1,1,33,0,0.653437," ","integrate(2/(3-cos(4+6*x)),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(6 \, x + 4\right) - \sqrt{2}}{4 \, \sin\left(6 \, x + 4\right)}\right)"," ",0,"-1/12*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(6*x + 4) - sqrt(2))/sin(6*x + 4))","A",0
2,1,33,0,0.688025," ","integrate(2*csc(4+6*x)/(-cot(4+6*x)+3*csc(4+6*x)),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(6 \, x + 4\right) - \sqrt{2}}{4 \, \sin\left(6 \, x + 4\right)}\right)"," ",0,"-1/12*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(6*x + 4) - sqrt(2))/sin(6*x + 4))","A",0
3,1,43,0,0.646601," ","integrate(1/(1+sin(2+3*x)^2),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(3 \, x + 2\right)^{2} - 2 \, \sqrt{2}}{4 \, \cos\left(3 \, x + 2\right) \sin\left(3 \, x + 2\right)}\right)"," ",0,"-1/12*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(3*x + 2)^2 - 2*sqrt(2))/(cos(3*x + 2)*sin(3*x + 2)))","A",0
4,1,43,0,0.731469," ","integrate(1/(2-cos(2+3*x)^2),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(3 \, x + 2\right)^{2} - 2 \, \sqrt{2}}{4 \, \cos\left(3 \, x + 2\right) \sin\left(3 \, x + 2\right)}\right)"," ",0,"-1/12*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(3*x + 2)^2 - 2*sqrt(2))/(cos(3*x + 2)*sin(3*x + 2)))","A",0
5,1,43,0,0.735001," ","integrate(1/(cos(2+3*x)^2+2*sin(2+3*x)^2),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(3 \, x + 2\right)^{2} - 2 \, \sqrt{2}}{4 \, \cos\left(3 \, x + 2\right) \sin\left(3 \, x + 2\right)}\right)"," ",0,"-1/12*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(3*x + 2)^2 - 2*sqrt(2))/(cos(3*x + 2)*sin(3*x + 2)))","A",0
6,1,43,0,0.509627," ","integrate(sec(2+3*x)^2/(1+2*tan(2+3*x)^2),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(3 \, x + 2\right)^{2} - 2 \, \sqrt{2}}{4 \, \cos\left(3 \, x + 2\right) \sin\left(3 \, x + 2\right)}\right)"," ",0,"-1/12*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(3*x + 2)^2 - 2*sqrt(2))/(cos(3*x + 2)*sin(3*x + 2)))","A",0
7,1,43,0,0.644195," ","integrate(csc(2+3*x)^2/(2+cot(2+3*x)^2),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(3 \, x + 2\right)^{2} - 2 \, \sqrt{2}}{4 \, \cos\left(3 \, x + 2\right) \sin\left(3 \, x + 2\right)}\right)"," ",0,"-1/12*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(3*x + 2)^2 - 2*sqrt(2))/(cos(3*x + 2)*sin(3*x + 2)))","A",0
8,1,74,0,0.506416," ","integrate(2/(1-3*cos(4+6*x)),x, algorithm=""fricas"")","\frac{1}{24} \, \sqrt{2} \log\left(-\frac{7 \, \cos\left(6 \, x + 4\right)^{2} - 4 \, {\left(\sqrt{2} \cos\left(6 \, x + 4\right) - 3 \, \sqrt{2}\right)} \sin\left(6 \, x + 4\right) + 6 \, \cos\left(6 \, x + 4\right) - 17}{9 \, \cos\left(6 \, x + 4\right)^{2} - 6 \, \cos\left(6 \, x + 4\right) + 1}\right)"," ",0,"1/24*sqrt(2)*log(-(7*cos(6*x + 4)^2 - 4*(sqrt(2)*cos(6*x + 4) - 3*sqrt(2))*sin(6*x + 4) + 6*cos(6*x + 4) - 17)/(9*cos(6*x + 4)^2 - 6*cos(6*x + 4) + 1))","A",0
9,1,74,0,0.912065," ","integrate(2*csc(4+6*x)/(-3*cot(4+6*x)+csc(4+6*x)),x, algorithm=""fricas"")","\frac{1}{24} \, \sqrt{2} \log\left(-\frac{7 \, \cos\left(6 \, x + 4\right)^{2} - 4 \, {\left(\sqrt{2} \cos\left(6 \, x + 4\right) - 3 \, \sqrt{2}\right)} \sin\left(6 \, x + 4\right) + 6 \, \cos\left(6 \, x + 4\right) - 17}{9 \, \cos\left(6 \, x + 4\right)^{2} - 6 \, \cos\left(6 \, x + 4\right) + 1}\right)"," ",0,"1/24*sqrt(2)*log(-(7*cos(6*x + 4)^2 - 4*(sqrt(2)*cos(6*x + 4) - 3*sqrt(2))*sin(6*x + 4) + 6*cos(6*x + 4) - 17)/(9*cos(6*x + 4)^2 - 6*cos(6*x + 4) + 1))","A",0
10,1,86,0,0.654422," ","integrate(1/(-1+3*sin(2+3*x)^2),x, algorithm=""fricas"")","\frac{1}{24} \, \sqrt{2} \log\left(-\frac{7 \, \cos\left(3 \, x + 2\right)^{4} - 4 \, \cos\left(3 \, x + 2\right)^{2} - 4 \, {\left(\sqrt{2} \cos\left(3 \, x + 2\right)^{3} - 2 \, \sqrt{2} \cos\left(3 \, x + 2\right)\right)} \sin\left(3 \, x + 2\right) - 4}{9 \, \cos\left(3 \, x + 2\right)^{4} - 12 \, \cos\left(3 \, x + 2\right)^{2} + 4}\right)"," ",0,"1/24*sqrt(2)*log(-(7*cos(3*x + 2)^4 - 4*cos(3*x + 2)^2 - 4*(sqrt(2)*cos(3*x + 2)^3 - 2*sqrt(2)*cos(3*x + 2))*sin(3*x + 2) - 4)/(9*cos(3*x + 2)^4 - 12*cos(3*x + 2)^2 + 4))","A",0
11,1,86,0,0.569416," ","integrate(1/(2-3*cos(2+3*x)^2),x, algorithm=""fricas"")","\frac{1}{24} \, \sqrt{2} \log\left(-\frac{7 \, \cos\left(3 \, x + 2\right)^{4} - 4 \, \cos\left(3 \, x + 2\right)^{2} - 4 \, {\left(\sqrt{2} \cos\left(3 \, x + 2\right)^{3} - 2 \, \sqrt{2} \cos\left(3 \, x + 2\right)\right)} \sin\left(3 \, x + 2\right) - 4}{9 \, \cos\left(3 \, x + 2\right)^{4} - 12 \, \cos\left(3 \, x + 2\right)^{2} + 4}\right)"," ",0,"1/24*sqrt(2)*log(-(7*cos(3*x + 2)^4 - 4*cos(3*x + 2)^2 - 4*(sqrt(2)*cos(3*x + 2)^3 - 2*sqrt(2)*cos(3*x + 2))*sin(3*x + 2) - 4)/(9*cos(3*x + 2)^4 - 12*cos(3*x + 2)^2 + 4))","A",0
12,1,86,0,0.780610," ","integrate(1/(-cos(2+3*x)^2+2*sin(2+3*x)^2),x, algorithm=""fricas"")","\frac{1}{24} \, \sqrt{2} \log\left(-\frac{7 \, \cos\left(3 \, x + 2\right)^{4} - 4 \, \cos\left(3 \, x + 2\right)^{2} - 4 \, {\left(\sqrt{2} \cos\left(3 \, x + 2\right)^{3} - 2 \, \sqrt{2} \cos\left(3 \, x + 2\right)\right)} \sin\left(3 \, x + 2\right) - 4}{9 \, \cos\left(3 \, x + 2\right)^{4} - 12 \, \cos\left(3 \, x + 2\right)^{2} + 4}\right)"," ",0,"1/24*sqrt(2)*log(-(7*cos(3*x + 2)^4 - 4*cos(3*x + 2)^2 - 4*(sqrt(2)*cos(3*x + 2)^3 - 2*sqrt(2)*cos(3*x + 2))*sin(3*x + 2) - 4)/(9*cos(3*x + 2)^4 - 12*cos(3*x + 2)^2 + 4))","A",0
13,1,86,0,0.771017," ","integrate(sec(2+3*x)^2/(-1+2*tan(2+3*x)^2),x, algorithm=""fricas"")","\frac{1}{24} \, \sqrt{2} \log\left(-\frac{7 \, \cos\left(3 \, x + 2\right)^{4} - 4 \, \cos\left(3 \, x + 2\right)^{2} - 4 \, {\left(\sqrt{2} \cos\left(3 \, x + 2\right)^{3} - 2 \, \sqrt{2} \cos\left(3 \, x + 2\right)\right)} \sin\left(3 \, x + 2\right) - 4}{9 \, \cos\left(3 \, x + 2\right)^{4} - 12 \, \cos\left(3 \, x + 2\right)^{2} + 4}\right)"," ",0,"1/24*sqrt(2)*log(-(7*cos(3*x + 2)^4 - 4*cos(3*x + 2)^2 - 4*(sqrt(2)*cos(3*x + 2)^3 - 2*sqrt(2)*cos(3*x + 2))*sin(3*x + 2) - 4)/(9*cos(3*x + 2)^4 - 12*cos(3*x + 2)^2 + 4))","A",0
14,1,86,0,0.683962," ","integrate(csc(2+3*x)^2/(2-cot(2+3*x)^2),x, algorithm=""fricas"")","\frac{1}{24} \, \sqrt{2} \log\left(-\frac{7 \, \cos\left(3 \, x + 2\right)^{4} - 4 \, \cos\left(3 \, x + 2\right)^{2} - 4 \, {\left(\sqrt{2} \cos\left(3 \, x + 2\right)^{3} - 2 \, \sqrt{2} \cos\left(3 \, x + 2\right)\right)} \sin\left(3 \, x + 2\right) - 4}{9 \, \cos\left(3 \, x + 2\right)^{4} - 12 \, \cos\left(3 \, x + 2\right)^{2} + 4}\right)"," ",0,"1/24*sqrt(2)*log(-(7*cos(3*x + 2)^4 - 4*cos(3*x + 2)^2 - 4*(sqrt(2)*cos(3*x + 2)^3 - 2*sqrt(2)*cos(3*x + 2))*sin(3*x + 2) - 4)/(9*cos(3*x + 2)^4 - 12*cos(3*x + 2)^2 + 4))","A",0
15,1,31,0,1.319428," ","integrate(2/(3+cos(4+6*x)),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(6 \, x + 4\right) + \sqrt{2}}{4 \, \sin\left(6 \, x + 4\right)}\right)"," ",0,"-1/12*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(6*x + 4) + sqrt(2))/sin(6*x + 4))","A",0
16,1,31,0,0.596890," ","integrate(2*csc(4+6*x)/(cot(4+6*x)+3*csc(4+6*x)),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(6 \, x + 4\right) + \sqrt{2}}{4 \, \sin\left(6 \, x + 4\right)}\right)"," ",0,"-1/12*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(6*x + 4) + sqrt(2))/sin(6*x + 4))","A",0
17,1,43,0,0.755137," ","integrate(1/(2-sin(2+3*x)^2),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(3 \, x + 2\right)^{2} - \sqrt{2}}{4 \, \cos\left(3 \, x + 2\right) \sin\left(3 \, x + 2\right)}\right)"," ",0,"-1/12*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(3*x + 2)^2 - sqrt(2))/(cos(3*x + 2)*sin(3*x + 2)))","A",0
18,1,43,0,0.684677," ","integrate(1/(1+cos(2+3*x)^2),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(3 \, x + 2\right)^{2} - \sqrt{2}}{4 \, \cos\left(3 \, x + 2\right) \sin\left(3 \, x + 2\right)}\right)"," ",0,"-1/12*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(3*x + 2)^2 - sqrt(2))/(cos(3*x + 2)*sin(3*x + 2)))","A",0
19,1,43,0,0.507915," ","integrate(1/(2*cos(2+3*x)^2+sin(2+3*x)^2),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(3 \, x + 2\right)^{2} - \sqrt{2}}{4 \, \cos\left(3 \, x + 2\right) \sin\left(3 \, x + 2\right)}\right)"," ",0,"-1/12*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(3*x + 2)^2 - sqrt(2))/(cos(3*x + 2)*sin(3*x + 2)))","A",0
20,1,43,0,0.608554," ","integrate(sec(2+3*x)^2/(2+tan(2+3*x)^2),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(3 \, x + 2\right)^{2} - \sqrt{2}}{4 \, \cos\left(3 \, x + 2\right) \sin\left(3 \, x + 2\right)}\right)"," ",0,"-1/12*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(3*x + 2)^2 - sqrt(2))/(cos(3*x + 2)*sin(3*x + 2)))","A",0
21,1,43,0,0.553777," ","integrate(csc(2+3*x)^2/(1+2*cot(2+3*x)^2),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(3 \, x + 2\right)^{2} - \sqrt{2}}{4 \, \cos\left(3 \, x + 2\right) \sin\left(3 \, x + 2\right)}\right)"," ",0,"-1/12*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(3*x + 2)^2 - sqrt(2))/(cos(3*x + 2)*sin(3*x + 2)))","A",0
22,1,74,0,0.541045," ","integrate(-2/(1+3*cos(4+6*x)),x, algorithm=""fricas"")","\frac{1}{24} \, \sqrt{2} \log\left(-\frac{7 \, \cos\left(6 \, x + 4\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(6 \, x + 4\right) + 3 \, \sqrt{2}\right)} \sin\left(6 \, x + 4\right) - 6 \, \cos\left(6 \, x + 4\right) - 17}{9 \, \cos\left(6 \, x + 4\right)^{2} + 6 \, \cos\left(6 \, x + 4\right) + 1}\right)"," ",0,"1/24*sqrt(2)*log(-(7*cos(6*x + 4)^2 + 4*(sqrt(2)*cos(6*x + 4) + 3*sqrt(2))*sin(6*x + 4) - 6*cos(6*x + 4) - 17)/(9*cos(6*x + 4)^2 + 6*cos(6*x + 4) + 1))","A",0
23,1,74,0,0.548550," ","integrate(-2*csc(4+6*x)/(3*cot(4+6*x)+csc(4+6*x)),x, algorithm=""fricas"")","\frac{1}{24} \, \sqrt{2} \log\left(-\frac{7 \, \cos\left(6 \, x + 4\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(6 \, x + 4\right) + 3 \, \sqrt{2}\right)} \sin\left(6 \, x + 4\right) - 6 \, \cos\left(6 \, x + 4\right) - 17}{9 \, \cos\left(6 \, x + 4\right)^{2} + 6 \, \cos\left(6 \, x + 4\right) + 1}\right)"," ",0,"1/24*sqrt(2)*log(-(7*cos(6*x + 4)^2 + 4*(sqrt(2)*cos(6*x + 4) + 3*sqrt(2))*sin(6*x + 4) - 6*cos(6*x + 4) - 17)/(9*cos(6*x + 4)^2 + 6*cos(6*x + 4) + 1))","A",0
24,1,85,0,0.587276," ","integrate(1/(-2+3*sin(2+3*x)^2),x, algorithm=""fricas"")","\frac{1}{24} \, \sqrt{2} \log\left(-\frac{7 \, \cos\left(3 \, x + 2\right)^{4} - 10 \, \cos\left(3 \, x + 2\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(3 \, x + 2\right)^{3} + \sqrt{2} \cos\left(3 \, x + 2\right)\right)} \sin\left(3 \, x + 2\right) - 1}{9 \, \cos\left(3 \, x + 2\right)^{4} - 6 \, \cos\left(3 \, x + 2\right)^{2} + 1}\right)"," ",0,"1/24*sqrt(2)*log(-(7*cos(3*x + 2)^4 - 10*cos(3*x + 2)^2 + 4*(sqrt(2)*cos(3*x + 2)^3 + sqrt(2)*cos(3*x + 2))*sin(3*x + 2) - 1)/(9*cos(3*x + 2)^4 - 6*cos(3*x + 2)^2 + 1))","A",0
25,1,85,0,0.594295," ","integrate(1/(1-3*cos(2+3*x)^2),x, algorithm=""fricas"")","\frac{1}{24} \, \sqrt{2} \log\left(-\frac{7 \, \cos\left(3 \, x + 2\right)^{4} - 10 \, \cos\left(3 \, x + 2\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(3 \, x + 2\right)^{3} + \sqrt{2} \cos\left(3 \, x + 2\right)\right)} \sin\left(3 \, x + 2\right) - 1}{9 \, \cos\left(3 \, x + 2\right)^{4} - 6 \, \cos\left(3 \, x + 2\right)^{2} + 1}\right)"," ",0,"1/24*sqrt(2)*log(-(7*cos(3*x + 2)^4 - 10*cos(3*x + 2)^2 + 4*(sqrt(2)*cos(3*x + 2)^3 + sqrt(2)*cos(3*x + 2))*sin(3*x + 2) - 1)/(9*cos(3*x + 2)^4 - 6*cos(3*x + 2)^2 + 1))","A",0
26,1,85,0,0.574625," ","integrate(1/(-2*cos(2+3*x)^2+sin(2+3*x)^2),x, algorithm=""fricas"")","\frac{1}{24} \, \sqrt{2} \log\left(-\frac{7 \, \cos\left(3 \, x + 2\right)^{4} - 10 \, \cos\left(3 \, x + 2\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(3 \, x + 2\right)^{3} + \sqrt{2} \cos\left(3 \, x + 2\right)\right)} \sin\left(3 \, x + 2\right) - 1}{9 \, \cos\left(3 \, x + 2\right)^{4} - 6 \, \cos\left(3 \, x + 2\right)^{2} + 1}\right)"," ",0,"1/24*sqrt(2)*log(-(7*cos(3*x + 2)^4 - 10*cos(3*x + 2)^2 + 4*(sqrt(2)*cos(3*x + 2)^3 + sqrt(2)*cos(3*x + 2))*sin(3*x + 2) - 1)/(9*cos(3*x + 2)^4 - 6*cos(3*x + 2)^2 + 1))","A",0
27,1,85,0,0.536407," ","integrate(sec(2+3*x)^2/(-2+tan(2+3*x)^2),x, algorithm=""fricas"")","\frac{1}{24} \, \sqrt{2} \log\left(-\frac{7 \, \cos\left(3 \, x + 2\right)^{4} - 10 \, \cos\left(3 \, x + 2\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(3 \, x + 2\right)^{3} + \sqrt{2} \cos\left(3 \, x + 2\right)\right)} \sin\left(3 \, x + 2\right) - 1}{9 \, \cos\left(3 \, x + 2\right)^{4} - 6 \, \cos\left(3 \, x + 2\right)^{2} + 1}\right)"," ",0,"1/24*sqrt(2)*log(-(7*cos(3*x + 2)^4 - 10*cos(3*x + 2)^2 + 4*(sqrt(2)*cos(3*x + 2)^3 + sqrt(2)*cos(3*x + 2))*sin(3*x + 2) - 1)/(9*cos(3*x + 2)^4 - 6*cos(3*x + 2)^2 + 1))","A",0
28,1,85,0,0.537748," ","integrate(csc(2+3*x)^2/(1-2*cot(2+3*x)^2),x, algorithm=""fricas"")","\frac{1}{24} \, \sqrt{2} \log\left(-\frac{7 \, \cos\left(3 \, x + 2\right)^{4} - 10 \, \cos\left(3 \, x + 2\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(3 \, x + 2\right)^{3} + \sqrt{2} \cos\left(3 \, x + 2\right)\right)} \sin\left(3 \, x + 2\right) - 1}{9 \, \cos\left(3 \, x + 2\right)^{4} - 6 \, \cos\left(3 \, x + 2\right)^{2} + 1}\right)"," ",0,"1/24*sqrt(2)*log(-(7*cos(3*x + 2)^4 - 10*cos(3*x + 2)^2 + 4*(sqrt(2)*cos(3*x + 2)^3 + sqrt(2)*cos(3*x + 2))*sin(3*x + 2) - 1)/(9*cos(3*x + 2)^4 - 6*cos(3*x + 2)^2 + 1))","A",0
29,1,22,0,0.507992," ","integrate((x+sin(x))^2,x, algorithm=""fricas"")","\frac{1}{3} \, x^{3} - 2 \, x \cos\left(x\right) - \frac{1}{2} \, {\left(\cos\left(x\right) - 4\right)} \sin\left(x\right) + \frac{1}{2} \, x"," ",0,"1/3*x^3 - 2*x*cos(x) - 1/2*(cos(x) - 4)*sin(x) + 1/2*x","A",0
30,1,46,0,0.486989," ","integrate((x+sin(x))^3,x, algorithm=""fricas"")","\frac{1}{4} \, x^{4} + \frac{1}{3} \, \cos\left(x\right)^{3} + \frac{3}{4} \, x^{2} - {\left(3 \, x^{2} - 5\right)} \cos\left(x\right) - \frac{3}{4} \, \cos\left(x\right)^{2} - \frac{3}{2} \, {\left(x \cos\left(x\right) - 4 \, x\right)} \sin\left(x\right)"," ",0,"1/4*x^4 + 1/3*cos(x)^3 + 3/4*x^2 - (3*x^2 - 5)*cos(x) - 3/4*cos(x)^2 - 3/2*(x*cos(x) - 4*x)*sin(x)","A",0
31,1,187,0,0.559123," ","integrate(sin(b*x+a)/(d*x^2+c),x, algorithm=""fricas"")","\frac{\sqrt{\frac{b^{2} c}{d}} {\rm Ei}\left(i \, b x - \sqrt{\frac{b^{2} c}{d}}\right) e^{\left(i \, a + \sqrt{\frac{b^{2} c}{d}}\right)} - \sqrt{\frac{b^{2} c}{d}} {\rm Ei}\left(i \, b x + \sqrt{\frac{b^{2} c}{d}}\right) e^{\left(i \, a - \sqrt{\frac{b^{2} c}{d}}\right)} + \sqrt{\frac{b^{2} c}{d}} {\rm Ei}\left(-i \, b x - \sqrt{\frac{b^{2} c}{d}}\right) e^{\left(-i \, a + \sqrt{\frac{b^{2} c}{d}}\right)} - \sqrt{\frac{b^{2} c}{d}} {\rm Ei}\left(-i \, b x + \sqrt{\frac{b^{2} c}{d}}\right) e^{\left(-i \, a - \sqrt{\frac{b^{2} c}{d}}\right)}}{4 \, b c}"," ",0,"1/4*(sqrt(b^2*c/d)*Ei(I*b*x - sqrt(b^2*c/d))*e^(I*a + sqrt(b^2*c/d)) - sqrt(b^2*c/d)*Ei(I*b*x + sqrt(b^2*c/d))*e^(I*a - sqrt(b^2*c/d)) + sqrt(b^2*c/d)*Ei(-I*b*x - sqrt(b^2*c/d))*e^(-I*a + sqrt(b^2*c/d)) - sqrt(b^2*c/d)*Ei(-I*b*x + sqrt(b^2*c/d))*e^(-I*a - sqrt(b^2*c/d)))/(b*c)","C",0
32,1,434,0,2.021482," ","integrate(sin(b*x+a)/(e*x^2+d*x+c),x, algorithm=""fricas"")","-\frac{e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}} {\rm Ei}\left(\frac{-2 i \, b e x - i \, b d - e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}}}{2 \, e}\right) e^{\left(\frac{i \, b d - 2 i \, a e + e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}}}{2 \, e}\right)} - e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}} {\rm Ei}\left(\frac{-2 i \, b e x - i \, b d + e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}}}{2 \, e}\right) e^{\left(\frac{i \, b d - 2 i \, a e - e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}}}{2 \, e}\right)} + e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}} {\rm Ei}\left(\frac{2 i \, b e x + i \, b d - e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}}}{2 \, e}\right) e^{\left(\frac{-i \, b d + 2 i \, a e + e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}}}{2 \, e}\right)} - e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}} {\rm Ei}\left(\frac{2 i \, b e x + i \, b d + e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}}}{2 \, e}\right) e^{\left(\frac{-i \, b d + 2 i \, a e - e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}}}{2 \, e}\right)}}{2 \, {\left(b d^{2} - 4 \, b c e\right)}}"," ",0,"-1/2*(e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2)*Ei(1/2*(-2*I*b*e*x - I*b*d - e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2))/e)*e^(1/2*(I*b*d - 2*I*a*e + e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2))/e) - e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2)*Ei(1/2*(-2*I*b*e*x - I*b*d + e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2))/e)*e^(1/2*(I*b*d - 2*I*a*e - e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2))/e) + e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2)*Ei(1/2*(2*I*b*e*x + I*b*d - e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2))/e)*e^(1/2*(-I*b*d + 2*I*a*e + e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2))/e) - e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2)*Ei(1/2*(2*I*b*e*x + I*b*d + e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2))/e)*e^(1/2*(-I*b*d + 2*I*a*e - e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2))/e))/(b*d^2 - 4*b*c*e)","C",0
33,1,8,0,0.588163," ","integrate(sin((-7+x)^(1/2))/(-7+x)^(1/2),x, algorithm=""fricas"")","-2 \, \cos\left(\sqrt{x - 7}\right)"," ",0,"-2*cos(sqrt(x - 7))","A",0
34,0,0,0,1.267142," ","integrate(sin(x)*(b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{2} + a} \sqrt{\frac{b x^{2} - a}{x^{2}}} \sin\left(x\right)}{b x^{2} - a}, x\right)"," ",0,"integral(-sqrt(-b*x^2 + a)*sqrt((b*x^2 - a)/x^2)*sin(x)/(b*x^2 - a), x)","F",0
35,1,22,0,0.625848," ","integrate(1/x/(1+sin(log(x))),x, algorithm=""fricas"")","-\frac{\cos\left(\log\left(x\right)\right) - \sin\left(\log\left(x\right)\right) + 1}{\cos\left(\log\left(x\right)\right) + \sin\left(\log\left(x\right)\right) + 1}"," ",0,"-(cos(log(x)) - sin(log(x)) + 1)/(cos(log(x)) + sin(log(x)) + 1)","A",0
36,1,139,0,1.086442," ","integrate(sin((b*x+a)/(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(b c - a d\right)} \sin\left(\frac{b}{d}\right) \operatorname{Si}\left(-\frac{b c - a d}{d^{2} x + c d}\right) - {\left({\left(b c - a d\right)} \operatorname{Ci}\left(\frac{b c - a d}{d^{2} x + c d}\right) + {\left(b c - a d\right)} \operatorname{Ci}\left(-\frac{b c - a d}{d^{2} x + c d}\right)\right)} \cos\left(\frac{b}{d}\right) - 2 \, {\left(d^{2} x + c d\right)} \sin\left(\frac{b x + a}{d x + c}\right)}{2 \, d^{2}}"," ",0,"-1/2*(2*(b*c - a*d)*sin(b/d)*sin_integral(-(b*c - a*d)/(d^2*x + c*d)) - ((b*c - a*d)*cos_integral((b*c - a*d)/(d^2*x + c*d)) + (b*c - a*d)*cos_integral(-(b*c - a*d)/(d^2*x + c*d)))*cos(b/d) - 2*(d^2*x + c*d)*sin((b*x + a)/(d*x + c)))/d^2","A",0
37,1,149,0,0.608186," ","integrate(sin((b*x+a)/(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, d^{2} x - 2 \, {\left(d^{2} x + c d\right)} \cos\left(\frac{b x + a}{d x + c}\right)^{2} + 2 \, {\left(b c - a d\right)} \cos\left(\frac{2 \, b}{d}\right) \operatorname{Si}\left(-\frac{2 \, {\left(b c - a d\right)}}{d^{2} x + c d}\right) + {\left({\left(b c - a d\right)} \operatorname{Ci}\left(\frac{2 \, {\left(b c - a d\right)}}{d^{2} x + c d}\right) + {\left(b c - a d\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(b c - a d\right)}}{d^{2} x + c d}\right)\right)} \sin\left(\frac{2 \, b}{d}\right)}{2 \, d^{2}}"," ",0,"1/2*(2*d^2*x - 2*(d^2*x + c*d)*cos((b*x + a)/(d*x + c))^2 + 2*(b*c - a*d)*cos(2*b/d)*sin_integral(-2*(b*c - a*d)/(d^2*x + c*d)) + ((b*c - a*d)*cos_integral(2*(b*c - a*d)/(d^2*x + c*d)) + (b*c - a*d)*cos_integral(-2*(b*c - a*d)/(d^2*x + c*d)))*sin(2*b/d))/d^2","A",0
38,1,277,0,1.136801," ","integrate(sin((b*x+a)/(d*x+c))^3,x, algorithm=""fricas"")","-\frac{6 \, {\left(b c - a d\right)} \sin\left(\frac{b}{d}\right) \operatorname{Si}\left(-\frac{b c - a d}{d^{2} x + c d}\right) - 6 \, {\left(b c - a d\right)} \sin\left(\frac{3 \, b}{d}\right) \operatorname{Si}\left(-\frac{3 \, {\left(b c - a d\right)}}{d^{2} x + c d}\right) + 3 \, {\left({\left(b c - a d\right)} \operatorname{Ci}\left(\frac{3 \, {\left(b c - a d\right)}}{d^{2} x + c d}\right) + {\left(b c - a d\right)} \operatorname{Ci}\left(-\frac{3 \, {\left(b c - a d\right)}}{d^{2} x + c d}\right)\right)} \cos\left(\frac{3 \, b}{d}\right) - 3 \, {\left({\left(b c - a d\right)} \operatorname{Ci}\left(\frac{b c - a d}{d^{2} x + c d}\right) + {\left(b c - a d\right)} \operatorname{Ci}\left(-\frac{b c - a d}{d^{2} x + c d}\right)\right)} \cos\left(\frac{b}{d}\right) - 8 \, {\left(d^{2} x - {\left(d^{2} x + c d\right)} \cos\left(\frac{b x + a}{d x + c}\right)^{2} + c d\right)} \sin\left(\frac{b x + a}{d x + c}\right)}{8 \, d^{2}}"," ",0,"-1/8*(6*(b*c - a*d)*sin(b/d)*sin_integral(-(b*c - a*d)/(d^2*x + c*d)) - 6*(b*c - a*d)*sin(3*b/d)*sin_integral(-3*(b*c - a*d)/(d^2*x + c*d)) + 3*((b*c - a*d)*cos_integral(3*(b*c - a*d)/(d^2*x + c*d)) + (b*c - a*d)*cos_integral(-3*(b*c - a*d)/(d^2*x + c*d)))*cos(3*b/d) - 3*((b*c - a*d)*cos_integral((b*c - a*d)/(d^2*x + c*d)) + (b*c - a*d)*cos_integral(-(b*c - a*d)/(d^2*x + c*d)))*cos(b/d) - 8*(d^2*x - (d^2*x + c*d)*cos((b*x + a)/(d*x + c))^2 + c*d)*sin((b*x + a)/(d*x + c)))/d^2","A",0
39,0,0,0,2.026055," ","integrate(sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))^3/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\cos\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{2} - 1\right)} \sin\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral((cos(sqrt(-a*x + 1)/sqrt(a*x + 1))^2 - 1)*sin(sqrt(-a*x + 1)/sqrt(a*x + 1))/(a^2*x^2 - 1), x)","F",0
40,0,0,0,0.965911," ","integrate(sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{2} - 1}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral((cos(sqrt(-a*x + 1)/sqrt(a*x + 1))^2 - 1)/(a^2*x^2 - 1), x)","F",0
41,0,0,0,0.948508," ","integrate(sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sin\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sin(sqrt(-a*x + 1)/sqrt(a*x + 1))/(a^2*x^2 - 1), x)","F",0
42,0,0,0,1.145413," ","integrate(1/(-a^2*x^2+1)/sin((-a*x+1)^(1/2)/(a*x+1)^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{{\left(a^{2} x^{2} - 1\right)} \sin\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)}, x\right)"," ",0,"integral(-1/((a^2*x^2 - 1)*sin(sqrt(-a*x + 1)/sqrt(a*x + 1))), x)","F",0
43,0,0,0,1.171373," ","integrate(1/(-a^2*x^2+1)/sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{a^{2} x^{2} - {\left(a^{2} x^{2} - 1\right)} \cos\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{2} - 1}, x\right)"," ",0,"integral(-1/(a^2*x^2 - (a^2*x^2 - 1)*cos(sqrt(-a*x + 1)/sqrt(a*x + 1))^2 - 1), x)","F",0
44,1,23,0,2.513101," ","integrate((x+cos(x))^2,x, algorithm=""fricas"")","\frac{1}{3} \, x^{3} + \frac{1}{2} \, {\left(4 \, x + \cos\left(x\right)\right)} \sin\left(x\right) + \frac{1}{2} \, x + 2 \, \cos\left(x\right)"," ",0,"1/3*x^3 + 1/2*(4*x + cos(x))*sin(x) + 1/2*x + 2*cos(x)","A",0
45,1,44,0,0.850869," ","integrate((x+cos(x))^3,x, algorithm=""fricas"")","\frac{1}{4} \, x^{4} + \frac{3}{4} \, x^{2} + 6 \, x \cos\left(x\right) + \frac{3}{4} \, \cos\left(x\right)^{2} + \frac{1}{6} \, {\left(18 \, x^{2} + 9 \, x \cos\left(x\right) + 2 \, \cos\left(x\right)^{2} - 32\right)} \sin\left(x\right)"," ",0,"1/4*x^4 + 3/4*x^2 + 6*x*cos(x) + 3/4*cos(x)^2 + 1/6*(18*x^2 + 9*x*cos(x) + 2*cos(x)^2 - 32)*sin(x)","A",0
46,1,189,0,1.123232," ","integrate(cos(b*x+a)/(d*x^2+c),x, algorithm=""fricas"")","\frac{2 i \, \sqrt{\frac{b^{2} c}{d}} {\rm Ei}\left(i \, b x - \sqrt{\frac{b^{2} c}{d}}\right) e^{\left(i \, a + \sqrt{\frac{b^{2} c}{d}}\right)} - 2 i \, \sqrt{\frac{b^{2} c}{d}} {\rm Ei}\left(i \, b x + \sqrt{\frac{b^{2} c}{d}}\right) e^{\left(i \, a - \sqrt{\frac{b^{2} c}{d}}\right)} - 2 i \, \sqrt{\frac{b^{2} c}{d}} {\rm Ei}\left(-i \, b x - \sqrt{\frac{b^{2} c}{d}}\right) e^{\left(-i \, a + \sqrt{\frac{b^{2} c}{d}}\right)} + 2 i \, \sqrt{\frac{b^{2} c}{d}} {\rm Ei}\left(-i \, b x + \sqrt{\frac{b^{2} c}{d}}\right) e^{\left(-i \, a - \sqrt{\frac{b^{2} c}{d}}\right)}}{8 \, b c}"," ",0,"1/8*(2*I*sqrt(b^2*c/d)*Ei(I*b*x - sqrt(b^2*c/d))*e^(I*a + sqrt(b^2*c/d)) - 2*I*sqrt(b^2*c/d)*Ei(I*b*x + sqrt(b^2*c/d))*e^(I*a - sqrt(b^2*c/d)) - 2*I*sqrt(b^2*c/d)*Ei(-I*b*x - sqrt(b^2*c/d))*e^(-I*a + sqrt(b^2*c/d)) + 2*I*sqrt(b^2*c/d)*Ei(-I*b*x + sqrt(b^2*c/d))*e^(-I*a - sqrt(b^2*c/d)))/(b*c)","C",0
47,1,436,0,1.035643," ","integrate(cos(b*x+a)/(e*x^2+d*x+c),x, algorithm=""fricas"")","-\frac{-i \, e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}} {\rm Ei}\left(\frac{-2 i \, b e x - i \, b d - e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}}}{2 \, e}\right) e^{\left(\frac{i \, b d - 2 i \, a e + e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}}}{2 \, e}\right)} + i \, e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}} {\rm Ei}\left(\frac{-2 i \, b e x - i \, b d + e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}}}{2 \, e}\right) e^{\left(\frac{i \, b d - 2 i \, a e - e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}}}{2 \, e}\right)} + i \, e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}} {\rm Ei}\left(\frac{2 i \, b e x + i \, b d - e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}}}{2 \, e}\right) e^{\left(\frac{-i \, b d + 2 i \, a e + e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}}}{2 \, e}\right)} - i \, e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}} {\rm Ei}\left(\frac{2 i \, b e x + i \, b d + e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}}}{2 \, e}\right) e^{\left(\frac{-i \, b d + 2 i \, a e - e \sqrt{-\frac{b^{2} d^{2} - 4 \, b^{2} c e}{e^{2}}}}{2 \, e}\right)}}{2 \, {\left(b d^{2} - 4 \, b c e\right)}}"," ",0,"-1/2*(-I*e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2)*Ei(1/2*(-2*I*b*e*x - I*b*d - e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2))/e)*e^(1/2*(I*b*d - 2*I*a*e + e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2))/e) + I*e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2)*Ei(1/2*(-2*I*b*e*x - I*b*d + e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2))/e)*e^(1/2*(I*b*d - 2*I*a*e - e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2))/e) + I*e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2)*Ei(1/2*(2*I*b*e*x + I*b*d - e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2))/e)*e^(1/2*(-I*b*d + 2*I*a*e + e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2))/e) - I*e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2)*Ei(1/2*(2*I*b*e*x + I*b*d + e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2))/e)*e^(1/2*(-I*b*d + 2*I*a*e - e*sqrt(-(b^2*d^2 - 4*b^2*c*e)/e^2))/e))/(b*d^2 - 4*b*c*e)","C",0
