{2}\right)^{\frac{7}{4}} \cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+b^{2}+c^{2}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"-1/4/(b^2+c^2)^(7/4)*(sin(e*x+d-arctan(-b,c))*2^(1/2)*arctanh(1/2*(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+(b^2+c^2)^(1/2))^(1/2)*2^(1/2)/(b^2+c^2)^(1/4))*(b^2+c^2)+2*(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+(b^2+c^2)^(1/2))^(1/2)*(b^2+c^2)^(3/4)+2^(1/2)*arctanh(1/2*(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+(b^2+c^2)^(1/2))^(1/2)*2^(1/2)/(b^2+c^2)^(1/4))*b^2+2^(1/2)*arctanh(1/2*(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+(b^2+c^2)^(1/2))^(1/2)*2^(1/2)/(b^2+c^2)^(1/4))*c^2)*(-(b^2+c^2)^(1/2)*(sin(e*x+d-arctan(-b,c))-1))^(1/2)/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))+b^2+c^2)/(b^2+c^2)^(1/2))^(1/2)/e","B"
436,1,350,197,0.402000," ","int(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(5/2),x)","\frac{\left(\sin \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+\sqrt{b^{2}+c^{2}}}\, \sqrt{2}}{2 \left(b^{2}+c^{2}\right)^{\frac{1}{4}}}\right) \left(b^{2}+c^{2}\right)+2 \sqrt{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+\sqrt{b^{2}+c^{2}}}\, \left(b^{2}+c^{2}\right)^{\frac{3}{4}}+\sqrt{2}\, \arctanh \left(\frac{\sqrt{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+\sqrt{b^{2}+c^{2}}}\, \sqrt{2}}{2 \left(b^{2}+c^{2}\right)^{\frac{1}{4}}}\right) b^{2}+\sqrt{2}\, \arctanh \left(\frac{\sqrt{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)+\sqrt{b^{2}+c^{2}}}\, \sqrt{2}}{2 \left(b^{2}+c^{2}\right)^{\frac{1}{4}}}\right) c^{2}\right) \sqrt{-\sqrt{b^{2}+c^{2}}\, \left(\sin \left(e x +d -\arctan \left(-b , c\right)\right)-1\right)}}{4 \left(b^{2}+c^{2}\right)^{\frac{5}{4}} \cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+b^{2}+c^{2}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"1/4*(sin(e*x+d-arctan(-b,c))*2^(1/2)*arctanh(1/2*(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+(b^2+c^2)^(1/2))^(1/2)*2^(1/2)/(b^2+c^2)^(1/4))*(b^2+c^2)+2*(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+(b^2+c^2)^(1/2))^(1/2)*(b^2+c^2)^(3/4)+2^(1/2)*arctanh(1/2*(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+(b^2+c^2)^(1/2))^(1/2)*2^(1/2)/(b^2+c^2)^(1/4))*b^2+2^(1/2)*arctanh(1/2*(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))+(b^2+c^2)^(1/2))^(1/2)*2^(1/2)/(b^2+c^2)^(1/4))*c^2)*(-(b^2+c^2)^(1/2)*(sin(e*x+d-arctan(-b,c))-1))^(1/2)/(b^2+c^2)^(5/4)/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))+b^2+c^2)/(b^2+c^2)^(1/2))^(1/2)/e","A"
437,1,204,176,0.375000," ","int((b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(5/2),x)","\frac{2 \left(\sin \left(e x +d -\arctan \left(-b , c\right)\right)-1\right) \sqrt{b^{2}+c^{2}}\, \left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(3 b^{2} \left(\sin^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)+3 c^{2} \left(\sin^{2}\left(e x +d -\arctan \left(-b , c\right)\right)\right)-14 b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)-14 c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+43 b^{2}+43 c^{2}\right)}{15 \cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)-b^{2}-c^{2}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"2/15*(sin(e*x+d-arctan(-b,c))-1)*(b^2+c^2)^(1/2)*(1+sin(e*x+d-arctan(-b,c)))*(3*b^2*sin(e*x+d-arctan(-b,c))^2+3*c^2*sin(e*x+d-arctan(-b,c))^2-14*b^2*sin(e*x+d-arctan(-b,c))-14*c^2*sin(e*x+d-arctan(-b,c))+43*b^2+43*c^2)/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))-b^2-c^2)/(b^2+c^2)^(1/2))^(1/2)/e","A"
438,1,130,116,0.379000," ","int((b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(3/2),x)","\frac{2 \left(\sin \left(e x +d -\arctan \left(-b , c\right)\right)-1\right) \left(b^{2}+c^{2}\right) \left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right) \left(\sin \left(e x +d -\arctan \left(-b , c\right)\right)-5\right)}{3 \cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)-b^{2}-c^{2}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"2/3*(sin(e*x+d-arctan(-b,c))-1)*(b^2+c^2)*(1+sin(e*x+d-arctan(-b,c)))*(sin(e*x+d-arctan(-b,c))-5)/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))-b^2-c^2)/(b^2+c^2)^(1/2))^(1/2)/e","A"
439,1,117,53,0.355000," ","int((b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(1/2),x)","\frac{2 \left(\sin \left(e x +d -\arctan \left(-b , c\right)\right)-1\right) \sqrt{b^{2}+c^{2}}\, \left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right)}{\cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)-b^{2}-c^{2}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"2*(sin(e*x+d-arctan(-b,c))-1)*(b^2+c^2)^(1/2)*(1+sin(e*x+d-arctan(-b,c)))/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))-b^2-c^2)/(b^2+c^2)^(1/2))^(1/2)/e","B"
440,1,175,78,0.302000," ","int(1/(b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(1/2),x)","\frac{\left(\sin \left(e x +d -\arctan \left(-b , c\right)\right)-1\right) \sqrt{-\sqrt{b^{2}+c^{2}}\, \left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right)}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{-\sqrt{b^{2}+c^{2}}\, \left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right)}\, \sqrt{2}}{2 \left(b^{2}+c^{2}\right)^{\frac{1}{4}}}\right)}{\left(b^{2}+c^{2}\right)^{\frac{1}{4}} \cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)-b^{2}-c^{2}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"(sin(e*x+d-arctan(-b,c))-1)*(-(b^2+c^2)^(1/2)*(1+sin(e*x+d-arctan(-b,c))))^(1/2)*2^(1/2)/(b^2+c^2)^(1/4)*arctan(1/2*(-(b^2+c^2)^(1/2)*(1+sin(e*x+d-arctan(-b,c))))^(1/2)*2^(1/2)/(b^2+c^2)^(1/4))/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))-b^2-c^2)/(b^2+c^2)^(1/2))^(1/2)/e","B"
441,1,363,141,0.362000," ","int(1/(b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(3/2),x)","\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-\sqrt{b^{2}+c^{2}}}\, \sqrt{2}}{2 \left(b^{2}+c^{2}\right)^{\frac{1}{4}}}\right) \left(b^{2}+c^{2}\right)+2 \sqrt{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-\sqrt{b^{2}+c^{2}}}\, \left(b^{2}+c^{2}\right)^{\frac{3}{4}}+\sqrt{2}\, \arctan \left(\frac{\sqrt{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-\sqrt{b^{2}+c^{2}}}\, \sqrt{2}}{2 \left(b^{2}+c^{2}\right)^{\frac{1}{4}}}\right) b^{2}+\sqrt{2}\, \arctan \left(\frac{\sqrt{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-\sqrt{b^{2}+c^{2}}}\, \sqrt{2}}{2 \left(b^{2}+c^{2}\right)^{\frac{1}{4}}}\right) c^{2}\right) \sqrt{-\sqrt{b^{2}+c^{2}}\, \left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right)}}{4 \left(b^{2}+c^{2}\right)^{\frac{7}{4}} \cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)-b^{2}-c^{2}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"1/4/(b^2+c^2)^(7/4)*(-sin(e*x+d-arctan(-b,c))*2^(1/2)*arctan(1/2*(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-(b^2+c^2)^(1/2))^(1/2)*2^(1/2)/(b^2+c^2)^(1/4))*(b^2+c^2)+2*(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-(b^2+c^2)^(1/2))^(1/2)*(b^2+c^2)^(3/4)+2^(1/2)*arctan(1/2*(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-(b^2+c^2)^(1/2))^(1/2)*2^(1/2)/(b^2+c^2)^(1/4))*b^2+2^(1/2)*arctan(1/2*(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-(b^2+c^2)^(1/2))^(1/2)*2^(1/2)/(b^2+c^2)^(1/4))*c^2)*(-(b^2+c^2)^(1/2)*(1+sin(e*x+d-arctan(-b,c))))^(1/2)/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))-b^2-c^2)/(b^2+c^2)^(1/2))^(1/2)/e","B"
442,1,363,203,0.454000," ","int(1/(b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(5/2),x)","-\frac{\left(-\sin \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-\sqrt{b^{2}+c^{2}}}\, \sqrt{2}}{2 \left(b^{2}+c^{2}\right)^{\frac{1}{4}}}\right) \left(b^{2}+c^{2}\right)+2 \sqrt{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-\sqrt{b^{2}+c^{2}}}\, \left(b^{2}+c^{2}\right)^{\frac{3}{4}}+\sqrt{2}\, \arctan \left(\frac{\sqrt{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-\sqrt{b^{2}+c^{2}}}\, \sqrt{2}}{2 \left(b^{2}+c^{2}\right)^{\frac{1}{4}}}\right) b^{2}+\sqrt{2}\, \arctan \left(\frac{\sqrt{-\sqrt{b^{2}+c^{2}}\, \sin \left(e x +d -\arctan \left(-b , c\right)\right)-\sqrt{b^{2}+c^{2}}}\, \sqrt{2}}{2 \left(b^{2}+c^{2}\right)^{\frac{1}{4}}}\right) c^{2}\right) \sqrt{-\sqrt{b^{2}+c^{2}}\, \left(1+\sin \left(e x +d -\arctan \left(-b , c\right)\right)\right)}}{4 \left(b^{2}+c^{2}\right)^{\frac{5}{4}} \cos \left(e x +d -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(e x +d -\arctan \left(-b , c\right)\right)-b^{2}-c^{2}}{\sqrt{b^{2}+c^{2}}}}\, e}"," ",0,"-1/4*(-sin(e*x+d-arctan(-b,c))*2^(1/2)*arctan(1/2*(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-(b^2+c^2)^(1/2))^(1/2)*2^(1/2)/(b^2+c^2)^(1/4))*(b^2+c^2)+2*(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-(b^2+c^2)^(1/2))^(1/2)*(b^2+c^2)^(3/4)+2^(1/2)*arctan(1/2*(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-(b^2+c^2)^(1/2))^(1/2)*2^(1/2)/(b^2+c^2)^(1/4))*b^2+2^(1/2)*arctan(1/2*(-(b^2+c^2)^(1/2)*sin(e*x+d-arctan(-b,c))-(b^2+c^2)^(1/2))^(1/2)*2^(1/2)/(b^2+c^2)^(1/4))*c^2)*(-(b^2+c^2)^(1/2)*(1+sin(e*x+d-arctan(-b,c))))^(1/2)/(b^2+c^2)^(5/4)/cos(e*x+d-arctan(-b,c))/((b^2*sin(e*x+d-arctan(-b,c))+c^2*sin(e*x+d-arctan(-b,c))-b^2-c^2)/(b^2+c^2)^(1/2))^(1/2)/e","A"
443,1,438,95,0.116000," ","int(sin(x)/(a+b*cos(x)+c*sin(x)),x)","-\frac{2 \ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right) a b}{\left(2 b^{2}+2 c^{2}\right) \left(a -b \right)}+\frac{2 \ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right) b^{2}}{\left(2 b^{2}+2 c^{2}\right) \left(a -b \right)}-\frac{4 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a c}{\left(2 b^{2}+2 c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}-\frac{4 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) c b}{\left(2 b^{2}+2 c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}+\frac{4 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) c a b}{\left(2 b^{2}+2 c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}\, \left(a -b \right)}-\frac{4 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) c \,b^{2}}{\left(2 b^{2}+2 c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}\, \left(a -b \right)}+\frac{2 b \ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{2 b^{2}+2 c^{2}}+\frac{4 c \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{2 b^{2}+2 c^{2}}"," ",0,"-2/(2*b^2+2*c^2)/(a-b)*ln(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)*a*b+2/(2*b^2+2*c^2)/(a-b)*ln(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)*b^2-4/(2*b^2+2*c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a*c-4/(2*b^2+2*c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*c*b+4/(2*b^2+2*c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*c/(a-b)*a*b-4/(2*b^2+2*c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*c/(a-b)*b^2+2/(2*b^2+2*c^2)*b*ln(1+tan(1/2*x)^2)+4/(2*b^2+2*c^2)*c*arctan(tan(1/2*x))","B"
444,1,25,16,0.112000," ","int(sin(x)/(1+cos(x)+sin(x)),x)","\frac{\ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{2}-\ln \left(1+\tan \left(\frac{x}{2}\right)\right)+\frac{x}{2}"," ",0,"1/2*ln(1+tan(1/2*x)^2)-ln(1+tan(1/2*x))+1/2*x","A"
445,1,414,91,0.151000," ","int(1/(a+c*sec(x)+b*tan(x)),x)","\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-c \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 b \tan \left(\frac{x}{2}\right)-a -c \right) a b}{\left(a^{2}+b^{2}\right) \left(a -c \right)}-\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-c \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 b \tan \left(\frac{x}{2}\right)-a -c \right) c b}{\left(a^{2}+b^{2}\right) \left(a -c \right)}+\frac{2 \arctan \left(\frac{2 \left(a -c \right) \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{-a^{2}-b^{2}+c^{2}}}\right) a c}{\left(a^{2}+b^{2}\right) \sqrt{-a^{2}-b^{2}+c^{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -c \right) \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{-a^{2}-b^{2}+c^{2}}}\right) b^{2}}{\left(a^{2}+b^{2}\right) \sqrt{-a^{2}-b^{2}+c^{2}}}+\frac{2 \arctan \left(\frac{2 \left(a -c \right) \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{-a^{2}-b^{2}+c^{2}}}\right) b^{2} a}{\left(a^{2}+b^{2}\right) \sqrt{-a^{2}-b^{2}+c^{2}}\, \left(a -c \right)}-\frac{2 \arctan \left(\frac{2 \left(a -c \right) \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{-a^{2}-b^{2}+c^{2}}}\right) b^{2} c}{\left(a^{2}+b^{2}\right) \sqrt{-a^{2}-b^{2}+c^{2}}\, \left(a -c \right)}-\frac{b \ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{a^{2}+b^{2}}+\frac{2 a \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a^{2}+b^{2}}"," ",0,"1/(a^2+b^2)/(a-c)*ln(a*tan(1/2*x)^2-c*tan(1/2*x)^2-2*b*tan(1/2*x)-a-c)*a*b-1/(a^2+b^2)/(a-c)*ln(a*tan(1/2*x)^2-c*tan(1/2*x)^2-2*b*tan(1/2*x)-a-c)*c*b+2/(a^2+b^2)/(-a^2-b^2+c^2)^(1/2)*arctan(1/2*(2*(a-c)*tan(1/2*x)-2*b)/(-a^2-b^2+c^2)^(1/2))*a*c-2/(a^2+b^2)/(-a^2-b^2+c^2)^(1/2)*arctan(1/2*(2*(a-c)*tan(1/2*x)-2*b)/(-a^2-b^2+c^2)^(1/2))*b^2+2/(a^2+b^2)/(-a^2-b^2+c^2)^(1/2)*arctan(1/2*(2*(a-c)*tan(1/2*x)-2*b)/(-a^2-b^2+c^2)^(1/2))*b^2/(a-c)*a-2/(a^2+b^2)/(-a^2-b^2+c^2)^(1/2)*arctan(1/2*(2*(a-c)*tan(1/2*x)-2*b)/(-a^2-b^2+c^2)^(1/2))*b^2/(a-c)*c-1/(a^2+b^2)*b*ln(1+tan(1/2*x)^2)+2/(a^2+b^2)*a*arctan(tan(1/2*x))","B"
446,1,53,45,0.129000," ","int(sec(x)/(a+c*sec(x)+b*tan(x)),x)","-\frac{2 \arctan \left(\frac{2 \left(a -c \right) \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{-a^{2}-b^{2}+c^{2}}}\right)}{\sqrt{-a^{2}-b^{2}+c^{2}}}"," ",0,"-2/(-a^2-b^2+c^2)^(1/2)*arctan(1/2*(2*(a-c)*tan(1/2*x)-2*b)/(-a^2-b^2+c^2)^(1/2))","A"
447,1,430,128,0.135000," ","int(sec(x)^2/(a+c*sec(x)+b*tan(x)),x)","-\frac{2 \ln \left(\tan \left(\frac{x}{2}\right)-1\right)}{2 b +2 c}+\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-c \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 b \tan \left(\frac{x}{2}\right)-a -c \right) a b}{\left(b -c \right) \left(b +c \right) \left(a -c \right)}-\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-c \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 b \tan \left(\frac{x}{2}\right)-a -c \right) c b}{\left(b -c \right) \left(b +c \right) \left(a -c \right)}-\frac{2 \arctan \left(\frac{2 \left(a -c \right) \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{-a^{2}-b^{2}+c^{2}}}\right) a c}{\left(b -c \right) \left(b +c \right) \sqrt{-a^{2}-b^{2}+c^{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -c \right) \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{-a^{2}-b^{2}+c^{2}}}\right) b^{2}}{\left(b -c \right) \left(b +c \right) \sqrt{-a^{2}-b^{2}+c^{2}}}+\frac{2 \arctan \left(\frac{2 \left(a -c \right) \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{-a^{2}-b^{2}+c^{2}}}\right) b^{2} a}{\left(b -c \right) \left(b +c \right) \sqrt{-a^{2}-b^{2}+c^{2}}\, \left(a -c \right)}-\frac{2 \arctan \left(\frac{2 \left(a -c \right) \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{-a^{2}-b^{2}+c^{2}}}\right) b^{2} c}{\left(b -c \right) \left(b +c \right) \sqrt{-a^{2}-b^{2}+c^{2}}\, \left(a -c \right)}-\frac{2 \ln \left(1+\tan \left(\frac{x}{2}\right)\right)}{-2 c +2 b}"," ",0,"-2/(2*b+2*c)*ln(tan(1/2*x)-1)+1/(b-c)/(b+c)/(a-c)*ln(a*tan(1/2*x)^2-c*tan(1/2*x)^2-2*b*tan(1/2*x)-a-c)*a*b-1/(b-c)/(b+c)/(a-c)*ln(a*tan(1/2*x)^2-c*tan(1/2*x)^2-2*b*tan(1/2*x)-a-c)*c*b-2/(b-c)/(b+c)/(-a^2-b^2+c^2)^(1/2)*arctan(1/2*(2*(a-c)*tan(1/2*x)-2*b)/(-a^2-b^2+c^2)^(1/2))*a*c-2/(b-c)/(b+c)/(-a^2-b^2+c^2)^(1/2)*arctan(1/2*(2*(a-c)*tan(1/2*x)-2*b)/(-a^2-b^2+c^2)^(1/2))*b^2+2/(b-c)/(b+c)/(-a^2-b^2+c^2)^(1/2)*arctan(1/2*(2*(a-c)*tan(1/2*x)-2*b)/(-a^2-b^2+c^2)^(1/2))*b^2/(a-c)*a-2/(b-c)/(b+c)/(-a^2-b^2+c^2)^(1/2)*arctan(1/2*(2*(a-c)*tan(1/2*x)-2*b)/(-a^2-b^2+c^2)^(1/2))*b^2/(a-c)*c-2/(-2*c+2*b)*ln(1+tan(1/2*x))","B"
448,1,21186,415,4.408000," ","int((a+b*sec(e*x+d)+c*tan(e*x+d))^(3/2)/sec(e*x+d)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
449,1,12462,145,1.886000," ","int((a+b*sec(e*x+d)+c*tan(e*x+d))^(1/2)/sec(e*x+d)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
450,1,722,145,1.862000," ","int(sec(e*x+d)^(1/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(1/2),x)","-\frac{4 i \EllipticF \left(\sqrt{\frac{\left(i \sin \left(e x +d \right)+\cos \left(e x +d \right)\right) \left(i a -i b -\sqrt{a^{2}-b^{2}+c^{2}}+c \right)}{i a -i b +\sqrt{a^{2}-b^{2}+c^{2}}-c}}, \sqrt{\frac{\left(i a -i b +\sqrt{a^{2}-b^{2}+c^{2}}-c \right) \left(i a -i b +\sqrt{a^{2}-b^{2}+c^{2}}+c \right)}{\left(i a -i b -\sqrt{a^{2}-b^{2}+c^{2}}+c \right) \left(i a -i b -\sqrt{a^{2}-b^{2}+c^{2}}-c \right)}}\right) \sqrt{\frac{1}{\cos \left(e x +d \right)}}\, \sqrt{\frac{b +a \cos \left(e x +d \right)+c \sin \left(e x +d \right)}{\cos \left(e x +d \right)}}\, \sqrt{\frac{\left(i \sin \left(e x +d \right)+\cos \left(e x +d \right)\right) \left(i a -i b -\sqrt{a^{2}-b^{2}+c^{2}}+c \right)}{i a -i b +\sqrt{a^{2}-b^{2}+c^{2}}-c}}\, \sqrt{-\frac{i \left(\cos \left(e x +d \right) \sqrt{a^{2}-b^{2}+c^{2}}-a \sin \left(e x +d \right)+b \sin \left(e x +d \right)+c \cos \left(e x +d \right)+\sqrt{a^{2}-b^{2}+c^{2}}+c \right)}{\left(i \cos \left(e x +d \right)+\sin \left(e x +d \right)+i\right) \left(i a -i b -\sqrt{a^{2}-b^{2}+c^{2}}-c \right)}}\, \sqrt{\frac{i \left(a \sin \left(e x +d \right)-b \sin \left(e x +d \right)+\cos \left(e x +d \right) \sqrt{a^{2}-b^{2}+c^{2}}-c \cos \left(e x +d \right)+\sqrt{a^{2}-b^{2}+c^{2}}-c \right)}{\left(i \cos \left(e x +d \right)+\sin \left(e x +d \right)+i\right) \left(i a -i b +\sqrt{a^{2}-b^{2}+c^{2}}-c \right)}}\, \left(\cos \left(e x +d \right)+1\right)^{2} \cos \left(e x +d \right) \left(\cos \left(e x +d \right)-1\right)^{2} \left(i a \cos \left(e x +d \right)-i \cos \left(e x +d \right) b -i \sqrt{a^{2}-b^{2}+c^{2}}\, \sin \left(e x +d \right)+i c \sin \left(e x +d \right)+\cos \left(e x +d \right) \sqrt{a^{2}-b^{2}+c^{2}}-c \cos \left(e x +d \right)+a \sin \left(e x +d \right)-b \sin \left(e x +d \right)\right)}{e \sin \left(e x +d \right)^{4} \left(b +a \cos \left(e x +d \right)+c \sin \left(e x +d \right)\right) \left(i a -i b -\sqrt{a^{2}-b^{2}+c^{2}}+c \right)}"," ",0,"-4*I/e*EllipticF(((I*sin(e*x+d)+cos(e*x+d))*(I*a-I*b-(a^2-b^2+c^2)^(1/2)+c)/(I*a-I*b+(a^2-b^2+c^2)^(1/2)-c))^(1/2),((I*a-I*b+(a^2-b^2+c^2)^(1/2)-c)*(I*a-I*b+(a^2-b^2+c^2)^(1/2)+c)/(I*a-I*b-(a^2-b^2+c^2)^(1/2)+c)/(I*a-I*b-(a^2-b^2+c^2)^(1/2)-c))^(1/2))*(1/cos(e*x+d))^(1/2)*((b+a*cos(e*x+d)+c*sin(e*x+d))/cos(e*x+d))^(1/2)*((I*sin(e*x+d)+cos(e*x+d))*(I*a-I*b-(a^2-b^2+c^2)^(1/2)+c)/(I*a-I*b+(a^2-b^2+c^2)^(1/2)-c))^(1/2)*(-I*(cos(e*x+d)*(a^2-b^2+c^2)^(1/2)-a*sin(e*x+d)+b*sin(e*x+d)+c*cos(e*x+d)+(a^2-b^2+c^2)^(1/2)+c)/(I*cos(e*x+d)+sin(e*x+d)+I)/(I*a-I*b-(a^2-b^2+c^2)^(1/2)-c))^(1/2)*(I*(a*sin(e*x+d)-b*sin(e*x+d)+cos(e*x+d)*(a^2-b^2+c^2)^(1/2)-c*cos(e*x+d)+(a^2-b^2+c^2)^(1/2)-c)/(I*cos(e*x+d)+sin(e*x+d)+I)/(I*a-I*b+(a^2-b^2+c^2)^(1/2)-c))^(1/2)*(cos(e*x+d)+1)^2*cos(e*x+d)*(cos(e*x+d)-1)^2*(I*a*cos(e*x+d)-I*cos(e*x+d)*b-I*(a^2-b^2+c^2)^(1/2)*sin(e*x+d)+I*c*sin(e*x+d)+cos(e*x+d)*(a^2-b^2+c^2)^(1/2)-c*cos(e*x+d)+a*sin(e*x+d)-b*sin(e*x+d))/sin(e*x+d)^4/(b+a*cos(e*x+d)+c*sin(e*x+d))/(I*a-I*b-(a^2-b^2+c^2)^(1/2)+c)","C"
451,1,12574,263,1.220000," ","int(sec(e*x+d)^(3/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
452,1,64693,530,2.549000," ","int(sec(e*x+d)^(5/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
453,1,20776,415,1.287000," ","int(cos(e*x+d)^(3/2)*(a+b*sec(e*x+d)+c*tan(e*x+d))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
454,1,12459,145,1.023000," ","int(cos(e*x+d)^(1/2)*(a+b*sec(e*x+d)+c*tan(e*x+d))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
455,1,714,145,1.527000," ","int(1/cos(e*x+d)^(1/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(1/2),x)","-\frac{4 i \sqrt{\frac{b +a \cos \left(e x +d \right)+c \sin \left(e x +d \right)}{\cos \left(e x +d \right)}}\, \sqrt{\frac{\left(i \sin \left(e x +d \right)+\cos \left(e x +d \right)\right) \left(i a -i b -\sqrt{a^{2}-b^{2}+c^{2}}+c \right)}{i a -i b +\sqrt{a^{2}-b^{2}+c^{2}}-c}}\, \sqrt{-\frac{i \left(\cos \left(e x +d \right) \sqrt{a^{2}-b^{2}+c^{2}}-a \sin \left(e x +d \right)+b \sin \left(e x +d \right)+c \cos \left(e x +d \right)+\sqrt{a^{2}-b^{2}+c^{2}}+c \right)}{\left(i \cos \left(e x +d \right)+\sin \left(e x +d \right)+i\right) \left(i a -i b -\sqrt{a^{2}-b^{2}+c^{2}}-c \right)}}\, \sqrt{\frac{i \left(a \sin \left(e x +d \right)-b \sin \left(e x +d \right)+\cos \left(e x +d \right) \sqrt{a^{2}-b^{2}+c^{2}}-c \cos \left(e x +d \right)+\sqrt{a^{2}-b^{2}+c^{2}}-c \right)}{\left(i \cos \left(e x +d \right)+\sin \left(e x +d \right)+i\right) \left(i a -i b +\sqrt{a^{2}-b^{2}+c^{2}}-c \right)}}\, \left(\cos \left(e x +d \right)+1\right)^{2} \EllipticF \left(\sqrt{\frac{\left(i \sin \left(e x +d \right)+\cos \left(e x +d \right)\right) \left(i a -i b -\sqrt{a^{2}-b^{2}+c^{2}}+c \right)}{i a -i b +\sqrt{a^{2}-b^{2}+c^{2}}-c}}, \sqrt{\frac{\left(i a -i b +\sqrt{a^{2}-b^{2}+c^{2}}-c \right) \left(i a -i b +\sqrt{a^{2}-b^{2}+c^{2}}+c \right)}{\left(i a -i b -\sqrt{a^{2}-b^{2}+c^{2}}+c \right) \left(i a -i b -\sqrt{a^{2}-b^{2}+c^{2}}-c \right)}}\right) \left(\sqrt{\cos}\left(e x +d \right)\right) \left(\cos \left(e x +d \right)-1\right)^{2} \left(i \sqrt{a^{2}-b^{2}+c^{2}}\, \sin \left(e x +d \right)-i a \cos \left(e x +d \right)+i \cos \left(e x +d \right) b -i c \sin \left(e x +d \right)-\cos \left(e x +d \right) \sqrt{a^{2}-b^{2}+c^{2}}+c \cos \left(e x +d \right)-a \sin \left(e x +d \right)+b \sin \left(e x +d \right)\right)}{e \sin \left(e x +d \right)^{4} \left(b +a \cos \left(e x +d \right)+c \sin \left(e x +d \right)\right) \left(-i a +i b +\sqrt{a^{2}-b^{2}+c^{2}}-c \right)}"," ",0,"-4*I/e*((b+a*cos(e*x+d)+c*sin(e*x+d))/cos(e*x+d))^(1/2)*((I*sin(e*x+d)+cos(e*x+d))*(I*a-I*b-(a^2-b^2+c^2)^(1/2)+c)/(I*a-I*b+(a^2-b^2+c^2)^(1/2)-c))^(1/2)*(-I*(cos(e*x+d)*(a^2-b^2+c^2)^(1/2)-a*sin(e*x+d)+b*sin(e*x+d)+c*cos(e*x+d)+(a^2-b^2+c^2)^(1/2)+c)/(I*cos(e*x+d)+sin(e*x+d)+I)/(I*a-I*b-(a^2-b^2+c^2)^(1/2)-c))^(1/2)*(I*(a*sin(e*x+d)-b*sin(e*x+d)+cos(e*x+d)*(a^2-b^2+c^2)^(1/2)-c*cos(e*x+d)+(a^2-b^2+c^2)^(1/2)-c)/(I*cos(e*x+d)+sin(e*x+d)+I)/(I*a-I*b+(a^2-b^2+c^2)^(1/2)-c))^(1/2)*(cos(e*x+d)+1)^2*EllipticF(((I*sin(e*x+d)+cos(e*x+d))*(I*a-I*b-(a^2-b^2+c^2)^(1/2)+c)/(I*a-I*b+(a^2-b^2+c^2)^(1/2)-c))^(1/2),((I*a-I*b+(a^2-b^2+c^2)^(1/2)-c)*(I*a-I*b+(a^2-b^2+c^2)^(1/2)+c)/(I*a-I*b-(a^2-b^2+c^2)^(1/2)+c)/(I*a-I*b-(a^2-b^2+c^2)^(1/2)-c))^(1/2))*cos(e*x+d)^(1/2)*(cos(e*x+d)-1)^2*(I*(a^2-b^2+c^2)^(1/2)*sin(e*x+d)-I*a*cos(e*x+d)+I*cos(e*x+d)*b-I*c*sin(e*x+d)-cos(e*x+d)*(a^2-b^2+c^2)^(1/2)+c*cos(e*x+d)-a*sin(e*x+d)+b*sin(e*x+d))/sin(e*x+d)^4/(b+a*cos(e*x+d)+c*sin(e*x+d))/(-I*a+I*b+(a^2-b^2+c^2)^(1/2)-c)","C"
456,1,12564,263,0.950000," ","int(1/cos(e*x+d)^(3/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
457,1,64683,530,1.745000," ","int(1/cos(e*x+d)^(5/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
458,1,446,92,0.132000," ","int(1/(a+b*cot(x)+c*csc(x)),x)","-\frac{2 \ln \left(b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-c \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 a \tan \left(\frac{x}{2}\right)-b -c \right) b^{2}}{\left(2 a^{2}+2 b^{2}\right) \left(b -c \right)}+\frac{2 \ln \left(b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-c \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 a \tan \left(\frac{x}{2}\right)-b -c \right) c b}{\left(2 a^{2}+2 b^{2}\right) \left(b -c \right)}+\frac{4 \arctan \left(\frac{2 \left(b -c \right) \tan \left(\frac{x}{2}\right)-2 a}{2 \sqrt{-a^{2}-b^{2}+c^{2}}}\right) a b}{\left(2 a^{2}+2 b^{2}\right) \sqrt{-a^{2}-b^{2}+c^{2}}}+\frac{4 \arctan \left(\frac{2 \left(b -c \right) \tan \left(\frac{x}{2}\right)-2 a}{2 \sqrt{-a^{2}-b^{2}+c^{2}}}\right) a c}{\left(2 a^{2}+2 b^{2}\right) \sqrt{-a^{2}-b^{2}+c^{2}}}-\frac{4 \arctan \left(\frac{2 \left(b -c \right) \tan \left(\frac{x}{2}\right)-2 a}{2 \sqrt{-a^{2}-b^{2}+c^{2}}}\right) a \,b^{2}}{\left(2 a^{2}+2 b^{2}\right) \sqrt{-a^{2}-b^{2}+c^{2}}\, \left(b -c \right)}+\frac{4 \arctan \left(\frac{2 \left(b -c \right) \tan \left(\frac{x}{2}\right)-2 a}{2 \sqrt{-a^{2}-b^{2}+c^{2}}}\right) a c b}{\left(2 a^{2}+2 b^{2}\right) \sqrt{-a^{2}-b^{2}+c^{2}}\, \left(b -c \right)}+\frac{2 b \ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{2 a^{2}+2 b^{2}}+\frac{4 a \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{2 a^{2}+2 b^{2}}"," ",0,"-2/(2*a^2+2*b^2)/(b-c)*ln(b*tan(1/2*x)^2-c*tan(1/2*x)^2-2*a*tan(1/2*x)-b-c)*b^2+2/(2*a^2+2*b^2)/(b-c)*ln(b*tan(1/2*x)^2-c*tan(1/2*x)^2-2*a*tan(1/2*x)-b-c)*c*b+4/(2*a^2+2*b^2)/(-a^2-b^2+c^2)^(1/2)*arctan(1/2*(2*(b-c)*tan(1/2*x)-2*a)/(-a^2-b^2+c^2)^(1/2))*a*b+4/(2*a^2+2*b^2)/(-a^2-b^2+c^2)^(1/2)*arctan(1/2*(2*(b-c)*tan(1/2*x)-2*a)/(-a^2-b^2+c^2)^(1/2))*a*c-4/(2*a^2+2*b^2)/(-a^2-b^2+c^2)^(1/2)*arctan(1/2*(2*(b-c)*tan(1/2*x)-2*a)/(-a^2-b^2+c^2)^(1/2))*a/(b-c)*b^2+4/(2*a^2+2*b^2)/(-a^2-b^2+c^2)^(1/2)*arctan(1/2*(2*(b-c)*tan(1/2*x)-2*a)/(-a^2-b^2+c^2)^(1/2))*a/(b-c)*c*b+2/(2*a^2+2*b^2)*b*ln(1+tan(1/2*x)^2)+4/(2*a^2+2*b^2)*a*arctan(tan(1/2*x))","B"
459,1,53,45,0.112000," ","int(csc(x)/(a+b*cot(x)+c*csc(x)),x)","-\frac{2 \arctan \left(\frac{2 \left(b -c \right) \tan \left(\frac{x}{2}\right)-2 a}{2 \sqrt{-a^{2}-b^{2}+c^{2}}}\right)}{\sqrt{-a^{2}-b^{2}+c^{2}}}"," ",0,"-2/(-a^2-b^2+c^2)^(1/2)*arctan(1/2*(2*(b-c)*tan(1/2*x)-2*a)/(-a^2-b^2+c^2)^(1/2))","A"
460,1,184,108,0.114000," ","int(csc(x)^2/(a+b*cot(x)+c*csc(x)),x)","-\frac{b \ln \left(b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-c \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 a \tan \left(\frac{x}{2}\right)-b -c \right)}{\left(b +c \right) \left(b -c \right)}+\frac{2 \arctan \left(\frac{2 \left(b -c \right) \tan \left(\frac{x}{2}\right)-2 a}{2 \sqrt{-a^{2}-b^{2}+c^{2}}}\right) a}{\left(b +c \right) \sqrt{-a^{2}-b^{2}+c^{2}}}-\frac{2 \arctan \left(\frac{2 \left(b -c \right) \tan \left(\frac{x}{2}\right)-2 a}{2 \sqrt{-a^{2}-b^{2}+c^{2}}}\right) b a}{\left(b +c \right) \sqrt{-a^{2}-b^{2}+c^{2}}\, \left(b -c \right)}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{b +c}"," ",0,"-1/(b+c)*b/(b-c)*ln(b*tan(1/2*x)^2-c*tan(1/2*x)^2-2*a*tan(1/2*x)-b-c)+2/(b+c)/(-a^2-b^2+c^2)^(1/2)*arctan(1/2*(2*(b-c)*tan(1/2*x)-2*a)/(-a^2-b^2+c^2)^(1/2))*a-2/(b+c)/(-a^2-b^2+c^2)^(1/2)*arctan(1/2*(2*(b-c)*tan(1/2*x)-2*a)/(-a^2-b^2+c^2)^(1/2))*b*a/(b-c)+ln(tan(1/2*x))/(b+c)","A"
461,1,10,21,0.118000," ","int(csc(x)/(2+2*cot(x)+3*csc(x)),x)","2 \arctan \left(2+\tan \left(\frac{x}{2}\right)\right)"," ",0,"2*arctan(2+tan(1/2*x))","A"
462,1,20463,415,3.116000," ","int((a+c*cot(e*x+d)+b*csc(e*x+d))^(3/2)/csc(e*x+d)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
463,1,12367,145,1.757000," ","int((a+c*cot(e*x+d)+b*csc(e*x+d))^(1/2)/csc(e*x+d)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
464,1,713,145,1.679000," ","int(csc(e*x+d)^(1/2)/(a+c*cot(e*x+d)+b*csc(e*x+d))^(1/2),x)","-\frac{4 i \sqrt{\frac{1}{\sin \left(e x +d \right)}}\, \sqrt{\frac{b +c \cos \left(e x +d \right)+a \sin \left(e x +d \right)}{\sin \left(e x +d \right)}}\, \sqrt{\frac{\left(i \sin \left(e x +d \right)+\cos \left(e x +d \right)\right) \left(i b -i c -\sqrt{a^{2}-b^{2}+c^{2}}-a \right)}{i b -i c +\sqrt{a^{2}-b^{2}+c^{2}}+a}}\, \sqrt{-\frac{i \left(\cos \left(e x +d \right) \sqrt{a^{2}-b^{2}+c^{2}}-b \sin \left(e x +d \right)+c \sin \left(e x +d \right)-a \cos \left(e x +d \right)+\sqrt{a^{2}-b^{2}+c^{2}}-a \right)}{\left(i \cos \left(e x +d \right)+\sin \left(e x +d \right)+i\right) \left(i b -i c -\sqrt{a^{2}-b^{2}+c^{2}}+a \right)}}\, \sqrt{\frac{i \left(b \sin \left(e x +d \right)-c \sin \left(e x +d \right)+\cos \left(e x +d \right) \sqrt{a^{2}-b^{2}+c^{2}}+a \cos \left(e x +d \right)+\sqrt{a^{2}-b^{2}+c^{2}}+a \right)}{\left(i \cos \left(e x +d \right)+\sin \left(e x +d \right)+i\right) \left(i b -i c +\sqrt{a^{2}-b^{2}+c^{2}}+a \right)}}\, \left(\cos \left(e x +d \right)+1\right)^{2} \EllipticF \left(\sqrt{\frac{\left(i \sin \left(e x +d \right)+\cos \left(e x +d \right)\right) \left(i b -i c -\sqrt{a^{2}-b^{2}+c^{2}}-a \right)}{i b -i c +\sqrt{a^{2}-b^{2}+c^{2}}+a}}, \sqrt{\frac{\left(i b -i c +\sqrt{a^{2}-b^{2}+c^{2}}+a \right) \left(i b -i c +\sqrt{a^{2}-b^{2}+c^{2}}-a \right)}{\left(i b -i c -\sqrt{a^{2}-b^{2}+c^{2}}-a \right) \left(i b -i c -\sqrt{a^{2}-b^{2}+c^{2}}+a \right)}}\right) \left(\cos \left(e x +d \right)-1\right)^{2} \left(i \cos \left(e x +d \right) b -i \cos \left(e x +d \right) c -i \sqrt{a^{2}-b^{2}+c^{2}}\, \sin \left(e x +d \right)-i \sin \left(e x +d \right) a +\cos \left(e x +d \right) \sqrt{a^{2}-b^{2}+c^{2}}+a \cos \left(e x +d \right)+b \sin \left(e x +d \right)-c \sin \left(e x +d \right)\right)}{e \sin \left(e x +d \right)^{3} \left(b +c \cos \left(e x +d \right)+a \sin \left(e x +d \right)\right) \left(i b -i c -\sqrt{a^{2}-b^{2}+c^{2}}-a \right)}"," ",0,"-4*I/e*(1/sin(e*x+d))^(1/2)*((b+c*cos(e*x+d)+a*sin(e*x+d))/sin(e*x+d))^(1/2)*((I*sin(e*x+d)+cos(e*x+d))*(I*b-I*c-(a^2-b^2+c^2)^(1/2)-a)/(I*b-I*c+(a^2-b^2+c^2)^(1/2)+a))^(1/2)*(-I*(cos(e*x+d)*(a^2-b^2+c^2)^(1/2)-b*sin(e*x+d)+c*sin(e*x+d)-a*cos(e*x+d)+(a^2-b^2+c^2)^(1/2)-a)/(I*cos(e*x+d)+sin(e*x+d)+I)/(I*b-I*c-(a^2-b^2+c^2)^(1/2)+a))^(1/2)*(I*(b*sin(e*x+d)-c*sin(e*x+d)+cos(e*x+d)*(a^2-b^2+c^2)^(1/2)+a*cos(e*x+d)+(a^2-b^2+c^2)^(1/2)+a)/(I*cos(e*x+d)+sin(e*x+d)+I)/(I*b-I*c+(a^2-b^2+c^2)^(1/2)+a))^(1/2)*(cos(e*x+d)+1)^2*EllipticF(((I*sin(e*x+d)+cos(e*x+d))*(I*b-I*c-(a^2-b^2+c^2)^(1/2)-a)/(I*b-I*c+(a^2-b^2+c^2)^(1/2)+a))^(1/2),((I*b-I*c+(a^2-b^2+c^2)^(1/2)+a)*(I*b-I*c+(a^2-b^2+c^2)^(1/2)-a)/(I*b-I*c-(a^2-b^2+c^2)^(1/2)-a)/(I*b-I*c-(a^2-b^2+c^2)^(1/2)+a))^(1/2))*(cos(e*x+d)-1)^2*(I*cos(e*x+d)*b-I*cos(e*x+d)*c-I*(a^2-b^2+c^2)^(1/2)*sin(e*x+d)-I*sin(e*x+d)*a+cos(e*x+d)*(a^2-b^2+c^2)^(1/2)+a*cos(e*x+d)+b*sin(e*x+d)-c*sin(e*x+d))/sin(e*x+d)^3/(b+c*cos(e*x+d)+a*sin(e*x+d))/(I*b-I*c-(a^2-b^2+c^2)^(1/2)-a)","C"
465,1,12236,263,1.122000," ","int(csc(e*x+d)^(3/2)/(a+c*cot(e*x+d)+b*csc(e*x+d))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
466,1,62955,530,2.163000," ","int(csc(e*x+d)^(5/2)/(a+c*cot(e*x+d)+b*csc(e*x+d))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
467,1,20454,415,1.098000," ","int((a+c*cot(e*x+d)+b*csc(e*x+d))^(3/2)*sin(e*x+d)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
468,1,12365,145,1.056000," ","int((a+c*cot(e*x+d)+b*csc(e*x+d))^(1/2)*sin(e*x+d)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
469,1,705,145,1.160000," ","int(1/(a+c*cot(e*x+d)+b*csc(e*x+d))^(1/2)/sin(e*x+d)^(1/2),x)","\frac{4 i \sqrt{\frac{b +c \cos \left(e x +d \right)+a \sin \left(e x +d \right)}{\sin \left(e x +d \right)}}\, \sqrt{\frac{\left(i \sin \left(e x +d \right)+\cos \left(e x +d \right)\right) \left(i b -i c -\sqrt{a^{2}-b^{2}+c^{2}}-a \right)}{i b -i c +\sqrt{a^{2}-b^{2}+c^{2}}+a}}\, \sqrt{-\frac{i \left(\cos \left(e x +d \right) \sqrt{a^{2}-b^{2}+c^{2}}-b \sin \left(e x +d \right)+c \sin \left(e x +d \right)-a \cos \left(e x +d \right)+\sqrt{a^{2}-b^{2}+c^{2}}-a \right)}{\left(i \cos \left(e x +d \right)+\sin \left(e x +d \right)+i\right) \left(i b -i c -\sqrt{a^{2}-b^{2}+c^{2}}+a \right)}}\, \sqrt{\frac{i \left(b \sin \left(e x +d \right)-c \sin \left(e x +d \right)+\cos \left(e x +d \right) \sqrt{a^{2}-b^{2}+c^{2}}+a \cos \left(e x +d \right)+\sqrt{a^{2}-b^{2}+c^{2}}+a \right)}{\left(i \cos \left(e x +d \right)+\sin \left(e x +d \right)+i\right) \left(i b -i c +\sqrt{a^{2}-b^{2}+c^{2}}+a \right)}}\, \left(\cos \left(e x +d \right)+1\right)^{2} \EllipticF \left(\sqrt{\frac{\left(i \sin \left(e x +d \right)+\cos \left(e x +d \right)\right) \left(i b -i c -\sqrt{a^{2}-b^{2}+c^{2}}-a \right)}{i b -i c +\sqrt{a^{2}-b^{2}+c^{2}}+a}}, \sqrt{\frac{\left(i b -i c +\sqrt{a^{2}-b^{2}+c^{2}}+a \right) \left(i b -i c +\sqrt{a^{2}-b^{2}+c^{2}}-a \right)}{\left(i b -i c -\sqrt{a^{2}-b^{2}+c^{2}}-a \right) \left(i b -i c -\sqrt{a^{2}-b^{2}+c^{2}}+a \right)}}\right) \left(\cos \left(e x +d \right)-1\right)^{2} \left(i \sqrt{a^{2}-b^{2}+c^{2}}\, \sin \left(e x +d \right)+i \sin \left(e x +d \right) a -i \cos \left(e x +d \right) b +i \cos \left(e x +d \right) c -b \sin \left(e x +d \right)+c \sin \left(e x +d \right)-\cos \left(e x +d \right) \sqrt{a^{2}-b^{2}+c^{2}}-a \cos \left(e x +d \right)\right)}{e \sin \left(e x +d \right)^{\frac{7}{2}} \left(b +c \cos \left(e x +d \right)+a \sin \left(e x +d \right)\right) \left(i b -i c -\sqrt{a^{2}-b^{2}+c^{2}}-a \right)}"," ",0,"4*I/e*((b+c*cos(e*x+d)+a*sin(e*x+d))/sin(e*x+d))^(1/2)*((I*sin(e*x+d)+cos(e*x+d))*(I*b-I*c-(a^2-b^2+c^2)^(1/2)-a)/(I*b-I*c+(a^2-b^2+c^2)^(1/2)+a))^(1/2)*(-I*(cos(e*x+d)*(a^2-b^2+c^2)^(1/2)-b*sin(e*x+d)+c*sin(e*x+d)-a*cos(e*x+d)+(a^2-b^2+c^2)^(1/2)-a)/(I*cos(e*x+d)+sin(e*x+d)+I)/(I*b-I*c-(a^2-b^2+c^2)^(1/2)+a))^(1/2)*(I*(b*sin(e*x+d)-c*sin(e*x+d)+cos(e*x+d)*(a^2-b^2+c^2)^(1/2)+a*cos(e*x+d)+(a^2-b^2+c^2)^(1/2)+a)/(I*cos(e*x+d)+sin(e*x+d)+I)/(I*b-I*c+(a^2-b^2+c^2)^(1/2)+a))^(1/2)*(cos(e*x+d)+1)^2*EllipticF(((I*sin(e*x+d)+cos(e*x+d))*(I*b-I*c-(a^2-b^2+c^2)^(1/2)-a)/(I*b-I*c+(a^2-b^2+c^2)^(1/2)+a))^(1/2),((I*b-I*c+(a^2-b^2+c^2)^(1/2)+a)*(I*b-I*c+(a^2-b^2+c^2)^(1/2)-a)/(I*b-I*c-(a^2-b^2+c^2)^(1/2)-a)/(I*b-I*c-(a^2-b^2+c^2)^(1/2)+a))^(1/2))*(cos(e*x+d)-1)^2*(I*(a^2-b^2+c^2)^(1/2)*sin(e*x+d)+I*sin(e*x+d)*a-I*cos(e*x+d)*b+I*cos(e*x+d)*c-b*sin(e*x+d)+c*sin(e*x+d)-cos(e*x+d)*(a^2-b^2+c^2)^(1/2)-a*cos(e*x+d))/sin(e*x+d)^(7/2)/(b+c*cos(e*x+d)+a*sin(e*x+d))/(I*b-I*c-(a^2-b^2+c^2)^(1/2)-a)","C"
470,1,12231,263,0.957000," ","int(1/(a+c*cot(e*x+d)+b*csc(e*x+d))^(3/2)/sin(e*x+d)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
471,1,62945,530,1.652000," ","int(1/(a+c*cot(e*x+d)+b*csc(e*x+d))^(5/2)/sin(e*x+d)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
472,1,2,1,0.059000," ","int(1/(cos(x)^2+sin(x)^2),x)","x"," ",0,"x","A"
473,1,2,1,0.047000," ","int(1/(cos(x)^2+sin(x)^2)^2,x)","x"," ",0,"x","A"
474,1,2,1,0.049000," ","int(1/(cos(x)^2+sin(x)^2)^3,x)","x"," ",0,"x","A"
475,1,4,9,0.098000," ","int(1/(cos(x)^2-sin(x)^2),x)","\arctanh \left(\tan \left(x \right)\right)"," ",0,"arctanh(tan(x))","A"
476,1,18,13,0.105000," ","int(1/(cos(x)^2-sin(x)^2)^2,x)","-\frac{1}{2 \left(1+\tan \left(x \right)\right)}-\frac{1}{2 \left(\tan \left(x \right)-1\right)}"," ",0,"-1/2/(1+tan(x))-1/2/(tan(x)-1)","A"
477,1,48,28,0.115000," ","int(1/(cos(x)^2-sin(x)^2)^3,x)","\frac{1}{4 \left(\tan \left(x \right)-1\right)^{2}}+\frac{1}{4 \tan \left(x \right)-4}-\frac{\ln \left(\tan \left(x \right)-1\right)}{4}-\frac{1}{4 \left(1+\tan \left(x \right)\right)^{2}}+\frac{1}{4+4 \tan \left(x \right)}+\frac{\ln \left(1+\tan \left(x \right)\right)}{4}"," ",0,"1/4/(tan(x)-1)^2+1/4/(tan(x)-1)-1/4*ln(tan(x)-1)-1/4/(1+tan(x))^2+1/4/(1+tan(x))+1/4*ln(1+tan(x))","A"
478,1,10,9,0.116000," ","int(1/(cos(x)^2+a^2*sin(x)^2),x)","\frac{\arctan \left(a \tan \left(x \right)\right)}{a}"," ",0,"arctan(a*tan(x))/a","A"
479,1,12,11,0.109000," ","int(1/(b^2*cos(x)^2+sin(x)^2),x)","\frac{\arctan \left(\frac{\tan \left(x \right)}{b}\right)}{b}"," ",0,"arctan(tan(x)/b)/b","A"
480,1,16,15,0.125000," ","int(1/(b^2*cos(x)^2+a^2*sin(x)^2),x)","\frac{\arctan \left(\frac{a \tan \left(x \right)}{b}\right)}{a b}"," ",0,"arctan(a*tan(x)/b)/a/b","A"
481,1,18,43,0.229000," ","int(1/(4*cos(1+2*x)^2+3*sin(1+2*x)^2),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \tan \left(1+2 x \right)}{2}\right)}{12}"," ",0,"1/12*3^(1/2)*arctan(1/2*3^(1/2)*tan(1+2*x))","A"
482,1,38,35,0.110000," ","int(sin(x)^2/(a*cos(x)^2+b*sin(x)^2),x)","\frac{a \arctan \left(\frac{\tan \left(x \right) b}{\sqrt{a b}}\right)}{\left(a -b \right) \sqrt{a b}}-\frac{\arctan \left(\tan \left(x \right)\right)}{a -b}"," ",0,"a/(a-b)/(a*b)^(1/2)*arctan(tan(x)*b/(a*b)^(1/2))-1/(a-b)*arctan(tan(x))","A"
483,1,36,35,0.105000," ","int(cos(x)^2/(a*cos(x)^2+b*sin(x)^2),x)","-\frac{b \arctan \left(\frac{\tan \left(x \right) b}{\sqrt{a b}}\right)}{\left(a -b \right) \sqrt{a b}}+\frac{x}{a -b}"," ",0,"-b/(a-b)/(a*b)^(1/2)*arctan(tan(x)*b/(a*b)^(1/2))+x/(a-b)","A"
484,1,16,30,0.118000," ","int(1/(sec(x)^2+tan(x)^2),x)","\sqrt{2}\, \arctan \left(\sqrt{2}\, \tan \left(x \right)\right)-x"," ",0,"2^(1/2)*arctan(2^(1/2)*tan(x))-x","A"
485,1,27,43,0.124000," ","int(1/(sec(x)^2+tan(x)^2)^2,x)","\frac{\tan \left(x \right)}{2 \left(\tan^{2}\left(x \right)\right)+1}-\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, \tan \left(x \right)\right)}{2}+x"," ",0,"1/2*tan(x)/(tan(x)^2+1/2)-1/2*2^(1/2)*arctan(2^(1/2)*tan(x))+x","A"
486,1,40,60,0.131000," ","int(1/(sec(x)^2+tan(x)^2)^3,x)","\frac{-\frac{\left(\tan^{3}\left(x \right)\right)}{2}+\frac{\tan \left(x \right)}{4}}{\left(2 \left(\tan^{2}\left(x \right)\right)+1\right)^{2}}+\frac{7 \sqrt{2}\, \arctan \left(\sqrt{2}\, \tan \left(x \right)\right)}{8}-x"," ",0,"8*(-1/16*tan(x)^3+1/32*tan(x))/(1+2*tan(x)^2)^2+7/8*2^(1/2)*arctan(2^(1/2)*tan(x))-x","A"
487,1,4,1,0.062000," ","int(1/(sec(x)^2-tan(x)^2),x)","\arctan \left(\tan \left(x \right)\right)"," ",0,"arctan(tan(x))","C"
488,1,4,1,0.062000," ","int(1/(sec(x)^2-tan(x)^2)^2,x)","\arctan \left(\tan \left(x \right)\right)"," ",0,"arctan(tan(x))","C"
489,1,4,1,0.066000," ","int(1/(sec(x)^2-tan(x)^2)^3,x)","\arctan \left(\tan \left(x \right)\right)"," ",0,"arctan(tan(x))","C"
490,1,17,31,0.159000," ","int(1/(cot(x)^2+csc(x)^2),x)","\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(x \right)}{2}\right)-x"," ",0,"2^(1/2)*arctan(1/2*2^(1/2)*tan(x))-x","A"
491,1,28,42,0.184000," ","int(1/(cot(x)^2+csc(x)^2)^2,x)","-\frac{\tan \left(x \right)}{2+\tan^{2}\left(x \right)}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(x \right)}{2}\right)}{2}+x"," ",0,"-tan(x)/(2+tan(x)^2)-1/2*2^(1/2)*arctan(1/2*2^(1/2)*tan(x))+x","A"
492,1,39,58,0.219000," ","int(1/(cot(x)^2+csc(x)^2)^3,x)","\frac{-\frac{\left(\tan^{3}\left(x \right)\right)}{4}+\frac{\tan \left(x \right)}{2}}{\left(2+\tan^{2}\left(x \right)\right)^{2}}+\frac{7 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(x \right)}{2}\right)}{8}-x"," ",0,"2*(-1/8*tan(x)^3+1/4*tan(x))/(2+tan(x)^2)^2+7/8*2^(1/2)*arctan(1/2*2^(1/2)*tan(x))-x","A"
493,1,6,3,0.061000," ","int(1/(cot(x)^2-csc(x)^2),x)","-\arctan \left(\tan \left(x \right)\right)"," ",0,"-arctan(tan(x))","C"
494,1,4,1,0.065000," ","int(1/(cot(x)^2-csc(x)^2)^2,x)","\arctan \left(\tan \left(x \right)\right)"," ",0,"arctan(tan(x))","C"
495,1,6,3,0.066000," ","int(1/(cot(x)^2-csc(x)^2)^3,x)","-\arctan \left(\tan \left(x \right)\right)"," ",0,"-arctan(tan(x))","C"
496,1,27,25,0.122000," ","int(1/(a+b*cos(x)^2+c*sin(x)^2),x)","\frac{\arctan \left(\frac{\left(a +c \right) \tan \left(x \right)}{\sqrt{\left(a +b \right) \left(a +c \right)}}\right)}{\sqrt{\left(a +b \right) \left(a +c \right)}}"," ",0,"1/((a+b)*(a+c))^(1/2)*arctan((a+c)*tan(x)/((a+b)*(a+c))^(1/2))","A"
497,1,820,189,0.299000," ","int(x/(a+b*cos(x)^2+c*sin(x)^2),x)","-\frac{i x \ln \left(1-\frac{\left(b -c \right) {\mathrm e}^{2 i x}}{2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{2 \sqrt{\left(a +b \right) \left(a +c \right)}}-\frac{x^{2}}{2 \sqrt{\left(a +b \right) \left(a +c \right)}}-\frac{\polylog \left(2, \frac{\left(b -c \right) {\mathrm e}^{2 i x}}{2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{4 \sqrt{\left(a +b \right) \left(a +c \right)}}-\frac{i \ln \left(1-\frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right) x}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}-\frac{i \ln \left(1-\frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right) a x}{\sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{i \ln \left(1-\frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right) b x}{2 \sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{i \ln \left(1-\frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right) c x}{2 \sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{x^{2}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}-\frac{a \,x^{2}}{\sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{b \,x^{2}}{2 \sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{c \,x^{2}}{2 \sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{\polylog \left(2, \frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{2 \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{\polylog \left(2, \frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right) a}{2 \sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{\polylog \left(2, \frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right) b}{4 \sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{\polylog \left(2, \frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right) c}{4 \sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}"," ",0,"-1/2*I/((a+b)*(a+c))^(1/2)*x*ln(1-(b-c)*exp(2*I*x)/(2*((a+b)*(a+c))^(1/2)-2*a-b-c))-1/2/((a+b)*(a+c))^(1/2)*x^2-1/4/((a+b)*(a+c))^(1/2)*polylog(2,(b-c)*exp(2*I*x)/(2*((a+b)*(a+c))^(1/2)-2*a-b-c))-I/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*ln(1-(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))*x-I/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*ln(1-(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))*a*x-1/2*I/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*ln(1-(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))*b*x-1/2*I/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*ln(1-(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))*c*x-1/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*x^2-1/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*a*x^2-1/2/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*b*x^2-1/2/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*c*x^2-1/2/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*polylog(2,(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))-1/2/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*polylog(2,(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))*a-1/4/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*polylog(2,(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))*b-1/4/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*polylog(2,(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))*c","B"
498,1,1161,289,0.288000," ","int(x^2/(a+b*cos(x)^2+c*sin(x)^2),x)","-\frac{x \polylog \left(2, \frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}-\frac{i \polylog \left(3, \frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{2 \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{a x \polylog \left(2, \frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{\sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{i b \,x^{2} \ln \left(1-\frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{2 \sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{x \polylog \left(2, \frac{\left(b -c \right) {\mathrm e}^{2 i x}}{2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{2 \sqrt{\left(a +b \right) \left(a +c \right)}}-\frac{i b \polylog \left(3, \frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{4 \sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{c x \polylog \left(2, \frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{2 \sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{i x^{2} \ln \left(1-\frac{\left(b -c \right) {\mathrm e}^{2 i x}}{2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{2 \sqrt{\left(a +b \right) \left(a +c \right)}}-\frac{b x \polylog \left(2, \frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{2 \sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{i a \,x^{2} \ln \left(1-\frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{\sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{2 a \,x^{3}}{3 \sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{i \polylog \left(3, \frac{\left(b -c \right) {\mathrm e}^{2 i x}}{2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{4 \sqrt{\left(a +b \right) \left(a +c \right)}}-\frac{2 x^{3}}{3 \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{i c \,x^{2} \ln \left(1-\frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{2 \sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{b \,x^{3}}{3 \sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{i c \polylog \left(3, \frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{4 \sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{c \,x^{3}}{3 \sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}-\frac{i x^{2} \ln \left(1-\frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}-\frac{x^{3}}{3 \sqrt{\left(a +b \right) \left(a +c \right)}}-\frac{i a \polylog \left(3, \frac{\left(b -c \right) {\mathrm e}^{2 i x}}{-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c}\right)}{2 \sqrt{\left(a +b \right) \left(a +c \right)}\, \left(-2 \sqrt{\left(a +b \right) \left(a +c \right)}-2 a -b -c \right)}"," ",0,"-1/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*x*polylog(2,(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))-1/4*I/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*c*polylog(3,(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))-1/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*a*x*polylog(2,(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))-1/2*I/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*b*x^2*ln(1-(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))-1/2/((a+b)*(a+c))^(1/2)*x*polylog(2,(b-c)*exp(2*I*x)/(2*((a+b)*(a+c))^(1/2)-2*a-b-c))-1/4*I/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*b*polylog(3,(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))-1/2/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*c*x*polylog(2,(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))-1/2*I/((a+b)*(a+c))^(1/2)*x^2*ln(1-(b-c)*exp(2*I*x)/(2*((a+b)*(a+c))^(1/2)-2*a-b-c))-1/2/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*b*x*polylog(2,(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))-1/4*I/((a+b)*(a+c))^(1/2)*polylog(3,(b-c)*exp(2*I*x)/(2*((a+b)*(a+c))^(1/2)-2*a-b-c))-2/3/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*a*x^3-1/2*I/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*polylog(3,(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))-2/3/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*x^3-I/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*a*x^2*ln(1-(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))-1/3/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*b*x^3-1/2*I/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*c*x^2*ln(1-(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))-1/3/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*c*x^3-I/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*x^2*ln(1-(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))-1/3/((a+b)*(a+c))^(1/2)*x^3-1/2*I/((a+b)*(a+c))^(1/2)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c)*a*polylog(3,(b-c)*exp(2*I*x)/(-2*((a+b)*(a+c))^(1/2)-2*a-b-c))","B"
499,1,255,183,0.100000," ","int((a+b*sin(e*x+d))*(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^2,x)","\frac{a \,b^{4} \left(e x +d \right)-4 \cos \left(e x +d \right) a^{2} b^{3}+6 a^{3} b^{2} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)-\frac{4 a^{4} b \left(2+\sin^{2}\left(e x +d \right)\right) \cos \left(e x +d \right)}{3}+a^{5} \left(-\frac{\left(\sin^{3}\left(e x +d \right)+\frac{3 \sin \left(e x +d \right)}{2}\right) \cos \left(e x +d \right)}{4}+\frac{3 e x}{8}+\frac{3 d}{8}\right)-\cos \left(e x +d \right) b^{5}+4 a \,b^{4} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)-2 a^{2} b^{3} \left(2+\sin^{2}\left(e x +d \right)\right) \cos \left(e x +d \right)+4 a^{3} b^{2} \left(-\frac{\left(\sin^{3}\left(e x +d \right)+\frac{3 \sin \left(e x +d \right)}{2}\right) \cos \left(e x +d \right)}{4}+\frac{3 e x}{8}+\frac{3 d}{8}\right)-\frac{a^{4} b \left(\frac{8}{3}+\sin^{4}\left(e x +d \right)+\frac{4 \left(\sin^{2}\left(e x +d \right)\right)}{3}\right) \cos \left(e x +d \right)}{5}}{e}"," ",0,"1/e*(a*b^4*(e*x+d)-4*cos(e*x+d)*a^2*b^3+6*a^3*b^2*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)-4/3*a^4*b*(2+sin(e*x+d)^2)*cos(e*x+d)+a^5*(-1/4*(sin(e*x+d)^3+3/2*sin(e*x+d))*cos(e*x+d)+3/8*e*x+3/8*d)-cos(e*x+d)*b^5+4*a*b^4*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)-2*a^2*b^3*(2+sin(e*x+d)^2)*cos(e*x+d)+4*a^3*b^2*(-1/4*(sin(e*x+d)^3+3/2*sin(e*x+d))*cos(e*x+d)+3/8*e*x+3/8*d)-1/5*a^4*b*(8/3+sin(e*x+d)^4+4/3*sin(e*x+d)^2)*cos(e*x+d))","A"
500,1,115,101,0.079000," ","int((a+b*sin(e*x+d))*(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2),x)","\frac{-\frac{a^{2} b \left(2+\sin^{2}\left(e x +d \right)\right) \cos \left(e x +d \right)}{3}+a^{3} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)+2 a \,b^{2} \left(-\frac{\sin \left(e x +d \right) \cos \left(e x +d \right)}{2}+\frac{e x}{2}+\frac{d}{2}\right)-2 \cos \left(e x +d \right) a^{2} b -b^{3} \cos \left(e x +d \right)+a \,b^{2} \left(e x +d \right)}{e}"," ",0,"1/e*(-1/3*a^2*b*(2+sin(e*x+d)^2)*cos(e*x+d)+a^3*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)+2*a*b^2*(-1/2*sin(e*x+d)*cos(e*x+d)+1/2*e*x+1/2*d)-2*cos(e*x+d)*a^2*b-b^3*cos(e*x+d)+a*b^2*(e*x+d))","A"