48,1,8,0,1.626219," ","integrate(x*cos((x^2+1)^(1/2))/(x^2+1)^(1/2),x, algorithm=""fricas"")","\sin\left(\sqrt{x^{2} + 1}\right)"," ",0,"sin(sqrt(x^2 + 1))","A",0
49,1,37,0,0.941138," ","integrate(x*cos(3^(1/2)*(x^2+2)^(1/2))/(x^2+2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} \tan\left(\frac{1}{2} \, \sqrt{3} \sqrt{x^{2} + 2}\right)}{3 \, {\left(\tan\left(\frac{1}{2} \, \sqrt{3} \sqrt{x^{2} + 2}\right)^{2} + 1\right)}}"," ",0,"2/3*sqrt(3)*tan(1/2*sqrt(3)*sqrt(x^2 + 2))/(tan(1/2*sqrt(3)*sqrt(x^2 + 2))^2 + 1)","B",0
50,1,15,0,1.704702," ","integrate((-1+2*x)*cos((6+3*(-1+2*x)^2)^(1/2))/(6+3*(-1+2*x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sin\left(\sqrt{12 \, x^{2} - 12 \, x + 9}\right)"," ",0,"1/6*sin(sqrt(12*x^2 - 12*x + 9))","A",0
51,1,138,0,4.118033," ","integrate(cos((b*x+a)/(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(b c - a d\right)} \cos\left(\frac{b}{d}\right) \operatorname{Si}\left(-\frac{b c - a d}{d^{2} x + c d}\right) - 2 \, {\left(d^{2} x + c d\right)} \cos\left(\frac{b x + a}{d x + c}\right) + {\left({\left(b c - a d\right)} \operatorname{Ci}\left(\frac{b c - a d}{d^{2} x + c d}\right) + {\left(b c - a d\right)} \operatorname{Ci}\left(-\frac{b c - a d}{d^{2} x + c d}\right)\right)} \sin\left(\frac{b}{d}\right)}{2 \, d^{2}}"," ",0,"-1/2*(2*(b*c - a*d)*cos(b/d)*sin_integral(-(b*c - a*d)/(d^2*x + c*d)) - 2*(d^2*x + c*d)*cos((b*x + a)/(d*x + c)) + ((b*c - a*d)*cos_integral((b*c - a*d)/(d^2*x + c*d)) + (b*c - a*d)*cos_integral(-(b*c - a*d)/(d^2*x + c*d)))*sin(b/d))/d^2","A",0
52,1,144,0,2.197018," ","integrate(cos((b*x+a)/(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(d^{2} x + c d\right)} \cos\left(\frac{b x + a}{d x + c}\right)^{2} - 2 \, {\left(b c - a d\right)} \cos\left(\frac{2 \, b}{d}\right) \operatorname{Si}\left(-\frac{2 \, {\left(b c - a d\right)}}{d^{2} x + c d}\right) - {\left({\left(b c - a d\right)} \operatorname{Ci}\left(\frac{2 \, {\left(b c - a d\right)}}{d^{2} x + c d}\right) + {\left(b c - a d\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(b c - a d\right)}}{d^{2} x + c d}\right)\right)} \sin\left(\frac{2 \, b}{d}\right)}{2 \, d^{2}}"," ",0,"1/2*(2*(d^2*x + c*d)*cos((b*x + a)/(d*x + c))^2 - 2*(b*c - a*d)*cos(2*b/d)*sin_integral(-2*(b*c - a*d)/(d^2*x + c*d)) - ((b*c - a*d)*cos_integral(2*(b*c - a*d)/(d^2*x + c*d)) + (b*c - a*d)*cos_integral(-2*(b*c - a*d)/(d^2*x + c*d)))*sin(2*b/d))/d^2","A",0
53,0,0,0,2.693686," ","integrate(cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))^3/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\cos\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{3}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-cos(sqrt(-a*x + 1)/sqrt(a*x + 1))^3/(a^2*x^2 - 1), x)","F",0
54,0,0,0,1.494272," ","integrate(cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\cos\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{2}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-cos(sqrt(-a*x + 1)/sqrt(a*x + 1))^2/(a^2*x^2 - 1), x)","F",0
55,0,0,0,1.773271," ","integrate(cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\cos\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-cos(sqrt(-a*x + 1)/sqrt(a*x + 1))/(a^2*x^2 - 1), x)","F",0
56,0,0,0,0.495583," ","integrate(1/(-a^2*x^2+1)/cos((-a*x+1)^(1/2)/(a*x+1)^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{{\left(a^{2} x^{2} - 1\right)} \cos\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)}, x\right)"," ",0,"integral(-1/((a^2*x^2 - 1)*cos(sqrt(-a*x + 1)/sqrt(a*x + 1))), x)","F",0
57,0,0,0,1.129041," ","integrate(1/(-a^2*x^2+1)/cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{{\left(a^{2} x^{2} - 1\right)} \cos\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{2}}, x\right)"," ",0,"integral(-1/((a^2*x^2 - 1)*cos(sqrt(-a*x + 1)/sqrt(a*x + 1))^2), x)","F",0
58,1,13,0,1.996018," ","integrate(tan(x^(1/2))/x^(1/2),x, algorithm=""fricas"")","-\log\left(\frac{1}{\tan\left(\sqrt{x}\right)^{2} + 1}\right)"," ",0,"-log(1/(tan(sqrt(x))^2 + 1))","A",0
59,1,12,0,1.972245," ","integrate(tan(x^(1/2))^2/x^(1/2),x, algorithm=""fricas"")","-2 \, \sqrt{x} + 2 \, \tan\left(\sqrt{x}\right)"," ",0,"-2*sqrt(x) + 2*tan(sqrt(x))","A",0
60,0,0,0,0.857540," ","integrate(x^(1/2)*tan(x^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{x} \tan\left(\sqrt{x}\right), x\right)"," ",0,"integral(sqrt(x)*tan(sqrt(x)), x)","F",0
61,1,23,0,1.661493," ","integrate(1/2*b*tan(c*x^2+b*x+a)/c+x*tan(c*x^2+b*x+a),x, algorithm=""fricas"")","-\frac{\log\left(\frac{1}{\tan\left(c x^{2} + b x + a\right)^{2} + 1}\right)}{4 \, c}"," ",0,"-1/4*log(1/(tan(c*x^2 + b*x + a)^2 + 1))/c","A",0
62,1,28,0,1.222389," ","integrate(cot(x^(1/2))^2/x^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(\sqrt{x} \sin\left(2 \, \sqrt{x}\right) + \cos\left(2 \, \sqrt{x}\right) + 1\right)}}{\sin\left(2 \, \sqrt{x}\right)}"," ",0,"-2*(sqrt(x)*sin(2*sqrt(x)) + cos(2*sqrt(x)) + 1)/sin(2*sqrt(x))","B",0
63,0,0,0,1.198923," ","integrate((a+b*sec(d*x+c))^(1/2)/(1+cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a}}{\cos\left(d x + c\right) + 1}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)/(cos(d*x + c) + 1), x)","F",0
64,1,72,0,0.942159," ","integrate(sec(b*x+a)*sec(2*b*x+2*a),x, algorithm=""fricas"")","\frac{\sqrt{2} \log\left(-\frac{2 \, \cos\left(b x + a\right)^{2} - 2 \, \sqrt{2} \sin\left(b x + a\right) - 3}{2 \, \cos\left(b x + a\right)^{2} - 1}\right) - \log\left(\sin\left(b x + a\right) + 1\right) + \log\left(-\sin\left(b x + a\right) + 1\right)}{2 \, b}"," ",0,"1/2*(sqrt(2)*log(-(2*cos(b*x + a)^2 - 2*sqrt(2)*sin(b*x + a) - 3)/(2*cos(b*x + a)^2 - 1)) - log(sin(b*x + a) + 1) + log(-sin(b*x + a) + 1))/b","B",0
65,1,72,0,0.980233," ","integrate(sec(b*x+a)*sec(2*b*x+2*a),x, algorithm=""fricas"")","\frac{\sqrt{2} \log\left(-\frac{2 \, \cos\left(b x + a\right)^{2} - 2 \, \sqrt{2} \sin\left(b x + a\right) - 3}{2 \, \cos\left(b x + a\right)^{2} - 1}\right) - \log\left(\sin\left(b x + a\right) + 1\right) + \log\left(-\sin\left(b x + a\right) + 1\right)}{2 \, b}"," ",0,"1/2*(sqrt(2)*log(-(2*cos(b*x + a)^2 - 2*sqrt(2)*sin(b*x + a) - 3)/(2*cos(b*x + a)^2 - 1)) - log(sin(b*x + a) + 1) + log(-sin(b*x + a) + 1))/b","B",0
66,1,10,0,2.012450," ","integrate(sin(x)*sin(2*x),x, algorithm=""fricas"")","-\frac{2}{3} \, {\left(\cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)"," ",0,"-2/3*(cos(x)^2 - 1)*sin(x)","A",0
67,1,13,0,0.585192," ","integrate(sin(x)*sin(3*x),x, algorithm=""fricas"")","-{\left(\cos\left(x\right)^{3} - \cos\left(x\right)\right)} \sin\left(x\right)"," ",0,"-(cos(x)^3 - cos(x))*sin(x)","A",0
68,1,18,0,1.122257," ","integrate(sin(x)*sin(4*x),x, algorithm=""fricas"")","-\frac{4}{15} \, {\left(6 \, \cos\left(x\right)^{4} - 7 \, \cos\left(x\right)^{2} + 1\right)} \sin\left(x\right)"," ",0,"-4/15*(6*cos(x)^4 - 7*cos(x)^2 + 1)*sin(x)","A",0
69,1,26,0,1.082572," ","integrate(sin(x)*sin(m*x),x, algorithm=""fricas"")","-\frac{m \cos\left(m x\right) \sin\left(x\right) - \cos\left(x\right) \sin\left(m x\right)}{m^{2} - 1}"," ",0,"-(m*cos(m*x)*sin(x) - cos(x)*sin(m*x))/(m^2 - 1)","A",0
70,1,9,0,0.784703," ","integrate(cos(2*x)*sin(x),x, algorithm=""fricas"")","-\frac{2}{3} \, \cos\left(x\right)^{3} + \cos\left(x\right)"," ",0,"-2/3*cos(x)^3 + cos(x)","A",0
71,1,13,0,0.829828," ","integrate(cos(3*x)*sin(x),x, algorithm=""fricas"")","-\cos\left(x\right)^{4} + \frac{3}{2} \, \cos\left(x\right)^{2}"," ",0,"-cos(x)^4 + 3/2*cos(x)^2","A",0
72,1,17,0,1.061016," ","integrate(cos(4*x)*sin(x),x, algorithm=""fricas"")","-\frac{8}{5} \, \cos\left(x\right)^{5} + \frac{8}{3} \, \cos\left(x\right)^{3} - \cos\left(x\right)"," ",0,"-8/5*cos(x)^5 + 8/3*cos(x)^3 - cos(x)","A",0
73,1,24,0,0.804940," ","integrate(cos(m*x)*sin(x),x, algorithm=""fricas"")","\frac{m \sin\left(m x\right) \sin\left(x\right) + \cos\left(m x\right) \cos\left(x\right)}{m^{2} - 1}"," ",0,"(m*sin(m*x)*sin(x) + cos(m*x)*cos(x))/(m^2 - 1)","A",0
74,1,38,0,2.060816," ","integrate(sin(x)*tan(2*x),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(-\frac{2 \, \cos\left(x\right)^{2} - 2 \, \sqrt{2} \sin\left(x\right) - 3}{2 \, \cos\left(x\right)^{2} - 1}\right) - \sin\left(x\right)"," ",0,"1/4*sqrt(2)*log(-(2*cos(x)^2 - 2*sqrt(2)*sin(x) - 3)/(2*cos(x)^2 - 1)) - sin(x)","B",0
75,1,39,0,1.907420," ","integrate(sin(x)*tan(3*x),x, algorithm=""fricas"")","\frac{1}{6} \, \log\left(2 \, \sin\left(x\right) + 1\right) + \frac{1}{6} \, \log\left(\sin\left(x\right) + 1\right) - \frac{1}{6} \, \log\left(-\sin\left(x\right) + 1\right) - \frac{1}{6} \, \log\left(-2 \, \sin\left(x\right) + 1\right) - \sin\left(x\right)"," ",0,"1/6*log(2*sin(x) + 1) + 1/6*log(sin(x) + 1) - 1/6*log(-sin(x) + 1) - 1/6*log(-2*sin(x) + 1) - sin(x)","A",0
76,1,101,0,2.459176," ","integrate(sin(x)*tan(4*x),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{\sqrt{2} + 2} \log\left(\sqrt{\sqrt{2} + 2} + 2 \, \sin\left(x\right)\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \log\left(\sqrt{\sqrt{2} + 2} - 2 \, \sin\left(x\right)\right) + \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \log\left(\sqrt{-\sqrt{2} + 2} + 2 \, \sin\left(x\right)\right) - \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \log\left(\sqrt{-\sqrt{2} + 2} - 2 \, \sin\left(x\right)\right) - \sin\left(x\right)"," ",0,"1/8*sqrt(sqrt(2) + 2)*log(sqrt(sqrt(2) + 2) + 2*sin(x)) - 1/8*sqrt(sqrt(2) + 2)*log(sqrt(sqrt(2) + 2) - 2*sin(x)) + 1/8*sqrt(-sqrt(2) + 2)*log(sqrt(-sqrt(2) + 2) + 2*sin(x)) - 1/8*sqrt(-sqrt(2) + 2)*log(sqrt(-sqrt(2) + 2) - 2*sin(x)) - sin(x)","A",0
77,1,136,0,0.835468," ","integrate(sin(x)*tan(5*x),x, algorithm=""fricas"")","\frac{1}{20} \, \sqrt{5} \log\left(\frac{8 \, \cos\left(x\right)^{2} - 4 \, {\left(\sqrt{5} - 1\right)} \sin\left(x\right) + \sqrt{5} - 11}{4 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right) - 3}\right) + \frac{1}{20} \, \sqrt{5} \log\left(-\frac{8 \, \cos\left(x\right)^{2} - 4 \, {\left(\sqrt{5} + 1\right)} \sin\left(x\right) - \sqrt{5} - 11}{4 \, \cos\left(x\right)^{2} - 2 \, \sin\left(x\right) - 3}\right) - \frac{1}{20} \, \log\left(4 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right) - 3\right) + \frac{1}{20} \, \log\left(4 \, \cos\left(x\right)^{2} - 2 \, \sin\left(x\right) - 3\right) + \frac{1}{10} \, \log\left(\sin\left(x\right) + 1\right) - \frac{1}{10} \, \log\left(-\sin\left(x\right) + 1\right) - \sin\left(x\right)"," ",0,"1/20*sqrt(5)*log((8*cos(x)^2 - 4*(sqrt(5) - 1)*sin(x) + sqrt(5) - 11)/(4*cos(x)^2 + 2*sin(x) - 3)) + 1/20*sqrt(5)*log(-(8*cos(x)^2 - 4*(sqrt(5) + 1)*sin(x) - sqrt(5) - 11)/(4*cos(x)^2 - 2*sin(x) - 3)) - 1/20*log(4*cos(x)^2 + 2*sin(x) - 3) + 1/20*log(4*cos(x)^2 - 2*sin(x) - 3) + 1/10*log(sin(x) + 1) - 1/10*log(-sin(x) + 1) - sin(x)","A",0
78,1,134,0,1.792536," ","integrate(sin(x)*tan(6*x),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{\sqrt{3} + 2} \log\left(\sqrt{\sqrt{3} + 2} + 2 \, \sin\left(x\right)\right) - \frac{1}{12} \, \sqrt{\sqrt{3} + 2} \log\left(\sqrt{\sqrt{3} + 2} - 2 \, \sin\left(x\right)\right) + \frac{1}{12} \, \sqrt{-\sqrt{3} + 2} \log\left(\sqrt{-\sqrt{3} + 2} + 2 \, \sin\left(x\right)\right) - \frac{1}{12} \, \sqrt{-\sqrt{3} + 2} \log\left(\sqrt{-\sqrt{3} + 2} - 2 \, \sin\left(x\right)\right) + \frac{1}{12} \, \sqrt{2} \log\left(-\frac{2 \, \cos\left(x\right)^{2} - 2 \, \sqrt{2} \sin\left(x\right) - 3}{2 \, \cos\left(x\right)^{2} - 1}\right) - \sin\left(x\right)"," ",0,"1/12*sqrt(sqrt(3) + 2)*log(sqrt(sqrt(3) + 2) + 2*sin(x)) - 1/12*sqrt(sqrt(3) + 2)*log(sqrt(sqrt(3) + 2) - 2*sin(x)) + 1/12*sqrt(-sqrt(3) + 2)*log(sqrt(-sqrt(3) + 2) + 2*sin(x)) - 1/12*sqrt(-sqrt(3) + 2)*log(sqrt(-sqrt(3) + 2) - 2*sin(x)) + 1/12*sqrt(2)*log(-(2*cos(x)^2 - 2*sqrt(2)*sin(x) - 3)/(2*cos(x)^2 - 1)) - sin(x)","A",0
79,0,0,0,0.731774," ","integrate(sin(x)*tan(n*x),x, algorithm=""fricas"")","{\rm integral}\left(\sin\left(x\right) \tan\left(n x\right), x\right)"," ",0,"integral(sin(x)*tan(n*x), x)","F",0
80,1,19,0,0.680464," ","integrate(cot(2*x)*sin(x),x, algorithm=""fricas"")","-\frac{1}{4} \, \log\left(\sin\left(x\right) + 1\right) + \frac{1}{4} \, \log\left(-\sin\left(x\right) + 1\right) + \sin\left(x\right)"," ",0,"-1/4*log(sin(x) + 1) + 1/4*log(-sin(x) + 1) + sin(x)","B",0
81,1,36,0,0.978449," ","integrate(cot(3*x)*sin(x),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \log\left(-\frac{4 \, \cos\left(x\right)^{2} + 4 \, \sqrt{3} \sin\left(x\right) - 7}{4 \, \cos\left(x\right)^{2} - 1}\right) + \sin\left(x\right)"," ",0,"1/6*sqrt(3)*log(-(4*cos(x)^2 + 4*sqrt(3)*sin(x) - 7)/(4*cos(x)^2 - 1)) + sin(x)","B",0
82,1,52,0,0.571227," ","integrate(cot(4*x)*sin(x),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{2} \log\left(-\frac{2 \, \cos\left(x\right)^{2} + 2 \, \sqrt{2} \sin\left(x\right) - 3}{2 \, \cos\left(x\right)^{2} - 1}\right) - \frac{1}{8} \, \log\left(\sin\left(x\right) + 1\right) + \frac{1}{8} \, \log\left(-\sin\left(x\right) + 1\right) + \sin\left(x\right)"," ",0,"1/8*sqrt(2)*log(-(2*cos(x)^2 + 2*sqrt(2)*sin(x) - 3)/(2*cos(x)^2 - 1)) - 1/8*log(sin(x) + 1) + 1/8*log(-sin(x) + 1) + sin(x)","B",0
83,1,127,0,0.562253," ","integrate(cot(5*x)*sin(x),x, algorithm=""fricas"")","-\frac{1}{20} \, \sqrt{2} \sqrt{\sqrt{5} + 5} \log\left(\sqrt{2} \sqrt{\sqrt{5} + 5} + 4 \, \sin\left(x\right)\right) + \frac{1}{20} \, \sqrt{2} \sqrt{\sqrt{5} + 5} \log\left(\sqrt{2} \sqrt{\sqrt{5} + 5} - 4 \, \sin\left(x\right)\right) - \frac{1}{20} \, \sqrt{2} \sqrt{-\sqrt{5} + 5} \log\left(\sqrt{2} \sqrt{-\sqrt{5} + 5} + 4 \, \sin\left(x\right)\right) + \frac{1}{20} \, \sqrt{2} \sqrt{-\sqrt{5} + 5} \log\left(\sqrt{2} \sqrt{-\sqrt{5} + 5} - 4 \, \sin\left(x\right)\right) + \sin\left(x\right)"," ",0,"-1/20*sqrt(2)*sqrt(sqrt(5) + 5)*log(sqrt(2)*sqrt(sqrt(5) + 5) + 4*sin(x)) + 1/20*sqrt(2)*sqrt(sqrt(5) + 5)*log(sqrt(2)*sqrt(sqrt(5) + 5) - 4*sin(x)) - 1/20*sqrt(2)*sqrt(-sqrt(5) + 5)*log(sqrt(2)*sqrt(-sqrt(5) + 5) + 4*sin(x)) + 1/20*sqrt(2)*sqrt(-sqrt(5) + 5)*log(sqrt(2)*sqrt(-sqrt(5) + 5) - 4*sin(x)) + sin(x)","B",0
84,1,70,0,0.868745," ","integrate(cot(6*x)*sin(x),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \log\left(-\frac{4 \, \cos\left(x\right)^{2} + 4 \, \sqrt{3} \sin\left(x\right) - 7}{4 \, \cos\left(x\right)^{2} - 1}\right) - \frac{1}{12} \, \log\left(2 \, \sin\left(x\right) + 1\right) - \frac{1}{12} \, \log\left(\sin\left(x\right) + 1\right) + \frac{1}{12} \, \log\left(-\sin\left(x\right) + 1\right) + \frac{1}{12} \, \log\left(-2 \, \sin\left(x\right) + 1\right) + \sin\left(x\right)"," ",0,"1/12*sqrt(3)*log(-(4*cos(x)^2 + 4*sqrt(3)*sin(x) - 7)/(4*cos(x)^2 - 1)) - 1/12*log(2*sin(x) + 1) - 1/12*log(sin(x) + 1) + 1/12*log(-sin(x) + 1) + 1/12*log(-2*sin(x) + 1) + sin(x)","B",0
85,1,33,0,0.602398," ","integrate(sec(2*x)*sin(x),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(-\frac{2 \, \cos\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 1}{2 \, \cos\left(x\right)^{2} - 1}\right)"," ",0,"1/4*sqrt(2)*log(-(2*cos(x)^2 + 2*sqrt(2)*cos(x) + 1)/(2*cos(x)^2 - 1))","B",0
86,1,19,0,0.876096," ","integrate(sec(3*x)*sin(x),x, algorithm=""fricas"")","-\frac{1}{6} \, \log\left(4 \, \cos\left(x\right)^{2} - 3\right) + \frac{1}{3} \, \log\left(-\cos\left(x\right)\right)"," ",0,"-1/6*log(4*cos(x)^2 - 3) + 1/3*log(-cos(x))","A",0
87,1,121,0,0.676780," ","integrate(sec(4*x)*sin(x),x, algorithm=""fricas"")","-\frac{1}{8} \, \sqrt{\sqrt{2} + 2} \log\left(\sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 1\right)} + 2 \, \cos\left(x\right)\right) + \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \log\left(\sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 1\right)} - 2 \, \cos\left(x\right)\right) + \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \log\left({\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 2} + 2 \, \cos\left(x\right)\right) - \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \log\left({\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 2} - 2 \, \cos\left(x\right)\right)"," ",0,"-1/8*sqrt(sqrt(2) + 2)*log(sqrt(sqrt(2) + 2)*(sqrt(2) - 1) + 2*cos(x)) + 1/8*sqrt(sqrt(2) + 2)*log(sqrt(sqrt(2) + 2)*(sqrt(2) - 1) - 2*cos(x)) + 1/8*sqrt(-sqrt(2) + 2)*log((sqrt(2) + 1)*sqrt(-sqrt(2) + 2) + 2*cos(x)) - 1/8*sqrt(-sqrt(2) + 2)*log((sqrt(2) + 1)*sqrt(-sqrt(2) + 2) - 2*cos(x))","B",0
88,1,72,0,0.688919," ","integrate(sec(5*x)*sin(x),x, algorithm=""fricas"")","\frac{1}{20} \, \sqrt{5} \log\left(\frac{32 \, \cos\left(x\right)^{4} + 8 \, {\left(\sqrt{5} - 5\right)} \cos\left(x\right)^{2} - 5 \, \sqrt{5} + 15}{16 \, \cos\left(x\right)^{4} - 20 \, \cos\left(x\right)^{2} + 5}\right) + \frac{1}{20} \, \log\left(16 \, \cos\left(x\right)^{4} - 20 \, \cos\left(x\right)^{2} + 5\right) - \frac{1}{5} \, \log\left(-\cos\left(x\right)\right)"," ",0,"1/20*sqrt(5)*log((32*cos(x)^4 + 8*(sqrt(5) - 5)*cos(x)^2 - 5*sqrt(5) + 15)/(16*cos(x)^4 - 20*cos(x)^2 + 5)) + 1/20*log(16*cos(x)^4 - 20*cos(x)^2 + 5) - 1/5*log(-cos(x))","A",0
89,1,153,0,1.054602," ","integrate(sec(6*x)*sin(x),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{\sqrt{3} + 2} \log\left(\sqrt{\sqrt{3} + 2} {\left(\sqrt{3} - 2\right)} + 2 \, \cos\left(x\right)\right) + \frac{1}{12} \, \sqrt{\sqrt{3} + 2} \log\left(\sqrt{\sqrt{3} + 2} {\left(\sqrt{3} - 2\right)} - 2 \, \cos\left(x\right)\right) + \frac{1}{12} \, \sqrt{-\sqrt{3} + 2} \log\left({\left(\sqrt{3} + 2\right)} \sqrt{-\sqrt{3} + 2} + 2 \, \cos\left(x\right)\right) - \frac{1}{12} \, \sqrt{-\sqrt{3} + 2} \log\left({\left(\sqrt{3} + 2\right)} \sqrt{-\sqrt{3} + 2} - 2 \, \cos\left(x\right)\right) + \frac{1}{12} \, \sqrt{2} \log\left(\frac{2 \, \cos\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 1}{2 \, \cos\left(x\right)^{2} - 1}\right)"," ",0,"-1/12*sqrt(sqrt(3) + 2)*log(sqrt(sqrt(3) + 2)*(sqrt(3) - 2) + 2*cos(x)) + 1/12*sqrt(sqrt(3) + 2)*log(sqrt(sqrt(3) + 2)*(sqrt(3) - 2) - 2*cos(x)) + 1/12*sqrt(-sqrt(3) + 2)*log((sqrt(3) + 2)*sqrt(-sqrt(3) + 2) + 2*cos(x)) - 1/12*sqrt(-sqrt(3) + 2)*log((sqrt(3) + 2)*sqrt(-sqrt(3) + 2) - 2*cos(x)) + 1/12*sqrt(2)*log((2*cos(x)^2 - 2*sqrt(2)*cos(x) + 1)/(2*cos(x)^2 - 1))","B",0
90,1,17,0,2.741535," ","integrate(csc(2*x)*sin(x),x, algorithm=""fricas"")","\frac{1}{4} \, \log\left(\sin\left(x\right) + 1\right) - \frac{1}{4} \, \log\left(-\sin\left(x\right) + 1\right)"," ",0,"1/4*log(sin(x) + 1) - 1/4*log(-sin(x) + 1)","B",0
91,1,58,0,1.090380," ","integrate(csc(3*x)*sin(x),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \log\left(-\frac{8 \, \cos\left(x\right)^{4} - 16 \, \cos\left(x\right)^{2} - 4 \, {\left(2 \, \sqrt{3} \cos\left(x\right)^{3} + \sqrt{3} \cos\left(x\right)\right)} \sin\left(x\right) - 1}{16 \, \cos\left(x\right)^{4} - 8 \, \cos\left(x\right)^{2} + 1}\right)"," ",0,"1/12*sqrt(3)*log(-(8*cos(x)^4 - 16*cos(x)^2 - 4*(2*sqrt(3)*cos(x)^3 + sqrt(3)*cos(x))*sin(x) - 1)/(16*cos(x)^4 - 8*cos(x)^2 + 1))","A",0
92,1,50,0,1.971783," ","integrate(csc(4*x)*sin(x),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{2} \log\left(-\frac{2 \, \cos\left(x\right)^{2} - 2 \, \sqrt{2} \sin\left(x\right) - 3}{2 \, \cos\left(x\right)^{2} - 1}\right) - \frac{1}{8} \, \log\left(\sin\left(x\right) + 1\right) + \frac{1}{8} \, \log\left(-\sin\left(x\right) + 1\right)"," ",0,"1/8*sqrt(2)*log(-(2*cos(x)^2 - 2*sqrt(2)*sin(x) - 3)/(2*cos(x)^2 - 1)) - 1/8*log(sin(x) + 1) + 1/8*log(-sin(x) + 1)","B",0
93,1,231,0,0.933244," ","integrate(csc(5*x)*sin(x),x, algorithm=""fricas"")","-\frac{1}{40} \, \sqrt{2} \sqrt{\sqrt{5} + 5} \log\left({\left(\sqrt{5} \sqrt{2} - \sqrt{2}\right)} \sqrt{\sqrt{5} + 5} \cos\left(x\right) \sin\left(x\right) + 2 \, {\left(\sqrt{5} + 1\right)} \cos\left(x\right)^{2} - \sqrt{5} + 3\right) + \frac{1}{40} \, \sqrt{2} \sqrt{\sqrt{5} + 5} \log\left(-{\left(\sqrt{5} \sqrt{2} - \sqrt{2}\right)} \sqrt{\sqrt{5} + 5} \cos\left(x\right) \sin\left(x\right) + 2 \, {\left(\sqrt{5} + 1\right)} \cos\left(x\right)^{2} - \sqrt{5} + 3\right) - \frac{1}{40} \, \sqrt{2} \sqrt{-\sqrt{5} + 5} \log\left({\left(\sqrt{5} \sqrt{2} + \sqrt{2}\right)} \sqrt{-\sqrt{5} + 5} \cos\left(x\right) \sin\left(x\right) + 2 \, {\left(\sqrt{5} - 1\right)} \cos\left(x\right)^{2} - \sqrt{5} - 3\right) + \frac{1}{40} \, \sqrt{2} \sqrt{-\sqrt{5} + 5} \log\left(-{\left(\sqrt{5} \sqrt{2} + \sqrt{2}\right)} \sqrt{-\sqrt{5} + 5} \cos\left(x\right) \sin\left(x\right) + 2 \, {\left(\sqrt{5} - 1\right)} \cos\left(x\right)^{2} - \sqrt{5} - 3\right)"," ",0,"-1/40*sqrt(2)*sqrt(sqrt(5) + 5)*log((sqrt(5)*sqrt(2) - sqrt(2))*sqrt(sqrt(5) + 5)*cos(x)*sin(x) + 2*(sqrt(5) + 1)*cos(x)^2 - sqrt(5) + 3) + 1/40*sqrt(2)*sqrt(sqrt(5) + 5)*log(-(sqrt(5)*sqrt(2) - sqrt(2))*sqrt(sqrt(5) + 5)*cos(x)*sin(x) + 2*(sqrt(5) + 1)*cos(x)^2 - sqrt(5) + 3) - 1/40*sqrt(2)*sqrt(-sqrt(5) + 5)*log((sqrt(5)*sqrt(2) + sqrt(2))*sqrt(-sqrt(5) + 5)*cos(x)*sin(x) + 2*(sqrt(5) - 1)*cos(x)^2 - sqrt(5) - 3) + 1/40*sqrt(2)*sqrt(-sqrt(5) + 5)*log(-(sqrt(5)*sqrt(2) + sqrt(2))*sqrt(-sqrt(5) + 5)*cos(x)*sin(x) + 2*(sqrt(5) - 1)*cos(x)^2 - sqrt(5) - 3)","B",0
94,1,68,0,1.239557," ","integrate(csc(6*x)*sin(x),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \log\left(-\frac{4 \, \cos\left(x\right)^{2} + 4 \, \sqrt{3} \sin\left(x\right) - 7}{4 \, \cos\left(x\right)^{2} - 1}\right) + \frac{1}{12} \, \log\left(2 \, \sin\left(x\right) + 1\right) + \frac{1}{12} \, \log\left(\sin\left(x\right) + 1\right) - \frac{1}{12} \, \log\left(-\sin\left(x\right) + 1\right) - \frac{1}{12} \, \log\left(-2 \, \sin\left(x\right) + 1\right)"," ",0,"1/12*sqrt(3)*log(-(4*cos(x)^2 + 4*sqrt(3)*sin(x) - 7)/(4*cos(x)^2 - 1)) + 1/12*log(2*sin(x) + 1) + 1/12*log(sin(x) + 1) - 1/12*log(-sin(x) + 1) - 1/12*log(-2*sin(x) + 1)","B",0
95,1,8,0,0.828865," ","integrate(csc(x)*sin(3*x),x, algorithm=""fricas"")","2 \, \cos\left(x\right) \sin\left(x\right) + x"," ",0,"2*cos(x)*sin(x) + x","A",0
96,1,6,0,2.971691," ","integrate(csc(3*x)*sin(6*x),x, algorithm=""fricas"")","\frac{2}{3} \, \sin\left(3 \, x\right)"," ",0,"2/3*sin(3*x)","A",0
97,1,6,0,1.484086," ","integrate(cos(x)*sin(2*x),x, algorithm=""fricas"")","-\frac{2}{3} \, \cos\left(x\right)^{3}"," ",0,"-2/3*cos(x)^3","A",0
98,1,13,0,0.899600," ","integrate(cos(x)*sin(3*x),x, algorithm=""fricas"")","-\cos\left(x\right)^{4} + \frac{1}{2} \, \cos\left(x\right)^{2}"," ",0,"-cos(x)^4 + 1/2*cos(x)^2","A",0
99,1,13,0,0.554469," ","integrate(cos(x)*sin(4*x),x, algorithm=""fricas"")","-\frac{8}{5} \, \cos\left(x\right)^{5} + \frac{4}{3} \, \cos\left(x\right)^{3}"," ",0,"-8/5*cos(x)^5 + 4/3*cos(x)^3","A",0
100,1,25,0,0.433964," ","integrate(cos(x)*sin(m*x),x, algorithm=""fricas"")","-\frac{m \cos\left(m x\right) \cos\left(x\right) + \sin\left(m x\right) \sin\left(x\right)}{m^{2} - 1}"," ",0,"-(m*cos(m*x)*cos(x) + sin(m*x)*sin(x))/(m^2 - 1)","A",0
101,1,12,0,1.585535," ","integrate(cos(x)*cos(2*x),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(2 \, \cos\left(x\right)^{2} + 1\right)} \sin\left(x\right)"," ",0,"1/3*(2*cos(x)^2 + 1)*sin(x)","A",0
102,1,7,0,0.565052," ","integrate(cos(x)*cos(3*x),x, algorithm=""fricas"")","\cos\left(x\right)^{3} \sin\left(x\right)"," ",0,"cos(x)^3*sin(x)","A",0
103,1,18,0,1.080877," ","integrate(cos(x)*cos(4*x),x, algorithm=""fricas"")","\frac{1}{15} \, {\left(24 \, \cos\left(x\right)^{4} - 8 \, \cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)"," ",0,"1/15*(24*cos(x)^4 - 8*cos(x)^2 - 1)*sin(x)","A",0
104,1,25,0,2.474856," ","integrate(cos(x)*cos(m*x),x, algorithm=""fricas"")","\frac{m \cos\left(x\right) \sin\left(m x\right) - \cos\left(m x\right) \sin\left(x\right)}{m^{2} - 1}"," ",0,"(m*cos(x)*sin(m*x) - cos(m*x)*sin(x))/(m^2 - 1)","A",0
105,1,38,0,2.029893," ","integrate(cos(x)*tan(2*x),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(-\frac{2 \, \cos\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 1}{2 \, \cos\left(x\right)^{2} - 1}\right) - \cos\left(x\right)"," ",0,"1/4*sqrt(2)*log(-(2*cos(x)^2 + 2*sqrt(2)*cos(x) + 1)/(2*cos(x)^2 - 1)) - cos(x)","B",0
106,1,38,0,1.507010," ","integrate(cos(x)*tan(3*x),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \log\left(-\frac{4 \, \cos\left(x\right)^{2} + 4 \, \sqrt{3} \cos\left(x\right) + 3}{4 \, \cos\left(x\right)^{2} - 3}\right) - \cos\left(x\right)"," ",0,"1/6*sqrt(3)*log(-(4*cos(x)^2 + 4*sqrt(3)*cos(x) + 3)/(4*cos(x)^2 - 3)) - cos(x)","B",0