501,1,52,23,0.336000," ","int((a+b*sin(e*x+d))/(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2),x)","\frac{-\frac{2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{b}-2}{e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)}"," ",0,"2/e*(-a*tan(1/2*d+1/2*e*x)/b-1)/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)","B"
502,1,1297,146,0.332000," ","int((a+b*sin(e*x+d))/(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^2,x)","-\frac{2 a^{5} \left(\tan^{5}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} b \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{4 a^{3} b \left(\tan^{5}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{4 a \,b^{3} \left(\tan^{5}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{4 \left(\tan^{4}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) a^{6}}{e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} b^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{6 \left(\tan^{4}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) a^{4}}{e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{10 b^{2} \left(\tan^{4}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) a^{2}}{e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{2 b^{4} \left(\tan^{4}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{8 a^{7} \left(\tan^{3}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{3 e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} b^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{4 a^{5} \left(\tan^{3}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{3 e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} b \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{4 a^{3} b \left(\tan^{3}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{12 a \,b^{3} \left(\tan^{3}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{4 \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) a^{6}}{e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} b^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{12 b^{2} \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) a^{2}}{e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{4 b^{4} \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{2 a^{5} \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} b \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{8 a \,b^{3} \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{2 a^{4}}{3 e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{2 a^{2} b^{2}}{3 e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{2 b^{4}}{e \left(b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+b \right)^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{2 a b \arctan \left(\frac{2 b \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{e \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{-a^{2}+b^{2}}}"," ",0,"-2/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3*a^5/b/(a^4-2*a^2*b^2+b^4)*tan(1/2*d+1/2*e*x)^5+4/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3*a^3*b/(a^4-2*a^2*b^2+b^4)*tan(1/2*d+1/2*e*x)^5-4/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3*a*b^3/(a^4-2*a^2*b^2+b^4)*tan(1/2*d+1/2*e*x)^5-4/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3/b^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*d+1/2*e*x)^4*a^6+6/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3/(a^4-2*a^2*b^2+b^4)*tan(1/2*d+1/2*e*x)^4*a^4-10/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3*b^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*d+1/2*e*x)^4*a^2-2/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3*b^4/(a^4-2*a^2*b^2+b^4)*tan(1/2*d+1/2*e*x)^4-8/3/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3*a^7/b^3/(a^4-2*a^2*b^2+b^4)*tan(1/2*d+1/2*e*x)^3-4/3/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3*a^5/b/(a^4-2*a^2*b^2+b^4)*tan(1/2*d+1/2*e*x)^3-4/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3*a^3*b/(a^4-2*a^2*b^2+b^4)*tan(1/2*d+1/2*e*x)^3-12/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3*a*b^3/(a^4-2*a^2*b^2+b^4)*tan(1/2*d+1/2*e*x)^3-4/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3/b^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*d+1/2*e*x)^2*a^6-12/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3*b^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*d+1/2*e*x)^2*a^2-4/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3*b^4/(a^4-2*a^2*b^2+b^4)*tan(1/2*d+1/2*e*x)^2-2/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3*a^5/b/(a^4-2*a^2*b^2+b^4)*tan(1/2*d+1/2*e*x)-8/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3*a*b^3/(a^4-2*a^2*b^2+b^4)*tan(1/2*d+1/2*e*x)-2/3/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3/(a^4-2*a^2*b^2+b^4)*a^4+2/3/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3/(a^4-2*a^2*b^2+b^4)*a^2*b^2-2/e/(b*tan(1/2*d+1/2*e*x)^2+2*a*tan(1/2*d+1/2*e*x)+b)^3/(a^4-2*a^2*b^2+b^4)*b^4-2/e*a*b/(a^4-2*a^2*b^2+b^4)/(-a^2+b^2)^(1/2)*arctan(1/2*(2*b*tan(1/2*d+1/2*e*x)+2*a)/(-a^2+b^2)^(1/2))","B"
503,1,832,206,0.178000," ","int((d+e*sin(x))/(a+b*sin(x)+c*sin(x)^2),x)","\frac{8 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 a c +b^{2}}}{\sqrt{4 a c -2 b^{2}-2 b \sqrt{-4 a c +b^{2}}+4 a^{2}}}\right) d c}{\left(4 a c -b^{2}\right) \sqrt{4 a c -2 b^{2}-2 b \sqrt{-4 a c +b^{2}}+4 a^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 a c +b^{2}}}{\sqrt{4 a c -2 b^{2}-2 b \sqrt{-4 a c +b^{2}}+4 a^{2}}}\right) d \,b^{2}}{\left(4 a c -b^{2}\right) \sqrt{4 a c -2 b^{2}-2 b \sqrt{-4 a c +b^{2}}+4 a^{2}}}+\frac{4 a \sqrt{-4 a c +b^{2}}\, \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 a c +b^{2}}}{\sqrt{4 a c -2 b^{2}-2 b \sqrt{-4 a c +b^{2}}+4 a^{2}}}\right) e}{\left(4 a c -b^{2}\right) \sqrt{4 a c -2 b^{2}-2 b \sqrt{-4 a c +b^{2}}+4 a^{2}}}-\frac{2 \sqrt{-4 a c +b^{2}}\, \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 a c +b^{2}}}{\sqrt{4 a c -2 b^{2}-2 b \sqrt{-4 a c +b^{2}}+4 a^{2}}}\right) d b}{\left(4 a c -b^{2}\right) \sqrt{4 a c -2 b^{2}-2 b \sqrt{-4 a c +b^{2}}+4 a^{2}}}-\frac{8 a \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 a c +b^{2}}-b}{\sqrt{4 a c -2 b^{2}+2 b \sqrt{-4 a c +b^{2}}+4 a^{2}}}\right) d c}{\left(4 a c -b^{2}\right) \sqrt{4 a c -2 b^{2}+2 b \sqrt{-4 a c +b^{2}}+4 a^{2}}}+\frac{2 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 a c +b^{2}}-b}{\sqrt{4 a c -2 b^{2}+2 b \sqrt{-4 a c +b^{2}}+4 a^{2}}}\right) d \,b^{2}}{\left(4 a c -b^{2}\right) \sqrt{4 a c -2 b^{2}+2 b \sqrt{-4 a c +b^{2}}+4 a^{2}}}+\frac{4 a \sqrt{-4 a c +b^{2}}\, \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 a c +b^{2}}-b}{\sqrt{4 a c -2 b^{2}+2 b \sqrt{-4 a c +b^{2}}+4 a^{2}}}\right) e}{\left(4 a c -b^{2}\right) \sqrt{4 a c -2 b^{2}+2 b \sqrt{-4 a c +b^{2}}+4 a^{2}}}-\frac{2 \sqrt{-4 a c +b^{2}}\, \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 a c +b^{2}}-b}{\sqrt{4 a c -2 b^{2}+2 b \sqrt{-4 a c +b^{2}}+4 a^{2}}}\right) d b}{\left(4 a c -b^{2}\right) \sqrt{4 a c -2 b^{2}+2 b \sqrt{-4 a c +b^{2}}+4 a^{2}}}"," ",0,"8*a/(4*a*c-b^2)/(4*a*c-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*a*c-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*d*c-2/(4*a*c-b^2)/(4*a*c-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*a*c-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*d*b^2+4*a*(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/(4*a*c-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*a*c-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*e-2*(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/(4*a*c-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*a*c-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*d*b-8*a/(4*a*c-b^2)/(4*a*c-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*a*c-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*d*c+2/(4*a*c-b^2)/(4*a*c-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*a*c-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*d*b^2+4*a*(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/(4*a*c-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*a*c-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*e-2*(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/(4*a*c-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*a*c-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*d*b","B"
504,1,269,311,0.786000," ","int((a+b*sin(e*x+d))*(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^(3/2),x)","-\frac{\left(-a^{2} \left(\cos^{2}\left(e x +d \right)\right)+2 a b \sin \left(e x +d \right)+a^{2}+b^{2}\right)^{\frac{3}{2}} \left(6 \left(\cos^{3}\left(e x +d \right)\right) \sin \left(e x +d \right) a^{3} b +8 a^{4} \left(\cos^{3}\left(e x +d \right)\right)+24 a^{2} b^{2} \left(\cos^{3}\left(e x +d \right)\right)-51 \sin \left(e x +d \right) \cos \left(e x +d \right) a^{3} b -36 \cos \left(e x +d \right) \sin \left(e x +d \right) a \,b^{3}-24 a^{4} \cos \left(e x +d \right)-144 a^{2} b^{2} \cos \left(e x +d \right)-24 \cos \left(e x +d \right) b^{4}+45 \left(e x +d \right) a^{3} b +60 \left(e x +d \right) a \,b^{3}-16 a^{4}-120 a^{2} b^{2}-24 b^{4}\right)}{24 e \left(\left(\cos^{2}\left(e x +d \right)\right) \sin \left(e x +d \right) a^{3}+3 \left(\cos^{2}\left(e x +d \right)\right) a^{2} b -a^{3} \sin \left(e x +d \right)-3 \sin \left(e x +d \right) a \,b^{2}-3 a^{2} b -b^{3}\right)}"," ",0,"-1/24/e*(-a^2*cos(e*x+d)^2+2*a*b*sin(e*x+d)+a^2+b^2)^(3/2)*(6*cos(e*x+d)^3*sin(e*x+d)*a^3*b+8*a^4*cos(e*x+d)^3+24*a^2*b^2*cos(e*x+d)^3-51*sin(e*x+d)*cos(e*x+d)*a^3*b-36*cos(e*x+d)*sin(e*x+d)*a*b^3-24*a^4*cos(e*x+d)-144*a^2*b^2*cos(e*x+d)-24*cos(e*x+d)*b^4+45*(e*x+d)*a^3*b+60*(e*x+d)*a*b^3-16*a^4-120*a^2*b^2-24*b^4)/(cos(e*x+d)^2*sin(e*x+d)*a^3+3*cos(e*x+d)^2*a^2*b-a^3*sin(e*x+d)-3*sin(e*x+d)*a*b^2-3*a^2*b-b^3)","A"
505,1,107,175,0.586000," ","int((a+b*sin(e*x+d))*(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^(1/2),x)","-\frac{\sqrt{-a^{2} \left(\cos^{2}\left(e x +d \right)\right)+2 a b \sin \left(e x +d \right)+a^{2}+b^{2}}\, \left(\sin \left(e x +d \right) \cos \left(e x +d \right) a b +2 a^{2} \cos \left(e x +d \right)+2 \cos \left(e x +d \right) b^{2}-3 \left(e x +d \right) a b +2 a^{2}+2 b^{2}\right)}{2 e \left(b +a \sin \left(e x +d \right)\right)}"," ",0,"-1/2/e*(-a^2*cos(e*x+d)^2+2*a*b*sin(e*x+d)+a^2+b^2)^(1/2)*(sin(e*x+d)*cos(e*x+d)*a*b+2*a^2*cos(e*x+d)+2*cos(e*x+d)*b^2-3*(e*x+d)*a*b+2*a^2+2*b^2)/(b+a*sin(e*x+d))","A"
506,1,176,128,0.458000," ","int((a+b*sin(e*x+d))/(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^(1/2),x)","-\frac{\left(2 \arctan \left(\frac{b \cos \left(e x +d \right)-a \sin \left(e x +d \right)-b}{\sin \left(e x +d \right) \sqrt{-a^{2}+b^{2}}}\right) a^{2}-2 \arctan \left(\frac{b \cos \left(e x +d \right)-a \sin \left(e x +d \right)-b}{\sin \left(e x +d \right) \sqrt{-a^{2}+b^{2}}}\right) b^{2}-b \left(e x +d \right) \sqrt{-a^{2}+b^{2}}\right) \left(b +a \sin \left(e x +d \right)\right)}{e \sqrt{-a^{2} \left(\cos^{2}\left(e x +d \right)\right)+2 a b \sin \left(e x +d \right)+a^{2}+b^{2}}\, a \sqrt{-a^{2}+b^{2}}}"," ",0,"-1/e*(2*arctan((b*cos(e*x+d)-a*sin(e*x+d)-b)/sin(e*x+d)/(-a^2+b^2)^(1/2))*a^2-2*arctan((b*cos(e*x+d)-a*sin(e*x+d)-b)/sin(e*x+d)/(-a^2+b^2)^(1/2))*b^2-b*(e*x+d)*(-a^2+b^2)^(1/2))*(b+a*sin(e*x+d))/(-a^2*cos(e*x+d)^2+2*a*b*sin(e*x+d)+a^2+b^2)^(1/2)/a/(-a^2+b^2)^(1/2)","A"
507,1,741,224,0.413000," ","int((a+b*sin(e*x+d))/(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^(3/2),x)","\frac{2 \sin \left(e x +d \right) \left(\cos^{2}\left(e x +d \right)\right) \arctan \left(\frac{b \cos \left(e x +d \right)-a \sin \left(e x +d \right)-b}{\sin \left(e x +d \right) \sqrt{-a^{2}+b^{2}}}\right) a^{4} b^{2}+\sqrt{-a^{2}+b^{2}}\, \sin \left(e x +d \right) \left(\cos^{2}\left(e x +d \right)\right) a^{5}-2 \sqrt{-a^{2}+b^{2}}\, \sin \left(e x +d \right) \left(\cos^{2}\left(e x +d \right)\right) a^{3} b^{2}-\sqrt{-a^{2}+b^{2}}\, \left(\cos^{3}\left(e x +d \right)\right) a^{2} b^{3}+6 \left(\cos^{2}\left(e x +d \right)\right) \arctan \left(\frac{b \cos \left(e x +d \right)-a \sin \left(e x +d \right)-b}{\sin \left(e x +d \right) \sqrt{-a^{2}+b^{2}}}\right) a^{3} b^{3}-\sqrt{-a^{2}+b^{2}}\, \sin \left(e x +d \right) \cos \left(e x +d \right) a^{3} b^{2}+3 \sqrt{-a^{2}+b^{2}}\, \sin \left(e x +d \right) \cos \left(e x +d \right) a \,b^{4}+3 \sqrt{-a^{2}+b^{2}}\, \left(\cos^{2}\left(e x +d \right)\right) a^{4} b -6 \sqrt{-a^{2}+b^{2}}\, \left(\cos^{2}\left(e x +d \right)\right) a^{2} b^{3}-2 \sin \left(e x +d \right) \arctan \left(\frac{b \cos \left(e x +d \right)-a \sin \left(e x +d \right)-b}{\sin \left(e x +d \right) \sqrt{-a^{2}+b^{2}}}\right) a^{4} b^{2}-6 \sin \left(e x +d \right) \arctan \left(\frac{b \cos \left(e x +d \right)-a \sin \left(e x +d \right)-b}{\sin \left(e x +d \right) \sqrt{-a^{2}+b^{2}}}\right) a^{2} b^{4}-\sqrt{-a^{2}+b^{2}}\, \sin \left(e x +d \right) a^{5}-\sqrt{-a^{2}+b^{2}}\, \sin \left(e x +d \right) a^{3} b^{2}+6 \sqrt{-a^{2}+b^{2}}\, \sin \left(e x +d \right) a \,b^{4}+2 \sqrt{-a^{2}+b^{2}}\, \cos \left(e x +d \right) b^{5}-6 \arctan \left(\frac{b \cos \left(e x +d \right)-a \sin \left(e x +d \right)-b}{\sin \left(e x +d \right) \sqrt{-a^{2}+b^{2}}}\right) a^{3} b^{3}-2 \arctan \left(\frac{b \cos \left(e x +d \right)-a \sin \left(e x +d \right)-b}{\sin \left(e x +d \right) \sqrt{-a^{2}+b^{2}}}\right) a \,b^{5}-3 \sqrt{-a^{2}+b^{2}}\, a^{4} b +5 \sqrt{-a^{2}+b^{2}}\, a^{2} b^{3}+2 \sqrt{-a^{2}+b^{2}}\, b^{5}}{2 e \left(-a^{2} \left(\cos^{2}\left(e x +d \right)\right)+2 a b \sin \left(e x +d \right)+a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{-a^{2}+b^{2}}\, \left(a^{2}-b^{2}\right) b^{2}}"," ",0,"1/2/e*(2*sin(e*x+d)*cos(e*x+d)^2*arctan((b*cos(e*x+d)-a*sin(e*x+d)-b)/sin(e*x+d)/(-a^2+b^2)^(1/2))*a^4*b^2+(-a^2+b^2)^(1/2)*sin(e*x+d)*cos(e*x+d)^2*a^5-2*(-a^2+b^2)^(1/2)*sin(e*x+d)*cos(e*x+d)^2*a^3*b^2-(-a^2+b^2)^(1/2)*cos(e*x+d)^3*a^2*b^3+6*cos(e*x+d)^2*arctan((b*cos(e*x+d)-a*sin(e*x+d)-b)/sin(e*x+d)/(-a^2+b^2)^(1/2))*a^3*b^3-(-a^2+b^2)^(1/2)*sin(e*x+d)*cos(e*x+d)*a^3*b^2+3*(-a^2+b^2)^(1/2)*sin(e*x+d)*cos(e*x+d)*a*b^4+3*(-a^2+b^2)^(1/2)*cos(e*x+d)^2*a^4*b-6*(-a^2+b^2)^(1/2)*cos(e*x+d)^2*a^2*b^3-2*sin(e*x+d)*arctan((b*cos(e*x+d)-a*sin(e*x+d)-b)/sin(e*x+d)/(-a^2+b^2)^(1/2))*a^4*b^2-6*sin(e*x+d)*arctan((b*cos(e*x+d)-a*sin(e*x+d)-b)/sin(e*x+d)/(-a^2+b^2)^(1/2))*a^2*b^4-(-a^2+b^2)^(1/2)*sin(e*x+d)*a^5-(-a^2+b^2)^(1/2)*sin(e*x+d)*a^3*b^2+6*(-a^2+b^2)^(1/2)*sin(e*x+d)*a*b^4+2*(-a^2+b^2)^(1/2)*cos(e*x+d)*b^5-6*arctan((b*cos(e*x+d)-a*sin(e*x+d)-b)/sin(e*x+d)/(-a^2+b^2)^(1/2))*a^3*b^3-2*arctan((b*cos(e*x+d)-a*sin(e*x+d)-b)/sin(e*x+d)/(-a^2+b^2)^(1/2))*a*b^5-3*(-a^2+b^2)^(1/2)*a^4*b+5*(-a^2+b^2)^(1/2)*a^2*b^3+2*(-a^2+b^2)^(1/2)*b^5)/(-a^2*cos(e*x+d)^2+2*a*b*sin(e*x+d)+a^2+b^2)^(3/2)/(-a^2+b^2)^(1/2)/(a^2-b^2)/b^2","B"
508,1,33,11,0.086000," ","int((a+b*cos(x))/(b^2+2*a*b*cos(x)+a^2*cos(x)^2),x)","-\frac{2 \tan \left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-a -b}"," ",0,"-2*tan(1/2*x)/(a*tan(1/2*x)^2-b*tan(1/2*x)^2-a-b)","B"
509,1,2556,204,0.124000," ","int((d+e*cos(x))/(a+b*cos(x)+c*cos(x)^2),x)","\text{Expression too large to display}"," ",0,"-2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2*e+2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2*e-1/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*d*b^2-1/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^2*e+1/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*d*b^2+1/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^2*e-2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2*d+2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2*d-b/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*d+b/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*e+c/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*d-c/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*e+c/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*d-c/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*e-a/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*e+a/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*d+a/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*d-a/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*e-b/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*d+b/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*e-a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*d*b-3*a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b*e+2*a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*d+3*b/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*d-3*b/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*d-2*c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a*e+c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b*e+2*c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a*e-c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b*e+a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*d*b+3*a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b*e-2*a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*d","B"
510,1,245,138,0.008000," ","int((a+b*tan(e*x+d))*(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^2,x)","\frac{a^{4} b \left(\tan^{4}\left(e x +d \right)\right)}{4 e}+\frac{\left(\tan^{3}\left(e x +d \right)\right) a^{5}}{3 e}+\frac{4 \left(\tan^{3}\left(e x +d \right)\right) a^{3} b^{2}}{3 e}+\frac{3 \left(\tan^{2}\left(e x +d \right)\right) a^{4} b}{2 e}+\frac{3 \left(\tan^{2}\left(e x +d \right)\right) a^{2} b^{3}}{e}-\frac{a^{5} \tan \left(e x +d \right)}{e}+\frac{2 a^{3} b^{2} \tan \left(e x +d \right)}{e}+\frac{4 a \,b^{4} \tan \left(e x +d \right)}{e}-\frac{3 \ln \left(1+\tan^{2}\left(e x +d \right)\right) a^{4} b}{2 e}-\frac{\ln \left(1+\tan^{2}\left(e x +d \right)\right) a^{2} b^{3}}{e}+\frac{\ln \left(1+\tan^{2}\left(e x +d \right)\right) b^{5}}{2 e}+\frac{\arctan \left(\tan \left(e x +d \right)\right) a^{5}}{e}-\frac{2 \arctan \left(\tan \left(e x +d \right)\right) a^{3} b^{2}}{e}-\frac{3 \arctan \left(\tan \left(e x +d \right)\right) a \,b^{4}}{e}"," ",0,"1/4/e*a^4*b*tan(e*x+d)^4+1/3/e*tan(e*x+d)^3*a^5+4/3/e*tan(e*x+d)^3*a^3*b^2+3/2/e*tan(e*x+d)^2*a^4*b+3/e*tan(e*x+d)^2*a^2*b^3-1/e*a^5*tan(e*x+d)+2/e*a^3*b^2*tan(e*x+d)+4/e*a*b^4*tan(e*x+d)-3/2/e*ln(1+tan(e*x+d)^2)*a^4*b-1/e*ln(1+tan(e*x+d)^2)*a^2*b^3+1/2/e*ln(1+tan(e*x+d)^2)*b^5+1/e*arctan(tan(e*x+d))*a^5-2/e*arctan(tan(e*x+d))*a^3*b^2-3/e*arctan(tan(e*x+d))*a*b^4","A"
511,1,117,70,0.007000," ","int((a+b*tan(e*x+d))*(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2),x)","\frac{a^{2} b \left(\tan^{2}\left(e x +d \right)\right)}{2 e}+\frac{a^{3} \tan \left(e x +d \right)}{e}+\frac{2 a \,b^{2} \tan \left(e x +d \right)}{e}+\frac{\ln \left(1+\tan^{2}\left(e x +d \right)\right) a^{2} b}{2 e}+\frac{\ln \left(1+\tan^{2}\left(e x +d \right)\right) b^{3}}{2 e}-\frac{\arctan \left(\tan \left(e x +d \right)\right) a^{3}}{e}-\frac{\arctan \left(\tan \left(e x +d \right)\right) a \,b^{2}}{e}"," ",0,"1/2/e*a^2*b*tan(e*x+d)^2+1/e*a^3*tan(e*x+d)+2*a*b^2*tan(e*x+d)/e+1/2/e*ln(1+tan(e*x+d)^2)*a^2*b+1/2/e*ln(1+tan(e*x+d)^2)*b^3-1/e*arctan(tan(e*x+d))*a^3-1/e*arctan(tan(e*x+d))*a*b^2","A"
512,1,222,100,0.164000," ","int((a+b*tan(e*x+d))/(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2),x)","-\frac{a^{2}}{e \left(a^{2}+b^{2}\right) \left(b +a \tan \left(e x +d \right)\right)}+\frac{b^{2}}{e \left(a^{2}+b^{2}\right) \left(b +a \tan \left(e x +d \right)\right)}+\frac{3 b \ln \left(b +a \tan \left(e x +d \right)\right) a^{2}}{e \left(a^{2}+b^{2}\right)^{2}}-\frac{b^{3} \ln \left(b +a \tan \left(e x +d \right)\right)}{e \left(a^{2}+b^{2}\right)^{2}}-\frac{3 \ln \left(1+\tan^{2}\left(e x +d \right)\right) a^{2} b}{2 e \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(e x +d \right)\right) b^{3}}{2 e \left(a^{2}+b^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(e x +d \right)\right) a^{3}}{e \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \arctan \left(\tan \left(e x +d \right)\right) a \,b^{2}}{e \left(a^{2}+b^{2}\right)^{2}}"," ",0,"-1/e/(a^2+b^2)/(b+a*tan(e*x+d))*a^2+1/e/(a^2+b^2)/(b+a*tan(e*x+d))*b^2+3/e*b/(a^2+b^2)^2*ln(b+a*tan(e*x+d))*a^2-1/e*b^3/(a^2+b^2)^2*ln(b+a*tan(e*x+d))-3/2/e/(a^2+b^2)^2*ln(1+tan(e*x+d)^2)*a^2*b+1/2/e/(a^2+b^2)^2*ln(1+tan(e*x+d)^2)*b^3-1/e/(a^2+b^2)^2*arctan(tan(e*x+d))*a^3+3/e/(a^2+b^2)^2*arctan(tan(e*x+d))*a*b^2","B"
513,1,458,193,0.176000," ","int((a+b*tan(e*x+d))/(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^2,x)","-\frac{a^{2}}{3 e \left(a^{2}+b^{2}\right) \left(b +a \tan \left(e x +d \right)\right)^{3}}+\frac{b^{2}}{3 e \left(a^{2}+b^{2}\right) \left(b +a \tan \left(e x +d \right)\right)^{3}}-\frac{3 b \,a^{2}}{2 e \left(a^{2}+b^{2}\right)^{2} \left(b +a \tan \left(e x +d \right)\right)^{2}}+\frac{b^{3}}{2 e \left(a^{2}+b^{2}\right)^{2} \left(b +a \tan \left(e x +d \right)\right)^{2}}+\frac{a^{4}}{e \left(a^{2}+b^{2}\right)^{3} \left(b +a \tan \left(e x +d \right)\right)}-\frac{6 a^{2} b^{2}}{e \left(a^{2}+b^{2}\right)^{3} \left(b +a \tan \left(e x +d \right)\right)}+\frac{b^{4}}{e \left(a^{2}+b^{2}\right)^{3} \left(b +a \tan \left(e x +d \right)\right)}-\frac{5 b \ln \left(b +a \tan \left(e x +d \right)\right) a^{4}}{e \left(a^{2}+b^{2}\right)^{4}}+\frac{10 b^{3} \ln \left(b +a \tan \left(e x +d \right)\right) a^{2}}{e \left(a^{2}+b^{2}\right)^{4}}-\frac{b^{5} \ln \left(b +a \tan \left(e x +d \right)\right)}{e \left(a^{2}+b^{2}\right)^{4}}+\frac{5 \ln \left(1+\tan^{2}\left(e x +d \right)\right) a^{4} b}{2 e \left(a^{2}+b^{2}\right)^{4}}-\frac{5 \ln \left(1+\tan^{2}\left(e x +d \right)\right) a^{2} b^{3}}{e \left(a^{2}+b^{2}\right)^{4}}+\frac{\ln \left(1+\tan^{2}\left(e x +d \right)\right) b^{5}}{2 e \left(a^{2}+b^{2}\right)^{4}}+\frac{\arctan \left(\tan \left(e x +d \right)\right) a^{5}}{e \left(a^{2}+b^{2}\right)^{4}}-\frac{10 \arctan \left(\tan \left(e x +d \right)\right) a^{3} b^{2}}{e \left(a^{2}+b^{2}\right)^{4}}+\frac{5 \arctan \left(\tan \left(e x +d \right)\right) a \,b^{4}}{e \left(a^{2}+b^{2}\right)^{4}}"," ",0,"-1/3/e/(a^2+b^2)/(b+a*tan(e*x+d))^3*a^2+1/3/e/(a^2+b^2)/(b+a*tan(e*x+d))^3*b^2-3/2/e*b/(a^2+b^2)^2/(b+a*tan(e*x+d))^2*a^2+1/2/e*b^3/(a^2+b^2)^2/(b+a*tan(e*x+d))^2+1/e/(a^2+b^2)^3/(b+a*tan(e*x+d))*a^4-6/e/(a^2+b^2)^3/(b+a*tan(e*x+d))*a^2*b^2+1/e/(a^2+b^2)^3/(b+a*tan(e*x+d))*b^4-5/e*b/(a^2+b^2)^4*ln(b+a*tan(e*x+d))*a^4+10/e*b^3/(a^2+b^2)^4*ln(b+a*tan(e*x+d))*a^2-1/e*b^5/(a^2+b^2)^4*ln(b+a*tan(e*x+d))+5/2/e/(a^2+b^2)^4*ln(1+tan(e*x+d)^2)*a^4*b-5/e/(a^2+b^2)^4*ln(1+tan(e*x+d)^2)*a^2*b^3+1/2/e/(a^2+b^2)^4*ln(1+tan(e*x+d)^2)*b^5+1/e/(a^2+b^2)^4*arctan(tan(e*x+d))*a^5-10/e/(a^2+b^2)^4*arctan(tan(e*x+d))*a^3*b^2+5/e/(a^2+b^2)^4*arctan(tan(e*x+d))*a*b^4","B"
514,1,158,270,0.309000," ","int((a+b*tan(e*x+d))*(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^(3/2),x)","-\frac{\left(b^{2}+2 a b \tan \left(e x +d \right)+a^{2} \left(\tan^{2}\left(e x +d \right)\right)\right)^{\frac{3}{2}} \left(-2 \left(\tan^{3}\left(e x +d \right)\right) a^{3} b -3 \left(\tan^{2}\left(e x +d \right)\right) a^{4}-9 \left(\tan^{2}\left(e x +d \right)\right) a^{2} b^{2}+3 \ln \left(1+\tan^{2}\left(e x +d \right)\right) a^{4}-3 \ln \left(1+\tan^{2}\left(e x +d \right)\right) b^{4}+12 \arctan \left(\tan \left(e x +d \right)\right) a^{3} b +12 \arctan \left(\tan \left(e x +d \right)\right) a \,b^{3}-12 \tan \left(e x +d \right) a^{3} b -18 \tan \left(e x +d \right) a \,b^{3}\right)}{6 e \left(b +a \tan \left(e x +d \right)\right)^{3}}"," ",0,"-1/6/e*((b+a*tan(e*x+d))^2)^(3/2)*(-2*tan(e*x+d)^3*a^3*b-3*tan(e*x+d)^2*a^4-9*tan(e*x+d)^2*a^2*b^2+3*ln(1+tan(e*x+d)^2)*a^4-3*ln(1+tan(e*x+d)^2)*b^4+12*arctan(tan(e*x+d))*a^3*b+12*arctan(tan(e*x+d))*a*b^3-12*tan(e*x+d)*a^3*b-18*tan(e*x+d)*a*b^3)/(b+a*tan(e*x+d))^3","A"
515,1,75,118,0.319000," ","int((b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^(1/2)*(a+b*tan(e*x+d)),x)","\frac{\mathrm{csgn}\left(b +a \tan \left(e x +d \right)\right) \left(\ln \left(a^{2} \left(\tan^{2}\left(e x +d \right)\right)+a^{2}\right) a^{2}+\ln \left(a^{2} \left(\tan^{2}\left(e x +d \right)\right)+a^{2}\right) b^{2}+2 a b \tan \left(e x +d \right)+2 b^{2}\right)}{2 e}"," ",0,"1/2/e*csgn(b+a*tan(e*x+d))*(ln(a^2*tan(e*x+d)^2+a^2)*a^2+ln(a^2*tan(e*x+d)^2+a^2)*b^2+2*a*b*tan(e*x+d)+2*b^2)","C"
516,1,114,134,0.227000," ","int((a+b*tan(e*x+d))/(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^(1/2),x)","\frac{\left(b +a \tan \left(e x +d \right)\right) \left(2 \ln \left(b +a \tan \left(e x +d \right)\right) a^{2}-2 \ln \left(b +a \tan \left(e x +d \right)\right) b^{2}-\ln \left(1+\tan^{2}\left(e x +d \right)\right) a^{2}+\ln \left(1+\tan^{2}\left(e x +d \right)\right) b^{2}+4 a b \arctan \left(\tan \left(e x +d \right)\right)\right)}{2 e \sqrt{b^{2}+2 a b \tan \left(e x +d \right)+a^{2} \left(\tan^{2}\left(e x +d \right)\right)}\, \left(a^{2}+b^{2}\right)}"," ",0,"1/2/e*(b+a*tan(e*x+d))*(2*ln(b+a*tan(e*x+d))*a^2-2*ln(b+a*tan(e*x+d))*b^2-ln(1+tan(e*x+d)^2)*a^2+ln(1+tan(e*x+d)^2)*b^2+4*a*b*arctan(tan(e*x+d)))/((b+a*tan(e*x+d))^2)^(1/2)/(a^2+b^2)","A"
517,1,622,306,0.190000," ","int((a+b*tan(e*x+d))/(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^(3/2),x)","-\frac{\left(3 a^{2} b^{4}+a^{6}-3 b^{6}+6 \ln \left(1+\tan^{2}\left(e x +d \right)\right) \left(\tan^{2}\left(e x +d \right)\right) a^{4} b^{2}+2 \ln \left(b +a \tan \left(e x +d \right)\right) \left(\tan^{2}\left(e x +d \right)\right) a^{2} b^{4}-12 \ln \left(b +a \tan \left(e x +d \right)\right) \left(\tan^{2}\left(e x +d \right)\right) a^{4} b^{2}-\ln \left(1+\tan^{2}\left(e x +d \right)\right) \left(\tan^{2}\left(e x +d \right)\right) a^{2} b^{4}+8 \arctan \left(\tan \left(e x +d \right)\right) \left(\tan^{2}\left(e x +d \right)\right) a^{5} b -8 \arctan \left(\tan \left(e x +d \right)\right) \left(\tan^{2}\left(e x +d \right)\right) a^{3} b^{3}-2 \ln \left(1+\tan^{2}\left(e x +d \right)\right) \tan \left(e x +d \right) a^{5} b +12 \ln \left(1+\tan^{2}\left(e x +d \right)\right) \tan \left(e x +d \right) a^{3} b^{3}-2 \ln \left(1+\tan^{2}\left(e x +d \right)\right) \tan \left(e x +d \right) a \,b^{5}+4 \ln \left(b +a \tan \left(e x +d \right)\right) \tan \left(e x +d \right) a^{5} b -24 \ln \left(b +a \tan \left(e x +d \right)\right) \tan \left(e x +d \right) a^{3} b^{3}+4 \ln \left(b +a \tan \left(e x +d \right)\right) \tan \left(e x +d \right) a \,b^{5}+16 \arctan \left(\tan \left(e x +d \right)\right) \tan \left(e x +d \right) a^{4} b^{2}-16 \arctan \left(\tan \left(e x +d \right)\right) \tan \left(e x +d \right) a^{2} b^{4}+6 \ln \left(1+\tan^{2}\left(e x +d \right)\right) a^{2} b^{4}-\ln \left(1+\tan^{2}\left(e x +d \right)\right) a^{4} b^{2}-\ln \left(1+\tan^{2}\left(e x +d \right)\right) \left(\tan^{2}\left(e x +d \right)\right) a^{6}+2 \ln \left(b +a \tan \left(e x +d \right)\right) b^{6}-\ln \left(1+\tan^{2}\left(e x +d \right)\right) b^{6}+2 \ln \left(b +a \tan \left(e x +d \right)\right) \left(\tan^{2}\left(e x +d \right)\right) a^{6}+6 \tan \left(e x +d \right) a^{5} b +4 \tan \left(e x +d \right) a^{3} b^{3}-2 \tan \left(e x +d \right) a \,b^{5}+2 \ln \left(b +a \tan \left(e x +d \right)\right) a^{4} b^{2}-12 \ln \left(b +a \tan \left(e x +d \right)\right) a^{2} b^{4}+8 \arctan \left(\tan \left(e x +d \right)\right) a^{3} b^{3}-8 \arctan \left(\tan \left(e x +d \right)\right) a \,b^{5}+7 a^{4} b^{2}\right) \left(b +a \tan \left(e x +d \right)\right)}{2 e \left(a^{2}+b^{2}\right)^{3} \left(b^{2}+2 a b \tan \left(e x +d \right)+a^{2} \left(\tan^{2}\left(e x +d \right)\right)\right)^{\frac{3}{2}}}"," ",0,"-1/2/e*(2*ln(b+a*tan(e*x+d))*tan(e*x+d)^2*a^6+3*a^2*b^4+a^6-3*b^6+6*ln(1+tan(e*x+d)^2)*tan(e*x+d)^2*a^4*b^2+2*ln(b+a*tan(e*x+d))*tan(e*x+d)^2*a^2*b^4-12*ln(b+a*tan(e*x+d))*tan(e*x+d)^2*a^4*b^2-ln(1+tan(e*x+d)^2)*tan(e*x+d)^2*a^2*b^4+8*arctan(tan(e*x+d))*tan(e*x+d)^2*a^5*b-8*arctan(tan(e*x+d))*tan(e*x+d)^2*a^3*b^3+4*ln(b+a*tan(e*x+d))*tan(e*x+d)*a^5*b-24*ln(b+a*tan(e*x+d))*tan(e*x+d)*a^3*b^3+4*ln(b+a*tan(e*x+d))*tan(e*x+d)*a*b^5-2*ln(1+tan(e*x+d)^2)*tan(e*x+d)*a^5*b+12*ln(1+tan(e*x+d)^2)*tan(e*x+d)*a^3*b^3-2*ln(1+tan(e*x+d)^2)*tan(e*x+d)*a*b^5+16*arctan(tan(e*x+d))*tan(e*x+d)*a^4*b^2-16*arctan(tan(e*x+d))*tan(e*x+d)*a^2*b^4+2*ln(b+a*tan(e*x+d))*b^6-ln(1+tan(e*x+d)^2)*b^6+6*tan(e*x+d)*a^5*b+4*tan(e*x+d)*a^3*b^3-2*tan(e*x+d)*a*b^5-ln(1+tan(e*x+d)^2)*tan(e*x+d)^2*a^6+2*ln(b+a*tan(e*x+d))*a^4*b^2-12*ln(b+a*tan(e*x+d))*a^2*b^4-ln(1+tan(e*x+d)^2)*a^4*b^2+6*ln(1+tan(e*x+d)^2)*a^2*b^4+8*arctan(tan(e*x+d))*a^3*b^3-8*arctan(tan(e*x+d))*a*b^5+7*a^4*b^2)*(b+a*tan(e*x+d))/(a^2+b^2)^3/((b+a*tan(e*x+d))^2)^(3/2)","B"
518,1,246,174,0.141000," ","int((a+b*sec(e*x+d))*(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^2,x)","a \,b^{4} x +\frac{a \,b^{4} d}{e}+\frac{7 a^{2} b^{3} \ln \left(\sec \left(e x +d \right)+\tan \left(e x +d \right)\right)}{e}+\frac{26 a^{3} b^{2} \tan \left(e x +d \right)}{3 e}+\frac{19 a^{4} b \sec \left(e x +d \right) \tan \left(e x +d \right)}{8 e}+\frac{19 a^{4} b \ln \left(\sec \left(e x +d \right)+\tan \left(e x +d \right)\right)}{8 e}+\frac{2 a^{5} \tan \left(e x +d \right)}{3 e}+\frac{a^{5} \tan \left(e x +d \right) \left(\sec^{2}\left(e x +d \right)\right)}{3 e}+\frac{b^{5} \ln \left(\sec \left(e x +d \right)+\tan \left(e x +d \right)\right)}{e}+\frac{4 a \,b^{4} \tan \left(e x +d \right)}{e}+\frac{3 a^{2} b^{3} \sec \left(e x +d \right) \tan \left(e x +d \right)}{e}+\frac{4 a^{3} b^{2} \tan \left(e x +d \right) \left(\sec^{2}\left(e x +d \right)\right)}{3 e}+\frac{a^{4} b \tan \left(e x +d \right) \left(\sec^{3}\left(e x +d \right)\right)}{4 e}"," ",0,"a*b^4*x+1/e*a*b^4*d+7/e*a^2*b^3*ln(sec(e*x+d)+tan(e*x+d))+26/3/e*a^3*b^2*tan(e*x+d)+19/8/e*a^4*b*sec(e*x+d)*tan(e*x+d)+19/8/e*a^4*b*ln(sec(e*x+d)+tan(e*x+d))+2/3/e*a^5*tan(e*x+d)+1/3/e*a^5*tan(e*x+d)*sec(e*x+d)^2+1/e*b^5*ln(sec(e*x+d)+tan(e*x+d))+4/e*a*b^4*tan(e*x+d)+3/e*a^2*b^3*sec(e*x+d)*tan(e*x+d)+4/3/e*a^3*b^2*tan(e*x+d)*sec(e*x+d)^2+1/4/e*a^4*b*tan(e*x+d)*sec(e*x+d)^3","A"
519,1,110,72,0.092000," ","int((a+b*sec(e*x+d))*(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2),x)","a \,b^{2} x +\frac{a \,b^{2} d}{e}+\frac{5 a^{2} b \ln \left(\sec \left(e x +d \right)+\tan \left(e x +d \right)\right)}{2 e}+\frac{a^{3} \tan \left(e x +d \right)}{e}+\frac{b^{3} \ln \left(\sec \left(e x +d \right)+\tan \left(e x +d \right)\right)}{e}+\frac{2 a \,b^{2} \tan \left(e x +d \right)}{e}+\frac{a^{2} b \sec \left(e x +d \right) \tan \left(e x +d \right)}{2 e}"," ",0,"a*b^2*x+1/e*a*b^2*d+5/2/e*a^2*b*ln(sec(e*x+d)+tan(e*x+d))+1/e*a^3*tan(e*x+d)+1/e*b^3*ln(sec(e*x+d)+tan(e*x+d))+2*a*b^2*tan(e*x+d)/e+1/2*a^2*b*sec(e*x+d)*tan(e*x+d)/e","A"
520,1,163,83,0.287000," ","int((a+b*sec(e*x+d))/(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2),x)","-\frac{2 \tan \left(\frac{d}{2}+\frac{e x}{2}\right) a}{e b \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+a +b \right)}-\frac{2 \arctan \left(\frac{\tan \left(\frac{d}{2}+\frac{e x}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right) a^{2}}{e \,b^{2} \sqrt{\left(a +b \right) \left(a -b \right)}}+\frac{2 \arctan \left(\frac{\tan \left(\frac{d}{2}+\frac{e x}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{e \sqrt{\left(a +b \right) \left(a -b \right)}}+\frac{2 a \arctan \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e \,b^{2}}"," ",0,"-2/e/b*tan(1/2*d+1/2*e*x)*a/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+a+b)-2/e/b^2/((a+b)*(a-b))^(1/2)*arctan(tan(1/2*d+1/2*e*x)*(a-b)/((a+b)*(a-b))^(1/2))*a^2+2/e/((a+b)*(a-b))^(1/2)*arctan(tan(1/2*d+1/2*e*x)*(a-b)/((a+b)*(a-b))^(1/2))+2/e*a/b^2*arctan(tan(1/2*d+1/2*e*x))","A"
521,1,1118,215,0.348000," ","int((a+b*sec(e*x+d))/(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^2,x)","-\frac{2 a^{5} \left(\tan^{5}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e \,b^{3} \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+a +b \right)^{3} \left(a^{2}+2 a b +b^{2}\right)}+\frac{a^{4} \left(\tan^{5}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e \,b^{2} \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+a +b \right)^{3} \left(a^{2}+2 a b +b^{2}\right)}+\frac{4 a^{3} \left(\tan^{5}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e b \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+a +b \right)^{3} \left(a^{2}+2 a b +b^{2}\right)}-\frac{3 a^{2} \left(\tan^{5}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+a +b \right)^{3} \left(a^{2}+2 a b +b^{2}\right)}-\frac{6 b a \left(\tan^{5}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+a +b \right)^{3} \left(a^{2}+2 a b +b^{2}\right)}-\frac{4 a^{5} \left(\tan^{3}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e \,b^{3} \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+a +b \right)^{3} \left(a +b \right) \left(a -b \right)}+\frac{32 a^{3} \left(\tan^{3}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{3 e b \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+a +b \right)^{3} \left(a +b \right) \left(a -b \right)}-\frac{12 b a \left(\tan^{3}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+a +b \right)^{3} \left(a +b \right) \left(a -b \right)}-\frac{2 a^{5} \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{e \,b^{3} \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+a +b \right)^{3} \left(a^{2}-2 a b +b^{2}\right)}-\frac{a^{4} \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{e \,b^{2} \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+a +b \right)^{3} \left(a^{2}-2 a b +b^{2}\right)}+\frac{4 a^{3} \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{e b \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+a +b \right)^{3} \left(a^{2}-2 a b +b^{2}\right)}+\frac{3 a^{2} \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+a +b \right)^{3} \left(a^{2}-2 a b +b^{2}\right)}-\frac{6 b a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+a +b \right)^{3} \left(a^{2}-2 a b +b^{2}\right)}-\frac{2 \arctan \left(\frac{\tan \left(\frac{d}{2}+\frac{e x}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right) a^{6}}{e \,b^{4} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a +b \right) \left(a -b \right)}}+\frac{5 \arctan \left(\frac{\tan \left(\frac{d}{2}+\frac{e x}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right) a^{4}}{e \,b^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a +b \right) \left(a -b \right)}}-\frac{3 \arctan \left(\frac{\tan \left(\frac{d}{2}+\frac{e x}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right) a^{2}}{e \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a +b \right) \left(a -b \right)}}+\frac{2 b^{2} \arctan \left(\frac{\tan \left(\frac{d}{2}+\frac{e x}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{e \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a +b \right) \left(a -b \right)}}+\frac{2 a \arctan \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e \,b^{4}}"," ",0,"-2/e/b^3/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+a+b)^3*a^5/(a^2+2*a*b+b^2)*tan(1/2*d+1/2*e*x)^5+1/e/b^2/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+a+b)^3*a^4/(a^2+2*a*b+b^2)*tan(1/2*d+1/2*e*x)^5+4/e/b/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+a+b)^3*a^3/(a^2+2*a*b+b^2)*tan(1/2*d+1/2*e*x)^5-3/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+a+b)^3*a^2/(a^2+2*a*b+b^2)*tan(1/2*d+1/2*e*x)^5-6/e*b/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+a+b)^3*a/(a^2+2*a*b+b^2)*tan(1/2*d+1/2*e*x)^5-4/e/b^3/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+a+b)^3*a^5/(a+b)/(a-b)*tan(1/2*d+1/2*e*x)^3+32/3/e/b/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+a+b)^3*a^3/(a+b)/(a-b)*tan(1/2*d+1/2*e*x)^3-12/e*b/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+a+b)^3*a/(a+b)/(a-b)*tan(1/2*d+1/2*e*x)^3-2/e/b^3/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+a+b)^3*a^5/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)-1/e/b^2/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+a+b)^3*a^4/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)+4/e/b/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+a+b)^3*a^3/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)+3/e/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+a+b)^3*a^2/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)-6/e*b/(a*tan(1/2*d+1/2*e*x)^2-b*tan(1/2*d+1/2*e*x)^2+a+b)^3*a/(a^2-2*a*b+b^2)*tan(1/2*d+1/2*e*x)-2/e/b^4/(a^4-2*a^2*b^2+b^4)/((a+b)*(a-b))^(1/2)*arctan(tan(1/2*d+1/2*e*x)*(a-b)/((a+b)*(a-b))^(1/2))*a^6+5/e/b^2/(a^4-2*a^2*b^2+b^4)/((a+b)*(a-b))^(1/2)*arctan(tan(1/2*d+1/2*e*x)*(a-b)/((a+b)*(a-b))^(1/2))*a^4-3/e/(a^4-2*a^2*b^2+b^4)/((a+b)*(a-b))^(1/2)*arctan(tan(1/2*d+1/2*e*x)*(a-b)/((a+b)*(a-b))^(1/2))*a^2+2/e*b^2/(a^4-2*a^2*b^2+b^4)/((a+b)*(a-b))^(1/2)*arctan(tan(1/2*d+1/2*e*x)*(a-b)/((a+b)*(a-b))^(1/2))+2/e*a/b^4*arctan(tan(1/2*d+1/2*e*x))","B"
522,1,387,341,0.608000," ","int((a+b*sec(e*x+d))*(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^(3/2),x)","\frac{\left(3 \ln \left(\frac{1-\cos \left(e x +d \right)+\sin \left(e x +d \right)}{\sin \left(e x +d \right)}\right) \left(\cos^{3}\left(e x +d \right)\right) a^{4}+27 \ln \left(\frac{1-\cos \left(e x +d \right)+\sin \left(e x +d \right)}{\sin \left(e x +d \right)}\right) \left(\cos^{3}\left(e x +d \right)\right) a^{2} b^{2}+6 \ln \left(\frac{1-\cos \left(e x +d \right)+\sin \left(e x +d \right)}{\sin \left(e x +d \right)}\right) \left(\cos^{3}\left(e x +d \right)\right) b^{4}-3 \ln \left(-\frac{\cos \left(e x +d \right)-1+\sin \left(e x +d \right)}{\sin \left(e x +d \right)}\right) \left(\cos^{3}\left(e x +d \right)\right) a^{4}-27 \ln \left(-\frac{\cos \left(e x +d \right)-1+\sin \left(e x +d \right)}{\sin \left(e x +d \right)}\right) \left(\cos^{3}\left(e x +d \right)\right) a^{2} b^{2}-6 \ln \left(-\frac{\cos \left(e x +d \right)-1+\sin \left(e x +d \right)}{\sin \left(e x +d \right)}\right) \left(\cos^{3}\left(e x +d \right)\right) b^{4}+6 \left(\cos^{3}\left(e x +d \right)\right) \left(e x +d \right) a \,b^{3}+22 \sin \left(e x +d \right) \left(\cos^{2}\left(e x +d \right)\right) a^{3} b +18 \sin \left(e x +d \right) \left(\cos^{2}\left(e x +d \right)\right) a \,b^{3}+3 \sin \left(e x +d \right) \cos \left(e x +d \right) a^{4}+9 \sin \left(e x +d \right) \cos \left(e x +d \right) a^{2} b^{2}+2 a^{3} b \sin \left(e x +d \right)\right) \left(\frac{\left(b \cos \left(e x +d \right)+a \right)^{2}}{\cos \left(e x +d \right)^{2}}\right)^{\frac{3}{2}}}{6 e \left(b \cos \left(e x +d \right)+a \right)^{3}}"," ",0,"1/6/e*(3*ln((1-cos(e*x+d)+sin(e*x+d))/sin(e*x+d))*cos(e*x+d)^3*a^4+27*ln((1-cos(e*x+d)+sin(e*x+d))/sin(e*x+d))*cos(e*x+d)^3*a^2*b^2+6*ln((1-cos(e*x+d)+sin(e*x+d))/sin(e*x+d))*cos(e*x+d)^3*b^4-3*ln(-(cos(e*x+d)-1+sin(e*x+d))/sin(e*x+d))*cos(e*x+d)^3*a^4-27*ln(-(cos(e*x+d)-1+sin(e*x+d))/sin(e*x+d))*cos(e*x+d)^3*a^2*b^2-6*ln(-(cos(e*x+d)-1+sin(e*x+d))/sin(e*x+d))*cos(e*x+d)^3*b^4+6*cos(e*x+d)^3*(e*x+d)*a*b^3+22*sin(e*x+d)*cos(e*x+d)^2*a^3*b+18*sin(e*x+d)*cos(e*x+d)^2*a*b^3+3*sin(e*x+d)*cos(e*x+d)*a^4+9*sin(e*x+d)*cos(e*x+d)*a^2*b^2+2*a^3*b*sin(e*x+d))*((b*cos(e*x+d)+a)^2/cos(e*x+d)^2)^(3/2)/(b*cos(e*x+d)+a)^3","A"
523,1,211,167,0.585000," ","int((a+b*sec(e*x+d))*(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^(1/2),x)","-\frac{\left(\cos \left(e x +d \right) \ln \left(-\frac{\cos \left(e x +d \right)-1+\sin \left(e x +d \right)}{\sin \left(e x +d \right)}\right) a^{2}+\cos \left(e x +d \right) \ln \left(-\frac{\cos \left(e x +d \right)-1+\sin \left(e x +d \right)}{\sin \left(e x +d \right)}\right) b^{2}-\cos \left(e x +d \right) \ln \left(\frac{1-\cos \left(e x +d \right)+\sin \left(e x +d \right)}{\sin \left(e x +d \right)}\right) a^{2}-\cos \left(e x +d \right) \ln \left(\frac{1-\cos \left(e x +d \right)+\sin \left(e x +d \right)}{\sin \left(e x +d \right)}\right) b^{2}-\cos \left(e x +d \right) \left(e x +d \right) a b -a b \sin \left(e x +d \right)\right) \sqrt{\frac{\left(b \cos \left(e x +d \right)+a \right)^{2}}{\cos \left(e x +d \right)^{2}}}}{e \left(b \cos \left(e x +d \right)+a \right)}"," ",0,"-1/e*(cos(e*x+d)*ln(-(cos(e*x+d)-1+sin(e*x+d))/sin(e*x+d))*a^2+cos(e*x+d)*ln(-(cos(e*x+d)-1+sin(e*x+d))/sin(e*x+d))*b^2-cos(e*x+d)*ln((1-cos(e*x+d)+sin(e*x+d))/sin(e*x+d))*a^2-cos(e*x+d)*ln((1-cos(e*x+d)+sin(e*x+d))/sin(e*x+d))*b^2-cos(e*x+d)*(e*x+d)*a*b-a*b*sin(e*x+d))*((b*cos(e*x+d)+a)^2/cos(e*x+d)^2)^(1/2)/(b*cos(e*x+d)+a)","A"
524,1,157,129,0.665000," ","int((a+b*sec(e*x+d))/(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^(1/2),x)","\frac{\left(b \cos \left(e x +d \right)+a \right) \left(2 \arctan \left(\frac{\left(\cos \left(e x +d \right)-1\right) \left(a -b \right)}{\sin \left(e x +d \right) \sqrt{\left(a +b \right) \left(a -b \right)}}\right) a^{2}-2 \arctan \left(\frac{\left(\cos \left(e x +d \right)-1\right) \left(a -b \right)}{\sin \left(e x +d \right) \sqrt{\left(a +b \right) \left(a -b \right)}}\right) b^{2}+a \left(e x +d \right) \sqrt{\left(a +b \right) \left(a -b \right)}\right)}{e \cos \left(e x +d \right) \sqrt{\frac{\left(b \cos \left(e x +d \right)+a \right)^{2}}{\cos \left(e x +d \right)^{2}}}\, b \sqrt{\left(a +b \right) \left(a -b \right)}}"," ",0,"1/e*(b*cos(e*x+d)+a)*(2*arctan((cos(e*x+d)-1)*(a-b)/sin(e*x+d)/((a+b)*(a-b))^(1/2))*a^2-2*arctan((cos(e*x+d)-1)*(a-b)/sin(e*x+d)/((a+b)*(a-b))^(1/2))*b^2+a*(e*x+d)*((a+b)*(a-b))^(1/2))/cos(e*x+d)/((b*cos(e*x+d)+a)^2/cos(e*x+d)^2)^(1/2)/b/((a+b)*(a-b))^(1/2)","A"
525,1,756,309,0.614000," ","int((a+b*sec(e*x+d))/(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^(3/2),x)","\frac{\left(b \cos \left(e x +d \right)+a \right) \left(4 \arctan \left(\frac{\left(\cos \left(e x +d \right)-1\right) \left(a -b \right)}{\sin \left(e x +d \right) \sqrt{\left(a +b \right) \left(a -b \right)}}\right) \left(\cos^{2}\left(e x +d \right)\right) a^{4} b^{2}-6 \arctan \left(\frac{\left(\cos \left(e x +d \right)-1\right) \left(a -b \right)}{\sin \left(e x +d \right) \sqrt{\left(a +b \right) \left(a -b \right)}}\right) \left(\cos^{2}\left(e x +d \right)\right) a^{2} b^{4}+4 \arctan \left(\frac{\left(\cos \left(e x +d \right)-1\right) \left(a -b \right)}{\sin \left(e x +d \right) \sqrt{\left(a +b \right) \left(a -b \right)}}\right) \left(\cos^{2}\left(e x +d \right)\right) b^{6}+2 \left(\cos^{2}\left(e x +d \right)\right) \sqrt{\left(a +b \right) \left(a -b \right)}\, \left(e x +d \right) a^{3} b^{2}-2 \left(\cos^{2}\left(e x +d \right)\right) \sqrt{\left(a +b \right) \left(a -b \right)}\, \left(e x +d \right) a \,b^{4}+8 \arctan \left(\frac{\left(\cos \left(e x +d \right)-1\right) \left(a -b \right)}{\sin \left(e x +d \right) \sqrt{\left(a +b \right) \left(a -b \right)}}\right) \cos \left(e x +d \right) a^{5} b -12 \arctan \left(\frac{\left(\cos \left(e x +d \right)-1\right) \left(a -b \right)}{\sin \left(e x +d \right) \sqrt{\left(a +b \right) \left(a -b \right)}}\right) \cos \left(e x +d \right) a^{3} b^{3}+8 \arctan \left(\frac{\left(\cos \left(e x +d \right)-1\right) \left(a -b \right)}{\sin \left(e x +d \right) \sqrt{\left(a +b \right) \left(a -b \right)}}\right) \cos \left(e x +d \right) a \,b^{5}-3 \cos \left(e x +d \right) \sqrt{\left(a +b \right) \left(a -b \right)}\, \sin \left(e x +d \right) a^{3} b^{2}+4 \cos \left(e x +d \right) \sqrt{\left(a +b \right) \left(a -b \right)}\, \sin \left(e x +d \right) a \,b^{4}+4 \cos \left(e x +d \right) \sqrt{\left(a +b \right) \left(a -b \right)}\, \left(e x +d \right) a^{4} b -4 \cos \left(e x +d \right) \sqrt{\left(a +b \right) \left(a -b \right)}\, \left(e x +d \right) a^{2} b^{3}+4 \arctan \left(\frac{\left(\cos \left(e x +d \right)-1\right) \left(a -b \right)}{\sin \left(e x +d \right) \sqrt{\left(a +b \right) \left(a -b \right)}}\right) a^{6}-6 \arctan \left(\frac{\left(\cos \left(e x +d \right)-1\right) \left(a -b \right)}{\sin \left(e x +d \right) \sqrt{\left(a +b \right) \left(a -b \right)}}\right) a^{4} b^{2}+4 \arctan \left(\frac{\left(\cos \left(e x +d \right)-1\right) \left(a -b \right)}{\sin \left(e x +d \right) \sqrt{\left(a +b \right) \left(a -b \right)}}\right) a^{2} b^{4}-2 \sqrt{\left(a +b \right) \left(a -b \right)}\, a^{4} b \sin \left(e x +d \right)+3 \sqrt{\left(a +b \right) \left(a -b \right)}\, a^{2} b^{3} \sin \left(e x +d \right)+2 \sqrt{\left(a +b \right) \left(a -b \right)}\, \left(e x +d \right) a^{5}-2 \sqrt{\left(a +b \right) \left(a -b \right)}\, \left(e x +d \right) a^{3} b^{2}\right)}{2 e \cos \left(e x +d \right)^{3} \left(\frac{\left(b \cos \left(e x +d \right)+a \right)^{2}}{\cos \left(e x +d \right)^{2}}\right)^{\frac{3}{2}} \sqrt{\left(a +b \right) \left(a -b \right)}\, \left(a^{2}-b^{2}\right) b^{3}}"," ",0,"1/2/e*(b*cos(e*x+d)+a)*(4*arctan((cos(e*x+d)-1)*(a-b)/sin(e*x+d)/((a+b)*(a-b))^(1/2))*cos(e*x+d)^2*a^4*b^2-6*arctan((cos(e*x+d)-1)*(a-b)/sin(e*x+d)/((a+b)*(a-b))^(1/2))*cos(e*x+d)^2*a^2*b^4+4*arctan((cos(e*x+d)-1)*(a-b)/sin(e*x+d)/((a+b)*(a-b))^(1/2))*cos(e*x+d)^2*b^6+2*cos(e*x+d)^2*((a+b)*(a-b))^(1/2)*(e*x+d)*a^3*b^2-2*cos(e*x+d)^2*((a+b)*(a-b))^(1/2)*(e*x+d)*a*b^4+8*arctan((cos(e*x+d)-1)*(a-b)/sin(e*x+d)/((a+b)*(a-b))^(1/2))*cos(e*x+d)*a^5*b-12*arctan((cos(e*x+d)-1)*(a-b)/sin(e*x+d)/((a+b)*(a-b))^(1/2))*cos(e*x+d)*a^3*b^3+8*arctan((cos(e*x+d)-1)*(a-b)/sin(e*x+d)/((a+b)*(a-b))^(1/2))*cos(e*x+d)*a*b^5-3*cos(e*x+d)*((a+b)*(a-b))^(1/2)*sin(e*x+d)*a^3*b^2+4*cos(e*x+d)*((a+b)*(a-b))^(1/2)*sin(e*x+d)*a*b^4+4*cos(e*x+d)*((a+b)*(a-b))^(1/2)*(e*x+d)*a^4*b-4*cos(e*x+d)*((a+b)*(a-b))^(1/2)*(e*x+d)*a^2*b^3+4*arctan((cos(e*x+d)-1)*(a-b)/sin(e*x+d)/((a+b)*(a-b))^(1/2))*a^6-6*arctan((cos(e*x+d)-1)*(a-b)/sin(e*x+d)/((a+b)*(a-b))^(1/2))*a^4*b^2+4*arctan((cos(e*x+d)-1)*(a-b)/sin(e*x+d)/((a+b)*(a-b))^(1/2))*a^2*b^4-2*((a+b)*(a-b))^(1/2)*a^4*b*sin(e*x+d)+3*((a+b)*(a-b))^(1/2)*a^2*b^3*sin(e*x+d)+2*((a+b)*(a-b))^(1/2)*(e*x+d)*a^5-2*((a+b)*(a-b))^(1/2)*(e*x+d)*a^3*b^2)/cos(e*x+d)^3/((b*cos(e*x+d)+a)^2/cos(e*x+d)^2)^(3/2)/((a+b)*(a-b))^(1/2)/(a^2-b^2)/b^3","B"
526,1,8,13,0.196000," ","int((cos(x)-I*sin(x))/(cos(x)+I*sin(x)),x)","\frac{1}{\tan \left(x \right)-i}"," ",0,"1/(tan(x)-I)","A"
527,1,8,13,0.174000," ","int((cos(x)+I*sin(x))/(cos(x)-I*sin(x)),x)","\frac{1}{\tan \left(x \right)+i}"," ",0,"1/(tan(x)+I)","A"
528,1,7,6,0.058000," ","int((cos(x)-sin(x))/(cos(x)+sin(x)),x)","\ln \left(\cos \left(x \right)+\sin \left(x \right)\right)"," ",0,"ln(cos(x)+sin(x))","A"
529,1,111,47,0.135000," ","int((B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x)),x)","\frac{\ln \left(c \tan \left(x \right)+b \right) B c}{b^{2}+c^{2}}-\frac{\ln \left(c \tan \left(x \right)+b \right) b C}{b^{2}+c^{2}}-\frac{\ln \left(1+\tan^{2}\left(x \right)\right) B c}{2 \left(b^{2}+c^{2}\right)}+\frac{\ln \left(1+\tan^{2}\left(x \right)\right) b C}{2 b^{2}+2 c^{2}}+\frac{B \arctan \left(\tan \left(x \right)\right) b}{b^{2}+c^{2}}+\frac{C \arctan \left(\tan \left(x \right)\right) c}{b^{2}+c^{2}}"," ",0,"1/(b^2+c^2)*ln(c*tan(x)+b)*B*c-1/(b^2+c^2)*ln(c*tan(x)+b)*b*C-1/2/(b^2+c^2)*ln(1+tan(x)^2)*B*c+1/2/(b^2+c^2)*ln(1+tan(x)^2)*b*C+1/(b^2+c^2)*B*arctan(tan(x))*b+1/(b^2+c^2)*C*arctan(tan(x))*c","B"
530,1,113,69,0.173000," ","int((B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))^2,x)","-\frac{2 \left(-\frac{c \left(B c -b C \right) \tan \left(\frac{x}{2}\right)}{b \left(b^{2}+c^{2}\right)}-\frac{B c -b C}{b^{2}+c^{2}}\right)}{b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 c \tan \left(\frac{x}{2}\right)-b}+\frac{2 \left(b B +C c \right) \arctanh \left(\frac{2 b \tan \left(\frac{x}{2}\right)-2 c}{2 \sqrt{b^{2}+c^{2}}}\right)}{\left(b^{2}+c^{2}\right)^{\frac{3}{2}}}"," ",0,"-2*(-c*(B*c-C*b)/b/(b^2+c^2)*tan(1/2*x)-(B*c-C*b)/(b^2+c^2))/(b*tan(1/2*x)^2-2*c*tan(1/2*x)-b)+2*(B*b+C*c)/(b^2+c^2)^(3/2)*arctanh(1/2*(2*b*tan(1/2*x)-2*c)/(b^2+c^2)^(1/2))","A"
531,1,37,64,0.188000," ","int((B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))^3,x)","-\frac{B c -b C}{2 c^{2} \left(c \tan \left(x \right)+b \right)^{2}}-\frac{C}{c^{2} \left(c \tan \left(x \right)+b \right)}"," ",0,"-1/2*(B*c-C*b)/c^2/(c*tan(x)+b)^2-C/c^2/(c*tan(x)+b)","A"
532,1,222,80,0.137000," ","int((A+B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x)),x)","\frac{B c \ln \left(b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 c \tan \left(\frac{x}{2}\right)-b \right)}{b^{2}+c^{2}}-\frac{b C \ln \left(b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 c \tan \left(\frac{x}{2}\right)-b \right)}{b^{2}+c^{2}}+\frac{2 \arctanh \left(\frac{2 b \tan \left(\frac{x}{2}\right)-2 c}{2 \sqrt{b^{2}+c^{2}}}\right) A \,b^{2}}{\left(b^{2}+c^{2}\right)^{\frac{3}{2}}}+\frac{2 \arctanh \left(\frac{2 b \tan \left(\frac{x}{2}\right)-2 c}{2 \sqrt{b^{2}+c^{2}}}\right) A \,c^{2}}{\left(b^{2}+c^{2}\right)^{\frac{3}{2}}}-\frac{B c \ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}+\frac{C b \ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}+\frac{2 B b \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}+\frac{2 C c \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}"," ",0,"1/(b^2+c^2)*B*c*ln(b*tan(1/2*x)^2-2*c*tan(1/2*x)-b)-1/(b^2+c^2)*b*C*ln(b*tan(1/2*x)^2-2*c*tan(1/2*x)-b)+2/(b^2+c^2)^(3/2)*arctanh(1/2*(2*b*tan(1/2*x)-2*c)/(b^2+c^2)^(1/2))*A*b^2+2/(b^2+c^2)^(3/2)*arctanh(1/2*(2*b*tan(1/2*x)-2*c)/(b^2+c^2)^(1/2))*A*c^2-B/(b^2+c^2)*c*ln(1+tan(1/2*x)^2)+C/(b^2+c^2)*b*ln(1+tan(1/2*x)^2)+2*B/(b^2+c^2)*b*arctan(tan(1/2*x))+2*C/(b^2+c^2)*c*arctan(tan(1/2*x))","B"
533,1,124,80,0.168000," ","int((A+B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))^2,x)","\frac{-\frac{2 \left(A \,b^{2}+A \,c^{2}-B \,c^{2}+C b c \right) \tan \left(\frac{x}{2}\right)}{b \left(b^{2}+c^{2}\right)}+\frac{2 \left(B c -b C \right)}{b^{2}+c^{2}}}{b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 c \tan \left(\frac{x}{2}\right)-b}+\frac{2 \left(b B +C c \right) \arctanh \left(\frac{2 b \tan \left(\frac{x}{2}\right)-2 c}{2 \sqrt{b^{2}+c^{2}}}\right)}{\left(b^{2}+c^{2}\right)^{\frac{3}{2}}}"," ",0,"2*(-(A*b^2+A*c^2-B*c^2+C*b*c)/b/(b^2+c^2)*tan(1/2*x)+(B*c-C*b)/(b^2+c^2))/(b*tan(1/2*x)^2-2*c*tan(1/2*x)-b)+2*(B*b+C*c)/(b^2+c^2)^(3/2)*arctanh(1/2*(2*b*tan(1/2*x)-2*c)/(b^2+c^2)^(1/2))","A"
534,1,218,120,0.195000," ","int((A+B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))^3,x)","-\frac{2 \left(-\frac{\left(A \,b^{2}+2 A \,c^{2}-2 B \,b^{2}-2 B \,c^{2}\right) \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{2 \left(b^{2}+c^{2}\right) b}-\frac{\left(A \,b^{2} c -2 A \,c^{3}+2 B \,b^{2} c +2 B \,c^{3}+2 C \,b^{3}+2 C b \,c^{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{2 \left(b^{2}+c^{2}\right) b^{2}}-\frac{\left(A \,b^{2}-2 A \,c^{2}+2 B \,b^{2}+2 B \,c^{2}\right) \tan \left(\frac{x}{2}\right)}{2 \left(b^{2}+c^{2}\right) b}+\frac{A c}{2 b^{2}+2 c^{2}}\right)}{\left(b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 c \tan \left(\frac{x}{2}\right)-b \right)^{2}}+\frac{A \arctanh \left(\frac{2 b \tan \left(\frac{x}{2}\right)-2 c}{2 \sqrt{b^{2}+c^{2}}}\right)}{\left(b^{2}+c^{2}\right)^{\frac{3}{2}}}"," ",0,"-2*(-1/2*(A*b^2+2*A*c^2-2*B*b^2-2*B*c^2)/(b^2+c^2)/b*tan(1/2*x)^3-1/2*(A*b^2*c-2*A*c^3+2*B*b^2*c+2*B*c^3+2*C*b^3+2*C*b*c^2)/(b^2+c^2)/b^2*tan(1/2*x)^2-1/2*(A*b^2-2*A*c^2+2*B*b^2+2*B*c^2)/(b^2+c^2)/b*tan(1/2*x)+1/2*A*c/(b^2+c^2))/(b*tan(1/2*x)^2-2*c*tan(1/2*x)-b)^2+A/(b^2+c^2)^(3/2)*arctanh(1/2*(2*b*tan(1/2*x)-2*c)/(b^2+c^2)^(1/2))","A"
535,1,544,109,0.124000," ","int((A+B*cos(x))/(a+b*cos(x)+c*sin(x)),x)","\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right) a B c}{\left(b^{2}+c^{2}\right) \left(a -b \right)}-\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right) b B c}{\left(b^{2}+c^{2}\right) \left(a -b \right)}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) A \,b^{2}}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) A \,c^{2}}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a b B}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) B \,c^{2}}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) c^{2} a B}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}\, \left(a -b \right)}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) c^{2} b B}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}\, \left(a -b \right)}-\frac{B c \ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}+\frac{2 B b \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}"," ",0,"1/(b^2+c^2)/(a-b)*ln(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)*a*B*c-1/(b^2+c^2)/(a-b)*ln(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)*b*B*c+2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*A*b^2+2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*A*c^2-2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a*b*B+2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*B*c^2-2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*c^2/(a-b)*a*B+2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*c^2/(a-b)*b*B-B/(b^2+c^2)*c*ln(1+tan(1/2*x)^2)+2*B/(b^2+c^2)*b*arctan(tan(1/2*x))","B"
536,1,254,107,0.175000," ","int((A+B*cos(x))/(a+b*cos(x)+c*sin(x))^2,x)","\frac{-\frac{2 \left(a A b -A \,b^{2}-A \,c^{2}-a^{2} B +a b B +B \,c^{2}\right) \tan \left(\frac{x}{2}\right)}{a^{3}-a^{2} b -a \,b^{2}-a \,c^{2}+b^{3}+c^{2} b}+\frac{2 \left(a A -b B \right) c}{a^{3}-a^{2} b -a \,b^{2}-a \,c^{2}+b^{3}+c^{2} b}}{a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a A}{\left(a^{2}-b^{2}-c^{2}\right)^{\frac{3}{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) b B}{\left(a^{2}-b^{2}-c^{2}\right)^{\frac{3}{2}}}"," ",0,"2*(-(A*a*b-A*b^2-A*c^2-B*a^2+B*a*b+B*c^2)/(a^3-a^2*b-a*b^2-a*c^2+b^3+b*c^2)*tan(1/2*x)+(A*a-B*b)*c/(a^3-a^2*b-a*b^2-a*c^2+b^3+b*c^2))/(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)+2/(a^2-b^2-c^2)^(3/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a*A-2/(a^2-b^2-c^2)^(3/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*b*B","B"
537,1,1109,190,0.210000," ","int((A+B*cos(x))/(a+b*cos(x)+c*sin(x))^3,x)","\frac{-\frac{\left(4 A \,a^{3} b -7 A \,a^{2} b^{2}-5 A \,a^{2} c^{2}+2 A a \,b^{3}+2 A a b \,c^{2}+A \,b^{4}+3 A \,b^{2} c^{2}+2 A \,c^{4}-2 B \,a^{4}+3 B \,a^{3} b -2 B \,a^{2} b^{2}+4 B \,a^{2} c^{2}+3 B a \,b^{3}-2 B \,b^{4}-4 B \,b^{2} c^{2}-2 B \,c^{4}\right) \left(\tan^{3}\left(\frac{x}{2}\right)\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{c \left(4 A \,a^{4}-12 A \,a^{3} b +13 A \,a^{2} b^{2}+7 A \,a^{2} c^{2}-6 A a \,b^{3}-6 A a b \,c^{2}+A \,b^{4}-A \,b^{2} c^{2}-2 A \,c^{4}+2 B \,a^{4}-9 B \,a^{3} b +14 B \,a^{2} b^{2}-4 B \,a^{2} c^{2}-9 B a \,b^{3}+2 B \,b^{4}+4 B \,b^{2} c^{2}+2 B \,c^{4}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{\left(4 A \,a^{4} b -5 A \,a^{3} b^{2}-11 A \,a^{3} c^{2}-3 A \,a^{2} b^{3}+3 A \,a^{2} b \,c^{2}+5 A a \,b^{4}+7 A a \,b^{2} c^{2}+2 A a \,c^{4}-A \,b^{5}+A \,b^{3} c^{2}+2 A b \,c^{4}-2 B \,a^{5}+3 B \,a^{4} b -B \,a^{3} b^{2}+4 B \,a^{3} c^{2}-B \,a^{2} b^{3}+8 B \,a^{2} b \,c^{2}+3 B a \,b^{4}-8 B a \,b^{2} c^{2}-2 B a \,c^{4}-2 B \,b^{5}-4 B \,b^{3} c^{2}-2 B b \,c^{4}\right) \tan \left(\frac{x}{2}\right)}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{c \left(4 A \,a^{4}-3 A \,a^{2} b^{2}-A \,a^{2} c^{2}-A \,b^{4}-A \,b^{2} c^{2}-5 B \,a^{3} b +5 B a \,b^{3}+2 B a b \,c^{2}\right)}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \left(a^{2}-2 a b +b^{2}\right)}}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right)^{2}}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a^{2} A}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-b^{2}-c^{2}}}+\frac{\arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) A \,b^{2}}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-b^{2}-c^{2}}}+\frac{\arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) A \,c^{2}}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-b^{2}-c^{2}}}-\frac{3 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a b B}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-b^{2}-c^{2}}}"," ",0,"2*(-1/2*(4*A*a^3*b-7*A*a^2*b^2-5*A*a^2*c^2+2*A*a*b^3+2*A*a*b*c^2+A*b^4+3*A*b^2*c^2+2*A*c^4-2*B*a^4+3*B*a^3*b-2*B*a^2*b^2+4*B*a^2*c^2+3*B*a*b^3-2*B*b^4-4*B*b^2*c^2-2*B*c^4)/(a-b)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)*tan(1/2*x)^3+1/2*c*(4*A*a^4-12*A*a^3*b+13*A*a^2*b^2+7*A*a^2*c^2-6*A*a*b^3-6*A*a*b*c^2+A*b^4-A*b^2*c^2-2*A*c^4+2*B*a^4-9*B*a^3*b+14*B*a^2*b^2-4*B*a^2*c^2-9*B*a*b^3+2*B*b^4+4*B*b^2*c^2+2*B*c^4)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*x)^2-1/2*(4*A*a^4*b-5*A*a^3*b^2-11*A*a^3*c^2-3*A*a^2*b^3+3*A*a^2*b*c^2+5*A*a*b^4+7*A*a*b^2*c^2+2*A*a*c^4-A*b^5+A*b^3*c^2+2*A*b*c^4-2*B*a^5+3*B*a^4*b-B*a^3*b^2+4*B*a^3*c^2-B*a^2*b^3+8*B*a^2*b*c^2+3*B*a*b^4-8*B*a*b^2*c^2-2*B*a*c^4-2*B*b^5-4*B*b^3*c^2-2*B*b*c^4)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*x)+1/2*c*(4*A*a^4-3*A*a^2*b^2-A*a^2*c^2-A*b^4-A*b^2*c^2-5*B*a^3*b+5*B*a*b^3+2*B*a*b*c^2)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2))/(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)^2+2/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a^2*A+1/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*A*b^2+1/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*A*c^2-3/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a*b*B","B"
538,1,153,73,0.183000," ","int((A+B*cos(x))/(a+b*cos(x)+I*b*sin(x)),x)","\frac{i B \ln \left(\tan \left(\frac{x}{2}\right)+i\right)}{2 b}-\frac{i \ln \left(\tan \left(\frac{x}{2}\right)-i\right) A}{a}+\frac{i \ln \left(\tan \left(\frac{x}{2}\right)-i\right) b B}{2 a^{2}}+\frac{B}{a \left(\tan \left(\frac{x}{2}\right)-i\right)}+\frac{i \ln \left(i a +i b +a \tan \left(\frac{x}{2}\right)-b \tan \left(\frac{x}{2}\right)\right) A}{a}-\frac{i \ln \left(i a +i b +a \tan \left(\frac{x}{2}\right)-b \tan \left(\frac{x}{2}\right)\right) B}{2 b}-\frac{i b \ln \left(i a +i b +a \tan \left(\frac{x}{2}\right)-b \tan \left(\frac{x}{2}\right)\right) B}{2 a^{2}}"," ",0,"1/2*I*B/b*ln(tan(1/2*x)+I)-I/a*ln(tan(1/2*x)-I)*A+1/2*I/a^2*ln(tan(1/2*x)-I)*b*B+B/a/(tan(1/2*x)-I)+I/a*ln(I*a+I*b+a*tan(1/2*x)-b*tan(1/2*x))*A-1/2*I/b*ln(I*a+I*b+a*tan(1/2*x)-b*tan(1/2*x))*B-1/2*I/a^2*b*ln(I*a+I*b+a*tan(1/2*x)-b*tan(1/2*x))*B","B"
539,1,284,73,0.185000," ","int((A+B*cos(x))/(a+b*cos(x)-I*b*sin(x)),x)","\frac{i \ln \left(\tan \left(\frac{x}{2}\right)+i\right) A}{a}-\frac{i \ln \left(\tan \left(\frac{x}{2}\right)+i\right) b B}{2 a^{2}}+\frac{B}{a \left(\tan \left(\frac{x}{2}\right)+i\right)}-\frac{i B \ln \left(\tan \left(\frac{x}{2}\right)-i\right)}{2 b}+\frac{i \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) A}{-a +b}-\frac{i b \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) A}{a \left(-a +b \right)}-\frac{i a \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) B}{2 b \left(-a +b \right)}+\frac{i \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) B}{-2 a +2 b}-\frac{i b \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) B}{2 a \left(-a +b \right)}+\frac{i b^{2} \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) B}{2 a^{2} \left(-a +b \right)}"," ",0,"I/a*ln(tan(1/2*x)+I)*A-1/2*I/a^2*ln(tan(1/2*x)+I)*b*B+B/a/(tan(1/2*x)+I)-1/2*I*B/b*ln(tan(1/2*x)-I)+I/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*A-I/a*b/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*A-1/2*I*a/b/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*B+1/2*I/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*B-1/2*I/a*b/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*B+1/2*I/a^2*b^2/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*B","B"
540,1,542,110,0.129000," ","int((A+C*sin(x))/(a+b*cos(x)+c*sin(x)),x)","-\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right) a b C}{\left(b^{2}+c^{2}\right) \left(a -b \right)}+\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right) b^{2} C}{\left(b^{2}+c^{2}\right) \left(a -b \right)}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) A \,b^{2}}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) A \,c^{2}}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a c C}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) C b c}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) c a b C}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}\, \left(a -b \right)}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) c \,b^{2} C}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}\, \left(a -b \right)}+\frac{C b \ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}+\frac{2 C c \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}"," ",0,"-1/(b^2+c^2)/(a-b)*ln(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)*a*b*C+1/(b^2+c^2)/(a-b)*ln(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)*b^2*C+2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*A*b^2+2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*A*c^2-2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a*c*C-2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*C*b*c+2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*c/(a-b)*a*b*C-2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*c/(a-b)*b^2*C+C/(b^2+c^2)*b*ln(1+tan(1/2*x)^2)+2*C/(b^2+c^2)*c*arctan(tan(1/2*x))","B"
541,1,255,108,0.183000," ","int((A+C*sin(x))/(a+b*cos(x)+c*sin(x))^2,x)","\frac{-\frac{2 \left(a A b -A \,b^{2}-A \,c^{2}+a c C -C b c \right) \tan \left(\frac{x}{2}\right)}{a^{3}-a^{2} b -a \,b^{2}-a \,c^{2}+b^{3}+c^{2} b}+\frac{2 \left(a A c -a^{2} C +b^{2} C \right)}{a^{3}-a^{2} b -a \,b^{2}-a \,c^{2}+b^{3}+c^{2} b}}{a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a A}{\left(a^{2}-b^{2}-c^{2}\right)^{\frac{3}{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) C c}{\left(a^{2}-b^{2}-c^{2}\right)^{\frac{3}{2}}}"," ",0,"2*(-(A*a*b-A*b^2-A*c^2+C*a*c-C*b*c)/(a^3-a^2*b-a*b^2-a*c^2+b^3+b*c^2)*tan(1/2*x)+(A*a*c-C*a^2+C*b^2)/(a^3-a^2*b-a*b^2-a*c^2+b^3+b*c^2))/(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)+2/(a^2-b^2-c^2)^(3/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a*A-2/(a^2-b^2-c^2)^(3/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*C*c","B"
542,1,1088,192,0.217000," ","int((A+C*sin(x))/(a+b*cos(x)+c*sin(x))^3,x)","\frac{-\frac{\left(4 A \,a^{3} b -7 A \,a^{2} b^{2}-5 A \,a^{2} c^{2}+2 A a \,b^{3}+2 A a b \,c^{2}+A \,b^{4}+3 A \,b^{2} c^{2}+2 A \,c^{4}+3 C \,a^{3} c -6 C \,a^{2} b c +3 C a \,b^{2} c \right) \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \left(a -b \right)}+\frac{\left(4 A \,a^{4} c -12 A \,a^{3} b c +13 A \,a^{2} b^{2} c +7 A \,a^{2} c^{3}-6 A a \,b^{3} c -6 A a b \,c^{3}+A \,b^{4} c -A \,b^{2} c^{3}-2 A \,c^{5}-2 C \,a^{5}+2 C \,a^{4} b +4 C \,a^{3} b^{2}-5 C \,a^{3} c^{2}-4 C \,a^{2} b^{3}+14 C \,a^{2} b \,c^{2}-2 C a \,b^{4}-13 C a \,b^{2} c^{2}-2 C a \,c^{4}+2 C \,b^{5}+4 C \,b^{3} c^{2}+2 C b \,c^{4}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{\left(4 A \,a^{4} b -5 A \,a^{3} b^{2}-11 A \,a^{3} c^{2}-3 A \,a^{2} b^{3}+3 A \,a^{2} b \,c^{2}+5 A a \,b^{4}+7 A a \,b^{2} c^{2}+2 A a \,c^{4}-A \,b^{5}+A \,b^{3} c^{2}+2 A b \,c^{4}+5 C \,a^{4} c -5 C \,a^{3} b c -5 C \,a^{2} b^{2} c +4 C \,a^{2} c^{3}+5 C a \,b^{3} c -4 C a b \,c^{3}\right) \tan \left(\frac{x}{2}\right)}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{4 A \,a^{4} c -3 A \,a^{2} b^{2} c -A \,a^{2} c^{3}-A \,b^{4} c -A \,b^{2} c^{3}-2 C \,a^{5}+4 C \,a^{3} b^{2}-C \,a^{3} c^{2}-2 C a \,b^{4}+C a \,b^{2} c^{2}}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \left(a^{2}-2 a b +b^{2}\right)}}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right)^{2}}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a^{2} A}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-b^{2}-c^{2}}}+\frac{\arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) A \,b^{2}}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-b^{2}-c^{2}}}+\frac{\arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) A \,c^{2}}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-b^{2}-c^{2}}}-\frac{3 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a c C}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-b^{2}-c^{2}}}"," ",0,"2*(-1/2*(4*A*a^3*b-7*A*a^2*b^2-5*A*a^2*c^2+2*A*a*b^3+2*A*a*b*c^2+A*b^4+3*A*b^2*c^2+2*A*c^4+3*C*a^3*c-6*C*a^2*b*c+3*C*a*b^2*c)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a-b)*tan(1/2*x)^3+1/2*(4*A*a^4*c-12*A*a^3*b*c+13*A*a^2*b^2*c+7*A*a^2*c^3-6*A*a*b^3*c-6*A*a*b*c^3+A*b^4*c-A*b^2*c^3-2*A*c^5-2*C*a^5+2*C*a^4*b+4*C*a^3*b^2-5*C*a^3*c^2-4*C*a^2*b^3+14*C*a^2*b*c^2-2*C*a*b^4-13*C*a*b^2*c^2-2*C*a*c^4+2*C*b^5+4*C*b^3*c^2+2*C*b*c^4)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*x)^2-1/2*(4*A*a^4*b-5*A*a^3*b^2-11*A*a^3*c^2-3*A*a^2*b^3+3*A*a^2*b*c^2+5*A*a*b^4+7*A*a*b^2*c^2+2*A*a*c^4-A*b^5+A*b^3*c^2+2*A*b*c^4+5*C*a^4*c-5*C*a^3*b*c-5*C*a^2*b^2*c+4*C*a^2*c^3+5*C*a*b^3*c-4*C*a*b*c^3)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*x)+1/2*(4*A*a^4*c-3*A*a^2*b^2*c-A*a^2*c^3-A*b^4*c-A*b^2*c^3-2*C*a^5+4*C*a^3*b^2-C*a^3*c^2-2*C*a*b^4+C*a*b^2*c^2)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2))/(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)^2+2/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a^2*A+1/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*A*b^2+1/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*A*c^2-3/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a*c*C","B"
543,1,151,73,0.184000," ","int((A+C*sin(x))/(a+b*cos(x)+I*b*sin(x)),x)","\frac{C \ln \left(\tan \left(\frac{x}{2}\right)+i\right)}{2 b}+\frac{i C}{a \left(\tan \left(\frac{x}{2}\right)-i\right)}-\frac{i \ln \left(\tan \left(\frac{x}{2}\right)-i\right) A}{a}-\frac{\ln \left(\tan \left(\frac{x}{2}\right)-i\right) b C}{2 a^{2}}-\frac{\ln \left(i a +i b +a \tan \left(\frac{x}{2}\right)-b \tan \left(\frac{x}{2}\right)\right) C}{2 b}+\frac{b \ln \left(i a +i b +a \tan \left(\frac{x}{2}\right)-b \tan \left(\frac{x}{2}\right)\right) C}{2 a^{2}}+\frac{i \ln \left(i a +i b +a \tan \left(\frac{x}{2}\right)-b \tan \left(\frac{x}{2}\right)\right) A}{a}"," ",0,"1/2*C/b*ln(tan(1/2*x)+I)+I*C/a/(tan(1/2*x)-I)-I/a*ln(tan(1/2*x)-I)*A-1/2/a^2*ln(tan(1/2*x)-I)*b*C-1/2/b*ln(I*a+I*b+a*tan(1/2*x)-b*tan(1/2*x))*C+1/2/a^2*b*ln(I*a+I*b+a*tan(1/2*x)-b*tan(1/2*x))*C+I/a*ln(I*a+I*b+a*tan(1/2*x)-b*tan(1/2*x))*A","B"
544,1,280,73,0.175000," ","int((A+C*sin(x))/(a+b*cos(x)-I*b*sin(x)),x)","-\frac{i C}{a \left(\tan \left(\frac{x}{2}\right)+i\right)}+\frac{i \ln \left(\tan \left(\frac{x}{2}\right)+i\right) A}{a}-\frac{\ln \left(\tan \left(\frac{x}{2}\right)+i\right) b C}{2 a^{2}}+\frac{C \ln \left(\tan \left(\frac{x}{2}\right)-i\right)}{2 b}+\frac{a \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) C}{2 b \left(-a +b \right)}-\frac{\ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) C}{2 \left(-a +b \right)}-\frac{b \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) C}{2 a \left(-a +b \right)}+\frac{b^{2} \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) C}{2 a^{2} \left(-a +b \right)}+\frac{i \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) A}{-a +b}-\frac{i b \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) A}{a \left(-a +b \right)}"," ",0,"-I*C/a/(tan(1/2*x)+I)+I/a*ln(tan(1/2*x)+I)*A-1/2/a^2*ln(tan(1/2*x)+I)*b*C+1/2*C/b*ln(tan(1/2*x)-I)+1/2*a/b/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*C-1/2/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*C-1/2/a*b/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*C+1/2/a^2*b^2/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*C+I/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*A-I/a*b/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*A","B"
545,1,824,113,0.123000," ","int((B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x)),x)","\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right) a B c}{\left(b^{2}+c^{2}\right) \left(a -b \right)}-\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right) b B c}{\left(b^{2}+c^{2}\right) \left(a -b \right)}-\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right) a b C}{\left(b^{2}+c^{2}\right) \left(a -b \right)}+\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right) b^{2} C}{\left(b^{2}+c^{2}\right) \left(a -b \right)}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a b B}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) B \,c^{2}}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a c C}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) C b c}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) c^{2} a B}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}\, \left(a -b \right)}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) c^{2} b B}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}\, \left(a -b \right)}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) c a b C}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}\, \left(a -b \right)}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) c \,b^{2} C}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}\, \left(a -b \right)}-\frac{B c \ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}+\frac{C b \ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}+\frac{2 B b \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}+\frac{2 C c \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}"," ",0,"1/(b^2+c^2)/(a-b)*ln(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)*a*B*c-1/(b^2+c^2)/(a-b)*ln(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)*b*B*c-1/(b^2+c^2)/(a-b)*ln(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)*a*b*C+1/(b^2+c^2)/(a-b)*ln(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)*b^2*C-2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a*b*B+2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*B*c^2-2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a*c*C-2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*C*b*c-2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*c^2/(a-b)*a*B+2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*c^2/(a-b)*b*B+2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*c/(a-b)*a*b*C-2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*c/(a-b)*b^2*C-B/(b^2+c^2)*c*ln(1+tan(1/2*x)^2)+C/(b^2+c^2)*b*ln(1+tan(1/2*x)^2)+2*B/(b^2+c^2)*b*arctan(tan(1/2*x))+2*C/(b^2+c^2)*c*arctan(tan(1/2*x))","B"
546,1,255,104,0.177000," ","int((B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^2,x)","-\frac{2 \left(-\frac{\left(a^{2} B -a b B -B \,c^{2}-a c C +C b c \right) \tan \left(\frac{x}{2}\right)}{a^{3}-a^{2} b -a \,b^{2}-a \,c^{2}+b^{3}+c^{2} b}+\frac{b B c +a^{2} C -b^{2} C}{a^{3}-a^{2} b -a \,b^{2}-a \,c^{2}+b^{3}+c^{2} b}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) b B}{\left(a^{2}-b^{2}-c^{2}\right)^{\frac{3}{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) C c}{\left(a^{2}-b^{2}-c^{2}\right)^{\frac{3}{2}}}"," ",0,"-2*(-(B*a^2-B*a*b-B*c^2-C*a*c+C*b*c)/(a^3-a^2*b-a*b^2-a*c^2+b^3+b*c^2)*tan(1/2*x)+(B*b*c+C*a^2-C*b^2)/(a^3-a^2*b-a*b^2-a*c^2+b^3+b*c^2))/(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)-2/(a^2-b^2-c^2)^(3/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*b*B-2/(a^2-b^2-c^2)^(3/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*C*c","B"
547,1,881,187,0.222000," ","int((B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^3,x)","-\frac{2 \left(-\frac{\left(2 B \,a^{4}-3 B \,a^{3} b +2 B \,a^{2} b^{2}-4 B \,a^{2} c^{2}-3 B a \,b^{3}+2 B \,b^{4}+4 B \,b^{2} c^{2}+2 B \,c^{4}-3 C \,a^{3} c +6 C \,a^{2} b c -3 C a \,b^{2} c \right) \left(\tan^{3}\left(\frac{x}{2}\right)\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) \left(a -b \right)}-\frac{\left(2 B \,a^{4} c -9 B \,a^{3} b c +14 B \,a^{2} b^{2} c -4 B \,a^{2} c^{3}-9 B a \,b^{3} c +2 B \,b^{4} c +4 B \,b^{2} c^{3}+2 B \,c^{5}-2 C \,a^{5}+2 C \,a^{4} b +4 C \,a^{3} b^{2}-5 C \,a^{3} c^{2}-4 C \,a^{2} b^{3}+14 C \,a^{2} b \,c^{2}-2 C a \,b^{4}-13 C a \,b^{2} c^{2}-2 C a \,c^{4}+2 C \,b^{5}+4 C \,b^{3} c^{2}+2 C b \,c^{4}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\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) \left(a^{2}-2 a b +b^{2}\right)}-\frac{\left(2 B \,a^{5}-3 B \,a^{4} b +B \,a^{3} b^{2}-4 B \,a^{3} c^{2}+B \,a^{2} b^{3}-8 B \,a^{2} b \,c^{2}-3 B a \,b^{4}+8 B a \,b^{2} c^{2}+2 B a \,c^{4}+2 B \,b^{5}+4 B \,b^{3} c^{2}+2 B b \,c^{4}-5 C \,a^{4} c +5 C \,a^{3} b c +5 C \,a^{2} b^{2} c -4 C \,a^{2} c^{3}-5 C a \,b^{3} c +4 C a b \,c^{3}\right) \tan \left(\frac{x}{2}\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) \left(a^{2}-2 a b +b^{2}\right)}+\frac{a \left(5 B \,a^{2} b c -5 B \,b^{3} c -2 B b \,c^{3}+2 C \,a^{4}-4 C \,a^{2} b^{2}+C \,a^{2} c^{2}+2 C \,b^{4}-C \,b^{2} c^{2}\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) \left(a^{2}-2 a b +b^{2}\right)}\right)}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right)^{2}}-\frac{3 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a b B}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-b^{2}-c^{2}}}-\frac{3 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a c C}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-b^{2}-c^{2}}}"," ",0,"-2*(-1/2*(2*B*a^4-3*B*a^3*b+2*B*a^2*b^2-4*B*a^2*c^2-3*B*a*b^3+2*B*b^4+4*B*b^2*c^2+2*B*c^4-3*C*a^3*c+6*C*a^2*b*c-3*C*a*b^2*c)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a-b)*tan(1/2*x)^3-1/2*(2*B*a^4*c-9*B*a^3*b*c+14*B*a^2*b^2*c-4*B*a^2*c^3-9*B*a*b^3*c+2*B*b^4*c+4*B*b^2*c^3+2*B*c^5-2*C*a^5+2*C*a^4*b+4*C*a^3*b^2-5*C*a^3*c^2-4*C*a^2*b^3+14*C*a^2*b*c^2-2*C*a*b^4-13*C*a*b^2*c^2-2*C*a*c^4+2*C*b^5+4*C*b^3*c^2+2*C*b*c^4)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*x)^2-1/2*(2*B*a^5-3*B*a^4*b+B*a^3*b^2-4*B*a^3*c^2+B*a^2*b^3-8*B*a^2*b*c^2-3*B*a*b^4+8*B*a*b^2*c^2+2*B*a*c^4+2*B*b^5+4*B*b^3*c^2+2*B*b*c^4-5*C*a^4*c+5*C*a^3*b*c+5*C*a^2*b^2*c-4*C*a^2*c^3-5*C*a*b^3*c+4*C*a*b*c^3)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*x)+1/2*a*(5*B*a^2*b*c-5*B*b^3*c-2*B*b*c^3+2*C*a^4-4*C*a^2*b^2+C*a^2*c^2+2*C*b^4-C*b^2*c^2)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2))/(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)^2-3/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a*b*B-3/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a*c*C","B"
548,1,212,79,0.195000," ","int((B*cos(x)+C*sin(x))/(a+b*cos(x)+I*b*sin(x)),x)","\frac{C \ln \left(\tan \left(\frac{x}{2}\right)+i\right)}{2 b}+\frac{i B \ln \left(\tan \left(\frac{x}{2}\right)+i\right)}{2 b}+\frac{i C}{a \left(\tan \left(\frac{x}{2}\right)-i\right)}+\frac{B}{a \left(\tan \left(\frac{x}{2}\right)-i\right)}+\frac{i \ln \left(\tan \left(\frac{x}{2}\right)-i\right) b B}{2 a^{2}}-\frac{\ln \left(\tan \left(\frac{x}{2}\right)-i\right) b C}{2 a^{2}}-\frac{\ln \left(i a +i b +a \tan \left(\frac{x}{2}\right)-b \tan \left(\frac{x}{2}\right)\right) C}{2 b}+\frac{b \ln \left(i a +i b +a \tan \left(\frac{x}{2}\right)-b \tan \left(\frac{x}{2}\right)\right) C}{2 a^{2}}-\frac{i \ln \left(i a +i b +a \tan \left(\frac{x}{2}\right)-b \tan \left(\frac{x}{2}\right)\right) B}{2 b}-\frac{i b \ln \left(i a +i b +a \tan \left(\frac{x}{2}\right)-b \tan \left(\frac{x}{2}\right)\right) B}{2 a^{2}}"," ",0,"1/2*C/b*ln(tan(1/2*x)+I)+1/2*I*B/b*ln(tan(1/2*x)+I)+I*C/a/(tan(1/2*x)-I)+B/a/(tan(1/2*x)-I)+1/2*I/a^2*ln(tan(1/2*x)-I)*b*B-1/2/a^2*ln(tan(1/2*x)-I)*b*C-1/2/b*ln(I*a+I*b+a*tan(1/2*x)-b*tan(1/2*x))*C+1/2/a^2*b*ln(I*a+I*b+a*tan(1/2*x)-b*tan(1/2*x))*C-1/2*I/b*ln(I*a+I*b+a*tan(1/2*x)-b*tan(1/2*x))*B-1/2*I/a^2*b*ln(I*a+I*b+a*tan(1/2*x)-b*tan(1/2*x))*B","B"
549,1,388,77,0.191000," ","int((B*cos(x)+C*sin(x))/(a+b*cos(x)-I*b*sin(x)),x)","-\frac{i C}{a \left(\tan \left(\frac{x}{2}\right)+i\right)}+\frac{B}{a \left(\tan \left(\frac{x}{2}\right)+i\right)}-\frac{i \ln \left(\tan \left(\frac{x}{2}\right)+i\right) b B}{2 a^{2}}-\frac{\ln \left(\tan \left(\frac{x}{2}\right)+i\right) b C}{2 a^{2}}+\frac{C \ln \left(\tan \left(\frac{x}{2}\right)-i\right)}{2 b}-\frac{i B \ln \left(\tan \left(\frac{x}{2}\right)-i\right)}{2 b}+\frac{a \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) C}{2 b \left(-a +b \right)}-\frac{\ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) C}{2 \left(-a +b \right)}-\frac{b \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) C}{2 a \left(-a +b \right)}+\frac{b^{2} \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) C}{2 a^{2} \left(-a +b \right)}-\frac{i a \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) B}{2 b \left(-a +b \right)}+\frac{i \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) B}{-2 a +2 b}-\frac{i b \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) B}{2 a \left(-a +b \right)}+\frac{i b^{2} \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) B}{2 a^{2} \left(-a +b \right)}"," ",0,"-I*C/a/(tan(1/2*x)+I)+B/a/(tan(1/2*x)+I)-1/2*I/a^2*ln(tan(1/2*x)+I)*b*B-1/2/a^2*ln(tan(1/2*x)+I)*b*C+1/2*C/b*ln(tan(1/2*x)-I)-1/2*I*B/b*ln(tan(1/2*x)-I)+1/2*a/b/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*C-1/2/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*C-1/2/a*b/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*C+1/2/a^2*b^2/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*C-1/2*I*a/b/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*B+1/2*I/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*B-1/2*I/a*b/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*B+1/2*I/a^2*b^2/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*B","B"
550,1,954,125,0.132000," ","int((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x)),x)","\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right) a B c}{\left(b^{2}+c^{2}\right) \left(a -b \right)}-\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right) b B c}{\left(b^{2}+c^{2}\right) \left(a -b \right)}-\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right) a b C}{\left(b^{2}+c^{2}\right) \left(a -b \right)}+\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right) b^{2} C}{\left(b^{2}+c^{2}\right) \left(a -b \right)}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) A \,b^{2}}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) A \,c^{2}}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a b B}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) B \,c^{2}}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a c C}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) C b c}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) c^{2} a B}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}\, \left(a -b \right)}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) c^{2} b B}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}\, \left(a -b \right)}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) c a b C}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}\, \left(a -b \right)}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) c \,b^{2} C}{\left(b^{2}+c^{2}\right) \sqrt{a^{2}-b^{2}-c^{2}}\, \left(a -b \right)}-\frac{B c \ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}+\frac{C b \ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}+\frac{2 B b \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}+\frac{2 C c \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b^{2}+c^{2}}"," ",0,"1/(b^2+c^2)/(a-b)*ln(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)*a*B*c-1/(b^2+c^2)/(a-b)*ln(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)*b*B*c-1/(b^2+c^2)/(a-b)*ln(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)*a*b*C+1/(b^2+c^2)/(a-b)*ln(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)*b^2*C+2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*A*b^2+2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*A*c^2-2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a*b*B+2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*B*c^2-2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a*c*C-2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*C*b*c-2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*c^2/(a-b)*a*B+2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*c^2/(a-b)*b*B+2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*c/(a-b)*a*b*C-2/(b^2+c^2)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*c/(a-b)*b^2*C-B/(b^2+c^2)*c*ln(1+tan(1/2*x)^2)+C/(b^2+c^2)*b*ln(1+tan(1/2*x)^2)+2*B/(b^2+c^2)*b*arctan(tan(1/2*x))+2*C/(b^2+c^2)*c*arctan(tan(1/2*x))","B"
551,1,329,121,0.183000," ","int((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^2,x)","\frac{-\frac{2 \left(a A b -A \,b^{2}-A \,c^{2}-a^{2} B +a b B +B \,c^{2}+a c C -C b c \right) \tan \left(\frac{x}{2}\right)}{a^{3}-a^{2} b -a \,b^{2}-a \,c^{2}+b^{3}+c^{2} b}+\frac{2 \left(a A c -b B c -a^{2} C +b^{2} C \right)}{a^{3}-a^{2} b -a \,b^{2}-a \,c^{2}+b^{3}+c^{2} b}}{a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a A}{\left(a^{2}-b^{2}-c^{2}\right)^{\frac{3}{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) b B}{\left(a^{2}-b^{2}-c^{2}\right)^{\frac{3}{2}}}-\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) C c}{\left(a^{2}-b^{2}-c^{2}\right)^{\frac{3}{2}}}"," ",0,"2*(-(A*a*b-A*b^2-A*c^2-B*a^2+B*a*b+B*c^2+C*a*c-C*b*c)/(a^3-a^2*b-a*b^2-a*c^2+b^3+b*c^2)*tan(1/2*x)+(A*a*c-B*b*c-C*a^2+C*b^2)/(a^3-a^2*b-a*b^2-a*c^2+b^3+b*c^2))/(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)+2/(a^2-b^2-c^2)^(3/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a*A-2/(a^2-b^2-c^2)^(3/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*b*B-2/(a^2-b^2-c^2)^(3/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*C*c","B"
552,1,1422,227,0.226000," ","int((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^3,x)","\frac{-\frac{\left(4 A \,a^{3} b -7 A \,a^{2} b^{2}-5 A \,a^{2} c^{2}+2 A a \,b^{3}+2 A a b \,c^{2}+A \,b^{4}+3 A \,b^{2} c^{2}+2 A \,c^{4}-2 B \,a^{4}+3 B \,a^{3} b -2 B \,a^{2} b^{2}+4 B \,a^{2} c^{2}+3 B a \,b^{3}-2 B \,b^{4}-4 B \,b^{2} c^{2}-2 B \,c^{4}+3 C \,a^{3} c -6 C \,a^{2} b c +3 C a \,b^{2} c \right) \left(\tan^{3}\left(\frac{x}{2}\right)\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{\left(4 A \,a^{4} c -12 A \,a^{3} b c +13 A \,a^{2} b^{2} c +7 A \,a^{2} c^{3}-6 A a \,b^{3} c -6 A a b \,c^{3}+A \,b^{4} c -A \,b^{2} c^{3}-2 A \,c^{5}+2 B \,a^{4} c -9 B \,a^{3} b c +14 B \,a^{2} b^{2} c -4 B \,a^{2} c^{3}-9 B a \,b^{3} c +2 B \,b^{4} c +4 B \,b^{2} c^{3}+2 B \,c^{5}-2 C \,a^{5}+2 C \,a^{4} b +4 C \,a^{3} b^{2}-5 C \,a^{3} c^{2}-4 C \,a^{2} b^{3}+14 C \,a^{2} b \,c^{2}-2 C a \,b^{4}-13 C a \,b^{2} c^{2}-2 C a \,c^{4}+2 C \,b^{5}+4 C \,b^{3} c^{2}+2 C b \,c^{4}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{\left(4 A \,a^{4} b -5 A \,a^{3} b^{2}-11 A \,a^{3} c^{2}-3 A \,a^{2} b^{3}+3 A \,a^{2} b \,c^{2}+5 A a \,b^{4}+7 A a \,b^{2} c^{2}+2 A a \,c^{4}-A \,b^{5}+A \,b^{3} c^{2}+2 A b \,c^{4}-2 B \,a^{5}+3 B \,a^{4} b -B \,a^{3} b^{2}+4 B \,a^{3} c^{2}-B \,a^{2} b^{3}+8 B \,a^{2} b \,c^{2}+3 B a \,b^{4}-8 B a \,b^{2} c^{2}-2 B a \,c^{4}-2 B \,b^{5}-4 B \,b^{3} c^{2}-2 B b \,c^{4}+5 C \,a^{4} c -5 C \,a^{3} b c -5 C \,a^{2} b^{2} c +4 C \,a^{2} c^{3}+5 C a \,b^{3} c -4 C a b \,c^{3}\right) \tan \left(\frac{x}{2}\right)}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{4 A \,a^{4} c -3 A \,a^{2} b^{2} c -A \,a^{2} c^{3}-A \,b^{4} c -A \,b^{2} c^{3}-5 B \,a^{3} b c +5 B a \,b^{3} c +2 B a b \,c^{3}-2 C \,a^{5}+4 C \,a^{3} b^{2}-C \,a^{3} c^{2}-2 C a \,b^{4}+C a \,b^{2} c^{2}}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \left(a^{2}-2 a b +b^{2}\right)}}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b \right)^{2}}+\frac{2 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a^{2} A}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-b^{2}-c^{2}}}+\frac{\arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) A \,b^{2}}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-b^{2}-c^{2}}}+\frac{\arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) A \,c^{2}}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-b^{2}-c^{2}}}-\frac{3 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a b B}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-b^{2}-c^{2}}}-\frac{3 \arctan \left(\frac{2 \left(a -b \right) \tan \left(\frac{x}{2}\right)+2 c}{2 \sqrt{a^{2}-b^{2}-c^{2}}}\right) a c C}{\left(a^{4}-2 a^{2} b^{2}-2 a^{2} c^{2}+b^{4}+2 b^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-b^{2}-c^{2}}}"," ",0,"2*(-1/2*(4*A*a^3*b-7*A*a^2*b^2-5*A*a^2*c^2+2*A*a*b^3+2*A*a*b*c^2+A*b^4+3*A*b^2*c^2+2*A*c^4-2*B*a^4+3*B*a^3*b-2*B*a^2*b^2+4*B*a^2*c^2+3*B*a*b^3-2*B*b^4-4*B*b^2*c^2-2*B*c^4+3*C*a^3*c-6*C*a^2*b*c+3*C*a*b^2*c)/(a-b)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)*tan(1/2*x)^3+1/2*(4*A*a^4*c-12*A*a^3*b*c+13*A*a^2*b^2*c+7*A*a^2*c^3-6*A*a*b^3*c-6*A*a*b*c^3+A*b^4*c-A*b^2*c^3-2*A*c^5+2*B*a^4*c-9*B*a^3*b*c+14*B*a^2*b^2*c-4*B*a^2*c^3-9*B*a*b^3*c+2*B*b^4*c+4*B*b^2*c^3+2*B*c^5-2*C*a^5+2*C*a^4*b+4*C*a^3*b^2-5*C*a^3*c^2-4*C*a^2*b^3+14*C*a^2*b*c^2-2*C*a*b^4-13*C*a*b^2*c^2-2*C*a*c^4+2*C*b^5+4*C*b^3*c^2+2*C*b*c^4)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*x)^2-1/2*(4*A*a^4*b-5*A*a^3*b^2-11*A*a^3*c^2-3*A*a^2*b^3+3*A*a^2*b*c^2+5*A*a*b^4+7*A*a*b^2*c^2+2*A*a*c^4-A*b^5+A*b^3*c^2+2*A*b*c^4-2*B*a^5+3*B*a^4*b-B*a^3*b^2+4*B*a^3*c^2-B*a^2*b^3+8*B*a^2*b*c^2+3*B*a*b^4-8*B*a*b^2*c^2-2*B*a*c^4-2*B*b^5-4*B*b^3*c^2-2*B*b*c^4+5*C*a^4*c-5*C*a^3*b*c-5*C*a^2*b^2*c+4*C*a^2*c^3+5*C*a*b^3*c-4*C*a*b*c^3)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2)*tan(1/2*x)+1/2*(4*A*a^4*c-3*A*a^2*b^2*c-A*a^2*c^3-A*b^4*c-A*b^2*c^3-5*B*a^3*b*c+5*B*a*b^3*c+2*B*a*b*c^3-2*C*a^5+4*C*a^3*b^2-C*a^3*c^2-2*C*a*b^4+C*a*b^2*c^2)/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-2*a*b+b^2))/(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)^2+2/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a^2*A+1/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*A*b^2+1/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*A*c^2-3/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a*b*B-3/(a^4-2*a^2*b^2-2*a^2*c^2+b^4+2*b^2*c^2+c^4)/(a^2-b^2-c^2)^(1/2)*arctan(1/2*(2*(a-b)*tan(1/2*x)+2*c)/(a^2-b^2-c^2)^(1/2))*a*c*C","B"
553,1,257,92,0.185000," ","int((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+I*b*sin(x)),x)","\frac{C \ln \left(\tan \left(\frac{x}{2}\right)+i\right)}{2 b}+\frac{i B \ln \left(\tan \left(\frac{x}{2}\right)+i\right)}{2 b}+\frac{i C}{a \left(\tan \left(\frac{x}{2}\right)-i\right)}+\frac{B}{a \left(\tan \left(\frac{x}{2}\right)-i\right)}-\frac{i \ln \left(\tan \left(\frac{x}{2}\right)-i\right) A}{a}+\frac{i \ln \left(\tan \left(\frac{x}{2}\right)-i\right) b B}{2 a^{2}}-\frac{\ln \left(\tan \left(\frac{x}{2}\right)-i\right) b C}{2 a^{2}}-\frac{\ln \left(i a +i b +a \tan \left(\frac{x}{2}\right)-b \tan \left(\frac{x}{2}\right)\right) C}{2 b}+\frac{b \ln \left(i a +i b +a \tan \left(\frac{x}{2}\right)-b \tan \left(\frac{x}{2}\right)\right) C}{2 a^{2}}+\frac{i \ln \left(i a +i b +a \tan \left(\frac{x}{2}\right)-b \tan \left(\frac{x}{2}\right)\right) A}{a}-\frac{i \ln \left(i a +i b +a \tan \left(\frac{x}{2}\right)-b \tan \left(\frac{x}{2}\right)\right) B}{2 b}-\frac{i b \ln \left(i a +i b +a \tan \left(\frac{x}{2}\right)-b \tan \left(\frac{x}{2}\right)\right) B}{2 a^{2}}"," ",0,"1/2*C/b*ln(tan(1/2*x)+I)+1/2*I*B/b*ln(tan(1/2*x)+I)+I*C/a/(tan(1/2*x)-I)+B/a/(tan(1/2*x)-I)-I/a*ln(tan(1/2*x)-I)*A+1/2*I/a^2*ln(tan(1/2*x)-I)*b*B-1/2/a^2*ln(tan(1/2*x)-I)*b*C-1/2/b*ln(I*a+I*b+a*tan(1/2*x)-b*tan(1/2*x))*C+1/2/a^2*b*ln(I*a+I*b+a*tan(1/2*x)-b*tan(1/2*x))*C+I/a*ln(I*a+I*b+a*tan(1/2*x)-b*tan(1/2*x))*A-1/2*I/b*ln(I*a+I*b+a*tan(1/2*x)-b*tan(1/2*x))*B-1/2*I/a^2*b*ln(I*a+I*b+a*tan(1/2*x)-b*tan(1/2*x))*B","B"
554,1,475,90,0.194000," ","int((A+B*cos(x)+C*sin(x))/(a+b*cos(x)-I*b*sin(x)),x)","\frac{i \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) B}{-2 a +2 b}+\frac{B}{a \left(\tan \left(\frac{x}{2}\right)+i\right)}-\frac{i b \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) A}{a \left(-a +b \right)}-\frac{i B \ln \left(\tan \left(\frac{x}{2}\right)-i\right)}{2 b}-\frac{\ln \left(\tan \left(\frac{x}{2}\right)+i\right) b C}{2 a^{2}}+\frac{C \ln \left(\tan \left(\frac{x}{2}\right)-i\right)}{2 b}-\frac{i C}{a \left(\tan \left(\frac{x}{2}\right)+i\right)}+\frac{a \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) C}{2 b \left(-a +b \right)}-\frac{\ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) C}{2 \left(-a +b \right)}-\frac{b \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) C}{2 a \left(-a +b \right)}+\frac{b^{2} \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) C}{2 a^{2} \left(-a +b \right)}-\frac{i \ln \left(\tan \left(\frac{x}{2}\right)+i\right) b B}{2 a^{2}}-\frac{i a \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) B}{2 b \left(-a +b \right)}+\frac{i \ln \left(\tan \left(\frac{x}{2}\right)+i\right) A}{a}-\frac{i b \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) B}{2 a \left(-a +b \right)}+\frac{i \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) A}{-a +b}+\frac{i b^{2} \ln \left(i a +i b -a \tan \left(\frac{x}{2}\right)+b \tan \left(\frac{x}{2}\right)\right) B}{2 a^{2} \left(-a +b \right)}"," ",0,"1/2*I/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*B+B/a/(tan(1/2*x)+I)-I/a*b/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*A-1/2*I*B/b*ln(tan(1/2*x)-I)-1/2/a^2*ln(tan(1/2*x)+I)*b*C+1/2*C/b*ln(tan(1/2*x)-I)-I*C/a/(tan(1/2*x)+I)+1/2*a/b/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*C-1/2/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*C-1/2/a*b/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*C+1/2/a^2*b^2/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*C-1/2*I/a^2*ln(tan(1/2*x)+I)*b*B-1/2*I*a/b/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*B+I/a*ln(tan(1/2*x)+I)*A-1/2*I/a*b/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*B+I/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*A+1/2*I/a^2*b^2/(-a+b)*ln(I*a+I*b-a*tan(1/2*x)+b*tan(1/2*x))*B","B"
555,1,70,23,0.189000," ","int((b^2+c^2+a*b*cos(x)+a*c*sin(x))/(a+b*cos(x)+c*sin(x))^2,x)","-\frac{2 \left(-\frac{\left(a b -b^{2}-c^{2}\right) \tan \left(\frac{x}{2}\right)}{a -b}+\frac{a c}{a -b}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 c \tan \left(\frac{x}{2}\right)+a +b}"," ",0,"-2*(-(a*b-b^2-c^2)/(a-b)*tan(1/2*x)+a*c/(a-b))/(a*tan(1/2*x)^2-b*tan(1/2*x)^2+2*c*tan(1/2*x)+a+b)","B"
556,1,3502,414,1.279000," ","int((a+b*cos(x)+c*sin(x))^(5/2)*(d+b*e*cos(x)+c*e*sin(x)),x)","\text{output too large to display}"," ",0,"(-(-b^2*sin(x-arctan(-b,c))-c^2*sin(x-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(x-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)/(b^2+c^2)*((b^6*e+3*b^4*c^2*e+3*b^2*c^4*e+c^6*e)*(-2/7/(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))^2*(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)+12/35/(b^2+c^2)*a*sin(x-arctan(-b,c))*(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)-2/3*(5/7+24/35/(b^2+c^2)*a^2)/(b^2+c^2)^(1/2)*(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)+2*(-4/35/(b^2+c^2)*a^2+5/21)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+2*(-48*a^3-44*a*b^2-44*a*c^2)/(105*(b^2+c^2)^(1/2)*b^2+105*(b^2+c^2)^(1/2)*c^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))))+(3*(b^2+c^2)^(1/2)*a*b^4*e+6*(b^2+c^2)^(1/2)*a*b^2*c^2*e+3*(b^2+c^2)^(1/2)*a*c^4*e+(b^2+c^2)^(1/2)*b^4*d+2*(b^2+c^2)^(1/2)*b^2*c^2*d+(b^2+c^2)^(1/2)*c^4*d)*(-2/5/(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))*(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)+8/15/(b^2+c^2)*a*(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)+4/15/(b^2+c^2)^(1/2)*a*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+2*(3/5+8/15/(b^2+c^2)*a^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))))+(3*a^2*b^4*e+6*a^2*b^2*c^2*e+3*a^2*c^4*e+3*a*b^4*d+6*a*b^2*c^2*d+3*a*c^4*d)*(-2/3/(b^2+c^2)^(1/2)*(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)+2/3*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))-4/3/(b^2+c^2)^(1/2)*a*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))))+2*((b^2+c^2)^(1/2)*a^3*b^2*e+(b^2+c^2)^(1/2)*a^3*c^2*e+(b^2+c^2)^(3/2)*a^2*d+2*a^2*b^2*d*(b^2+c^2)^(1/2)+2*a^2*c^2*d*(b^2+c^2)^(1/2))*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))+2*a^3*b^2*d*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-b^2*sin(x-arctan(-b,c))-c^2*sin(x-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(x-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+2*a^3*c^2*d*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-b^2*sin(x-arctan(-b,c))-c^2*sin(x-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(x-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))/cos(x-arctan(-b,c))/((b^2*sin(x-arctan(-b,c))+c^2*sin(x-arctan(-b,c))+a*(b^2+c^2)^(1/2))/(b^2+c^2)^(1/2))^(1/2)","B"
557,1,2238,322,1.011000," ","int((a+b*cos(x)+c*sin(x))^(3/2)*(d+b*e*cos(x)+c*e*sin(x)),x)","\frac{\sqrt{-\frac{\left(-b^{2} \sin \left(x -\arctan \left(-b , c\right)\right)-c^{2} \sin \left(x -\arctan \left(-b , c\right)\right)-a \sqrt{b^{2}+c^{2}}\right) \left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right)}{\sqrt{b^{2}+c^{2}}}}\, \left(\left(b^{4} e +2 b^{2} c^{2} e +c^{4} e \right) \left(-\frac{2 \sin \left(x -\arctan \left(-b , c\right)\right) \sqrt{\left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)+a \right)}}{5 \sqrt{b^{2}+c^{2}}}+\frac{8 a \sqrt{\left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)+a \right)}}{15 \left(b^{2}+c^{2}\right)}+\frac{4 a \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(x -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(x -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)}{15 \sqrt{b^{2}+c^{2}}\, \sqrt{\left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)+a \right)}}+\frac{2 \left(\frac{3}{5}+\frac{8 a^{2}}{15 \left(b^{2}+c^{2}\right)}\right) \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(x -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(x -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \left(\left(-\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \EllipticE \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)+\EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)\right)}{\sqrt{\left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)+a \right)}}\right)+\left(2 \sqrt{b^{2}+c^{2}}\, a \,b^{2} e +2 \sqrt{b^{2}+c^{2}}\, a \,c^{2} e +\sqrt{b^{2}+c^{2}}\, b^{2} d +\sqrt{b^{2}+c^{2}}\, c^{2} d \right) \left(-\frac{2 \sqrt{\left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)+a \right)}}{3 \sqrt{b^{2}+c^{2}}}+\frac{2 \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(x -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(x -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)}{3 \sqrt{\left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)+a \right)}}-\frac{4 a \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(x -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(x -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \left(\left(-\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \EllipticE \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)+\EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)\right)}{3 \sqrt{b^{2}+c^{2}}\, \sqrt{\left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)+a \right)}}\right)+\frac{2 \left(a^{2} b^{2} e +a^{2} c^{2} e +2 a \,b^{2} d +2 a \,c^{2} d \right) \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(x -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(x -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \left(\left(-\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \EllipticE \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)+\EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)\right)}{\sqrt{\left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)+a \right)}}+\frac{2 d \,a^{2} \sqrt{b^{2}+c^{2}}\, \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(x -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(x -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)}{\sqrt{-\frac{\left(-b^{2} \sin \left(x -\arctan \left(-b , c\right)\right)-c^{2} \sin \left(x -\arctan \left(-b , c\right)\right)-a \sqrt{b^{2}+c^{2}}\right) \left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right)}{\sqrt{b^{2}+c^{2}}}}}\right)}{\sqrt{b^{2}+c^{2}}\, \cos \left(x -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(x -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(x -\arctan \left(-b , c\right)\right)+a \sqrt{b^{2}+c^{2}}}{\sqrt{b^{2}+c^{2}}}}}"," ",0,"(-(-b^2*sin(x-arctan(-b,c))-c^2*sin(x-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(x-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)/(b^2+c^2)^(1/2)*((b^4*e+2*b^2*c^2*e+c^4*e)*(-2/5/(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))*(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)+8/15/(b^2+c^2)*a*(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)+4/15/(b^2+c^2)^(1/2)*a*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+2*(3/5+8/15/(b^2+c^2)*a^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))))+(2*(b^2+c^2)^(1/2)*a*b^2*e+2*(b^2+c^2)^(1/2)*a*c^2*e+(b^2+c^2)^(1/2)*b^2*d+(b^2+c^2)^(1/2)*c^2*d)*(-2/3/(b^2+c^2)^(1/2)*(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)+2/3*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))-4/3/(b^2+c^2)^(1/2)*a*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))))+2*(a^2*b^2*e+a^2*c^2*e+2*a*b^2*d+2*a*c^2*d)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))+2*d*a^2*(b^2+c^2)^(1/2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-b^2*sin(x-arctan(-b,c))-c^2*sin(x-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(x-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))/cos(x-arctan(-b,c))/((b^2*sin(x-arctan(-b,c))+c^2*sin(x-arctan(-b,c))+a*(b^2+c^2)^(1/2))/(b^2+c^2)^(1/2))^(1/2)","B"