107,1,101,0,0.944551," ","integrate(cos(x)*tan(4*x),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{\sqrt{2} + 2} \log\left(\sqrt{\sqrt{2} + 2} + 2 \, \cos\left(x\right)\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \log\left(\sqrt{\sqrt{2} + 2} - 2 \, \cos\left(x\right)\right) + \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \log\left(\sqrt{-\sqrt{2} + 2} + 2 \, \cos\left(x\right)\right) - \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \log\left(\sqrt{-\sqrt{2} + 2} - 2 \, \cos\left(x\right)\right) - \cos\left(x\right)"," ",0,"1/8*sqrt(sqrt(2) + 2)*log(sqrt(sqrt(2) + 2) + 2*cos(x)) - 1/8*sqrt(sqrt(2) + 2)*log(sqrt(sqrt(2) + 2) - 2*cos(x)) + 1/8*sqrt(-sqrt(2) + 2)*log(sqrt(-sqrt(2) + 2) + 2*cos(x)) - 1/8*sqrt(-sqrt(2) + 2)*log(sqrt(-sqrt(2) + 2) - 2*cos(x)) - cos(x)","A",0
108,1,129,0,1.201409," ","integrate(cos(x)*tan(5*x),x, algorithm=""fricas"")","\frac{1}{20} \, \sqrt{2} \sqrt{\sqrt{5} + 5} \log\left(\sqrt{2} \sqrt{\sqrt{5} + 5} + 4 \, \cos\left(x\right)\right) - \frac{1}{20} \, \sqrt{2} \sqrt{\sqrt{5} + 5} \log\left(\sqrt{2} \sqrt{\sqrt{5} + 5} - 4 \, \cos\left(x\right)\right) + \frac{1}{20} \, \sqrt{2} \sqrt{-\sqrt{5} + 5} \log\left(\sqrt{2} \sqrt{-\sqrt{5} + 5} + 4 \, \cos\left(x\right)\right) - \frac{1}{20} \, \sqrt{2} \sqrt{-\sqrt{5} + 5} \log\left(\sqrt{2} \sqrt{-\sqrt{5} + 5} - 4 \, \cos\left(x\right)\right) - \cos\left(x\right)"," ",0,"1/20*sqrt(2)*sqrt(sqrt(5) + 5)*log(sqrt(2)*sqrt(sqrt(5) + 5) + 4*cos(x)) - 1/20*sqrt(2)*sqrt(sqrt(5) + 5)*log(sqrt(2)*sqrt(sqrt(5) + 5) - 4*cos(x)) + 1/20*sqrt(2)*sqrt(-sqrt(5) + 5)*log(sqrt(2)*sqrt(-sqrt(5) + 5) + 4*cos(x)) - 1/20*sqrt(2)*sqrt(-sqrt(5) + 5)*log(sqrt(2)*sqrt(-sqrt(5) + 5) - 4*cos(x)) - cos(x)","B",0
109,1,134,0,0.851552," ","integrate(cos(x)*tan(6*x),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{\sqrt{3} + 2} \log\left(\sqrt{\sqrt{3} + 2} + 2 \, \cos\left(x\right)\right) - \frac{1}{12} \, \sqrt{\sqrt{3} + 2} \log\left(\sqrt{\sqrt{3} + 2} - 2 \, \cos\left(x\right)\right) + \frac{1}{12} \, \sqrt{-\sqrt{3} + 2} \log\left(\sqrt{-\sqrt{3} + 2} + 2 \, \cos\left(x\right)\right) - \frac{1}{12} \, \sqrt{-\sqrt{3} + 2} \log\left(\sqrt{-\sqrt{3} + 2} - 2 \, \cos\left(x\right)\right) + \frac{1}{12} \, \sqrt{2} \log\left(-\frac{2 \, \cos\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 1}{2 \, \cos\left(x\right)^{2} - 1}\right) - \cos\left(x\right)"," ",0,"1/12*sqrt(sqrt(3) + 2)*log(sqrt(sqrt(3) + 2) + 2*cos(x)) - 1/12*sqrt(sqrt(3) + 2)*log(sqrt(sqrt(3) + 2) - 2*cos(x)) + 1/12*sqrt(-sqrt(3) + 2)*log(sqrt(-sqrt(3) + 2) + 2*cos(x)) - 1/12*sqrt(-sqrt(3) + 2)*log(sqrt(-sqrt(3) + 2) - 2*cos(x)) + 1/12*sqrt(2)*log(-(2*cos(x)^2 + 2*sqrt(2)*cos(x) + 1)/(2*cos(x)^2 - 1)) - cos(x)","A",0
110,1,21,0,1.297163," ","integrate(cos(x)*cot(2*x),x, algorithm=""fricas"")","\cos\left(x\right) - \frac{1}{4} \, \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{4} \, \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"cos(x) - 1/4*log(1/2*cos(x) + 1/2) + 1/4*log(-1/2*cos(x) + 1/2)","B",0
111,1,39,0,3.044628," ","integrate(cos(x)*cot(3*x),x, algorithm=""fricas"")","\cos\left(x\right) - \frac{1}{6} \, \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{6} \, \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{6} \, \log\left(-2 \, \cos\left(x\right) + 1\right) - \frac{1}{6} \, \log\left(-2 \, \cos\left(x\right) - 1\right)"," ",0,"cos(x) - 1/6*log(1/2*cos(x) + 1/2) + 1/6*log(-1/2*cos(x) + 1/2) + 1/6*log(-2*cos(x) + 1) - 1/6*log(-2*cos(x) - 1)","A",0
112,1,53,0,1.007338," ","integrate(cos(x)*cot(4*x),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{2} \log\left(\frac{2 \, \cos\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 1}{2 \, \cos\left(x\right)^{2} - 1}\right) + \cos\left(x\right) - \frac{1}{8} \, \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{8} \, \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"1/8*sqrt(2)*log((2*cos(x)^2 - 2*sqrt(2)*cos(x) + 1)/(2*cos(x)^2 - 1)) + cos(x) - 1/8*log(1/2*cos(x) + 1/2) + 1/8*log(-1/2*cos(x) + 1/2)","B",0
113,1,137,0,0.624672," ","integrate(cos(x)*cot(5*x),x, algorithm=""fricas"")","\frac{1}{20} \, \sqrt{5} \log\left(-\frac{4 \, {\left(\sqrt{5} - 1\right)} \cos\left(x\right) - 8 \, \cos\left(x\right)^{2} + \sqrt{5} - 3}{4 \, \cos\left(x\right)^{2} + 2 \, \cos\left(x\right) - 1}\right) + \frac{1}{20} \, \sqrt{5} \log\left(-\frac{4 \, {\left(\sqrt{5} + 1\right)} \cos\left(x\right) - 8 \, \cos\left(x\right)^{2} - \sqrt{5} - 3}{4 \, \cos\left(x\right)^{2} - 2 \, \cos\left(x\right) - 1}\right) + \cos\left(x\right) - \frac{1}{20} \, \log\left(4 \, \cos\left(x\right)^{2} + 2 \, \cos\left(x\right) - 1\right) + \frac{1}{20} \, \log\left(4 \, \cos\left(x\right)^{2} - 2 \, \cos\left(x\right) - 1\right) - \frac{1}{10} \, \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{10} \, \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"1/20*sqrt(5)*log(-(4*(sqrt(5) - 1)*cos(x) - 8*cos(x)^2 + sqrt(5) - 3)/(4*cos(x)^2 + 2*cos(x) - 1)) + 1/20*sqrt(5)*log(-(4*(sqrt(5) + 1)*cos(x) - 8*cos(x)^2 - sqrt(5) - 3)/(4*cos(x)^2 - 2*cos(x) - 1)) + cos(x) - 1/20*log(4*cos(x)^2 + 2*cos(x) - 1) + 1/20*log(4*cos(x)^2 - 2*cos(x) - 1) - 1/10*log(1/2*cos(x) + 1/2) + 1/10*log(-1/2*cos(x) + 1/2)","A",0
114,1,71,0,0.691357," ","integrate(cos(x)*cot(6*x),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \log\left(\frac{4 \, \cos\left(x\right)^{2} - 4 \, \sqrt{3} \cos\left(x\right) + 3}{4 \, \cos\left(x\right)^{2} - 3}\right) + \cos\left(x\right) - \frac{1}{12} \, \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{12} \, \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{12} \, \log\left(-2 \, \cos\left(x\right) + 1\right) - \frac{1}{12} \, \log\left(-2 \, \cos\left(x\right) - 1\right)"," ",0,"1/12*sqrt(3)*log((4*cos(x)^2 - 4*sqrt(3)*cos(x) + 3)/(4*cos(x)^2 - 3)) + cos(x) - 1/12*log(1/2*cos(x) + 1/2) + 1/12*log(-1/2*cos(x) + 1/2) + 1/12*log(-2*cos(x) + 1) - 1/12*log(-2*cos(x) - 1)","B",0
115,0,0,0,1.065623," ","integrate(cos(x)*cot(n*x),x, algorithm=""fricas"")","{\rm integral}\left(\cos\left(x\right) \cot\left(n x\right), x\right)"," ",0,"integral(cos(x)*cot(n*x), x)","F",0
116,1,33,0,1.128013," ","integrate(cos(x)*sec(2*x),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(-\frac{2 \, \cos\left(x\right)^{2} - 2 \, \sqrt{2} \sin\left(x\right) - 3}{2 \, \cos\left(x\right)^{2} - 1}\right)"," ",0,"1/4*sqrt(2)*log(-(2*cos(x)^2 - 2*sqrt(2)*sin(x) - 3)/(2*cos(x)^2 - 1))","B",0
117,1,53,0,1.487514," ","integrate(cos(x)*sec(3*x),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \log\left(-\frac{8 \, \cos\left(x\right)^{4} + 4 \, {\left(2 \, \sqrt{3} \cos\left(x\right)^{3} - 3 \, \sqrt{3} \cos\left(x\right)\right)} \sin\left(x\right) - 9}{16 \, \cos\left(x\right)^{4} - 24 \, \cos\left(x\right)^{2} + 9}\right)"," ",0,"1/12*sqrt(3)*log(-(8*cos(x)^4 + 4*(2*sqrt(3)*cos(x)^3 - 3*sqrt(3)*cos(x))*sin(x) - 9)/(16*cos(x)^4 - 24*cos(x)^2 + 9))","A",0
118,1,121,0,1.982786," ","integrate(cos(x)*sec(4*x),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{\sqrt{2} + 2} \log\left(\sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 1\right)} + 2 \, \sin\left(x\right)\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \log\left(\sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 1\right)} - 2 \, \sin\left(x\right)\right) - \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \log\left({\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 2} + 2 \, \sin\left(x\right)\right) + \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \log\left({\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 2} - 2 \, \sin\left(x\right)\right)"," ",0,"1/8*sqrt(sqrt(2) + 2)*log(sqrt(sqrt(2) + 2)*(sqrt(2) - 1) + 2*sin(x)) - 1/8*sqrt(sqrt(2) + 2)*log(sqrt(sqrt(2) + 2)*(sqrt(2) - 1) - 2*sin(x)) - 1/8*sqrt(-sqrt(2) + 2)*log((sqrt(2) + 1)*sqrt(-sqrt(2) + 2) + 2*sin(x)) + 1/8*sqrt(-sqrt(2) + 2)*log((sqrt(2) + 1)*sqrt(-sqrt(2) + 2) - 2*sin(x))","B",0
119,1,231,0,2.070394," ","integrate(cos(x)*sec(5*x),x, algorithm=""fricas"")","-\frac{1}{40} \, \sqrt{2} \sqrt{\sqrt{5} + 5} \log\left({\left(\sqrt{5} \sqrt{2} - \sqrt{2}\right)} \sqrt{\sqrt{5} + 5} \cos\left(x\right) \sin\left(x\right) + 2 \, {\left(\sqrt{5} + 1\right)} \cos\left(x\right)^{2} - \sqrt{5} - 5\right) + \frac{1}{40} \, \sqrt{2} \sqrt{\sqrt{5} + 5} \log\left(-{\left(\sqrt{5} \sqrt{2} - \sqrt{2}\right)} \sqrt{\sqrt{5} + 5} \cos\left(x\right) \sin\left(x\right) + 2 \, {\left(\sqrt{5} + 1\right)} \cos\left(x\right)^{2} - \sqrt{5} - 5\right) - \frac{1}{40} \, \sqrt{2} \sqrt{-\sqrt{5} + 5} \log\left({\left(\sqrt{5} \sqrt{2} + \sqrt{2}\right)} \sqrt{-\sqrt{5} + 5} \cos\left(x\right) \sin\left(x\right) + 2 \, {\left(\sqrt{5} - 1\right)} \cos\left(x\right)^{2} - \sqrt{5} + 5\right) + \frac{1}{40} \, \sqrt{2} \sqrt{-\sqrt{5} + 5} \log\left(-{\left(\sqrt{5} \sqrt{2} + \sqrt{2}\right)} \sqrt{-\sqrt{5} + 5} \cos\left(x\right) \sin\left(x\right) + 2 \, {\left(\sqrt{5} - 1\right)} \cos\left(x\right)^{2} - \sqrt{5} + 5\right)"," ",0,"-1/40*sqrt(2)*sqrt(sqrt(5) + 5)*log((sqrt(5)*sqrt(2) - sqrt(2))*sqrt(sqrt(5) + 5)*cos(x)*sin(x) + 2*(sqrt(5) + 1)*cos(x)^2 - sqrt(5) - 5) + 1/40*sqrt(2)*sqrt(sqrt(5) + 5)*log(-(sqrt(5)*sqrt(2) - sqrt(2))*sqrt(sqrt(5) + 5)*cos(x)*sin(x) + 2*(sqrt(5) + 1)*cos(x)^2 - sqrt(5) - 5) - 1/40*sqrt(2)*sqrt(-sqrt(5) + 5)*log((sqrt(5)*sqrt(2) + sqrt(2))*sqrt(-sqrt(5) + 5)*cos(x)*sin(x) + 2*(sqrt(5) - 1)*cos(x)^2 - sqrt(5) + 5) + 1/40*sqrt(2)*sqrt(-sqrt(5) + 5)*log(-(sqrt(5)*sqrt(2) + sqrt(2))*sqrt(-sqrt(5) + 5)*cos(x)*sin(x) + 2*(sqrt(5) - 1)*cos(x)^2 - sqrt(5) + 5)","B",0
120,1,154,0,4.125019," ","integrate(cos(x)*sec(6*x),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{\sqrt{3} + 2} \log\left(\sqrt{\sqrt{3} + 2} {\left(\sqrt{3} - 2\right)} + 2 \, \sin\left(x\right)\right) + \frac{1}{12} \, \sqrt{\sqrt{3} + 2} \log\left(\sqrt{\sqrt{3} + 2} {\left(\sqrt{3} - 2\right)} - 2 \, \sin\left(x\right)\right) + \frac{1}{12} \, \sqrt{-\sqrt{3} + 2} \log\left({\left(\sqrt{3} + 2\right)} \sqrt{-\sqrt{3} + 2} + 2 \, \sin\left(x\right)\right) - \frac{1}{12} \, \sqrt{-\sqrt{3} + 2} \log\left({\left(\sqrt{3} + 2\right)} \sqrt{-\sqrt{3} + 2} - 2 \, \sin\left(x\right)\right) + \frac{1}{12} \, \sqrt{2} \log\left(-\frac{2 \, \cos\left(x\right)^{2} + 2 \, \sqrt{2} \sin\left(x\right) - 3}{2 \, \cos\left(x\right)^{2} - 1}\right)"," ",0,"-1/12*sqrt(sqrt(3) + 2)*log(sqrt(sqrt(3) + 2)*(sqrt(3) - 2) + 2*sin(x)) + 1/12*sqrt(sqrt(3) + 2)*log(sqrt(sqrt(3) + 2)*(sqrt(3) - 2) - 2*sin(x)) + 1/12*sqrt(-sqrt(3) + 2)*log((sqrt(3) + 2)*sqrt(-sqrt(3) + 2) + 2*sin(x)) - 1/12*sqrt(-sqrt(3) + 2)*log((sqrt(3) + 2)*sqrt(-sqrt(3) + 2) - 2*sin(x)) + 1/12*sqrt(2)*log(-(2*cos(x)^2 + 2*sqrt(2)*sin(x) - 3)/(2*cos(x)^2 - 1))","B",0
121,1,21,0,0.679601," ","integrate(cos(2*x)*sec(x),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(\sin\left(x\right) + 1\right) + \frac{1}{2} \, \log\left(-\sin\left(x\right) + 1\right) + 2 \, \sin\left(x\right)"," ",0,"-1/2*log(sin(x) + 1) + 1/2*log(-sin(x) + 1) + 2*sin(x)","B",0
122,1,25,0,1.471904," ","integrate(cos(4*x)*sec(2*x),x, algorithm=""fricas"")","-\frac{1}{4} \, \log\left(\sin\left(2 \, x\right) + 1\right) + \frac{1}{4} \, \log\left(-\sin\left(2 \, x\right) + 1\right) + \sin\left(2 \, x\right)"," ",0,"-1/4*log(sin(2*x) + 1) + 1/4*log(-sin(2*x) + 1) + sin(2*x)","B",0
123,1,19,0,2.121125," ","integrate(cos(x)*csc(2*x),x, algorithm=""fricas"")","-\frac{1}{4} \, \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{4} \, \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"-1/4*log(1/2*cos(x) + 1/2) + 1/4*log(-1/2*cos(x) + 1/2)","B",0
124,1,19,0,1.273801," ","integrate(cos(x)*csc(3*x),x, algorithm=""fricas"")","-\frac{1}{6} \, \log\left(4 \, \cos\left(x\right)^{2} - 1\right) + \frac{1}{3} \, \log\left(\frac{1}{2} \, \sin\left(x\right)\right)"," ",0,"-1/6*log(4*cos(x)^2 - 1) + 1/3*log(1/2*sin(x))","A",0
125,1,52,0,0.828868," ","integrate(cos(x)*csc(4*x),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{2} \log\left(-\frac{2 \, \cos\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 1}{2 \, \cos\left(x\right)^{2} - 1}\right) - \frac{1}{8} \, \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{8} \, \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"1/8*sqrt(2)*log(-(2*cos(x)^2 + 2*sqrt(2)*cos(x) + 1)/(2*cos(x)^2 - 1)) - 1/8*log(1/2*cos(x) + 1/2) + 1/8*log(-1/2*cos(x) + 1/2)","B",0
126,1,72,0,1.393745," ","integrate(cos(x)*csc(5*x),x, algorithm=""fricas"")","\frac{1}{20} \, \sqrt{5} \log\left(\frac{32 \, \cos\left(x\right)^{4} + 8 \, {\left(\sqrt{5} - 3\right)} \cos\left(x\right)^{2} - 3 \, \sqrt{5} + 7}{16 \, \cos\left(x\right)^{4} - 12 \, \cos\left(x\right)^{2} + 1}\right) - \frac{1}{20} \, \log\left(16 \, \cos\left(x\right)^{4} - 12 \, \cos\left(x\right)^{2} + 1\right) + \frac{1}{5} \, \log\left(\frac{1}{2} \, \sin\left(x\right)\right)"," ",0,"1/20*sqrt(5)*log((32*cos(x)^4 + 8*(sqrt(5) - 3)*cos(x)^2 - 3*sqrt(5) + 7)/(16*cos(x)^4 - 12*cos(x)^2 + 1)) - 1/20*log(16*cos(x)^4 - 12*cos(x)^2 + 1) + 1/5*log(1/2*sin(x))","A",0
127,1,70,0,0.707435," ","integrate(cos(x)*csc(6*x),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \log\left(-\frac{4 \, \cos\left(x\right)^{2} + 4 \, \sqrt{3} \cos\left(x\right) + 3}{4 \, \cos\left(x\right)^{2} - 3}\right) - \frac{1}{12} \, \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{12} \, \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{12} \, \log\left(-2 \, \cos\left(x\right) + 1\right) - \frac{1}{12} \, \log\left(-2 \, \cos\left(x\right) - 1\right)"," ",0,"1/12*sqrt(3)*log(-(4*cos(x)^2 + 4*sqrt(3)*cos(x) + 3)/(4*cos(x)^2 - 3)) - 1/12*log(1/2*cos(x) + 1/2) + 1/12*log(-1/2*cos(x) + 1/2) + 1/12*log(-2*cos(x) + 1) - 1/12*log(-2*cos(x) - 1)","B",0
128,1,57,0,3.969463," ","integrate(cos(6*x)^3*sin(x),x, algorithm=""fricas"")","-\frac{32768}{19} \, \cos\left(x\right)^{19} + \frac{147456}{17} \, \cos\left(x\right)^{17} - 18432 \, \cos\left(x\right)^{15} + 21504 \, \cos\left(x\right)^{13} - 14976 \, \cos\left(x\right)^{11} + 6336 \, \cos\left(x\right)^{9} - \frac{11112}{7} \, \cos\left(x\right)^{7} + \frac{1116}{5} \, \cos\left(x\right)^{5} - 18 \, \cos\left(x\right)^{3} + \cos\left(x\right)"," ",0,"-32768/19*cos(x)^19 + 147456/17*cos(x)^17 - 18432*cos(x)^15 + 21504*cos(x)^13 - 14976*cos(x)^11 + 6336*cos(x)^9 - 11112/7*cos(x)^7 + 1116/5*cos(x)^5 - 18*cos(x)^3 + cos(x)","B",0
129,1,39,0,0.578923," ","integrate(cos(6*x)^3*sin(9*x),x, algorithm=""fricas"")","-\frac{32}{27} \, \cos\left(3 \, x\right)^{9} + \frac{8}{3} \, \cos\left(3 \, x\right)^{7} - \frac{12}{5} \, \cos\left(3 \, x\right)^{5} + \frac{10}{9} \, \cos\left(3 \, x\right)^{3} - \frac{1}{3} \, \cos\left(3 \, x\right)"," ",0,"-32/27*cos(3*x)^9 + 8/3*cos(3*x)^7 - 12/5*cos(3*x)^5 + 10/9*cos(3*x)^3 - 1/3*cos(3*x)","A",0
130,1,32,0,2.008771," ","integrate(cos(2*x)*sin(6*x)^2,x, algorithm=""fricas"")","-\frac{1}{70} \, {\left(80 \, \cos\left(2 \, x\right)^{6} - 72 \, \cos\left(2 \, x\right)^{4} + 9 \, \cos\left(2 \, x\right)^{2} - 17\right)} \sin\left(2 \, x\right)"," ",0,"-1/70*(80*cos(2*x)^6 - 72*cos(2*x)^4 + 9*cos(2*x)^2 - 17)*sin(2*x)","A",0
131,1,42,0,0.603397," ","integrate(cos(x)*sin(6*x)^2,x, algorithm=""fricas"")","-\frac{4}{143} \, {\left(2816 \, \cos\left(x\right)^{12} - 6912 \, \cos\left(x\right)^{10} + 6048 \, \cos\left(x\right)^{8} - 2240 \, \cos\left(x\right)^{6} + 315 \, \cos\left(x\right)^{4} - 9 \, \cos\left(x\right)^{2} - 18\right)} \sin\left(x\right)"," ",0,"-4/143*(2816*cos(x)^12 - 6912*cos(x)^10 + 6048*cos(x)^8 - 2240*cos(x)^6 + 315*cos(x)^4 - 9*cos(x)^2 - 18)*sin(x)","B",0
132,1,49,0,0.612120," ","integrate(cos(x)*sin(6*x)^3,x, algorithm=""fricas"")","\frac{32768}{19} \, \cos\left(x\right)^{19} - \frac{131072}{17} \, \cos\left(x\right)^{17} + 14336 \, \cos\left(x\right)^{15} - 14336 \, \cos\left(x\right)^{13} + 8320 \, \cos\left(x\right)^{11} - 2816 \, \cos\left(x\right)^{9} + \frac{3672}{7} \, \cos\left(x\right)^{7} - \frac{216}{5} \, \cos\left(x\right)^{5}"," ",0,"32768/19*cos(x)^19 - 131072/17*cos(x)^17 + 14336*cos(x)^15 - 14336*cos(x)^13 + 8320*cos(x)^11 - 2816*cos(x)^9 + 3672/7*cos(x)^7 - 216/5*cos(x)^5","A",0
133,1,67,0,1.288797," ","integrate(cos(7*x)*sin(6*x)^3,x, algorithm=""fricas"")","\frac{2097152}{25} \, \cos\left(x\right)^{25} - 524288 \, \cos\left(x\right)^{23} + 1441792 \, \cos\left(x\right)^{21} - 2293760 \, \cos\left(x\right)^{19} + 2334720 \, \cos\left(x\right)^{17} - \frac{7938048}{5} \, \cos\left(x\right)^{15} + \frac{9503232}{13} \, \cos\left(x\right)^{13} - \frac{2484992}{11} \, \cos\left(x\right)^{11} + 45248 \, \cos\left(x\right)^{9} - 5400 \, \cos\left(x\right)^{7} + \frac{1512}{5} \, \cos\left(x\right)^{5}"," ",0,"2097152/25*cos(x)^25 - 524288*cos(x)^23 + 1441792*cos(x)^21 - 2293760*cos(x)^19 + 2334720*cos(x)^17 - 7938048/5*cos(x)^15 + 9503232/13*cos(x)^13 - 2484992/11*cos(x)^11 + 45248*cos(x)^9 - 5400*cos(x)^7 + 1512/5*cos(x)^5","B",0
134,1,25,0,0.987408," ","integrate(cos(3*x)^2*sin(2*x)^3,x, algorithm=""fricas"")","\frac{32}{3} \, \cos\left(x\right)^{12} - 32 \, \cos\left(x\right)^{10} + 33 \, \cos\left(x\right)^{8} - 12 \, \cos\left(x\right)^{6}"," ",0,"32/3*cos(x)^12 - 32*cos(x)^10 + 33*cos(x)^8 - 12*cos(x)^6","A",0
135,1,50,0,0.622841," ","integrate(sin(b*x+a)*sin(b*x+c),x, algorithm=""fricas"")","\frac{b x \cos\left(-a + c\right) - \cos\left(b x + c\right) \cos\left(-a + c\right) \sin\left(b x + c\right) + \cos\left(b x + c\right)^{2} \sin\left(-a + c\right)}{2 \, b}"," ",0,"1/2*(b*x*cos(-a + c) - cos(b*x + c)*cos(-a + c)*sin(b*x + c) + cos(b*x + c)^2*sin(-a + c))/b","B",0
136,1,44,0,0.819942," ","integrate(-sin(b*x-c)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{b x \cos\left(a + c\right) - \cos\left(b x + a\right) \cos\left(a + c\right) \sin\left(b x + a\right) + \cos\left(b x + a\right)^{2} \sin\left(a + c\right)}{2 \, b}"," ",0,"-1/2*(b*x*cos(a + c) - cos(b*x + a)*cos(a + c)*sin(b*x + a) + cos(b*x + a)^2*sin(a + c))/b","A",0
137,1,50,0,0.557975," ","integrate(cos(b*x+a)*cos(b*x+c),x, algorithm=""fricas"")","\frac{b x \cos\left(-a + c\right) + \cos\left(b x + c\right) \cos\left(-a + c\right) \sin\left(b x + c\right) - \cos\left(b x + c\right)^{2} \sin\left(-a + c\right)}{2 \, b}"," ",0,"1/2*(b*x*cos(-a + c) + cos(b*x + c)*cos(-a + c)*sin(b*x + c) - cos(b*x + c)^2*sin(-a + c))/b","B",0
138,1,44,0,2.125550," ","integrate(cos(b*x-c)*cos(b*x+a),x, algorithm=""fricas"")","\frac{b x \cos\left(a + c\right) + \cos\left(b x + a\right) \cos\left(a + c\right) \sin\left(b x + a\right) - \cos\left(b x + a\right)^{2} \sin\left(a + c\right)}{2 \, b}"," ",0,"1/2*(b*x*cos(a + c) + cos(b*x + a)*cos(a + c)*sin(b*x + a) - cos(b*x + a)^2*sin(a + c))/b","A",0
139,1,145,0,0.634883," ","integrate(tan(b*x+a)*tan(b*x+c),x, algorithm=""fricas"")","-\frac{2 \, b x \sin\left(-2 \, a + 2 \, c\right) - {\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \log\left(-\frac{{\left(\cos\left(-2 \, a + 2 \, c\right) - 1\right)} \tan\left(b x + c\right)^{2} - 2 \, \sin\left(-2 \, a + 2 \, c\right) \tan\left(b x + c\right) - \cos\left(-2 \, a + 2 \, c\right) - 1}{{\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \tan\left(b x + c\right)^{2} + \cos\left(-2 \, a + 2 \, c\right) + 1}\right) + {\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \log\left(\frac{1}{\tan\left(b x + c\right)^{2} + 1}\right)}{2 \, b \sin\left(-2 \, a + 2 \, c\right)}"," ",0,"-1/2*(2*b*x*sin(-2*a + 2*c) - (cos(-2*a + 2*c) + 1)*log(-((cos(-2*a + 2*c) - 1)*tan(b*x + c)^2 - 2*sin(-2*a + 2*c)*tan(b*x + c) - cos(-2*a + 2*c) - 1)/((cos(-2*a + 2*c) + 1)*tan(b*x + c)^2 + cos(-2*a + 2*c) + 1)) + (cos(-2*a + 2*c) + 1)*log(1/(tan(b*x + c)^2 + 1)))/(b*sin(-2*a + 2*c))","B",0
140,1,145,0,2.006973," ","integrate(-tan(b*x-c)*tan(b*x+a),x, algorithm=""fricas"")","\frac{2 \, b x \sin\left(2 \, a + 2 \, c\right) - {\left(\cos\left(2 \, a + 2 \, c\right) + 1\right)} \log\left(-\frac{{\left(\cos\left(2 \, a + 2 \, c\right) - 1\right)} \tan\left(b x + a\right)^{2} - 2 \, \sin\left(2 \, a + 2 \, c\right) \tan\left(b x + a\right) - \cos\left(2 \, a + 2 \, c\right) - 1}{{\left(\cos\left(2 \, a + 2 \, c\right) + 1\right)} \tan\left(b x + a\right)^{2} + \cos\left(2 \, a + 2 \, c\right) + 1}\right) + {\left(\cos\left(2 \, a + 2 \, c\right) + 1\right)} \log\left(\frac{1}{\tan\left(b x + a\right)^{2} + 1}\right)}{2 \, b \sin\left(2 \, a + 2 \, c\right)}"," ",0,"1/2*(2*b*x*sin(2*a + 2*c) - (cos(2*a + 2*c) + 1)*log(-((cos(2*a + 2*c) - 1)*tan(b*x + a)^2 - 2*sin(2*a + 2*c)*tan(b*x + a) - cos(2*a + 2*c) - 1)/((cos(2*a + 2*c) + 1)*tan(b*x + a)^2 + cos(2*a + 2*c) + 1)) + (cos(2*a + 2*c) + 1)*log(1/(tan(b*x + a)^2 + 1)))/(b*sin(2*a + 2*c))","B",0
141,1,118,0,1.525649," ","integrate(cot(b*x+a)*cot(b*x+c),x, algorithm=""fricas"")","-\frac{2 \, b x \sin\left(-2 \, a + 2 \, c\right) - {\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \log\left(-\frac{\cos\left(2 \, b x + 2 \, c\right) \cos\left(-2 \, a + 2 \, c\right) + \sin\left(2 \, b x + 2 \, c\right) \sin\left(-2 \, a + 2 \, c\right) - 1}{\cos\left(-2 \, a + 2 \, c\right) + 1}\right) + {\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, c\right) + \frac{1}{2}\right)}{2 \, b \sin\left(-2 \, a + 2 \, c\right)}"," ",0,"-1/2*(2*b*x*sin(-2*a + 2*c) - (cos(-2*a + 2*c) + 1)*log(-(cos(2*b*x + 2*c)*cos(-2*a + 2*c) + sin(2*b*x + 2*c)*sin(-2*a + 2*c) - 1)/(cos(-2*a + 2*c) + 1)) + (cos(-2*a + 2*c) + 1)*log(-1/2*cos(2*b*x + 2*c) + 1/2))/(b*sin(-2*a + 2*c))","B",0
142,1,118,0,2.944771," ","integrate(-cot(b*x-c)*cot(b*x+a),x, algorithm=""fricas"")","\frac{2 \, b x \sin\left(2 \, a + 2 \, c\right) - {\left(\cos\left(2 \, a + 2 \, c\right) + 1\right)} \log\left(-\frac{\cos\left(2 \, b x + 2 \, a\right) \cos\left(2 \, a + 2 \, c\right) + \sin\left(2 \, b x + 2 \, a\right) \sin\left(2 \, a + 2 \, c\right) - 1}{\cos\left(2 \, a + 2 \, c\right) + 1}\right) + {\left(\cos\left(2 \, a + 2 \, c\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right)}{2 \, b \sin\left(2 \, a + 2 \, c\right)}"," ",0,"1/2*(2*b*x*sin(2*a + 2*c) - (cos(2*a + 2*c) + 1)*log(-(cos(2*b*x + 2*a)*cos(2*a + 2*c) + sin(2*b*x + 2*a)*sin(2*a + 2*c) - 1)/(cos(2*a + 2*c) + 1)) + (cos(2*a + 2*c) + 1)*log(-1/2*cos(2*b*x + 2*a) + 1/2))/(b*sin(2*a + 2*c))","B",0
143,1,107,0,1.988214," ","integrate(sec(b*x+a)*sec(b*x+c),x, algorithm=""fricas"")","-\frac{\log\left(\cos\left(b x + c\right)^{2}\right) - \log\left(\frac{4 \, {\left(2 \, \cos\left(b x + c\right) \cos\left(-a + c\right) \sin\left(b x + c\right) \sin\left(-a + c\right) + {\left(2 \, \cos\left(-a + c\right)^{2} - 1\right)} \cos\left(b x + c\right)^{2} - \cos\left(-a + c\right)^{2} + 1\right)}}{\cos\left(-a + c\right)^{2} + 2 \, \cos\left(-a + c\right) + 1}\right)}{2 \, b \sin\left(-a + c\right)}"," ",0,"-1/2*(log(cos(b*x + c)^2) - log(4*(2*cos(b*x + c)*cos(-a + c)*sin(b*x + c)*sin(-a + c) + (2*cos(-a + c)^2 - 1)*cos(b*x + c)^2 - cos(-a + c)^2 + 1)/(cos(-a + c)^2 + 2*cos(-a + c) + 1)))/(b*sin(-a + c))","B",0
144,1,93,0,0.650368," ","integrate(sec(b*x-c)*sec(b*x+a),x, algorithm=""fricas"")","-\frac{\log\left(\cos\left(b x + a\right)^{2}\right) - \log\left(\frac{4 \, {\left(2 \, \cos\left(b x + a\right) \cos\left(a + c\right) \sin\left(b x + a\right) \sin\left(a + c\right) + {\left(2 \, \cos\left(a + c\right)^{2} - 1\right)} \cos\left(b x + a\right)^{2} - \cos\left(a + c\right)^{2} + 1\right)}}{\cos\left(a + c\right)^{2} + 2 \, \cos\left(a + c\right) + 1}\right)}{2 \, b \sin\left(a + c\right)}"," ",0,"-1/2*(log(cos(b*x + a)^2) - log(4*(2*cos(b*x + a)*cos(a + c)*sin(b*x + a)*sin(a + c) + (2*cos(a + c)^2 - 1)*cos(b*x + a)^2 - cos(a + c)^2 + 1)/(cos(a + c)^2 + 2*cos(a + c) + 1)))/(b*sin(a + c))","B",0
145,1,110,0,0.754338," ","integrate(csc(b*x+a)*csc(b*x+c),x, algorithm=""fricas"")","-\frac{\log\left(-\frac{1}{4} \, \cos\left(b x + c\right)^{2} + \frac{1}{4}\right) - \log\left(-\frac{2 \, \cos\left(b x + c\right) \cos\left(-a + c\right) \sin\left(b x + c\right) \sin\left(-a + c\right) + {\left(2 \, \cos\left(-a + c\right)^{2} - 1\right)} \cos\left(b x + c\right)^{2} - \cos\left(-a + c\right)^{2}}{\cos\left(-a + c\right)^{2} + 2 \, \cos\left(-a + c\right) + 1}\right)}{2 \, b \sin\left(-a + c\right)}"," ",0,"-1/2*(log(-1/4*cos(b*x + c)^2 + 1/4) - log(-(2*cos(b*x + c)*cos(-a + c)*sin(b*x + c)*sin(-a + c) + (2*cos(-a + c)^2 - 1)*cos(b*x + c)^2 - cos(-a + c)^2)/(cos(-a + c)^2 + 2*cos(-a + c) + 1)))/(b*sin(-a + c))","B",0
146,1,96,0,0.784519," ","integrate(-csc(b*x-c)*csc(b*x+a),x, algorithm=""fricas"")","\frac{\log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right) - \log\left(-\frac{2 \, \cos\left(b x + a\right) \cos\left(a + c\right) \sin\left(b x + a\right) \sin\left(a + c\right) + {\left(2 \, \cos\left(a + c\right)^{2} - 1\right)} \cos\left(b x + a\right)^{2} - \cos\left(a + c\right)^{2}}{\cos\left(a + c\right)^{2} + 2 \, \cos\left(a + c\right) + 1}\right)}{2 \, b \sin\left(a + c\right)}"," ",0,"1/2*(log(-1/4*cos(b*x + a)^2 + 1/4) - log(-(2*cos(b*x + a)*cos(a + c)*sin(b*x + a)*sin(a + c) + (2*cos(a + c)^2 - 1)*cos(b*x + a)^2 - cos(a + c)^2)/(cos(a + c)^2 + 2*cos(a + c) + 1)))/(b*sin(a + c))","B",0
147,1,22,0,0.743227," ","integrate((sin(x)*tan(x))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}} \cos\left(x\right)}{\sin\left(x\right)}"," ",0,"-2*sqrt(-(cos(x)^2 - 1)/cos(x))*cos(x)/sin(x)","A",0
148,1,26,0,0.487712," ","integrate((sin(x)*tan(x))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\cos\left(x\right)^{2} + 3\right)} \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}}}{3 \, \sin\left(x\right)}"," ",0,"2/3*(cos(x)^2 + 3)*sqrt(-(cos(x)^2 - 1)/cos(x))/sin(x)","A",0
149,1,38,0,0.717608," ","integrate((sin(x)*tan(x))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, \cos\left(x\right)^{4} - 30 \, \cos\left(x\right)^{2} - 5\right)} \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}}}{15 \, \cos\left(x\right) \sin\left(x\right)}"," ",0,"-2/15*(3*cos(x)^4 - 30*cos(x)^2 - 5)*sqrt(-(cos(x)^2 - 1)/cos(x))/(cos(x)*sin(x))","A",0