558,1,1460,261,0.774000," ","int((a+b*cos(x)+c*sin(x))^(1/2)*(d+b*e*cos(x)+c*e*sin(x)),x)","\frac{\sqrt{-\frac{\left(-b^{2} \sin \left(x -\arctan \left(-b , c\right)\right)-c^{2} \sin \left(x -\arctan \left(-b , c\right)\right)-a \sqrt{b^{2}+c^{2}}\right) \left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right)}{\sqrt{b^{2}+c^{2}}}}\, \left(\left(\sqrt{b^{2}+c^{2}}\, b^{2} e +\sqrt{b^{2}+c^{2}}\, c^{2} e \right) \left(-\frac{2 \sqrt{\left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)+a \right)}}{3 \sqrt{b^{2}+c^{2}}}+\frac{2 \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(x -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(x -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)}{3 \sqrt{\left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)+a \right)}}-\frac{4 a \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(x -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(x -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \left(\left(-\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \EllipticE \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)+\EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)\right)}{3 \sqrt{b^{2}+c^{2}}\, \sqrt{\left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)+a \right)}}\right)+\frac{2 \left(a \,b^{2} e +a \,c^{2} e +b^{2} d +c^{2} d \right) \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(x -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(x -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \left(\left(-\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \EllipticE \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)+\EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)\right)}{\sqrt{\left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)+a \right)}}+\frac{2 d a \sqrt{b^{2}+c^{2}}\, \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(x -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(x -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)}{\sqrt{-\frac{\left(-b^{2} \sin \left(x -\arctan \left(-b , c\right)\right)-c^{2} \sin \left(x -\arctan \left(-b , c\right)\right)-a \sqrt{b^{2}+c^{2}}\right) \left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right)}{\sqrt{b^{2}+c^{2}}}}}\right)}{\sqrt{b^{2}+c^{2}}\, \cos \left(x -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(x -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(x -\arctan \left(-b , c\right)\right)+a \sqrt{b^{2}+c^{2}}}{\sqrt{b^{2}+c^{2}}}}}"," ",0,"(-(-b^2*sin(x-arctan(-b,c))-c^2*sin(x-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(x-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)/(b^2+c^2)^(1/2)*(((b^2+c^2)^(1/2)*b^2*e+(b^2+c^2)^(1/2)*c^2*e)*(-2/3/(b^2+c^2)^(1/2)*(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)+2/3*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))-4/3/(b^2+c^2)^(1/2)*a*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))))+2*(a*b^2*e+a*c^2*e+b^2*d+c^2*d)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))+2*d*a*(b^2+c^2)^(1/2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-b^2*sin(x-arctan(-b,c))-c^2*sin(x-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(x-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))/cos(x-arctan(-b,c))/((b^2*sin(x-arctan(-b,c))+c^2*sin(x-arctan(-b,c))+a*(b^2+c^2)^(1/2))/(b^2+c^2)^(1/2))^(1/2)","B"
559,1,777,220,0.654000," ","int((d+b*e*cos(x)+c*e*sin(x))/(a+b*cos(x)+c*sin(x))^(1/2),x)","\frac{\sqrt{-\frac{\left(-b^{2} \sin \left(x -\arctan \left(-b , c\right)\right)-c^{2} \sin \left(x -\arctan \left(-b , c\right)\right)-a \sqrt{b^{2}+c^{2}}\right) \left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right)}{\sqrt{b^{2}+c^{2}}}}\, \left(\frac{2 \left(b^{2} e +c^{2} e \right) \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(x -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(x -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \left(\left(-\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \EllipticE \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)+\EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)\right)}{\sqrt{\left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right) \left(\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)+a \right)}}+\frac{2 d \sqrt{b^{2}+c^{2}}\, \left(\frac{a}{\sqrt{b^{2}+c^{2}}}-1\right) \sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(-\sin \left(x -\arctan \left(-b , c\right)\right)+1\right) \sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\, \sqrt{\frac{\left(1+\sin \left(x -\arctan \left(-b , c\right)\right)\right) \sqrt{b^{2}+c^{2}}}{-a +\sqrt{b^{2}+c^{2}}}}\, \EllipticF \left(\sqrt{\frac{-\sqrt{b^{2}+c^{2}}\, \sin \left(x -\arctan \left(-b , c\right)\right)-a}{-a +\sqrt{b^{2}+c^{2}}}}, \sqrt{\frac{a -\sqrt{b^{2}+c^{2}}}{a +\sqrt{b^{2}+c^{2}}}}\right)}{\sqrt{-\frac{\left(-b^{2} \sin \left(x -\arctan \left(-b , c\right)\right)-c^{2} \sin \left(x -\arctan \left(-b , c\right)\right)-a \sqrt{b^{2}+c^{2}}\right) \left(\cos^{2}\left(x -\arctan \left(-b , c\right)\right)\right)}{\sqrt{b^{2}+c^{2}}}}}\right)}{\sqrt{b^{2}+c^{2}}\, \cos \left(x -\arctan \left(-b , c\right)\right) \sqrt{\frac{b^{2} \sin \left(x -\arctan \left(-b , c\right)\right)+c^{2} \sin \left(x -\arctan \left(-b , c\right)\right)+a \sqrt{b^{2}+c^{2}}}{\sqrt{b^{2}+c^{2}}}}}"," ",0,"(-(-b^2*sin(x-arctan(-b,c))-c^2*sin(x-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(x-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)/(b^2+c^2)^(1/2)*(2*(b^2*e+c^2*e)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))+2*d*(b^2+c^2)^(1/2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-b^2*sin(x-arctan(-b,c))-c^2*sin(x-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(x-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))/cos(x-arctan(-b,c))/((b^2*sin(x-arctan(-b,c))+c^2*sin(x-arctan(-b,c))+a*(b^2+c^2)^(1/2))/(b^2+c^2)^(1/2))^(1/2)","B"
560,1,2596,288,1.070000," ","int((d+b*e*cos(x)+c*e*sin(x))/(a+b*cos(x)+c*sin(x))^(3/2),x)","\text{Expression too large to display}"," ",0,"(-(-b^2*sin(x-arctan(-b,c))-c^2*sin(x-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(x-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)/(b^2+c^2)^(1/2)*(2*(b^2+c^2)^(1/2)*e*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-b^2*sin(x-arctan(-b,c))-c^2*sin(x-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(x-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+(b^2+c^2)^(1/2)*(-b^2-c^2)*cos(x-arctan(-b,c))^2/(a^2-b^2-c^2)*(a*e-d)/(-(-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)*cos(x-arctan(-b,c))^2*(b^2+c^2))^(1/2)-a*(b^2+c^2)*(a*e-d)/(a^2-b^2-c^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)*cos(x-arctan(-b,c))^2*(b^2+c^2))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))-2*(-1/2*(b^2+c^2)^(3/2)*(a*e-d)/(a^2-b^2-c^2)+1/2*(b^2+c^2)^(1/2)*(2*b^2+2*c^2)/(a^2-b^2-c^2)*(a*e-d))*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)*cos(x-arctan(-b,c))^2*(b^2+c^2))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))-1/2*(a*b^2*e+a*c^2*e-b^2*d-c^2*d)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)*cos(x-arctan(-b,c))^2*(b^2+c^2))^(1/2)/a*EllipticPi(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),-1/2*(-1/(b^2+c^2)^(1/2)*a+1)*(b^2+c^2)^(1/2)/a,((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))-(b^2+c^2)*cos(x-arctan(-b,c))^2*(a*e-d)/(a^2-b^2-c^2)/(-(-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)*cos(x-arctan(-b,c))^2)^(1/2)-a*(b^2+c^2)^(1/2)*(a*e-d)/(a^2-b^2-c^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)*cos(x-arctan(-b,c))^2)^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))-(b^2+c^2)*(a*e-d)/(a^2-b^2-c^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)*cos(x-arctan(-b,c))^2)^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))+(1/2*a*e-1/2*d)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(-(-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)*cos(x-arctan(-b,c))^2)^(1/2)*(b^2+c^2)^(1/2)/a*EllipticPi(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),-1/2*(-1/(b^2+c^2)^(1/2)*a+1)*(b^2+c^2)^(1/2)/a,((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))/cos(x-arctan(-b,c))/((b^2*sin(x-arctan(-b,c))+c^2*sin(x-arctan(-b,c))+a*(b^2+c^2)^(1/2))/(b^2+c^2)^(1/2))^(1/2)","B"
561,1,3164,406,3.886000," ","int((d+b*e*cos(x)+c*e*sin(x))/(a+b*cos(x)+c*sin(x))^(5/2),x)","\text{output too large to display}"," ",0,"(-(-b^2*sin(x-arctan(-b,c))-c^2*sin(x-arctan(-b,c))-a*(b^2+c^2)^(1/2))*cos(x-arctan(-b,c))^2/(b^2+c^2)^(1/2))^(1/2)/(b^2+c^2)^(1/2)*(-1/4*(a*b^2*e+a*c^2*e-b^2*d-c^2*d)/a/(a^2-b^2-c^2)*(cos(x-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)/(b^2*sin(x-arctan(-b,c))+c^2*sin(x-arctan(-b,c))-a*(b^2+c^2)^(1/2))-1/3*(a*e-d)/(a^2-b^2-c^2)/(b^2+c^2)^(1/2)*(cos(x-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)/(sin(x-arctan(-b,c))+1/(b^2+c^2)^(1/2)*a)^2+1/3*(b^2+c^2)^(1/2)*(-b^2-c^2)*cos(x-arctan(-b,c))^2/(a^2-b^2-c^2)^2*(a^2*e+3*b^2*e+3*c^2*e-4*a*d)/(cos(x-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)+2*(7/24*(a*b^2*e+a*c^2*e-b^2*d-c^2*d)/(a^2-b^2-c^2)-1/6*a*(b^2+c^2)*(a^2*e+3*b^2*e+3*c^2*e-4*a*d)/(a^2-b^2-c^2)^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+2*(-1/8*(b^2+c^2)^(1/2)*(a*b^2*e+a*c^2*e-b^2*d-c^2*d)/a/(a^2-b^2-c^2)+1/6*(b^2+c^2)^(3/2)*(a^2*e+3*b^2*e+3*c^2*e-4*a*d)/(a^2-b^2-c^2)^2-1/6*(b^2+c^2)^(1/2)*(2*b^2+2*c^2)/(a^2-b^2-c^2)^2*(a^2*e+3*b^2*e+3*c^2*e-4*a*d))*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))-1/8*(a^3*b^2*e+a^3*c^2*e+3*a*b^4*e+6*a*b^2*c^2*e+3*a*c^4*e-5*a^2*b^2*d-5*a^2*c^2*d+b^4*d+2*b^2*c^2*d+c^4*d)/a^2/(a^2-b^2-c^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*(b^2+c^2)*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*EllipticPi(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),-1/2*(-1/(b^2+c^2)^(1/2)*a+1)*(b^2+c^2)^(1/2)/a,((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+1/4*(b^2+c^2)^(3/2)*(a*e-d)/a/(a^2-b^2-c^2)*(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)/(b^2*sin(x-arctan(-b,c))+c^2*sin(x-arctan(-b,c))-a*(b^2+c^2)^(1/2))-1/3*(a*e-d)/(a^2-b^2-c^2)*(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)/(sin(x-arctan(-b,c))+1/(b^2+c^2)^(1/2)*a)^2-1/3*(b^2+c^2)*cos(x-arctan(-b,c))^2/(a^2-b^2-c^2)^2*(a^2*e+3*b^2*e+3*c^2*e-4*a*d)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)+2*(1/24*(b^2+c^2)^(1/2)*(a*e-d)/(a^2-b^2-c^2)-1/6*a*(b^2+c^2)^(1/2)*(a^2*e+3*b^2*e+3*c^2*e-4*a*d)/(a^2-b^2-c^2)^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+2*(1/8*(a*b^2*e+a*c^2*e-b^2*d-c^2*d)/a/(a^2-b^2-c^2)-1/6*(b^2+c^2)*(a^2*e+3*b^2*e+3*c^2*e-4*a*d)/(a^2-b^2-c^2)^2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*((-1/(b^2+c^2)^(1/2)*a-1)*EllipticE(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2))+EllipticF(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))+1/8*(a^3*b^2*e+a^3*c^2*e+3*a*b^4*e+6*a*b^2*c^2*e+3*a*c^4*e-5*a^2*b^2*d-5*a^2*c^2*d+b^4*d+2*b^2*c^2*d+c^4*d)/a^2/(a^2-b^2-c^2)/(b^2+c^2)^(1/2)*(1/(b^2+c^2)^(1/2)*a-1)*((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2)*((-sin(x-arctan(-b,c))+1)*(b^2+c^2)^(1/2)/(a+(b^2+c^2)^(1/2)))^(1/2)*((1+sin(x-arctan(-b,c)))*(b^2+c^2)^(1/2)/(-a+(b^2+c^2)^(1/2)))^(1/2)/(cos(x-arctan(-b,c))^2*((b^2+c^2)^(1/2)*sin(x-arctan(-b,c))+a))^(1/2)*EllipticPi(((-(b^2+c^2)^(1/2)*sin(x-arctan(-b,c))-a)/(-a+(b^2+c^2)^(1/2)))^(1/2),-1/2*(-1/(b^2+c^2)^(1/2)*a+1)*(b^2+c^2)^(1/2)/a,((a-(b^2+c^2)^(1/2))/(a+(b^2+c^2)^(1/2)))^(1/2)))/cos(x-arctan(-b,c))/((b^2*sin(x-arctan(-b,c))+c^2*sin(x-arctan(-b,c))+a*(b^2+c^2)^(1/2))/(b^2+c^2)^(1/2))^(1/2)","B"
562,1,178,79,0.253000," ","int((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d)),x)","\frac{B \ln \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)}{e c}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+2 c}{2 \sqrt{a^{2}-c^{2}}}\right) A}{e \sqrt{a^{2}-c^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+2 c}{2 \sqrt{a^{2}-c^{2}}}\right) C a}{e c \sqrt{a^{2}-c^{2}}}-\frac{B \ln \left(1+\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e c}+\frac{2 C \arctan \left(\tan \left(\frac{d}{2}+\frac{e x}{2}\right)\right)}{e c}"," ",0,"1/e/c*B*ln(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)+2/e/(a^2-c^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d+1/2*e*x)+2*c)/(a^2-c^2)^(1/2))*A-2/e/c/(a^2-c^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d+1/2*e*x)+2*c)/(a^2-c^2)^(1/2))*C*a-1/e/c*B*ln(1+tan(1/2*d+1/2*e*x)^2)+2/e/c*C*arctan(tan(1/2*d+1/2*e*x))","B"
563,1,426,113,0.395000," ","int((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d))^2,x)","\frac{2 \tan \left(\frac{d}{2}+\frac{e x}{2}\right) A \,c^{2}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right) a \left(a^{2}-c^{2}\right)}+\frac{2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right) B}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right) \left(a^{2}-c^{2}\right)}-\frac{2 \tan \left(\frac{d}{2}+\frac{e x}{2}\right) B \,c^{2}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right) a \left(a^{2}-c^{2}\right)}-\frac{2 \tan \left(\frac{d}{2}+\frac{e x}{2}\right) c C}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right) \left(a^{2}-c^{2}\right)}+\frac{2 A c}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right) \left(a^{2}-c^{2}\right)}-\frac{2 C a}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right) \left(a^{2}-c^{2}\right)}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+2 c}{2 \sqrt{a^{2}-c^{2}}}\right) a A}{e \left(a^{2}-c^{2}\right)^{\frac{3}{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+2 c}{2 \sqrt{a^{2}-c^{2}}}\right) C c}{e \left(a^{2}-c^{2}\right)^{\frac{3}{2}}}"," ",0,"2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)/a/(a^2-c^2)*tan(1/2*d+1/2*e*x)*A*c^2+2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)*a/(a^2-c^2)*tan(1/2*d+1/2*e*x)*B-2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)/a/(a^2-c^2)*tan(1/2*d+1/2*e*x)*B*c^2-2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)/(a^2-c^2)*tan(1/2*d+1/2*e*x)*c*C+2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)/(a^2-c^2)*A*c-2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)/(a^2-c^2)*C*a+2/e/(a^2-c^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d+1/2*e*x)+2*c)/(a^2-c^2)^(1/2))*a*A-2/e/(a^2-c^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d+1/2*e*x)+2*c)/(a^2-c^2)^(1/2))*C*c","B"
564,1,1891,174,0.428000," ","int((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d))^3,x)","-\frac{4 a \left(\tan^{3}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) B \,c^{2}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}+\frac{2 \left(\tan^{3}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) B \,c^{4}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right) a}-\frac{3 a^{2} \left(\tan^{3}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) C c}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}+\frac{4 a^{2} \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) A c}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}-\frac{2 \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) A \,c^{5}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right) a^{2}}+\frac{2 a^{2} \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) B c}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}+\frac{2 \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) B \,c^{5}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right) a^{2}}-\frac{5 a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) C \,c^{2}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}-\frac{2 \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) C \,c^{4}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right) a}+\frac{11 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right) A \,c^{2}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}-\frac{2 \tan \left(\frac{d}{2}+\frac{e x}{2}\right) A \,c^{4}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} a \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}-\frac{4 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right) B \,c^{2}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}+\frac{2 \tan \left(\frac{d}{2}+\frac{e x}{2}\right) B \,c^{4}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} a \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}-\frac{5 a^{2} \tan \left(\frac{d}{2}+\frac{e x}{2}\right) C c}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}+\frac{5 a \left(\tan^{3}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) A \,c^{2}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}-\frac{2 \left(\tan^{3}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) A \,c^{4}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right) a}-\frac{C a \,c^{2}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}+\frac{7 \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) A \,c^{3}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}-\frac{4 \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) B \,c^{3}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}-\frac{4 \tan \left(\frac{d}{2}+\frac{e x}{2}\right) C \,c^{3}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}+\frac{2 a^{3} \left(\tan^{3}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) B}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}-\frac{2 a^{3} \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right) C}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}+\frac{2 a^{3} \tan \left(\frac{d}{2}+\frac{e x}{2}\right) B}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}+\frac{4 A \,a^{2} c}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}-\frac{2 C \,a^{3}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}-\frac{A \,c^{3}}{e \left(a \left(\tan^{2}\left(\frac{d}{2}+\frac{e x}{2}\right)\right)+2 c \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+a \right)^{2} \left(a^{4}-2 a^{2} c^{2}+c^{4}\right)}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+2 c}{2 \sqrt{a^{2}-c^{2}}}\right) a^{2} A}{e \left(a^{4}-2 a^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-c^{2}}}+\frac{\arctan \left(\frac{2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+2 c}{2 \sqrt{a^{2}-c^{2}}}\right) A \,c^{2}}{e \left(a^{4}-2 a^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-c^{2}}}-\frac{3 \arctan \left(\frac{2 a \tan \left(\frac{d}{2}+\frac{e x}{2}\right)+2 c}{2 \sqrt{a^{2}-c^{2}}}\right) a c C}{e \left(a^{4}-2 a^{2} c^{2}+c^{4}\right) \sqrt{a^{2}-c^{2}}}"," ",0,"-2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)*C*a^3-1/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)*A*c^3-2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)*a^3*tan(1/2*d+1/2*e*x)^2*C+2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2*a^3/(a^4-2*a^2*c^2+c^4)*tan(1/2*d+1/2*e*x)*B+4/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)*A*a^2*c-1/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)*C*a*c^2+7/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)*tan(1/2*d+1/2*e*x)^2*A*c^3-4/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)*tan(1/2*d+1/2*e*x)^2*B*c^3-4/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)*tan(1/2*d+1/2*e*x)*C*c^3+2/e/(a^4-2*a^2*c^2+c^4)/(a^2-c^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d+1/2*e*x)+2*c)/(a^2-c^2)^(1/2))*a^2*A+1/e/(a^4-2*a^2*c^2+c^4)/(a^2-c^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d+1/2*e*x)+2*c)/(a^2-c^2)^(1/2))*A*c^2+2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)*a^3*tan(1/2*d+1/2*e*x)^3*B-4/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)*a*tan(1/2*d+1/2*e*x)^3*B*c^2+2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)/a*tan(1/2*d+1/2*e*x)^3*B*c^4-3/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)*a^2*tan(1/2*d+1/2*e*x)^3*C*c+4/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)*a^2*tan(1/2*d+1/2*e*x)^2*A*c-2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)/a^2*tan(1/2*d+1/2*e*x)^2*A*c^5+2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)*a^2*tan(1/2*d+1/2*e*x)^2*B*c+2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)/a^2*tan(1/2*d+1/2*e*x)^2*B*c^5-5/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)*a*tan(1/2*d+1/2*e*x)^2*C*c^2-2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)/a*tan(1/2*d+1/2*e*x)^2*C*c^4+11/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2*a/(a^4-2*a^2*c^2+c^4)*tan(1/2*d+1/2*e*x)*A*c^2-2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/a/(a^4-2*a^2*c^2+c^4)*tan(1/2*d+1/2*e*x)*A*c^4-4/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2*a/(a^4-2*a^2*c^2+c^4)*tan(1/2*d+1/2*e*x)*B*c^2+2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/a/(a^4-2*a^2*c^2+c^4)*tan(1/2*d+1/2*e*x)*B*c^4-5/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2*a^2/(a^4-2*a^2*c^2+c^4)*tan(1/2*d+1/2*e*x)*C*c-3/e/(a^4-2*a^2*c^2+c^4)/(a^2-c^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d+1/2*e*x)+2*c)/(a^2-c^2)^(1/2))*a*c*C+5/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)*a*tan(1/2*d+1/2*e*x)^3*A*c^2-2/e/(a*tan(1/2*d+1/2*e*x)^2+2*c*tan(1/2*d+1/2*e*x)+a)^2/(a^4-2*a^2*c^2+c^4)/a*tan(1/2*d+1/2*e*x)^3*A*c^4","B"
565,1,5051,245,0.463000," ","int((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d))^4,x)","\text{output too large to display}"," ",0,"result too large to display","B"
566,0,0,115,1.111000," ","int((a+b*cos(d*x+c)*sin(d*x+c))^m,x)","\int \left(a +b \cos \left(d x +c \right) \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+b*cos(d*x+c)*sin(d*x+c))^m,x)","F"
567,1,106,99,0.248000," ","int((a+b*cos(d*x+c)*sin(d*x+c))^3,x)","\frac{b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)+3 a \,b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\sin \left(d x +c \right) \cos \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\frac{3 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b}{2}+a^{3} \left(d x +c \right)}{d}"," ",0,"1/d*(b^3*(-1/6*sin(d*x+c)^2*cos(d*x+c)^4-1/12*cos(d*x+c)^4)+3*a*b^2*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*sin(d*x+c)*cos(d*x+c)+1/8*d*x+1/8*c)-3/2*cos(d*x+c)^2*a^2*b+a^3*(d*x+c))","A"
568,1,69,55,0.242000," ","int((a+b*cos(d*x+c)*sin(d*x+c))^2,x)","\frac{b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\sin \left(d x +c \right) \cos \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\left(\cos^{2}\left(d x +c \right)\right) a b +a^{2} \left(d x +c \right)}{d}"," ",0,"1/d*(b^2*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*sin(d*x+c)*cos(d*x+c)+1/8*d*x+1/8*c)-cos(d*x+c)^2*a*b+a^2*(d*x+c))","A"
569,1,19,18,0.003000," ","int(a+b*cos(d*x+c)*sin(d*x+c),x)","a x +\frac{b \left(\sin^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"a*x+1/2*b*sin(d*x+c)^2/d","A"
570,1,45,44,0.313000," ","int(1/(a+b*cos(d*x+c)*sin(d*x+c)),x)","\frac{2 \arctan \left(\frac{b +2 a \tan \left(d x +c \right)}{\sqrt{4 a^{2}-b^{2}}}\right)}{d \sqrt{4 a^{2}-b^{2}}}"," ",0,"2*arctan((b+2*a*tan(d*x+c))/(4*a^2-b^2)^(1/2))/d/(4*a^2-b^2)^(1/2)","A"
571,1,139,91,0.445000," ","int(1/(a+b*cos(d*x+c)*sin(d*x+c))^2,x)","\frac{b^{2} \tan \left(d x +c \right)}{d \left(\left(\tan^{2}\left(d x +c \right)\right) a +b \tan \left(d x +c \right)+a \right) a \left(4 a^{2}-b^{2}\right)}+\frac{2 b}{d \left(\left(\tan^{2}\left(d x +c \right)\right) a +b \tan \left(d x +c \right)+a \right) \left(4 a^{2}-b^{2}\right)}+\frac{8 a \arctan \left(\frac{b +2 a \tan \left(d x +c \right)}{\sqrt{4 a^{2}-b^{2}}}\right)}{\left(4 a^{2}-b^{2}\right)^{\frac{3}{2}} d}"," ",0,"1/d/(tan(d*x+c)^2*a+b*tan(d*x+c)+a)*b^2/a/(4*a^2-b^2)*tan(d*x+c)+2/d/(tan(d*x+c)^2*a+b*tan(d*x+c)+a)*b/(4*a^2-b^2)+8*a*arctan((b+2*a*tan(d*x+c))/(4*a^2-b^2)^(1/2))/(4*a^2-b^2)^(3/2)/d","A"
572,1,640,145,0.488000," ","int(1/(a+b*cos(d*x+c)*sin(d*x+c))^3,x)","\frac{10 b^{2} a \left(\tan^{3}\left(d x +c \right)\right)}{d \left(\left(\tan^{2}\left(d x +c \right)\right) a +b \tan \left(d x +c \right)+a \right)^{2} \left(16 a^{4}-8 a^{2} b^{2}+b^{4}\right)}-\frac{b^{4} \left(\tan^{3}\left(d x +c \right)\right)}{d \left(\left(\tan^{2}\left(d x +c \right)\right) a +b \tan \left(d x +c \right)+a \right)^{2} \left(16 a^{4}-8 a^{2} b^{2}+b^{4}\right) a}+\frac{16 b \,a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{d \left(\left(\tan^{2}\left(d x +c \right)\right) a +b \tan \left(d x +c \right)+a \right)^{2} \left(16 a^{4}-8 a^{2} b^{2}+b^{4}\right)}+\frac{7 b^{3} \left(\tan^{2}\left(d x +c \right)\right)}{d \left(\left(\tan^{2}\left(d x +c \right)\right) a +b \tan \left(d x +c \right)+a \right)^{2} \left(16 a^{4}-8 a^{2} b^{2}+b^{4}\right)}-\frac{b^{5} \left(\tan^{2}\left(d x +c \right)\right)}{2 d \left(\left(\tan^{2}\left(d x +c \right)\right) a +b \tan \left(d x +c \right)+a \right)^{2} \left(16 a^{4}-8 a^{2} b^{2}+b^{4}\right) a^{2}}+\frac{22 b^{2} a \tan \left(d x +c \right)}{d \left(\left(\tan^{2}\left(d x +c \right)\right) a +b \tan \left(d x +c \right)+a \right)^{2} \left(16 a^{4}-8 a^{2} b^{2}+b^{4}\right)}-\frac{b^{4} \tan \left(d x +c \right)}{d \left(\left(\tan^{2}\left(d x +c \right)\right) a +b \tan \left(d x +c \right)+a \right)^{2} a \left(16 a^{4}-8 a^{2} b^{2}+b^{4}\right)}+\frac{16 b \,a^{2}}{d \left(\left(\tan^{2}\left(d x +c \right)\right) a +b \tan \left(d x +c \right)+a \right)^{2} \left(16 a^{4}-8 a^{2} b^{2}+b^{4}\right)}-\frac{b^{3}}{d \left(\left(\tan^{2}\left(d x +c \right)\right) a +b \tan \left(d x +c \right)+a \right)^{2} \left(16 a^{4}-8 a^{2} b^{2}+b^{4}\right)}+\frac{32 \arctan \left(\frac{b +2 a \tan \left(d x +c \right)}{\sqrt{4 a^{2}-b^{2}}}\right) a^{2}}{d \left(16 a^{4}-8 a^{2} b^{2}+b^{4}\right) \sqrt{4 a^{2}-b^{2}}}+\frac{4 \arctan \left(\frac{b +2 a \tan \left(d x +c \right)}{\sqrt{4 a^{2}-b^{2}}}\right) b^{2}}{d \left(16 a^{4}-8 a^{2} b^{2}+b^{4}\right) \sqrt{4 a^{2}-b^{2}}}"," ",0,"10/d/(tan(d*x+c)^2*a+b*tan(d*x+c)+a)^2*b^2/(16*a^4-8*a^2*b^2+b^4)*a*tan(d*x+c)^3-1/d/(tan(d*x+c)^2*a+b*tan(d*x+c)+a)^2*b^4/(16*a^4-8*a^2*b^2+b^4)/a*tan(d*x+c)^3+16/d/(tan(d*x+c)^2*a+b*tan(d*x+c)+a)^2*b/(16*a^4-8*a^2*b^2+b^4)*a^2*tan(d*x+c)^2+7/d/(tan(d*x+c)^2*a+b*tan(d*x+c)+a)^2*b^3/(16*a^4-8*a^2*b^2+b^4)*tan(d*x+c)^2-1/2/d/(tan(d*x+c)^2*a+b*tan(d*x+c)+a)^2*b^5/(16*a^4-8*a^2*b^2+b^4)/a^2*tan(d*x+c)^2+22/d/(tan(d*x+c)^2*a+b*tan(d*x+c)+a)^2*b^2*a/(16*a^4-8*a^2*b^2+b^4)*tan(d*x+c)-1/d/(tan(d*x+c)^2*a+b*tan(d*x+c)+a)^2*b^4/a/(16*a^4-8*a^2*b^2+b^4)*tan(d*x+c)+16/d/(tan(d*x+c)^2*a+b*tan(d*x+c)+a)^2*b/(16*a^4-8*a^2*b^2+b^4)*a^2-1/d/(tan(d*x+c)^2*a+b*tan(d*x+c)+a)^2*b^3/(16*a^4-8*a^2*b^2+b^4)+32/d/(16*a^4-8*a^2*b^2+b^4)/(4*a^2-b^2)^(1/2)*arctan((b+2*a*tan(d*x+c))/(4*a^2-b^2)^(1/2))*a^2+4/d/(16*a^4-8*a^2*b^2+b^4)/(4*a^2-b^2)^(1/2)*arctan((b+2*a*tan(d*x+c))/(4*a^2-b^2)^(1/2))*b^2","B"
573,1,1138,293,0.521000," ","int((a+b*cos(d*x+c)*sin(d*x+c))^(5/2),x)","\frac{240 a^{4} \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, \EllipticF \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right)+64 \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \EllipticF \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) a^{3} b -24 a^{2} \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, \EllipticF \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) b^{2}-16 a \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, \EllipticF \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) b^{3}-9 \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \EllipticF \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) b^{4}-368 \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \EllipticE \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) a^{4}+56 \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \EllipticE \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) a^{2} b^{2}+9 \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \EllipticE \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) b^{4}+3 b^{4} \left(\sin^{4}\left(2 d x +2 c \right)\right)+28 a \,b^{3} \left(\sin^{3}\left(2 d x +2 c \right)\right)+44 a^{2} b^{2} \left(\sin^{2}\left(2 d x +2 c \right)\right)-3 b^{4} \left(\sin^{2}\left(2 d x +2 c \right)\right)-28 \sin \left(2 d x +2 c \right) a \,b^{3}-44 a^{2} b^{2}}{60 b \cos \left(2 d x +2 c \right) \sqrt{4 a +2 b \sin \left(2 d x +2 c \right)}\, d}"," ",0,"1/60*(240*a^4*((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*EllipticF(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))+64*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*EllipticF(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*a^3*b-24*a^2*((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*EllipticF(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*b^2-16*a*((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*EllipticF(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*b^3-9*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*EllipticF(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*b^4-368*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*EllipticE(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*a^4+56*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*EllipticE(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*a^2*b^2+9*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*EllipticE(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*b^4+3*b^4*sin(2*d*x+2*c)^4+28*a*b^3*sin(2*d*x+2*c)^3+44*a^2*b^2*sin(2*d*x+2*c)^2-3*b^4*sin(2*d*x+2*c)^2-28*sin(2*d*x+2*c)*a*b^3-44*a^2*b^2)/b/cos(2*d*x+2*c)/(4*a+2*b*sin(2*d*x+2*c))^(1/2)/d","B"
574,1,844,246,0.442000," ","int((a+b*cos(d*x+c)*sin(d*x+c))^(3/2),x)","\frac{24 a^{3} \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, \EllipticF \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right)+4 \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \EllipticF \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, a^{2} b -6 \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, \EllipticF \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) b^{2} a -\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, \EllipticF \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) b^{3}-32 \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \EllipticE \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, a^{3}+8 \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \EllipticE \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, a \,b^{2}+b^{3} \left(\sin^{3}\left(2 d x +2 c \right)\right)+2 a \,b^{2} \left(\sin^{2}\left(2 d x +2 c \right)\right)-\sin \left(2 d x +2 c \right) b^{3}-2 a \,b^{2}}{6 b \cos \left(2 d x +2 c \right) \sqrt{4 a +2 b \sin \left(2 d x +2 c \right)}\, d}"," ",0,"1/6*(24*a^3*((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*EllipticF(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))+4*((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*EllipticF(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*a^2*b-6*((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*EllipticF(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*b^2*a-((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*EllipticF(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*b^3-32*((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*EllipticE(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*a^3+8*((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*EllipticE(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*a*b^2+b^3*sin(2*d*x+2*c)^3+2*a*b^2*sin(2*d*x+2*c)^2-sin(2*d*x+2*c)*b^3-2*a*b^2)/b/cos(2*d*x+2*c)/(4*a+2*b*sin(2*d*x+2*c))^(1/2)/d","B"
575,1,312,99,0.407000," ","int((a+b*cos(d*x+c)*sin(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, \left(2 a -b \right) \left(2 \EllipticE \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) a +\EllipticE \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) b -2 a \EllipticF \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right)-\EllipticF \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) b \right)}{b \cos \left(2 d x +2 c \right) \sqrt{4 a +2 b \sin \left(2 d x +2 c \right)}\, d}"," ",0,"-((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)/b*(2*a-b)*(2*EllipticE(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*a+EllipticE(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*b-2*a*EllipticF(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))-EllipticF(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*b)/cos(2*d*x+2*c)/(4*a+2*b*sin(2*d*x+2*c))^(1/2)/d","B"
576,1,165,99,0.426000," ","int(1/(a+b*cos(d*x+c)*sin(d*x+c))^(1/2),x)","\frac{2 \left(2 a -b \right) \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, \EllipticF \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right)}{b \cos \left(2 d x +2 c \right) \sqrt{4 a +2 b \sin \left(2 d x +2 c \right)}\, d}"," ",0,"2*(2*a-b)*((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*EllipticF(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))/b/cos(2*d*x+2*c)/(4*a+2*b*sin(2*d*x+2*c))^(1/2)/d","A"
577,1,570,161,0.501000," ","int(1/(a+b*cos(d*x+c)*sin(d*x+c))^(3/2),x)","\frac{16 a^{2} \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, \EllipticF \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right)-4 \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \EllipticF \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, b^{2}-16 \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \EllipticE \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, a^{2}+4 \sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}\, \EllipticE \left(\sqrt{\frac{2 a +b \sin \left(2 d x +2 c \right)}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) \sqrt{-\frac{\left(\sin \left(2 d x +2 c \right)-1\right) b}{2 a +b}}\, \sqrt{-\frac{\left(1+\sin \left(2 d x +2 c \right)\right) b}{2 a -b}}\, b^{2}-4 b^{2} \left(\sin^{2}\left(2 d x +2 c \right)\right)+4 b^{2}}{b \left(4 a^{2}-b^{2}\right) \cos \left(2 d x +2 c \right) \sqrt{4 a +2 b \sin \left(2 d x +2 c \right)}\, d}"," ",0,"4/b*(4*a^2*((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*EllipticF(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))-((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*EllipticF(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*b^2-4*((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*EllipticE(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*a^2+((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2)*EllipticE(((2*a+b*sin(2*d*x+2*c))/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*(-(sin(2*d*x+2*c)-1)*b/(2*a+b))^(1/2)*(-(1+sin(2*d*x+2*c))*b/(2*a-b))^(1/2)*b^2-b^2*sin(2*d*x+2*c)^2+b^2)/(4*a^2-b^2)/cos(2*d*x+2*c)/(4*a+2*b*sin(2*d*x+2*c))^(1/2)/d","B"
578,1,1554,323,0.515000," ","int(1/(a+b*cos(d*x+c)*sin(d*x+c))^(5/2),x)","\frac{\frac{64 \sin \left(2 d x +2 c \right) \left(\cos^{2}\left(2 d x +2 c \right)\right) a \,b^{3}}{3}+\frac{8 \sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}\, \sqrt{-\frac{b \sin \left(2 d x +2 c \right)}{2 a +b}+\frac{b}{2 a +b}}\, \sqrt{-\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}-\frac{b}{2 a -b}}\, b \left(24 \EllipticF \left(\sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) a^{3}+4 \EllipticF \left(\sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) a^{2} b -6 \EllipticF \left(\sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) a \,b^{2}-\EllipticF \left(\sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) b^{3}-32 \EllipticE \left(\sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) a^{3}+8 \EllipticE \left(\sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) a \,b^{2}\right) \sin \left(2 d x +2 c \right)}{3}+\frac{8 \left(20 a^{2} b^{2}-b^{4}\right) \left(\cos^{2}\left(2 d x +2 c \right)\right)}{3}+128 \sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) \sqrt{-\frac{b \sin \left(2 d x +2 c \right)}{2 a +b}+\frac{b}{2 a +b}}\, \sqrt{-\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}-\frac{b}{2 a -b}}\, a^{4}+\frac{64 \sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) \sqrt{-\frac{b \sin \left(2 d x +2 c \right)}{2 a +b}+\frac{b}{2 a +b}}\, \sqrt{-\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}-\frac{b}{2 a -b}}\, a^{3} b}{3}-32 \sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) \sqrt{-\frac{b \sin \left(2 d x +2 c \right)}{2 a +b}+\frac{b}{2 a +b}}\, \sqrt{-\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}-\frac{b}{2 a -b}}\, a^{2} b^{2}-\frac{16 \sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) \sqrt{-\frac{b \sin \left(2 d x +2 c \right)}{2 a +b}+\frac{b}{2 a +b}}\, \sqrt{-\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}-\frac{b}{2 a -b}}\, a \,b^{3}}{3}-\frac{512 \sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}\, \sqrt{-\frac{b \sin \left(2 d x +2 c \right)}{2 a +b}+\frac{b}{2 a +b}}\, \sqrt{-\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}-\frac{b}{2 a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) a^{4}}{3}+\frac{128 \sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}\, \sqrt{-\frac{b \sin \left(2 d x +2 c \right)}{2 a +b}+\frac{b}{2 a +b}}\, \sqrt{-\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}-\frac{b}{2 a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(2 d x +2 c \right)}{2 a -b}+\frac{2 a}{2 a -b}}, \sqrt{\frac{2 a -b}{2 a +b}}\right) a^{2} b^{2}}{3}}{\left(2 a +b \sin \left(2 d x +2 c \right)\right) \left(4 a^{2}-b^{2}\right)^{2} b \cos \left(2 d x +2 c \right) \sqrt{4 a +2 b \sin \left(2 d x +2 c \right)}\, d}"," ",0,"8/3*(8*sin(2*d*x+2*c)*cos(2*d*x+2*c)^2*a*b^3+(b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2)*(-b/(2*a+b)*sin(2*d*x+2*c)+b/(2*a+b))^(1/2)*(-b/(2*a-b)*sin(2*d*x+2*c)-b/(2*a-b))^(1/2)*b*(24*EllipticF((b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*a^3+4*EllipticF((b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*a^2*b-6*EllipticF((b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*a*b^2-EllipticF((b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*b^3-32*EllipticE((b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*a^3+8*EllipticE((b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*a*b^2)*sin(2*d*x+2*c)+(20*a^2*b^2-b^4)*cos(2*d*x+2*c)^2+48*(b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2)*EllipticF((b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*(-b/(2*a+b)*sin(2*d*x+2*c)+b/(2*a+b))^(1/2)*(-b/(2*a-b)*sin(2*d*x+2*c)-b/(2*a-b))^(1/2)*a^4+8*(b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2)*EllipticF((b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*(-b/(2*a+b)*sin(2*d*x+2*c)+b/(2*a+b))^(1/2)*(-b/(2*a-b)*sin(2*d*x+2*c)-b/(2*a-b))^(1/2)*a^3*b-12*(b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2)*EllipticF((b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*(-b/(2*a+b)*sin(2*d*x+2*c)+b/(2*a+b))^(1/2)*(-b/(2*a-b)*sin(2*d*x+2*c)-b/(2*a-b))^(1/2)*a^2*b^2-2*(b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2)*EllipticF((b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*(-b/(2*a+b)*sin(2*d*x+2*c)+b/(2*a+b))^(1/2)*(-b/(2*a-b)*sin(2*d*x+2*c)-b/(2*a-b))^(1/2)*a*b^3-64*(b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2)*(-b/(2*a+b)*sin(2*d*x+2*c)+b/(2*a+b))^(1/2)*(-b/(2*a-b)*sin(2*d*x+2*c)-b/(2*a-b))^(1/2)*EllipticE((b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*a^4+16*(b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2)*(-b/(2*a+b)*sin(2*d*x+2*c)+b/(2*a+b))^(1/2)*(-b/(2*a-b)*sin(2*d*x+2*c)-b/(2*a-b))^(1/2)*EllipticE((b/(2*a-b)*sin(2*d*x+2*c)+2*a/(2*a-b))^(1/2),((2*a-b)/(2*a+b))^(1/2))*a^2*b^2)/(2*a+b*sin(2*d*x+2*c))/(4*a^2-b^2)^2/b/cos(2*d*x+2*c)/(4*a+2*b*sin(2*d*x+2*c))^(1/2)/d","B"
579,1,2282,389,0.297000," ","int(x^3/(a+b*cos(x)*sin(x)),x)","\frac{12 \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2} x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{3 \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2} x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{3 \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, \polylog \left(4, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{6 i \polylog \left(4, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{3 i \polylog \left(4, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2}}{2 \left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{6 i \polylog \left(4, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{3 i \polylog \left(4, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2}}{2 \left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{3 \polylog \left(4, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{3 i \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2} x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{12 i \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2} x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{12 i \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2} x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{4 i \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a \,x^{3}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{6 i \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{6 i \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{4 i \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a \,x^{3}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{8 \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2} x^{3}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{2 \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2} x^{3}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{2 \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a \,x^{4}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{8 \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2} x^{3}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{2 \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2} x^{3}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{2 \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a \,x^{4}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{i b^{2} x^{4}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{i b^{2} x^{4}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{4 i a^{2} x^{4}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{4 i a^{2} x^{4}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{12 \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2} x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{3 \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2} x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{3 i \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2} x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{6 \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a \,x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{6 \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a \,x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}"," ",0,"8/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*ln(1-b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*a^2*x^3-2/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*ln(1-b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*b^2*x^3-2/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*(-(2*a-b)*(2*a+b))^(1/2)*a*x^4+12/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(3,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*a^2*x-3/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(3,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*b^2*x+3*I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(2,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*b^2*x^2-12*I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(2,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*a^2*x^2-12*I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*polylog(2,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*a^2*x^2+3*I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*polylog(2,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*b^2*x^2+6/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*polylog(2,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*(-(2*a-b)*(2*a+b))^(1/2)*a*x^2-6/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(2,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*(-(2*a-b)*(2*a+b))^(1/2)*a*x^2+4*I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*ln(1-b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*(-(2*a-b)*(2*a+b))^(1/2)*a*x^3+6*I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*(-(2*a-b)*(2*a+b))^(1/2)*polylog(3,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*a*x-4*I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*ln(1-b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*(-(2*a-b)*(2*a+b))^(1/2)*a*x^3-6*I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(3,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*(-(2*a-b)*(2*a+b))^(1/2)*a*x+8/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*ln(1-b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*a^2*x^3-2/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*ln(1-b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*b^2*x^3+2/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*(-(2*a-b)*(2*a+b))^(1/2)*a*x^4+12/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*polylog(3,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*a^2*x-3/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*polylog(3,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*b^2*x-3/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*(-(2*a-b)*(2*a+b))^(1/2)*polylog(4,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*a+I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*b^2*x^4+I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*b^2*x^4-4*I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*a^2*x^4+6*I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*polylog(4,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*a^2-3/2*I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*polylog(4,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*b^2-4*I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*a^2*x^4+6*I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(4,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*a^2-3/2*I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(4,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*b^2+3/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(4,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*(-(2*a-b)*(2*a+b))^(1/2)*a","B"
580,1,1782,290,0.227000," ","int(x^2/(a+b*cos(x)*sin(x)),x)","\frac{8 \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a \,x^{3}}{3 \left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{2 i \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2} x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{2 i \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2} x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{8 i \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2} x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{8 \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2} x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{2 \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2} x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{4 \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{2 i \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{2 i \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{4 i \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a \,x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{4 \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{\polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{8 \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a \,x^{3}}{3 \left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{16 i a^{2} x^{3}}{3 \left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{16 i a^{2} x^{3}}{3 \left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{4 i b^{2} x^{3}}{3 \left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{8 \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2} x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{2 \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2} x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{4 \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{8 i \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2} x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{4 i b^{2} x^{3}}{3 \left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{4 i \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a \,x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{4 \polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{\polylog \left(3, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}"," ",0,"8/3/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*(-(2*a-b)*(2*a+b))^(1/2)*a*x^3+2*I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*polylog(2,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*b^2*x-8*I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*polylog(2,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*a^2*x+2*I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(2,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*b^2*x+8/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*ln(1-b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*a^2*x^2-2/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*ln(1-b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*b^2*x^2+4/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*(-(2*a-b)*(2*a+b))^(1/2)*polylog(2,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*a*x-4*I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*ln(1-b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*(-(2*a-b)*(2*a+b))^(1/2)*a*x^2+2*I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*polylog(3,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*(-(2*a-b)*(2*a+b))^(1/2)*a-16/3*I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*a^2*x^3+4/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*polylog(3,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*a^2-1/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*polylog(3,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*b^2-8/3/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*(-(2*a-b)*(2*a+b))^(1/2)*a*x^3-16/3*I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*a^2*x^3+4/3*I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*b^2*x^3-8*I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(2,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*a^2*x+8/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*ln(1-b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*a^2*x^2-2/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*ln(1-b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*b^2*x^2-4/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(2,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*(-(2*a-b)*(2*a+b))^(1/2)*a*x+4/3*I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*b^2*x^3-2*I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(3,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*(-(2*a-b)*(2*a+b))^(1/2)*a+4*I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*(-(2*a-b)*(2*a+b))^(1/2)*ln(1-b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*a*x^2+4/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(3,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*a^2-1/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(3,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*b^2","B"
581,1,1284,191,0.217000," ","int(x/(a+b*cos(x)*sin(x)),x)","-\frac{4 i \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{4 \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a \,x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{2 \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2} x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{4 \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a \,x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{2 \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{i \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{4 i \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{8 i a^{2} x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{4 i \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{2 i b^{2} x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{2 \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{8 \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2} x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{8 \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) a^{2} x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{2 \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2} x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{i \polylog \left(2, \frac{b \,{\mathrm e}^{2 i x}}{-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) b^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a +\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{4 i \ln \left(1-\frac{b \,{\mathrm e}^{2 i x}}{-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}}\right) \sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\, a x}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}-\frac{8 i a^{2} x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}+\frac{2 i b^{2} x^{2}}{\left(8 a^{2}-2 b^{2}\right) \left(-2 i a -\sqrt{-\left(2 a -b \right) \left(2 a +b \right)}\right)}"," ",0,"4*I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*ln(1-b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*(-(2*a-b)*(2*a+b))^(1/2)*a*x-4/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*(-(2*a-b)*(2*a+b))^(1/2)*a*x^2-2/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*ln(1-b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*b^2*x+4/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*(-(2*a-b)*(2*a+b))^(1/2)*a*x^2-2/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(2,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*(-(2*a-b)*(2*a+b))^(1/2)*a-8*I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*a^2*x^2+2*I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*b^2*x^2-4*I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*polylog(2,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*a^2+I/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*polylog(2,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*b^2-4*I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*ln(1-b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*(-(2*a-b)*(2*a+b))^(1/2)*a*x+2/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*polylog(2,b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*(-(2*a-b)*(2*a+b))^(1/2)*a+8/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*ln(1-b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*a^2*x+8/(8*a^2-2*b^2)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2))*ln(1-b*exp(2*I*x)/(-2*I*a+(-(2*a-b)*(2*a+b))^(1/2)))*a^2*x-2/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*ln(1-b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*b^2*x-8*I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*a^2*x^2-4*I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(2,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*a^2+I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*polylog(2,b*exp(2*I*x)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2)))*b^2+2*I/(8*a^2-2*b^2)/(-2*I*a-(-(2*a-b)*(2*a+b))^(1/2))*b^2*x^2","B"
582,0,0,17,0.246000," ","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)}\, dx"," ",0,"int(1/x/(a+b*cos(x)*sin(x)),x)","F"
583,0,0,78,2.193000," ","int((b*x)^(2-n)*sin(a*x)^n/(a*c*x*cos(a*x)-c*sin(a*x))^2,x)","\int \frac{\left(b x \right)^{2-n} \left(\sin^{n}\left(a x \right)\right)}{\left(a c x \cos \left(a x \right)-c \sin \left(a x \right)\right)^{2}}\, dx"," ",0,"int((b*x)^(2-n)*sin(a*x)^n/(a*c*x*cos(a*x)-c*sin(a*x))^2,x)","F"
584,0,0,78,2.187000," ","int((b*x)^(2-n)*cos(a*x)^n/(c*cos(a*x)+a*c*x*sin(a*x))^2,x)","\int \frac{\left(b x \right)^{2-n} \left(\cos^{n}\left(a x \right)\right)}{\left(c \cos \left(a x \right)+a c x \sin \left(a x \right)\right)^{2}}\, dx"," ",0,"int((b*x)^(2-n)*cos(a*x)^n/(c*cos(a*x)+a*c*x*sin(a*x))^2,x)","F"
585,-1,0,165,180.000000," ","int(sin(a*x)^6/x^4/(a*x*cos(a*x)-sin(a*x))^2,x)","\int \frac{\sin^{6}\left(a x \right)}{x^{4} \left(a x \cos \left(a x \right)-\sin \left(a x \right)\right)^{2}}\, dx"," ",0,"int(sin(a*x)^6/x^4/(a*x*cos(a*x)-sin(a*x))^2,x)","F"
586,-1,0,123,180.000000," ","int(sin(a*x)^5/x^3/(a*x*cos(a*x)-sin(a*x))^2,x)","\int \frac{\sin^{5}\left(a x \right)}{x^{3} \left(a x \cos \left(a x \right)-\sin \left(a x \right)\right)^{2}}\, dx"," ",0,"int(sin(a*x)^5/x^3/(a*x*cos(a*x)-sin(a*x))^2,x)","F"
587,-1,0,80,180.000000," ","int(sin(a*x)^4/x^2/(a*x*cos(a*x)-sin(a*x))^2,x)","\int \frac{\sin^{4}\left(a x \right)}{x^{2} \left(a x \cos \left(a x \right)-\sin \left(a x \right)\right)^{2}}\, dx"," ",0,"int(sin(a*x)^4/x^2/(a*x*cos(a*x)-sin(a*x))^2,x)","F"
588,1,108,56,4.279000," ","int(sin(a*x)^3/x/(a*x*cos(a*x)-sin(a*x))^2,x)","\frac{i \Ei \left(1, -i a x \right)}{2}+\frac{i {\mathrm e}^{i a x}}{2 i a x -2}+\frac{i {\mathrm e}^{-i a x}}{2 i a x +2}-\frac{i \Ei \left(1, i a x \right)}{2}+\frac{2 \,{\mathrm e}^{i a x}}{\left(a x +i\right) \left(a x -i\right) \left(a x \,{\mathrm e}^{2 i a x}+i {\mathrm e}^{2 i a x}+a x -i\right)}"," ",0,"1/2*I*Ei(1,-I*a*x)+1/2*I*exp(I*a*x)/(-1+I*a*x)+1/2*I*exp(-I*a*x)/(I*a*x+1)-1/2*I*Ei(1,I*a*x)+2*exp(I*a*x)/(a*x+I)/(a*x-I)/(a*x*exp(2*I*a*x)+I*exp(2*I*a*x)+a*x-I)","C"
589,1,77,35,1.471000," ","int(sin(a*x)^2/(a*x*cos(a*x)-sin(a*x))^2,x)","\frac{\frac{\tan^{4}\left(\frac{a x}{2}\right)}{a}+\frac{\tan^{6}\left(\frac{a x}{2}\right)}{a}-\frac{1}{a}-\frac{\tan^{2}\left(\frac{a x}{2}\right)}{a}}{\left(1+\tan^{2}\left(\frac{a x}{2}\right)\right)^{2} \left(a x \left(\tan^{2}\left(\frac{a x}{2}\right)\right)-a x +2 \tan \left(\frac{a x}{2}\right)\right)}"," ",0,"(1/a*tan(1/2*a*x)^4+1/a*tan(1/2*a*x)^6-1/a-1/a*tan(1/2*a*x)^2)/(1+tan(1/2*a*x)^2)^2/(a*x*tan(1/2*a*x)^2-a*x+2*tan(1/2*a*x))","B"
590,1,21,20,0.195000," ","int(x*sin(a*x)/(a*x*cos(a*x)-sin(a*x))^2,x)","\frac{1}{a^{2} \left(a x \cos \left(a x \right)-\sin \left(a x \right)\right)}"," ",0,"1/a^2/(a*x*cos(a*x)-sin(a*x))","A"
591,1,54,35,1.226000," ","int(x^2/(a*x*cos(a*x)-sin(a*x))^2,x)","\frac{\frac{\tan^{2}\left(\frac{a x}{2}\right)}{a^{3}}-\frac{1}{a^{3}}-\frac{2 x \tan \left(\frac{a x}{2}\right)}{a^{2}}}{a x \left(\tan^{2}\left(\frac{a x}{2}\right)\right)-a x +2 \tan \left(\frac{a x}{2}\right)}"," ",0,"(1/a^3*tan(1/2*a*x)^2-1/a^3-2*x/a^2*tan(1/2*a*x))/(a*x*tan(1/2*a*x)^2-a*x+2*tan(1/2*a*x))","A"
592,0,0,96,2.473000," ","int(x^3*csc(a*x)/(a*x*cos(a*x)-sin(a*x))^2,x)","\int \frac{x^{3} \csc \left(a x \right)}{\left(a x \cos \left(a x \right)-\sin \left(a x \right)\right)^{2}}\, dx"," ",0,"int(x^3*csc(a*x)/(a*x*cos(a*x)-sin(a*x))^2,x)","F"
593,1,172,121,1.105000," ","int(x^4*csc(a*x)^2/(a*x*cos(a*x)-sin(a*x))^2,x)","-\frac{2 i \left(2 i a^{2} x^{2} {\mathrm e}^{2 i a x}+2 x^{3} a^{3}-2 i a^{2} x^{2}-a x \,{\mathrm e}^{2 i a x}+i {\mathrm e}^{2 i a x}+a x -i\right)}{\left({\mathrm e}^{2 i a x}-1\right) \left(a x \,{\mathrm e}^{2 i a x}+i {\mathrm e}^{2 i a x}+a x -i\right) a^{5}}-\frac{4 i x^{2}}{a^{3}}+\frac{4 x \ln \left({\mathrm e}^{i a x}+1\right)}{a^{4}}-\frac{4 i \polylog \left(2, -{\mathrm e}^{i a x}\right)}{a^{5}}+\frac{4 x \ln \left(1-{\mathrm e}^{i a x}\right)}{a^{4}}-\frac{4 i \polylog \left(2, {\mathrm e}^{i a x}\right)}{a^{5}}"," ",0,"-2*I*(2*I*a^2*x^2*exp(2*I*a*x)+2*x^3*a^3-2*I*a^2*x^2-a*x*exp(2*I*a*x)+I*exp(2*I*a*x)+a*x-I)/(exp(2*I*a*x)-1)/(a*x*exp(2*I*a*x)+I*exp(2*I*a*x)+a*x-I)/a^5-4*I/a^3*x^2+4/a^4*x*ln(exp(I*a*x)+1)-4*I/a^5*polylog(2,-exp(I*a*x))+4/a^4*x*ln(1-exp(I*a*x))-4*I/a^5*polylog(2,exp(I*a*x))","A"
594,-1,0,166,180.000000," ","int(cos(a*x)^6/x^4/(cos(a*x)+a*x*sin(a*x))^2,x)","\int \frac{\cos^{6}\left(a x \right)}{x^{4} \left(\cos \left(a x \right)+a x \sin \left(a x \right)\right)^{2}}\, dx"," ",0,"int(cos(a*x)^6/x^4/(cos(a*x)+a*x*sin(a*x))^2,x)","F"
595,-1,0,124,180.000000," ","int(cos(a*x)^5/x^3/(cos(a*x)+a*x*sin(a*x))^2,x)","\int \frac{\cos^{5}\left(a x \right)}{x^{3} \left(\cos \left(a x \right)+a x \sin \left(a x \right)\right)^{2}}\, dx"," ",0,"int(cos(a*x)^5/x^3/(cos(a*x)+a*x*sin(a*x))^2,x)","F"
596,-1,0,80,180.000000," ","int(cos(a*x)^4/x^2/(cos(a*x)+a*x*sin(a*x))^2,x)","\int \frac{\cos^{4}\left(a x \right)}{x^{2} \left(\cos \left(a x \right)+a x \sin \left(a x \right)\right)^{2}}\, dx"," ",0,"int(cos(a*x)^4/x^2/(cos(a*x)+a*x*sin(a*x))^2,x)","F"
597,1,106,56,5.142000," ","int(cos(a*x)^3/x/(cos(a*x)+a*x*sin(a*x))^2,x)","-\frac{\Ei \left(1, -i a x \right)}{2}-\frac{{\mathrm e}^{i a x}}{2 \left(i a x -1\right)}+\frac{{\mathrm e}^{-i a x}}{2 i a x +2}-\frac{\Ei \left(1, i a x \right)}{2}-\frac{2 i {\mathrm e}^{i a x}}{\left(a x +i\right) \left(a x -i\right) \left(a x \,{\mathrm e}^{2 i a x}-a x +i {\mathrm e}^{2 i a x}+i\right)}"," ",0,"-1/2*Ei(1,-I*a*x)-1/2*exp(I*a*x)/(-1+I*a*x)+1/2*exp(-I*a*x)/(I*a*x+1)-1/2*Ei(1,I*a*x)-2*I*exp(I*a*x)/(a*x+I)/(a*x-I)/(a*x*exp(2*I*a*x)-a*x+I*exp(2*I*a*x)+I)","C"
598,1,70,34,1.787000," ","int(cos(a*x)^2/(cos(a*x)+a*x*sin(a*x))^2,x)","\frac{\frac{2 \tan \left(\frac{a x}{2}\right)}{a}+\frac{4 \left(\tan^{3}\left(\frac{a x}{2}\right)\right)}{a}+\frac{2 \left(\tan^{5}\left(\frac{a x}{2}\right)\right)}{a}}{\left(1+\tan^{2}\left(\frac{a x}{2}\right)\right)^{2} \left(2 \tan \left(\frac{a x}{2}\right) x a -\left(\tan^{2}\left(\frac{a x}{2}\right)\right)+1\right)}"," ",0,"(2/a*tan(1/2*a*x)+4/a*tan(1/2*a*x)^3+2/a*tan(1/2*a*x)^5)/(1+tan(1/2*a*x)^2)^2/(2*tan(1/2*a*x)*x*a-tan(1/2*a*x)^2+1)","B"
599,1,20,19,0.238000," ","int(x*cos(a*x)/(cos(a*x)+a*x*sin(a*x))^2,x)","-\frac{1}{a^{2} \left(\cos \left(a x \right)+a x \sin \left(a x \right)\right)}"," ",0,"-1/a^2/(cos(a*x)+a*x*sin(a*x))","A"
600,1,53,33,1.187000," ","int(x^2/(cos(a*x)+a*x*sin(a*x))^2,x)","\frac{\frac{x \left(\tan^{2}\left(\frac{a x}{2}\right)\right)}{a^{2}}-\frac{x}{a^{2}}+\frac{2 \tan \left(\frac{a x}{2}\right)}{a^{3}}}{2 \tan \left(\frac{a x}{2}\right) x a -\left(\tan^{2}\left(\frac{a x}{2}\right)\right)+1}"," ",0,"(x/a^2*tan(1/2*a*x)^2-x/a^2+2/a^3*tan(1/2*a*x))/(2*tan(1/2*a*x)*x*a-tan(1/2*a*x)^2+1)","A"
601,0,0,99,2.540000," ","int(x^3*sec(a*x)/(cos(a*x)+a*x*sin(a*x))^2,x)","\int \frac{x^{3} \sec \left(a x \right)}{\left(\cos \left(a x \right)+a x \sin \left(a x \right)\right)^{2}}\, dx"," ",0,"int(x^3*sec(a*x)/(cos(a*x)+a*x*sin(a*x))^2,x)","F"
602,1,141,118,1.242000," ","int(x^4*sec(a*x)^2/(cos(a*x)+a*x*sin(a*x))^2,x)","-\frac{2 i \left(-2 i a^{2} x^{2} {\mathrm e}^{2 i a x}+2 x^{3} a^{3}-2 i a^{2} x^{2}+a x \,{\mathrm e}^{2 i a x}-i {\mathrm e}^{2 i a x}+a x -i\right)}{\left(1+{\mathrm e}^{2 i a x}\right) \left(a x \,{\mathrm e}^{2 i a x}-a x +i {\mathrm e}^{2 i a x}+i\right) a^{5}}-\frac{4 i x^{2}}{a^{3}}+\frac{4 x \ln \left(1+{\mathrm e}^{2 i a x}\right)}{a^{4}}-\frac{2 i \polylog \left(2, -{\mathrm e}^{2 i a x}\right)}{a^{5}}"," ",0,"-2*I*(-2*I*a^2*x^2*exp(2*I*a*x)+2*x^3*a^3-2*I*a^2*x^2+a*x*exp(2*I*a*x)-I*exp(2*I*a*x)+a*x-I)/(1+exp(2*I*a*x))/(a*x*exp(2*I*a*x)-a*x+I*exp(2*I*a*x)+I)/a^5-4*I/a^3*x^2+4*x*ln(1+exp(2*I*a*x))/a^4-2*I*polylog(2,-exp(2*I*a*x))/a^5","A"
603,1,98,141,1.589000," ","int(sec(2*b*x+2*a)^4*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x)","-\frac{\sqrt{2}\, \cos \left(b x +a \right) \sqrt{\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \left(128 \left(\cos^{6}\left(b x +a \right)\right)-224 \left(\cos^{4}\left(b x +a \right)\right)+140 \left(\cos^{2}\left(b x +a \right)\right)-35\right) \sqrt{4}}{70 b \sin \left(b x +a \right) \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right)^{3}}"," ",0,"-1/70*2^(1/2)/b*cos(b*x+a)*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(1/2)*(128*cos(b*x+a)^6-224*cos(b*x+a)^4+140*cos(b*x+a)^2-35)/sin(b*x+a)/(2*cos(b*x+a)^2-1)^3*4^(1/2)","A"
604,1,88,98,1.167000," ","int(sec(2*b*x+2*a)^3*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x)","\frac{\sqrt{2}\, \sqrt{\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \cos \left(b x +a \right) \left(32 \left(\cos^{4}\left(b x +a \right)\right)-40 \left(\cos^{2}\left(b x +a \right)\right)+15\right) \sqrt{4}}{30 b \sin \left(b x +a \right) \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right)^{2}}"," ",0,"1/30*2^(1/2)/b*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(1/2)*cos(b*x+a)*(32*cos(b*x+a)^4-40*cos(b*x+a)^2+15)/sin(b*x+a)/(2*cos(b*x+a)^2-1)^2*4^(1/2)","A"
605,1,78,64,1.095000," ","int(sec(2*b*x+2*a)^2*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \cos \left(b x +a \right) \left(4 \left(\cos^{2}\left(b x +a \right)\right)-3\right) \sqrt{4}}{6 b \sin \left(b x +a \right) \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right)}"," ",0,"-1/6*2^(1/2)/b*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(1/2)*cos(b*x+a)*(4*cos(b*x+a)^2-3)/sin(b*x+a)/(2*cos(b*x+a)^2-1)*4^(1/2)","A"
606,1,52,31,0.971000," ","int(sec(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x)","\frac{\sqrt{2}\, \sqrt{\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \cos \left(b x +a \right) \sqrt{4}}{2 b \sin \left(b x +a \right)}"," ",0,"1/2*2^(1/2)/b*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(1/2)*cos(b*x+a)/sin(b*x+a)*4^(1/2)","A"
607,1,136,39,0.944000," ","int((c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x)","-\frac{\sqrt{\frac{c \left(1-\left(\cos^{2}\left(b x +a \right)\right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \sin \left(b x +a \right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \sqrt{4}}{2 b \left(-1+\cos \left(b x +a \right)\right)}"," ",0,"-1/2/b*(c*(1-cos(b*x+a)^2)/(2*cos(b*x+a)^2-1))^(1/2)*sin(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))/(-1+cos(b*x+a))*4^(1/2)","B"
608,1,391,72,1.139000," ","int(cos(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x)","\frac{\sqrt{\frac{c \left(1-\left(\cos^{2}\left(b x +a \right)\right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \sin \left(b x +a \right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \sqrt{4}}{2 b \left(-1+\cos \left(b x +a \right)\right)}-\frac{\sqrt{2}\, \sin \left(b x +a \right) \sqrt{\frac{c \left(1-\left(\cos^{2}\left(b x +a \right)\right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \left(\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \cos \left(b x +a \right)+\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)-4 \left(\cos^{3}\left(b x +a \right)\right)+2 \cos \left(b x +a \right)\right) \sqrt{4}}{8 b \left(-1+\cos^{2}\left(b x +a \right)\right)}"," ",0,"1/2/b*(c*(1-cos(b*x+a)^2)/(2*cos(b*x+a)^2-1))^(1/2)*sin(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))/(-1+cos(b*x+a))*4^(1/2)-1/8*2^(1/2)/b*sin(b*x+a)*(c*(1-cos(b*x+a)^2)/(2*cos(b*x+a)^2-1))^(1/2)*(2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))*cos(b*x+a)+2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-4*cos(b*x+a)^3+2*cos(b*x+a))/(-1+cos(b*x+a)^2)*4^(1/2)","B"
609,1,657,113,1.218000," ","int(cos(2*b*x+2*a)^2*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x)","-\frac{\sqrt{\frac{c \left(1-\left(\cos^{2}\left(b x +a \right)\right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \sin \left(b x +a \right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \sqrt{4}}{2 b \left(-1+\cos \left(b x +a \right)\right)}+\frac{\sqrt{2}\, \sin \left(b x +a \right) \sqrt{\frac{c \left(1-\left(\cos^{2}\left(b x +a \right)\right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \left(\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \cos \left(b x +a \right)+\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)-4 \left(\cos^{3}\left(b x +a \right)\right)+2 \cos \left(b x +a \right)\right) \sqrt{4}}{4 b \left(-1+\cos^{2}\left(b x +a \right)\right)}-\frac{\sqrt{2}\, \sin \left(b x +a \right) \sqrt{\frac{c \left(1-\left(\cos^{2}\left(b x +a \right)\right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \left(-16 \left(\cos^{5}\left(b x +a \right)\right)+3 \sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \cos \left(b x +a \right)+3 \sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)-4 \left(\cos^{3}\left(b x +a \right)\right)+6 \cos \left(b x +a \right)\right) \sqrt{4}}{32 b \left(-1+\cos^{2}\left(b x +a \right)\right)}"," ",0,"-1/2/b*(c*(1-cos(b*x+a)^2)/(2*cos(b*x+a)^2-1))^(1/2)*sin(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))/(-1+cos(b*x+a))*4^(1/2)+1/4*2^(1/2)/b*sin(b*x+a)*(c*(1-cos(b*x+a)^2)/(2*cos(b*x+a)^2-1))^(1/2)*(2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))*cos(b*x+a)+2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-4*cos(b*x+a)^3+2*cos(b*x+a))/(-1+cos(b*x+a)^2)*4^(1/2)-1/32*2^(1/2)/b*sin(b*x+a)*(c*(1-cos(b*x+a)^2)/(2*cos(b*x+a)^2-1))^(1/2)*(-16*cos(b*x+a)^5+3*2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))*cos(b*x+a)+3*2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-4*cos(b*x+a)^3+6*cos(b*x+a))/(-1+cos(b*x+a)^2)*4^(1/2)","B"
610,1,933,156,1.171000," ","int(cos(2*b*x+2*a)^3*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x)","\frac{\sqrt{\frac{c \left(1-\left(\cos^{2}\left(b x +a \right)\right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \sin \left(b x +a \right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \sqrt{4}}{2 b \left(-1+\cos \left(b x +a \right)\right)}-\frac{3 \sqrt{2}\, \sin \left(b x +a \right) \sqrt{\frac{c \left(1-\left(\cos^{2}\left(b x +a \right)\right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \left(\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \cos \left(b x +a \right)+\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)-4 \left(\cos^{3}\left(b x +a \right)\right)+2 \cos \left(b x +a \right)\right) \sqrt{4}}{8 b \left(-1+\cos^{2}\left(b x +a \right)\right)}+\frac{3 \sqrt{2}\, \sin \left(b x +a \right) \sqrt{\frac{c \left(1-\left(\cos^{2}\left(b x +a \right)\right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \left(-16 \left(\cos^{5}\left(b x +a \right)\right)+3 \sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \cos \left(b x +a \right)+3 \sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)-4 \left(\cos^{3}\left(b x +a \right)\right)+6 \cos \left(b x +a \right)\right) \sqrt{4}}{32 b \left(-1+\cos^{2}\left(b x +a \right)\right)}-\frac{\sqrt{2}\, \sin \left(b x +a \right) \sqrt{\frac{c \left(1-\left(\cos^{2}\left(b x +a \right)\right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \left(-128 \left(\cos^{7}\left(b x +a \right)\right)-16 \left(\cos^{5}\left(b x +a \right)\right)+15 \sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \cos \left(b x +a \right)+15 \sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)-20 \left(\cos^{3}\left(b x +a \right)\right)+30 \cos \left(b x +a \right)\right) \sqrt{4}}{192 b \left(-1+\cos^{2}\left(b x +a \right)\right)}"," ",0,"1/2/b*(c*(1-cos(b*x+a)^2)/(2*cos(b*x+a)^2-1))^(1/2)*sin(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))/(-1+cos(b*x+a))*4^(1/2)-3/8*2^(1/2)/b*sin(b*x+a)*(c*(1-cos(b*x+a)^2)/(2*cos(b*x+a)^2-1))^(1/2)*(2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))*cos(b*x+a)+2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-4*cos(b*x+a)^3+2*cos(b*x+a))/(-1+cos(b*x+a)^2)*4^(1/2)+3/32*2^(1/2)/b*sin(b*x+a)*(c*(1-cos(b*x+a)^2)/(2*cos(b*x+a)^2-1))^(1/2)*(-16*cos(b*x+a)^5+3*2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))*cos(b*x+a)+3*2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-4*cos(b*x+a)^3+6*cos(b*x+a))/(-1+cos(b*x+a)^2)*4^(1/2)-1/192*2^(1/2)/b*sin(b*x+a)*(c*(1-cos(b*x+a)^2)/(2*cos(b*x+a)^2-1))^(1/2)*(-128*cos(b*x+a)^7-16*cos(b*x+a)^5+15*2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))*cos(b*x+a)+15*2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-20*cos(b*x+a)^3+30*cos(b*x+a))/(-1+cos(b*x+a)^2)*4^(1/2)","B"
611,1,105,188,1.119000," ","int(sec(2*b*x+2*a)^4*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x)","\frac{2 \sqrt{2}\, \left(2176 \left(\cos^{8}\left(b x +a \right)\right)-4896 \left(\cos^{6}\left(b x +a \right)\right)+4284 \left(\cos^{4}\left(b x +a \right)\right)-1785 \left(\cos^{2}\left(b x +a \right)\right)+315\right) \cos \left(b x +a \right) \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}}}{315 b \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right)^{3} \sin \left(b x +a \right)^{3}}"," ",0,"2/315*2^(1/2)/b*(2176*cos(b*x+a)^8-4896*cos(b*x+a)^6+4284*cos(b*x+a)^4-1785*cos(b*x+a)^2+315)*cos(b*x+a)*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/(2*cos(b*x+a)^2-1)^3/sin(b*x+a)^3","A"
612,1,95,132,0.944000," ","int(sec(2*b*x+2*a)^3*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x)","-\frac{2 \sqrt{2}\, \left(416 \left(\cos^{6}\left(b x +a \right)\right)-728 \left(\cos^{4}\left(b x +a \right)\right)+455 \left(\cos^{2}\left(b x +a \right)\right)-105\right) \cos \left(b x +a \right) \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}}}{105 b \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right)^{2} \sin \left(b x +a \right)^{3}}"," ",0,"-2/105*2^(1/2)/b*(416*cos(b*x+a)^6-728*cos(b*x+a)^4+455*cos(b*x+a)^2-105)*cos(b*x+a)*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/(2*cos(b*x+a)^2-1)^2/sin(b*x+a)^3","A"
613,1,85,98,0.863000," ","int(sec(2*b*x+2*a)^2*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x)","\frac{2 \sqrt{2}\, \left(12 \left(\cos^{4}\left(b x +a \right)\right)-15 \left(\cos^{2}\left(b x +a \right)\right)+5\right) \cos \left(b x +a \right) \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}}}{5 b \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right) \sin \left(b x +a \right)^{3}}"," ",0,"2/5*2^(1/2)/b*(12*cos(b*x+a)^4-15*cos(b*x+a)^2+5)*cos(b*x+a)*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/(2*cos(b*x+a)^2-1)/sin(b*x+a)^3","A"
614,1,61,67,0.832000," ","int(sec(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x)","-\frac{2 \sqrt{2}\, \left(5 \left(\cos^{2}\left(b x +a \right)\right)-3\right) \cos \left(b x +a \right) \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}}}{3 b \sin \left(b x +a \right)^{3}}"," ",0,"-2/3*2^(1/2)/b*(5*cos(b*x+a)^2-3)*cos(b*x+a)*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3","A"
615,1,253,72,0.950000," ","int((c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x)","\frac{\sqrt{2}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right) \left(\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \cos \left(b x +a \right)+\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)-2 \cos \left(b x +a \right)\right) \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}}}{b \sin \left(b x +a \right)^{3} \left(2+\sqrt{2}\right) \left(\sqrt{2}-2\right)}"," ",0,"2^(1/2)/b*(2*cos(b*x+a)^2-1)*(2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))*cos(b*x+a)+2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-2*cos(b*x+a))*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3/(2+2^(1/2))/(2^(1/2)-2)","B"
616,1,518,74,1.087000," ","int(cos(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x)","-\frac{\sqrt{2}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right) \left(\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \cos \left(b x +a \right)+\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)-2 \cos \left(b x +a \right)\right) \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}}}{b \sin \left(b x +a \right)^{3} \left(2+\sqrt{2}\right) \left(\sqrt{2}-2\right)}-\frac{2 \sqrt{2}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right) \left(\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \cos \left(b x +a \right)+\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)+4 \left(\cos^{3}\left(b x +a \right)\right)+2 \cos \left(b x +a \right)\right) \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}}}{b \sin \left(b x +a \right)^{3} \left(2+\sqrt{2}\right)^{3} \left(\sqrt{2}-2\right)^{3}}"," ",0,"-2^(1/2)/b*(2*cos(b*x+a)^2-1)*(2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))*cos(b*x+a)+2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-2*cos(b*x+a))*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3/(2+2^(1/2))/(2^(1/2)-2)-2*2^(1/2)/b*(2*cos(b*x+a)^2-1)*(2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))*cos(b*x+a)+2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+4*cos(b*x+a)^3+2*cos(b*x+a))*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3/(2+2^(1/2))^3/(2^(1/2)-2)^3","B"
617,1,792,117,1.022000," ","int(cos(2*b*x+2*a)^2*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x)","\frac{\sqrt{2}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right) \left(\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \cos \left(b x +a \right)+\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)-2 \cos \left(b x +a \right)\right) \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}}}{b \sin \left(b x +a \right)^{3} \left(2+\sqrt{2}\right) \left(\sqrt{2}-2\right)}+\frac{4 \sqrt{2}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right) \left(\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \cos \left(b x +a \right)+\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)+4 \left(\cos^{3}\left(b x +a \right)\right)+2 \cos \left(b x +a \right)\right) \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}}}{b \sin \left(b x +a \right)^{3} \left(2+\sqrt{2}\right)^{3} \left(\sqrt{2}-2\right)^{3}}-\frac{2 \sqrt{2}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right) \left(16 \left(\cos^{5}\left(b x +a \right)\right)+9 \sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \cos \left(b x +a \right)-12 \left(\cos^{3}\left(b x +a \right)\right)+9 \sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)+18 \cos \left(b x +a \right)\right) \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}}}{b \sin \left(b x +a \right)^{3} \left(2+\sqrt{2}\right)^{5} \left(\sqrt{2}-2\right)^{5}}"," ",0,"2^(1/2)/b*(2*cos(b*x+a)^2-1)*(2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))*cos(b*x+a)+2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-2*cos(b*x+a))*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3/(2+2^(1/2))/(2^(1/2)-2)+4*2^(1/2)/b*(2*cos(b*x+a)^2-1)*(2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))*cos(b*x+a)+2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+4*cos(b*x+a)^3+2*cos(b*x+a))*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3/(2+2^(1/2))^3/(2^(1/2)-2)^3-2*2^(1/2)/b*(2*cos(b*x+a)^2-1)*(16*cos(b*x+a)^5+9*2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))*cos(b*x+a)-12*cos(b*x+a)^3+9*2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+18*cos(b*x+a))*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3/(2+2^(1/2))^5/(2^(1/2)-2)^5","B"
618,1,1078,162,1.112000," ","int(cos(2*b*x+2*a)^3*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x)","-\frac{\sqrt{2}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right) \left(\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \cos \left(b x +a \right)+\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)-2 \cos \left(b x +a \right)\right) \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}}}{b \sin \left(b x +a \right)^{3} \left(2+\sqrt{2}\right) \left(\sqrt{2}-2\right)}-\frac{6 \sqrt{2}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right) \left(\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \cos \left(b x +a \right)+\sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)+4 \left(\cos^{3}\left(b x +a \right)\right)+2 \cos \left(b x +a \right)\right) \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}}}{b \sin \left(b x +a \right)^{3} \left(2+\sqrt{2}\right)^{3} \left(\sqrt{2}-2\right)^{3}}+\frac{6 \sqrt{2}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right) \left(16 \left(\cos^{5}\left(b x +a \right)\right)+9 \sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \cos \left(b x +a \right)-12 \left(\cos^{3}\left(b x +a \right)\right)+9 \sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)+18 \cos \left(b x +a \right)\right) \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}}}{b \sin \left(b x +a \right)^{3} \left(2+\sqrt{2}\right)^{5} \left(\sqrt{2}-2\right)^{5}}-\frac{4 \sqrt{2}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right) \left(128 \left(\cos^{7}\left(b x +a \right)\right)-80 \left(\cos^{5}\left(b x +a \right)\right)+75 \sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right) \cos \left(b x +a \right)+75 \sqrt{2}\, \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)-100 \left(\cos^{3}\left(b x +a \right)\right)+150 \cos \left(b x +a \right)\right) \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}}}{3 b \sin \left(b x +a \right)^{3} \left(2+\sqrt{2}\right)^{7} \left(\sqrt{2}-2\right)^{7}}"," ",0,"-2^(1/2)/b*(2*cos(b*x+a)^2-1)*(2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))*cos(b*x+a)+2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-2*cos(b*x+a))*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3/(2+2^(1/2))/(2^(1/2)-2)-6*2^(1/2)/b*(2*cos(b*x+a)^2-1)*(2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))*cos(b*x+a)+2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+4*cos(b*x+a)^3+2*cos(b*x+a))*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3/(2+2^(1/2))^3/(2^(1/2)-2)^3+6*2^(1/2)/b*(2*cos(b*x+a)^2-1)*(16*cos(b*x+a)^5+9*2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))*cos(b*x+a)-12*cos(b*x+a)^3+9*2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+18*cos(b*x+a))*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3/(2+2^(1/2))^5/(2^(1/2)-2)^5-4/3*2^(1/2)/b*(2*cos(b*x+a)^2-1)*(128*cos(b*x+a)^7-80*cos(b*x+a)^5+75*2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))*cos(b*x+a)+75*2^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-100*cos(b*x+a)^3+150*cos(b*x+a))*(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3/(2+2^(1/2))^7/(2^(1/2)-2)^7","B"
619,1,984,154,1.357000," ","int(sec(2*b*x+2*a)^4/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x)","\frac{\sqrt{2}\, \left(-1+\cos \left(b x +a \right)\right) \left(208 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \left(\cos^{6}\left(b x +a \right)\right)+120 \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right) \left(\cos^{6}\left(b x +a \right)\right)+120 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right) \left(\cos^{6}\left(b x +a \right)\right)+208 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \left(\cos^{5}\left(b x +a \right)\right)-200 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \left(\cos^{4}\left(b x +a \right)\right)-180 \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right) \left(\cos^{4}\left(b x +a \right)\right)-180 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right) \left(\cos^{4}\left(b x +a \right)\right)-200 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \left(\cos^{3}\left(b x +a \right)\right)+60 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+90 \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right) \left(\cos^{2}\left(b x +a \right)\right)+90 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right) \left(\cos^{2}\left(b x +a \right)\right)+60 \cos \left(b x +a \right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-15 \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)-15 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)\right) \sqrt{4}}{120 b \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right)^{3} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sqrt{\frac{c \left(1-\left(\cos^{2}\left(b x +a \right)\right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \sin \left(b x +a \right) \left(-3+2 \sqrt{2}\right)^{3} \left(3+2 \sqrt{2}\right)^{3}}"," ",0,"1/120*2^(1/2)/b*(-1+cos(b*x+a))*(208*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*cos(b*x+a)^6+120*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)*cos(b*x+a)^6+120*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)*cos(b*x+a)^6+208*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*cos(b*x+a)^5-200*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*cos(b*x+a)^4-180*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)*cos(b*x+a)^4-180*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)*cos(b*x+a)^4-200*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*cos(b*x+a)^3+60*cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+90*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)*cos(b*x+a)^2+90*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)*cos(b*x+a)^2+60*cos(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-15*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)-15*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2))/(2*cos(b*x+a)^2-1)^3/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/(c*(1-cos(b*x+a)^2)/(2*cos(b*x+a)^2-1))^(1/2)/sin(b*x+a)*4^(1/2)/(-3+2*2^(1/2))^3/(3+2*2^(1/2))^3","B"
620,1,677,112,1.208000," ","int(sec(2*b*x+2*a)^3/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x)","-\frac{\sqrt{2}\, \left(-1+\cos \left(b x +a \right)\right) \left(12 \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right) \left(\cos^{4}\left(b x +a \right)\right)+12 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right) \left(\cos^{4}\left(b x +a \right)\right)+8 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \left(\cos^{4}\left(b x +a \right)\right)+8 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \left(\cos^{3}\left(b x +a \right)\right)-12 \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right) \left(\cos^{2}\left(b x +a \right)\right)-12 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right) \left(\cos^{2}\left(b x +a \right)\right)+3 \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)+3 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)\right) \sqrt{4}}{24 b \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sqrt{\frac{c \left(1-\left(\cos^{2}\left(b x +a \right)\right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \sin \left(b x +a \right) \left(-3+2 \sqrt{2}\right)^{2} \left(3+2 \sqrt{2}\right)^{2}}"," ",0,"-1/24*2^(1/2)/b*(-1+cos(b*x+a))*(12*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)*cos(b*x+a)^4+12*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)*cos(b*x+a)^4+8*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*cos(b*x+a)^4+8*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*cos(b*x+a)^3-12*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)*cos(b*x+a)^2-12*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)*cos(b*x+a)^2+3*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)+3*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2))/(2*cos(b*x+a)^2-1)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/(c*(1-cos(b*x+a)^2)/(2*cos(b*x+a)^2-1))^(1/2)/sin(b*x+a)*4^(1/2)/(-3+2*2^(1/2))^2/(3+2*2^(1/2))^2","B"
621,1,478,77,1.194000," ","int(sec(2*b*x+2*a)^2/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x)","\frac{\sqrt{2}\, \left(\cos \left(b x +a \right) \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+\cos \left(b x +a \right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)+\ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+\arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+4 \cos \left(b x +a \right)\right) \sin \left(b x +a \right)}{4 b \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right) \sqrt{\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}}"," ",0,"1/4*2^(1/2)/b*(cos(b*x+a)*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+cos(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)+ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+4*cos(b*x+a))*sin(b*x+a)/(2*cos(b*x+a)^2-1)/(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(1/2)","B"
622,1,236,46,1.067000," ","int(sec(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x)","\frac{\sqrt{2}\, \left(\cos \left(b x +a \right)+1\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sqrt{\frac{c \left(1-\left(\cos^{2}\left(b x +a \right)\right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \left(\ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)+\arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)\right) \sqrt{4}}{8 b \sin \left(b x +a \right) c}"," ",0,"1/8*2^(1/2)/b*(cos(b*x+a)+1)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*(c*(1-cos(b*x+a)^2)/(2*cos(b*x+a)^2-1))^(1/2)*(ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)+arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2))/sin(b*x+a)/c*4^(1/2)","B"
623,1,301,85,1.007000," ","int(1/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x)","-\frac{\sqrt{2}\, \left(\cos \left(b x +a \right)+1\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sqrt{\frac{c \left(1-\left(\cos^{2}\left(b x +a \right)\right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \left(2 \sqrt{2}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)-\ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)-\arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)\right) \sqrt{4}}{8 b \sin \left(b x +a \right) c}"," ",0,"-1/8*2^(1/2)/b*(cos(b*x+a)+1)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*(c*(1-cos(b*x+a)^2)/(2*cos(b*x+a)^2-1))^(1/2)*(2*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)-arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2))/sin(b*x+a)/c*4^(1/2)","B"
624,1,1030,117,1.171000," ","int(cos(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x)","\frac{\sqrt{2}\, \left(-1+\cos \left(b x +a \right)\right)^{2} \left(\left(\cos^{3}\left(b x +a \right)\right) \sqrt{4}\, \left(\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}\right)^{\frac{3}{2}}+4 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{4}\, \left(\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}\right)^{\frac{3}{2}}+5 \cos \left(b x +a \right) \sqrt{4}\, \left(\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}\right)^{\frac{3}{2}}+2 \sqrt{4}\, \left(\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}\right)^{\frac{3}{2}}-6 \cos \left(b x +a \right) \sqrt{2}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)+6 \cos \left(b x +a \right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+4 \cos \left(b x +a \right) \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)+4 \cos \left(b x +a \right) \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)-6 \sqrt{2}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)+4 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+4 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)+4 \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)\right) \sqrt{4}}{16 b \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sqrt{\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \sin \left(b x +a \right)^{3}}+\frac{\sqrt{2}\, \left(\cos \left(b x +a \right)+1\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sqrt{\frac{c \left(1-\left(\cos^{2}\left(b x +a \right)\right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}}\, \left(2 \sqrt{2}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)-\ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)-\arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)\right) \sqrt{4}}{8 b \sin \left(b x +a \right) c}"," ",0,"1/16*2^(1/2)/b*(-1+cos(b*x+a))^2*(cos(b*x+a)^3*4^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)+4*cos(b*x+a)^2*4^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)+5*cos(b*x+a)*4^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)+2*4^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)-6*cos(b*x+a)*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+6*cos(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+4*cos(b*x+a)*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)+4*cos(b*x+a)*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)-6*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+4*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+4*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)+4*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2))/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(1/2)/sin(b*x+a)^3*4^(1/2)+1/8*2^(1/2)/b*(cos(b*x+a)+1)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*(c*(1-cos(b*x+a)^2)/(2*cos(b*x+a)^2-1))^(1/2)*(2*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)-arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2))/sin(b*x+a)/c*4^(1/2)","B"
625,1,1835,157,1.095000," ","int(cos(2*b*x+2*a)^2/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x)","\text{Expression too large to display}"," ",0,"-1/8*2^(1/2)/b*(cos(b*x+a)+1)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*(c*(1-cos(b*x+a)^2)/(2*cos(b*x+a)^2-1))^(1/2)*(2*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)-arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2))/sin(b*x+a)/c*4^(1/2)-1/8*2^(1/2)/b*(-1+cos(b*x+a))^2*(cos(b*x+a)^3*4^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)+4*cos(b*x+a)^2*4^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)+5*cos(b*x+a)*4^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)+2*4^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)-6*cos(b*x+a)*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+6*cos(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+4*cos(b*x+a)*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)+4*cos(b*x+a)*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)-6*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+4*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+4*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)+4*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2))/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(1/2)/sin(b*x+a)^3*4^(1/2)-1/64*2^(1/2)/b*(-1+cos(b*x+a))^2*(-4*4^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)*cos(b*x+a)^5-16*4^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)*cos(b*x+a)^4-33*cos(b*x+a)^3*4^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)-52*cos(b*x+a)^2*4^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)-49*cos(b*x+a)*4^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)-18*4^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)+46*cos(b*x+a)*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+46*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-54*cos(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-32*cos(b*x+a)*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)-32*cos(b*x+a)*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)-36*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-32*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)-32*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2))/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(1/2)/sin(b*x+a)^3*4^(1/2)","B"
626,1,1211,157,1.129000," ","int(sec(2*b*x+2*a)^4/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x)","\frac{\sqrt{2}\, \left(-1+\cos \left(b x +a \right)\right)^{2} \left(152 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \left(\cos^{5}\left(b x +a \right)\right)+132 \left(\cos^{5}\left(b x +a \right)\right) \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)+132 \left(\cos^{5}\left(b x +a \right)\right) \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)-132 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right) \left(\cos^{4}\left(b x +a \right)\right)-132 \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right) \left(\cos^{4}\left(b x +a \right)\right)-200 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \left(\cos^{3}\left(b x +a \right)\right)-132 \left(\cos^{3}\left(b x +a \right)\right) \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)-132 \left(\cos^{3}\left(b x +a \right)\right) \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)+132 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right) \left(\cos^{2}\left(b x +a \right)\right)+132 \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right) \left(\cos^{2}\left(b x +a \right)\right)+54 \cos \left(b x +a \right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+33 \cos \left(b x +a \right) \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)+33 \cos \left(b x +a \right) \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)-33 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)-33 \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)\right) \sqrt{4}}{96 b \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right)^{2} \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}} \sin \left(b x +a \right)^{3} \left(\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}\right)^{\frac{3}{2}} \left(-3+2 \sqrt{2}\right)^{3} \left(3+2 \sqrt{2}\right)^{3}}"," ",0,"1/96*2^(1/2)/b*(-1+cos(b*x+a))^2*(152*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*cos(b*x+a)^5+132*cos(b*x+a)^5*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)+132*cos(b*x+a)^5*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)-132*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)*cos(b*x+a)^4-132*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)*cos(b*x+a)^4-200*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*cos(b*x+a)^3-132*cos(b*x+a)^3*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)-132*cos(b*x+a)^3*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)+132*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)*cos(b*x+a)^2+132*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)*cos(b*x+a)^2+54*cos(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+33*cos(b*x+a)*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)+33*cos(b*x+a)*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)-33*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)-33*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2))/(2*cos(b*x+a)^2-1)^2/(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)*4^(1/2)/(-3+2*2^(1/2))^3/(3+2*2^(1/2))^3","B"