150,1,19,0,0.663544," ","integrate((cos(x)*cot(x))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}} \sin\left(x\right)}{\cos\left(x\right)}"," ",0,"2*sqrt(cos(x)^2/sin(x))*sin(x)/cos(x)","A",0
151,1,23,0,0.728115," ","integrate((cos(x)*cot(x))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\cos\left(x\right)^{2} - 4\right)} \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}}}{3 \, \cos\left(x\right)}"," ",0,"2/3*(cos(x)^2 - 4)*sqrt(cos(x)^2/sin(x))/cos(x)","A",0
152,1,35,0,0.598787," ","integrate((cos(x)*cot(x))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, \cos\left(x\right)^{4} + 24 \, \cos\left(x\right)^{2} - 32\right)} \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}}}{15 \, \cos\left(x\right) \sin\left(x\right)}"," ",0,"2/15*(3*cos(x)^4 + 24*cos(x)^2 - 32)*sqrt(cos(x)^2/sin(x))/(cos(x)*sin(x))","A",0
153,1,236,0,1.556851," ","integrate(x*cos(x)/(a+b*sin(x))^2,x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \sin\left(x\right) + a\right)} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a b \sin\left(x\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(x\right) \sin\left(x\right) + b \cos\left(x\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(x\right)^{2} - 2 \, a b \sin\left(x\right) - a^{2} - b^{2}}\right) + 2 \, {\left(a^{2} - b^{2}\right)} x}{2 \, {\left(a^{3} b - a b^{3} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(x\right)\right)}}, -\frac{\sqrt{a^{2} - b^{2}} {\left(b \sin\left(x\right) + a\right)} \arctan\left(-\frac{a \sin\left(x\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(x\right)}\right) + {\left(a^{2} - b^{2}\right)} x}{a^{3} b - a b^{3} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(x\right)}\right]"," ",0,"[-1/2*(sqrt(-a^2 + b^2)*(b*sin(x) + a)*log(((2*a^2 - b^2)*cos(x)^2 - 2*a*b*sin(x) - a^2 - b^2 + 2*(a*cos(x)*sin(x) + b*cos(x))*sqrt(-a^2 + b^2))/(b^2*cos(x)^2 - 2*a*b*sin(x) - a^2 - b^2)) + 2*(a^2 - b^2)*x)/(a^3*b - a*b^3 + (a^2*b^2 - b^4)*sin(x)), -(sqrt(a^2 - b^2)*(b*sin(x) + a)*arctan(-(a*sin(x) + b)/(sqrt(a^2 - b^2)*cos(x))) + (a^2 - b^2)*x)/(a^3*b - a*b^3 + (a^2*b^2 - b^4)*sin(x))]","A",0
154,1,459,0,0.629776," ","integrate(x*cos(x)/(a+b*sin(x))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(x\right) \sin\left(x\right) - {\left(a b^{2} \cos\left(x\right)^{2} - 2 \, a^{2} b \sin\left(x\right) - a^{3} - a b^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a b \sin\left(x\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(x\right) \sin\left(x\right) + b \cos\left(x\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(x\right)^{2} - 2 \, a b \sin\left(x\right) - a^{2} - b^{2}}\right) - 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x + 2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(x\right)}{4 \, {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7} - {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \sin\left(x\right)\right)}}, \frac{{\left(a^{2} b^{2} - b^{4}\right)} \cos\left(x\right) \sin\left(x\right) + {\left(a b^{2} \cos\left(x\right)^{2} - 2 \, a^{2} b \sin\left(x\right) - a^{3} - a b^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(x\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(x\right)}\right) - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x + {\left(a^{3} b - a b^{3}\right)} \cos\left(x\right)}{2 \, {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7} - {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \sin\left(x\right)\right)}}\right]"," ",0,"[1/4*(2*(a^2*b^2 - b^4)*cos(x)*sin(x) - (a*b^2*cos(x)^2 - 2*a^2*b*sin(x) - a^3 - a*b^2)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(x)^2 - 2*a*b*sin(x) - a^2 - b^2 - 2*(a*cos(x)*sin(x) + b*cos(x))*sqrt(-a^2 + b^2))/(b^2*cos(x)^2 - 2*a*b*sin(x) - a^2 - b^2)) - 2*(a^4 - 2*a^2*b^2 + b^4)*x + 2*(a^3*b - a*b^3)*cos(x))/(a^6*b - a^4*b^3 - a^2*b^5 + b^7 - (a^4*b^3 - 2*a^2*b^5 + b^7)*cos(x)^2 + 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*sin(x)), 1/2*((a^2*b^2 - b^4)*cos(x)*sin(x) + (a*b^2*cos(x)^2 - 2*a^2*b*sin(x) - a^3 - a*b^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(x) + b)/(sqrt(a^2 - b^2)*cos(x))) - (a^4 - 2*a^2*b^2 + b^4)*x + (a^3*b - a*b^3)*cos(x))/(a^6*b - a^4*b^3 - a^2*b^5 + b^7 - (a^4*b^3 - 2*a^2*b^5 + b^7)*cos(x)^2 + 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*sin(x))]","B",0
155,1,227,0,0.571325," ","integrate(x*sin(x)/(a+b*cos(x))^2,x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(x\right) + a\right)} \log\left(\frac{2 \, a b \cos\left(x\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(x\right) + b\right)} \sin\left(x\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(x\right)^{2} + 2 \, a b \cos\left(x\right) + a^{2}}\right) - 2 \, {\left(a^{2} - b^{2}\right)} x}{2 \, {\left(a^{3} b - a b^{3} + {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(x\right)\right)}}, -\frac{\sqrt{a^{2} - b^{2}} {\left(b \cos\left(x\right) + a\right)} \arctan\left(-\frac{a \cos\left(x\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(x\right)}\right) - {\left(a^{2} - b^{2}\right)} x}{a^{3} b - a b^{3} + {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(x\right)}\right]"," ",0,"[-1/2*(sqrt(-a^2 + b^2)*(b*cos(x) + a)*log((2*a*b*cos(x) + (2*a^2 - b^2)*cos(x)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(x) + b)*sin(x) - a^2 + 2*b^2)/(b^2*cos(x)^2 + 2*a*b*cos(x) + a^2)) - 2*(a^2 - b^2)*x)/(a^3*b - a*b^3 + (a^2*b^2 - b^4)*cos(x)), -(sqrt(a^2 - b^2)*(b*cos(x) + a)*arctan(-(a*cos(x) + b)/(sqrt(a^2 - b^2)*sin(x))) - (a^2 - b^2)*x)/(a^3*b - a*b^3 + (a^2*b^2 - b^4)*cos(x))]","A",0
156,1,417,0,0.658872," ","integrate(x*sin(x)/(a+b*cos(x))^3,x, algorithm=""fricas"")","\left[\frac{{\left(a b^{2} \cos\left(x\right)^{2} + 2 \, a^{2} b \cos\left(x\right) + a^{3}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(x\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(x\right) + b\right)} \sin\left(x\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(x\right)^{2} + 2 \, a b \cos\left(x\right) + a^{2}}\right) + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x + 2 \, {\left(a^{3} b - a b^{3} + {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{4 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5} + {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(x\right)\right)}}, -\frac{{\left(a b^{2} \cos\left(x\right)^{2} + 2 \, a^{2} b \cos\left(x\right) + a^{3}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(x\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(x\right)}\right) - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x - {\left(a^{3} b - a b^{3} + {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5} + {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(x\right)\right)}}\right]"," ",0,"[1/4*((a*b^2*cos(x)^2 + 2*a^2*b*cos(x) + a^3)*sqrt(-a^2 + b^2)*log((2*a*b*cos(x) + (2*a^2 - b^2)*cos(x)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(x) + b)*sin(x) - a^2 + 2*b^2)/(b^2*cos(x)^2 + 2*a*b*cos(x) + a^2)) + 2*(a^4 - 2*a^2*b^2 + b^4)*x + 2*(a^3*b - a*b^3 + (a^2*b^2 - b^4)*cos(x))*sin(x))/(a^6*b - 2*a^4*b^3 + a^2*b^5 + (a^4*b^3 - 2*a^2*b^5 + b^7)*cos(x)^2 + 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*cos(x)), -1/2*((a*b^2*cos(x)^2 + 2*a^2*b*cos(x) + a^3)*sqrt(a^2 - b^2)*arctan(-(a*cos(x) + b)/(sqrt(a^2 - b^2)*sin(x))) - (a^4 - 2*a^2*b^2 + b^4)*x - (a^3*b - a*b^3 + (a^2*b^2 - b^4)*cos(x))*sin(x))/(a^6*b - 2*a^4*b^3 + a^2*b^5 + (a^4*b^3 - 2*a^2*b^5 + b^7)*cos(x)^2 + 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*cos(x))]","B",0
157,1,80,0,0.588220," ","integrate(x*sec(x)^2/(a+b*tan(x))^2,x, algorithm=""fricas"")","-\frac{2 \, b x \cos\left(x\right) - 2 \, a x \sin\left(x\right) - {\left(a \cos\left(x\right) + b \sin\left(x\right)\right)} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right)}{2 \, {\left({\left(a^{3} + a b^{2}\right)} \cos\left(x\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(x\right)\right)}}"," ",0,"-1/2*(2*b*x*cos(x) - 2*a*x*sin(x) - (a*cos(x) + b*sin(x))*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2))/((a^3 + a*b^2)*cos(x) + (a^2*b + b^3)*sin(x))","A",0
158,1,81,0,0.743499," ","integrate(x*csc(x)^2/(a+b*cot(x))^2,x, algorithm=""fricas"")","-\frac{2 \, a x \cos\left(x\right) - 2 \, b x \sin\left(x\right) - {\left(b \cos\left(x\right) + a \sin\left(x\right)\right)} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2}\right)}{2 \, {\left({\left(a^{2} b + b^{3}\right)} \cos\left(x\right) + {\left(a^{3} + a b^{2}\right)} \sin\left(x\right)\right)}}"," ",0,"-1/2*(2*a*x*cos(x) - 2*b*x*sin(x) - (b*cos(x) + a*sin(x))*log(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 + a^2))/((a^2*b + b^3)*cos(x) + (a^3 + a*b^2)*sin(x))","A",0
159,1,205,0,0.623301," ","integrate(sec(d*x+c)^2/(a+b*tan(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b} \log\left(\frac{{\left(a^{2} + 6 \, a b + b^{2}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a b + b^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a + b\right)} \cos\left(d x + c\right)^{3} - b \cos\left(d x + c\right)\right)} \sqrt{-a b} \sin\left(d x + c\right) + b^{2}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(a b - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right)}{4 \, a b d}, -\frac{\sqrt{a b} \arctan\left(\frac{{\left({\left(a + b\right)} \cos\left(d x + c\right)^{2} - b\right)} \sqrt{a b}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right)}\right)}{2 \, a b d}\right]"," ",0,"[-1/4*sqrt(-a*b)*log(((a^2 + 6*a*b + b^2)*cos(d*x + c)^4 - 2*(3*a*b + b^2)*cos(d*x + c)^2 + 4*((a + b)*cos(d*x + c)^3 - b*cos(d*x + c))*sqrt(-a*b)*sin(d*x + c) + b^2)/((a^2 - 2*a*b + b^2)*cos(d*x + c)^4 + 2*(a*b - b^2)*cos(d*x + c)^2 + b^2))/(a*b*d), -1/2*sqrt(a*b)*arctan(1/2*((a + b)*cos(d*x + c)^2 - b)*sqrt(a*b)/(a*b*cos(d*x + c)*sin(d*x + c)))/(a*b*d)]","B",0
160,1,3344,0,1.298630," ","integrate(x*sec(d*x+c)^2/(a+b*tan(d*x+c)^2),x, algorithm=""fricas"")","\frac{-4 i \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} c \log\left(2 \, \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} + 2 \, \cos\left(d x + c\right) + 2 i \, \sin\left(d x + c\right)\right) + 4 i \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} c \log\left(2 \, \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} + 2 \, \cos\left(d x + c\right) - 2 i \, \sin\left(d x + c\right)\right) + 4 i \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} c \log\left(2 \, \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} - 2 \, \cos\left(d x + c\right) + 2 i \, \sin\left(d x + c\right)\right) - 4 i \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} c \log\left(2 \, \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} - 2 \, \cos\left(d x + c\right) - 2 i \, \sin\left(d x + c\right)\right) + 4 i \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} c \log\left(2 \, \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} + 2 \, \cos\left(d x + c\right) + 2 i \, \sin\left(d x + c\right)\right) - 4 i \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} c \log\left(2 \, \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} + 2 \, \cos\left(d x + c\right) - 2 i \, \sin\left(d x + c\right)\right) - 4 i \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} c \log\left(2 \, \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} - 2 \, \cos\left(d x + c\right) + 2 i \, \sin\left(d x + c\right)\right) + 4 i \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} c \log\left(2 \, \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} - 2 \, \cos\left(d x + c\right) - 2 i \, \sin\left(d x + c\right)\right) + 4 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) + 4 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) + 4 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) + 4 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) - 4 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) - 4 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) - 4 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) - 4 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) + 4 \, {\left(i \, {\left(a - b\right)} d x + i \, {\left(a - b\right)} c\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} \log\left(-\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-i \, {\left(a - b\right)} d x - i \, {\left(a - b\right)} c\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} \log\left(\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-i \, {\left(a - b\right)} d x - i \, {\left(a - b\right)} c\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} \log\left(-\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(i \, {\left(a - b\right)} d x + i \, {\left(a - b\right)} c\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} \log\left(\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-i \, {\left(a - b\right)} d x - i \, {\left(a - b\right)} c\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} \log\left(-\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(i \, {\left(a - b\right)} d x + i \, {\left(a - b\right)} c\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} \log\left(\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(i \, {\left(a - b\right)} d x + i \, {\left(a - b\right)} c\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} \log\left(-\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-i \, {\left(a - b\right)} d x - i \, {\left(a - b\right)} c\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} \log\left(\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}}\right)}{16 \, a b d^{2}}"," ",0,"1/16*(-4*I*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*c*log(2*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) + 2*cos(d*x + c) + 2*I*sin(d*x + c)) + 4*I*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*c*log(2*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) + 2*cos(d*x + c) - 2*I*sin(d*x + c)) + 4*I*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*c*log(2*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) - 2*cos(d*x + c) + 2*I*sin(d*x + c)) - 4*I*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*c*log(2*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) - 2*cos(d*x + c) - 2*I*sin(d*x + c)) + 4*I*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*c*log(2*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) + 2*cos(d*x + c) + 2*I*sin(d*x + c)) - 4*I*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*c*log(2*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) + 2*cos(d*x + c) - 2*I*sin(d*x + c)) - 4*I*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*c*log(2*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) - 2*cos(d*x + c) + 2*I*sin(d*x + c)) + 4*I*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*c*log(2*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) - 2*cos(d*x + c) - 2*I*sin(d*x + c)) + 4*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*dilog(1/2*((2*(a + b)*cos(d*x + c) + (2*I*a + 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) - 2*a + 2*b)/(a - b) + 1) + 4*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*dilog(-1/2*((2*(a + b)*cos(d*x + c) - (2*I*a + 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) + 2*a - 2*b)/(a - b) + 1) + 4*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*dilog(1/2*((2*(a + b)*cos(d*x + c) + (-2*I*a - 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) - 2*a + 2*b)/(a - b) + 1) + 4*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*dilog(-1/2*((2*(a + b)*cos(d*x + c) - (-2*I*a - 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) + 2*a - 2*b)/(a - b) + 1) - 4*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*dilog(1/2*((2*(a + b)*cos(d*x + c) + (2*I*a + 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) - 2*a + 2*b)/(a - b) + 1) - 4*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*dilog(-1/2*((2*(a + b)*cos(d*x + c) - (2*I*a + 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) + 2*a - 2*b)/(a - b) + 1) - 4*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*dilog(1/2*((2*(a + b)*cos(d*x + c) + (-2*I*a - 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) - 2*a + 2*b)/(a - b) + 1) - 4*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*dilog(-1/2*((2*(a + b)*cos(d*x + c) - (-2*I*a - 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) + 2*a - 2*b)/(a - b) + 1) + 4*(I*(a - b)*d*x + I*(a - b)*c)*sqrt(a*b/(a^2 - 2*a*b + b^2))*log(-1/2*((2*(a + b)*cos(d*x + c) + (2*I*a + 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) - 2*a + 2*b)/(a - b)) + 4*(-I*(a - b)*d*x - I*(a - b)*c)*sqrt(a*b/(a^2 - 2*a*b + b^2))*log(1/2*((2*(a + b)*cos(d*x + c) - (2*I*a + 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) + 2*a - 2*b)/(a - b)) + 4*(-I*(a - b)*d*x - I*(a - b)*c)*sqrt(a*b/(a^2 - 2*a*b + b^2))*log(-1/2*((2*(a + b)*cos(d*x + c) + (-2*I*a - 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) - 2*a + 2*b)/(a - b)) + 4*(I*(a - b)*d*x + I*(a - b)*c)*sqrt(a*b/(a^2 - 2*a*b + b^2))*log(1/2*((2*(a + b)*cos(d*x + c) - (-2*I*a - 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) + 2*a - 2*b)/(a - b)) + 4*(-I*(a - b)*d*x - I*(a - b)*c)*sqrt(a*b/(a^2 - 2*a*b + b^2))*log(-1/2*((2*(a + b)*cos(d*x + c) + (2*I*a + 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) - 2*a + 2*b)/(a - b)) + 4*(I*(a - b)*d*x + I*(a - b)*c)*sqrt(a*b/(a^2 - 2*a*b + b^2))*log(1/2*((2*(a + b)*cos(d*x + c) - (2*I*a + 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) + 2*a - 2*b)/(a - b)) + 4*(I*(a - b)*d*x + I*(a - b)*c)*sqrt(a*b/(a^2 - 2*a*b + b^2))*log(-1/2*((2*(a + b)*cos(d*x + c) + (-2*I*a - 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) - 2*a + 2*b)/(a - b)) + 4*(-I*(a - b)*d*x - I*(a - b)*c)*sqrt(a*b/(a^2 - 2*a*b + b^2))*log(1/2*((2*(a + b)*cos(d*x + c) - (-2*I*a - 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) + 2*a - 2*b)/(a - b)))/(a*b*d^2)","B",0
161,1,4644,0,2.281135," ","integrate(x^2*sec(d*x+c)^2/(a+b*tan(d*x+c)^2),x, algorithm=""fricas"")","\frac{8 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} d x {\rm Li}_2\left(\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) + 8 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} d x {\rm Li}_2\left(-\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) + 8 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} d x {\rm Li}_2\left(\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) + 8 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} d x {\rm Li}_2\left(-\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) - 8 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} d x {\rm Li}_2\left(\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) - 8 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} d x {\rm Li}_2\left(-\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) - 8 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} d x {\rm Li}_2\left(\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) - 8 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} d x {\rm Li}_2\left(-\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) + 4 i \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} c^{2} \log\left(2 \, \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} + 2 \, \cos\left(d x + c\right) + 2 i \, \sin\left(d x + c\right)\right) - 4 i \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} c^{2} \log\left(2 \, \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} + 2 \, \cos\left(d x + c\right) - 2 i \, \sin\left(d x + c\right)\right) - 4 i \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} c^{2} \log\left(2 \, \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} - 2 \, \cos\left(d x + c\right) + 2 i \, \sin\left(d x + c\right)\right) + 4 i \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} c^{2} \log\left(2 \, \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} - 2 \, \cos\left(d x + c\right) - 2 i \, \sin\left(d x + c\right)\right) - 4 i \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} c^{2} \log\left(2 \, \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} + 2 \, \cos\left(d x + c\right) + 2 i \, \sin\left(d x + c\right)\right) + 4 i \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} c^{2} \log\left(2 \, \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} + 2 \, \cos\left(d x + c\right) - 2 i \, \sin\left(d x + c\right)\right) + 4 i \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} c^{2} \log\left(2 \, \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} - 2 \, \cos\left(d x + c\right) + 2 i \, \sin\left(d x + c\right)\right) - 4 i \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} c^{2} \log\left(2 \, \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} - 2 \, \cos\left(d x + c\right) - 2 i \, \sin\left(d x + c\right)\right) + 4 \, {\left(i \, {\left(a - b\right)} d^{2} x^{2} - i \, {\left(a - b\right)} c^{2}\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} \log\left(-\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-i \, {\left(a - b\right)} d^{2} x^{2} + i \, {\left(a - b\right)} c^{2}\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} \log\left(\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-i \, {\left(a - b\right)} d^{2} x^{2} + i \, {\left(a - b\right)} c^{2}\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} \log\left(-\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(i \, {\left(a - b\right)} d^{2} x^{2} - i \, {\left(a - b\right)} c^{2}\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} \log\left(\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-i \, {\left(a - b\right)} d^{2} x^{2} + i \, {\left(a - b\right)} c^{2}\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} \log\left(-\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(i \, {\left(a - b\right)} d^{2} x^{2} - i \, {\left(a - b\right)} c^{2}\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} \log\left(\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(i \, {\left(a - b\right)} d^{2} x^{2} - i \, {\left(a - b\right)} c^{2}\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} \log\left(-\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-i \, {\left(a - b\right)} d^{2} x^{2} + i \, {\left(a - b\right)} c^{2}\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} \log\left(\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(2 i \, a - 2 i \, b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} {\rm polylog}\left(3, -\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}}}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-2 i \, a + 2 i \, b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} {\rm polylog}\left(3, \frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}}}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-2 i \, a + 2 i \, b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} {\rm polylog}\left(3, -\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}}}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(2 i \, a - 2 i \, b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} {\rm polylog}\left(3, \frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} + a + b}{a - b}}}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-2 i \, a + 2 i \, b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} {\rm polylog}\left(3, -\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}}}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(2 i \, a - 2 i \, b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} {\rm polylog}\left(3, \frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}}}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(2 i \, a - 2 i \, b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} {\rm polylog}\left(3, -\frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}}}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-2 i \, a + 2 i \, b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} {\rm polylog}\left(3, \frac{{\left(2 \, {\left(a + b\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b}{a^{2} - 2 \, a b + b^{2}}} - a - b}{a - b}}}{2 \, {\left(a - b\right)}}\right)}{16 \, a b d^{3}}"," ",0,"1/16*(8*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*d*x*dilog(1/2*((2*(a + b)*cos(d*x + c) + (2*I*a + 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) - 2*a + 2*b)/(a - b) + 1) + 8*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*d*x*dilog(-1/2*((2*(a + b)*cos(d*x + c) - (2*I*a + 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) + 2*a - 2*b)/(a - b) + 1) + 8*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*d*x*dilog(1/2*((2*(a + b)*cos(d*x + c) + (-2*I*a - 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) - 2*a + 2*b)/(a - b) + 1) + 8*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*d*x*dilog(-1/2*((2*(a + b)*cos(d*x + c) - (-2*I*a - 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) + 2*a - 2*b)/(a - b) + 1) - 8*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*d*x*dilog(1/2*((2*(a + b)*cos(d*x + c) + (2*I*a + 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) - 2*a + 2*b)/(a - b) + 1) - 8*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*d*x*dilog(-1/2*((2*(a + b)*cos(d*x + c) - (2*I*a + 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) + 2*a - 2*b)/(a - b) + 1) - 8*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*d*x*dilog(1/2*((2*(a + b)*cos(d*x + c) + (-2*I*a - 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) - 2*a + 2*b)/(a - b) + 1) - 8*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*d*x*dilog(-1/2*((2*(a + b)*cos(d*x + c) - (-2*I*a - 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) + 2*a - 2*b)/(a - b) + 1) + 4*I*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*c^2*log(2*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) + 2*cos(d*x + c) + 2*I*sin(d*x + c)) - 4*I*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*c^2*log(2*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) + 2*cos(d*x + c) - 2*I*sin(d*x + c)) - 4*I*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*c^2*log(2*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) - 2*cos(d*x + c) + 2*I*sin(d*x + c)) + 4*I*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*c^2*log(2*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) - 2*cos(d*x + c) - 2*I*sin(d*x + c)) - 4*I*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*c^2*log(2*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) + 2*cos(d*x + c) + 2*I*sin(d*x + c)) + 4*I*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*c^2*log(2*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) + 2*cos(d*x + c) - 2*I*sin(d*x + c)) + 4*I*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*c^2*log(2*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) - 2*cos(d*x + c) + 2*I*sin(d*x + c)) - 4*I*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*c^2*log(2*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) - 2*cos(d*x + c) - 2*I*sin(d*x + c)) + 4*(I*(a - b)*d^2*x^2 - I*(a - b)*c^2)*sqrt(a*b/(a^2 - 2*a*b + b^2))*log(-1/2*((2*(a + b)*cos(d*x + c) + (2*I*a + 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) - 2*a + 2*b)/(a - b)) + 4*(-I*(a - b)*d^2*x^2 + I*(a - b)*c^2)*sqrt(a*b/(a^2 - 2*a*b + b^2))*log(1/2*((2*(a + b)*cos(d*x + c) - (2*I*a + 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) + 2*a - 2*b)/(a - b)) + 4*(-I*(a - b)*d^2*x^2 + I*(a - b)*c^2)*sqrt(a*b/(a^2 - 2*a*b + b^2))*log(-1/2*((2*(a + b)*cos(d*x + c) + (-2*I*a - 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) - 2*a + 2*b)/(a - b)) + 4*(I*(a - b)*d^2*x^2 - I*(a - b)*c^2)*sqrt(a*b/(a^2 - 2*a*b + b^2))*log(1/2*((2*(a + b)*cos(d*x + c) - (-2*I*a - 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b)) + 2*a - 2*b)/(a - b)) + 4*(-I*(a - b)*d^2*x^2 + I*(a - b)*c^2)*sqrt(a*b/(a^2 - 2*a*b + b^2))*log(-1/2*((2*(a + b)*cos(d*x + c) + (2*I*a + 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) - 2*a + 2*b)/(a - b)) + 4*(I*(a - b)*d^2*x^2 - I*(a - b)*c^2)*sqrt(a*b/(a^2 - 2*a*b + b^2))*log(1/2*((2*(a + b)*cos(d*x + c) - (2*I*a + 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) + 2*a - 2*b)/(a - b)) + 4*(I*(a - b)*d^2*x^2 - I*(a - b)*c^2)*sqrt(a*b/(a^2 - 2*a*b + b^2))*log(-1/2*((2*(a + b)*cos(d*x + c) + (-2*I*a - 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) - 2*a + 2*b)/(a - b)) + 4*(-I*(a - b)*d^2*x^2 + I*(a - b)*c^2)*sqrt(a*b/(a^2 - 2*a*b + b^2))*log(1/2*((2*(a + b)*cos(d*x + c) - (-2*I*a - 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b)) + 2*a - 2*b)/(a - b)) + 4*(2*I*a - 2*I*b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*polylog(3, -1/2*(2*(a + b)*cos(d*x + c) + (2*I*a + 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b))/(a - b)) + 4*(-2*I*a + 2*I*b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*polylog(3, 1/2*(2*(a + b)*cos(d*x + c) - (2*I*a + 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b))/(a - b)) + 4*(-2*I*a + 2*I*b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*polylog(3, -1/2*(2*(a + b)*cos(d*x + c) + (-2*I*a - 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b))/(a - b)) + 4*(2*I*a - 2*I*b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*polylog(3, 1/2*(2*(a + b)*cos(d*x + c) - (-2*I*a - 2*I*b)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) + a + b)/(a - b))/(a - b)) + 4*(-2*I*a + 2*I*b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*polylog(3, -1/2*(2*(a + b)*cos(d*x + c) + (2*I*a + 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b))/(a - b)) + 4*(2*I*a - 2*I*b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*polylog(3, 1/2*(2*(a + b)*cos(d*x + c) - (2*I*a + 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b))/(a - b)) + 4*(2*I*a - 2*I*b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*polylog(3, -1/2*(2*(a + b)*cos(d*x + c) + (-2*I*a - 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b))/(a - b)) + 4*(-2*I*a + 2*I*b)*sqrt(a*b/(a^2 - 2*a*b + b^2))*polylog(3, 1/2*(2*(a + b)*cos(d*x + c) - (-2*I*a - 2*I*b)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt(a*b/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt(a*b/(a^2 - 2*a*b + b^2)) - a - b)/(a - b))/(a - b)))/(a*b*d^3)","C",0
162,1,300,0,0.749800," ","integrate(sec(d*x+c)^2/(a+c*sec(d*x+c)^2+b*tan(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b - {\left(a + b\right)} c - c^{2}} \log\left(\frac{{\left(a^{2} + 6 \, a b + b^{2} + 8 \, {\left(a + b\right)} c + 8 \, c^{2}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a b + b^{2} + {\left(3 \, a + 5 \, b\right)} c + 4 \, c^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a + b + 2 \, c\right)} \cos\left(d x + c\right)^{3} - {\left(b + c\right)} \cos\left(d x + c\right)\right)} \sqrt{-a b - {\left(a + b\right)} c - c^{2}} \sin\left(d x + c\right) + b^{2} + 2 \, b c + c^{2}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(a b - b^{2} + {\left(a - b\right)} c\right)} \cos\left(d x + c\right)^{2} + b^{2} + 2 \, b c + c^{2}}\right)}{4 \, {\left(a b + {\left(a + b\right)} c + c^{2}\right)} d}, -\frac{\arctan\left(\frac{{\left(a + b + 2 \, c\right)} \cos\left(d x + c\right)^{2} - b - c}{2 \, \sqrt{a b + {\left(a + b\right)} c + c^{2}} \cos\left(d x + c\right) \sin\left(d x + c\right)}\right)}{2 \, \sqrt{a b + {\left(a + b\right)} c + c^{2}} d}\right]"," ",0,"[-1/4*sqrt(-a*b - (a + b)*c - c^2)*log(((a^2 + 6*a*b + b^2 + 8*(a + b)*c + 8*c^2)*cos(d*x + c)^4 - 2*(3*a*b + b^2 + (3*a + 5*b)*c + 4*c^2)*cos(d*x + c)^2 + 4*((a + b + 2*c)*cos(d*x + c)^3 - (b + c)*cos(d*x + c))*sqrt(-a*b - (a + b)*c - c^2)*sin(d*x + c) + b^2 + 2*b*c + c^2)/((a^2 - 2*a*b + b^2)*cos(d*x + c)^4 + 2*(a*b - b^2 + (a - b)*c)*cos(d*x + c)^2 + b^2 + 2*b*c + c^2))/((a*b + (a + b)*c + c^2)*d), -1/2*arctan(1/2*((a + b + 2*c)*cos(d*x + c)^2 - b - c)/(sqrt(a*b + (a + b)*c + c^2)*cos(d*x + c)*sin(d*x + c)))/(sqrt(a*b + (a + b)*c + c^2)*d)]","B",0
163,1,4160,0,1.382658," ","integrate(x*sec(d*x+c)^2/(a+c*sec(d*x+c)^2+b*tan(d*x+c)^2),x, algorithm=""fricas"")","\frac{-4 i \, {\left(a - b\right)} c \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(2 \, \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} + 2 \, \cos\left(d x + c\right) + 2 i \, \sin\left(d x + c\right)\right) + 4 i \, {\left(a - b\right)} c \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(2 \, \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} + 2 \, \cos\left(d x + c\right) - 2 i \, \sin\left(d x + c\right)\right) + 4 i \, {\left(a - b\right)} c \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(2 \, \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} - 2 \, \cos\left(d x + c\right) + 2 i \, \sin\left(d x + c\right)\right) - 4 i \, {\left(a - b\right)} c \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(2 \, \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} - 2 \, \cos\left(d x + c\right) - 2 i \, \sin\left(d x + c\right)\right) + 4 i \, {\left(a - b\right)} c \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(2 \, \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} + 2 \, \cos\left(d x + c\right) + 2 i \, \sin\left(d x + c\right)\right) - 4 i \, {\left(a - b\right)} c \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(2 \, \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} + 2 \, \cos\left(d x + c\right) - 2 i \, \sin\left(d x + c\right)\right) - 4 i \, {\left(a - b\right)} c \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(2 \, \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} - 2 \, \cos\left(d x + c\right) + 2 i \, \sin\left(d x + c\right)\right) + 4 i \, {\left(a - b\right)} c \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(2 \, \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} - 2 \, \cos\left(d x + c\right) - 2 i \, \sin\left(d x + c\right)\right) + 4 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) + 4 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) + 4 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) + 4 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) - 4 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) - 4 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) - 4 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) - 4 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) + 4 \, {\left(i \, {\left(a - b\right)} d x + i \, {\left(a - b\right)} c\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(-\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-i \, {\left(a - b\right)} d x - i \, {\left(a - b\right)} c\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-i \, {\left(a - b\right)} d x - i \, {\left(a - b\right)} c\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(-\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(i \, {\left(a - b\right)} d x + i \, {\left(a - b\right)} c\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-i \, {\left(a - b\right)} d x - i \, {\left(a - b\right)} c\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(-\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(i \, {\left(a - b\right)} d x + i \, {\left(a - b\right)} c\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(i \, {\left(a - b\right)} d x + i \, {\left(a - b\right)} c\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(-\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-i \, {\left(a - b\right)} d x - i \, {\left(a - b\right)} c\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}}\right)}{16 \, {\left(a b + {\left(a + b\right)} c + c^{2}\right)} d^{2}}"," ",0,"1/16*(-4*I*(a - b)*c*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(2*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) + 2*cos(d*x + c) + 2*I*sin(d*x + c)) + 4*I*(a - b)*c*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(2*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) + 2*cos(d*x + c) - 2*I*sin(d*x + c)) + 4*I*(a - b)*c*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(2*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) - 2*cos(d*x + c) + 2*I*sin(d*x + c)) - 4*I*(a - b)*c*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(2*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) - 2*cos(d*x + c) - 2*I*sin(d*x + c)) + 4*I*(a - b)*c*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(2*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) + 2*cos(d*x + c) + 2*I*sin(d*x + c)) - 4*I*(a - b)*c*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(2*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) + 2*cos(d*x + c) - 2*I*sin(d*x + c)) - 4*I*(a - b)*c*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(2*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) - 2*cos(d*x + c) + 2*I*sin(d*x + c)) + 4*I*(a - b)*c*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(2*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) - 2*cos(d*x + c) - 2*I*sin(d*x + c)) + 4*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*dilog(1/2*((2*(a + b + 2*c)*cos(d*x + c) + (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) - 2*a + 2*b)/(a - b) + 1) + 4*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*dilog(-1/2*((2*(a + b + 2*c)*cos(d*x + c) - (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) + 2*a - 2*b)/(a - b) + 1) + 4*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*dilog(1/2*((2*(a + b + 2*c)*cos(d*x + c) + (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) - 2*a + 2*b)/(a - b) + 1) + 4*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*dilog(-1/2*((2*(a + b + 2*c)*cos(d*x + c) - (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) + 2*a - 2*b)/(a - b) + 1) - 4*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*dilog(1/2*((2*(a + b + 2*c)*cos(d*x + c) + (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) - 2*a + 2*b)/(a - b) + 1) - 4*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*dilog(-1/2*((2*(a + b + 2*c)*cos(d*x + c) - (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) + 2*a - 2*b)/(a - b) + 1) - 4*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*dilog(1/2*((2*(a + b + 2*c)*cos(d*x + c) + (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) - 2*a + 2*b)/(a - b) + 1) - 4*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*dilog(-1/2*((2*(a + b + 2*c)*cos(d*x + c) - (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) + 2*a - 2*b)/(a - b) + 1) + 4*(I*(a - b)*d*x + I*(a - b)*c)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(-1/2*((2*(a + b + 2*c)*cos(d*x + c) + (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) - 2*a + 2*b)/(a - b)) + 4*(-I*(a - b)*d*x - I*(a - b)*c)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(1/2*((2*(a + b + 2*c)*cos(d*x + c) - (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) + 2*a - 2*b)/(a - b)) + 4*(-I*(a - b)*d*x - I*(a - b)*c)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(-1/2*((2*(a + b + 2*c)*cos(d*x + c) + (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) - 2*a + 2*b)/(a - b)) + 4*(I*(a - b)*d*x + I*(a - b)*c)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(1/2*((2*(a + b + 2*c)*cos(d*x + c) - (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) + 2*a - 2*b)/(a - b)) + 4*(-I*(a - b)*d*x - I*(a - b)*c)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(-1/2*((2*(a + b + 2*c)*cos(d*x + c) + (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) - 2*a + 2*b)/(a - b)) + 4*(I*(a - b)*d*x + I*(a - b)*c)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(1/2*((2*(a + b + 2*c)*cos(d*x + c) - (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) + 2*a - 2*b)/(a - b)) + 4*(I*(a - b)*d*x + I*(a - b)*c)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(-1/2*((2*(a + b + 2*c)*cos(d*x + c) + (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) - 2*a + 2*b)/(a - b)) + 4*(-I*(a - b)*d*x - I*(a - b)*c)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(1/2*((2*(a + b + 2*c)*cos(d*x + c) - (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) + 2*a - 2*b)/(a - b)))/((a*b + (a + b)*c + c^2)*d^2)","B",0
164,1,5772,0,1.284989," ","integrate(x^2*sec(d*x+c)^2/(a+c*sec(d*x+c)^2+b*tan(d*x+c)^2),x, algorithm=""fricas"")","\frac{8 \, {\left(a - b\right)} d x \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) + 8 \, {\left(a - b\right)} d x \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) + 8 \, {\left(a - b\right)} d x \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) + 8 \, {\left(a - b\right)} d x \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) - 8 \, {\left(a - b\right)} d x \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) - 8 \, {\left(a - b\right)} d x \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) - 8 \, {\left(a - b\right)} d x \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) - 8 \, {\left(a - b\right)} d x \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}} + 1\right) + 4 i \, {\left(a - b\right)} c^{2} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(2 \, \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} + 2 \, \cos\left(d x + c\right) + 2 i \, \sin\left(d x + c\right)\right) - 4 i \, {\left(a - b\right)} c^{2} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(2 \, \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} + 2 \, \cos\left(d x + c\right) - 2 i \, \sin\left(d x + c\right)\right) - 4 i \, {\left(a - b\right)} c^{2} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(2 \, \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} - 2 \, \cos\left(d x + c\right) + 2 i \, \sin\left(d x + c\right)\right) + 4 i \, {\left(a - b\right)} c^{2} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(2 \, \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} - 2 \, \cos\left(d x + c\right) - 2 i \, \sin\left(d x + c\right)\right) - 4 i \, {\left(a - b\right)} c^{2} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(2 \, \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} + 2 \, \cos\left(d x + c\right) + 2 i \, \sin\left(d x + c\right)\right) + 4 i \, {\left(a - b\right)} c^{2} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(2 \, \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} + 2 \, \cos\left(d x + c\right) - 2 i \, \sin\left(d x + c\right)\right) + 4 i \, {\left(a - b\right)} c^{2} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(2 \, \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} - 2 \, \cos\left(d x + c\right) + 2 i \, \sin\left(d x + c\right)\right) - 4 i \, {\left(a - b\right)} c^{2} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(2 \, \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} - 2 \, \cos\left(d x + c\right) - 2 i \, \sin\left(d x + c\right)\right) + 4 \, {\left(i \, {\left(a - b\right)} d^{2} x^{2} - i \, {\left(a - b\right)} c^{2}\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(-\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-i \, {\left(a - b\right)} d^{2} x^{2} + i \, {\left(a - b\right)} c^{2}\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-i \, {\left(a - b\right)} d^{2} x^{2} + i \, {\left(a - b\right)} c^{2}\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(-\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(i \, {\left(a - b\right)} d^{2} x^{2} - i \, {\left(a - b\right)} c^{2}\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-i \, {\left(a - b\right)} d^{2} x^{2} + i \, {\left(a - b\right)} c^{2}\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(-\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(i \, {\left(a - b\right)} d^{2} x^{2} - i \, {\left(a - b\right)} c^{2}\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(i \, {\left(a - b\right)} d^{2} x^{2} - i \, {\left(a - b\right)} c^{2}\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(-\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} - 2 \, a + 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-i \, {\left(a - b\right)} d^{2} x^{2} + i \, {\left(a - b\right)} c^{2}\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} \log\left(\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}} + 2 \, a - 2 \, b}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(2 i \, a - 2 i \, b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm polylog}\left(3, -\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}}}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-2 i \, a + 2 i \, b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm polylog}\left(3, \frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}}}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-2 i \, a + 2 i \, b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm polylog}\left(3, -\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}}}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(2 i \, a - 2 i \, b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm polylog}\left(3, \frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{-\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} + a + b + 2 \, c}{a - b}}}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-2 i \, a + 2 i \, b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm polylog}\left(3, -\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}}}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(2 i \, a - 2 i \, b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm polylog}\left(3, \frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(2 i \, a + 2 i \, b + 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(i \, a - i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}}}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(2 i \, a - 2 i \, b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm polylog}\left(3, -\frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) + {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) + {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}}}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(-2 i \, a + 2 i \, b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} {\rm polylog}\left(3, \frac{{\left(2 \, {\left(a + b + 2 \, c\right)} \cos\left(d x + c\right) - {\left(-2 i \, a - 2 i \, b - 4 i \, c\right)} \sin\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cos\left(d x + c\right) - {\left(-i \, a + i \, b\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}}\right)} \sqrt{\frac{2 \, {\left(a - b\right)} \sqrt{\frac{a b + {\left(a + b\right)} c + c^{2}}{a^{2} - 2 \, a b + b^{2}}} - a - b - 2 \, c}{a - b}}}{2 \, {\left(a - b\right)}}\right)}{16 \, {\left(a b + {\left(a + b\right)} c + c^{2}\right)} d^{3}}"," ",0,"1/16*(8*(a - b)*d*x*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*dilog(1/2*((2*(a + b + 2*c)*cos(d*x + c) + (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) - 2*a + 2*b)/(a - b) + 1) + 8*(a - b)*d*x*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*dilog(-1/2*((2*(a + b + 2*c)*cos(d*x + c) - (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) + 2*a - 2*b)/(a - b) + 1) + 8*(a - b)*d*x*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*dilog(1/2*((2*(a + b + 2*c)*cos(d*x + c) + (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) - 2*a + 2*b)/(a - b) + 1) + 8*(a - b)*d*x*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*dilog(-1/2*((2*(a + b + 2*c)*cos(d*x + c) - (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) + 2*a - 2*b)/(a - b) + 1) - 8*(a - b)*d*x*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*dilog(1/2*((2*(a + b + 2*c)*cos(d*x + c) + (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) - 2*a + 2*b)/(a - b) + 1) - 8*(a - b)*d*x*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*dilog(-1/2*((2*(a + b + 2*c)*cos(d*x + c) - (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) + 2*a - 2*b)/(a - b) + 1) - 8*(a - b)*d*x*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*dilog(1/2*((2*(a + b + 2*c)*cos(d*x + c) + (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) - 2*a + 2*b)/(a - b) + 1) - 8*(a - b)*d*x*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*dilog(-1/2*((2*(a + b + 2*c)*cos(d*x + c) - (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) + 2*a - 2*b)/(a - b) + 1) + 4*I*(a - b)*c^2*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(2*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) + 2*cos(d*x + c) + 2*I*sin(d*x + c)) - 4*I*(a - b)*c^2*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(2*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) + 2*cos(d*x + c) - 2*I*sin(d*x + c)) - 4*I*(a - b)*c^2*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(2*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) - 2*cos(d*x + c) + 2*I*sin(d*x + c)) + 4*I*(a - b)*c^2*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(2*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) - 2*cos(d*x + c) - 2*I*sin(d*x + c)) - 4*I*(a - b)*c^2*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(2*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) + 2*cos(d*x + c) + 2*I*sin(d*x + c)) + 4*I*(a - b)*c^2*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(2*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) + 2*cos(d*x + c) - 2*I*sin(d*x + c)) + 4*I*(a - b)*c^2*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(2*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) - 2*cos(d*x + c) + 2*I*sin(d*x + c)) - 4*I*(a - b)*c^2*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(2*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) - 2*cos(d*x + c) - 2*I*sin(d*x + c)) + 4*(I*(a - b)*d^2*x^2 - I*(a - b)*c^2)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(-1/2*((2*(a + b + 2*c)*cos(d*x + c) + (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) - 2*a + 2*b)/(a - b)) + 4*(-I*(a - b)*d^2*x^2 + I*(a - b)*c^2)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(1/2*((2*(a + b + 2*c)*cos(d*x + c) - (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) + 2*a - 2*b)/(a - b)) + 4*(-I*(a - b)*d^2*x^2 + I*(a - b)*c^2)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(-1/2*((2*(a + b + 2*c)*cos(d*x + c) + (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) - 2*a + 2*b)/(a - b)) + 4*(I*(a - b)*d^2*x^2 - I*(a - b)*c^2)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(1/2*((2*(a + b + 2*c)*cos(d*x + c) - (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b)) + 2*a - 2*b)/(a - b)) + 4*(-I*(a - b)*d^2*x^2 + I*(a - b)*c^2)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(-1/2*((2*(a + b + 2*c)*cos(d*x + c) + (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) - 2*a + 2*b)/(a - b)) + 4*(I*(a - b)*d^2*x^2 - I*(a - b)*c^2)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(1/2*((2*(a + b + 2*c)*cos(d*x + c) - (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) + 2*a - 2*b)/(a - b)) + 4*(I*(a - b)*d^2*x^2 - I*(a - b)*c^2)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(-1/2*((2*(a + b + 2*c)*cos(d*x + c) + (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) - 2*a + 2*b)/(a - b)) + 4*(-I*(a - b)*d^2*x^2 + I*(a - b)*c^2)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*log(1/2*((2*(a + b + 2*c)*cos(d*x + c) - (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b)) + 2*a - 2*b)/(a - b)) + 4*(2*I*a - 2*I*b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*polylog(3, -1/2*(2*(a + b + 2*c)*cos(d*x + c) + (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b))/(a - b)) + 4*(-2*I*a + 2*I*b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*polylog(3, 1/2*(2*(a + b + 2*c)*cos(d*x + c) - (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b))/(a - b)) + 4*(-2*I*a + 2*I*b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*polylog(3, -1/2*(2*(a + b + 2*c)*cos(d*x + c) + (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b))/(a - b)) + 4*(2*I*a - 2*I*b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*polylog(3, 1/2*(2*(a + b + 2*c)*cos(d*x + c) - (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) - 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt(-(2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) + a + b + 2*c)/(a - b))/(a - b)) + 4*(-2*I*a + 2*I*b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*polylog(3, -1/2*(2*(a + b + 2*c)*cos(d*x + c) + (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b))/(a - b)) + 4*(2*I*a - 2*I*b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*polylog(3, 1/2*(2*(a + b + 2*c)*cos(d*x + c) - (2*I*a + 2*I*b + 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (I*a - I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b))/(a - b)) + 4*(2*I*a - 2*I*b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*polylog(3, -1/2*(2*(a + b + 2*c)*cos(d*x + c) + (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) + (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b))/(a - b)) + 4*(-2*I*a + 2*I*b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2))*polylog(3, 1/2*(2*(a + b + 2*c)*cos(d*x + c) - (-2*I*a - 2*I*b - 4*I*c)*sin(d*x + c) + 4*((a - b)*cos(d*x + c) - (-I*a + I*b)*sin(d*x + c))*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)))*sqrt((2*(a - b)*sqrt((a*b + (a + b)*c + c^2)/(a^2 - 2*a*b + b^2)) - a - b - 2*c)/(a - b))/(a - b)))/((a*b + (a + b)*c + c^2)*d^3)","C",0