627,1,930,111,1.148000," ","int(sec(2*b*x+2*a)^3/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x)","-\frac{\sqrt{2}\, \left(7 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \left(\cos^{3}\left(b x +a \right)\right)+7 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right) \left(\cos^{3}\left(b x +a \right)\right)+7 \left(\cos^{2}\left(b x +a \right)\right) \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+7 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)-7 \cos \left(b x +a \right) \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-7 \cos \left(b x +a \right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)+20 \left(\cos^{3}\left(b x +a \right)\right)-7 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-7 \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-18 \cos \left(b x +a \right)\right) \sin \left(b x +a \right)}{16 b \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}} \left(2 \left(\cos^{2}\left(b x +a \right)\right)-1\right)^{2}}"," ",0,"-1/16*2^(1/2)/b*(7*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*cos(b*x+a)^3+7*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)*cos(b*x+a)^3+7*cos(b*x+a)^2*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+7*cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)-7*cos(b*x+a)*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-7*cos(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)+20*cos(b*x+a)^3-7*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-7*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-18*cos(b*x+a))*sin(b*x+a)/(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/(2*cos(b*x+a)^2-1)^2","B"
628,1,433,78,1.041000," ","int(sec(2*b*x+2*a)^2/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x)","-\frac{\sqrt{2}\, \left(-1+\cos \left(b x +a \right)\right)^{2} \left(2 \cos \left(b x +a \right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+3 \cos \left(b x +a \right) \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)+3 \cos \left(b x +a \right) \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)-3 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)-3 \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)\right) \sqrt{4}}{32 b \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}} \sin \left(b x +a \right)^{3} \left(\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}\right)^{\frac{3}{2}}}"," ",0,"-1/32*2^(1/2)/b*(-1+cos(b*x+a))^2*(2*cos(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+3*cos(b*x+a)*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)+3*cos(b*x+a)*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)-3*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)-3*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2))/(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)*4^(1/2)","B"
629,1,599,78,1.036000," ","int(sec(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x)","\frac{\sqrt{2}\, \left(-1+\cos \left(b x +a \right)\right)^{3} \left(2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{4}\, \left(\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}\right)^{\frac{3}{2}}+4 \cos \left(b x +a \right) \sqrt{4}\, \left(\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}\right)^{\frac{3}{2}}+2 \sqrt{4}\, \left(\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}\right)^{\frac{3}{2}}-6 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-\ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right) \left(\cos^{2}\left(b x +a \right)\right)-\arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right) \left(\cos^{2}\left(b x +a \right)\right)+2 \cos \left(b x +a \right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+4 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+\ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)+\arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)\right) \sqrt{4}}{32 b \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}} \sin \left(b x +a \right)^{5} \left(\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}\right)^{\frac{3}{2}}}"," ",0,"1/32*2^(1/2)/b*(-1+cos(b*x+a))^3*(2*cos(b*x+a)^2*4^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)+4*cos(b*x+a)*4^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)+2*4^(1/2)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)-6*cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)*cos(b*x+a)^2-arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)*cos(b*x+a)^2+2*cos(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+4*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)+arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2))/(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^5/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)*4^(1/2)","B"
630,1,561,117,1.015000," ","int(1/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x)","-\frac{\sqrt{2}\, \left(-1+\cos \left(b x +a \right)\right)^{2} \left(8 \cos \left(b x +a \right) \sqrt{2}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)+2 \cos \left(b x +a \right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-5 \cos \left(b x +a \right) \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)-5 \cos \left(b x +a \right) \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)-8 \sqrt{2}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)+5 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)+5 \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)\right) \sqrt{4}}{32 b \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}} \sin \left(b x +a \right)^{3} \left(\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}\right)^{\frac{3}{2}}}"," ",0,"-1/32*2^(1/2)/b*(-1+cos(b*x+a))^2*(8*cos(b*x+a)*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+2*cos(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-5*cos(b*x+a)*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)-5*cos(b*x+a)*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)-8*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+5*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)+5*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2))/(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)*4^(1/2)","B"
631,1,1157,151,1.073000," ","int(cos(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x)","\frac{\sqrt{2}\, \left(-1+\cos \left(b x +a \right)\right)^{2} \left(8 \cos \left(b x +a \right) \sqrt{2}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)+2 \cos \left(b x +a \right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-5 \cos \left(b x +a \right) \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)-5 \cos \left(b x +a \right) \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)-8 \sqrt{2}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)+5 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)+5 \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)\right) \sqrt{4}}{32 b \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}} \sin \left(b x +a \right)^{3} \left(\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}\right)^{\frac{3}{2}}}+\frac{\sqrt{2}\, \left(-1+\cos \left(b x +a \right)\right)^{2} \left(4 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \left(\cos^{3}\left(b x +a \right)\right)-10 \cos \left(b x +a \right) \sqrt{2}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)+7 \cos \left(b x +a \right) \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)+7 \cos \left(b x +a \right) \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)-6 \cos \left(b x +a \right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+10 \sqrt{2}\, \arctanh \left(\frac{\cos \left(b x +a \right) \sqrt{4}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{2}}{2 \sin \left(b x +a \right)^{2} \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}}\right)-7 \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}\right)-7 \ln \left(-\frac{2 \left(\left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-2 \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)-\sqrt{\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+1\right)}{\sin \left(b x +a \right)^{2}}\right)\right) \sqrt{4}}{16 b \left(\frac{2 \left(\cos^{2}\left(b x +a \right)\right)-1}{\left(\cos \left(b x +a \right)+1\right)^{2}}\right)^{\frac{3}{2}} \left(\frac{c \left(\sin^{2}\left(b x +a \right)\right)}{2 \left(\cos^{2}\left(b x +a \right)\right)-1}\right)^{\frac{3}{2}} \sin \left(b x +a \right)^{3}}"," ",0,"1/32*2^(1/2)/b*(-1+cos(b*x+a))^2*(8*cos(b*x+a)*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+2*cos(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-5*cos(b*x+a)*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)-5*cos(b*x+a)*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)-8*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+5*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)+5*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2))/(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)*4^(1/2)+1/16*2^(1/2)/b*(-1+cos(b*x+a))^2*(4*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*cos(b*x+a)^3-10*cos(b*x+a)*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+7*cos(b*x+a)*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)+7*cos(b*x+a)*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)-6*cos(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+10*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-7*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)-7*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2))/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)/(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3*4^(1/2)","B"
632,1,1787,203,1.024000," ","int(cos(2*b*x+2*a)^2/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x)","\text{Expression too large to display}"," ",0,"-1/32*2^(1/2)/b*(-1+cos(b*x+a))^2*(-8*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*cos(b*x+a)^5-14*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*cos(b*x+a)^3+51*cos(b*x+a)*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-51*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-36*cos(b*x+a)*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)-36*cos(b*x+a)*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)+30*cos(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+36*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)+36*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2))/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)/(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3*4^(1/2)-1/32*2^(1/2)/b*(-1+cos(b*x+a))^2*(8*cos(b*x+a)*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+2*cos(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-5*cos(b*x+a)*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)-5*cos(b*x+a)*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)-8*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+5*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)+5*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2))/(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)*4^(1/2)-1/8*2^(1/2)/b*(-1+cos(b*x+a))^2*(4*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*cos(b*x+a)^3-10*cos(b*x+a)*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))+7*cos(b*x+a)*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)+7*cos(b*x+a)*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2)-6*cos(b*x+a)*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+10*2^(1/2)*arctanh(1/2*cos(b*x+a)*4^(1/2)*(-1+cos(b*x+a))/sin(b*x+a)^2/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)*2^(1/2))-7*arctanh(1/2*4^(1/2)*(2*cos(b*x+a)^2-3*cos(b*x+a)+1)/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2)-7*ln(-2*(cos(b*x+a)^2*((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)-2*cos(b*x+a)^2+cos(b*x+a)-((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(1/2)+1)/sin(b*x+a)^2))/((2*cos(b*x+a)^2-1)/(cos(b*x+a)+1)^2)^(3/2)/(c*sin(b*x+a)^2/(2*cos(b*x+a)^2-1))^(3/2)/sin(b*x+a)^3*4^(1/2)","B"
633,1,119,12,0.213000," ","int(cot(x)*csc(x)/sin(2*x)^(1/2),x)","\frac{\sqrt{-\frac{\tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \left(4 \sqrt{1+\tan \left(\frac{x}{2}\right)}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{1+\tan \left(\frac{x}{2}\right)}, \frac{\sqrt{2}}{2}\right) \tan \left(\frac{x}{2}\right)+\tan^{4}\left(\frac{x}{2}\right)-1\right)}{6 \tan \left(\frac{x}{2}\right) \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}}"," ",0,"1/6*(-tan(1/2*x)/(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)^2-1)/tan(1/2*x)*(4*(1+tan(1/2*x))^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((1+tan(1/2*x))^(1/2),1/2*2^(1/2))*tan(1/2*x)+tan(1/2*x)^4-1)/((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)/(tan(1/2*x)^3-tan(1/2*x))^(1/2)","C"
634,1,397,50,0.313000," ","int(csc(x)^2*sec(x)/sin(2*x)^(1/2)/(-2+tan(x)),x)","\frac{\sqrt{-\frac{\tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)-1}}\, \left(140 \sqrt{1+\tan \left(\frac{x}{2}\right)}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \EllipticF \left(\sqrt{1+\tan \left(\frac{x}{2}\right)}, \frac{\sqrt{2}}{2}\right) \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \tan \left(\frac{x}{2}\right)-240 \sqrt{1+\tan \left(\frac{x}{2}\right)}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \EllipticE \left(\sqrt{1+\tan \left(\frac{x}{2}\right)}, \frac{\sqrt{2}}{2}\right) \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \tan \left(\frac{x}{2}\right)-\sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\textit{\_Z}^{3}+2 \textit{\_Z}^{2}-\textit{\_Z} +1\right)}{\sum}\frac{\left(14 \underline{\hspace{1.25 ex}}\alpha^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{2}+14 \underline{\hspace{1.25 ex}}\alpha  -11\right) \left(\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha  -3\right) \sqrt{1+\tan \left(\frac{x}{2}\right)}\, \sqrt{1-\tan \left(\frac{x}{2}\right)}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticPi \left(\sqrt{1+\tan \left(\frac{x}{2}\right)}, -\frac{1}{4} \underline{\hspace{1.25 ex}}\alpha^{3}-\frac{1}{2} \underline{\hspace{1.25 ex}}\alpha  +\frac{3}{4}, \frac{\sqrt{2}}{2}\right)}{\sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}}\right) \tan \left(\frac{x}{2}\right)-40 \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \left(\tan^{4}\left(\frac{x}{2}\right)\right)-120 \left(\tan^{3}\left(\frac{x}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}+120 \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \tan \left(\frac{x}{2}\right)+40 \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\right)}{480 \tan \left(\frac{x}{2}\right)^{2} \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}}"," ",0,"1/480*(-tan(1/2*x)/(tan(1/2*x)^2-1))^(1/2)/tan(1/2*x)^2*(140*(1+tan(1/2*x))^(1/2)*(-tan(1/2*x))^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*EllipticF((1+tan(1/2*x))^(1/2),1/2*2^(1/2))*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*tan(1/2*x)-240*(1+tan(1/2*x))^(1/2)*(-tan(1/2*x))^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*EllipticE((1+tan(1/2*x))^(1/2),1/2*2^(1/2))*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*tan(1/2*x)-(tan(1/2*x)^3-tan(1/2*x))^(1/2)*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*2^(1/2)*sum((14*_alpha^3+3*_alpha^2+14*_alpha-11)*(_alpha^3+2*_alpha-3)*(1+tan(1/2*x))^(1/2)*(1-tan(1/2*x))^(1/2)*(-tan(1/2*x))^(1/2)/((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*EllipticPi((1+tan(1/2*x))^(1/2),-1/4*_alpha^3-1/2*_alpha+3/4,1/2*2^(1/2)),_alpha=RootOf(_Z^4+_Z^3+2*_Z^2-_Z+1))*tan(1/2*x)-40*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*tan(1/2*x)^4-120*tan(1/2*x)^3*(tan(1/2*x)^3-tan(1/2*x))^(1/2)+120*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*tan(1/2*x)+40*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2))/(tan(1/2*x)^3-tan(1/2*x))^(1/2)","C"
635,1,397,60,0.280000," ","int(cos(x)^2*sin(x)/(sin(x)^2-sin(2*x))/sin(2*x)^(5/2),x)","\frac{\sqrt{-\frac{\tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)-1}}\, \left(140 \sqrt{1+\tan \left(\frac{x}{2}\right)}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \EllipticF \left(\sqrt{1+\tan \left(\frac{x}{2}\right)}, \frac{\sqrt{2}}{2}\right) \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \tan \left(\frac{x}{2}\right)-240 \sqrt{1+\tan \left(\frac{x}{2}\right)}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \EllipticE \left(\sqrt{1+\tan \left(\frac{x}{2}\right)}, \frac{\sqrt{2}}{2}\right) \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \tan \left(\frac{x}{2}\right)-\sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\textit{\_Z}^{3}+2 \textit{\_Z}^{2}-\textit{\_Z} +1\right)}{\sum}\frac{\left(14 \underline{\hspace{1.25 ex}}\alpha^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{2}+14 \underline{\hspace{1.25 ex}}\alpha  -11\right) \left(\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha  -3\right) \sqrt{1+\tan \left(\frac{x}{2}\right)}\, \sqrt{1-\tan \left(\frac{x}{2}\right)}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticPi \left(\sqrt{1+\tan \left(\frac{x}{2}\right)}, -\frac{1}{4} \underline{\hspace{1.25 ex}}\alpha^{3}-\frac{1}{2} \underline{\hspace{1.25 ex}}\alpha  +\frac{3}{4}, \frac{\sqrt{2}}{2}\right)}{\sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}}\right) \tan \left(\frac{x}{2}\right)-40 \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \left(\tan^{4}\left(\frac{x}{2}\right)\right)-120 \left(\tan^{3}\left(\frac{x}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}+120 \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \tan \left(\frac{x}{2}\right)+40 \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\right)}{1920 \tan \left(\frac{x}{2}\right)^{2} \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}}"," ",0,"1/1920*(-tan(1/2*x)/(tan(1/2*x)^2-1))^(1/2)/tan(1/2*x)^2*(140*(1+tan(1/2*x))^(1/2)*(-tan(1/2*x))^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*EllipticF((1+tan(1/2*x))^(1/2),1/2*2^(1/2))*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*tan(1/2*x)-240*(1+tan(1/2*x))^(1/2)*(-tan(1/2*x))^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*EllipticE((1+tan(1/2*x))^(1/2),1/2*2^(1/2))*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*tan(1/2*x)-(tan(1/2*x)^3-tan(1/2*x))^(1/2)*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*2^(1/2)*sum((14*_alpha^3+3*_alpha^2+14*_alpha-11)*(_alpha^3+2*_alpha-3)*(1+tan(1/2*x))^(1/2)*(1-tan(1/2*x))^(1/2)*(-tan(1/2*x))^(1/2)/((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*EllipticPi((1+tan(1/2*x))^(1/2),-1/4*_alpha^3-1/2*_alpha+3/4,1/2*2^(1/2)),_alpha=RootOf(_Z^4+_Z^3+2*_Z^2-_Z+1))*tan(1/2*x)-40*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*tan(1/2*x)^4-120*tan(1/2*x)^3*(tan(1/2*x)^3-tan(1/2*x))^(1/2)+120*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*tan(1/2*x)+40*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2))/(tan(1/2*x)^3-tan(1/2*x))^(1/2)","C"
636,1,761,72,0.383000," ","int(cos(x)^3*cos(2*x)/(sin(x)^2-sin(2*x))/sin(2*x)^(5/2),x)","\frac{\sqrt{-\frac{\tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)-1}}\, \left(1772 \sqrt{\left(\tan \left(\frac{x}{2}\right)-1\right) \left(1+\tan \left(\frac{x}{2}\right)\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \EllipticF \left(\sqrt{1+\tan \left(\frac{x}{2}\right)}, \frac{\sqrt{2}}{2}\right) \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{1+\tan \left(\frac{x}{2}\right)}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)-4464 \sqrt{\left(\tan \left(\frac{x}{2}\right)-1\right) \left(1+\tan \left(\frac{x}{2}\right)\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \EllipticE \left(\sqrt{1+\tan \left(\frac{x}{2}\right)}, \frac{\sqrt{2}}{2}\right) \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{1+\tan \left(\frac{x}{2}\right)}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)+24 \sqrt{\left(\tan \left(\frac{x}{2}\right)-1\right) \left(1+\tan \left(\frac{x}{2}\right)\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \left(\tan^{6}\left(\frac{x}{2}\right)\right)+3 \sqrt{\left(\tan \left(\frac{x}{2}\right)-1\right) \left(1+\tan \left(\frac{x}{2}\right)\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\textit{\_Z}^{3}+2 \textit{\_Z}^{2}-\textit{\_Z} +1\right)}{\sum}\frac{\left(6 \underline{\hspace{1.25 ex}}\alpha^{3}+7 \underline{\hspace{1.25 ex}}\alpha^{2}+6 \underline{\hspace{1.25 ex}}\alpha  +1\right) \left(\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha  -3\right) \sqrt{1+\tan \left(\frac{x}{2}\right)}\, \sqrt{1-\tan \left(\frac{x}{2}\right)}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticPi \left(\sqrt{1+\tan \left(\frac{x}{2}\right)}, -\frac{1}{4} \underline{\hspace{1.25 ex}}\alpha^{3}-\frac{1}{2} \underline{\hspace{1.25 ex}}\alpha  +\frac{3}{4}, \frac{\sqrt{2}}{2}\right)}{\sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}}\right) \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{2}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)-40 \sqrt{\left(\tan \left(\frac{x}{2}\right)-1\right) \left(1+\tan \left(\frac{x}{2}\right)\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \left(\tan^{5}\left(\frac{x}{2}\right)\right)-1272 \left(\tan^{4}\left(\frac{x}{2}\right)\right) \sqrt{\left(\tan \left(\frac{x}{2}\right)-1\right) \left(1+\tan \left(\frac{x}{2}\right)\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}-24 \left(\tan^{4}\left(\frac{x}{2}\right)\right) \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{\left(\tan \left(\frac{x}{2}\right)-1\right) \left(1+\tan \left(\frac{x}{2}\right)\right) \tan \left(\frac{x}{2}\right)}-1920 \left(\tan^{4}\left(\frac{x}{2}\right)\right) \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}+1272 \sqrt{\left(\tan \left(\frac{x}{2}\right)-1\right) \left(1+\tan \left(\frac{x}{2}\right)\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)-24 \sqrt{\left(\tan \left(\frac{x}{2}\right)-1\right) \left(1+\tan \left(\frac{x}{2}\right)\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)+40 \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{\left(\tan \left(\frac{x}{2}\right)-1\right) \left(1+\tan \left(\frac{x}{2}\right)\right) \tan \left(\frac{x}{2}\right)}\, \tan \left(\frac{x}{2}\right)+24 \sqrt{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{\left(\tan \left(\frac{x}{2}\right)-1\right) \left(1+\tan \left(\frac{x}{2}\right)\right) \tan \left(\frac{x}{2}\right)}\right)}{3840 \tan \left(\frac{x}{2}\right)^{3} \sqrt{\left(\tan \left(\frac{x}{2}\right)-1\right) \left(1+\tan \left(\frac{x}{2}\right)\right) \tan \left(\frac{x}{2}\right)}\, \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}}"," ",0,"1/3840*(-tan(1/2*x)/(tan(1/2*x)^2-1))^(1/2)/tan(1/2*x)^3*(1772*((tan(1/2*x)-1)*(1+tan(1/2*x))*tan(1/2*x))^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*EllipticF((1+tan(1/2*x))^(1/2),1/2*2^(1/2))*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*(1+tan(1/2*x))^(1/2)*(-tan(1/2*x))^(1/2)*tan(1/2*x)^2-4464*((tan(1/2*x)-1)*(1+tan(1/2*x))*tan(1/2*x))^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*EllipticE((1+tan(1/2*x))^(1/2),1/2*2^(1/2))*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*(1+tan(1/2*x))^(1/2)*(-tan(1/2*x))^(1/2)*tan(1/2*x)^2+24*((tan(1/2*x)-1)*(1+tan(1/2*x))*tan(1/2*x))^(1/2)*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*tan(1/2*x)^6+3*((tan(1/2*x)-1)*(1+tan(1/2*x))*tan(1/2*x))^(1/2)*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*sum((6*_alpha^3+7*_alpha^2+6*_alpha+1)*(_alpha^3+2*_alpha-3)*(1+tan(1/2*x))^(1/2)*(1-tan(1/2*x))^(1/2)*(-tan(1/2*x))^(1/2)*EllipticPi((1+tan(1/2*x))^(1/2),-1/4*_alpha^3-1/2*_alpha+3/4,1/2*2^(1/2))/((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2),_alpha=RootOf(_Z^4+_Z^3+2*_Z^2-_Z+1))*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*2^(1/2)*tan(1/2*x)^2-40*((tan(1/2*x)-1)*(1+tan(1/2*x))*tan(1/2*x))^(1/2)*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*tan(1/2*x)^5-1272*tan(1/2*x)^4*((tan(1/2*x)-1)*(1+tan(1/2*x))*tan(1/2*x))^(1/2)*(tan(1/2*x)^3-tan(1/2*x))^(1/2)-24*tan(1/2*x)^4*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*((tan(1/2*x)-1)*(1+tan(1/2*x))*tan(1/2*x))^(1/2)-1920*tan(1/2*x)^4*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*(tan(1/2*x)^3-tan(1/2*x))^(1/2)+1272*((tan(1/2*x)-1)*(1+tan(1/2*x))*tan(1/2*x))^(1/2)*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*tan(1/2*x)^2-24*((tan(1/2*x)-1)*(1+tan(1/2*x))*tan(1/2*x))^(1/2)*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*tan(1/2*x)^2+40*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*((tan(1/2*x)-1)*(1+tan(1/2*x))*tan(1/2*x))^(1/2)*tan(1/2*x)+24*((tan(1/2*x)^2-1)*tan(1/2*x))^(1/2)*((tan(1/2*x)-1)*(1+tan(1/2*x))*tan(1/2*x))^(1/2))/((tan(1/2*x)-1)*(1+tan(1/2*x))*tan(1/2*x))^(1/2)/(tan(1/2*x)^3-tan(1/2*x))^(1/2)","C"
637,1,31,30,0.461000," ","int((b*sec(d*x+c)+a*sin(d*x+c))^n*(a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c)),x)","\frac{\left(b \sec \left(d x +c \right)+a \sin \left(d x +c \right)\right)^{n +1}}{d \left(n +1\right)}"," ",0,"(b*sec(d*x+c)+a*sin(d*x+c))^(n+1)/d/(n+1)","A"
638,1,137,24,0.608000," ","int((b*sec(d*x+c)+a*sin(d*x+c))^3*(a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c)),x)","\frac{a^{4} \left(\sin^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{3} b \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{a^{3} b \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{d}+\frac{3 a^{2} b^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \,b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{3}}+\frac{a \,b^{3} \tan \left(d x +c \right)}{d}+\frac{b^{4}}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/4/d*a^4*sin(d*x+c)^4+1/d*a^3*b*sin(d*x+c)^5/cos(d*x+c)+1/d*a^3*b*cos(d*x+c)*sin(d*x+c)^3+3/2/d*a^2*b^2*tan(d*x+c)^2+1/d*a*b^3*sin(d*x+c)^3/cos(d*x+c)^3+1/d*a*b^3*tan(d*x+c)+1/4/d*b^4/cos(d*x+c)^4","B"
639,1,118,24,0.556000," ","int((b*sec(d*x+c)+a*sin(d*x+c))^2*(a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c)),x)","\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} b \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{a^{2} b \left(\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{d}+\frac{a \,b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{a \,b^{2} \sin \left(d x +c \right)}{d}+\frac{b^{3}}{3 d \cos \left(d x +c \right)^{3}}"," ",0,"1/3/d*a^3*sin(d*x+c)^3+1/d*a^2*b*sin(d*x+c)^4/cos(d*x+c)+1/d*a^2*b*sin(d*x+c)^2*cos(d*x+c)+1/d*a*b^2*sin(d*x+c)^3/cos(d*x+c)^2+1/d*a*b^2*sin(d*x+c)+1/3/d*b^3/cos(d*x+c)^3","B"
640,1,57,24,0.460000," ","int((b*sec(d*x+c)+a*sin(d*x+c))*(a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c)),x)","\frac{-\frac{\left(\cos^{2}\left(d x +c \right)\right) a^{2}}{2}+a b \left(\tan \left(d x +c \right)-d x -c \right)+\left(d x +c \right) a b +\frac{b^{2}}{2 \cos \left(d x +c \right)^{2}}}{d}"," ",0,"1/d*(-1/2*cos(d*x+c)^2*a^2+a*b*(tan(d*x+c)-d*x-c)+(d*x+c)*a*b+1/2*b^2/cos(d*x+c)^2)","B"
641,1,23,22,0.519000," ","int((a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c))/(b*sec(d*x+c)+a*sin(d*x+c)),x)","\frac{\ln \left(b \sec \left(d x +c \right)+a \sin \left(d x +c \right)\right)}{d}"," ",0,"ln(b*sec(d*x+c)+a*sin(d*x+c))/d","A"
642,1,25,24,0.631000," ","int((a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c))/(b*sec(d*x+c)+a*sin(d*x+c))^2,x)","-\frac{1}{d \left(b \sec \left(d x +c \right)+a \sin \left(d x +c \right)\right)}"," ",0,"-1/d/(b*sec(d*x+c)+a*sin(d*x+c))","A"
643,1,25,24,0.658000," ","int((a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c))/(b*sec(d*x+c)+a*sin(d*x+c))^3,x)","-\frac{1}{2 d \left(b \sec \left(d x +c \right)+a \sin \left(d x +c \right)\right)^{2}}"," ",0,"-1/2/d/(b*sec(d*x+c)+a*sin(d*x+c))^2","A"
644,0,0,20,0.053000," ","int(F(c,d,cos(b*x+a),r,s)*sin(b*x+a),x)","\int F \left(c , d , \cos \left(b x +a \right), r , s\right) \sin \left(b x +a \right)\, dx"," ",0,"int(F(c,d,cos(b*x+a),r,s)*sin(b*x+a),x)","F"
645,0,0,20,0.030000," ","int(cos(b*x+a)*F(c,d,sin(b*x+a),r,s),x)","\int \cos \left(b x +a \right) F \left(c , d , \sin \left(b x +a \right), r , s\right)\, dx"," ",0,"int(cos(b*x+a)*F(c,d,sin(b*x+a),r,s),x)","F"
646,0,0,22,0.056000," ","int(F(c,d,tan(b*x+a),r,s)*sec(b*x+a)^2,x)","\int F \left(c , d , \tan \left(b x +a \right), r , s\right) \left(\sec^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(F(c,d,tan(b*x+a),r,s)*sec(b*x+a)^2,x)","F"
647,0,0,22,0.053000," ","int(csc(b*x+a)^2*F(c,d,cot(b*x+a),r,s),x)","\int \left(\csc^{2}\left(b x +a \right)\right) F \left(c , d , \cot \left(b x +a \right), r , s\right)\, dx"," ",0,"int(csc(b*x+a)^2*F(c,d,cot(b*x+a),r,s),x)","F"
648,1,13,12,0.033000," ","int(sin(x)/(a+b*cos(x)),x)","-\frac{\ln \left(a +b \cos \left(x \right)\right)}{b}"," ",0,"-ln(a+b*cos(x))/b","A"
649,1,21,20,0.032000," ","int((a+b*cos(x))^n*sin(x),x)","-\frac{\left(a +b \cos \left(x \right)\right)^{n +1}}{b \left(n +1\right)}"," ",0,"-(a+b*cos(x))^(n+1)/b/(n+1)","A"
650,1,6,5,0.059000," ","int(sin(x)/(1+cos(x)^2)^(1/2),x)","-\arcsinh \left(\cos \left(x \right)\right)"," ",0,"-arcsinh(cos(x))","A"
651,1,6,5,0.007000," ","int(cos(cos(x))*sin(x),x)","-\sin \left(\cos \left(x \right)\right)"," ",0,"-sin(cos(x))","A"
652,1,23,22,0.010000," ","int(cos(x)*cos(cos(x))*sin(x)*sin(cos(x)),x)","\frac{\left(\cos^{2}\left(\cos \left(x \right)\right)\right) \cos \left(x \right)}{2}-\frac{\cos \left(\cos \left(x \right)\right) \sin \left(\cos \left(x \right)\right)}{4}-\frac{\cos \left(x \right)}{4}"," ",0,"1/2*cos(cos(x))^2*cos(x)-1/4*cos(cos(x))*sin(cos(x))-1/4*cos(x)","A"
653,1,21,20,0.155000," ","int(cos(cos(x))*sin(x)*sin(6*cos(x))^2,x)","-\frac{\sin \left(\cos \left(x \right)\right)}{2}+\frac{\sin \left(11 \cos \left(x \right)\right)}{44}+\frac{\sin \left(13 \cos \left(x \right)\right)}{52}"," ",0,"-1/2*sin(cos(x))+1/44*sin(11*cos(x))+1/52*sin(13*cos(x))","A"
654,1,40,32,0.013000," ","int(cos(x)^3*(a+b*cos(x)^2)^3*sin(x),x)","-\frac{b^{3} \left(\cos^{10}\left(x \right)\right)}{10}-\frac{3 a \,b^{2} \left(\cos^{8}\left(x \right)\right)}{8}-\frac{a^{2} b \left(\cos^{6}\left(x \right)\right)}{2}-\frac{a^{3} \left(\cos^{4}\left(x \right)\right)}{4}"," ",0,"-1/10*b^3*cos(x)^10-3/8*a*b^2*cos(x)^8-1/2*a^2*b*cos(x)^6-1/4*a^3*cos(x)^4","A"
655,1,8,7,0.007000," ","int(sin(3*x)*sin(cos(3*x)),x)","\frac{\cos \left(\cos \left(3 x \right)\right)}{3}"," ",0,"1/3*cos(cos(3*x))","A"
656,1,26,25,0.012000," ","int(exp(cos(1+3*x))*cos(1+3*x)*sin(1+3*x),x)","\frac{{\mathrm e}^{\cos \left(1+3 x \right)}}{3}-\frac{{\mathrm e}^{\cos \left(1+3 x \right)} \cos \left(1+3 x \right)}{3}"," ",0,"1/3*exp(cos(1+3*x))-1/3*exp(cos(1+3*x))*cos(1+3*x)","A"
657,0,0,7,1.263000," ","int(cos(x)^2*sin(x)/(1-cos(x)^6)^(1/2),x)","\int \frac{\left(\cos^{2}\left(x \right)\right) \sin \left(x \right)}{\sqrt{1-\left(\cos^{6}\left(x \right)\right)}}\, dx"," ",0,"int(cos(x)^2*sin(x)/(1-cos(x)^6)^(1/2),x)","F"
658,1,49,51,0.173000," ","int(sin(x)^5/(1-5*cos(x))^(1/2),x)","\frac{32 \sqrt{10 \left(\sin^{2}\left(\frac{x}{2}\right)\right)-4}\, \left(21875 \left(\sin^{8}\left(\frac{x}{2}\right)\right)-46250 \left(\sin^{6}\left(\frac{x}{2}\right)\right)+17175 \left(\sin^{4}\left(\frac{x}{2}\right)\right)+9160 \left(\sin^{2}\left(\frac{x}{2}\right)\right)+7328\right)}{984375}"," ",0,"32/984375*(10*sin(1/2*x)^2-4)^(1/2)*(21875*sin(1/2*x)^8-46250*sin(1/2*x)^6+17175*sin(1/2*x)^4+9160*sin(1/2*x)^2+7328)","A"
659,1,18,17,0.006000," ","int(exp(n*cos(b*x+a))*sin(b*x+a),x)","-\frac{{\mathrm e}^{n \cos \left(b x +a \right)}}{b n}"," ",0,"-exp(n*cos(b*x+a))/b/n","A"
660,1,24,22,0.057000," ","int(exp(n*cos(b*c*x+a*c))*sin(c*(b*x+a)),x)","-\frac{{\mathrm e}^{n \cos \left(b c x +a c \right)}}{b c n}"," ",0,"-exp(n*cos(b*c*x+a*c))/b/c/n","A"
661,1,24,23,0.033000," ","int(exp(n*cos(c*(b*x+a)))*sin(b*c*x+a*c),x)","-\frac{{\mathrm e}^{n \cos \left(b c x +a c \right)}}{b c n}"," ",0,"-exp(n*cos(b*c*x+a*c))/b/c/n","A"
662,1,16,14,0.033000," ","int(exp(n*cos(b*x+a))*tan(b*x+a),x)","\frac{\Ei \left(1, -n \cos \left(b x +a \right)\right)}{b}"," ",0,"1/b*Ei(1,-n*cos(b*x+a))","A"
663,1,22,19,0.074000," ","int(exp(n*cos(b*c*x+a*c))*tan(c*(b*x+a)),x)","\frac{\Ei \left(1, -n \cos \left(b c x +a c \right)\right)}{c b}"," ",0,"1/c/b*Ei(1,-n*cos(b*c*x+a*c))","A"
664,1,22,20,0.050000," ","int(exp(n*cos(c*(b*x+a)))*tan(b*c*x+a*c),x)","\frac{\Ei \left(1, -n \cos \left(b c x +a c \right)\right)}{c b}"," ",0,"1/c/b*Ei(1,-n*cos(b*c*x+a*c))","A"
665,1,12,11,0.034000," ","int(cos(x)/(a+b*sin(x)),x)","\frac{\ln \left(a +b \sin \left(x \right)\right)}{b}"," ",0,"ln(a+b*sin(x))/b","A"
666,1,20,19,0.026000," ","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)}"," ",0,"(a+b*sin(x))^(n+1)/b/(n+1)","A"
667,1,4,3,0.057000," ","int(cos(x)/(1+sin(x)^2)^(1/2),x)","\arcsinh \left(\sin \left(x \right)\right)"," ",0,"arcsinh(sin(x))","A"
668,1,6,5,0.076000," ","int(cos(x)/(4-sin(x)^2)^(1/2),x)","\arcsin \left(\frac{\sin \left(x \right)}{2}\right)"," ",0,"arcsin(1/2*sin(x))","A"
669,1,10,9,0.084000," ","int(cos(3*x)/(4-sin(3*x)^2)^(1/2),x)","\frac{\arcsin \left(\frac{\sin \left(3 x \right)}{2}\right)}{3}"," ",0,"1/3*arcsin(1/2*sin(3*x))","A"
670,1,48,17,0.079000," ","int(cos(x)*(1+csc(x))^(1/2),x)","\frac{1}{2 \sqrt{1+\csc \left(x \right)}-2}-\frac{\ln \left(\sqrt{1+\csc \left(x \right)}-1\right)}{2}+\frac{1}{2 \sqrt{1+\csc \left(x \right)}+2}+\frac{\ln \left(\sqrt{1+\csc \left(x \right)}+1\right)}{2}"," ",0,"1/2/((1+csc(x))^(1/2)-1)-1/2*ln((1+csc(x))^(1/2)-1)+1/2/((1+csc(x))^(1/2)+1)+1/2*ln((1+csc(x))^(1/2)+1)","B"
671,1,23,22,0.072000," ","int(cos(x)*(4-sin(x)^2)^(1/2),x)","2 \arcsin \left(\frac{\sin \left(x \right)}{2}\right)+\frac{\sin \left(x \right) \sqrt{4-\left(\sin^{2}\left(x \right)\right)}}{2}"," ",0,"2*arcsin(1/2*sin(x))+1/2*sin(x)*(4-sin(x)^2)^(1/2)","A"
672,1,11,10,0.007000," ","int(cos(x)*sin(x)*(1+sin(x)^2)^(1/2),x)","\frac{\left(1+\sin^{2}\left(x \right)\right)^{\frac{3}{2}}}{3}"," ",0,"1/3*(1+sin(x)^2)^(3/2)","A"
673,1,17,17,0.099000," ","int(cos(x)/(2*sin(x)+sin(x)^2)^(1/2),x)","\ln \left(\sin \left(x \right)+1+\sqrt{2 \sin \left(x \right)+\sin^{2}\left(x \right)}\right)"," ",0,"ln(sin(x)+1+(2*sin(x)+sin(x)^2)^(1/2))","A"
674,1,4,3,0.009000," ","int(cos(x)*cos(sin(x)),x)","\sin \left(\sin \left(x \right)\right)"," ",0,"sin(sin(x))","A"
675,1,5,4,0.013000," ","int(cos(x)*cos(sin(x))*cos(sin(sin(x))),x)","\sin \left(\sin \left(\sin \left(x \right)\right)\right)"," ",0,"sin(sin(sin(x)))","A"
676,1,9,4,0.010000," ","int(cos(x)*sec(sin(x)),x)","\ln \left(\sec \left(\sin \left(x \right)\right)+\tan \left(\sin \left(x \right)\right)\right)"," ",0,"ln(sec(sin(x))+tan(sin(x)))","A"
677,1,40,32,0.014000," ","int(cos(x)*sin(x)^3*(a+b*sin(x)^2)^3,x)","\frac{b^{3} \left(\sin^{10}\left(x \right)\right)}{10}+\frac{3 a \,b^{2} \left(\sin^{8}\left(x \right)\right)}{8}+\frac{a^{2} b \left(\sin^{6}\left(x \right)\right)}{2}+\frac{a^{3} \left(\sin^{4}\left(x \right)\right)}{4}"," ",0,"1/10*b^3*sin(x)^10+3/8*a*b^2*sin(x)^8+1/2*a^2*b*sin(x)^6+1/4*a^3*sin(x)^4","A"
678,1,13,12,0.004000," ","int(exp(sin(x))*cos(x)*sin(x),x)","-{\mathrm e}^{\sin \left(x \right)}+{\mathrm e}^{\sin \left(x \right)} \sin \left(x \right)"," ",0,"-exp(sin(x))+exp(sin(x))*sin(x)","A"
679,1,14,19,0.157000," ","int(cos(x)^3/(sin(x)^3)^(1/2),x)","-\frac{2 \left(\sin^{\frac{3}{2}}\left(x \right)\right)}{3}-\frac{2}{\sqrt{\sin \left(x \right)}}"," ",0,"-2/3*sin(x)^(3/2)-2/sin(x)^(1/2)","A"
680,1,8,7,0.019000," ","int(exp(sin(x)^(1/2))*cos(x)/sin(x)^(1/2),x)","2 \,{\mathrm e}^{\sqrt{\sin}\left(x \right)}"," ",0,"2*exp(sin(x)^(1/2))","A"
681,1,6,5,0.028000," ","int(exp(4+sin(x))*cos(x),x)","{\mathrm e}^{4+\sin \left(x \right)}"," ",0,"exp(4+sin(x))","A"
682,1,7,7,0.079000," ","int(exp(cos(x)*sin(x))*cos(2*x),x)","{\mathrm e}^{\cos \left(x \right) \sin \left(x \right)}"," ",0,"exp(cos(x)*sin(x))","A"
683,1,13,7,0.079000," ","int(exp(cos(1/2*x)*sin(1/2*x))*cos(x),x)","2 \,{\mathrm e}^{\cos \left(\frac{x}{2}\right) \sin \left(\frac{x}{2}\right)}"," ",0,"2*exp(cos(1/2*x)*sin(1/2*x))","A"
684,1,17,16,0.008000," ","int(exp(n*sin(b*x+a))*cos(b*x+a),x)","\frac{{\mathrm e}^{n \sin \left(b x +a \right)}}{b n}"," ",0,"exp(n*sin(b*x+a))/b/n","A"
685,1,23,21,0.058000," ","int(exp(n*sin(b*c*x+a*c))*cos(c*(b*x+a)),x)","\frac{{\mathrm e}^{n \sin \left(b c x +a c \right)}}{b c n}"," ",0,"exp(n*sin(b*c*x+a*c))/b/c/n","A"
686,1,23,22,0.033000," ","int(exp(n*sin(c*(b*x+a)))*cos(b*c*x+a*c),x)","\frac{{\mathrm e}^{n \sin \left(b c x +a c \right)}}{b c n}"," ",0,"exp(n*sin(b*c*x+a*c))/b/c/n","A"
687,1,17,13,0.032000," ","int(exp(n*sin(b*x+a))*cot(b*x+a),x)","-\frac{\Ei \left(1, -n \sin \left(b x +a \right)\right)}{b}"," ",0,"-1/b*Ei(1,-n*sin(b*x+a))","A"
688,1,23,18,0.104000," ","int(exp(n*sin(b*c*x+a*c))*cot(c*(b*x+a)),x)","-\frac{\Ei \left(1, -n \sin \left(b c x +a c \right)\right)}{c b}"," ",0,"-1/c/b*Ei(1,-n*sin(b*c*x+a*c))","A"
689,1,23,19,0.066000," ","int(exp(n*sin(c*(b*x+a)))*cot(b*c*x+a*c),x)","-\frac{\Ei \left(1, -n \sin \left(b c x +a c \right)\right)}{c b}"," ",0,"-1/c/b*Ei(1,-n*sin(b*c*x+a*c))","A"
690,1,12,11,0.073000," ","int(sec(x)^2/(a+b*tan(x)),x)","\frac{\ln \left(a +b \tan \left(x \right)\right)}{b}"," ",0,"ln(a+b*tan(x))/b","A"
691,1,4,9,0.099000," ","int(sec(x)^2/(1-tan(x)^2),x)","\arctanh \left(\tan \left(x \right)\right)"," ",0,"arctanh(tan(x))","A"
692,1,8,23,0.102000," ","int(sec(x)^2/(9+tan(x)^2),x)","\frac{\arctan \left(\frac{\tan \left(x \right)}{3}\right)}{3}"," ",0,"1/3*arctan(1/3*tan(x))","A"
693,1,20,19,0.079000," ","int(sec(x)^2*(a+b*tan(x))^n,x)","\frac{\left(a +b \tan \left(x \right)\right)^{n +1}}{b \left(n +1\right)}"," ",0,"(a+b*tan(x))^(n+1)/b/(n+1)","A"
694,1,5,4,0.115000," ","int(sec(x)^2*(1+1/(1+tan(x)^2)),x)","x +\tan \left(x \right)"," ",0,"x+tan(x)","A"
695,1,5,4,0.114000," ","int(sec(x)^2*(2+tan(x)^2)/(1+tan(x)^2),x)","x +\tan \left(x \right)"," ",0,"x+tan(x)","A"
696,1,6,33,0.135000," ","int(sec(x)^2/(2+2*tan(x)+tan(x)^2),x)","\arctan \left(1+\tan \left(x \right)\right)"," ",0,"arctan(1+tan(x))","A"
697,1,18,10,0.129000," ","int(sec(x)^2/(tan(x)^2+tan(x)^3),x)","-\frac{1}{\tan \left(x \right)}-\ln \left(\tan \left(x \right)\right)+\ln \left(1+\tan \left(x \right)\right)"," ",0,"-1/tan(x)-ln(tan(x))+ln(1+tan(x))","A"
698,1,16,10,0.136000," ","int(sec(x)^2/(-tan(x)^2+tan(x)^3),x)","\frac{1}{\tan \left(x \right)}-\ln \left(\tan \left(x \right)\right)+\ln \left(\tan \left(x \right)-1\right)"," ",0,"1/tan(x)-ln(tan(x))+ln(tan(x)-1)","A"
699,1,80,128,0.123000," ","int(sec(x)^2/(3-4*tan(x)^3),x)","-\frac{3^{\frac{1}{3}} 4^{\frac{2}{3}} \ln \left(\tan \left(x \right)-\frac{3^{\frac{1}{3}} 4^{\frac{2}{3}}}{4}\right)}{36}+\frac{3^{\frac{1}{3}} 4^{\frac{2}{3}} \ln \left(\tan^{2}\left(x \right)+\frac{3^{\frac{1}{3}} 4^{\frac{2}{3}} \tan \left(x \right)}{4}+\frac{3^{\frac{2}{3}} 4^{\frac{1}{3}}}{4}\right)}{72}+\frac{3^{\frac{5}{6}} 4^{\frac{2}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,3^{\frac{2}{3}} 4^{\frac{1}{3}} \tan \left(x \right)}{3}+1\right)}{3}\right)}{36}"," ",0,"-1/36*3^(1/3)*4^(2/3)*ln(tan(x)-1/4*3^(1/3)*4^(2/3))+1/72*3^(1/3)*4^(2/3)*ln(tan(x)^2+1/4*3^(1/3)*4^(2/3)*tan(x)+1/4*3^(2/3)*4^(1/3))+1/36*3^(5/6)*4^(2/3)*arctan(1/3*3^(1/2)*(2/3*3^(2/3)*4^(1/3)*tan(x)+1))","A"
700,1,18,47,0.148000," ","int(sec(x)^2/(11-5*tan(x)+5*tan(x)^2),x)","\frac{2 \sqrt{195}\, \arctan \left(\frac{\left(10 \tan \left(x \right)-5\right) \sqrt{195}}{195}\right)}{195}"," ",0,"2/195*195^(1/2)*arctan(1/195*(10*tan(x)-5)*195^(1/2))","A"
701,1,35,28,0.119000," ","int(sec(x)^2*(a+b*tan(x))/(c+d*tan(x)),x)","\frac{b \tan \left(x \right)}{d}+\frac{\ln \left(c +d \tan \left(x \right)\right) a}{d}-\frac{\ln \left(c +d \tan \left(x \right)\right) c b}{d^{2}}"," ",0,"b*tan(x)/d+1/d*ln(c+d*tan(x))*a-1/d^2*ln(c+d*tan(x))*c*b","A"
702,1,80,51,0.133000," ","int(sec(x)^2*(a+b*tan(x))^2/(c+d*tan(x)),x)","\frac{b^{2} \left(\tan^{2}\left(x \right)\right)}{2 d}+\frac{2 b a \tan \left(x \right)}{d}-\frac{b^{2} \tan \left(x \right) c}{d^{2}}+\frac{\ln \left(c +d \tan \left(x \right)\right) a^{2}}{d}-\frac{2 \ln \left(c +d \tan \left(x \right)\right) a b c}{d^{2}}+\frac{\ln \left(c +d \tan \left(x \right)\right) b^{2} c^{2}}{d^{3}}"," ",0,"1/2*b^2/d*tan(x)^2+2*b/d*a*tan(x)-b^2/d^2*tan(x)*c+1/d*ln(c+d*tan(x))*a^2-2/d^2*ln(c+d*tan(x))*a*b*c+1/d^3*ln(c+d*tan(x))*b^2*c^2","A"
703,1,143,74,0.162000," ","int(sec(x)^2*(a+b*tan(x))^3/(c+d*tan(x)),x)","\frac{b^{3} \left(\tan^{3}\left(x \right)\right)}{3 d}+\frac{3 b^{2} \left(\tan^{2}\left(x \right)\right) a}{2 d}-\frac{b^{3} \left(\tan^{2}\left(x \right)\right) c}{2 d^{2}}+\frac{3 b \,a^{2} \tan \left(x \right)}{d}-\frac{3 b^{2} a c \tan \left(x \right)}{d^{2}}+\frac{b^{3} c^{2} \tan \left(x \right)}{d^{3}}+\frac{\ln \left(c +d \tan \left(x \right)\right) a^{3}}{d}-\frac{3 \ln \left(c +d \tan \left(x \right)\right) a^{2} b c}{d^{2}}+\frac{3 \ln \left(c +d \tan \left(x \right)\right) a \,b^{2} c^{2}}{d^{3}}-\frac{\ln \left(c +d \tan \left(x \right)\right) b^{3} c^{3}}{d^{4}}"," ",0,"1/3*b^3/d*tan(x)^3+3/2*b^2/d*tan(x)^2*a-1/2*b^3/d^2*tan(x)^2*c+3*b/d*a^2*tan(x)-3*b^2/d^2*a*c*tan(x)+b^3/d^3*c^2*tan(x)+1/d*ln(c+d*tan(x))*a^3-3/d^2*ln(c+d*tan(x))*a^2*b*c+3/d^3*ln(c+d*tan(x))*a*b^2*c^2-1/d^4*ln(c+d*tan(x))*b^3*c^3","A"
704,1,11,10,0.129000," ","int(sec(x)^2*tan(x)^2/(2+tan(x)^3)^2,x)","-\frac{1}{3 \left(2+\tan^{3}\left(x \right)\right)}"," ",0,"-1/3/(2+tan(x)^3)","A"
705,1,42,25,0.064000," ","int(sec(x)^2*tan(x)^6*(1+tan(x)^2)^3,x)","\frac{\sin^{7}\left(x \right)}{7 \cos \left(x \right)^{7}}+\frac{\sin^{9}\left(x \right)}{3 \cos \left(x \right)^{9}}+\frac{3 \left(\sin^{11}\left(x \right)\right)}{11 \cos \left(x \right)^{11}}+\frac{\sin^{13}\left(x \right)}{13 \cos \left(x \right)^{13}}"," ",0,"1/7*sin(x)^7/cos(x)^7+1/3*sin(x)^9/cos(x)^9+3/11*sin(x)^11/cos(x)^11+1/13*sin(x)^13/cos(x)^13","A"
706,1,24,40,0.204000," ","int(sec(x)^2*(2+tan(x)^2)/(1+tan(x)^3),x)","\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(-1+2 \tan \left(x \right)\right) \sqrt{3}}{3}\right)}{3}+\ln \left(1+\tan \left(x \right)\right)"," ",0,"2/3*3^(1/2)*arctan(1/3*(-1+2*tan(x))*3^(1/2))+ln(1+tan(x))","A"
707,1,5,4,0.076000," ","int((1+cos(x)^2)*sec(x)^2,x)","x +\tan \left(x \right)"," ",0,"x+tan(x)","A"
708,1,14,21,0.131000," ","int(sec(x)^2/(1+sec(x)^2-3*tan(x)),x)","\ln \left(-2+\tan \left(x \right)\right)-\ln \left(\tan \left(x \right)-1\right)"," ",0,"ln(-2+tan(x))-ln(tan(x)-1)","A"
709,1,103,8,0.282000," ","int(sec(x)^2/(4-sec(x)^2)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{\frac{2 \cos \left(x \right)-1}{1+\cos \left(x \right)}}\, \sqrt{6}\, \sqrt{\frac{1+2 \cos \left(x \right)}{1+\cos \left(x \right)}}\, \left(\EllipticF \left(\frac{\sqrt{3}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, \frac{1}{3}\right)-2 \EllipticPi \left(\frac{\sqrt{3}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, \frac{1}{3}, \frac{1}{3}\right)\right) \left(\sin^{2}\left(x \right)\right) \sqrt{3}}{9 \sqrt{\frac{4 \left(\cos^{2}\left(x \right)\right)-1}{\cos \left(x \right)^{2}}}\, \cos \left(x \right) \left(-1+\cos \left(x \right)\right)}"," ",0,"-1/9*2^(1/2)*((2*cos(x)-1)/(1+cos(x)))^(1/2)*6^(1/2)*((1+2*cos(x))/(1+cos(x)))^(1/2)*(EllipticF(3^(1/2)*(-1+cos(x))/sin(x),1/3)-2*EllipticPi(3^(1/2)*(-1+cos(x))/sin(x),1/3,1/3))*sin(x)^2/((4*cos(x)^2-1)/cos(x)^2)^(1/2)/cos(x)/(-1+cos(x))*3^(1/2)","C"
710,1,171,7,0.687000," ","int(sec(x)^2/(1-4*tan(x)^2)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{\frac{2 \cos \left(x \right) \sqrt{5}+5 \cos \left(x \right)-2 \sqrt{5}-4}{1+\cos \left(x \right)}}\, \sqrt{-\frac{2 \left(2 \cos \left(x \right) \sqrt{5}-5 \cos \left(x \right)-2 \sqrt{5}+4\right)}{1+\cos \left(x \right)}}\, \left(\EllipticF \left(\frac{\left(-1+\cos \left(x \right)\right) \left(\sqrt{5}+2\right)}{\sin \left(x \right)}, 9-4 \sqrt{5}\right)-2 \EllipticPi \left(\frac{\sqrt{9+4 \sqrt{5}}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, \frac{1}{9+4 \sqrt{5}}, \frac{\sqrt{9-4 \sqrt{5}}}{\sqrt{9+4 \sqrt{5}}}\right)\right) \left(\sin^{2}\left(x \right)\right)}{\sqrt{\frac{5 \left(\cos^{2}\left(x \right)\right)-4}{\cos \left(x \right)^{2}}}\, \cos \left(x \right) \left(-1+\cos \left(x \right)\right) \sqrt{9+4 \sqrt{5}}}"," ",0,"-2^(1/2)*((2*cos(x)*5^(1/2)+5*cos(x)-2*5^(1/2)-4)/(1+cos(x)))^(1/2)*(-2*(2*cos(x)*5^(1/2)-5*cos(x)-2*5^(1/2)+4)/(1+cos(x)))^(1/2)*(EllipticF((-1+cos(x))*(5^(1/2)+2)/sin(x),9-4*5^(1/2))-2*EllipticPi((9+4*5^(1/2))^(1/2)*(-1+cos(x))/sin(x),1/(9+4*5^(1/2)),(9-4*5^(1/2))^(1/2)/(9+4*5^(1/2))^(1/2)))*sin(x)^2/((5*cos(x)^2-4)/cos(x)^2)^(1/2)/cos(x)/(-1+cos(x))/(9+4*5^(1/2))^(1/2)","C"
711,1,171,12,0.720000," ","int(sec(x)^2/(-4+tan(x)^2)^(1/2),x)","-\frac{\sqrt{-\frac{2 \left(\cos \left(x \right) \sqrt{5}-5 \cos \left(x \right)-\sqrt{5}+1\right)}{1+\cos \left(x \right)}}\, \sqrt{2}\, \sqrt{\frac{\cos \left(x \right) \sqrt{5}-\sqrt{5}+5 \cos \left(x \right)-1}{1+\cos \left(x \right)}}\, \left(\EllipticF \left(\frac{\left(-1+\cos \left(x \right)\right) \left(\sqrt{5}-1\right)}{2 \sin \left(x \right)}, \frac{3}{2}+\frac{\sqrt{5}}{2}\right)-2 \EllipticPi \left(\frac{\sqrt{\frac{3}{2}-\frac{\sqrt{5}}{2}}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, -\frac{2}{\sqrt{5}-3}, \frac{\sqrt{\frac{3}{2}+\frac{\sqrt{5}}{2}}}{\sqrt{\frac{3}{2}-\frac{\sqrt{5}}{2}}}\right)\right) \left(\sin^{2}\left(x \right)\right)}{4 \sqrt{-\frac{5 \left(\cos^{2}\left(x \right)\right)-1}{\cos \left(x \right)^{2}}}\, \cos \left(x \right) \left(-1+\cos \left(x \right)\right) \sqrt{\frac{3}{2}-\frac{\sqrt{5}}{2}}}"," ",0,"-1/4*(-2*(cos(x)*5^(1/2)-5*cos(x)-5^(1/2)+1)/(1+cos(x)))^(1/2)*2^(1/2)*((cos(x)*5^(1/2)-5^(1/2)+5*cos(x)-1)/(1+cos(x)))^(1/2)*(EllipticF(1/2*(-1+cos(x))*(5^(1/2)-1)/sin(x),3/2+1/2*5^(1/2))-2*EllipticPi((3/2-1/2*5^(1/2))^(1/2)*(-1+cos(x))/sin(x),-2/(5^(1/2)-3),(3/2+1/2*5^(1/2))^(1/2)/(3/2-1/2*5^(1/2))^(1/2)))*sin(x)^2/(-(5*cos(x)^2-1)/cos(x)^2)^(1/2)/cos(x)/(-1+cos(x))/(3/2-1/2*5^(1/2))^(1/2)","C"
712,1,223,17,0.612000," ","int(sec(x)^2*(1-cot(x)^2)^(1/2),x)","-\frac{\left(-1+\cos \left(x \right)\right) \left(4 i \cos \left(x \right) \ln \left(\frac{4 \left(-1+\cos \left(x \right)\right) \left(2 i \cos \left(x \right)-\cos \left(x \right) \sqrt{-\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}+i-\sqrt{-\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}\right)}{\sin \left(x \right)^{2}}\right)-3 \cos \left(x \right) \arcsin \left(\frac{\left(1+2 \cos \left(x \right)\right) \sqrt{2}}{2+2 \cos \left(x \right)}\right)-\cos \left(x \right) \arctan \left(\frac{2 \left(\cos^{2}\left(x \right)\right)-3 \cos \left(x \right)+1}{\sqrt{-\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}\, \sin \left(x \right)^{2}}\right)+2 \cos \left(x \right) \sqrt{-\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}+2 \sqrt{-\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}\right) \sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{-1+\cos^{2}\left(x \right)}}}{2 \cos \left(x \right) \sin \left(x \right) \sqrt{-\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}}"," ",0,"-1/2*(-1+cos(x))*(4*I*cos(x)*ln(4*(-1+cos(x))*(2*I*cos(x)-cos(x)*(-(2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)+I-(-(2*cos(x)^2-1)/(1+cos(x))^2)^(1/2))/sin(x)^2)-3*cos(x)*arcsin(1/2*(1+2*cos(x))/(1+cos(x))*2^(1/2))-cos(x)*arctan((2*cos(x)^2-3*cos(x)+1)/(-(2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)/sin(x)^2)+2*cos(x)*(-(2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)+2*(-(2*cos(x)^2-1)/(1+cos(x))^2)^(1/2))*((2*cos(x)^2-1)/(-1+cos(x)^2))^(1/2)/cos(x)/sin(x)/(-(2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)","C"
713,1,492,20,0.427000," ","int(sec(x)^2*(1-tan(x)^2)^(1/2),x)","\frac{\sin \left(x \right) \left(2 \left(\cos^{2}\left(x \right)\right) \sin \left(x \right) \sqrt{2}\, \sqrt{\frac{\cos \left(x \right) \sqrt{2}-\sqrt{2}+2 \cos \left(x \right)-1}{1+\cos \left(x \right)}}\, \sqrt{-\frac{2 \left(\cos \left(x \right) \sqrt{2}-\sqrt{2}-2 \cos \left(x \right)+1\right)}{1+\cos \left(x \right)}}\, \EllipticPi \left(\frac{\sqrt{3+2 \sqrt{2}}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, \frac{1}{3+2 \sqrt{2}}, \frac{\sqrt{3-2 \sqrt{2}}}{\sqrt{3+2 \sqrt{2}}}\right)-\left(\cos^{2}\left(x \right)\right) \sin \left(x \right) \sqrt{2}\, \sqrt{\frac{\cos \left(x \right) \sqrt{2}-\sqrt{2}+2 \cos \left(x \right)-1}{1+\cos \left(x \right)}}\, \sqrt{-\frac{2 \left(\cos \left(x \right) \sqrt{2}-\sqrt{2}-2 \cos \left(x \right)+1\right)}{1+\cos \left(x \right)}}\, \EllipticF \left(\frac{\left(1+\sqrt{2}\right) \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, 3-2 \sqrt{2}\right)+4 \left(\cos^{2}\left(x \right)\right) \sin \left(x \right) \sqrt{\frac{\cos \left(x \right) \sqrt{2}-\sqrt{2}+2 \cos \left(x \right)-1}{1+\cos \left(x \right)}}\, \sqrt{-\frac{2 \left(\cos \left(x \right) \sqrt{2}-\sqrt{2}-2 \cos \left(x \right)+1\right)}{1+\cos \left(x \right)}}\, \EllipticPi \left(\frac{\sqrt{3+2 \sqrt{2}}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, \frac{1}{3+2 \sqrt{2}}, \frac{\sqrt{3-2 \sqrt{2}}}{\sqrt{3+2 \sqrt{2}}}\right)-2 \left(\cos^{2}\left(x \right)\right) \sin \left(x \right) \sqrt{\frac{\cos \left(x \right) \sqrt{2}-\sqrt{2}+2 \cos \left(x \right)-1}{1+\cos \left(x \right)}}\, \sqrt{-\frac{2 \left(\cos \left(x \right) \sqrt{2}-\sqrt{2}-2 \cos \left(x \right)+1\right)}{1+\cos \left(x \right)}}\, \EllipticF \left(\frac{\left(1+\sqrt{2}\right) \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, 3-2 \sqrt{2}\right)+4 \left(\cos^{3}\left(x \right)\right) \sqrt{2}-4 \left(\cos^{2}\left(x \right)\right) \sqrt{2}+6 \left(\cos^{3}\left(x \right)\right)-2 \cos \left(x \right) \sqrt{2}-6 \left(\cos^{2}\left(x \right)\right)+2 \sqrt{2}-3 \cos \left(x \right)+3\right) \sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\cos \left(x \right)^{2}}}}{2 \left(-1+\cos \left(x \right)\right) \left(2 \left(\cos^{2}\left(x \right)\right)-1\right) \cos \left(x \right) \left(1+\sqrt{2}\right) \sqrt{3+2 \sqrt{2}}}"," ",0,"1/2*sin(x)*(2*cos(x)^2*sin(x)*2^(1/2)*((cos(x)*2^(1/2)-2^(1/2)+2*cos(x)-1)/(1+cos(x)))^(1/2)*(-2*(cos(x)*2^(1/2)-2^(1/2)-2*cos(x)+1)/(1+cos(x)))^(1/2)*EllipticPi((3+2*2^(1/2))^(1/2)*(-1+cos(x))/sin(x),1/(3+2*2^(1/2)),(3-2*2^(1/2))^(1/2)/(3+2*2^(1/2))^(1/2))-cos(x)^2*sin(x)*2^(1/2)*((cos(x)*2^(1/2)-2^(1/2)+2*cos(x)-1)/(1+cos(x)))^(1/2)*(-2*(cos(x)*2^(1/2)-2^(1/2)-2*cos(x)+1)/(1+cos(x)))^(1/2)*EllipticF((1+2^(1/2))*(-1+cos(x))/sin(x),3-2*2^(1/2))+4*cos(x)^2*sin(x)*((cos(x)*2^(1/2)-2^(1/2)+2*cos(x)-1)/(1+cos(x)))^(1/2)*(-2*(cos(x)*2^(1/2)-2^(1/2)-2*cos(x)+1)/(1+cos(x)))^(1/2)*EllipticPi((3+2*2^(1/2))^(1/2)*(-1+cos(x))/sin(x),1/(3+2*2^(1/2)),(3-2*2^(1/2))^(1/2)/(3+2*2^(1/2))^(1/2))-2*cos(x)^2*sin(x)*((cos(x)*2^(1/2)-2^(1/2)+2*cos(x)-1)/(1+cos(x)))^(1/2)*(-2*(cos(x)*2^(1/2)-2^(1/2)-2*cos(x)+1)/(1+cos(x)))^(1/2)*EllipticF((1+2^(1/2))*(-1+cos(x))/sin(x),3-2*2^(1/2))+4*cos(x)^3*2^(1/2)-4*cos(x)^2*2^(1/2)+6*cos(x)^3-2*cos(x)*2^(1/2)-6*cos(x)^2+2*2^(1/2)-3*cos(x)+3)*((2*cos(x)^2-1)/cos(x)^2)^(1/2)/(-1+cos(x))/(2*cos(x)^2-1)/cos(x)/(1+2^(1/2))/(3+2*2^(1/2))^(1/2)","C"