165,-2,0,0,0.000000," ","integrate(x^3*(a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
166,-2,0,0,0.000000," ","integrate(x^2*(a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
167,-2,0,0,0.000000," ","integrate(x*(a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
168,-2,0,0,0.000000," ","integrate((a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
169,-2,0,0,0.000000," ","integrate((a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
170,-2,0,0,0.000000," ","integrate((a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2)/x^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
171,-2,0,0,0.000000," ","integrate(x^3*(c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
172,-2,0,0,0.000000," ","integrate(x^2*(c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
173,-2,0,0,0.000000," ","integrate(x*(c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
174,-2,0,0,0.000000," ","integrate((c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
175,-2,0,0,0.000000," ","integrate((c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
176,-2,0,0,0.000000," ","integrate((c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2)/x^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
177,-2,0,0,0.000000," ","integrate((h*x+g)^3*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
178,-2,0,0,0.000000," ","integrate((h*x+g)^2*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
179,-2,0,0,0.000000," ","integrate((h*x+g)*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
180,-2,0,0,0.000000," ","integrate((a-a*sin(f*x+e))^(1/2)/(h*x+g)/(c+c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
181,0,0,0,0.728716," ","integrate(x^3*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a \sin\left(f x + e\right) + a} \sqrt{c \sin\left(f x + e\right) + c} x^{3}}{c^{2} \cos\left(f x + e\right)^{2} - 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral(-sqrt(-a*sin(f*x + e) + a)*sqrt(c*sin(f*x + e) + c)*x^3/(c^2*cos(f*x + e)^2 - 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
182,-2,0,0,0.000000," ","integrate(x^2*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
183,1,72,0,0.555557," ","integrate(x*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(f x + \cos\left(f x + e\right)\right)} \sqrt{-a \sin\left(f x + e\right) + a} \sqrt{c \sin\left(f x + e\right) + c}}{c^{2} f^{2} \cos\left(f x + e\right) \sin\left(f x + e\right) + c^{2} f^{2} \cos\left(f x + e\right)}"," ",0,"-(f*x + cos(f*x + e))*sqrt(-a*sin(f*x + e) + a)*sqrt(c*sin(f*x + e) + c)/(c^2*f^2*cos(f*x + e)*sin(f*x + e) + c^2*f^2*cos(f*x + e))","A",0
184,1,75,0,0.771133," ","integrate(z^2*(1+cos(z))^(1/2)/(1-cos(z))^(1/2),z, algorithm=""fricas"")","z^{2} \log\left(-\cos\left(z\right) + i \, \sin\left(z\right) + 1\right) + z^{2} \log\left(-\cos\left(z\right) - i \, \sin\left(z\right) + 1\right) - 2 i \, z {\rm Li}_2\left(\cos\left(z\right) + i \, \sin\left(z\right)\right) + 2 i \, z {\rm Li}_2\left(\cos\left(z\right) - i \, \sin\left(z\right)\right) + 2 \, {\rm polylog}\left(3, \cos\left(z\right) + i \, \sin\left(z\right)\right) + 2 \, {\rm polylog}\left(3, \cos\left(z\right) - i \, \sin\left(z\right)\right)"," ",0,"z^2*log(-cos(z) + I*sin(z) + 1) + z^2*log(-cos(z) - I*sin(z) + 1) - 2*I*z*dilog(cos(z) + I*sin(z)) + 2*I*z*dilog(cos(z) - I*sin(z)) + 2*polylog(3, cos(z) + I*sin(z)) + 2*polylog(3, cos(z) - I*sin(z))","C",0
185,1,32,0,0.665197," ","integrate((a+a*cos(x))*(A+B*sec(x)),x, algorithm=""fricas"")","{\left(A + B\right)} a x + \frac{1}{2} \, B a \log\left(\sin\left(x\right) + 1\right) - \frac{1}{2} \, B a \log\left(-\sin\left(x\right) + 1\right) + A a \sin\left(x\right)"," ",0,"(A + B)*a*x + 1/2*B*a*log(sin(x) + 1) - 1/2*B*a*log(-sin(x) + 1) + A*a*sin(x)","A",0
186,1,60,0,0.766335," ","integrate((a+a*cos(x))^2*(A+B*sec(x)),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(3 \, A + 4 \, B\right)} a^{2} x + \frac{1}{2} \, B a^{2} \log\left(\sin\left(x\right) + 1\right) - \frac{1}{2} \, B a^{2} \log\left(-\sin\left(x\right) + 1\right) + \frac{1}{2} \, {\left(A a^{2} \cos\left(x\right) + 2 \, {\left(2 \, A + B\right)} a^{2}\right)} \sin\left(x\right)"," ",0,"1/2*(3*A + 4*B)*a^2*x + 1/2*B*a^2*log(sin(x) + 1) - 1/2*B*a^2*log(-sin(x) + 1) + 1/2*(A*a^2*cos(x) + 2*(2*A + B)*a^2)*sin(x)","A",0
187,1,77,0,1.192924," ","integrate((a+a*cos(x))^3*(A+B*sec(x)),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(5 \, A + 7 \, B\right)} a^{3} x + \frac{1}{2} \, B a^{3} \log\left(\sin\left(x\right) + 1\right) - \frac{1}{2} \, B a^{3} \log\left(-\sin\left(x\right) + 1\right) + \frac{1}{6} \, {\left(2 \, A a^{3} \cos\left(x\right)^{2} + 3 \, {\left(3 \, A + B\right)} a^{3} \cos\left(x\right) + 2 \, {\left(11 \, A + 9 \, B\right)} a^{3}\right)} \sin\left(x\right)"," ",0,"1/2*(5*A + 7*B)*a^3*x + 1/2*B*a^3*log(sin(x) + 1) - 1/2*B*a^3*log(-sin(x) + 1) + 1/6*(2*A*a^3*cos(x)^2 + 3*(3*A + B)*a^3*cos(x) + 2*(11*A + 9*B)*a^3)*sin(x)","A",0
188,1,89,0,0.695291," ","integrate((a+a*cos(x))^4*(A+B*sec(x)),x, algorithm=""fricas"")","\frac{1}{8} \, {\left(35 \, A + 48 \, B\right)} a^{4} x + \frac{1}{2} \, B a^{4} \log\left(\sin\left(x\right) + 1\right) - \frac{1}{2} \, B a^{4} \log\left(-\sin\left(x\right) + 1\right) + \frac{1}{24} \, {\left(6 \, A a^{4} \cos\left(x\right)^{3} + 8 \, {\left(4 \, A + B\right)} a^{4} \cos\left(x\right)^{2} + 3 \, {\left(27 \, A + 16 \, B\right)} a^{4} \cos\left(x\right) + 160 \, {\left(A + B\right)} a^{4}\right)} \sin\left(x\right)"," ",0,"1/8*(35*A + 48*B)*a^4*x + 1/2*B*a^4*log(sin(x) + 1) - 1/2*B*a^4*log(-sin(x) + 1) + 1/24*(6*A*a^4*cos(x)^3 + 8*(4*A + B)*a^4*cos(x)^2 + 3*(27*A + 16*B)*a^4*cos(x) + 160*(A + B)*a^4)*sin(x)","A",0
189,1,47,0,1.141345," ","integrate((A+B*sec(x))/(a+a*cos(x)),x, algorithm=""fricas"")","\frac{{\left(B \cos\left(x\right) + B\right)} \log\left(\sin\left(x\right) + 1\right) - {\left(B \cos\left(x\right) + B\right)} \log\left(-\sin\left(x\right) + 1\right) + 2 \, {\left(A - B\right)} \sin\left(x\right)}{2 \, {\left(a \cos\left(x\right) + a\right)}}"," ",0,"1/2*((B*cos(x) + B)*log(sin(x) + 1) - (B*cos(x) + B)*log(-sin(x) + 1) + 2*(A - B)*sin(x))/(a*cos(x) + a)","A",0
190,1,85,0,0.741090," ","integrate((A+B*sec(x))/(a+a*cos(x))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(B \cos\left(x\right)^{2} + 2 \, B \cos\left(x\right) + B\right)} \log\left(\sin\left(x\right) + 1\right) - 3 \, {\left(B \cos\left(x\right)^{2} + 2 \, B \cos\left(x\right) + B\right)} \log\left(-\sin\left(x\right) + 1\right) + 2 \, {\left({\left(A - 4 \, B\right)} \cos\left(x\right) + 2 \, A - 5 \, B\right)} \sin\left(x\right)}{6 \, {\left(a^{2} \cos\left(x\right)^{2} + 2 \, a^{2} \cos\left(x\right) + a^{2}\right)}}"," ",0,"1/6*(3*(B*cos(x)^2 + 2*B*cos(x) + B)*log(sin(x) + 1) - 3*(B*cos(x)^2 + 2*B*cos(x) + B)*log(-sin(x) + 1) + 2*((A - 4*B)*cos(x) + 2*A - 5*B)*sin(x))/(a^2*cos(x)^2 + 2*a^2*cos(x) + a^2)","A",0
191,1,122,0,0.742485," ","integrate((A+B*sec(x))/(a+a*cos(x))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(B \cos\left(x\right)^{3} + 3 \, B \cos\left(x\right)^{2} + 3 \, B \cos\left(x\right) + B\right)} \log\left(\sin\left(x\right) + 1\right) - 15 \, {\left(B \cos\left(x\right)^{3} + 3 \, B \cos\left(x\right)^{2} + 3 \, B \cos\left(x\right) + B\right)} \log\left(-\sin\left(x\right) + 1\right) + 2 \, {\left(2 \, {\left(A - 11 \, B\right)} \cos\left(x\right)^{2} + 3 \, {\left(2 \, A - 17 \, B\right)} \cos\left(x\right) + 7 \, A - 32 \, B\right)} \sin\left(x\right)}{30 \, {\left(a^{3} \cos\left(x\right)^{3} + 3 \, a^{3} \cos\left(x\right)^{2} + 3 \, a^{3} \cos\left(x\right) + a^{3}\right)}}"," ",0,"1/30*(15*(B*cos(x)^3 + 3*B*cos(x)^2 + 3*B*cos(x) + B)*log(sin(x) + 1) - 15*(B*cos(x)^3 + 3*B*cos(x)^2 + 3*B*cos(x) + B)*log(-sin(x) + 1) + 2*(2*(A - 11*B)*cos(x)^2 + 3*(2*A - 17*B)*cos(x) + 7*A - 32*B)*sin(x))/(a^3*cos(x)^3 + 3*a^3*cos(x)^2 + 3*a^3*cos(x) + a^3)","A",0
192,1,158,0,0.567747," ","integrate((A+B*sec(x))/(a+a*cos(x))^4,x, algorithm=""fricas"")","\frac{105 \, {\left(B \cos\left(x\right)^{4} + 4 \, B \cos\left(x\right)^{3} + 6 \, B \cos\left(x\right)^{2} + 4 \, B \cos\left(x\right) + B\right)} \log\left(\sin\left(x\right) + 1\right) - 105 \, {\left(B \cos\left(x\right)^{4} + 4 \, B \cos\left(x\right)^{3} + 6 \, B \cos\left(x\right)^{2} + 4 \, B \cos\left(x\right) + B\right)} \log\left(-\sin\left(x\right) + 1\right) + 2 \, {\left(2 \, {\left(3 \, A - 80 \, B\right)} \cos\left(x\right)^{3} + {\left(24 \, A - 535 \, B\right)} \cos\left(x\right)^{2} + {\left(39 \, A - 620 \, B\right)} \cos\left(x\right) + 36 \, A - 260 \, B\right)} \sin\left(x\right)}{210 \, {\left(a^{4} \cos\left(x\right)^{4} + 4 \, a^{4} \cos\left(x\right)^{3} + 6 \, a^{4} \cos\left(x\right)^{2} + 4 \, a^{4} \cos\left(x\right) + a^{4}\right)}}"," ",0,"1/210*(105*(B*cos(x)^4 + 4*B*cos(x)^3 + 6*B*cos(x)^2 + 4*B*cos(x) + B)*log(sin(x) + 1) - 105*(B*cos(x)^4 + 4*B*cos(x)^3 + 6*B*cos(x)^2 + 4*B*cos(x) + B)*log(-sin(x) + 1) + 2*(2*(3*A - 80*B)*cos(x)^3 + (24*A - 535*B)*cos(x)^2 + (39*A - 620*B)*cos(x) + 36*A - 260*B)*sin(x))/(a^4*cos(x)^4 + 4*a^4*cos(x)^3 + 6*a^4*cos(x)^2 + 4*a^4*cos(x) + a^4)","A",0
193,1,123,0,0.730325," ","integrate((a+a*cos(x))^(5/2)*(A+B*sec(x)),x, algorithm=""fricas"")","\frac{15 \, {\left(B a^{2} \cos\left(x\right) + B a^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(x\right)^{3} - 7 \, a \cos\left(x\right)^{2} - 4 \, \sqrt{a \cos\left(x\right) + a} \sqrt{a} {\left(\cos\left(x\right) - 2\right)} \sin\left(x\right) + 8 \, a}{\cos\left(x\right)^{3} + \cos\left(x\right)^{2}}\right) + 4 \, {\left(3 \, A a^{2} \cos\left(x\right)^{2} + {\left(14 \, A + 5 \, B\right)} a^{2} \cos\left(x\right) + {\left(43 \, A + 40 \, B\right)} a^{2}\right)} \sqrt{a \cos\left(x\right) + a} \sin\left(x\right)}{30 \, {\left(\cos\left(x\right) + 1\right)}}"," ",0,"1/30*(15*(B*a^2*cos(x) + B*a^2)*sqrt(a)*log((a*cos(x)^3 - 7*a*cos(x)^2 - 4*sqrt(a*cos(x) + a)*sqrt(a)*(cos(x) - 2)*sin(x) + 8*a)/(cos(x)^3 + cos(x)^2)) + 4*(3*A*a^2*cos(x)^2 + (14*A + 5*B)*a^2*cos(x) + (43*A + 40*B)*a^2)*sqrt(a*cos(x) + a)*sin(x))/(cos(x) + 1)","A",0
194,1,99,0,0.656318," ","integrate((a+a*cos(x))^(3/2)*(A+B*sec(x)),x, algorithm=""fricas"")","\frac{3 \, {\left(B a \cos\left(x\right) + B a\right)} \sqrt{a} \log\left(\frac{a \cos\left(x\right)^{3} - 7 \, a \cos\left(x\right)^{2} - 4 \, \sqrt{a \cos\left(x\right) + a} \sqrt{a} {\left(\cos\left(x\right) - 2\right)} \sin\left(x\right) + 8 \, a}{\cos\left(x\right)^{3} + \cos\left(x\right)^{2}}\right) + 4 \, {\left(A a \cos\left(x\right) + {\left(5 \, A + 3 \, B\right)} a\right)} \sqrt{a \cos\left(x\right) + a} \sin\left(x\right)}{6 \, {\left(\cos\left(x\right) + 1\right)}}"," ",0,"1/6*(3*(B*a*cos(x) + B*a)*sqrt(a)*log((a*cos(x)^3 - 7*a*cos(x)^2 - 4*sqrt(a*cos(x) + a)*sqrt(a)*(cos(x) - 2)*sin(x) + 8*a)/(cos(x)^3 + cos(x)^2)) + 4*(A*a*cos(x) + (5*A + 3*B)*a)*sqrt(a*cos(x) + a)*sin(x))/(cos(x) + 1)","A",0
195,1,81,0,0.778623," ","integrate((a+a*cos(x))^(1/2)*(A+B*sec(x)),x, algorithm=""fricas"")","\frac{{\left(B \cos\left(x\right) + B\right)} \sqrt{a} \log\left(\frac{a \cos\left(x\right)^{3} - 7 \, a \cos\left(x\right)^{2} - 4 \, \sqrt{a \cos\left(x\right) + a} \sqrt{a} {\left(\cos\left(x\right) - 2\right)} \sin\left(x\right) + 8 \, a}{\cos\left(x\right)^{3} + \cos\left(x\right)^{2}}\right) + 4 \, \sqrt{a \cos\left(x\right) + a} A \sin\left(x\right)}{2 \, {\left(\cos\left(x\right) + 1\right)}}"," ",0,"1/2*((B*cos(x) + B)*sqrt(a)*log((a*cos(x)^3 - 7*a*cos(x)^2 - 4*sqrt(a*cos(x) + a)*sqrt(a)*(cos(x) - 2)*sin(x) + 8*a)/(cos(x)^3 + cos(x)^2)) + 4*sqrt(a*cos(x) + a)*A*sin(x))/(cos(x) + 1)","B",0
196,1,116,0,0.605592," ","integrate((A+B*sec(x))/(a+a*cos(x))^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(A - B\right)} \sqrt{a} \log\left(-\frac{\cos\left(x\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{a \cos\left(x\right) + a} \sin\left(x\right)}{\sqrt{a}} - 2 \, \cos\left(x\right) - 3}{\cos\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1}\right) - B \sqrt{a} \log\left(\frac{a \cos\left(x\right)^{3} - 7 \, a \cos\left(x\right)^{2} - 4 \, \sqrt{a \cos\left(x\right) + a} \sqrt{a} {\left(\cos\left(x\right) - 2\right)} \sin\left(x\right) + 8 \, a}{\cos\left(x\right)^{3} + \cos\left(x\right)^{2}}\right)}{2 \, a}"," ",0,"-1/2*(sqrt(2)*(A - B)*sqrt(a)*log(-(cos(x)^2 + 2*sqrt(2)*sqrt(a*cos(x) + a)*sin(x)/sqrt(a) - 2*cos(x) - 3)/(cos(x)^2 + 2*cos(x) + 1)) - B*sqrt(a)*log((a*cos(x)^3 - 7*a*cos(x)^2 - 4*sqrt(a*cos(x) + a)*sqrt(a)*(cos(x) - 2)*sin(x) + 8*a)/(cos(x)^3 + cos(x)^2)))/a","B",0
197,1,187,0,0.697619," ","integrate((A+B*sec(x))/(a+a*cos(x))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(A - 5 \, B\right)} \cos\left(x\right)^{2} + 2 \, {\left(A - 5 \, B\right)} \cos\left(x\right) + A - 5 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(x\right)^{2} + 2 \, \sqrt{2} \sqrt{a \cos\left(x\right) + a} \sqrt{a} \sin\left(x\right) - 2 \, a \cos\left(x\right) - 3 \, a}{\cos\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1}\right) - 4 \, {\left(B \cos\left(x\right)^{2} + 2 \, B \cos\left(x\right) + B\right)} \sqrt{a} \log\left(\frac{a \cos\left(x\right)^{3} - 7 \, a \cos\left(x\right)^{2} - 4 \, \sqrt{a \cos\left(x\right) + a} \sqrt{a} {\left(\cos\left(x\right) - 2\right)} \sin\left(x\right) + 8 \, a}{\cos\left(x\right)^{3} + \cos\left(x\right)^{2}}\right) - 4 \, \sqrt{a \cos\left(x\right) + a} {\left(A - B\right)} \sin\left(x\right)}{8 \, {\left(a^{2} \cos\left(x\right)^{2} + 2 \, a^{2} \cos\left(x\right) + a^{2}\right)}}"," ",0,"-1/8*(sqrt(2)*((A - 5*B)*cos(x)^2 + 2*(A - 5*B)*cos(x) + A - 5*B)*sqrt(a)*log(-(a*cos(x)^2 + 2*sqrt(2)*sqrt(a*cos(x) + a)*sqrt(a)*sin(x) - 2*a*cos(x) - 3*a)/(cos(x)^2 + 2*cos(x) + 1)) - 4*(B*cos(x)^2 + 2*B*cos(x) + B)*sqrt(a)*log((a*cos(x)^3 - 7*a*cos(x)^2 - 4*sqrt(a*cos(x) + a)*sqrt(a)*(cos(x) - 2)*sin(x) + 8*a)/(cos(x)^3 + cos(x)^2)) - 4*sqrt(a*cos(x) + a)*(A - B)*sin(x))/(a^2*cos(x)^2 + 2*a^2*cos(x) + a^2)","B",0
198,1,234,0,0.728001," ","integrate((A+B*sec(x))/(a+a*cos(x))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(3 \, A - 43 \, B\right)} \cos\left(x\right)^{3} + 3 \, {\left(3 \, A - 43 \, B\right)} \cos\left(x\right)^{2} + 3 \, {\left(3 \, A - 43 \, B\right)} \cos\left(x\right) + 3 \, A - 43 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(x\right)^{2} + 2 \, \sqrt{2} \sqrt{a \cos\left(x\right) + a} \sqrt{a} \sin\left(x\right) - 2 \, a \cos\left(x\right) - 3 \, a}{\cos\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1}\right) - 32 \, {\left(B \cos\left(x\right)^{3} + 3 \, B \cos\left(x\right)^{2} + 3 \, B \cos\left(x\right) + B\right)} \sqrt{a} \log\left(\frac{a \cos\left(x\right)^{3} - 7 \, a \cos\left(x\right)^{2} - 4 \, \sqrt{a \cos\left(x\right) + a} \sqrt{a} {\left(\cos\left(x\right) - 2\right)} \sin\left(x\right) + 8 \, a}{\cos\left(x\right)^{3} + \cos\left(x\right)^{2}}\right) - 4 \, {\left({\left(3 \, A - 11 \, B\right)} \cos\left(x\right) + 7 \, A - 15 \, B\right)} \sqrt{a \cos\left(x\right) + a} \sin\left(x\right)}{64 \, {\left(a^{3} \cos\left(x\right)^{3} + 3 \, a^{3} \cos\left(x\right)^{2} + 3 \, a^{3} \cos\left(x\right) + a^{3}\right)}}"," ",0,"-1/64*(sqrt(2)*((3*A - 43*B)*cos(x)^3 + 3*(3*A - 43*B)*cos(x)^2 + 3*(3*A - 43*B)*cos(x) + 3*A - 43*B)*sqrt(a)*log(-(a*cos(x)^2 + 2*sqrt(2)*sqrt(a*cos(x) + a)*sqrt(a)*sin(x) - 2*a*cos(x) - 3*a)/(cos(x)^2 + 2*cos(x) + 1)) - 32*(B*cos(x)^3 + 3*B*cos(x)^2 + 3*B*cos(x) + B)*sqrt(a)*log((a*cos(x)^3 - 7*a*cos(x)^2 - 4*sqrt(a*cos(x) + a)*sqrt(a)*(cos(x) - 2)*sin(x) + 8*a)/(cos(x)^3 + cos(x)^2)) - 4*((3*A - 11*B)*cos(x) + 7*A - 15*B)*sqrt(a*cos(x) + a)*sin(x))/(a^3*cos(x)^3 + 3*a^3*cos(x)^2 + 3*a^3*cos(x) + a^3)","B",0
199,1,35,0,0.714272," ","integrate(x*(b+a*sin(x))/(a+b*sin(x))^2,x, algorithm=""fricas"")","-\frac{b x \cos\left(x\right) - {\left(b \sin\left(x\right) + a\right)} \log\left(b \sin\left(x\right) + a\right)}{b^{2} \sin\left(x\right) + a b}"," ",0,"-(b*x*cos(x) - (b*sin(x) + a)*log(b*sin(x) + a))/(b^2*sin(x) + a*b)","A",0
200,1,36,0,0.740657," ","integrate(x*(b+a*cos(x))/(a+b*cos(x))^2,x, algorithm=""fricas"")","\frac{b x \sin\left(x\right) + {\left(b \cos\left(x\right) + a\right)} \log\left(-b \cos\left(x\right) - a\right)}{b^{2} \cos\left(x\right) + a b}"," ",0,"(b*x*sin(x) + (b*cos(x) + a)*log(-b*cos(x) - a))/(b^2*cos(x) + a*b)","A",0
201,1,15,0,0.649084," ","integrate((1+sin(x)^2)/(1-sin(x)^2),x, algorithm=""fricas"")","-\frac{x \cos\left(x\right) - 2 \, \sin\left(x\right)}{\cos\left(x\right)}"," ",0,"-(x*cos(x) - 2*sin(x))/cos(x)","A",0
202,1,35,0,0.654699," ","integrate((1-sin(x)^2)/(1+sin(x)^2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(x\right)^{2} - 2 \, \sqrt{2}}{4 \, \cos\left(x\right) \sin\left(x\right)}\right) - x"," ",0,"-1/2*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(x)^2 - 2*sqrt(2))/(cos(x)*sin(x))) - x","A",0
203,1,15,0,0.645972," ","integrate((1+cos(x)^2)/(1-cos(x)^2),x, algorithm=""fricas"")","-\frac{x \sin\left(x\right) + 2 \, \cos\left(x\right)}{\sin\left(x\right)}"," ",0,"-(x*sin(x) + 2*cos(x))/sin(x)","A",0
204,1,35,0,1.142728," ","integrate((1-cos(x)^2)/(1+cos(x)^2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(x\right)^{2} - \sqrt{2}}{4 \, \cos\left(x\right) \sin\left(x\right)}\right) - x"," ",0,"-1/2*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(x)^2 - sqrt(2))/(cos(x)*sin(x))) - x","A",0
205,1,13,0,0.634725," ","integrate((-1+c^2/d^2+sin(x)^2)/(c+d*cos(x)),x, algorithm=""fricas"")","\frac{c x - d \sin\left(x\right)}{d^{2}}"," ",0,"(c*x - d*sin(x))/d^2","A",0
206,1,254,0,1.016542," ","integrate((a+b*sin(x)^2)/(c+d*cos(x)),x, algorithm=""fricas"")","\left[\frac{{\left(b c^{2} - {\left(a + b\right)} d^{2}\right)} \sqrt{-c^{2} + d^{2}} \log\left(\frac{2 \, c d \cos\left(x\right) + {\left(2 \, c^{2} - d^{2}\right)} \cos\left(x\right)^{2} + 2 \, \sqrt{-c^{2} + d^{2}} {\left(c \cos\left(x\right) + d\right)} \sin\left(x\right) - c^{2} + 2 \, d^{2}}{d^{2} \cos\left(x\right)^{2} + 2 \, c d \cos\left(x\right) + c^{2}}\right) + 2 \, {\left(b c^{3} - b c d^{2}\right)} x - 2 \, {\left(b c^{2} d - b d^{3}\right)} \sin\left(x\right)}{2 \, {\left(c^{2} d^{2} - d^{4}\right)}}, -\frac{{\left(b c^{2} - {\left(a + b\right)} d^{2}\right)} \sqrt{c^{2} - d^{2}} \arctan\left(-\frac{c \cos\left(x\right) + d}{\sqrt{c^{2} - d^{2}} \sin\left(x\right)}\right) - {\left(b c^{3} - b c d^{2}\right)} x + {\left(b c^{2} d - b d^{3}\right)} \sin\left(x\right)}{c^{2} d^{2} - d^{4}}\right]"," ",0,"[1/2*((b*c^2 - (a + b)*d^2)*sqrt(-c^2 + d^2)*log((2*c*d*cos(x) + (2*c^2 - d^2)*cos(x)^2 + 2*sqrt(-c^2 + d^2)*(c*cos(x) + d)*sin(x) - c^2 + 2*d^2)/(d^2*cos(x)^2 + 2*c*d*cos(x) + c^2)) + 2*(b*c^3 - b*c*d^2)*x - 2*(b*c^2*d - b*d^3)*sin(x))/(c^2*d^2 - d^4), -((b*c^2 - (a + b)*d^2)*sqrt(c^2 - d^2)*arctan(-(c*cos(x) + d)/(sqrt(c^2 - d^2)*sin(x))) - (b*c^3 - b*c*d^2)*x + (b*c^2*d - b*d^3)*sin(x))/(c^2*d^2 - d^4)]","A",0
207,1,45,0,1.327752," ","integrate((a+b*sin(x)^2)/(c+c*cos(x)^2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(a + 2 \, b\right)} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(x\right)^{2} - \sqrt{2}}{4 \, \cos\left(x\right) \sin\left(x\right)}\right) + 4 \, b x}{4 \, c}"," ",0,"-1/4*(sqrt(2)*(a + 2*b)*arctan(1/4*(3*sqrt(2)*cos(x)^2 - sqrt(2))/(cos(x)*sin(x))) + 4*b*x)/c","A",0
208,1,19,0,0.611642," ","integrate((a+b*sin(x)^2)/(c-c*cos(x)^2),x, algorithm=""fricas"")","\frac{b x \sin\left(x\right) - a \cos\left(x\right)}{c \sin\left(x\right)}"," ",0,"(b*x*sin(x) - a*cos(x))/(c*sin(x))","A",0
209,1,228,0,0.790716," ","integrate((a+b*sin(x)^2)/(c+d*cos(x)^2),x, algorithm=""fricas"")","\left[-\frac{{\left(b c + {\left(a + b\right)} d\right)} \sqrt{-c^{2} - c d} \log\left(\frac{{\left(8 \, c^{2} + 8 \, c d + d^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, c^{2} + 3 \, c d\right)} \cos\left(x\right)^{2} + 4 \, {\left({\left(2 \, c + d\right)} \cos\left(x\right)^{3} - c \cos\left(x\right)\right)} \sqrt{-c^{2} - c d} \sin\left(x\right) + c^{2}}{d^{2} \cos\left(x\right)^{4} + 2 \, c d \cos\left(x\right)^{2} + c^{2}}\right) + 4 \, {\left(b c^{2} + b c d\right)} x}{4 \, {\left(c^{2} d + c d^{2}\right)}}, -\frac{{\left(b c + {\left(a + b\right)} d\right)} \sqrt{c^{2} + c d} \arctan\left(\frac{{\left(2 \, c + d\right)} \cos\left(x\right)^{2} - c}{2 \, \sqrt{c^{2} + c d} \cos\left(x\right) \sin\left(x\right)}\right) + 2 \, {\left(b c^{2} + b c d\right)} x}{2 \, {\left(c^{2} d + c d^{2}\right)}}\right]"," ",0,"[-1/4*((b*c + (a + b)*d)*sqrt(-c^2 - c*d)*log(((8*c^2 + 8*c*d + d^2)*cos(x)^4 - 2*(4*c^2 + 3*c*d)*cos(x)^2 + 4*((2*c + d)*cos(x)^3 - c*cos(x))*sqrt(-c^2 - c*d)*sin(x) + c^2)/(d^2*cos(x)^4 + 2*c*d*cos(x)^2 + c^2)) + 4*(b*c^2 + b*c*d)*x)/(c^2*d + c*d^2), -1/2*((b*c + (a + b)*d)*sqrt(c^2 + c*d)*arctan(1/2*((2*c + d)*cos(x)^2 - c)/(sqrt(c^2 + c*d)*cos(x)*sin(x))) + 2*(b*c^2 + b*c*d)*x)/(c^2*d + c*d^2)]","A",0
210,1,12,0,0.679501," ","integrate((-1+c^2/d^2+cos(x)^2)/(c+d*sin(x)),x, algorithm=""fricas"")","\frac{c x + d \cos\left(x\right)}{d^{2}}"," ",0,"(c*x + d*cos(x))/d^2","A",0
211,1,262,0,0.782320," ","integrate((a+b*cos(x)^2)/(c+d*sin(x)),x, algorithm=""fricas"")","\left[\frac{{\left(b c^{2} - {\left(a + b\right)} d^{2}\right)} \sqrt{-c^{2} + d^{2}} \log\left(\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(x\right)^{2} - 2 \, c d \sin\left(x\right) - c^{2} - d^{2} + 2 \, {\left(c \cos\left(x\right) \sin\left(x\right) + d \cos\left(x\right)\right)} \sqrt{-c^{2} + d^{2}}}{d^{2} \cos\left(x\right)^{2} - 2 \, c d \sin\left(x\right) - c^{2} - d^{2}}\right) + 2 \, {\left(b c^{3} - b c d^{2}\right)} x + 2 \, {\left(b c^{2} d - b d^{3}\right)} \cos\left(x\right)}{2 \, {\left(c^{2} d^{2} - d^{4}\right)}}, \frac{{\left(b c^{2} - {\left(a + b\right)} d^{2}\right)} \sqrt{c^{2} - d^{2}} \arctan\left(-\frac{c \sin\left(x\right) + d}{\sqrt{c^{2} - d^{2}} \cos\left(x\right)}\right) + {\left(b c^{3} - b c d^{2}\right)} x + {\left(b c^{2} d - b d^{3}\right)} \cos\left(x\right)}{c^{2} d^{2} - d^{4}}\right]"," ",0,"[1/2*((b*c^2 - (a + b)*d^2)*sqrt(-c^2 + d^2)*log(((2*c^2 - d^2)*cos(x)^2 - 2*c*d*sin(x) - c^2 - d^2 + 2*(c*cos(x)*sin(x) + d*cos(x))*sqrt(-c^2 + d^2))/(d^2*cos(x)^2 - 2*c*d*sin(x) - c^2 - d^2)) + 2*(b*c^3 - b*c*d^2)*x + 2*(b*c^2*d - b*d^3)*cos(x))/(c^2*d^2 - d^4), ((b*c^2 - (a + b)*d^2)*sqrt(c^2 - d^2)*arctan(-(c*sin(x) + d)/(sqrt(c^2 - d^2)*cos(x))) + (b*c^3 - b*c*d^2)*x + (b*c^2*d - b*d^3)*cos(x))/(c^2*d^2 - d^4)]","A",0
212,1,45,0,1.010961," ","integrate((a+b*cos(x)^2)/(c+c*sin(x)^2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(a + 2 \, b\right)} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(x\right)^{2} - 2 \, \sqrt{2}}{4 \, \cos\left(x\right) \sin\left(x\right)}\right) + 4 \, b x}{4 \, c}"," ",0,"-1/4*(sqrt(2)*(a + 2*b)*arctan(1/4*(3*sqrt(2)*cos(x)^2 - 2*sqrt(2))/(cos(x)*sin(x))) + 4*b*x)/c","A",0
213,1,18,0,1.076748," ","integrate((a+b*cos(x)^2)/(c-c*sin(x)^2),x, algorithm=""fricas"")","\frac{b x \cos\left(x\right) + a \sin\left(x\right)}{c \cos\left(x\right)}"," ",0,"(b*x*cos(x) + a*sin(x))/(c*cos(x))","A",0
214,1,255,0,2.032308," ","integrate((a+b*cos(x)^2)/(c+d*sin(x)^2),x, algorithm=""fricas"")","\left[-\frac{{\left(b c + {\left(a + b\right)} d\right)} \sqrt{-c^{2} - c d} \log\left(\frac{{\left(8 \, c^{2} + 8 \, c d + d^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, c^{2} + 5 \, c d + d^{2}\right)} \cos\left(x\right)^{2} + 4 \, {\left({\left(2 \, c + d\right)} \cos\left(x\right)^{3} - {\left(c + d\right)} \cos\left(x\right)\right)} \sqrt{-c^{2} - c d} \sin\left(x\right) + c^{2} + 2 \, c d + d^{2}}{d^{2} \cos\left(x\right)^{4} - 2 \, {\left(c d + d^{2}\right)} \cos\left(x\right)^{2} + c^{2} + 2 \, c d + d^{2}}\right) + 4 \, {\left(b c^{2} + b c d\right)} x}{4 \, {\left(c^{2} d + c d^{2}\right)}}, -\frac{{\left(b c + {\left(a + b\right)} d\right)} \sqrt{c^{2} + c d} \arctan\left(\frac{{\left(2 \, c + d\right)} \cos\left(x\right)^{2} - c - d}{2 \, \sqrt{c^{2} + c d} \cos\left(x\right) \sin\left(x\right)}\right) + 2 \, {\left(b c^{2} + b c d\right)} x}{2 \, {\left(c^{2} d + c d^{2}\right)}}\right]"," ",0,"[-1/4*((b*c + (a + b)*d)*sqrt(-c^2 - c*d)*log(((8*c^2 + 8*c*d + d^2)*cos(x)^4 - 2*(4*c^2 + 5*c*d + d^2)*cos(x)^2 + 4*((2*c + d)*cos(x)^3 - (c + d)*cos(x))*sqrt(-c^2 - c*d)*sin(x) + c^2 + 2*c*d + d^2)/(d^2*cos(x)^4 - 2*(c*d + d^2)*cos(x)^2 + c^2 + 2*c*d + d^2)) + 4*(b*c^2 + b*c*d)*x)/(c^2*d + c*d^2), -1/2*((b*c + (a + b)*d)*sqrt(c^2 + c*d)*arctan(1/2*((2*c + d)*cos(x)^2 - c - d)/(sqrt(c^2 + c*d)*cos(x)*sin(x))) + 2*(b*c^2 + b*c*d)*x)/(c^2*d + c*d^2)]","B",0