714,1,4,3,0.048000," ","int(exp(tan(x))*sec(x)^2,x)","{\mathrm e}^{\tan \left(x \right)}"," ",0,"exp(tan(x))","A"
715,1,20,13,0.046000," ","int(sec(x)^4*(-1+sec(x)^2)^2*tan(x),x)","\frac{\left(\sec^{8}\left(x \right)\right)}{8}-\frac{\left(\sec^{6}\left(x \right)\right)}{3}+\frac{\left(\sec^{4}\left(x \right)\right)}{4}"," ",0,"1/8*sec(x)^8-1/3*sec(x)^6+1/4*sec(x)^4","A"
716,1,13,12,0.073000," ","int(csc(x)^2/(a+b*cot(x)),x)","-\frac{\ln \left(a +b \cot \left(x \right)\right)}{b}"," ",0,"-ln(a+b*cot(x))/b","A"
717,1,21,20,0.080000," ","int((a+b*cot(x))^n*csc(x)^2,x)","-\frac{\left(a +b \cot \left(x \right)\right)^{n +1}}{b \left(n +1\right)}"," ",0,"-(a+b*cot(x))^(n+1)/b/(n+1)","A"
718,1,7,6,0.064000," ","int(csc(x)^2*(1+sin(x)^2),x)","x -\cot \left(x \right)"," ",0,"x-cot(x)","A"
719,1,7,6,0.088000," ","int((1+1/(1+cot(x)^2))*csc(x)^2,x)","x -\cot \left(x \right)"," ",0,"x-cot(x)","A"
720,1,56,28,0.103000," ","int((a+b*cot(x))*csc(x)^2/(c+d*cot(x)),x)","-\frac{b}{d \tan \left(x \right)}+\frac{\ln \left(\tan \left(x \right)\right) a}{d}-\frac{\ln \left(\tan \left(x \right)\right) c b}{d^{2}}-\frac{\ln \left(c \tan \left(x \right)+d \right) a}{d}+\frac{\ln \left(c \tan \left(x \right)+d \right) c b}{d^{2}}"," ",0,"-b/d/tan(x)+1/d*ln(tan(x))*a-1/d^2*ln(tan(x))*c*b-1/d*ln(c*tan(x)+d)*a+1/d^2*ln(c*tan(x)+d)*c*b","A"
721,1,119,51,0.131000," ","int((a+b*cot(x))^2*csc(x)^2/(c+d*cot(x)),x)","-\frac{b^{2}}{2 d \tan \left(x \right)^{2}}+\frac{\ln \left(\tan \left(x \right)\right) a^{2}}{d}-\frac{2 \ln \left(\tan \left(x \right)\right) a b c}{d^{2}}+\frac{\ln \left(\tan \left(x \right)\right) b^{2} c^{2}}{d^{3}}-\frac{2 b a}{d \tan \left(x \right)}+\frac{b^{2} c}{d^{2} \tan \left(x \right)}-\frac{\ln \left(c \tan \left(x \right)+d \right) a^{2}}{d}+\frac{2 \ln \left(c \tan \left(x \right)+d \right) a b c}{d^{2}}-\frac{\ln \left(c \tan \left(x \right)+d \right) b^{2} c^{2}}{d^{3}}"," ",0,"-1/2*b^2/d/tan(x)^2+1/d*ln(tan(x))*a^2-2/d^2*ln(tan(x))*a*b*c+1/d^3*ln(tan(x))*b^2*c^2-2*b/d/tan(x)*a+b^2/d^2/tan(x)*c-1/d*ln(c*tan(x)+d)*a^2+2/d^2*ln(c*tan(x)+d)*a*b*c-1/d^3*ln(c*tan(x)+d)*b^2*c^2","B"
722,1,202,74,0.164000," ","int((a+b*cot(x))^3*csc(x)^2/(c+d*cot(x)),x)","-\frac{b^{3}}{3 d \tan \left(x \right)^{3}}+\frac{\ln \left(\tan \left(x \right)\right) a^{3}}{d}-\frac{3 \ln \left(\tan \left(x \right)\right) a^{2} b c}{d^{2}}+\frac{3 \ln \left(\tan \left(x \right)\right) a \,b^{2} c^{2}}{d^{3}}-\frac{\ln \left(\tan \left(x \right)\right) b^{3} c^{3}}{d^{4}}-\frac{3 b \,a^{2}}{d \tan \left(x \right)}+\frac{3 b^{2} a c}{d^{2} \tan \left(x \right)}-\frac{b^{3} c^{2}}{d^{3} \tan \left(x \right)}-\frac{3 b^{2} a}{2 d \tan \left(x \right)^{2}}+\frac{b^{3} c}{2 d^{2} \tan \left(x \right)^{2}}-\frac{\ln \left(c \tan \left(x \right)+d \right) a^{3}}{d}+\frac{3 \ln \left(c \tan \left(x \right)+d \right) a^{2} b c}{d^{2}}-\frac{3 \ln \left(c \tan \left(x \right)+d \right) a \,b^{2} c^{2}}{d^{3}}+\frac{\ln \left(c \tan \left(x \right)+d \right) b^{3} c^{3}}{d^{4}}"," ",0,"-1/3*b^3/d/tan(x)^3+1/d*ln(tan(x))*a^3-3/d^2*ln(tan(x))*a^2*b*c+3/d^3*ln(tan(x))*a*b^2*c^2-1/d^4*ln(tan(x))*b^3*c^3-3*b/d/tan(x)*a^2+3*b^2/d^2/tan(x)*a*c-b^3/d^3/tan(x)*c^2-3/2*b^2/d/tan(x)^2*a+1/2*b^3/d^2/tan(x)^2*c-1/d*ln(c*tan(x)+d)*a^3+3/d^2*ln(c*tan(x)+d)*a^2*b*c-3/d^3*ln(c*tan(x)+d)*a*b^2*c^2+1/d^4*ln(c*tan(x)+d)*b^3*c^3","B"
723,1,6,5,0.049000," ","int(csc(x)^2/exp(cot(x)),x)","{\mathrm e}^{-\cot \left(x \right)}"," ",0,"1/exp(cot(x))","A"
724,1,12,11,0.040000," ","int(sec(x)*tan(x)/(a+b*sec(x)),x)","\frac{\ln \left(a +b \sec \left(x \right)\right)}{b}"," ",0,"ln(a+b*sec(x))/b","A"
725,1,4,5,0.070000," ","int(sec(x)*tan(x)/(1+sec(x)^2),x)","\arctan \left(\sec \left(x \right)\right)"," ",0,"arctan(sec(x))","A"
726,1,8,7,0.059000," ","int(sec(x)*tan(x)/(9+4*sec(x)^2),x)","\frac{\arctan \left(\frac{2 \sec \left(x \right)}{3}\right)}{6}"," ",0,"1/6*arctan(2/3*sec(x))","A"
727,1,12,7,0.082000," ","int(sec(x)*tan(x)/(sec(x)+sec(x)^2),x)","\ln \left(\sec \left(x \right)\right)-\ln \left(1+\sec \left(x \right)\right)"," ",0,"ln(sec(x))-ln(1+sec(x))","A"
728,1,6,5,0.099000," ","int(sec(x)*tan(x)/(4+sec(x)^2)^(1/2),x)","\arcsinh \left(\frac{\sec \left(x \right)}{2}\right)"," ",0,"arcsinh(1/2*sec(x))","A"
729,1,25,11,0.109000," ","int(sec(x)*tan(x)/(1+cos(x)^2)^(1/2),x)","\frac{1+\sec^{2}\left(x \right)}{\sqrt{\frac{1+\sec^{2}\left(x \right)}{\sec \left(x \right)^{2}}}\, \sec \left(x \right)}"," ",0,"1/((1+sec(x)^2)/sec(x)^2)^(1/2)/sec(x)*(1+sec(x)^2)","B"
730,1,4,3,0.020000," ","int(exp(sec(x))*sec(x)*tan(x),x)","{\mathrm e}^{\sec \left(x \right)}"," ",0,"exp(sec(x))","A"
731,1,10,9,0.022000," ","int(2^sec(x)*sec(x)*tan(x),x)","\frac{2^{\sec \left(x \right)}}{\ln \left(2\right)}"," ",0,"2^sec(x)/ln(2)","A"
732,1,11,10,0.076000," ","int(sec(2*x)*tan(2*x)/(1+sec(2*x))^(3/2),x)","-\frac{1}{\sqrt{1+\sec \left(2 x \right)}}"," ",0,"-1/(1+sec(2*x))^(1/2)","A"
733,1,65,33,0.116000," ","int(sec(3*x)*(1+5*cos(3*x)^2)^(1/2)*tan(3*x),x)","\frac{\sqrt{\frac{\sec^{2}\left(3 x \right)+5}{\sec \left(3 x \right)^{2}}}\, \sec \left(3 x \right) \left(\sqrt{\sec^{2}\left(3 x \right)+5}-\sqrt{5}\, \arctanh \left(\frac{\sqrt{5}}{\sqrt{\sec^{2}\left(3 x \right)+5}}\right)\right)}{3 \sqrt{\sec^{2}\left(3 x \right)+5}}"," ",0,"1/3*((sec(3*x)^2+5)/sec(3*x)^2)^(1/2)*sec(3*x)/(sec(3*x)^2+5)^(1/2)*((sec(3*x)^2+5)^(1/2)-5^(1/2)*arctanh(5^(1/2)/(sec(3*x)^2+5)^(1/2)))","A"
734,1,34,18,0.114000," ","int(sec(3*x)*tan(3*x)/(1+5*cos(3*x)^2)^(1/2),x)","\frac{\sec^{2}\left(3 x \right)+5}{3 \sqrt{\frac{\sec^{2}\left(3 x \right)+5}{\sec \left(3 x \right)^{2}}}\, \sec \left(3 x \right)}"," ",0,"1/3/((sec(3*x)^2+5)/sec(3*x)^2)^(1/2)/sec(3*x)*(sec(3*x)^2+5)","A"
735,1,13,12,0.049000," ","int(cot(x)*csc(x)/(a+b*csc(x)),x)","-\frac{\ln \left(a +b \csc \left(x \right)\right)}{b}"," ",0,"-ln(a+b*csc(x))/b","A"
736,1,13,12,0.036000," ","int(5^csc(3*x)*cot(3*x)*csc(3*x),x)","-\frac{5^{\csc \left(3 x \right)}}{3 \ln \left(5\right)}"," ",0,"-1/3*5^csc(3*x)/ln(5)","A"
737,1,6,3,0.053000," ","int(cot(x)*csc(x)/(1+csc(x)^2),x)","-\arctan \left(\csc \left(x \right)\right)"," ",0,"-arctan(csc(x))","A"
738,1,35,34,0.080000," ","int(cot(6*x)*csc(6*x)/(5-11*csc(6*x)^2)^2,x)","\frac{\csc \left(6 x \right)}{660 \left(\csc^{2}\left(6 x \right)\right)-300}-\frac{\sqrt{55}\, \arctanh \left(\frac{\csc \left(6 x \right) \sqrt{55}}{5}\right)}{3300}"," ",0,"1/60*csc(6*x)/(11*csc(6*x)^2-5)-1/3300*55^(1/2)*arctanh(1/5*csc(6*x)*55^(1/2))","A"
739,1,15,12,0.164000," ","int(cot(x)*csc(x)/(1+sin(x)^2)^(1/2),x)","-\frac{\sqrt{1+\sin^{2}\left(x \right)}}{\sin \left(x \right)}"," ",0,"-1/sin(x)*(1+sin(x)^2)^(1/2)","A"
740,1,38,35,0.237000," ","int(cot(5*x)*csc(5*x)^3/(1+sin(5*x)^2)^(1/2),x)","-\frac{\sqrt{1+\sin^{2}\left(5 x \right)}}{15 \sin \left(5 x \right)^{3}}+\frac{2 \sqrt{1+\sin^{2}\left(5 x \right)}}{15 \sin \left(5 x \right)}"," ",0,"-1/15/sin(5*x)^3*(1+sin(5*x)^2)^(1/2)+2/15/sin(5*x)*(1+sin(5*x)^2)^(1/2)","A"
741,1,104,41,0.144000," ","int(exp(n*sin(b*x+a))*sin(2*b*x+2*a),x)","-\frac{i {\mathrm e}^{n \sin \left(b x \right) \cos \left(a \right)+n \cos \left(b x \right) \sin \left(a \right)} {\mathrm e}^{i b x} {\mathrm e}^{i a}}{n b}+\frac{i {\mathrm e}^{n \sin \left(b x \right) \cos \left(a \right)+n \cos \left(b x \right) \sin \left(a \right)} {\mathrm e}^{-i b x} {\mathrm e}^{-i a}}{n b}-\frac{2 \,{\mathrm e}^{n \left(\sin \left(b x \right) \cos \left(a \right)+\cos \left(b x \right) \sin \left(a \right)\right)}}{n^{2} b}"," ",0,"-I/n/b*exp(n*sin(b*x)*cos(a)+n*cos(b*x)*sin(a))*exp(I*b*x)*exp(I*a)+I/n/b*exp(n*sin(b*x)*cos(a)+n*cos(b*x)*sin(a))*exp(-I*b*x)*exp(-I*a)-2/n^2/b*exp(n*(sin(b*x)*cos(a)+cos(b*x)*sin(a)))","C"
742,1,104,41,0.000000," ","int(exp(n*sin(b*x+a))*sin(2*b*x+2*a),x)","-\frac{i {\mathrm e}^{n \sin \left(b x \right) \cos \left(a \right)+n \cos \left(b x \right) \sin \left(a \right)} {\mathrm e}^{i b x} {\mathrm e}^{i a}}{n b}+\frac{i {\mathrm e}^{n \sin \left(b x \right) \cos \left(a \right)+n \cos \left(b x \right) \sin \left(a \right)} {\mathrm e}^{-i b x} {\mathrm e}^{-i a}}{n b}-\frac{2 \,{\mathrm e}^{n \left(\sin \left(b x \right) \cos \left(a \right)+\cos \left(b x \right) \sin \left(a \right)\right)}}{n^{2} b}"," ",0,"-I/n/b*exp(n*sin(b*x)*cos(a)+n*cos(b*x)*sin(a))*exp(I*b*x)*exp(I*a)+I/n/b*exp(n*sin(b*x)*cos(a)+n*cos(b*x)*sin(a))*exp(-I*b*x)*exp(-I*a)-2/n^2/b*exp(n*(sin(b*x)*cos(a)+cos(b*x)*sin(a)))","C"
743,1,122,50,0.130000," ","int(exp(n*sin(1/2*b*x+1/2*a))*sin(b*x+a),x)","\frac{2 i {\mathrm e}^{n \sin \left(\frac{b x}{2}\right) \cos \left(\frac{a}{2}\right)+n \cos \left(\frac{b x}{2}\right) \sin \left(\frac{a}{2}\right)} {\mathrm e}^{-\frac{i b x}{2}} {\mathrm e}^{-\frac{i a}{2}}}{n b}-\frac{2 i {\mathrm e}^{n \sin \left(\frac{b x}{2}\right) \cos \left(\frac{a}{2}\right)+n \cos \left(\frac{b x}{2}\right) \sin \left(\frac{a}{2}\right)} {\mathrm e}^{\frac{i b x}{2}} {\mathrm e}^{\frac{i a}{2}}}{n b}-\frac{4 \,{\mathrm e}^{n \left(\sin \left(\frac{b x}{2}\right) \cos \left(\frac{a}{2}\right)+\cos \left(\frac{b x}{2}\right) \sin \left(\frac{a}{2}\right)\right)}}{n^{2} b}"," ",0,"2*I/n/b*exp(n*sin(1/2*b*x)*cos(1/2*a)+n*cos(1/2*b*x)*sin(1/2*a))*exp(-1/2*I*b*x)*exp(-1/2*I*a)-2*I/n/b*exp(n*sin(1/2*b*x)*cos(1/2*a)+n*cos(1/2*b*x)*sin(1/2*a))*exp(1/2*I*b*x)*exp(1/2*I*a)-4/n^2/b*exp(n*(sin(1/2*b*x)*cos(1/2*a)+cos(1/2*b*x)*sin(1/2*a)))","C"
744,1,122,50,0.001000," ","int(exp(n*sin(1/2*b*x+1/2*a))*sin(b*x+a),x)","\frac{2 i {\mathrm e}^{n \sin \left(\frac{b x}{2}\right) \cos \left(\frac{a}{2}\right)+n \cos \left(\frac{b x}{2}\right) \sin \left(\frac{a}{2}\right)} {\mathrm e}^{-\frac{i b x}{2}} {\mathrm e}^{-\frac{i a}{2}}}{n b}-\frac{2 i {\mathrm e}^{n \sin \left(\frac{b x}{2}\right) \cos \left(\frac{a}{2}\right)+n \cos \left(\frac{b x}{2}\right) \sin \left(\frac{a}{2}\right)} {\mathrm e}^{\frac{i b x}{2}} {\mathrm e}^{\frac{i a}{2}}}{n b}-\frac{4 \,{\mathrm e}^{n \left(\sin \left(\frac{b x}{2}\right) \cos \left(\frac{a}{2}\right)+\cos \left(\frac{b x}{2}\right) \sin \left(\frac{a}{2}\right)\right)}}{n^{2} b}"," ",0,"2*I/n/b*exp(n*sin(1/2*b*x)*cos(1/2*a)+n*cos(1/2*b*x)*sin(1/2*a))*exp(-1/2*I*b*x)*exp(-1/2*I*a)-2*I/n/b*exp(n*sin(1/2*b*x)*cos(1/2*a)+n*cos(1/2*b*x)*sin(1/2*a))*exp(1/2*I*b*x)*exp(1/2*I*a)-4/n^2/b*exp(n*(sin(1/2*b*x)*cos(1/2*a)+cos(1/2*b*x)*sin(1/2*a)))","C"
745,1,105,41,0.109000," ","int(exp(n*cos(b*x+a))*sin(2*b*x+2*a),x)","-\frac{{\mathrm e}^{n \cos \left(b x \right) \cos \left(a \right)-n \sin \left(b x \right) \sin \left(a \right)} {\mathrm e}^{i b x} {\mathrm e}^{i a}}{b n}-\frac{{\mathrm e}^{n \cos \left(b x \right) \cos \left(a \right)-n \sin \left(b x \right) \sin \left(a \right)} {\mathrm e}^{-i b x} {\mathrm e}^{-i a}}{b n}+\frac{2 \,{\mathrm e}^{n \left(\cos \left(b x \right) \cos \left(a \right)-\sin \left(b x \right) \sin \left(a \right)\right)}}{b \,n^{2}}"," ",0,"-1/b/n*exp(n*cos(b*x)*cos(a)-n*sin(b*x)*sin(a))*exp(I*b*x)*exp(I*a)-1/b/n*exp(n*cos(b*x)*cos(a)-n*sin(b*x)*sin(a))*exp(-I*b*x)*exp(-I*a)+2/b/n^2*exp(n*(cos(b*x)*cos(a)-sin(b*x)*sin(a)))","C"
746,1,105,41,0.000000," ","int(exp(n*cos(b*x+a))*sin(2*b*x+2*a),x)","-\frac{{\mathrm e}^{n \cos \left(b x \right) \cos \left(a \right)-n \sin \left(b x \right) \sin \left(a \right)} {\mathrm e}^{i b x} {\mathrm e}^{i a}}{b n}-\frac{{\mathrm e}^{n \cos \left(b x \right) \cos \left(a \right)-n \sin \left(b x \right) \sin \left(a \right)} {\mathrm e}^{-i b x} {\mathrm e}^{-i a}}{b n}+\frac{2 \,{\mathrm e}^{n \left(\cos \left(b x \right) \cos \left(a \right)-\sin \left(b x \right) \sin \left(a \right)\right)}}{b \,n^{2}}"," ",0,"-1/b/n*exp(n*cos(b*x)*cos(a)-n*sin(b*x)*sin(a))*exp(I*b*x)*exp(I*a)-1/b/n*exp(n*cos(b*x)*cos(a)-n*sin(b*x)*sin(a))*exp(-I*b*x)*exp(-I*a)+2/b/n^2*exp(n*(cos(b*x)*cos(a)-sin(b*x)*sin(a)))","C"
747,1,123,50,0.122000," ","int(exp(n*cos(1/2*b*x+1/2*a))*sin(b*x+a),x)","-\frac{2 \,{\mathrm e}^{n \cos \left(\frac{b x}{2}\right) \cos \left(\frac{a}{2}\right)-n \sin \left(\frac{b x}{2}\right) \sin \left(\frac{a}{2}\right)} {\mathrm e}^{\frac{i b x}{2}} {\mathrm e}^{\frac{i a}{2}}}{b n}-\frac{2 \,{\mathrm e}^{n \cos \left(\frac{b x}{2}\right) \cos \left(\frac{a}{2}\right)-n \sin \left(\frac{b x}{2}\right) \sin \left(\frac{a}{2}\right)} {\mathrm e}^{-\frac{i b x}{2}} {\mathrm e}^{-\frac{i a}{2}}}{b n}+\frac{4 \,{\mathrm e}^{n \left(\cos \left(\frac{b x}{2}\right) \cos \left(\frac{a}{2}\right)-\sin \left(\frac{b x}{2}\right) \sin \left(\frac{a}{2}\right)\right)}}{b \,n^{2}}"," ",0,"-2/b/n*exp(n*cos(1/2*b*x)*cos(1/2*a)-n*sin(1/2*b*x)*sin(1/2*a))*exp(1/2*I*b*x)*exp(1/2*I*a)-2/b/n*exp(n*cos(1/2*b*x)*cos(1/2*a)-n*sin(1/2*b*x)*sin(1/2*a))*exp(-1/2*I*b*x)*exp(-1/2*I*a)+4/b/n^2*exp(n*(cos(1/2*b*x)*cos(1/2*a)-sin(1/2*b*x)*sin(1/2*a)))","C"
748,1,123,50,0.000000," ","int(exp(n*cos(1/2*b*x+1/2*a))*sin(b*x+a),x)","-\frac{2 \,{\mathrm e}^{n \cos \left(\frac{b x}{2}\right) \cos \left(\frac{a}{2}\right)-n \sin \left(\frac{b x}{2}\right) \sin \left(\frac{a}{2}\right)} {\mathrm e}^{\frac{i b x}{2}} {\mathrm e}^{\frac{i a}{2}}}{b n}-\frac{2 \,{\mathrm e}^{n \cos \left(\frac{b x}{2}\right) \cos \left(\frac{a}{2}\right)-n \sin \left(\frac{b x}{2}\right) \sin \left(\frac{a}{2}\right)} {\mathrm e}^{-\frac{i b x}{2}} {\mathrm e}^{-\frac{i a}{2}}}{b n}+\frac{4 \,{\mathrm e}^{n \left(\cos \left(\frac{b x}{2}\right) \cos \left(\frac{a}{2}\right)-\sin \left(\frac{b x}{2}\right) \sin \left(\frac{a}{2}\right)\right)}}{b \,n^{2}}"," ",0,"-2/b/n*exp(n*cos(1/2*b*x)*cos(1/2*a)-n*sin(1/2*b*x)*sin(1/2*a))*exp(1/2*I*b*x)*exp(1/2*I*a)-2/b/n*exp(n*cos(1/2*b*x)*cos(1/2*a)-n*sin(1/2*b*x)*sin(1/2*a))*exp(-1/2*I*b*x)*exp(-1/2*I*a)+4/b/n^2*exp(n*(cos(1/2*b*x)*cos(1/2*a)-sin(1/2*b*x)*sin(1/2*a)))","C"
749,1,8,7,0.079000," ","int(csc(x)*ln(tan(x))*sec(x),x)","\frac{\ln \left(\tan \left(x \right)\right)^{2}}{2}"," ",0,"1/2*ln(tan(x))^2","A"
750,1,8,7,0.062000," ","int(csc(2*x)*ln(tan(x)),x)","\frac{\ln \left(\tan \left(x \right)\right)^{2}}{4}"," ",0,"1/4*ln(tan(x))^2","A"
751,1,5,3,0.060000," ","int(exp(cos(x)^2+sin(x)^2),x)","{\mathrm e} x"," ",0,"exp(1)*x","C"
752,1,9,8,0.024000," ","int(x*sec(x)^2,x)","\ln \left(\cos \left(x \right)\right)+x \tan \left(x \right)"," ",0,"ln(cos(x))+x*tan(x)","A"
753,1,26,28,0.069000," ","int(x*cos(x^2)^4,x)","\frac{\left(\cos^{3}\left(x^{2}\right)+\frac{3 \cos \left(x^{2}\right)}{2}\right) \sin \left(x^{2}\right)}{8}+\frac{3 x^{2}}{16}"," ",0,"1/8*(cos(x^2)^3+3/2*cos(x^2))*sin(x^2)+3/16*x^2","A"
754,1,7,6,0.017000," ","int(sin(x)*cos(x)^(1/2),x)","-\frac{2 \left(\cos^{\frac{3}{2}}\left(x \right)\right)}{3}"," ",0,"-2/3*cos(x)^(3/2)","A"
755,1,9,8,0.049000," ","int(tan(exp(-2*x))/exp(2*x),x)","\frac{\ln \left(\cos \left({\mathrm e}^{-2 x}\right)\right)}{2}"," ",0,"1/2*ln(cos(exp(-2*x)))","A"
756,1,8,7,0.078000," ","int(sec(x)*sin(2*x)/(1+cos(x)),x)","-2 \ln \left(1+\cos \left(x \right)\right)"," ",0,"-2*ln(1+cos(x))","A"
757,1,16,15,0.025000," ","int(x*sec(3*x)^2,x)","\frac{\ln \left(\cos \left(3 x \right)\right)}{9}+\frac{x \tan \left(3 x \right)}{3}"," ",0,"1/9*ln(cos(3*x))+1/3*x*tan(3*x)","A"
758,1,31,35,0.058000," ","int(cos(2*Pi*x)/exp(2*Pi*x),x)","\frac{-\frac{{\mathrm e}^{-2 \pi  x} \cos \left(2 \pi  x \right)}{2}+\frac{{\mathrm e}^{-2 \pi  x} \sin \left(2 \pi  x \right)}{2}}{2 \pi}"," ",0,"1/2/Pi*(-1/2*exp(-2*Pi*x)*cos(2*Pi*x)+1/2*exp(-2*Pi*x)*sin(2*Pi*x))","A"
759,1,176,10,0.205000," ","int(cos(x)^12*sin(x)^10-cos(x)^10*sin(x)^12,x)","-\frac{\left(\cos^{13}\left(x \right)\right) \left(\sin^{9}\left(x \right)\right)}{22}-\frac{9 \left(\sin^{7}\left(x \right)\right) \left(\cos^{13}\left(x \right)\right)}{440}-\frac{7 \left(\sin^{5}\left(x \right)\right) \left(\cos^{13}\left(x \right)\right)}{880}-\frac{7 \left(\sin^{3}\left(x \right)\right) \left(\cos^{13}\left(x \right)\right)}{2816}-\frac{3 \sin \left(x \right) \left(\cos^{13}\left(x \right)\right)}{5632}+\frac{\left(\cos^{11}\left(x \right)+\frac{11 \left(\cos^{9}\left(x \right)\right)}{10}+\frac{99 \left(\cos^{7}\left(x \right)\right)}{80}+\frac{231 \left(\cos^{5}\left(x \right)\right)}{160}+\frac{231 \left(\cos^{3}\left(x \right)\right)}{128}+\frac{693 \cos \left(x \right)}{256}\right) \sin \left(x \right)}{22528}+\frac{\left(\cos^{11}\left(x \right)\right) \left(\sin^{11}\left(x \right)\right)}{22}+\frac{\left(\sin^{9}\left(x \right)\right) \left(\cos^{11}\left(x \right)\right)}{40}+\frac{\left(\sin^{7}\left(x \right)\right) \left(\cos^{11}\left(x \right)\right)}{80}+\frac{7 \left(\sin^{5}\left(x \right)\right) \left(\cos^{11}\left(x \right)\right)}{1280}+\frac{\left(\sin^{3}\left(x \right)\right) \left(\cos^{11}\left(x \right)\right)}{512}+\frac{\sin \left(x \right) \left(\cos^{11}\left(x \right)\right)}{2048}-\frac{\left(\cos^{9}\left(x \right)+\frac{9 \left(\cos^{7}\left(x \right)\right)}{8}+\frac{21 \left(\cos^{5}\left(x \right)\right)}{16}+\frac{105 \left(\cos^{3}\left(x \right)\right)}{64}+\frac{315 \cos \left(x \right)}{128}\right) \sin \left(x \right)}{20480}"," ",0,"-1/22*cos(x)^13*sin(x)^9-9/440*sin(x)^7*cos(x)^13-7/880*sin(x)^5*cos(x)^13-7/2816*sin(x)^3*cos(x)^13-3/5632*sin(x)*cos(x)^13+1/22528*(cos(x)^11+11/10*cos(x)^9+99/80*cos(x)^7+231/160*cos(x)^5+231/128*cos(x)^3+693/256*cos(x))*sin(x)+1/22*cos(x)^11*sin(x)^11+1/40*sin(x)^9*cos(x)^11+1/80*sin(x)^7*cos(x)^11+7/1280*sin(x)^5*cos(x)^11+1/512*sin(x)^3*cos(x)^11+1/2048*sin(x)*cos(x)^11-1/20480*(cos(x)^9+9/8*cos(x)^7+21/16*cos(x)^5+105/64*cos(x)^3+315/128*cos(x))*sin(x)","B"
760,1,8,7,0.003000," ","int(x*cot(x^2),x)","\frac{\ln \left(\sin \left(x^{2}\right)\right)}{2}"," ",0,"1/2*ln(sin(x^2))","A"
761,1,7,6,0.030000," ","int(x*sec(x^2)^2,x)","\frac{\tan \left(x^{2}\right)}{2}"," ",0,"1/2*tan(x^2)","A"
762,1,12,11,0.172000," ","int(sin(8*x)/(9+sin(4*x)^4),x)","\frac{\arctan \left(\frac{\left(\sin^{2}\left(4 x \right)\right)}{3}\right)}{12}"," ",0,"1/12*arctan(1/3*sin(4*x)^2)","A"
763,1,16,15,0.040000," ","int(cos(2*x)/(8+sin(2*x)^2),x)","\frac{\arctan \left(\frac{\sin \left(2 x \right) \sqrt{2}}{4}\right) \sqrt{2}}{8}"," ",0,"1/8*arctan(1/4*sin(2*x)*2^(1/2))*2^(1/2)","A"
764,1,30,29,0.171000," ","int(x*(cos(x^2)^3-sin(x^2)^3),x)","\frac{\left(2+\cos^{2}\left(x^{2}\right)\right) \sin \left(x^{2}\right)}{6}+\frac{\left(2+\sin^{2}\left(x^{2}\right)\right) \cos \left(x^{2}\right)}{6}"," ",0,"1/6*(2+cos(x^2)^2)*sin(x^2)+1/6*(2+sin(x^2)^2)*cos(x^2)","A"
765,1,9,10,0.040000," ","int(cos(x)*sin(x)/(1-cos(x)),x)","\cos \left(x \right)+\ln \left(-1+\cos \left(x \right)\right)"," ",0,"cos(x)+ln(-1+cos(x))","A"
766,1,7,6,0.039000," ","int(x*cos(x^2),x)","\frac{\sin \left(x^{2}\right)}{2}"," ",0,"1/2*sin(x^2)","A"
767,1,9,8,0.039000," ","int(x^2*cos(4*x^3),x)","\frac{\sin \left(4 x^{3}\right)}{12}"," ",0,"1/12*sin(4*x^3)","A"
768,1,7,6,0.039000," ","int(x^3*cos(x^4),x)","\frac{\sin \left(x^{4}\right)}{4}"," ",0,"1/4*sin(x^4)","A"
769,1,9,8,0.004000," ","int(x*sin(1/2*x^2),x)","-\cos \left(\frac{x^{2}}{2}\right)"," ",0,"-cos(1/2*x^2)","A"
770,1,7,6,0.026000," ","int(x*sec(x^2)*tan(x^2),x)","\frac{\sec \left(x^{2}\right)}{2}"," ",0,"1/2*sec(x^2)","A"
771,1,11,10,0.006000," ","int(tan(1/x)^2/x^2,x)","\frac{1}{x}-\tan \left(\frac{1}{x}\right)"," ",0,"1/x-tan(1/x)","A"
772,1,10,9,0.002000," ","int(x*tan(x^2+1),x)","-\frac{\ln \left(\cos \left(x^{2}+1\right)\right)}{2}"," ",0,"-1/2*ln(cos(x^2+1))","A"
773,1,11,10,0.039000," ","int(sin(Pi*(1+2*x)),x)","\frac{\cos \left(2 \pi  x \right)}{2 \pi}"," ",0,"1/2*cos(2*Pi*x)/Pi","A"
774,1,20,17,0.150000," ","int((cot(x)+csc(x)^2)/(1-cos(x)^2),x)","-\frac{1}{2 \tan \left(x \right)^{2}}-\frac{1}{\tan \left(x \right)}-\frac{1}{3 \tan \left(x \right)^{3}}"," ",0,"-1/2/tan(x)^2-1/tan(x)-1/3/tan(x)^3","A"
775,1,16,15,0.230000," ","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}"," ",0,"1/6*sin(x^3)+1/54*sin(9*x^3)","A"
776,1,33,43,0.029000," ","int(x^14*sin(x^3),x)","\left(-\frac{1}{3} x^{12}+4 x^{6}-8\right) \cos \left(x^{3}\right)+\frac{4 x^{3} \left(x^{6}-6\right) \sin \left(x^{3}\right)}{3}"," ",0,"(-1/3*x^12+4*x^6-8)*cos(x^3)+4/3*x^3*(x^6-6)*sin(x^3)","A"
777,1,36,33,0.026000," ","int(x^2*sin(2*x^3)/exp(3*x^3),x)","\frac{\left(-\frac{2}{39}+\frac{2 \left(\tan^{2}\left(x^{3}\right)\right)}{39}-\frac{2 \tan \left(x^{3}\right)}{13}\right) {\mathrm e}^{-3 x^{3}}}{1+\tan^{2}\left(x^{3}\right)}"," ",0,"(-2/39+2/39*tan(x^3)^2-2/13*tan(x^3))/(1+tan(x^3)^2)/exp(3*x^3)","A"
778,1,5,4,0.001000," ","int(2*x*cos(x^2),x)","\sin \left(x^{2}\right)"," ",0,"sin(x^2)","A"
779,1,7,6,0.040000," ","int(3*x^2*cos(x^3+7),x)","\sin \left(x^{3}+7\right)"," ",0,"sin(x^3+7)","A"
780,1,8,7,0.001000," ","int(1/(x^2+1)+sin(x),x)","\arctan \left(x \right)-\cos \left(x \right)"," ",0,"arctan(x)-cos(x)","A"
781,1,9,8,0.004000," ","int(x*sin(x^2+1),x)","-\frac{\cos \left(x^{2}+1\right)}{2}"," ",0,"-1/2*cos(x^2+1)","A"
782,1,9,8,0.040000," ","int(x*cos(x^2+1),x)","\frac{\sin \left(x^{2}+1\right)}{2}"," ",0,"1/2*sin(x^2+1)","A"
783,1,9,8,0.001000," ","int(1+x^2*cos(x^3),x)","x +\frac{\sin \left(x^{3}\right)}{3}"," ",0,"x+1/3*sin(x^3)","A"
784,1,9,8,0.004000," ","int(x^2*sin(x^3+1),x)","-\frac{\cos \left(x^{3}+1\right)}{3}"," ",0,"-1/3*cos(x^3+1)","A"
785,1,7,6,0.000000," ","int(12*x^2*cos(x^3),x)","4 \sin \left(x^{3}\right)"," ",0,"4*sin(x^3)","A"
786,1,15,14,0.028000," ","int((1+x)*sin(1+x),x)","-\left(1+x \right) \cos \left(1+x \right)+\sin \left(1+x \right)"," ",0,"-(1+x)*cos(1+x)+sin(1+x)","A"
787,1,17,16,0.053000," ","int(x^5*cos(x^3),x)","\frac{\cos \left(x^{3}\right)}{3}+\frac{x^{3} \sin \left(x^{3}\right)}{3}"," ",0,"1/3*cos(x^3)+1/3*x^3*sin(x^3)","A"
788,1,18,21,0.025000," ","int(cos(x)/exp(3*x),x)","-\frac{3 \,{\mathrm e}^{-3 x} \cos \left(x \right)}{10}+\frac{{\mathrm e}^{-3 x} \sin \left(x \right)}{10}"," ",0,"-3/10*exp(-3*x)*cos(x)+1/10*exp(-3*x)*sin(x)","A"
789,1,17,16,0.005000," ","int(x^3*sin(x^2),x)","-\frac{x^{2} \cos \left(x^{2}\right)}{2}+\frac{\sin \left(x^{2}\right)}{2}"," ",0,"-1/2*x^2*cos(x^2)+1/2*sin(x^2)","A"
790,1,17,16,0.039000," ","int(x^3*cos(x^2),x)","\frac{\cos \left(x^{2}\right)}{2}+\frac{x^{2} \sin \left(x^{2}\right)}{2}"," ",0,"1/2*cos(x^2)+1/2*x^2*sin(x^2)","A"
791,1,8,7,0.033000," ","int(cos(x)*cos(2*sin(x)),x)","\frac{\sin \left(2 \sin \left(x \right)\right)}{2}"," ",0,"1/2*sin(2*sin(x))","A"
792,1,10,9,0.032000," ","int(cos(x)*sin(x)/(1+cos(x)^2),x)","-\frac{\ln \left(1+\cos^{2}\left(x \right)\right)}{2}"," ",0,"-1/2*ln(1+cos(x)^2)","A"
793,1,65,8,0.089000," ","int((1+cos(x))*(x+sin(x))^3,x)","x^{3} \sin \left(x \right)-\frac{3 \left(\cos^{2}\left(x \right)\right) x^{2}}{2}+3 x \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)-\frac{3 x^{2}}{2}+x \left(\sin^{3}\left(x \right)\right)+\frac{\left(\sin^{4}\left(x \right)\right)}{4}+\frac{x^{4}}{4}+3 x \left(-\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)"," ",0,"x^3*sin(x)-3/2*cos(x)^2*x^2+3*x*(1/2*cos(x)*sin(x)+1/2*x)-3/2*x^2+x*sin(x)^3+1/4*sin(x)^4+1/4*x^4+3*x*(-1/2*cos(x)*sin(x)+1/2*x)","B"
794,1,12,9,0.065000," ","int((1+cos(x))*csc(x)^2,x)","-\frac{1}{\sin \left(x \right)}-\cot \left(x \right)"," ",0,"-1/sin(x)-cot(x)","A"
795,1,20,5,0.038000," ","int(sin(x)*tan(x)^2,x)","\frac{\sin^{4}\left(x \right)}{\cos \left(x \right)}+\left(2+\sin^{2}\left(x \right)\right) \cos \left(x \right)"," ",0,"sin(x)^4/cos(x)+(2+sin(x)^2)*cos(x)","B"
796,1,30,12,0.393000," ","int(exp(sin(x))*sec(x)^2*(x*cos(x)^3-sin(x)),x)","\frac{\left(x \,{\mathrm e}^{2 i x}+x -2 \,{\mathrm e}^{i x}\right) {\mathrm e}^{\sin \left(x \right)}}{{\mathrm e}^{2 i x}+1}"," ",0,"(x*exp(2*I*x)+x-2*exp(I*x))/(exp(2*I*x)+1)*exp(sin(x))","C"
797,1,10,9,0.026000," ","int(x*csc(x)^2,x)","-x \cot \left(x \right)+\ln \left(\sin \left(x \right)\right)"," ",0,"-x*cot(x)+ln(sin(x))","A"
798,1,15,14,0.146000," ","int(cos(x)*sin(1/6*Pi+x),x)","\frac{x}{4}-\frac{\cos \left(\frac{\pi}{6}+2 x \right)}{4}"," ",0,"1/4*x-1/4*cos(1/6*Pi+2*x)","A"
799,1,15,15,0.023000," ","int(x*sin(x^2)^3,x)","-\frac{\left(2+\sin^{2}\left(x^{2}\right)\right) \cos \left(x^{2}\right)}{6}"," ",0,"-1/6*(2+sin(x^2)^2)*cos(x^2)","A"
800,1,13,12,0.039000," ","int(sin(x)^2*tan(x),x)","-\frac{\left(\sin^{2}\left(x \right)\right)}{2}-\ln \left(\cos \left(x \right)\right)"," ",0,"-1/2*sin(x)^2-ln(cos(x))","A"
801,1,29,18,0.059000," ","int(cos(x)^2*cot(x)^3,x)","-\frac{\cos^{6}\left(x \right)}{2 \sin \left(x \right)^{2}}-\frac{\left(\cos^{4}\left(x \right)\right)}{2}-\left(\cos^{2}\left(x \right)\right)-2 \ln \left(\sin \left(x \right)\right)"," ",0,"-1/2/sin(x)^2*cos(x)^6-1/2*cos(x)^4-cos(x)^2-2*ln(sin(x))","A"
802,1,6,5,0.053000," ","int(sec(x)*(1-sin(x)),x)","\ln \left(1+\sin \left(x \right)\right)"," ",0,"ln(1+sin(x))","A"
803,1,6,7,0.050000," ","int((1+cos(x))*csc(x),x)","\ln \left(-1+\cos \left(x \right)\right)"," ",0,"ln(-1+cos(x))","A"
804,1,6,5,0.047000," ","int(cos(x)^2*(1-tan(x)^2),x)","\cos \left(x \right) \sin \left(x \right)"," ",0,"cos(x)*sin(x)","A"
805,1,20,11,0.263000," ","int(csc(2*x)*(cos(x)+sin(x)),x)","\frac{\ln \left(\sec \left(x \right)+\tan \left(x \right)\right)}{2}+\frac{\ln \left(\csc \left(x \right)-\cot \left(x \right)\right)}{2}"," ",0,"1/2*ln(sec(x)+tan(x))+1/2*ln(csc(x)-cot(x))","A"
806,1,12,11,0.053000," ","int(cos(x)*(-3+2*sin(x))/(2-3*sin(x)+sin(x)^2),x)","\ln \left(2-3 \sin \left(x \right)+\sin^{2}\left(x \right)\right)"," ",0,"ln(2-3*sin(x)+sin(x)^2)","A"
807,1,18,17,0.036000," ","int(cos(x)^2*sin(x)/(5+cos(x)^2),x)","-\cos \left(x \right)+\arctan \left(\frac{\cos \left(x \right) \sqrt{5}}{5}\right) \sqrt{5}"," ",0,"-cos(x)+arctan(1/5*cos(x)*5^(1/2))*5^(1/2)","A"
808,1,12,11,0.084000," ","int(cos(x)/(sin(x)+sin(x)^2),x)","\ln \left(\sin \left(x \right)\right)-\ln \left(1+\sin \left(x \right)\right)"," ",0,"ln(sin(x))-ln(1+sin(x))","A"
809,1,1856,22,0.750000," ","int(cos(x)/(sin(x)+sin(x)^(2^(1/2))),x)","\text{Expression too large to display}"," ",0,"-1/2*I*2^(1/2)*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))*csgn(I*(exp(I*x)-1))*csgn(I*(1+exp(I*x)))*Pi+1/2*I*2^(1/2)*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))*csgn(I*exp(-I*x))*Pi-2*ln(2)-I*Pi+1/2*I*2^(1/2)*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))^2*csgn(I*(exp(I*x)-1))*Pi+1/2*I*2^(1/2)*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))^2*csgn(I*(1+exp(I*x)))*Pi+1/2*I*2^(1/2)*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))^2*Pi+1/2*I*2^(1/2)*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))^2*csgn(I*exp(-I*x))*Pi-1/2*I*2^(1/2)*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))*csgn((1+exp(I*x))*(-1+exp(-I*x)))^2*Pi-1/2*I*2^(1/2)*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))*csgn((1+exp(I*x))*(-1+exp(-I*x)))*Pi+I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))*csgn(I*exp(-I*x))*Pi-I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))*csgn(I*(exp(I*x)-1))*csgn(I*(1+exp(I*x)))*Pi-1/2*I*2^(1/2)*Pi-I*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))*csgn((1+exp(I*x))*(-1+exp(-I*x)))^2*Pi-I*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))*csgn((1+exp(I*x))*(-1+exp(-I*x)))*Pi-I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))^3*Pi+I*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))^3*Pi+I*csgn((1+exp(I*x))*(-1+exp(-I*x)))^3*Pi+I*csgn((1+exp(I*x))*(-1+exp(-I*x)))^2*Pi-ln(exp(-1/2*2^(1/2)*(I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))*csgn(I*(exp(I*x)-1))*csgn(I*(1+exp(I*x)))*Pi+I*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))*csgn((1+exp(I*x))*(-1+exp(-I*x)))^2*Pi+I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))^3*Pi-I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))*csgn(I*exp(-I*x))*Pi-I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))^2*csgn(I*(1+exp(I*x)))*Pi+I*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))*csgn((1+exp(I*x))*(-1+exp(-I*x)))*Pi-I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))^2*csgn(I*(exp(I*x)-1))*Pi-I*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))^2*csgn(I*exp(-I*x))*Pi+I*Pi-I*csgn((1+exp(I*x))*(-1+exp(-I*x)))^2*Pi-I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))^2*Pi-I*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))^3*Pi-I*csgn((1+exp(I*x))*(-1+exp(-I*x)))^3*Pi+2*ln(exp(I*x))-2*ln(exp(I*x)-1)-2*ln(1+exp(I*x))+2*ln(2)))+sin(x))+2*ln(1+exp(I*x))-ln(exp(-1/2*2^(1/2)*(I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))*csgn(I*(exp(I*x)-1))*csgn(I*(1+exp(I*x)))*Pi+I*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))*csgn((1+exp(I*x))*(-1+exp(-I*x)))^2*Pi+I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))^3*Pi-I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))*csgn(I*exp(-I*x))*Pi-I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))^2*csgn(I*(1+exp(I*x)))*Pi+I*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))*csgn((1+exp(I*x))*(-1+exp(-I*x)))*Pi-I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))^2*csgn(I*(exp(I*x)-1))*Pi-I*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))^2*csgn(I*exp(-I*x))*Pi+I*Pi-I*csgn((1+exp(I*x))*(-1+exp(-I*x)))^2*Pi-I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))^2*Pi-I*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))^3*Pi-I*csgn((1+exp(I*x))*(-1+exp(-I*x)))^3*Pi+2*ln(exp(I*x))-2*ln(exp(I*x)-1)-2*ln(1+exp(I*x))+2*ln(2)))+sin(x))*2^(1/2)-1/2*I*2^(1/2)*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))^3*Pi+1/2*I*2^(1/2)*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))^3*Pi+1/2*I*2^(1/2)*csgn((1+exp(I*x))*(-1+exp(-I*x)))^3*Pi+1/2*I*2^(1/2)*csgn((1+exp(I*x))*(-1+exp(-I*x)))^2*Pi-2*ln(exp(I*x))+I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))^2*csgn(I*(exp(I*x)-1))*Pi+I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))^2*csgn(I*(1+exp(I*x)))*Pi+I*csgn(I*(exp(I*x)-1)*(1+exp(I*x)))*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))^2*Pi+I*csgn(I*(1+exp(I*x))*(-1+exp(-I*x)))^2*csgn(I*exp(-I*x))*Pi+2*ln(exp(I*x)-1)-2^(1/2)*ln(exp(I*x))+2^(1/2)*ln(exp(I*x)-1)+2^(1/2)*ln(1+exp(I*x))-2^(1/2)*ln(2)","C"
810,1,24,16,0.242000," ","int(1/(2*sin(x)+sin(2*x)),x)","\frac{\ln \left(-1+\cos \left(x \right)\right)}{8}+\frac{1}{4+4 \cos \left(x \right)}-\frac{\ln \left(1+\cos \left(x \right)\right)}{8}"," ",0,"1/8*ln(-1+cos(x))+1/4/(1+cos(x))-1/8*ln(1+cos(x))","A"
811,1,35,34,0.043000," ","int((x^2+4*x-3)*sin(2*x),x)","\frac{7 \cos \left(2 x \right)}{4}-2 x \cos \left(2 x \right)-\frac{x^{2} \cos \left(2 x \right)}{2}+\sin \left(2 x \right)+\frac{x \sin \left(2 x \right)}{2}"," ",0,"7/4*cos(2*x)-2*x*cos(2*x)-1/2*x^2*cos(2*x)+sin(2*x)+1/2*x*sin(2*x)","A"
812,1,22,25,0.028000," ","int(cos(4*x)/exp(3*x),x)","-\frac{3 \,{\mathrm e}^{-3 x} \cos \left(4 x \right)}{25}+\frac{4 \,{\mathrm e}^{-3 x} \sin \left(4 x \right)}{25}"," ",0,"-3/25*exp(-3*x)*cos(4*x)+4/25*exp(-3*x)*sin(4*x)","A"
813,1,18,17,0.026000," ","int(cos(x)*sin(x)/(1+sin(x))^(1/2),x)","\frac{2 \left(1+\sin \left(x \right)\right)^{\frac{3}{2}}}{3}-2 \sqrt{1+\sin \left(x \right)}"," ",0,"2/3*(1+sin(x))^(3/2)-2*(1+sin(x))^(1/2)","A"
814,1,41,24,0.008000," ","int(x+60*cos(x)^5*sin(x)^4,x)","\frac{x^{2}}{2}-\frac{20 \left(\cos^{6}\left(x \right)\right) \left(\sin^{3}\left(x \right)\right)}{3}-\frac{20 \sin \left(x \right) \left(\cos^{6}\left(x \right)\right)}{7}+\frac{4 \left(\frac{8}{3}+\cos^{4}\left(x \right)+\frac{4 \left(\cos^{2}\left(x \right)\right)}{3}\right) \sin \left(x \right)}{7}"," ",0,"1/2*x^2-20/3*cos(x)^6*sin(x)^3-20/7*sin(x)*cos(x)^6+4/7*(8/3+cos(x)^4+4/3*cos(x)^2)*sin(x)","A"
815,1,7,6,0.082000," ","int(cos(x)*(sec(x)+tan(x)),x)","x -\cos \left(x \right)"," ",0,"x-cos(x)","A"
816,1,8,7,0.095000," ","int(cos(x)*(sec(x)^3+tan(x)),x)","-\cos \left(x \right)+\tan \left(x \right)"," ",0,"-cos(x)+tan(x)","A"
817,1,10,9,0.036000," ","int(-1/2*cot(x)*csc(x)+1/2*csc(x)^2,x)","-\frac{\cot \left(x \right)}{2}+\frac{\csc \left(x \right)}{2}"," ",0,"-1/2*cot(x)+1/2*csc(x)","A"
818,1,10,9,0.032000," ","int(-csc(x)^2+sin(2*x),x)","-\frac{\cos \left(2 x \right)}{2}+\cot \left(x \right)"," ",0,"-1/2*cos(2*x)+cot(x)","A"
819,1,17,10,0.027000," ","int(2*cot(2*x)-3*sin(3*x),x)","-\frac{\ln \left(\cot^{2}\left(2 x \right)+1\right)}{2}+\cos \left(3 x \right)"," ",0,"-1/2*ln(cot(2*x)^2+1)+cos(3*x)","A"
820,1,9,8,0.004000," ","int(x*sin(2*x^2),x)","-\frac{\cos \left(2 x^{2}\right)}{4}"," ",0,"-1/4*cos(2*x^2)","A"
821,1,13,12,0.066000," ","int(cos(-1+x)*sin(-1+x)*(1+sin(-1+x)^2)^(1/2),x)","\frac{\left(1+\sin^{2}\left(-1+x \right)\right)^{\frac{3}{2}}}{3}"," ",0,"1/3*(1+sin(-1+x)^2)^(3/2)","A"
822,1,9,8,0.003000," ","int(cos(1/x)*sin(1/x)/x^2,x)","\frac{\left(\cos^{2}\left(\frac{1}{x}\right)\right)}{2}"," ",0,"1/2*cos(1/x)^2","A"
823,1,11,10,0.037000," ","int(cos(1/2+3/2*x)*sin(1/2+3/2*x)^3,x)","\frac{\left(\sin^{4}\left(\frac{1}{2}+\frac{3 x}{2}\right)\right)}{6}"," ",0,"1/6*sin(1/2+3/2*x)^4","A"
824,1,8,7,0.003000," ","int(4*x*tan(x^2),x)","-2 \ln \left(\cos \left(x^{2}\right)\right)"," ",0,"-2*ln(cos(x^2))","A"
825,1,17,9,0.003000," ","int(x*sec(x^2-5),x)","\frac{\ln \left(\sec \left(x^{2}-5\right)+\tan \left(x^{2}-5\right)\right)}{2}"," ",0,"1/2*ln(sec(x^2-5)+tan(x^2-5))","A"
826,1,11,5,0.003000," ","int(csc(1/x)/x^2,x)","\ln \left(\csc \left(\frac{1}{x}\right)+\cot \left(\frac{1}{x}\right)\right)"," ",0,"ln(csc(1/x)+cot(1/x))","A"
827,1,8,7,0.118000," ","int((csc(x)-sec(x))*(cos(x)+sin(x)),x)","\ln \left(\cos \left(x \right)\right)+\ln \left(\sin \left(x \right)\right)"," ",0,"ln(cos(x))+ln(sin(x))","A"
828,1,5,4,0.161000," ","int(-cos(3*x)*sin(2*x)+cos(2*x)*sin(3*x),x)","-\cos \left(x \right)"," ",0,"-cos(x)","A"
829,1,14,13,0.027000," ","int(4*x*sec(2*x)^2,x)","\ln \left(\cos \left(2 x \right)\right)+2 x \tan \left(2 x \right)"," ",0,"ln(cos(2*x))+2*x*tan(2*x)","A"
830,1,28,16,0.039000," ","int(4*sin(x)^2*tan(x)^2,x)","\frac{4 \left(\sin^{5}\left(x \right)\right)}{\cos \left(x \right)}+4 \left(\sin^{3}\left(x \right)+\frac{3 \sin \left(x \right)}{2}\right) \cos \left(x \right)-6 x"," ",0,"4*sin(x)^5/cos(x)+4*(sin(x)^3+3/2*sin(x))*cos(x)-6*x","A"
831,1,34,24,0.041000," ","int(cos(x)^4*cot(x)^2,x)","-\frac{\cos^{7}\left(x \right)}{\sin \left(x \right)}-\left(\cos^{5}\left(x \right)+\frac{5 \left(\cos^{3}\left(x \right)\right)}{4}+\frac{15 \cos \left(x \right)}{8}\right) \sin \left(x \right)-\frac{15 x}{8}"," ",0,"-1/sin(x)*cos(x)^7-(cos(x)^5+5/4*cos(x)^3+15/8*cos(x))*sin(x)-15/8*x","A"
832,1,19,18,0.009000," ","int(16*cos(x)^2*sin(x)^2,x)","2 x +2 \cos \left(x \right) \sin \left(x \right)-4 \left(\cos^{3}\left(x \right)\right) \sin \left(x \right)"," ",0,"2*x+2*cos(x)*sin(x)-4*cos(x)^3*sin(x)","A"
833,1,29,28,0.009000," ","int(8*cos(x)^2*sin(x)^4,x)","\frac{x}{2}+\frac{\cos \left(x \right) \sin \left(x \right)}{2}-\left(\cos^{3}\left(x \right)\right) \sin \left(x \right)-\frac{4 \left(\cos^{3}\left(x \right)\right) \left(\sin^{3}\left(x \right)\right)}{3}"," ",0,"1/2*x+1/2*cos(x)*sin(x)-cos(x)^3*sin(x)-4/3*cos(x)^3*sin(x)^3","A"
834,1,29,13,0.009000," ","int(35*cos(x)^3*sin(x)^4,x)","-5 \left(\cos^{4}\left(x \right)\right) \left(\sin^{3}\left(x \right)\right)-3 \sin \left(x \right) \left(\cos^{4}\left(x \right)\right)+\left(2+\cos^{2}\left(x \right)\right) \sin \left(x \right)"," ",0,"-5*cos(x)^4*sin(x)^3-3*sin(x)*cos(x)^4+(2+cos(x)^2)*sin(x)","B"
835,1,36,36,0.011000," ","int(4*cos(x)^4*sin(x)^4,x)","-\frac{\left(\cos^{5}\left(x \right)\right) \left(\sin^{3}\left(x \right)\right)}{2}-\frac{\left(\cos^{5}\left(x \right)\right) \sin \left(x \right)}{4}+\frac{\left(\cos^{3}\left(x \right)+\frac{3 \cos \left(x \right)}{2}\right) \sin \left(x \right)}{16}+\frac{3 x}{32}"," ",0,"-1/2*cos(x)^5*sin(x)^3-1/4*cos(x)^5*sin(x)+1/16*(cos(x)^3+3/2*cos(x))*sin(x)+3/32*x","A"
836,1,21,9,0.076000," ","int(cos(x)/(-sin(x)+sin(x)^3),x)","-\ln \left(\sin \left(x \right)\right)+\frac{\ln \left(\sin \left(x \right)-1\right)}{2}+\frac{\ln \left(1+\sin \left(x \right)\right)}{2}"," ",0,"-ln(sin(x))+1/2*ln(sin(x)-1)+1/2*ln(1+sin(x))","B"
837,1,13,12,0.024000," ","int(-1+2*cos(x)^2+cos(x)*sin(x),x)","\cos \left(x \right) \sin \left(x \right)+\frac{\left(\sin^{2}\left(x \right)\right)}{2}"," ",0,"cos(x)*sin(x)+1/2*sin(x)^2","A"
838,1,2,1,0.016000," ","int(cos(x)^2+sin(x)^2,x)","x"," ",0,"x","A"
839,1,7,6,0.001000," ","int(-cos(x)^2+sin(x)^2,x)","-\cos \left(x \right) \sin \left(x \right)"," ",0,"-cos(x)*sin(x)","A"
840,1,10,9,0.026000," ","int(2^sin(x)*cos(x),x)","\frac{2^{\sin \left(x \right)}}{\ln \left(2\right)}"," ",0,"2^sin(x)/ln(2)","A"
841,1,7,6,0.003000," ","int(tan(x)^3+tan(x)^5,x)","\frac{\left(\tan^{4}\left(x \right)\right)}{4}"," ",0,"1/4*tan(x)^4","A"
842,1,9,6,0.021000," ","int(x*sec(x)*(2+x*tan(x)),x)","\frac{x^{2}}{\cos \left(x \right)}"," ",0,"x^2/cos(x)","A"
843,1,7,6,0.085000," ","int(cot(x^(1/2))*csc(x^(1/2))/x^(1/2),x)","-2 \csc \left(\sqrt{x}\right)"," ",0,"-2*csc(x^(1/2))","A"
844,1,9,6,0.039000," ","int(cos(x^(1/2))*sin(x^(1/2))/x^(1/2),x)","-\left(\cos^{2}\left(\sqrt{x}\right)\right)"," ",0,"-cos(x^(1/2))^2","A"
845,1,7,6,0.058000," ","int(sec(x^(1/2))*tan(x^(1/2))/x^(1/2),x)","2 \sec \left(\sqrt{x}\right)"," ",0,"2*sec(x^(1/2))","A"
846,1,69,47,0.191000," ","int(sin(x)^2/(a+b*sin(2*x)),x)","-\frac{\ln \left(a +2 b \tan \left(x \right)+a \left(\tan^{2}\left(x \right)\right)\right)}{4 b}+\frac{\arctan \left(\frac{2 a \tan \left(x \right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{2 \sqrt{a^{2}-b^{2}}}+\frac{\ln \left(1+\tan^{2}\left(x \right)\right)}{4 b}"," ",0,"-1/4*ln(a+2*b*tan(x)+a*tan(x)^2)/b+1/2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(x)+2*b)/(a^2-b^2)^(1/2))+1/4/b*ln(1+tan(x)^2)","A"
847,1,69,47,0.172000," ","int(cos(x)^2/(a+b*sin(2*x)),x)","\frac{\ln \left(a +2 b \tan \left(x \right)+a \left(\tan^{2}\left(x \right)\right)\right)}{4 b}+\frac{\arctan \left(\frac{2 a \tan \left(x \right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{2 \sqrt{a^{2}-b^{2}}}-\frac{\ln \left(1+\tan^{2}\left(x \right)\right)}{4 b}"," ",0,"1/4*ln(a+2*b*tan(x)+a*tan(x)^2)/b+1/2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(x)+2*b)/(a^2-b^2)^(1/2))-1/4/b*ln(1+tan(x)^2)","A"
848,1,80,40,0.134000," ","int(sin(x)^2/(a+b*cos(2*x)),x)","\frac{\arctan \left(\frac{\tan \left(x \right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right) a}{2 b \sqrt{\left(a +b \right) \left(a -b \right)}}+\frac{\arctan \left(\frac{\tan \left(x \right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{2 \sqrt{\left(a +b \right) \left(a -b \right)}}-\frac{\arctan \left(\tan \left(x \right)\right)}{2 b}"," ",0,"1/2/b/((a+b)*(a-b))^(1/2)*arctan(tan(x)*(a-b)/((a+b)*(a-b))^(1/2))*a+1/2/((a+b)*(a-b))^(1/2)*arctan(tan(x)*(a-b)/((a+b)*(a-b))^(1/2))-1/2/b*arctan(tan(x))","A"
849,1,80,40,0.131000," ","int(cos(x)^2/(a+b*cos(2*x)),x)","-\frac{\arctan \left(\frac{\tan \left(x \right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right) a}{2 b \sqrt{\left(a +b \right) \left(a -b \right)}}+\frac{\arctan \left(\frac{\tan \left(x \right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{2 \sqrt{\left(a +b \right) \left(a -b \right)}}+\frac{\arctan \left(\tan \left(x \right)\right)}{2 b}"," ",0,"-1/2/b/((a+b)*(a-b))^(1/2)*arctan(tan(x)*(a-b)/((a+b)*(a-b))^(1/2))*a+1/2/((a+b)*(a-b))^(1/2)*arctan(tan(x)*(a-b)/((a+b)*(a-b))^(1/2))+1/2/b*arctan(tan(x))","A"
850,1,30,24,0.146000," ","int(tan(d*x+c)/(a*sin(d*x+c)^2)^(1/2),x)","\frac{\sin \left(d x +c \right) \arctanh \left(\sin \left(d x +c \right)\right)}{\sqrt{a \left(\sin^{2}\left(d x +c \right)\right)}\, d}"," ",0,"1/(a*sin(d*x+c)^2)^(1/2)*sin(d*x+c)*arctanh(sin(d*x+c))/d","A"
851,1,31,25,0.159000," ","int(cot(d*x+c)/(a*cos(d*x+c)^2)^(1/2),x)","-\frac{\cos \left(d x +c \right) \arctanh \left(\cos \left(d x +c \right)\right)}{\sqrt{a \left(\cos^{2}\left(d x +c \right)\right)}\, d}"," ",0,"-1/(a*cos(d*x+c)^2)^(1/2)*cos(d*x+c)*arctanh(cos(d*x+c))/d","A"
852,1,7,6,0.020000," ","int(x*cos(x^2)/sin(x^2)^(1/2),x)","\sqrt{\sin}\left(x^{2}\right)"," ",0,"sin(x^2)^(1/2)","A"
853,1,25,16,0.448000," ","int(cos(x)/(1-cos(2*x))^(1/2),x)","\frac{\sin \left(x \right) \left(\ln \left(-1+\cos \left(x \right)\right)+\ln \left(1+\cos \left(x \right)\right)\right) \sqrt{2}}{2 \sqrt{2-2 \cos \left(2 x \right)}}"," ",0,"1/4*sin(x)*(ln(-1+cos(x))+ln(1+cos(x)))*2^(1/2)/(sin(x)^2)^(1/2)","A"
854,1,24,23,0.042000," ","int(cos(ln(x))^2*sin(ln(x))^2/x,x)","\frac{\ln \left(x \right)}{8}+\frac{\cos \left(\ln \left(x \right)\right) \sin \left(\ln \left(x \right)\right)}{8}-\frac{\left(\cos^{3}\left(\ln \left(x \right)\right)\right) \sin \left(\ln \left(x \right)\right)}{4}"," ",0,"1/8*ln(x)+1/8*cos(ln(x))*sin(ln(x))-1/4*cos(ln(x))^3*sin(ln(x))","A"
855,1,34,23,0.140000," ","int(sin(x)^3/(cos(x)^3+sin(x)^3),x)","\frac{\ln \left(1-\tan \left(x \right)+\tan^{2}\left(x \right)\right)}{3}-\frac{\ln \left(1+\tan^{2}\left(x \right)\right)}{4}-\frac{\ln \left(1+\tan \left(x \right)\right)}{6}+\frac{x}{2}"," ",0,"1/3*ln(1-tan(x)+tan(x)^2)-1/4*ln(1+tan(x)^2)-1/6*ln(1+tan(x))+1/2*x","A"
856,1,34,23,0.136000," ","int(cos(x)^3/(cos(x)^3+sin(x)^3),x)","-\frac{\ln \left(1-\tan \left(x \right)+\tan^{2}\left(x \right)\right)}{3}+\frac{\ln \left(1+\tan^{2}\left(x \right)\right)}{4}+\frac{\ln \left(1+\tan \left(x \right)\right)}{6}+\frac{x}{2}"," ",0,"-1/3*ln(1-tan(x)+tan(x)^2)+1/4*ln(1+tan(x)^2)+1/6*ln(1+tan(x))+1/2*x","A"
857,1,31,36,0.161000," ","int(sec(x)/(-5+cos(x)^2+4*sin(x)),x)","-\frac{1}{3 \left(\sin \left(x \right)-2\right)}-\frac{4 \ln \left(\sin \left(x \right)-2\right)}{9}+\frac{\ln \left(\sin \left(x \right)-1\right)}{2}-\frac{\ln \left(1+\sin \left(x \right)\right)}{18}"," ",0,"-1/3/(sin(x)-2)-4/9*ln(sin(x)-2)+1/2*ln(sin(x)-1)-1/18*ln(1+sin(x))","A"
858,1,16,15,0.381000," ","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)}}"," ",0,"2*(3*cos(x)+sin(x))^(1/2)/cos(x)^(1/2)","A"
859,1,917,36,0.767000," ","int(csc(x)*(cos(x)+sin(x))^(1/2)/cos(x)^(3/2),x)","\frac{\left(-1+\cos \left(x \right)\right)^{2} \left(1+\cos \left(x \right)\right)^{2} \left(-\EllipticF \left(\frac{\sqrt{\frac{\left(\sin \left(x \right)-1\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(x \right)}}\, \sqrt{2}}{2}, \frac{i \sqrt{\left(2-\sqrt{2}\right) \left(2+\sqrt{2}\right)}}{2+\sqrt{2}}\right) \sqrt{\frac{\left(\cos \left(x \right) \sqrt{2}-\sin \left(x \right) \sqrt{2}+2 \sin \left(x \right)+\sqrt{2}-2\right) \sqrt{2}}{\cos \left(x \right)}}\, \sqrt{\frac{\left(\cos \left(x \right) \sqrt{2}-\sin \left(x \right) \sqrt{2}-2 \sin \left(x \right)+\sqrt{2}+2\right) \sqrt{2}}{\cos \left(x \right)}}\, \sqrt{\frac{\left(\sin \left(x \right)-1\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(x \right)}}\, \sin \left(x \right)+\EllipticPi \left(\frac{\sqrt{\frac{\left(\sin \left(x \right)-1\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(x \right)}}\, \sqrt{2}}{2}, \frac{\sqrt{2}}{2+\sqrt{2}}, \frac{i \sqrt{\left(2-\sqrt{2}\right) \left(2+\sqrt{2}\right)}}{2+\sqrt{2}}\right) \sqrt{\frac{\left(\cos \left(x \right) \sqrt{2}-\sin \left(x \right) \sqrt{2}+2 \sin \left(x \right)+\sqrt{2}-2\right) \sqrt{2}}{\cos \left(x \right)}}\, \sqrt{\frac{\left(\cos \left(x \right) \sqrt{2}-\sin \left(x \right) \sqrt{2}-2 \sin \left(x \right)+\sqrt{2}+2\right) \sqrt{2}}{\cos \left(x \right)}}\, \sqrt{\frac{\left(\sin \left(x \right)-1\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(x \right)}}\, \sin \left(x \right)+\EllipticPi \left(\frac{\sqrt{\frac{\left(\sin \left(x \right)-1\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(x \right)}}\, \sqrt{2}}{2}, -\frac{\sqrt{2}}{2+\sqrt{2}}, \frac{i \sqrt{\left(2-\sqrt{2}\right) \left(2+\sqrt{2}\right)}}{2+\sqrt{2}}\right) \sqrt{\frac{\left(\cos \left(x \right) \sqrt{2}-\sin \left(x \right) \sqrt{2}+2 \sin \left(x \right)+\sqrt{2}-2\right) \sqrt{2}}{\cos \left(x \right)}}\, \sqrt{\frac{\left(\cos \left(x \right) \sqrt{2}-\sin \left(x \right) \sqrt{2}-2 \sin \left(x \right)+\sqrt{2}+2\right) \sqrt{2}}{\cos \left(x \right)}}\, \sqrt{\frac{\left(\sin \left(x \right)-1\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(x \right)}}\, \sin \left(x \right)-\sqrt{\frac{\left(\cos \left(x \right) \sqrt{2}-\sin \left(x \right) \sqrt{2}+2 \sin \left(x \right)+\sqrt{2}-2\right) \sqrt{2}}{\cos \left(x \right)}}\, \sqrt{\frac{\left(\cos \left(x \right) \sqrt{2}-\sin \left(x \right) \sqrt{2}-2 \sin \left(x \right)+\sqrt{2}+2\right) \sqrt{2}}{\cos \left(x \right)}}\, \EllipticF \left(\frac{\sqrt{\frac{\left(\sin \left(x \right)-1\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(x \right)}}\, \sqrt{2}}{2}, \frac{i \sqrt{\left(2-\sqrt{2}\right) \left(2+\sqrt{2}\right)}}{2+\sqrt{2}}\right) \sqrt{\frac{\left(\sin \left(x \right)-1\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(x \right)}}+\sqrt{\frac{\left(\cos \left(x \right) \sqrt{2}-\sin \left(x \right) \sqrt{2}+2 \sin \left(x \right)+\sqrt{2}-2\right) \sqrt{2}}{\cos \left(x \right)}}\, \sqrt{\frac{\left(\cos \left(x \right) \sqrt{2}-\sin \left(x \right) \sqrt{2}-2 \sin \left(x \right)+\sqrt{2}+2\right) \sqrt{2}}{\cos \left(x \right)}}\, \EllipticPi \left(\frac{\sqrt{\frac{\left(\sin \left(x \right)-1\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(x \right)}}\, \sqrt{2}}{2}, \frac{\sqrt{2}}{2+\sqrt{2}}, \frac{i \sqrt{\left(2-\sqrt{2}\right) \left(2+\sqrt{2}\right)}}{2+\sqrt{2}}\right) \sqrt{\frac{\left(\sin \left(x \right)-1\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(x \right)}}+\sqrt{\frac{\left(\cos \left(x \right) \sqrt{2}-\sin \left(x \right) \sqrt{2}+2 \sin \left(x \right)+\sqrt{2}-2\right) \sqrt{2}}{\cos \left(x \right)}}\, \sqrt{\frac{\left(\cos \left(x \right) \sqrt{2}-\sin \left(x \right) \sqrt{2}-2 \sin \left(x \right)+\sqrt{2}+2\right) \sqrt{2}}{\cos \left(x \right)}}\, \EllipticPi \left(\frac{\sqrt{\frac{\left(\sin \left(x \right)-1\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(x \right)}}\, \sqrt{2}}{2}, -\frac{\sqrt{2}}{2+\sqrt{2}}, \frac{i \sqrt{\left(2-\sqrt{2}\right) \left(2+\sqrt{2}\right)}}{2+\sqrt{2}}\right) \sqrt{\frac{\left(\sin \left(x \right)-1\right) \left(2+\sqrt{2}\right) \sqrt{2}}{\cos \left(x \right)}}+2 \cos \left(x \right) \sqrt{2}+2 \sin \left(x \right) \sqrt{2}+4 \cos \left(x \right)+4 \sin \left(x \right)\right)}{\sin \left(x \right)^{4} \sqrt{\cos \left(x \right)+\sin \left(x \right)}\, \sqrt{\cos \left(x \right)}\, \left(2+\sqrt{2}\right)}"," ",0,"(-1+cos(x))^2*(1+cos(x))^2*(-EllipticF(1/2*((sin(x)-1)/cos(x)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I/(2+2^(1/2))*((2-2^(1/2))*(2+2^(1/2)))^(1/2))*((cos(x)*2^(1/2)-sin(x)*2^(1/2)+2*sin(x)+2^(1/2)-2)/cos(x)*2^(1/2))^(1/2)*((cos(x)*2^(1/2)-sin(x)*2^(1/2)-2*sin(x)+2^(1/2)+2)/cos(x)*2^(1/2))^(1/2)*((sin(x)-1)/cos(x)*(2+2^(1/2))*2^(1/2))^(1/2)*sin(x)+EllipticPi(1/2*((sin(x)-1)/cos(x)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),2^(1/2)/(2+2^(1/2)),I/(2+2^(1/2))*((2-2^(1/2))*(2+2^(1/2)))^(1/2))*((cos(x)*2^(1/2)-sin(x)*2^(1/2)+2*sin(x)+2^(1/2)-2)/cos(x)*2^(1/2))^(1/2)*((cos(x)*2^(1/2)-sin(x)*2^(1/2)-2*sin(x)+2^(1/2)+2)/cos(x)*2^(1/2))^(1/2)*((sin(x)-1)/cos(x)*(2+2^(1/2))*2^(1/2))^(1/2)*sin(x)+EllipticPi(1/2*((sin(x)-1)/cos(x)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),-2^(1/2)/(2+2^(1/2)),I/(2+2^(1/2))*((2-2^(1/2))*(2+2^(1/2)))^(1/2))*((cos(x)*2^(1/2)-sin(x)*2^(1/2)+2*sin(x)+2^(1/2)-2)/cos(x)*2^(1/2))^(1/2)*((cos(x)*2^(1/2)-sin(x)*2^(1/2)-2*sin(x)+2^(1/2)+2)/cos(x)*2^(1/2))^(1/2)*((sin(x)-1)/cos(x)*(2+2^(1/2))*2^(1/2))^(1/2)*sin(x)-((cos(x)*2^(1/2)-sin(x)*2^(1/2)+2*sin(x)+2^(1/2)-2)/cos(x)*2^(1/2))^(1/2)*((cos(x)*2^(1/2)-sin(x)*2^(1/2)-2*sin(x)+2^(1/2)+2)/cos(x)*2^(1/2))^(1/2)*EllipticF(1/2*((sin(x)-1)/cos(x)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),I/(2+2^(1/2))*((2-2^(1/2))*(2+2^(1/2)))^(1/2))*((sin(x)-1)/cos(x)*(2+2^(1/2))*2^(1/2))^(1/2)+((cos(x)*2^(1/2)-sin(x)*2^(1/2)+2*sin(x)+2^(1/2)-2)/cos(x)*2^(1/2))^(1/2)*((cos(x)*2^(1/2)-sin(x)*2^(1/2)-2*sin(x)+2^(1/2)+2)/cos(x)*2^(1/2))^(1/2)*EllipticPi(1/2*((sin(x)-1)/cos(x)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),2^(1/2)/(2+2^(1/2)),I/(2+2^(1/2))*((2-2^(1/2))*(2+2^(1/2)))^(1/2))*((sin(x)-1)/cos(x)*(2+2^(1/2))*2^(1/2))^(1/2)+((cos(x)*2^(1/2)-sin(x)*2^(1/2)+2*sin(x)+2^(1/2)-2)/cos(x)*2^(1/2))^(1/2)*((cos(x)*2^(1/2)-sin(x)*2^(1/2)-2*sin(x)+2^(1/2)+2)/cos(x)*2^(1/2))^(1/2)*EllipticPi(1/2*((sin(x)-1)/cos(x)*(2+2^(1/2))*2^(1/2))^(1/2)*2^(1/2),-2^(1/2)/(2+2^(1/2)),I/(2+2^(1/2))*((2-2^(1/2))*(2+2^(1/2)))^(1/2))*((sin(x)-1)/cos(x)*(2+2^(1/2))*2^(1/2))^(1/2)+2*cos(x)*2^(1/2)+2*sin(x)*2^(1/2)+4*cos(x)+4*sin(x))/sin(x)^4/(cos(x)+sin(x))^(1/2)/cos(x)^(1/2)/(2+2^(1/2))","C"
860,1,12372,17,0.417000," ","int((cos(x)+sin(x))/(1+sin(2*x))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
861,1,10,11,0.144000," ","int(sec(x)*(sec(x)+tan(x))^(1/2),x)","2 \sqrt{\sec \left(x \right)+\tan \left(x \right)}"," ",0,"2*(sec(x)+tan(x))^(1/2)","A"
862,1,11,10,0.063000," ","int(sec(x)*(4+3*sec(x))^(1/2)*tan(x),x)","\frac{2 \left(4+3 \sec \left(x \right)\right)^{\frac{3}{2}}}{9}"," ",0,"2/9*(4+3*sec(x))^(3/2)","A"
863,1,34,17,0.168000," ","int(sec(x)*(1+sec(x))^(1/2)*tan(x)^3,x)","-\frac{2 \left(9 \cos \left(x \right)-5\right) \sqrt{\frac{1+\cos \left(x \right)}{\cos \left(x \right)}}\, \left(\sin^{4}\left(x \right)\right)}{35 \left(-1+\cos \left(x \right)\right)^{2} \cos \left(x \right)^{3}}"," ",0,"-2/35*(9*cos(x)-5)*((1+cos(x))/cos(x))^(1/2)*sin(x)^4/(-1+cos(x))^2/cos(x)^3","A"
864,1,38,17,0.181000," ","int(cot(x)^3*csc(x)*(1+csc(x))^(1/2),x)","-\frac{2 \left(9 \left(\cos^{2}\left(x \right)\right) \sin \left(x \right)+13 \left(\cos^{2}\left(x \right)\right)-8 \sin \left(x \right)-8\right) \sqrt{\frac{1+\sin \left(x \right)}{\sin \left(x \right)}}}{35 \sin \left(x \right)^{3}}"," ",0,"-2/35*(9*cos(x)^2*sin(x)+13*cos(x)^2-8*sin(x)-8)*((1+sin(x))/sin(x))^(1/2)/sin(x)^3","B"
865,0,0,16,0.501000," ","int(csc(x)^(1/2)*(x*cos(x)-4*sec(x)*tan(x)),x)","\int \left(\sqrt{\csc}\left(x \right)\right) \left(x \cos \left(x \right)-4 \sec \left(x \right) \tan \left(x \right)\right)\, dx"," ",0,"int(csc(x)^(1/2)*(x*cos(x)-4*sec(x)*tan(x)),x)","F"
866,1,54,56,0.375000," ","int(cot(x)*(1-sin(x)^2)^3*(-1+csc(x)^2)^(1/2),x)","-\frac{\left(-8 \left(\cos^{7}\left(x \right)\right)-14 \left(\cos^{5}\left(x \right)\right)-35 \left(\cos^{3}\left(x \right)\right)+105 x \sin \left(x \right)+105 \cos \left(x \right)\right) \sqrt{-\frac{\cos^{2}\left(x \right)}{-1+\cos^{2}\left(x \right)}}\, \sqrt{4}}{96 \cos \left(x \right)}"," ",0,"-1/96*(-8*cos(x)^7-14*cos(x)^5-35*cos(x)^3+105*x*sin(x)+105*cos(x))*(-cos(x)^2/(-1+cos(x)^2))^(1/2)/cos(x)*4^(1/2)","A"
867,1,65,65,0.270000," ","int(cos(x)*(1-sin(x)^2)^3*(-1+csc(x)^2)^(1/2),x)","\frac{\left(15 \left(\cos^{7}\left(x \right)\right)+21 \left(\cos^{5}\left(x \right)\right)+35 \left(\cos^{3}\left(x \right)\right)+105 \cos \left(x \right)+105 \ln \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)+176\right) \sin \left(x \right) \sqrt{-\frac{\cos^{2}\left(x \right)}{-1+\cos^{2}\left(x \right)}}\, \sqrt{4}}{210 \cos \left(x \right)}"," ",0,"1/210*(15*cos(x)^7+21*cos(x)^5+35*cos(x)^3+105*cos(x)+105*ln(-(-1+cos(x))/sin(x))+176)*sin(x)*(-cos(x)^2/(-1+cos(x)^2))^(1/2)/cos(x)*4^(1/2)","A"
868,1,98,62,0.228000," ","int(x*csc(x)*sec(x)/(a*sec(x)^2)^(1/2),x)","-\frac{2 i \left(-\frac{i {\mathrm e}^{i x} x \ln \left(1+{\mathrm e}^{i x}\right)}{2}-\frac{{\mathrm e}^{i x} \polylog \left(2, -{\mathrm e}^{i x}\right)}{2}+\frac{i {\mathrm e}^{i x} x \ln \left(1-{\mathrm e}^{i x}\right)}{2}+\frac{{\mathrm e}^{i x} \polylog \left(2, {\mathrm e}^{i x}\right)}{2}\right)}{\sqrt{\frac{a \,{\mathrm e}^{2 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{2}}}\, \left({\mathrm e}^{2 i x}+1\right)}"," ",0,"-2*I/(a*exp(2*I*x)/(exp(2*I*x)+1)^2)^(1/2)/(exp(2*I*x)+1)*(-1/2*I*exp(I*x)*x*ln(1+exp(I*x))-1/2*exp(I*x)*polylog(2,-exp(I*x))+1/2*I*exp(I*x)*x*ln(1-exp(I*x))+1/2*exp(I*x)*polylog(2,exp(I*x)))","A"
869,1,132,106,0.205000," ","int(x^2*csc(x)*sec(x)/(a*sec(x)^2)^(1/2),x)","-\frac{2 \left(\frac{{\mathrm e}^{i x} x^{2} \ln \left(1+{\mathrm e}^{i x}\right)}{2}-i {\mathrm e}^{i x} x \polylog \left(2, -{\mathrm e}^{i x}\right)+{\mathrm e}^{i x} \polylog \left(3, -{\mathrm e}^{i x}\right)-\frac{{\mathrm e}^{i x} x^{2} \ln \left(1-{\mathrm e}^{i x}\right)}{2}+i {\mathrm e}^{i x} x \polylog \left(2, {\mathrm e}^{i x}\right)-{\mathrm e}^{i x} \polylog \left(3, {\mathrm e}^{i x}\right)\right)}{\sqrt{\frac{a \,{\mathrm e}^{2 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{2}}}\, \left({\mathrm e}^{2 i x}+1\right)}"," ",0,"-2/(a*exp(2*I*x)/(exp(2*I*x)+1)^2)^(1/2)/(exp(2*I*x)+1)*(1/2*exp(I*x)*x^2*ln(1+exp(I*x))-I*exp(I*x)*x*polylog(2,-exp(I*x))+exp(I*x)*polylog(3,-exp(I*x))-1/2*exp(I*x)*x^2*ln(1-exp(I*x))+I*exp(I*x)*x*polylog(2,exp(I*x))-exp(I*x)*polylog(3,exp(I*x)))","A"
870,1,172,154,0.188000," ","int(x^3*csc(x)*sec(x)/(a*sec(x)^2)^(1/2),x)","\frac{2 i \left(\frac{i {\mathrm e}^{i x} x^{3} \ln \left(1+{\mathrm e}^{i x}\right)}{2}+\frac{3 \,{\mathrm e}^{i x} x^{2} \polylog \left(2, -{\mathrm e}^{i x}\right)}{2}+3 i {\mathrm e}^{i x} x \polylog \left(3, -{\mathrm e}^{i x}\right)-3 \,{\mathrm e}^{i x} \polylog \left(4, -{\mathrm e}^{i x}\right)-\frac{i {\mathrm e}^{i x} x^{3} \ln \left(1-{\mathrm e}^{i x}\right)}{2}-\frac{3 \,{\mathrm e}^{i x} x^{2} \polylog \left(2, {\mathrm e}^{i x}\right)}{2}-3 i {\mathrm e}^{i x} x \polylog \left(3, {\mathrm e}^{i x}\right)+3 \,{\mathrm e}^{i x} \polylog \left(4, {\mathrm e}^{i x}\right)\right)}{\sqrt{\frac{a \,{\mathrm e}^{2 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{2}}}\, \left({\mathrm e}^{2 i x}+1\right)}"," ",0,"2*I/(a*exp(2*I*x)/(exp(2*I*x)+1)^2)^(1/2)/(exp(2*I*x)+1)*(1/2*I*exp(I*x)*x^3*ln(1+exp(I*x))+3/2*exp(I*x)*x^2*polylog(2,-exp(I*x))+3*I*exp(I*x)*x*polylog(3,-exp(I*x))-3*exp(I*x)*polylog(4,-exp(I*x))-1/2*I*exp(I*x)*x^3*ln(1-exp(I*x))-3/2*exp(I*x)*x^2*polylog(2,exp(I*x))-3*I*exp(I*x)*x*polylog(3,exp(I*x))+3*exp(I*x)*polylog(4,exp(I*x)))","A"
871,1,147,65,0.204000," ","int(x*csc(x)*sec(x)/(a*sec(x)^4)^(1/2),x)","\frac{i {\mathrm e}^{2 i x} x^{2}}{2 \sqrt{\frac{a \,{\mathrm e}^{4 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{4}}}\, \left({\mathrm e}^{2 i x}+1\right)^{2}}-\frac{2 i \left(\frac{{\mathrm e}^{2 i x} x^{2}}{2}+\frac{i {\mathrm e}^{2 i x} x \ln \left(1+{\mathrm e}^{i x}\right)}{2}+\frac{{\mathrm e}^{2 i x} \polylog \left(2, -{\mathrm e}^{i x}\right)}{2}+\frac{i {\mathrm e}^{2 i x} x \ln \left(1-{\mathrm e}^{i x}\right)}{2}+\frac{{\mathrm e}^{2 i x} \polylog \left(2, {\mathrm e}^{i x}\right)}{2}\right)}{\sqrt{\frac{a \,{\mathrm e}^{4 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{4}}}\, \left({\mathrm e}^{2 i x}+1\right)^{2}}"," ",0,"1/2*I/(a*exp(4*I*x)/(exp(2*I*x)+1)^4)^(1/2)/(exp(2*I*x)+1)^2*exp(2*I*x)*x^2-2*I/(a*exp(4*I*x)/(exp(2*I*x)+1)^4)^(1/2)/(exp(2*I*x)+1)^2*(1/2*exp(2*I*x)*x^2+1/2*I*exp(2*I*x)*x*ln(1+exp(I*x))+1/2*exp(2*I*x)*polylog(2,-exp(I*x))+1/2*I*exp(2*I*x)*x*ln(1-exp(I*x))+1/2*exp(2*I*x)*polylog(2,exp(I*x)))","B"
872,1,183,89,0.185000," ","int(x^2*csc(x)*sec(x)/(a*sec(x)^4)^(1/2),x)","\frac{i {\mathrm e}^{2 i x} x^{3}}{3 \sqrt{\frac{a \,{\mathrm e}^{4 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{4}}}\, \left({\mathrm e}^{2 i x}+1\right)^{2}}-\frac{2 \left(\frac{i {\mathrm e}^{2 i x} x^{3}}{3}-\frac{{\mathrm e}^{2 i x} x^{2} \ln \left(1+{\mathrm e}^{i x}\right)}{2}+i {\mathrm e}^{2 i x} x \polylog \left(2, -{\mathrm e}^{i x}\right)-{\mathrm e}^{2 i x} \polylog \left(3, -{\mathrm e}^{i x}\right)-\frac{{\mathrm e}^{2 i x} x^{2} \ln \left(1-{\mathrm e}^{i x}\right)}{2}+i {\mathrm e}^{2 i x} x \polylog \left(2, {\mathrm e}^{i x}\right)-{\mathrm e}^{2 i x} \polylog \left(3, {\mathrm e}^{i x}\right)\right)}{\sqrt{\frac{a \,{\mathrm e}^{4 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{4}}}\, \left({\mathrm e}^{2 i x}+1\right)^{2}}"," ",0,"1/3*I/(a*exp(4*I*x)/(exp(2*I*x)+1)^4)^(1/2)/(exp(2*I*x)+1)^2*exp(2*I*x)*x^3-2/(a*exp(4*I*x)/(exp(2*I*x)+1)^4)^(1/2)/(exp(2*I*x)+1)^2*(1/3*I*exp(2*I*x)*x^3-1/2*exp(2*I*x)*x^2*ln(1+exp(I*x))+I*exp(2*I*x)*x*polylog(2,-exp(I*x))-exp(2*I*x)*polylog(3,-exp(I*x))-1/2*exp(2*I*x)*x^2*ln(1-exp(I*x))+I*exp(2*I*x)*x*polylog(2,exp(I*x))-exp(2*I*x)*polylog(3,exp(I*x)))","B"
873,1,221,114,0.190000," ","int(x^3*csc(x)*sec(x)/(a*sec(x)^4)^(1/2),x)","\frac{i {\mathrm e}^{2 i x} x^{4}}{4 \sqrt{\frac{a \,{\mathrm e}^{4 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{4}}}\, \left({\mathrm e}^{2 i x}+1\right)^{2}}+\frac{2 i \left(-\frac{{\mathrm e}^{2 i x} x^{4}}{4}-\frac{i {\mathrm e}^{2 i x} x^{3} \ln \left(1+{\mathrm e}^{i x}\right)}{2}-\frac{3 \,{\mathrm e}^{2 i x} x^{2} \polylog \left(2, -{\mathrm e}^{i x}\right)}{2}-3 i {\mathrm e}^{2 i x} x \polylog \left(3, -{\mathrm e}^{i x}\right)+3 \,{\mathrm e}^{2 i x} \polylog \left(4, -{\mathrm e}^{i x}\right)-\frac{i {\mathrm e}^{2 i x} x^{3} \ln \left(1-{\mathrm e}^{i x}\right)}{2}-\frac{3 \,{\mathrm e}^{2 i x} x^{2} \polylog \left(2, {\mathrm e}^{i x}\right)}{2}-3 i {\mathrm e}^{2 i x} x \polylog \left(3, {\mathrm e}^{i x}\right)+3 \,{\mathrm e}^{2 i x} \polylog \left(4, {\mathrm e}^{i x}\right)\right)}{\sqrt{\frac{a \,{\mathrm e}^{4 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{4}}}\, \left({\mathrm e}^{2 i x}+1\right)^{2}}"," ",0,"1/4*I/(a*exp(4*I*x)/(exp(2*I*x)+1)^4)^(1/2)/(exp(2*I*x)+1)^2*exp(2*I*x)*x^4+2*I/(a*exp(4*I*x)/(exp(2*I*x)+1)^4)^(1/2)/(exp(2*I*x)+1)^2*(-1/4*exp(2*I*x)*x^4-1/2*I*exp(2*I*x)*x^3*ln(1+exp(I*x))-3/2*exp(2*I*x)*x^2*polylog(2,-exp(I*x))-3*I*exp(2*I*x)*x*polylog(3,-exp(I*x))+3*exp(2*I*x)*polylog(4,-exp(I*x))-1/2*I*exp(2*I*x)*x^3*ln(1-exp(I*x))-3/2*exp(2*I*x)*x^2*polylog(2,exp(I*x))-3*I*exp(2*I*x)*x*polylog(3,exp(I*x))+3*exp(2*I*x)*polylog(4,exp(I*x)))","A"
874,1,86,87,0.253000," ","int(x*csc(x)*sec(x)*(a*sec(x)^2)^(1/2),x)","2 \sqrt{\frac{a \,{\mathrm e}^{2 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{2}}}\, x +4 \sqrt{\frac{a \,{\mathrm e}^{2 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{2}}}\, \left(i \arctan \left({\mathrm e}^{i x}\right)+\frac{i \dilog \left(1+{\mathrm e}^{i x}\right)}{2}-\frac{x \ln \left(1+{\mathrm e}^{i x}\right)}{2}+\frac{i \dilog \left({\mathrm e}^{i x}\right)}{2}\right) \cos \left(x \right)"," ",0,"2*(a*exp(2*I*x)/(exp(2*I*x)+1)^2)^(1/2)*x+4*(a*exp(2*I*x)/(exp(2*I*x)+1)^2)^(1/2)*(I*arctan(exp(I*x))+1/2*I*dilog(1+exp(I*x))-1/2*x*ln(1+exp(I*x))+1/2*I*dilog(exp(I*x)))*cos(x)","A"
875,1,200,184,0.302000," ","int(x^2*csc(x)*sec(x)*(a*sec(x)^2)^(1/2),x)","2 \sqrt{\frac{a \,{\mathrm e}^{2 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{2}}}\, x^{2}-4 i \sqrt{\frac{a \,{\mathrm e}^{2 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{2}}}\, \left(2 i \left(\frac{x \ln \left(1+i {\mathrm e}^{i x}\right)}{2}-\frac{x \ln \left(1-i {\mathrm e}^{i x}\right)}{2}-\frac{i \dilog \left(1+i {\mathrm e}^{i x}\right)}{2}+\frac{i \dilog \left(1-i {\mathrm e}^{i x}\right)}{2}\right)-\frac{i \left(-\frac{i x^{3}}{3}+x^{2} \ln \left(1+{\mathrm e}^{i x}\right)-2 i x \polylog \left(2, -{\mathrm e}^{i x}\right)+2 \polylog \left(3, -{\mathrm e}^{i x}\right)\right)}{2}-\frac{i \left(\frac{i x^{3}}{3}-x^{2} \ln \left(1-{\mathrm e}^{i x}\right)+2 i x \polylog \left(2, {\mathrm e}^{i x}\right)-2 \polylog \left(3, {\mathrm e}^{i x}\right)\right)}{2}\right) \cos \left(x \right)"," ",0,"2*(a*exp(2*I*x)/(exp(2*I*x)+1)^2)^(1/2)*x^2-4*I*(a*exp(2*I*x)/(exp(2*I*x)+1)^2)^(1/2)*(2*I*(1/2*x*ln(1+I*exp(I*x))-1/2*x*ln(1-I*exp(I*x))-1/2*I*dilog(1+I*exp(I*x))+1/2*I*dilog(1-I*exp(I*x)))-1/2*I*(-1/3*I*x^3+x^2*ln(1+exp(I*x))-2*I*x*polylog(2,-exp(I*x))+2*polylog(3,-exp(I*x)))-1/2*I*(1/3*I*x^3-x^2*ln(1-exp(I*x))+2*I*x*polylog(2,exp(I*x))-2*polylog(3,exp(I*x))))*cos(x)","A"
876,1,250,280,0.418000," ","int(x^3*csc(x)*sec(x)*(a*sec(x)^2)^(1/2),x)","2 \sqrt{\frac{a \,{\mathrm e}^{2 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{2}}}\, x^{3}+4 \sqrt{\frac{a \,{\mathrm e}^{2 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{2}}}\, \left(\frac{3 x^{2} \ln \left(1+i {\mathrm e}^{i x}\right)}{2}-3 i x \polylog \left(2, -i {\mathrm e}^{i x}\right)+3 \polylog \left(3, -i {\mathrm e}^{i x}\right)-\frac{3 x^{2} \ln \left(1-i {\mathrm e}^{i x}\right)}{2}+3 i x \polylog \left(2, i {\mathrm e}^{i x}\right)-3 \polylog \left(3, i {\mathrm e}^{i x}\right)+\frac{i \left(\frac{x^{4}}{4}+i x^{3} \ln \left(1+{\mathrm e}^{i x}\right)+3 x^{2} \polylog \left(2, -{\mathrm e}^{i x}\right)+6 i x \polylog \left(3, -{\mathrm e}^{i x}\right)-6 \polylog \left(4, -{\mathrm e}^{i x}\right)\right)}{2}+\frac{i \left(-\frac{x^{4}}{4}-i x^{3} \ln \left(1-{\mathrm e}^{i x}\right)-3 x^{2} \polylog \left(2, {\mathrm e}^{i x}\right)-6 i x \polylog \left(3, {\mathrm e}^{i x}\right)+6 \polylog \left(4, {\mathrm e}^{i x}\right)\right)}{2}\right) \cos \left(x \right)"," ",0,"2*(a*exp(2*I*x)/(exp(2*I*x)+1)^2)^(1/2)*x^3+4*(a*exp(2*I*x)/(exp(2*I*x)+1)^2)^(1/2)*(3/2*x^2*ln(1+I*exp(I*x))-3*I*x*polylog(2,-I*exp(I*x))+3*polylog(3,-I*exp(I*x))-3/2*x^2*ln(1-I*exp(I*x))+3*I*x*polylog(2,I*exp(I*x))-3*polylog(3,I*exp(I*x))+1/2*I*(1/4*x^4+I*x^3*ln(1+exp(I*x))+3*x^2*polylog(2,-exp(I*x))+6*I*x*polylog(3,-exp(I*x))-6*polylog(4,-exp(I*x)))+1/2*I*(-1/4*x^4-I*x^3*ln(1-exp(I*x))-3*x^2*polylog(2,exp(I*x))-6*I*x*polylog(3,exp(I*x))+6*polylog(4,exp(I*x))))*cos(x)","A"
877,1,165,112,0.195000," ","int(x*csc(x)*sec(x)*(a*sec(x)^4)^(1/2),x)","\sqrt{\frac{a \,{\mathrm e}^{4 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{4}}}\, \left(-i+2 x -i {\mathrm e}^{-2 i x}\right)-4 i \sqrt{\frac{a \,{\mathrm e}^{4 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{4}}}\, \left({\mathrm e}^{2 i x}+1\right)^{2} \left(\frac{i {\mathrm e}^{-2 i x} x \ln \left(1+{\mathrm e}^{i x}\right)}{4}+\frac{{\mathrm e}^{-2 i x} \polylog \left(2, -{\mathrm e}^{i x}\right)}{4}-\frac{i {\mathrm e}^{-2 i x} x \ln \left({\mathrm e}^{2 i x}+1\right)}{4}-\frac{{\mathrm e}^{-2 i x} \polylog \left(2, -{\mathrm e}^{2 i x}\right)}{8}+\frac{i {\mathrm e}^{-2 i x} x \ln \left(1-{\mathrm e}^{i x}\right)}{4}+\frac{{\mathrm e}^{-2 i x} \polylog \left(2, {\mathrm e}^{i x}\right)}{4}\right)"," ",0,"(a*exp(4*I*x)/(exp(2*I*x)+1)^4)^(1/2)*(-I+2*x-I*exp(-2*I*x))-4*I*(a*exp(4*I*x)/(exp(2*I*x)+1)^4)^(1/2)*(exp(2*I*x)+1)^2*(1/4*I*exp(-2*I*x)*x*ln(1+exp(I*x))+1/4*exp(-2*I*x)*polylog(2,-exp(I*x))-1/4*I*exp(-2*I*x)*x*ln(exp(2*I*x)+1)-1/8*exp(-2*I*x)*polylog(2,-exp(2*I*x))+1/4*I*exp(-2*I*x)*x*ln(1-exp(I*x))+1/4*exp(-2*I*x)*polylog(2,exp(I*x)))","A"
878,1,254,182,0.231000," ","int(x^2*csc(x)*sec(x)*(a*sec(x)^4)^(1/2),x)","2 \sqrt{\frac{a \,{\mathrm e}^{4 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{4}}}\, x \left(x -i-i {\mathrm e}^{-2 i x}\right)+2 \sqrt{\frac{a \,{\mathrm e}^{4 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{4}}}\, \left({\mathrm e}^{2 i x}+1\right)^{2} \left(-\frac{{\mathrm e}^{-2 i x} \ln \left({\mathrm e}^{2 i x}+1\right)}{2}-{\mathrm e}^{-2 i x} \Im \left(x \right)+{\mathrm e}^{-2 i x} \ln \left({\mathrm e}^{i \Re \left(x \right)}\right)+\frac{{\mathrm e}^{-2 i x} x^{2} \ln \left(1+{\mathrm e}^{i x}\right)}{2}-i {\mathrm e}^{-2 i x} x \polylog \left(2, -{\mathrm e}^{i x}\right)+{\mathrm e}^{-2 i x} \polylog \left(3, -{\mathrm e}^{i x}\right)-\frac{{\mathrm e}^{-2 i x} x^{2} \ln \left({\mathrm e}^{2 i x}+1\right)}{2}+\frac{i {\mathrm e}^{-2 i x} x \polylog \left(2, -{\mathrm e}^{2 i x}\right)}{2}-\frac{{\mathrm e}^{-2 i x} \polylog \left(3, -{\mathrm e}^{2 i x}\right)}{4}+\frac{{\mathrm e}^{-2 i x} x^{2} \ln \left(1-{\mathrm e}^{i x}\right)}{2}-i {\mathrm e}^{-2 i x} x \polylog \left(2, {\mathrm e}^{i x}\right)+{\mathrm e}^{-2 i x} \polylog \left(3, {\mathrm e}^{i x}\right)\right)"," ",0,"2*(a*exp(4*I*x)/(exp(2*I*x)+1)^4)^(1/2)*x*(x-I-I*exp(-2*I*x))+2*(a*exp(4*I*x)/(exp(2*I*x)+1)^4)^(1/2)*(exp(2*I*x)+1)^2*(-1/2*exp(-2*I*x)*ln(exp(2*I*x)+1)-exp(-2*I*x)*Im(x)+exp(-2*I*x)*ln(exp(I*Re(x)))+1/2*exp(-2*I*x)*x^2*ln(1+exp(I*x))-I*exp(-2*I*x)*x*polylog(2,-exp(I*x))+exp(-2*I*x)*polylog(3,-exp(I*x))-1/2*exp(-2*I*x)*x^2*ln(exp(2*I*x)+1)+1/2*I*exp(-2*I*x)*x*polylog(2,-exp(2*I*x))-1/4*exp(-2*I*x)*polylog(3,-exp(2*I*x))+1/2*exp(-2*I*x)*x^2*ln(1-exp(I*x))-I*exp(-2*I*x)*x*polylog(2,exp(I*x))+exp(-2*I*x)*polylog(3,exp(I*x)))","C"
879,1,324,284,0.213000," ","int(x^3*csc(x)*sec(x)*(a*sec(x)^4)^(1/2),x)","\sqrt{\frac{a \,{\mathrm e}^{4 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{4}}}\, x^{2} \left(2 x -3 i-3 i {\mathrm e}^{-2 i x}\right)-2 i \sqrt{\frac{a \,{\mathrm e}^{4 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{4}}}\, \left({\mathrm e}^{2 i x}+1\right)^{2} \left(-\frac{3 \,{\mathrm e}^{-2 i x} x^{2}}{2}-\frac{3 i {\mathrm e}^{-2 i x} x \ln \left({\mathrm e}^{2 i x}+1\right)}{2}-\frac{3 \,{\mathrm e}^{-2 i x} \polylog \left(2, -{\mathrm e}^{2 i x}\right)}{4}+\frac{i {\mathrm e}^{-2 i x} x^{3} \ln \left(1+{\mathrm e}^{i x}\right)}{2}+\frac{3 \,{\mathrm e}^{-2 i x} x^{2} \polylog \left(2, -{\mathrm e}^{i x}\right)}{2}+3 i {\mathrm e}^{-2 i x} x \polylog \left(3, -{\mathrm e}^{i x}\right)-3 \,{\mathrm e}^{-2 i x} \polylog \left(4, -{\mathrm e}^{i x}\right)-\frac{i {\mathrm e}^{-2 i x} x^{3} \ln \left({\mathrm e}^{2 i x}+1\right)}{2}-\frac{3 \,{\mathrm e}^{-2 i x} x^{2} \polylog \left(2, -{\mathrm e}^{2 i x}\right)}{4}-\frac{3 i {\mathrm e}^{-2 i x} x \polylog \left(3, -{\mathrm e}^{2 i x}\right)}{4}+\frac{3 \,{\mathrm e}^{-2 i x} \polylog \left(4, -{\mathrm e}^{2 i x}\right)}{8}+\frac{i {\mathrm e}^{-2 i x} x^{3} \ln \left(1-{\mathrm e}^{i x}\right)}{2}+\frac{3 \,{\mathrm e}^{-2 i x} x^{2} \polylog \left(2, {\mathrm e}^{i x}\right)}{2}+3 i {\mathrm e}^{-2 i x} x \polylog \left(3, {\mathrm e}^{i x}\right)-3 \,{\mathrm e}^{-2 i x} \polylog \left(4, {\mathrm e}^{i x}\right)\right)"," ",0,"(a*exp(4*I*x)/(exp(2*I*x)+1)^4)^(1/2)*x^2*(2*x-3*I-3*I*exp(-2*I*x))-2*I*(a*exp(4*I*x)/(exp(2*I*x)+1)^4)^(1/2)*(exp(2*I*x)+1)^2*(-3/2*exp(-2*I*x)*x^2-3/2*I*exp(-2*I*x)*x*ln(exp(2*I*x)+1)-3/4*exp(-2*I*x)*polylog(2,-exp(2*I*x))+1/2*I*exp(-2*I*x)*x^3*ln(1+exp(I*x))+3/2*exp(-2*I*x)*x^2*polylog(2,-exp(I*x))+3*I*exp(-2*I*x)*x*polylog(3,-exp(I*x))-3*exp(-2*I*x)*polylog(4,-exp(I*x))-1/2*I*exp(-2*I*x)*x^3*ln(exp(2*I*x)+1)-3/4*exp(-2*I*x)*x^2*polylog(2,-exp(2*I*x))-3/4*I*exp(-2*I*x)*x*polylog(3,-exp(2*I*x))+3/8*exp(-2*I*x)*polylog(4,-exp(2*I*x))+1/2*I*exp(-2*I*x)*x^3*ln(1-exp(I*x))+3/2*exp(-2*I*x)*x^2*polylog(2,exp(I*x))+3*I*exp(-2*I*x)*x*polylog(3,exp(I*x))-3*exp(-2*I*x)*polylog(4,exp(I*x)))","A"
880,1,20,19,0.129000," ","int(sin(x)*sin(2*x)*sin(3*x),x)","-\frac{\cos \left(2 x \right)}{8}-\frac{\cos \left(4 x \right)}{16}+\frac{\cos \left(6 x \right)}{24}"," ",0,"-1/8*cos(2*x)-1/16*cos(4*x)+1/24*cos(6*x)","A"
881,1,23,22,0.141000," ","int(cos(x)*cos(2*x)*cos(3*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}"," ",0,"1/4*x+1/8*sin(2*x)+1/16*sin(4*x)+1/24*sin(6*x)","A"
882,1,23,22,0.093000," ","int(cos(x)*sin(2*x)*sin(3*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}"," ",0,"1/4*x+1/8*sin(2*x)-1/16*sin(4*x)-1/24*sin(6*x)","A"
883,1,20,19,0.085000," ","int(cos(2*x)*cos(3*x)*sin(x),x)","-\frac{\cos \left(2 x \right)}{8}+\frac{\cos \left(4 x \right)}{16}-\frac{\cos \left(6 x \right)}{24}"," ",0,"-1/8*cos(2*x)+1/16*cos(4*x)-1/24*cos(6*x)","A"
884,1,7,6,0.004000," ","int(x*sin(x^2),x)","-\frac{\cos \left(x^{2}\right)}{2}"," ",0,"-1/2*cos(x^2)","A"
885,1,97,9,0.082000," ","int((-cos(x)+sin(x))*(cos(x)+sin(x))^5,x)","-\frac{\left(\sin^{5}\left(x \right)+\frac{5 \left(\sin^{3}\left(x \right)\right)}{4}+\frac{15 \sin \left(x \right)}{8}\right) \cos \left(x \right)}{6}+\frac{2 \left(\sin^{6}\left(x \right)\right)}{3}-\frac{5 \left(\cos^{3}\left(x \right)\right) \left(\sin^{3}\left(x \right)\right)}{6}-\frac{5 \left(\cos^{3}\left(x \right)\right) \sin \left(x \right)}{8}+\frac{5 \cos \left(x \right) \sin \left(x \right)}{16}+\frac{5 \left(\cos^{5}\left(x \right)\right) \sin \left(x \right)}{6}-\frac{5 \left(\cos^{3}\left(x \right)+\frac{3 \cos \left(x \right)}{2}\right) \sin \left(x \right)}{24}+\frac{2 \left(\cos^{6}\left(x \right)\right)}{3}-\frac{\left(\cos^{5}\left(x \right)+\frac{5 \left(\cos^{3}\left(x \right)\right)}{4}+\frac{15 \cos \left(x \right)}{8}\right) \sin \left(x \right)}{6}"," ",0,"-1/6*(sin(x)^5+5/4*sin(x)^3+15/8*sin(x))*cos(x)+2/3*sin(x)^6-5/6*cos(x)^3*sin(x)^3-5/8*cos(x)^3*sin(x)+5/16*cos(x)*sin(x)+5/6*cos(x)^5*sin(x)-5/24*(cos(x)^3+3/2*cos(x))*sin(x)+2/3*cos(x)^6-1/6*(cos(x)^5+5/4*cos(x)^3+15/8*cos(x))*sin(x)","B"
886,1,12,11,0.044000," ","int(2*x*sec(x)^2*tan(x),x)","\frac{x}{\cos \left(x \right)^{2}}-\tan \left(x \right)"," ",0,"x/cos(x)^2-tan(x)","A"
887,1,9,8,0.124000," ","int((1+cos(x)^2)/(1+cos(2*x)),x)","\frac{x}{2}+\frac{\tan \left(x \right)}{2}"," ",0,"1/2*x+1/2*tan(x)","A"
888,1,27,10,0.076000," ","int(sin(x)/(cos(x)^3-cos(x)^5),x)","\frac{1}{2 \cos \left(x \right)^{2}}-\ln \left(\cos \left(x \right)\right)+\frac{\ln \left(-1+\cos \left(x \right)\right)}{2}+\frac{\ln \left(1+\cos \left(x \right)\right)}{2}"," ",0,"1/2/cos(x)^2-ln(cos(x))+1/2*ln(-1+cos(x))+1/2*ln(1+cos(x))","B"
889,1,18,17,0.049000," ","int(sec(x)*(5-11*sec(x)^5)^2*tan(x),x)","25 \sec \left(x \right)-\frac{55 \left(\sec^{6}\left(x \right)\right)}{3}+11 \left(\sec^{11}\left(x \right)\right)"," ",0,"25*sec(x)-55/3*sec(x)^6+11*sec(x)^11","A"
890,1,50,36,0.108000," ","int(sin(5*x)^3*tan(5*x)^3,x)","\frac{\sin^{7}\left(5 x \right)}{10 \cos \left(5 x \right)^{2}}+\frac{\left(\sin^{5}\left(5 x \right)\right)}{10}+\frac{\left(\sin^{3}\left(5 x \right)\right)}{6}+\frac{\sin \left(5 x \right)}{2}-\frac{\ln \left(\sec \left(5 x \right)+\tan \left(5 x \right)\right)}{2}"," ",0,"1/10*sin(5*x)^7/cos(5*x)^2+1/10*sin(5*x)^5+1/6*sin(5*x)^3+1/2*sin(5*x)-1/2*ln(sec(5*x)+tan(5*x))","A"
891,1,60,29,0.111000," ","int(sin(5*x)^3*tan(5*x)^4,x)","\frac{\sin^{8}\left(5 x \right)}{15 \cos \left(5 x \right)^{3}}-\frac{\sin^{8}\left(5 x \right)}{3 \cos \left(5 x \right)}-\frac{\left(\frac{16}{5}+\sin^{6}\left(5 x \right)+\frac{6 \left(\sin^{4}\left(5 x \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(5 x \right)\right)}{5}\right) \cos \left(5 x \right)}{3}"," ",0,"1/15*sin(5*x)^8/cos(5*x)^3-1/3*sin(5*x)^8/cos(5*x)-1/3*(16/5+sin(5*x)^6+6/5*sin(5*x)^4+8/5*sin(5*x)^2)*cos(5*x)","B"
892,1,58,44,0.121000," ","int(sin(6*x)^5*tan(6*x)^3,x)","\frac{\sin^{9}\left(6 x \right)}{12 \cos \left(6 x \right)^{2}}+\frac{\left(\sin^{7}\left(6 x \right)\right)}{12}+\frac{7 \left(\sin^{5}\left(6 x \right)\right)}{60}+\frac{7 \left(\sin^{3}\left(6 x \right)\right)}{36}+\frac{7 \sin \left(6 x \right)}{12}-\frac{7 \ln \left(\sec \left(6 x \right)+\tan \left(6 x \right)\right)}{12}"," ",0,"1/12*sin(6*x)^9/cos(6*x)^2+1/12*sin(6*x)^7+7/60*sin(6*x)^5+7/36*sin(6*x)^3+7/12*sin(6*x)-7/12*ln(sec(6*x)+tan(6*x))","A"
893,1,32,29,0.096000," ","int((-1+sec(2*x)^2)^3*sin(2*x),x)","\frac{1}{10 \cos \left(2 x \right)^{5}}-\frac{1}{2 \cos \left(2 x \right)^{3}}+\frac{3}{2 \cos \left(2 x \right)}+\frac{\cos \left(2 x \right)}{2}"," ",0,"1/10/cos(2*x)^5-1/2/cos(2*x)^3+3/2/cos(2*x)+1/2*cos(2*x)","A"
894,1,46,26,0.056000," ","int(sin(x)*tan(x)^5,x)","\frac{\sin^{7}\left(x \right)}{4 \cos \left(x \right)^{4}}-\frac{3 \left(\sin^{7}\left(x \right)\right)}{8 \cos \left(x \right)^{2}}-\frac{3 \left(\sin^{5}\left(x \right)\right)}{8}-\frac{5 \left(\sin^{3}\left(x \right)\right)}{8}-\frac{15 \sin \left(x \right)}{8}+\frac{15 \ln \left(\sec \left(x \right)+\tan \left(x \right)\right)}{8}"," ",0,"1/4*sin(x)^7/cos(x)^4-3/8*sin(x)^7/cos(x)^2-3/8*sin(x)^5-5/8*sin(x)^3-15/8*sin(x)+15/8*ln(sec(x)+tan(x))","A"
895,1,68,37,0.169000," ","int(cos(2*x)^5*cot(2*x)^4,x)","-\frac{\cos^{10}\left(2 x \right)}{6 \sin \left(2 x \right)^{3}}+\frac{7 \left(\cos^{10}\left(2 x \right)\right)}{6 \sin \left(2 x \right)}+\frac{7 \left(\frac{128}{35}+\cos^{8}\left(2 x \right)+\frac{8 \left(\cos^{6}\left(2 x \right)\right)}{7}+\frac{48 \left(\cos^{4}\left(2 x \right)\right)}{35}+\frac{64 \left(\cos^{2}\left(2 x \right)\right)}{35}\right) \sin \left(2 x \right)}{6}"," ",0,"-1/6/sin(2*x)^3*cos(2*x)^10+7/6/sin(2*x)*cos(2*x)^10+7/6*(128/35+cos(2*x)^8+8/7*cos(2*x)^6+48/35*cos(2*x)^4+64/35*cos(2*x)^2)*sin(2*x)","A"
896,1,72,69,0.156000," ","int(cos(3*x)*(-1+csc(3*x)^2)^3*(1-sin(3*x)^2)^5,x)","\frac{\left(\sin^{11}\left(3 x \right)\right)}{33}-\frac{8 \left(\sin^{9}\left(3 x \right)\right)}{27}+\frac{4 \left(\sin^{7}\left(3 x \right)\right)}{3}-\frac{56 \left(\sin^{5}\left(3 x \right)\right)}{15}+\frac{70 \left(\sin^{3}\left(3 x \right)\right)}{9}-\frac{56 \sin \left(3 x \right)}{3}-\frac{28}{3 \sin \left(3 x \right)}+\frac{8}{9 \sin \left(3 x \right)^{3}}-\frac{1}{15 \sin \left(3 x \right)^{5}}"," ",0,"1/33*sin(3*x)^11-8/27*sin(3*x)^9+4/3*sin(3*x)^7-56/15*sin(3*x)^5+70/9*sin(3*x)^3-56/3*sin(3*x)-28/3/sin(3*x)+8/9/sin(3*x)^3-1/15/sin(3*x)^5","A"
897,1,37,38,0.155000," ","int(cot(2*x)*(-1+csc(2*x)^2)^2*(1-sin(2*x)^2)^2,x)","\frac{\left(\sin^{4}\left(2 x \right)\right)}{8}+\cos^{2}\left(2 x \right)+3 \ln \left(\sin \left(2 x \right)\right)+\frac{1}{\sin \left(2 x \right)^{2}}-\frac{1}{8 \sin \left(2 x \right)^{4}}"," ",0,"1/8*sin(2*x)^4+cos(2*x)^2+3*ln(sin(2*x))+1/sin(2*x)^2-1/8/sin(2*x)^4","A"
898,1,56,53,0.151000," ","int(cos(2*x)*(-1+csc(2*x)^2)^4*(1-sin(2*x)^2)^2,x)","\frac{\left(\sin^{5}\left(2 x \right)\right)}{10}-\left(\sin^{3}\left(2 x \right)\right)+\frac{15 \sin \left(2 x \right)}{2}+\frac{10}{\sin \left(2 x \right)}-\frac{5}{2 \sin \left(2 x \right)^{3}}+\frac{3}{5 \sin \left(2 x \right)^{5}}-\frac{1}{14 \sin \left(2 x \right)^{7}}"," ",0,"1/10*sin(2*x)^5-sin(2*x)^3+15/2*sin(2*x)+10/sin(2*x)-5/2/sin(2*x)^3+3/5/sin(2*x)^5-1/14/sin(2*x)^7","A"
899,1,49,48,0.158000," ","int(cot(3*x)*(-1+csc(3*x)^2)^3*(1-sin(3*x)^2)^2,x)","-\frac{\left(\sin^{4}\left(3 x \right)\right)}{12}-\frac{5 \left(\cos^{2}\left(3 x \right)\right)}{6}-\frac{10 \ln \left(\sin \left(3 x \right)\right)}{3}-\frac{5}{3 \sin \left(3 x \right)^{2}}+\frac{5}{12 \sin \left(3 x \right)^{4}}-\frac{1}{18 \sin \left(3 x \right)^{6}}"," ",0,"-1/12*sin(3*x)^4-5/6*cos(3*x)^2-10/3*ln(sin(3*x))-5/3/sin(3*x)^2+5/12/sin(3*x)^4-1/18/sin(3*x)^6","A"
900,1,38,37,0.137000," ","int((1+cot(9*x)^2)^2*(1+tan(9*x)^2)^3,x)","-\frac{4 \cot \left(9 x \right)}{9}-\frac{\left(\cot^{3}\left(9 x \right)\right)}{27}+\frac{2 \tan \left(9 x \right)}{3}+\frac{4 \left(\tan^{3}\left(9 x \right)\right)}{27}+\frac{\left(\tan^{5}\left(9 x \right)\right)}{45}"," ",0,"-4/9*cot(9*x)-1/27*cot(9*x)^3+2/3*tan(9*x)+4/27*tan(9*x)^3+1/45*tan(9*x)^5","A"
901,1,38,39,0.062000," ","int(cos(x)*(9-7*sin(x)^3)^2/(1-sin(x)^2),x)","-\frac{49 \left(\sin^{5}\left(x \right)\right)}{5}-\frac{49 \left(\sin^{3}\left(x \right)\right)}{3}+63 \left(\sin^{2}\left(x \right)\right)-49 \sin \left(x \right)-2 \ln \left(\sin \left(x \right)-1\right)+128 \ln \left(1+\sin \left(x \right)\right)"," ",0,"-49/5*sin(x)^5-49/3*sin(x)^3+63*sin(x)^2-49*sin(x)-2*ln(sin(x)-1)+128*ln(1+sin(x))","A"
902,1,69,38,0.109000," ","int(cos(2*x)^4*cot(2*x)^5,x)","-\frac{\cos^{10}\left(2 x \right)}{8 \sin \left(2 x \right)^{4}}+\frac{3 \left(\cos^{10}\left(2 x \right)\right)}{8 \sin \left(2 x \right)^{2}}+\frac{3 \left(\cos^{8}\left(2 x \right)\right)}{8}+\frac{\left(\cos^{6}\left(2 x \right)\right)}{2}+\frac{3 \left(\cos^{4}\left(2 x \right)\right)}{4}+\frac{3 \left(\cos^{2}\left(2 x \right)\right)}{2}+3 \ln \left(\sin \left(2 x \right)\right)"," ",0,"-1/8/sin(2*x)^4*cos(2*x)^10+3/8/sin(2*x)^2*cos(2*x)^10+3/8*cos(2*x)^8+1/2*cos(2*x)^6+3/4*cos(2*x)^4+3/2*cos(2*x)^2+3*ln(sin(2*x))","A"
903,1,55,50,0.072000," ","int(sec(x)*tan(x)^2/(4+3*sec(x)),x)","\frac{2 \sqrt{7}\, \arctanh \left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{7}}{7}\right)}{9}-\frac{1}{3 \left(\tan \left(\frac{x}{2}\right)-1\right)}+\frac{4 \ln \left(\tan \left(\frac{x}{2}\right)-1\right)}{9}-\frac{1}{3 \left(1+\tan \left(\frac{x}{2}\right)\right)}-\frac{4 \ln \left(1+\tan \left(\frac{x}{2}\right)\right)}{9}"," ",0,"2/9*7^(1/2)*arctanh(1/7*tan(1/2*x)*7^(1/2))-1/3/(tan(1/2*x)-1)+4/9*ln(tan(1/2*x)-1)-1/3/(1+tan(1/2*x))-4/9*ln(1+tan(1/2*x))","A"
904,1,32,14,0.039000," ","int(x*sec(1+x)*tan(1+x),x)","\frac{1+x}{\cos \left(1+x \right)}-\ln \left(\sec \left(1+x \right)+\tan \left(1+x \right)\right)-\frac{1}{\cos \left(1+x \right)}"," ",0,"(1+x)/cos(1+x)-ln(sec(1+x)+tan(1+x))-1/cos(1+x)","B"
905,1,13,12,0.079000," ","int(sin(2*x)/(9-sin(x)^2)^(1/2),x)","-2 \sqrt{9-\left(\sin^{2}\left(x \right)\right)}"," ",0,"-2*(9-sin(x)^2)^(1/2)","A"
906,1,10,9,0.113000," ","int(sin(2*x)/(9-cos(x)^4)^(1/2),x)","-\arcsin \left(\frac{\left(\cos^{2}\left(x \right)\right)}{3}\right)"," ",0,"-arcsin(1/3*cos(x)^2)","A"
907,1,35,34,0.059000," ","int(cos(1/x)/x^5,x)","6 \cos \left(\frac{1}{x}\right)-\frac{3 \cos \left(\frac{1}{x}\right)}{x^{2}}-\frac{\sin \left(\frac{1}{x}\right)}{x^{3}}+\frac{6 \sin \left(\frac{1}{x}\right)}{x}"," ",0,"6*cos(1/x)-3*cos(1/x)/x^2-sin(1/x)/x^3+6*sin(1/x)/x","A"
908,1,24,17,0.075000," ","int(cos(1+x)^3*sin(1+x)^3,x)","-\frac{\left(\cos^{4}\left(1+x \right)\right) \left(\sin^{2}\left(1+x \right)\right)}{6}-\frac{\left(\cos^{4}\left(1+x \right)\right)}{12}"," ",0,"-1/6*cos(1+x)^4*sin(1+x)^2-1/12*cos(1+x)^4","A"
909,1,97,85,0.042000," ","int((1+2*x)^3*sin(1+2*x)^2,x)","\frac{\left(1+2 x \right)^{3} \left(-\frac{\sin \left(1+2 x \right) \cos \left(1+2 x \right)}{2}+x +\frac{1}{2}\right)}{2}-\frac{3 \left(\cos^{2}\left(1+2 x \right)\right) \left(1+2 x \right)^{2}}{8}+\frac{3 \left(1+2 x \right) \left(\frac{\sin \left(1+2 x \right) \cos \left(1+2 x \right)}{2}+x +\frac{1}{2}\right)}{4}-\frac{3 \left(1+2 x \right)^{2}}{16}-\frac{3 \left(\sin^{2}\left(1+2 x \right)\right)}{16}-\frac{3 \left(1+2 x \right)^{4}}{16}"," ",0,"1/2*(1+2*x)^3*(-1/2*sin(1+2*x)*cos(1+2*x)+x+1/2)-3/8*cos(1+2*x)^2*(1+2*x)^2+3/4*(1+2*x)*(1/2*sin(1+2*x)*cos(1+2*x)+x+1/2)-3/16*(1+2*x)^2-3/16*sin(1+2*x)^2-3/16*(1+2*x)^4","A"
910,1,51,31,0.108000," ","int((-1+sec(x))/(1-tan(x)),x)","\frac{\ln \left(\tan^{2}\left(\frac{x}{2}\right)+2 \tan \left(\frac{x}{2}\right)-1\right)}{2}+\sqrt{2}\, \arctanh \left(\frac{\left(2 \tan \left(\frac{x}{2}\right)+2\right) \sqrt{2}}{4}\right)-\frac{\ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{2}-\frac{x}{2}"," ",0,"1/2*ln(tan(1/2*x)^2+2*tan(1/2*x)-1)+2^(1/2)*arctanh(1/4*(2*tan(1/2*x)+2)*2^(1/2))-1/2*ln(1+tan(1/2*x)^2)-1/2*x","A"
911,1,46,45,0.140000," ","int(x^2*cos(3*x)*cos(5*x),x)","\frac{x \cos \left(2 x \right)}{4}+\frac{x \cos \left(8 x \right)}{64}-\frac{\sin \left(2 x \right)}{8}+\frac{x^{2} \sin \left(2 x \right)}{4}-\frac{\sin \left(8 x \right)}{512}+\frac{x^{2} \sin \left(8 x \right)}{16}"," ",0,"1/4*x*cos(2*x)+1/64*x*cos(8*x)-1/8*sin(2*x)+1/4*x^2*sin(2*x)-1/512*sin(8*x)+1/16*x^2*sin(8*x)","A"
912,1,134,41,0.256000," ","int((cos(x)+sin(x))/cos(x)^(1/2)/sin(x)^(1/2),x)","\frac{\sqrt{\frac{1-\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}}\, \sqrt{2}\, \sqrt{\frac{\cos \left(x \right)-1+\sin \left(x \right)}{\sin \left(x \right)}}\, \sqrt{\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \left(\sin^{\frac{3}{2}}\left(x \right)\right) \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{\frac{1-\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right)\right)}{\sqrt{\cos \left(x \right)}\, \left(-1+\cos \left(x \right)\right)}"," ",0,"((1-cos(x)+sin(x))/sin(x))^(1/2)*2^(1/2)*((cos(x)-1+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*sin(x)^(3/2)*(I*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))-I*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))+EllipticF(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2*2^(1/2)))/cos(x)^(1/2)/(-1+cos(x))","C"
913,1,8,5,0.063000," ","int(sec(x)^2*(1+sin(x)),x)","\tan \left(x \right)+\frac{1}{\cos \left(x \right)}"," ",0,"tan(x)+1/cos(x)","A"
914,1,30,11,0.194000," ","int(10*x^9*cos(x^5*ln(x))-x^10*(x^4+5*x^4*ln(x))*sin(x^5*ln(x)),x)","\frac{x^{10} x^{i x^{5}}}{2}+\frac{x^{10} x^{-i x^{5}}}{2}"," ",0,"1/2*x^10*x^(I*x^5)+1/2*x^10/(x^(I*x^5))","C"
915,1,22,19,0.360000," ","int(cos(1/2*x)^2*tan(1/4*Pi+1/2*x),x)","\frac{x}{2}-\frac{\cos \left(x \right)}{2}+\frac{\ln \left(\sec \left(x \right)+\tan \left(x \right)\right)}{2}-\frac{\ln \left(\cos \left(x \right)\right)}{2}"," ",0,"1/2*x-1/2*cos(x)+1/2*ln(sec(x)+tan(x))-1/2*ln(cos(x))","A"
916,1,62,57,0.026000," ","int((2+3*x)^2*sin(x)^3,x)","-3 x^{2} \left(2+\sin^{2}\left(x \right)\right) \cos \left(x \right)+12 \cos \left(x \right)+12 x \sin \left(x \right)+2 \left(\sin^{3}\left(x \right)\right) x -\frac{2 \left(2+\sin^{2}\left(x \right)\right) \cos \left(x \right)}{3}-4 x \left(2+\sin^{2}\left(x \right)\right) \cos \left(x \right)+\frac{4 \left(\sin^{3}\left(x \right)\right)}{3}+8 \sin \left(x \right)"," ",0,"-3*x^2*(2+sin(x)^2)*cos(x)+12*cos(x)+12*x*sin(x)+2*sin(x)^3*x-2/3*(2+sin(x)^2)*cos(x)-4*x*(2+sin(x)^2)*cos(x)+4/3*sin(x)^3+8*sin(x)","A"
917,1,11,8,0.085000," ","int(sec(x)^(1+m)*sin(x),x)","\frac{\left(\frac{1}{\cos \left(x \right)}\right)^{m}}{m}"," ",0,"1/m*(1/cos(x))^m","A"
918,0,0,32,0.368000," ","int(cos(b*x+a)^n*sin(b*x+a)^(-2-n),x)","\int \left(\cos^{n}\left(b x +a \right)\right) \left(\sin^{-2-n}\left(b x +a \right)\right)\, dx"," ",0,"int(cos(b*x+a)^n*sin(b*x+a)^(-2-n),x)","F"
919,1,4,3,0.152000," ","int(1/(sec(x)+sin(x)*tan(x)),x)","\arctan \left(\sin \left(x \right)\right)"," ",0,"arctan(sin(x))","A"
920,1,36,35,0.032000," ","int((c*x^2+b*x+a)*sin(x),x)","c \left(-x^{2} \cos \left(x \right)+2 \cos \left(x \right)+2 x \sin \left(x \right)\right)+b \left(\sin \left(x \right)-x \cos \left(x \right)\right)-a \cos \left(x \right)"," ",0,"c*(-x^2*cos(x)+2*cos(x)+2*x*sin(x))+b*(sin(x)-x*cos(x))-a*cos(x)","A"
921,1,7,6,0.026000," ","int(sin(x^5)/x,x)","\frac{\Si \left(x^{5}\right)}{5}"," ",0,"1/5*Si(x^5)","A"
922,1,38,37,0.034000," ","int(sin(2^x)/(1+2^x),x)","\frac{\Si \left(2^{x}\right)}{\ln \left(2\right)}-\frac{\cos \left(1\right) \Si \left(1+2^{x}\right)}{\ln \left(2\right)}+\frac{\Ci \left(1+2^{x}\right) \sin \left(1\right)}{\ln \left(2\right)}"," ",0,"Si(2^x)/ln(2)-cos(1)*Si(1+2^x)/ln(2)+Ci(1+2^x)*sin(1)/ln(2)","A"
923,1,11,10,0.019000," ","int(x*cos(2*x^2)*sin(2*x^2)^(3/4),x)","\frac{\left(\sin^{\frac{7}{4}}\left(2 x^{2}\right)\right)}{7}"," ",0,"1/7*sin(2*x^2)^(7/4)","A"
924,1,15,8,0.098000," ","int(x*sec(x^2)^2*tan(x^2)^2,x)","\frac{\sin^{3}\left(x^{2}\right)}{6 \cos \left(x^{2}\right)^{3}}"," ",0,"1/6*sin(x^2)^3/cos(x^2)^3","A"
925,1,16,15,0.049000," ","int(x^2*cos(b*x^3+a)^7*sin(b*x^3+a),x)","-\frac{\cos^{8}\left(b \,x^{3}+a \right)}{24 b}"," ",0,"-1/24*cos(b*x^3+a)^8/b","A"
926,1,403,117,0.950000," ","int(x^5*cos(b*x^3+a)^7*sin(b*x^3+a),x)","\frac{-\frac{4 x^{3}}{3 b}+\frac{4 \tan \left(b \,x^{3}+a \right)}{3 b^{2}}+\frac{4 x^{3} \left(\tan^{2}\left(b \,x^{3}+a \right)\right)}{3 b}}{128+128 \left(\tan^{2}\left(b \,x^{3}+a \right)\right)}+\frac{\frac{\tan \left(b \,x^{3}+a \right)}{b^{2}}-\frac{x^{3}}{b}-\frac{\tan^{3}\left(b \,x^{3}+a \right)}{b^{2}}+\frac{6 x^{3} \left(\tan^{2}\left(b \,x^{3}+a \right)\right)}{b}-\frac{x^{3} \left(\tan^{4}\left(b \,x^{3}+a \right)\right)}{b}}{128 \left(1+\tan^{2}\left(b \,x^{3}+a \right)\right)^{2}}+\frac{-6 x^{3} b \left(\cos^{2}\left(3 b \,x^{3}+3 a \right)\right)-18 \left(\cos^{2}\left(b \,x^{3}+a \right)\right) b \,x^{3}+12 b \,x^{3}+\sin \left(3 b \,x^{3}+3 a \right) \cos \left(3 b \,x^{3}+3 a \right)+9 \cos \left(b \,x^{3}+a \right) \sin \left(b \,x^{3}+a \right)}{1152 b^{2}}+\frac{-\frac{x^{3}}{6 b}+\frac{\tan \left(2 b \,x^{3}+2 a \right)}{12 b^{2}}+\frac{x^{3} \left(\tan^{2}\left(2 b \,x^{3}+2 a \right)\right)}{6 b}}{128+128 \left(\tan^{2}\left(2 b \,x^{3}+2 a \right)\right)}+\frac{-\frac{x^{3}}{24 b}+\frac{\tan \left(2 b \,x^{3}+2 a \right)}{48 b^{2}}-\frac{\tan^{3}\left(2 b \,x^{3}+2 a \right)}{48 b^{2}}+\frac{x^{3} \left(\tan^{2}\left(2 b \,x^{3}+2 a \right)\right)}{4 b}-\frac{x^{3} \left(\tan^{4}\left(2 b \,x^{3}+2 a \right)\right)}{24 b}}{128 \left(1+\tan^{2}\left(2 b \,x^{3}+2 a \right)\right)^{2}}"," ",0,"1/128*(-4/3*x^3/b+4/3/b^2*tan(b*x^3+a)+4/3*x^3/b*tan(b*x^3+a)^2)/(1+tan(b*x^3+a)^2)+1/128*(1/b^2*tan(b*x^3+a)-x^3/b-1/b^2*tan(b*x^3+a)^3+6*x^3/b*tan(b*x^3+a)^2-x^3/b*tan(b*x^3+a)^4)/(1+tan(b*x^3+a)^2)^2+1/1152*(-6*x^3*b*cos(3*b*x^3+3*a)^2-18*cos(b*x^3+a)^2*b*x^3+12*b*x^3+sin(3*b*x^3+3*a)*cos(3*b*x^3+3*a)+9*cos(b*x^3+a)*sin(b*x^3+a))/b^2+1/128*(-1/6*x^3/b+1/12/b^2*tan(2*b*x^3+2*a)+1/6*x^3/b*tan(2*b*x^3+2*a)^2)/(1+tan(2*b*x^3+2*a)^2)+1/128*(-1/24*x^3/b+1/48/b^2*tan(2*b*x^3+2*a)-1/48/b^2*tan(2*b*x^3+2*a)^3+1/4*x^3/b*tan(2*b*x^3+2*a)^2-1/24*x^3/b*tan(2*b*x^3+2*a)^4)/(1+tan(2*b*x^3+2*a)^2)^2","B"
927,1,160,100,0.309000," ","int(x^5*sec(b*x^3+a)^7*tan(b*x^3+a),x)","\frac{i \left(15 \,{\mathrm e}^{13 i \left(b \,x^{3}+a \right)}-3072 i b \,x^{3} {\mathrm e}^{7 i \left(b \,x^{3}+a \right)}+100 \,{\mathrm e}^{11 i \left(b \,x^{3}+a \right)}+283 \,{\mathrm e}^{9 i \left(b \,x^{3}+a \right)}-283 \,{\mathrm e}^{5 i \left(b \,x^{3}+a \right)}-100 \,{\mathrm e}^{3 i \left(b \,x^{3}+a \right)}-15 \,{\mathrm e}^{i \left(b \,x^{3}+a \right)}\right)}{504 b^{2} \left({\mathrm e}^{2 i \left(b \,x^{3}+a \right)}+1\right)^{7}}+\frac{5 \ln \left({\mathrm e}^{i \left(b \,x^{3}+a \right)}-i\right)}{336 b^{2}}-\frac{5 \ln \left({\mathrm e}^{i \left(b \,x^{3}+a \right)}+i\right)}{336 b^{2}}"," ",0,"1/504*I/b^2/(exp(2*I*(b*x^3+a))+1)^7*(15*exp(13*I*(b*x^3+a))-3072*I*b*x^3*exp(7*I*(b*x^3+a))+100*exp(11*I*(b*x^3+a))+283*exp(9*I*(b*x^3+a))-283*exp(5*I*(b*x^3+a))-100*exp(3*I*(b*x^3+a))-15*exp(I*(b*x^3+a)))+5/336/b^2*ln(exp(I*(b*x^3+a))-I)-5/336/b^2*ln(exp(I*(b*x^3+a))+I)","C"
928,1,7,6,0.035000," ","int(sec(1/x)^2/x^2,x)","-\tan \left(\frac{1}{x}\right)"," ",0,"-tan(1/x)","A"
929,1,5,4,0.001000," ","int(3*x^2*cos(x^3),x)","\sin \left(x^{3}\right)"," ",0,"sin(x^3)","A"
930,1,24,23,0.041000," ","int((1+2*x)*sec(1+2*x)^2,x)","\frac{\ln \left(\cos \left(1+2 x \right)\right)}{2}+\frac{\left(1+2 x \right) \tan \left(1+2 x \right)}{2}"," ",0,"1/2*ln(cos(1+2*x))+1/2*(1+2*x)*tan(1+2*x)","A"
931,1,28,22,1.042000," ","int(x^4/b/(x^3+3*sin(b*x+a))^(1/2)+x^2*cos(b*x+a)/(x^3+3*sin(b*x+a))^(1/2)+4/3*x*(x^3+3*sin(b*x+a))^(1/2)/b,x)","\frac{\sqrt{2 x^{3}+6 \sin \left(b x +a \right)}\, \sqrt{2}\, x^{2}}{3 b}"," ",0,"1/3*(2*x^3+6*sin(b*x+a))^(1/2)/b*2^(1/2)*x^2","A"
932,0,0,26,1.096000," ","int(x^2*cos(b*x+a)/(x^3+3*sin(b*x+a))^(1/2),x)","\int \frac{x^{2} \cos \left(b x +a \right)}{\sqrt{x^{3}+3 \sin \left(b x +a \right)}}\, dx"," ",0,"int(x^2*cos(b*x+a)/(x^3+3*sin(b*x+a))^(1/2),x)","F"
933,1,57,8,0.188000," ","int((cos(x)+sin(x))/(exp(-x)+sin(x)),x)","\frac{x +x \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{1+\tan^{2}\left(\frac{x}{2}\right)}-\ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)+\ln \left({\mathrm e}^{-x} \left(\tan^{2}\left(\frac{x}{2}\right)\right)+{\mathrm e}^{-x}+2 \tan \left(\frac{x}{2}\right)\right)"," ",0,"(x+x*tan(1/2*x)^2)/(1+tan(1/2*x)^2)-ln(1+tan(1/2*x)^2)+ln(exp(-x)*tan(1/2*x)^2+exp(-x)+2*tan(1/2*x))","B"
934,1,60,69,0.051000," ","int(sin(d*x+c)*(a*sin(d*x+c)^2+b*sin(d*x+c)^3),x)","\frac{b \left(-\frac{\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)-\frac{a \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(b*(-1/4*(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)+3/8*d*x+3/8*c)-1/3*a*(2+sin(d*x+c)^2)*cos(d*x+c))","A"
935,1,125,147,0.076000," ","int(sin(d*x+c)*(a*sin(d*x+c)^2+b*sin(d*x+c)^3)^2,x)","\frac{-\frac{b^{2} \left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)}{7}+2 a b \left(-\frac{\left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)-\frac{a^{2} \left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(-1/7*b^2*(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c)+2*a*b*(-1/6*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/16*d*x+5/16*c)-1/5*a^2*(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))","A"
936,1,84,81,0.076000," ","int(sin(d*x+c)*(a*sin(d*x+c)+b*sin(d*x+c)^2+c*sin(d*x+c)^3),x)","\frac{c \left(-\frac{\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)-\frac{b \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}+a \left(-\frac{\sin \left(d x +c \right) \cos \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(c*(-1/4*(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)+3/8*d*x+3/8*c)-1/3*b*(2+sin(d*x+c)^2)*cos(d*x+c)+a*(-1/2*sin(d*x+c)*cos(d*x+c)+1/2*d*x+1/2*c))","A"
937,1,213,264,0.086000," ","int(sin(d*x+c)*(a*sin(d*x+c)+b*sin(d*x+c)^2+c*sin(d*x+c)^3)^2,x)","\frac{-\frac{c^{2} \left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)}{7}+2 c b \left(-\frac{\left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)-\frac{2 a c \left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)}{5}-\frac{b^{2} \left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)}{5}+2 a b \left(-\frac{\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)-\frac{a^{2} \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(-1/7*c^2*(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c)+2*c*b*(-1/6*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/16*d*x+5/16*c)-2/5*a*c*(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c)-1/5*b^2*(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c)+2*a*b*(-1/4*(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)+3/8*d*x+3/8*c)-1/3*a^2*(2+sin(d*x+c)^2)*cos(d*x+c))","A"
938,1,136,87,0.338000," ","int(sin(d*x+c)*(a+c*sin(d*x+c)+b/sin(d*x+c)^(1/2)),x)","c x -\frac{a \cos \left(d x +c \right)}{d}-\frac{c \left(\frac{\sin \left(d x +c \right) \cos \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}-\frac{b \sqrt{1+\sin \left(d x +c \right)}\, \sqrt{-2 \sin \left(d x +c \right)+2}\, \sqrt{-\sin \left(d x +c \right)}\, \left(2 \EllipticE \left(\sqrt{1+\sin \left(d x +c \right)}, \frac{\sqrt{2}}{2}\right)-\EllipticF \left(\sqrt{1+\sin \left(d x +c \right)}, \frac{\sqrt{2}}{2}\right)\right)}{\cos \left(d x +c \right) \sqrt{\sin \left(d x +c \right)}\, d}"," ",0,"c*x-a*cos(d*x+c)/d-c/d*(1/2*sin(d*x+c)*cos(d*x+c)+1/2*d*x+1/2*c)-b*(1+sin(d*x+c))^(1/2)*(-2*sin(d*x+c)+2)^(1/2)*(-sin(d*x+c))^(1/2)*(2*EllipticE((1+sin(d*x+c))^(1/2),1/2*2^(1/2))-EllipticF((1+sin(d*x+c))^(1/2),1/2*2^(1/2)))/cos(d*x+c)/sin(d*x+c)^(1/2)/d","A"
939,1,266,200,0.325000," ","int(sin(d*x+c)*(a+c*sin(d*x+c)+b/sin(d*x+c)^(1/2))^2,x)","b^{2} x -\frac{a^{2} \cos \left(d x +c \right)}{d}-\frac{c^{2} \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3 d}+\frac{2 a c \left(-\frac{\sin \left(d x +c \right) \cos \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}+\frac{2 b \left(3 a \sqrt{1+\sin \left(d x +c \right)}\, \sqrt{-2 \sin \left(d x +c \right)+2}\, \sqrt{-\sin \left(d x +c \right)}\, \EllipticF \left(\sqrt{1+\sin \left(d x +c \right)}, \frac{\sqrt{2}}{2}\right)+\sqrt{1+\sin \left(d x +c \right)}\, \sqrt{-2 \sin \left(d x +c \right)+2}\, \sqrt{-\sin \left(d x +c \right)}\, \EllipticF \left(\sqrt{1+\sin \left(d x +c \right)}, \frac{\sqrt{2}}{2}\right) c -6 a \sqrt{1+\sin \left(d x +c \right)}\, \sqrt{-2 \sin \left(d x +c \right)+2}\, \sqrt{-\sin \left(d x +c \right)}\, \EllipticE \left(\sqrt{1+\sin \left(d x +c \right)}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) c \right)}{3 \cos \left(d x +c \right) \sqrt{\sin \left(d x +c \right)}\, d}"," ",0,"b^2*x-a^2*cos(d*x+c)/d-1/3*c^2/d*(2+sin(d*x+c)^2)*cos(d*x+c)+2*a*c/d*(-1/2*sin(d*x+c)*cos(d*x+c)+1/2*d*x+1/2*c)+2/3*b*(3*a*(1+sin(d*x+c))^(1/2)*(-2*sin(d*x+c)+2)^(1/2)*(-sin(d*x+c))^(1/2)*EllipticF((1+sin(d*x+c))^(1/2),1/2*2^(1/2))+(1+sin(d*x+c))^(1/2)*(-2*sin(d*x+c)+2)^(1/2)*(-sin(d*x+c))^(1/2)*EllipticF((1+sin(d*x+c))^(1/2),1/2*2^(1/2))*c-6*a*(1+sin(d*x+c))^(1/2)*(-2*sin(d*x+c)+2)^(1/2)*(-sin(d*x+c))^(1/2)*EllipticE((1+sin(d*x+c))^(1/2),1/2*2^(1/2))-2*cos(d*x+c)^2*sin(d*x+c)*c)/cos(d*x+c)/sin(d*x+c)^(1/2)/d","A"
940,1,86,31,0.437000," ","int(f^(b*x+a)*(cos(d*x+c)+I*sin(d*x+c))^n,x)","\frac{{\mathrm e}^{\left(b x +a \right) \ln \left(f \right)} {\mathrm e}^{n \ln \left(\frac{2 i \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{1-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\right)}}{i d n +b \ln \left(f \right)}"," ",0,"1/(I*d*n+b*ln(f))*exp((b*x+a)*ln(f))*exp(n*ln(2*I*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)+(1-tan(1/2*d*x+1/2*c)^2)/(1+tan(1/2*d*x+1/2*c)^2)))","B"
941,1,86,33,0.393000," ","int(f^(b*x+a)*(cos(d*x+c)-I*sin(d*x+c))^n,x)","\frac{{\mathrm e}^{\left(b x +a \right) \ln \left(f \right)} {\mathrm e}^{n \ln \left(\frac{1-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 i \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\right)}}{-i d n +b \ln \left(f \right)}"," ",0,"1/(-I*d*n+b*ln(f))*exp((b*x+a)*ln(f))*exp(n*ln((1-tan(1/2*d*x+1/2*c)^2)/(1+tan(1/2*d*x+1/2*c)^2)-2*I*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)))","B"
942,1,184,106,0.736000," ","int((cos(b*x+a)^5-sin(b*x+a)^5)/(cos(b*x+a)^5+sin(b*x+a)^5),x)","\frac{\ln \left(\tan \left(b x +a \right) \sqrt{5}+2 \left(\tan^{2}\left(b x +a \right)\right)-\tan \left(b x +a \right)+2\right) \sqrt{5}}{5 b}+\frac{\ln \left(\tan \left(b x +a \right) \sqrt{5}+2 \left(\tan^{2}\left(b x +a \right)\right)-\tan \left(b x +a \right)+2\right)}{5 b}-\frac{\ln \left(-\tan \left(b x +a \right) \sqrt{5}+2 \left(\tan^{2}\left(b x +a \right)\right)-\tan \left(b x +a \right)+2\right) \sqrt{5}}{5 b}+\frac{\ln \left(-\tan \left(b x +a \right) \sqrt{5}+2 \left(\tan^{2}\left(b x +a \right)\right)-\tan \left(b x +a \right)+2\right)}{5 b}-\frac{\ln \left(1+\tan^{2}\left(b x +a \right)\right)}{2 b}+\frac{\ln \left(1+\tan \left(b x +a \right)\right)}{5 b}"," ",0,"1/5/b*ln(tan(b*x+a)*5^(1/2)+2*tan(b*x+a)^2-tan(b*x+a)+2)*5^(1/2)+1/5/b*ln(tan(b*x+a)*5^(1/2)+2*tan(b*x+a)^2-tan(b*x+a)+2)-1/5/b*ln(-tan(b*x+a)*5^(1/2)+2*tan(b*x+a)^2-tan(b*x+a)+2)*5^(1/2)+1/5/b*ln(-tan(b*x+a)*5^(1/2)+2*tan(b*x+a)^2-tan(b*x+a)+2)-1/2/b*ln(1+tan(b*x+a)^2)+1/5*ln(1+tan(b*x+a))/b","A"
943,1,108,60,0.385000," ","int((cos(b*x+a)^4-sin(b*x+a)^4)/(cos(b*x+a)^4+sin(b*x+a)^4),x)","\frac{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \tan \left(b x +a \right)+\tan^{2}\left(b x +a \right)}{1-\sqrt{2}\, \tan \left(b x +a \right)+\tan^{2}\left(b x +a \right)}\right)}{8 b}-\frac{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \tan \left(b x +a \right)+\tan^{2}\left(b x +a \right)}{1+\sqrt{2}\, \tan \left(b x +a \right)+\tan^{2}\left(b x +a \right)}\right)}{8 b}"," ",0,"1/8/b*2^(1/2)*ln((1+2^(1/2)*tan(b*x+a)+tan(b*x+a)^2)/(1-2^(1/2)*tan(b*x+a)+tan(b*x+a)^2))-1/8/b*2^(1/2)*ln((1-2^(1/2)*tan(b*x+a)+tan(b*x+a)^2)/(1+2^(1/2)*tan(b*x+a)+tan(b*x+a)^2))","A"
944,1,56,51,0.648000," ","int((cos(b*x+a)^3-sin(b*x+a)^3)/(cos(b*x+a)^3+sin(b*x+a)^3),x)","-\frac{2 \ln \left(1-\tan \left(b x +a \right)+\tan^{2}\left(b x +a \right)\right)}{3 b}+\frac{\ln \left(1+\tan^{2}\left(b x +a \right)\right)}{2 b}+\frac{\ln \left(1+\tan \left(b x +a \right)\right)}{3 b}"," ",0,"-2/3*ln(1-tan(b*x+a)+tan(b*x+a)^2)/b+1/2/b*ln(1+tan(b*x+a)^2)+1/3*ln(1+tan(b*x+a))/b","A"
945,1,17,16,0.230000," ","int((cos(b*x+a)^2-sin(b*x+a)^2)/(cos(b*x+a)^2+sin(b*x+a)^2),x)","\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{b}"," ",0,"cos(b*x+a)*sin(b*x+a)/b","A"
946,1,19,18,0.246000," ","int((cos(b*x+a)-sin(b*x+a))/(cos(b*x+a)+sin(b*x+a)),x)","\frac{\ln \left(\cos \left(b x +a \right)+\sin \left(b x +a \right)\right)}{b}"," ",0,"ln(cos(b*x+a)+sin(b*x+a))/b","A"
947,1,32,19,0.746000," ","int((-csc(b*x+a)+sec(b*x+a))/(csc(b*x+a)+sec(b*x+a)),x)","\frac{\ln \left(1+\tan^{2}\left(b x +a \right)\right)}{2 b}-\frac{\ln \left(1+\tan \left(b x +a \right)\right)}{b}"," ",0,"1/2/b*ln(1+tan(b*x+a)^2)-ln(1+tan(b*x+a))/b","A"
948,1,18,17,0.342000," ","int((-csc(b*x+a)^2+sec(b*x+a)^2)/(csc(b*x+a)^2+sec(b*x+a)^2),x)","-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{b}"," ",0,"-cos(b*x+a)*sin(b*x+a)/b","A"
949,1,56,50,0.827000," ","int((-csc(b*x+a)^3+sec(b*x+a)^3)/(csc(b*x+a)^3+sec(b*x+a)^3),x)","\frac{2 \ln \left(1-\tan \left(b x +a \right)+\tan^{2}\left(b x +a \right)\right)}{3 b}-\frac{\ln \left(1+\tan^{2}\left(b x +a \right)\right)}{2 b}-\frac{\ln \left(1+\tan \left(b x +a \right)\right)}{3 b}"," ",0,"2/3*ln(1-tan(b*x+a)+tan(b*x+a)^2)/b-1/2/b*ln(1+tan(b*x+a)^2)-1/3*ln(1+tan(b*x+a))/b","A"
950,1,108,60,0.511000," ","int((-csc(b*x+a)^4+sec(b*x+a)^4)/(csc(b*x+a)^4+sec(b*x+a)^4),x)","-\frac{\sqrt{2}\, \ln \left(\frac{1+\sqrt{2}\, \tan \left(b x +a \right)+\tan^{2}\left(b x +a \right)}{1-\sqrt{2}\, \tan \left(b x +a \right)+\tan^{2}\left(b x +a \right)}\right)}{8 b}+\frac{\sqrt{2}\, \ln \left(\frac{1-\sqrt{2}\, \tan \left(b x +a \right)+\tan^{2}\left(b x +a \right)}{1+\sqrt{2}\, \tan \left(b x +a \right)+\tan^{2}\left(b x +a \right)}\right)}{8 b}"," ",0,"-1/8/b*2^(1/2)*ln((1+2^(1/2)*tan(b*x+a)+tan(b*x+a)^2)/(1-2^(1/2)*tan(b*x+a)+tan(b*x+a)^2))+1/8/b*2^(1/2)*ln((1-2^(1/2)*tan(b*x+a)+tan(b*x+a)^2)/(1+2^(1/2)*tan(b*x+a)+tan(b*x+a)^2))","A"