215,1,318,0,3.458213," ","integrate((a+b*sec(x)^2)/(c+d*cos(x)),x, algorithm=""fricas"")","\left[-\frac{{\left(a c^{2} + b d^{2}\right)} \sqrt{-c^{2} + d^{2}} \cos\left(x\right) \log\left(\frac{2 \, c d \cos\left(x\right) + {\left(2 \, c^{2} - d^{2}\right)} \cos\left(x\right)^{2} + 2 \, \sqrt{-c^{2} + d^{2}} {\left(c \cos\left(x\right) + d\right)} \sin\left(x\right) - c^{2} + 2 \, d^{2}}{d^{2} \cos\left(x\right)^{2} + 2 \, c d \cos\left(x\right) + c^{2}}\right) + {\left(b c^{2} d - b d^{3}\right)} \cos\left(x\right) \log\left(\sin\left(x\right) + 1\right) - {\left(b c^{2} d - b d^{3}\right)} \cos\left(x\right) \log\left(-\sin\left(x\right) + 1\right) - 2 \, {\left(b c^{3} - b c d^{2}\right)} \sin\left(x\right)}{2 \, {\left(c^{4} - c^{2} d^{2}\right)} \cos\left(x\right)}, \frac{2 \, {\left(a c^{2} + b d^{2}\right)} \sqrt{c^{2} - d^{2}} \arctan\left(-\frac{c \cos\left(x\right) + d}{\sqrt{c^{2} - d^{2}} \sin\left(x\right)}\right) \cos\left(x\right) - {\left(b c^{2} d - b d^{3}\right)} \cos\left(x\right) \log\left(\sin\left(x\right) + 1\right) + {\left(b c^{2} d - b d^{3}\right)} \cos\left(x\right) \log\left(-\sin\left(x\right) + 1\right) + 2 \, {\left(b c^{3} - b c d^{2}\right)} \sin\left(x\right)}{2 \, {\left(c^{4} - c^{2} d^{2}\right)} \cos\left(x\right)}\right]"," ",0,"[-1/2*((a*c^2 + b*d^2)*sqrt(-c^2 + d^2)*cos(x)*log((2*c*d*cos(x) + (2*c^2 - d^2)*cos(x)^2 + 2*sqrt(-c^2 + d^2)*(c*cos(x) + d)*sin(x) - c^2 + 2*d^2)/(d^2*cos(x)^2 + 2*c*d*cos(x) + c^2)) + (b*c^2*d - b*d^3)*cos(x)*log(sin(x) + 1) - (b*c^2*d - b*d^3)*cos(x)*log(-sin(x) + 1) - 2*(b*c^3 - b*c*d^2)*sin(x))/((c^4 - c^2*d^2)*cos(x)), 1/2*(2*(a*c^2 + b*d^2)*sqrt(c^2 - d^2)*arctan(-(c*cos(x) + d)/(sqrt(c^2 - d^2)*sin(x)))*cos(x) - (b*c^2*d - b*d^3)*cos(x)*log(sin(x) + 1) + (b*c^2*d - b*d^3)*cos(x)*log(-sin(x) + 1) + 2*(b*c^3 - b*c*d^2)*sin(x))/((c^4 - c^2*d^2)*cos(x))]","B",0
216,1,332,0,3.954817," ","integrate((a+b*csc(x)^2)/(c+d*sin(x)),x, algorithm=""fricas"")","\left[-\frac{{\left(a c^{2} + b d^{2}\right)} \sqrt{-c^{2} + d^{2}} \log\left(\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(x\right)^{2} - 2 \, c d \sin\left(x\right) - c^{2} - d^{2} + 2 \, {\left(c \cos\left(x\right) \sin\left(x\right) + d \cos\left(x\right)\right)} \sqrt{-c^{2} + d^{2}}}{d^{2} \cos\left(x\right)^{2} - 2 \, c d \sin\left(x\right) - c^{2} - d^{2}}\right) \sin\left(x\right) - {\left(b c^{2} d - b d^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) \sin\left(x\right) + {\left(b c^{2} d - b d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) \sin\left(x\right) + 2 \, {\left(b c^{3} - b c d^{2}\right)} \cos\left(x\right)}{2 \, {\left(c^{4} - c^{2} d^{2}\right)} \sin\left(x\right)}, -\frac{2 \, {\left(a c^{2} + b d^{2}\right)} \sqrt{c^{2} - d^{2}} \arctan\left(-\frac{c \sin\left(x\right) + d}{\sqrt{c^{2} - d^{2}} \cos\left(x\right)}\right) \sin\left(x\right) - {\left(b c^{2} d - b d^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) \sin\left(x\right) + {\left(b c^{2} d - b d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) \sin\left(x\right) + 2 \, {\left(b c^{3} - b c d^{2}\right)} \cos\left(x\right)}{2 \, {\left(c^{4} - c^{2} d^{2}\right)} \sin\left(x\right)}\right]"," ",0,"[-1/2*((a*c^2 + b*d^2)*sqrt(-c^2 + d^2)*log(((2*c^2 - d^2)*cos(x)^2 - 2*c*d*sin(x) - c^2 - d^2 + 2*(c*cos(x)*sin(x) + d*cos(x))*sqrt(-c^2 + d^2))/(d^2*cos(x)^2 - 2*c*d*sin(x) - c^2 - d^2))*sin(x) - (b*c^2*d - b*d^3)*log(1/2*cos(x) + 1/2)*sin(x) + (b*c^2*d - b*d^3)*log(-1/2*cos(x) + 1/2)*sin(x) + 2*(b*c^3 - b*c*d^2)*cos(x))/((c^4 - c^2*d^2)*sin(x)), -1/2*(2*(a*c^2 + b*d^2)*sqrt(c^2 - d^2)*arctan(-(c*sin(x) + d)/(sqrt(c^2 - d^2)*cos(x)))*sin(x) - (b*c^2*d - b*d^3)*log(1/2*cos(x) + 1/2)*sin(x) + (b*c^2*d - b*d^3)*log(-1/2*cos(x) + 1/2)*sin(x) + 2*(b*c^3 - b*c*d^2)*cos(x))/((c^4 - c^2*d^2)*sin(x))]","B",0
217,0,0,0,1.855231," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(d x + c\right) + b \sin\left(d x + c\right)\right)}^{n}, x\right)"," ",0,"integral((a*cos(d*x + c) + b*sin(d*x + c))^n, x)","F",0
218,0,0,0,1.176810," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)\right)}^{n}, x\right)"," ",0,"integral((2*cos(d*x + c) + 3*sin(d*x + c))^n, x)","F",0
219,1,257,0,1.010126," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^7,x, algorithm=""fricas"")","-\frac{35 \, b^{7} \cos\left(d x + c\right) + 5 \, {\left(7 \, a^{6} b - 35 \, a^{4} b^{3} + 21 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{7} + 7 \, {\left(35 \, a^{4} b^{3} - 42 \, a^{2} b^{5} + 3 \, b^{7}\right)} \cos\left(d x + c\right)^{5} + 35 \, {\left(7 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{3} - {\left(16 \, a^{7} + 56 \, a^{5} b^{2} + 70 \, a^{3} b^{4} + 35 \, a b^{6} + 5 \, {\left(a^{7} - 21 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 7 \, a b^{6}\right)} \cos\left(d x + c\right)^{6} + {\left(6 \, a^{7} + 21 \, a^{5} b^{2} - 280 \, a^{3} b^{4} + 105 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(8 \, a^{7} + 28 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 105 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{35 \, d}"," ",0,"-1/35*(35*b^7*cos(d*x + c) + 5*(7*a^6*b - 35*a^4*b^3 + 21*a^2*b^5 - b^7)*cos(d*x + c)^7 + 7*(35*a^4*b^3 - 42*a^2*b^5 + 3*b^7)*cos(d*x + c)^5 + 35*(7*a^2*b^5 - b^7)*cos(d*x + c)^3 - (16*a^7 + 56*a^5*b^2 + 70*a^3*b^4 + 35*a*b^6 + 5*(a^7 - 21*a^5*b^2 + 35*a^3*b^4 - 7*a*b^6)*cos(d*x + c)^6 + (6*a^7 + 21*a^5*b^2 - 280*a^3*b^4 + 105*a*b^6)*cos(d*x + c)^4 + (8*a^7 + 28*a^5*b^2 + 35*a^3*b^4 - 105*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))/d","B",0
220,1,219,0,1.184398," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^6,x, algorithm=""fricas"")","-\frac{144 \, a b^{5} \cos\left(d x + c\right)^{2} + 16 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{6} + 48 \, {\left(5 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} - 15 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d x - {\left(8 \, {\left(a^{6} - 15 \, a^{4} b^{2} + 15 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(5 \, a^{6} + 15 \, a^{4} b^{2} - 105 \, a^{2} b^{4} + 13 \, b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{6} + 15 \, a^{4} b^{2} + 15 \, a^{2} b^{4} - 11 \, b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, d}"," ",0,"-1/48*(144*a*b^5*cos(d*x + c)^2 + 16*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^6 + 48*(5*a^3*b^3 - 3*a*b^5)*cos(d*x + c)^4 - 15*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d*x - (8*(a^6 - 15*a^4*b^2 + 15*a^2*b^4 - b^6)*cos(d*x + c)^5 + 2*(5*a^6 + 15*a^4*b^2 - 105*a^2*b^4 + 13*b^6)*cos(d*x + c)^3 + 3*(5*a^6 + 15*a^4*b^2 + 15*a^2*b^4 - 11*b^6)*cos(d*x + c))*sin(d*x + c))/d","A",0
221,1,155,0,0.862722," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","-\frac{15 \, b^{5} \cos\left(d x + c\right) + 3 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{5} + 10 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{3} - {\left(8 \, a^{5} + 20 \, a^{3} b^{2} + 15 \, a b^{4} + 3 \, {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{5} + 5 \, a^{3} b^{2} - 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{15 \, d}"," ",0,"-1/15*(15*b^5*cos(d*x + c) + 3*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^5 + 10*(5*a^2*b^3 - b^5)*cos(d*x + c)^3 - (8*a^5 + 20*a^3*b^2 + 15*a*b^4 + 3*(a^5 - 10*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^4 + 2*(2*a^5 + 5*a^3*b^2 - 15*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
222,1,121,0,1.110467," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{16 \, a b^{3} \cos\left(d x + c\right)^{2} + 8 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d x - {\left(2 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 6 \, a^{2} b^{2} - 5 \, b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/8*(16*a*b^3*cos(d*x + c)^2 + 8*(a^3*b - a*b^3)*cos(d*x + c)^4 - 3*(a^4 + 2*a^2*b^2 + b^4)*d*x - (2*(a^4 - 6*a^2*b^2 + b^4)*cos(d*x + c)^3 + (3*a^4 + 6*a^2*b^2 - 5*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
223,1,77,0,1.318158," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, b^{3} \cos\left(d x + c\right) + {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(2 \, a^{3} + 3 \, a b^{2} + {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, d}"," ",0,"-1/3*(3*b^3*cos(d*x + c) + (3*a^2*b - b^3)*cos(d*x + c)^3 - (2*a^3 + 3*a*b^2 + (a^3 - 3*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
224,1,52,0,1.096204," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, a b \cos\left(d x + c\right)^{2} - {\left(a^{2} + b^{2}\right)} d x - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(2*a*b*cos(d*x + c)^2 - (a^2 + b^2)*d*x - (a^2 - b^2)*cos(d*x + c)*sin(d*x + c))/d","A",0
225,1,23,0,1.268870," ","integrate(a*cos(d*x+c)+b*sin(d*x+c),x, algorithm=""fricas"")","-\frac{b \cos\left(d x + c\right) - a \sin\left(d x + c\right)}{d}"," ",0,"-(b*cos(d*x + c) - a*sin(d*x + c))/d","A",0
226,1,131,0,1.740249," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right)}{2 \, \sqrt{a^{2} + b^{2}} d}"," ",0,"1/2*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2))/(sqrt(a^2 + b^2)*d)","B",0
227,1,57,0,0.586412," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{b \cos\left(d x + c\right) - a \sin\left(d x + c\right)}{{\left(a^{3} + a b^{2}\right)} d \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} d \sin\left(d x + c\right)}"," ",0,"-(b*cos(d*x + c) - a*sin(d*x + c))/((a^3 + a*b^2)*d*cos(d*x + c) + (a^2*b + b^3)*d*sin(d*x + c))","A",0
228,1,294,0,1.375056," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 2 \, {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right) + 2 \, {\left(a^{3} + a b^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d\right)}}"," ",0,"1/4*((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)*sqrt(a^2 + b^2)*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 2*(a^2*b + b^3)*cos(d*x + c) + 2*(a^3 + a*b^2)*sin(d*x + c))/((a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*d)","B",0
229,1,217,0,0.673690," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right) - {\left(a^{3} + 3 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left({\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) + {\left({\left(3 \, a^{6} b + 5 \, a^{4} b^{3} + a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/3*(2*(3*a^2*b - b^3)*cos(d*x + c)^3 - 3*(a^2*b - b^3)*cos(d*x + c) - (a^3 + 3*a*b^2 + 2*(a^3 - 3*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/((a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*d*cos(d*x + c)^3 + 3*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d*cos(d*x + c) + ((3*a^6*b + 5*a^4*b^3 + a^2*b^5 - b^7)*d*cos(d*x + c)^2 + (a^4*b^3 + 2*a^2*b^5 + b^7)*d)*sin(d*x + c))","B",0
230,1,544,0,1.126240," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","-\frac{6 \, {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} + b^{4} + 2 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} \cos\left(d x + c\right) + {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 2 \, {\left(4 \, a^{4} b - a^{2} b^{3} - 5 \, b^{5}\right)} \cos\left(d x + c\right) - 2 \, {\left(2 \, a^{5} + 7 \, a^{3} b^{2} + 5 \, a b^{4} + 3 \, {\left(a^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left({\left(a^{10} - 3 \, a^{8} b^{2} - 14 \, a^{6} b^{4} - 14 \, a^{4} b^{6} - 3 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{8} b^{2} + 8 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - b^{10}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{6} b^{4} + 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} + b^{10}\right)} d + 4 \, {\left({\left(a^{9} b + 2 \, a^{7} b^{3} - 2 \, a^{3} b^{7} - a b^{9}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{7} b^{3} + 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/16*(6*(3*a^4*b + 2*a^2*b^3 - b^5)*cos(d*x + c)^3 - 3*((a^4 - 6*a^2*b^2 + b^4)*cos(d*x + c)^4 + b^4 + 2*(3*a^2*b^2 - b^4)*cos(d*x + c)^2 + 4*(a*b^3*cos(d*x + c) + (a^3*b - a*b^3)*cos(d*x + c)^3)*sin(d*x + c))*sqrt(a^2 + b^2)*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 2*(4*a^4*b - a^2*b^3 - 5*b^5)*cos(d*x + c) - 2*(2*a^5 + 7*a^3*b^2 + 5*a*b^4 + 3*(a^5 - 2*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/((a^10 - 3*a^8*b^2 - 14*a^6*b^4 - 14*a^4*b^6 - 3*a^2*b^8 + b^10)*d*cos(d*x + c)^4 + 2*(3*a^8*b^2 + 8*a^6*b^4 + 6*a^4*b^6 - b^10)*d*cos(d*x + c)^2 + (a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10)*d + 4*((a^9*b + 2*a^7*b^3 - 2*a^3*b^7 - a*b^9)*d*cos(d*x + c)^3 + (a^7*b^3 + 3*a^5*b^5 + 3*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sin(d*x + c))","B",0
231,1,441,0,2.051642," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^6,x, algorithm=""fricas"")","-\frac{8 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{5} - 20 \, {\left(a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{3} - 5 \, {\left(a^{4} b + 6 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(d x + c\right) - {\left(3 \, a^{5} + 10 \, a^{3} b^{2} + 15 \, a b^{4} + 8 \, {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + 10 \, a^{3} b^{2} - 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{15 \, {\left({\left(a^{11} - 7 \, a^{9} b^{2} - 22 \, a^{7} b^{4} - 14 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + 5 \, a b^{10}\right)} d \cos\left(d x + c\right)^{5} + 10 \, {\left(a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{3} b^{8} - a b^{10}\right)} d \cos\left(d x + c\right)^{3} + 5 \, {\left(a^{7} b^{4} + 3 \, a^{5} b^{6} + 3 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right) + {\left({\left(5 \, a^{10} b + 5 \, a^{8} b^{3} - 14 \, a^{6} b^{5} - 22 \, a^{4} b^{7} - 7 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(5 \, a^{8} b^{3} + 14 \, a^{6} b^{5} + 12 \, a^{4} b^{7} + 2 \, a^{2} b^{9} - b^{11}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{6} b^{5} + 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} + b^{11}\right)} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/15*(8*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^5 - 20*(a^4*b - 6*a^2*b^3 + b^5)*cos(d*x + c)^3 - 5*(a^4*b + 6*a^2*b^3 - 3*b^5)*cos(d*x + c) - (3*a^5 + 10*a^3*b^2 + 15*a*b^4 + 8*(a^5 - 10*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^4 + 4*(a^5 + 10*a^3*b^2 - 15*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/((a^11 - 7*a^9*b^2 - 22*a^7*b^4 - 14*a^5*b^6 + 5*a^3*b^8 + 5*a*b^10)*d*cos(d*x + c)^5 + 10*(a^9*b^2 + 2*a^7*b^4 - 2*a^3*b^8 - a*b^10)*d*cos(d*x + c)^3 + 5*(a^7*b^4 + 3*a^5*b^6 + 3*a^3*b^8 + a*b^10)*d*cos(d*x + c) + ((5*a^10*b + 5*a^8*b^3 - 14*a^6*b^5 - 22*a^4*b^7 - 7*a^2*b^9 + b^11)*d*cos(d*x + c)^4 + 2*(5*a^8*b^3 + 14*a^6*b^5 + 12*a^4*b^7 + 2*a^2*b^9 - b^11)*d*cos(d*x + c)^2 + (a^6*b^5 + 3*a^4*b^7 + 3*a^2*b^9 + b^11)*d)*sin(d*x + c))","B",0
232,0,0,0,1.095033," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(3 \, a b^{2} \cos\left(d x + c\right) + {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(b^{3} + {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}, x\right)"," ",0,"integral((3*a*b^2*cos(d*x + c) + (a^3 - 3*a*b^2)*cos(d*x + c)^3 + (b^3 + (3*a^2*b - b^3)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a*cos(d*x + c) + b*sin(d*x + c)), x)","F",0
233,0,0,0,0.928756," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right)} \sqrt{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}, x\right)"," ",0,"integral((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)*sqrt(a*cos(d*x + c) + b*sin(d*x + c)), x)","F",0
234,0,0,0,0.810622," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(d x + c\right) + b \sin\left(d x + c\right)\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((a*cos(d*x + c) + b*sin(d*x + c))^(3/2), x)","F",0
235,0,0,0,0.800912," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(a*cos(d*x + c) + b*sin(d*x + c)), x)","F",0
236,0,0,0,0.871108," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}}, x\right)"," ",0,"integral(1/sqrt(a*cos(d*x + c) + b*sin(d*x + c)), x)","F",0
237,0,0,0,1.931293," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}, x\right)"," ",0,"integral(sqrt(a*cos(d*x + c) + b*sin(d*x + c))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2), x)","F",0
238,0,0,0,1.884261," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}}{3 \, a b^{2} \cos\left(d x + c\right) + {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(b^{3} + {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(a*cos(d*x + c) + b*sin(d*x + c))/(3*a*b^2*cos(d*x + c) + (a^3 - 3*a*b^2)*cos(d*x + c)^3 + (b^3 + (3*a^2*b - b^3)*cos(d*x + c)^2)*sin(d*x + c)), x)","F",0
239,0,0,0,1.393640," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}}{{\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} + b^{4} + 2 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} \cos\left(d x + c\right) + {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(a*cos(d*x + c) + b*sin(d*x + c))/((a^4 - 6*a^2*b^2 + b^4)*cos(d*x + c)^4 + b^4 + 2*(3*a^2*b^2 - b^4)*cos(d*x + c)^2 + 4*(a*b^3*cos(d*x + c) + (a^3*b - a*b^3)*cos(d*x + c)^3)*sin(d*x + c)), x)","F",0
240,0,0,0,0.597888," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(46 \, \cos\left(d x + c\right)^{3} - 9 \, {\left(\cos\left(d x + c\right)^{2} + 3\right)} \sin\left(d x + c\right) - 54 \, \cos\left(d x + c\right)\right)} \sqrt{2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-(46*cos(d*x + c)^3 - 9*(cos(d*x + c)^2 + 3)*sin(d*x + c) - 54*cos(d*x + c))*sqrt(2*cos(d*x + c) + 3*sin(d*x + c)), x)","F",0
241,0,0,0,0.971157," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(5 \, \cos\left(d x + c\right)^{2} - 12 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 9\right)} \sqrt{2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-(5*cos(d*x + c)^2 - 12*cos(d*x + c)*sin(d*x + c) - 9)*sqrt(2*cos(d*x + c) + 3*sin(d*x + c)), x)","F",0
242,0,0,0,1.246723," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((2*cos(d*x + c) + 3*sin(d*x + c))^(3/2), x)","F",0
243,0,0,0,1.187040," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(2*cos(d*x + c) + 3*sin(d*x + c)), x)","F",0
244,0,0,0,1.767996," ","integrate(1/(2*cos(d*x+c)+3*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)}}, x\right)"," ",0,"integral(1/sqrt(2*cos(d*x + c) + 3*sin(d*x + c)), x)","F",0
245,0,0,0,1.090194," ","integrate(1/(2*cos(d*x+c)+3*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)}}{5 \, \cos\left(d x + c\right)^{2} - 12 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 9}, x\right)"," ",0,"integral(-sqrt(2*cos(d*x + c) + 3*sin(d*x + c))/(5*cos(d*x + c)^2 - 12*cos(d*x + c)*sin(d*x + c) - 9), x)","F",0
246,0,0,0,0.504876," ","integrate(1/(2*cos(d*x+c)+3*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)}}{46 \, \cos\left(d x + c\right)^{3} - 9 \, {\left(\cos\left(d x + c\right)^{2} + 3\right)} \sin\left(d x + c\right) - 54 \, \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(2*cos(d*x + c) + 3*sin(d*x + c))/(46*cos(d*x + c)^3 - 9*(cos(d*x + c)^2 + 3)*sin(d*x + c) - 54*cos(d*x + c)), x)","F",0
247,0,0,0,1.544210," ","integrate(1/(2*cos(d*x+c)+3*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)}}{119 \, \cos\left(d x + c\right)^{4} - 54 \, \cos\left(d x + c\right)^{2} + 24 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 9 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 81}, x\right)"," ",0,"integral(-sqrt(2*cos(d*x + c) + 3*sin(d*x + c))/(119*cos(d*x + c)^4 - 54*cos(d*x + c)^2 + 24*(5*cos(d*x + c)^3 - 9*cos(d*x + c))*sin(d*x + c) - 81), x)","F",0
248,1,23,0,1.829091," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^n,x, algorithm=""fricas"")","-\frac{i \, e^{\left(i \, d n x + i \, c n + n \log\left(a\right)\right)}}{d n}"," ",0,"-I*e^(I*d*n*x + I*c*n + n*log(a))/(d*n)","A",0
249,1,17,0,1.833637," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)}}{4 \, d}"," ",0,"-1/4*I*a^4*e^(4*I*d*x + 4*I*c)/d","A",0
250,1,17,0,0.851959," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{i \, a^{3} e^{\left(3 i \, d x + 3 i \, c\right)}}{3 \, d}"," ",0,"-1/3*I*a^3*e^(3*I*d*x + 3*I*c)/d","A",0
251,1,17,0,1.691420," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)}}{2 \, d}"," ",0,"-1/2*I*a^2*e^(2*I*d*x + 2*I*c)/d","A",0
252,1,15,0,1.932111," ","integrate(a*cos(d*x+c)+I*a*sin(d*x+c),x, algorithm=""fricas"")","-\frac{i \, a e^{\left(i \, d x + i \, c\right)}}{d}"," ",0,"-I*a*e^(I*d*x + I*c)/d","A",0
253,1,17,0,0.916807," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{i \, e^{\left(-i \, d x - i \, c\right)}}{a d}"," ",0,"I*e^(-I*d*x - I*c)/(a*d)","A",0
254,1,17,0,0.934704," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{i \, e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a^{2} d}"," ",0,"1/2*I*e^(-2*I*d*x - 2*I*c)/(a^2*d)","A",0
255,1,17,0,1.620879," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{i \, e^{\left(-3 i \, d x - 3 i \, c\right)}}{3 \, a^{3} d}"," ",0,"1/3*I*e^(-3*I*d*x - 3*I*c)/(a^3*d)","A",0
256,1,17,0,1.328645," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{i \, e^{\left(-4 i \, d x - 4 i \, c\right)}}{4 \, a^{4} d}"," ",0,"1/4*I*e^(-4*I*d*x - 4*I*c)/(a^4*d)","A",0
257,1,17,0,1.469279," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 i \, a^{\frac{5}{2}} e^{\left(\frac{5}{2} i \, d x + \frac{5}{2} i \, c\right)}}{5 \, d}"," ",0,"-2/5*I*a^(5/2)*e^(5/2*I*d*x + 5/2*I*c)/d","A",0
258,1,17,0,1.080187," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 i \, a^{\frac{3}{2}} e^{\left(\frac{3}{2} i \, d x + \frac{3}{2} i \, c\right)}}{3 \, d}"," ",0,"-2/3*I*a^(3/2)*e^(3/2*I*d*x + 3/2*I*c)/d","A",0
259,1,17,0,2.385276," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 i \, \sqrt{a} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{d}"," ",0,"-2*I*sqrt(a)*e^(1/2*I*d*x + 1/2*I*c)/d","A",0
260,1,17,0,1.039013," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 i \, e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{\sqrt{a} d}"," ",0,"2*I*e^(-1/2*I*d*x - 1/2*I*c)/(sqrt(a)*d)","A",0
261,1,17,0,1.486815," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 i \, e^{\left(-\frac{3}{2} i \, d x - \frac{3}{2} i \, c\right)}}{3 \, a^{\frac{3}{2}} d}"," ",0,"2/3*I*e^(-3/2*I*d*x - 3/2*I*c)/(a^(3/2)*d)","A",0
262,1,17,0,0.968736," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 i \, e^{\left(-\frac{5}{2} i \, d x - \frac{5}{2} i \, c\right)}}{5 \, a^{\frac{5}{2}} d}"," ",0,"2/5*I*e^(-5/2*I*d*x - 5/2*I*c)/(a^(5/2)*d)","A",0
263,1,166,0,0.924614," ","integrate((a*sec(x)+b*tan(x))^5,x, algorithm=""fricas"")","\frac{{\left(3 \, a^{5} - 10 \, a^{3} b^{2} + 15 \, a b^{4} - 8 \, b^{5}\right)} \cos\left(x\right)^{4} \log\left(\sin\left(x\right) + 1\right) - {\left(3 \, a^{5} - 10 \, a^{3} b^{2} + 15 \, a b^{4} + 8 \, b^{5}\right)} \cos\left(x\right)^{4} \log\left(-\sin\left(x\right) + 1\right) + 20 \, a^{4} b + 40 \, a^{2} b^{3} + 4 \, b^{5} - 16 \, {\left(5 \, a^{2} b^{3} + b^{5}\right)} \cos\left(x\right)^{2} + 2 \, {\left(2 \, a^{5} + 20 \, a^{3} b^{2} + 10 \, a b^{4} + {\left(3 \, a^{5} - 10 \, a^{3} b^{2} - 25 \, a b^{4}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{16 \, \cos\left(x\right)^{4}}"," ",0,"1/16*((3*a^5 - 10*a^3*b^2 + 15*a*b^4 - 8*b^5)*cos(x)^4*log(sin(x) + 1) - (3*a^5 - 10*a^3*b^2 + 15*a*b^4 + 8*b^5)*cos(x)^4*log(-sin(x) + 1) + 20*a^4*b + 40*a^2*b^3 + 4*b^5 - 16*(5*a^2*b^3 + b^5)*cos(x)^2 + 2*(2*a^5 + 20*a^3*b^2 + 10*a*b^4 + (3*a^5 - 10*a^3*b^2 - 25*a*b^4)*cos(x)^2)*sin(x))/cos(x)^4","A",0
264,1,80,0,0.839445," ","integrate((a*sec(x)+b*tan(x))^4,x, algorithm=""fricas"")","\frac{3 \, b^{4} x \cos\left(x\right)^{3} - 12 \, a b^{3} \cos\left(x\right)^{2} + 4 \, a^{3} b + 4 \, a b^{3} + {\left(a^{4} + 6 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{4} - 3 \, a^{2} b^{2} - 2 \, b^{4}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{3 \, \cos\left(x\right)^{3}}"," ",0,"1/3*(3*b^4*x*cos(x)^3 - 12*a*b^3*cos(x)^2 + 4*a^3*b + 4*a*b^3 + (a^4 + 6*a^2*b^2 + b^4 + 2*(a^4 - 3*a^2*b^2 - 2*b^4)*cos(x)^2)*sin(x))/cos(x)^3","A",0
265,1,85,0,2.072354," ","integrate((a*sec(x)+b*tan(x))^3,x, algorithm=""fricas"")","\frac{{\left(a^{3} - 3 \, a b^{2} + 2 \, b^{3}\right)} \cos\left(x\right)^{2} \log\left(\sin\left(x\right) + 1\right) - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cos\left(x\right)^{2} \log\left(-\sin\left(x\right) + 1\right) + 6 \, a^{2} b + 2 \, b^{3} + 2 \, {\left(a^{3} + 3 \, a b^{2}\right)} \sin\left(x\right)}{4 \, \cos\left(x\right)^{2}}"," ",0,"1/4*((a^3 - 3*a*b^2 + 2*b^3)*cos(x)^2*log(sin(x) + 1) - (a^3 - 3*a*b^2 - 2*b^3)*cos(x)^2*log(-sin(x) + 1) + 6*a^2*b + 2*b^3 + 2*(a^3 + 3*a*b^2)*sin(x))/cos(x)^2","A",0
266,1,29,0,1.621897," ","integrate((a*sec(x)+b*tan(x))^2,x, algorithm=""fricas"")","-\frac{b^{2} x \cos\left(x\right) - 2 \, a b - {\left(a^{2} + b^{2}\right)} \sin\left(x\right)}{\cos\left(x\right)}"," ",0,"-(b^2*x*cos(x) - 2*a*b - (a^2 + b^2)*sin(x))/cos(x)","A",0
267,1,25,0,1.494550," ","integrate(a*sec(x)+b*tan(x),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(a - b\right)} \log\left(\sin\left(x\right) + 1\right) - \frac{1}{2} \, {\left(a + b\right)} \log\left(-\sin\left(x\right) + 1\right)"," ",0,"1/2*(a - b)*log(sin(x) + 1) - 1/2*(a + b)*log(-sin(x) + 1)","B",0
268,1,11,0,1.019662," ","integrate(1/(a*sec(x)+b*tan(x)),x, algorithm=""fricas"")","\frac{\log\left(b \sin\left(x\right) + a\right)}{b}"," ",0,"log(b*sin(x) + a)/b","A",0
269,1,308,0,1.057583," ","integrate(1/(a*sec(x)+b*tan(x))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a^{2} b - b^{3}\right)} x \sin\left(x\right) + {\left(a b \sin\left(x\right) + a^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a b \sin\left(x\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(x\right) \sin\left(x\right) + b \cos\left(x\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(x\right)^{2} - 2 \, a b \sin\left(x\right) - a^{2} - b^{2}}\right) + 2 \, {\left(a^{3} - a b^{2}\right)} x + 2 \, {\left(a^{2} b - b^{3}\right)} \cos\left(x\right)}{2 \, {\left(a^{3} b^{2} - a b^{4} + {\left(a^{2} b^{3} - b^{5}\right)} \sin\left(x\right)\right)}}, -\frac{{\left(a^{2} b - b^{3}\right)} x \sin\left(x\right) + {\left(a b \sin\left(x\right) + a^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(x\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(x\right)}\right) + {\left(a^{3} - a b^{2}\right)} x + {\left(a^{2} b - b^{3}\right)} \cos\left(x\right)}{a^{3} b^{2} - a b^{4} + {\left(a^{2} b^{3} - b^{5}\right)} \sin\left(x\right)}\right]"," ",0,"[-1/2*(2*(a^2*b - b^3)*x*sin(x) + (a*b*sin(x) + a^2)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(x)^2 - 2*a*b*sin(x) - a^2 - b^2 + 2*(a*cos(x)*sin(x) + b*cos(x))*sqrt(-a^2 + b^2))/(b^2*cos(x)^2 - 2*a*b*sin(x) - a^2 - b^2)) + 2*(a^3 - a*b^2)*x + 2*(a^2*b - b^3)*cos(x))/(a^3*b^2 - a*b^4 + (a^2*b^3 - b^5)*sin(x)), -((a^2*b - b^3)*x*sin(x) + (a*b*sin(x) + a^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(x) + b)/(sqrt(a^2 - b^2)*cos(x))) + (a^3 - a*b^2)*x + (a^2*b - b^3)*cos(x))/(a^3*b^2 - a*b^4 + (a^2*b^3 - b^5)*sin(x))]","B",0
270,1,83,0,0.946669," ","integrate(1/(a*sec(x)+b*tan(x))^3,x, algorithm=""fricas"")","\frac{4 \, a b \sin\left(x\right) + 3 \, a^{2} + b^{2} - 2 \, {\left(b^{2} \cos\left(x\right)^{2} - 2 \, a b \sin\left(x\right) - a^{2} - b^{2}\right)} \log\left(b \sin\left(x\right) + a\right)}{2 \, {\left(b^{5} \cos\left(x\right)^{2} - 2 \, a b^{4} \sin\left(x\right) - a^{2} b^{3} - b^{5}\right)}}"," ",0,"1/2*(4*a*b*sin(x) + 3*a^2 + b^2 - 2*(b^2*cos(x)^2 - 2*a*b*sin(x) - a^2 - b^2)*log(b*sin(x) + a))/(b^5*cos(x)^2 - 2*a*b^4*sin(x) - a^2*b^3 - b^5)","A",0
271,1,931,0,1.402684," ","integrate(1/(a*sec(x)+b*tan(x))^4,x, algorithm=""fricas"")","\left[-\frac{36 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} x \cos\left(x\right)^{2} + 2 \, {\left(11 \, a^{4} b^{3} - 19 \, a^{2} b^{5} + 8 \, b^{7}\right)} \cos\left(x\right)^{3} + 3 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} - 9 \, a^{2} b^{4} - 3 \, {\left(2 \, a^{4} b^{2} - 3 \, a^{2} b^{4}\right)} \cos\left(x\right)^{2} + {\left(6 \, a^{5} b - 7 \, a^{3} b^{3} - 3 \, a b^{5} - {\left(2 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a b \sin\left(x\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(x\right) \sin\left(x\right) + b \cos\left(x\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(x\right)^{2} - 2 \, a b \sin\left(x\right) - a^{2} - b^{2}}\right) - 12 \, {\left(a^{7} + a^{5} b^{2} - 5 \, a^{3} b^{4} + 3 \, a b^{6}\right)} x - 12 \, {\left(a^{6} b - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(x\right) + 6 \, {\left(2 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} x \cos\left(x\right)^{2} - 2 \, {\left(3 \, a^{6} b - 5 \, a^{4} b^{3} + a^{2} b^{5} + b^{7}\right)} x - {\left(5 \, a^{5} b^{2} - 8 \, a^{3} b^{4} + 3 \, a b^{6}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{12 \, {\left(a^{7} b^{4} + a^{5} b^{6} - 5 \, a^{3} b^{8} + 3 \, a b^{10} - 3 \, {\left(a^{5} b^{6} - 2 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(x\right)^{2} + {\left(3 \, a^{6} b^{5} - 5 \, a^{4} b^{7} + a^{2} b^{9} + b^{11} - {\left(a^{4} b^{7} - 2 \, a^{2} b^{9} + b^{11}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)\right)}}, -\frac{18 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} x \cos\left(x\right)^{2} + {\left(11 \, a^{4} b^{3} - 19 \, a^{2} b^{5} + 8 \, b^{7}\right)} \cos\left(x\right)^{3} - 3 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} - 9 \, a^{2} b^{4} - 3 \, {\left(2 \, a^{4} b^{2} - 3 \, a^{2} b^{4}\right)} \cos\left(x\right)^{2} + {\left(6 \, a^{5} b - 7 \, a^{3} b^{3} - 3 \, a b^{5} - {\left(2 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(x\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(x\right)}\right) - 6 \, {\left(a^{7} + a^{5} b^{2} - 5 \, a^{3} b^{4} + 3 \, a b^{6}\right)} x - 6 \, {\left(a^{6} b - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(x\right) + 3 \, {\left(2 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} x \cos\left(x\right)^{2} - 2 \, {\left(3 \, a^{6} b - 5 \, a^{4} b^{3} + a^{2} b^{5} + b^{7}\right)} x - {\left(5 \, a^{5} b^{2} - 8 \, a^{3} b^{4} + 3 \, a b^{6}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{6 \, {\left(a^{7} b^{4} + a^{5} b^{6} - 5 \, a^{3} b^{8} + 3 \, a b^{10} - 3 \, {\left(a^{5} b^{6} - 2 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(x\right)^{2} + {\left(3 \, a^{6} b^{5} - 5 \, a^{4} b^{7} + a^{2} b^{9} + b^{11} - {\left(a^{4} b^{7} - 2 \, a^{2} b^{9} + b^{11}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)\right)}}\right]"," ",0,"[-1/12*(36*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*x*cos(x)^2 + 2*(11*a^4*b^3 - 19*a^2*b^5 + 8*b^7)*cos(x)^3 + 3*(2*a^6 + 3*a^4*b^2 - 9*a^2*b^4 - 3*(2*a^4*b^2 - 3*a^2*b^4)*cos(x)^2 + (6*a^5*b - 7*a^3*b^3 - 3*a*b^5 - (2*a^3*b^3 - 3*a*b^5)*cos(x)^2)*sin(x))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(x)^2 - 2*a*b*sin(x) - a^2 - b^2 - 2*(a*cos(x)*sin(x) + b*cos(x))*sqrt(-a^2 + b^2))/(b^2*cos(x)^2 - 2*a*b*sin(x) - a^2 - b^2)) - 12*(a^7 + a^5*b^2 - 5*a^3*b^4 + 3*a*b^6)*x - 12*(a^6*b - 2*a^2*b^5 + b^7)*cos(x) + 6*(2*(a^4*b^3 - 2*a^2*b^5 + b^7)*x*cos(x)^2 - 2*(3*a^6*b - 5*a^4*b^3 + a^2*b^5 + b^7)*x - (5*a^5*b^2 - 8*a^3*b^4 + 3*a*b^6)*cos(x))*sin(x))/(a^7*b^4 + a^5*b^6 - 5*a^3*b^8 + 3*a*b^10 - 3*(a^5*b^6 - 2*a^3*b^8 + a*b^10)*cos(x)^2 + (3*a^6*b^5 - 5*a^4*b^7 + a^2*b^9 + b^11 - (a^4*b^7 - 2*a^2*b^9 + b^11)*cos(x)^2)*sin(x)), -1/6*(18*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*x*cos(x)^2 + (11*a^4*b^3 - 19*a^2*b^5 + 8*b^7)*cos(x)^3 - 3*(2*a^6 + 3*a^4*b^2 - 9*a^2*b^4 - 3*(2*a^4*b^2 - 3*a^2*b^4)*cos(x)^2 + (6*a^5*b - 7*a^3*b^3 - 3*a*b^5 - (2*a^3*b^3 - 3*a*b^5)*cos(x)^2)*sin(x))*sqrt(a^2 - b^2)*arctan(-(a*sin(x) + b)/(sqrt(a^2 - b^2)*cos(x))) - 6*(a^7 + a^5*b^2 - 5*a^3*b^4 + 3*a*b^6)*x - 6*(a^6*b - 2*a^2*b^5 + b^7)*cos(x) + 3*(2*(a^4*b^3 - 2*a^2*b^5 + b^7)*x*cos(x)^2 - 2*(3*a^6*b - 5*a^4*b^3 + a^2*b^5 + b^7)*x - (5*a^5*b^2 - 8*a^3*b^4 + 3*a*b^6)*cos(x))*sin(x))/(a^7*b^4 + a^5*b^6 - 5*a^3*b^8 + 3*a*b^10 - 3*(a^5*b^6 - 2*a^3*b^8 + a*b^10)*cos(x)^2 + (3*a^6*b^5 - 5*a^4*b^7 + a^2*b^9 + b^11 - (a^4*b^7 - 2*a^2*b^9 + b^11)*cos(x)^2)*sin(x))]","B",0
272,1,217,0,1.057809," ","integrate(1/(a*sec(x)+b*tan(x))^5,x, algorithm=""fricas"")","\frac{25 \, a^{4} + 110 \, a^{2} b^{2} + 9 \, b^{4} - 12 \, {\left(9 \, a^{2} b^{2} + b^{4}\right)} \cos\left(x\right)^{2} + 12 \, {\left(b^{4} \cos\left(x\right)^{4} + a^{4} + 6 \, a^{2} b^{2} + b^{4} - 2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} \cos\left(x\right)^{2} - 4 \, {\left(a b^{3} \cos\left(x\right)^{2} - a^{3} b - a b^{3}\right)} \sin\left(x\right)\right)} \log\left(b \sin\left(x\right) + a\right) - 8 \, {\left(6 \, a b^{3} \cos\left(x\right)^{2} - 11 \, a^{3} b - 7 \, a b^{3}\right)} \sin\left(x\right)}{12 \, {\left(b^{9} \cos\left(x\right)^{4} + a^{4} b^{5} + 6 \, a^{2} b^{7} + b^{9} - 2 \, {\left(3 \, a^{2} b^{7} + b^{9}\right)} \cos\left(x\right)^{2} - 4 \, {\left(a b^{8} \cos\left(x\right)^{2} - a^{3} b^{6} - a b^{8}\right)} \sin\left(x\right)\right)}}"," ",0,"1/12*(25*a^4 + 110*a^2*b^2 + 9*b^4 - 12*(9*a^2*b^2 + b^4)*cos(x)^2 + 12*(b^4*cos(x)^4 + a^4 + 6*a^2*b^2 + b^4 - 2*(3*a^2*b^2 + b^4)*cos(x)^2 - 4*(a*b^3*cos(x)^2 - a^3*b - a*b^3)*sin(x))*log(b*sin(x) + a) - 8*(6*a*b^3*cos(x)^2 - 11*a^3*b - 7*a*b^3)*sin(x))/(b^9*cos(x)^4 + a^4*b^5 + 6*a^2*b^7 + b^9 - 2*(3*a^2*b^7 + b^9)*cos(x)^2 - 4*(a*b^8*cos(x)^2 - a^3*b^6 - a*b^8)*sin(x))","B",0
273,1,38,0,0.956933," ","integrate((sec(x)+tan(x))^5,x, algorithm=""fricas"")","-\frac{{\left(\cos\left(x\right)^{2} + 2 \, \sin\left(x\right) - 2\right)} \log\left(-\sin\left(x\right) + 1\right) + 4 \, \sin\left(x\right) - 2}{\cos\left(x\right)^{2} + 2 \, \sin\left(x\right) - 2}"," ",0,"-((cos(x)^2 + 2*sin(x) - 2)*log(-sin(x) + 1) + 4*sin(x) - 2)/(cos(x)^2 + 2*sin(x) - 2)","A",0
274,1,61,0,0.910781," ","integrate((sec(x)+tan(x))^4,x, algorithm=""fricas"")","\frac{{\left(3 \, x + 8\right)} \cos\left(x\right)^{2} - {\left(3 \, x - 4\right)} \cos\left(x\right) + {\left({\left(3 \, x - 8\right)} \cos\left(x\right) + 6 \, x - 4\right)} \sin\left(x\right) - 6 \, x - 4}{3 \, {\left(\cos\left(x\right)^{2} + {\left(\cos\left(x\right) + 2\right)} \sin\left(x\right) - \cos\left(x\right) - 2\right)}}"," ",0,"1/3*((3*x + 8)*cos(x)^2 - (3*x - 4)*cos(x) + ((3*x - 8)*cos(x) + 6*x - 4)*sin(x) - 6*x - 4)/(cos(x)^2 + (cos(x) + 2)*sin(x) - cos(x) - 2)","B",0
275,1,21,0,0.907350," ","integrate((sec(x)+tan(x))^3,x, algorithm=""fricas"")","\frac{{\left(\sin\left(x\right) - 1\right)} \log\left(-\sin\left(x\right) + 1\right) - 2}{\sin\left(x\right) - 1}"," ",0,"((sin(x) - 1)*log(-sin(x) + 1) - 2)/(sin(x) - 1)","A",0
276,1,28,0,0.890285," ","integrate((sec(x)+tan(x))^2,x, algorithm=""fricas"")","-\frac{{\left(x - 2\right)} \cos\left(x\right) - {\left(x + 2\right)} \sin\left(x\right) + x - 2}{\cos\left(x\right) - \sin\left(x\right) + 1}"," ",0,"-((x - 2)*cos(x) - (x + 2)*sin(x) + x - 2)/(cos(x) - sin(x) + 1)","A",0
277,1,9,0,3.008558," ","integrate(sec(x)+tan(x),x, algorithm=""fricas"")","-\log\left(-\sin\left(x\right) + 1\right)"," ",0,"-log(-sin(x) + 1)","A",0
278,1,5,0,0.610305," ","integrate(1/(sec(x)+tan(x)),x, algorithm=""fricas"")","\log\left(\sin\left(x\right) + 1\right)"," ",0,"log(sin(x) + 1)","A",0
279,1,25,0,1.006384," ","integrate(1/(sec(x)+tan(x))^2,x, algorithm=""fricas"")","-\frac{{\left(x + 2\right)} \cos\left(x\right) + {\left(x - 2\right)} \sin\left(x\right) + x + 2}{\cos\left(x\right) + \sin\left(x\right) + 1}"," ",0,"-((x + 2)*cos(x) + (x - 2)*sin(x) + x + 2)/(cos(x) + sin(x) + 1)","A",0
280,1,20,0,1.066832," ","integrate(1/(sec(x)+tan(x))^3,x, algorithm=""fricas"")","-\frac{{\left(\sin\left(x\right) + 1\right)} \log\left(\sin\left(x\right) + 1\right) + 2}{\sin\left(x\right) + 1}"," ",0,"-((sin(x) + 1)*log(sin(x) + 1) + 2)/(sin(x) + 1)","A",0
281,1,63,0,0.861887," ","integrate(1/(sec(x)+tan(x))^4,x, algorithm=""fricas"")","\frac{{\left(3 \, x - 8\right)} \cos\left(x\right)^{2} - {\left(3 \, x + 4\right)} \cos\left(x\right) - {\left({\left(3 \, x + 8\right)} \cos\left(x\right) + 6 \, x + 4\right)} \sin\left(x\right) - 6 \, x + 4}{3 \, {\left(\cos\left(x\right)^{2} - {\left(\cos\left(x\right) + 2\right)} \sin\left(x\right) - \cos\left(x\right) - 2\right)}}"," ",0,"1/3*((3*x - 8)*cos(x)^2 - (3*x + 4)*cos(x) - ((3*x + 8)*cos(x) + 6*x + 4)*sin(x) - 6*x + 4)/(cos(x)^2 - (cos(x) + 2)*sin(x) - cos(x) - 2)","B",0
282,1,35,0,1.057092," ","integrate(1/(sec(x)+tan(x))^5,x, algorithm=""fricas"")","\frac{{\left(\cos\left(x\right)^{2} - 2 \, \sin\left(x\right) - 2\right)} \log\left(\sin\left(x\right) + 1\right) - 4 \, \sin\left(x\right) - 2}{\cos\left(x\right)^{2} - 2 \, \sin\left(x\right) - 2}"," ",0,"((cos(x)^2 - 2*sin(x) - 2)*log(sin(x) + 1) - 4*sin(x) - 2)/(cos(x)^2 - 2*sin(x) - 2)","A",0
283,1,292,0,0.872066," ","integrate((a*cot(x)+b*csc(x))^5,x, algorithm=""fricas"")","\frac{12 \, a^{5} + 40 \, a^{3} b^{2} - 20 \, a b^{4} - 2 \, {\left(25 \, a^{4} b + 10 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(x\right)^{3} - 16 \, {\left(a^{5} + 5 \, a^{3} b^{2}\right)} \cos\left(x\right)^{2} + 10 \, {\left(3 \, a^{4} b - 2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(x\right) + {\left(8 \, a^{5} - 15 \, a^{4} b + 10 \, a^{2} b^{3} - 3 \, b^{5} + {\left(8 \, a^{5} - 15 \, a^{4} b + 10 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(x\right)^{4} - 2 \, {\left(8 \, a^{5} - 15 \, a^{4} b + 10 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(x\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + {\left(8 \, a^{5} + 15 \, a^{4} b - 10 \, a^{2} b^{3} + 3 \, b^{5} + {\left(8 \, a^{5} + 15 \, a^{4} b - 10 \, a^{2} b^{3} + 3 \, b^{5}\right)} \cos\left(x\right)^{4} - 2 \, {\left(8 \, a^{5} + 15 \, a^{4} b - 10 \, a^{2} b^{3} + 3 \, b^{5}\right)} \cos\left(x\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{16 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)}}"," ",0,"1/16*(12*a^5 + 40*a^3*b^2 - 20*a*b^4 - 2*(25*a^4*b + 10*a^2*b^3 - 3*b^5)*cos(x)^3 - 16*(a^5 + 5*a^3*b^2)*cos(x)^2 + 10*(3*a^4*b - 2*a^2*b^3 - b^5)*cos(x) + (8*a^5 - 15*a^4*b + 10*a^2*b^3 - 3*b^5 + (8*a^5 - 15*a^4*b + 10*a^2*b^3 - 3*b^5)*cos(x)^4 - 2*(8*a^5 - 15*a^4*b + 10*a^2*b^3 - 3*b^5)*cos(x)^2)*log(1/2*cos(x) + 1/2) + (8*a^5 + 15*a^4*b - 10*a^2*b^3 + 3*b^5 + (8*a^5 + 15*a^4*b - 10*a^2*b^3 + 3*b^5)*cos(x)^4 - 2*(8*a^5 + 15*a^4*b - 10*a^2*b^3 + 3*b^5)*cos(x)^2)*log(-1/2*cos(x) + 1/2))/(cos(x)^4 - 2*cos(x)^2 + 1)","B",0
284,1,95,0,0.951467," ","integrate((a*cot(x)+b*csc(x))^4,x, algorithm=""fricas"")","\frac{12 \, a^{3} b \cos\left(x\right)^{2} - 8 \, a^{3} b + 4 \, a b^{3} + 2 \, {\left(2 \, a^{4} + 3 \, a^{2} b^{2} - b^{4}\right)} \cos\left(x\right)^{3} - 3 \, {\left(a^{4} - b^{4}\right)} \cos\left(x\right) + 3 \, {\left(a^{4} x \cos\left(x\right)^{2} - a^{4} x\right)} \sin\left(x\right)}{3 \, {\left(\cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}"," ",0,"1/3*(12*a^3*b*cos(x)^2 - 8*a^3*b + 4*a*b^3 + 2*(2*a^4 + 3*a^2*b^2 - b^4)*cos(x)^3 - 3*(a^4 - b^4)*cos(x) + 3*(a^4*x*cos(x)^2 - a^4*x)*sin(x))/((cos(x)^2 - 1)*sin(x))","A",0
285,1,128,0,0.968732," ","integrate((a*cot(x)+b*csc(x))^3,x, algorithm=""fricas"")","\frac{2 \, a^{3} + 6 \, a b^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} \cos\left(x\right) + {\left(2 \, a^{3} - 3 \, a^{2} b + b^{3} - {\left(2 \, a^{3} - 3 \, a^{2} b + b^{3}\right)} \cos\left(x\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cos\left(x\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{4 \, {\left(\cos\left(x\right)^{2} - 1\right)}}"," ",0,"1/4*(2*a^3 + 6*a*b^2 + 2*(3*a^2*b + b^3)*cos(x) + (2*a^3 - 3*a^2*b + b^3 - (2*a^3 - 3*a^2*b + b^3)*cos(x)^2)*log(1/2*cos(x) + 1/2) + (2*a^3 + 3*a^2*b - b^3 - (2*a^3 + 3*a^2*b - b^3)*cos(x)^2)*log(-1/2*cos(x) + 1/2))/(cos(x)^2 - 1)","A",0
286,1,28,0,0.923319," ","integrate((a*cot(x)+b*csc(x))^2,x, algorithm=""fricas"")","-\frac{a^{2} x \sin\left(x\right) + 2 \, a b + {\left(a^{2} + b^{2}\right)} \cos\left(x\right)}{\sin\left(x\right)}"," ",0,"-(a^2*x*sin(x) + 2*a*b + (a^2 + b^2)*cos(x))/sin(x)","A",0
287,1,27,0,0.923466," ","integrate(a*cot(x)+b*csc(x),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(a - b\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{2} \, {\left(a + b\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"1/2*(a - b)*log(1/2*cos(x) + 1/2) + 1/2*(a + b)*log(-1/2*cos(x) + 1/2)","B",0
288,1,12,0,1.204174," ","integrate(1/(a*cot(x)+b*csc(x)),x, algorithm=""fricas"")","-\frac{\log\left(a \cos\left(x\right) + b\right)}{a}"," ",0,"-log(a*cos(x) + b)/a","A",0
289,1,307,0,1.045131," ","integrate(1/(a*cot(x)+b*csc(x))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a^{3} - a b^{2}\right)} x \cos\left(x\right) - {\left(a b \cos\left(x\right) + b^{2}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(x\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(x\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(x\right) + a\right)} \sin\left(x\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(x\right)^{2} + 2 \, a b \cos\left(x\right) + b^{2}}\right) + 2 \, {\left(a^{2} b - b^{3}\right)} x - 2 \, {\left(a^{3} - a b^{2}\right)} \sin\left(x\right)}{2 \, {\left(a^{4} b - a^{2} b^{3} + {\left(a^{5} - a^{3} b^{2}\right)} \cos\left(x\right)\right)}}, -\frac{{\left(a^{3} - a b^{2}\right)} x \cos\left(x\right) - {\left(a b \cos\left(x\right) + b^{2}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(x\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(x\right)}\right) + {\left(a^{2} b - b^{3}\right)} x - {\left(a^{3} - a b^{2}\right)} \sin\left(x\right)}{a^{4} b - a^{2} b^{3} + {\left(a^{5} - a^{3} b^{2}\right)} \cos\left(x\right)}\right]"," ",0,"[-1/2*(2*(a^3 - a*b^2)*x*cos(x) - (a*b*cos(x) + b^2)*sqrt(a^2 - b^2)*log((2*a*b*cos(x) - (a^2 - 2*b^2)*cos(x)^2 + 2*sqrt(a^2 - b^2)*(b*cos(x) + a)*sin(x) + 2*a^2 - b^2)/(a^2*cos(x)^2 + 2*a*b*cos(x) + b^2)) + 2*(a^2*b - b^3)*x - 2*(a^3 - a*b^2)*sin(x))/(a^4*b - a^2*b^3 + (a^5 - a^3*b^2)*cos(x)), -((a^3 - a*b^2)*x*cos(x) - (a*b*cos(x) + b^2)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(x) + a)/((a^2 - b^2)*sin(x))) + (a^2*b - b^3)*x - (a^3 - a*b^2)*sin(x))/(a^4*b - a^2*b^3 + (a^5 - a^3*b^2)*cos(x))]","B",0
290,1,70,0,0.843772," ","integrate(1/(a*cot(x)+b*csc(x))^3,x, algorithm=""fricas"")","\frac{4 \, a b \cos\left(x\right) + a^{2} + 3 \, b^{2} + 2 \, {\left(a^{2} \cos\left(x\right)^{2} + 2 \, a b \cos\left(x\right) + b^{2}\right)} \log\left(a \cos\left(x\right) + b\right)}{2 \, {\left(a^{5} \cos\left(x\right)^{2} + 2 \, a^{4} b \cos\left(x\right) + a^{3} b^{2}\right)}}"," ",0,"1/2*(4*a*b*cos(x) + a^2 + 3*b^2 + 2*(a^2*cos(x)^2 + 2*a*b*cos(x) + b^2)*log(a*cos(x) + b))/(a^5*cos(x)^2 + 2*a^4*b*cos(x) + a^3*b^2)","A",0
291,1,878,0,2.075531," ","integrate(1/(a*cot(x)+b*csc(x))^4,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} x \cos\left(x\right)^{3} + 36 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} x \cos\left(x\right)^{2} + 36 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} x \cos\left(x\right) + 3 \, {\left(3 \, a^{2} b^{4} - 2 \, b^{6} + {\left(3 \, a^{5} b - 2 \, a^{3} b^{3}\right)} \cos\left(x\right)^{3} + 3 \, {\left(3 \, a^{4} b^{2} - 2 \, a^{2} b^{4}\right)} \cos\left(x\right)^{2} + 3 \, {\left(3 \, a^{3} b^{3} - 2 \, a b^{5}\right)} \cos\left(x\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(x\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(x\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(x\right) + a\right)} \sin\left(x\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(x\right)^{2} + 2 \, a b \cos\left(x\right) + b^{2}}\right) + 12 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} x + 2 \, {\left(2 \, a^{7} - 7 \, a^{5} b^{2} + 11 \, a^{3} b^{4} - 6 \, a b^{6} - {\left(8 \, a^{7} - 19 \, a^{5} b^{2} + 11 \, a^{3} b^{4}\right)} \cos\left(x\right)^{2} - 3 \, {\left(3 \, a^{6} b - 8 \, a^{4} b^{3} + 5 \, a^{2} b^{5}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{12 \, {\left(a^{8} b^{3} - 2 \, a^{6} b^{5} + a^{4} b^{7} + {\left(a^{11} - 2 \, a^{9} b^{2} + a^{7} b^{4}\right)} \cos\left(x\right)^{3} + 3 \, {\left(a^{10} b - 2 \, a^{8} b^{3} + a^{6} b^{5}\right)} \cos\left(x\right)^{2} + 3 \, {\left(a^{9} b^{2} - 2 \, a^{7} b^{4} + a^{5} b^{6}\right)} \cos\left(x\right)\right)}}, \frac{6 \, {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} x \cos\left(x\right)^{3} + 18 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} x \cos\left(x\right)^{2} + 18 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} x \cos\left(x\right) - 3 \, {\left(3 \, a^{2} b^{4} - 2 \, b^{6} + {\left(3 \, a^{5} b - 2 \, a^{3} b^{3}\right)} \cos\left(x\right)^{3} + 3 \, {\left(3 \, a^{4} b^{2} - 2 \, a^{2} b^{4}\right)} \cos\left(x\right)^{2} + 3 \, {\left(3 \, a^{3} b^{3} - 2 \, a b^{5}\right)} \cos\left(x\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(x\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(x\right)}\right) + 6 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} x + {\left(2 \, a^{7} - 7 \, a^{5} b^{2} + 11 \, a^{3} b^{4} - 6 \, a b^{6} - {\left(8 \, a^{7} - 19 \, a^{5} b^{2} + 11 \, a^{3} b^{4}\right)} \cos\left(x\right)^{2} - 3 \, {\left(3 \, a^{6} b - 8 \, a^{4} b^{3} + 5 \, a^{2} b^{5}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{6 \, {\left(a^{8} b^{3} - 2 \, a^{6} b^{5} + a^{4} b^{7} + {\left(a^{11} - 2 \, a^{9} b^{2} + a^{7} b^{4}\right)} \cos\left(x\right)^{3} + 3 \, {\left(a^{10} b - 2 \, a^{8} b^{3} + a^{6} b^{5}\right)} \cos\left(x\right)^{2} + 3 \, {\left(a^{9} b^{2} - 2 \, a^{7} b^{4} + a^{5} b^{6}\right)} \cos\left(x\right)\right)}}\right]"," ",0,"[1/12*(12*(a^7 - 2*a^5*b^2 + a^3*b^4)*x*cos(x)^3 + 36*(a^6*b - 2*a^4*b^3 + a^2*b^5)*x*cos(x)^2 + 36*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*x*cos(x) + 3*(3*a^2*b^4 - 2*b^6 + (3*a^5*b - 2*a^3*b^3)*cos(x)^3 + 3*(3*a^4*b^2 - 2*a^2*b^4)*cos(x)^2 + 3*(3*a^3*b^3 - 2*a*b^5)*cos(x))*sqrt(a^2 - b^2)*log((2*a*b*cos(x) - (a^2 - 2*b^2)*cos(x)^2 - 2*sqrt(a^2 - b^2)*(b*cos(x) + a)*sin(x) + 2*a^2 - b^2)/(a^2*cos(x)^2 + 2*a*b*cos(x) + b^2)) + 12*(a^4*b^3 - 2*a^2*b^5 + b^7)*x + 2*(2*a^7 - 7*a^5*b^2 + 11*a^3*b^4 - 6*a*b^6 - (8*a^7 - 19*a^5*b^2 + 11*a^3*b^4)*cos(x)^2 - 3*(3*a^6*b - 8*a^4*b^3 + 5*a^2*b^5)*cos(x))*sin(x))/(a^8*b^3 - 2*a^6*b^5 + a^4*b^7 + (a^11 - 2*a^9*b^2 + a^7*b^4)*cos(x)^3 + 3*(a^10*b - 2*a^8*b^3 + a^6*b^5)*cos(x)^2 + 3*(a^9*b^2 - 2*a^7*b^4 + a^5*b^6)*cos(x)), 1/6*(6*(a^7 - 2*a^5*b^2 + a^3*b^4)*x*cos(x)^3 + 18*(a^6*b - 2*a^4*b^3 + a^2*b^5)*x*cos(x)^2 + 18*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*x*cos(x) - 3*(3*a^2*b^4 - 2*b^6 + (3*a^5*b - 2*a^3*b^3)*cos(x)^3 + 3*(3*a^4*b^2 - 2*a^2*b^4)*cos(x)^2 + 3*(3*a^3*b^3 - 2*a*b^5)*cos(x))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(x) + a)/((a^2 - b^2)*sin(x))) + 6*(a^4*b^3 - 2*a^2*b^5 + b^7)*x + (2*a^7 - 7*a^5*b^2 + 11*a^3*b^4 - 6*a*b^6 - (8*a^7 - 19*a^5*b^2 + 11*a^3*b^4)*cos(x)^2 - 3*(3*a^6*b - 8*a^4*b^3 + 5*a^2*b^5)*cos(x))*sin(x))/(a^8*b^3 - 2*a^6*b^5 + a^4*b^7 + (a^11 - 2*a^9*b^2 + a^7*b^4)*cos(x)^3 + 3*(a^10*b - 2*a^8*b^3 + a^6*b^5)*cos(x)^2 + 3*(a^9*b^2 - 2*a^7*b^4 + a^5*b^6)*cos(x))]","B",0
292,1,166,0,2.029604," ","integrate(1/(a*cot(x)+b*csc(x))^5,x, algorithm=""fricas"")","-\frac{48 \, a^{3} b \cos\left(x\right)^{3} - 3 \, a^{4} + 2 \, a^{2} b^{2} + 25 \, b^{4} + 12 \, {\left(a^{4} + 9 \, a^{2} b^{2}\right)} \cos\left(x\right)^{2} + 8 \, {\left(a^{3} b + 11 \, a b^{3}\right)} \cos\left(x\right) + 12 \, {\left(a^{4} \cos\left(x\right)^{4} + 4 \, a^{3} b \cos\left(x\right)^{3} + 6 \, a^{2} b^{2} \cos\left(x\right)^{2} + 4 \, a b^{3} \cos\left(x\right) + b^{4}\right)} \log\left(a \cos\left(x\right) + b\right)}{12 \, {\left(a^{9} \cos\left(x\right)^{4} + 4 \, a^{8} b \cos\left(x\right)^{3} + 6 \, a^{7} b^{2} \cos\left(x\right)^{2} + 4 \, a^{6} b^{3} \cos\left(x\right) + a^{5} b^{4}\right)}}"," ",0,"-1/12*(48*a^3*b*cos(x)^3 - 3*a^4 + 2*a^2*b^2 + 25*b^4 + 12*(a^4 + 9*a^2*b^2)*cos(x)^2 + 8*(a^3*b + 11*a*b^3)*cos(x) + 12*(a^4*cos(x)^4 + 4*a^3*b*cos(x)^3 + 6*a^2*b^2*cos(x)^2 + 4*a*b^3*cos(x) + b^4)*log(a*cos(x) + b))/(a^9*cos(x)^4 + 4*a^8*b*cos(x)^3 + 6*a^7*b^2*cos(x)^2 + 4*a^6*b^3*cos(x) + a^5*b^4)","A",0
293,1,37,0,1.583530," ","integrate((cot(x)+csc(x))^5,x, algorithm=""fricas"")","\frac{{\left(\cos\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - 4 \, \cos\left(x\right) + 2}{\cos\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1}"," ",0,"((cos(x)^2 - 2*cos(x) + 1)*log(-1/2*cos(x) + 1/2) - 4*cos(x) + 2)/(cos(x)^2 - 2*cos(x) + 1)","A",0
294,1,36,0,1.702292," ","integrate((cot(x)+csc(x))^4,x, algorithm=""fricas"")","\frac{8 \, \cos\left(x\right)^{2} + 3 \, {\left(x \cos\left(x\right) - x\right)} \sin\left(x\right) + 4 \, \cos\left(x\right) - 4}{3 \, {\left(\cos\left(x\right) - 1\right)} \sin\left(x\right)}"," ",0,"1/3*(8*cos(x)^2 + 3*(x*cos(x) - x)*sin(x) + 4*cos(x) - 4)/((cos(x) - 1)*sin(x))","A",0
295,1,22,0,1.675334," ","integrate((cot(x)+csc(x))^3,x, algorithm=""fricas"")","-\frac{{\left(\cos\left(x\right) - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - 2}{\cos\left(x\right) - 1}"," ",0,"-((cos(x) - 1)*log(-1/2*cos(x) + 1/2) - 2)/(cos(x) - 1)","A",0
296,1,16,0,1.156546," ","integrate((cot(x)+csc(x))^2,x, algorithm=""fricas"")","-\frac{x \sin\left(x\right) + 2 \, \cos\left(x\right) + 2}{\sin\left(x\right)}"," ",0,"-(x*sin(x) + 2*cos(x) + 2)/sin(x)","A",0
297,1,7,0,1.030233," ","integrate(cot(x)+csc(x),x, algorithm=""fricas"")","\log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"log(-1/2*cos(x) + 1/2)","A",0
298,1,9,0,0.914822," ","integrate(1/(cot(x)+csc(x)),x, algorithm=""fricas"")","-\log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"-log(1/2*cos(x) + 1/2)","A",0
299,1,18,0,1.095584," ","integrate(1/(cot(x)+csc(x))^2,x, algorithm=""fricas"")","-\frac{x \cos\left(x\right) + x - 2 \, \sin\left(x\right)}{\cos\left(x\right) + 1}"," ",0,"-(x*cos(x) + x - 2*sin(x))/(cos(x) + 1)","A",0
300,1,21,0,0.862878," ","integrate(1/(cot(x)+csc(x))^3,x, algorithm=""fricas"")","\frac{{\left(\cos\left(x\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + 2}{\cos\left(x\right) + 1}"," ",0,"((cos(x) + 1)*log(1/2*cos(x) + 1/2) + 2)/(cos(x) + 1)","A",0
301,1,40,0,0.954237," ","integrate(1/(cot(x)+csc(x))^4,x, algorithm=""fricas"")","\frac{3 \, x \cos\left(x\right)^{2} + 6 \, x \cos\left(x\right) - 4 \, {\left(2 \, \cos\left(x\right) + 1\right)} \sin\left(x\right) + 3 \, x}{3 \, {\left(\cos\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)}}"," ",0,"1/3*(3*x*cos(x)^2 + 6*x*cos(x) - 4*(2*cos(x) + 1)*sin(x) + 3*x)/(cos(x)^2 + 2*cos(x) + 1)","A",0
302,1,38,0,1.990203," ","integrate(1/(cot(x)+csc(x))^5,x, algorithm=""fricas"")","-\frac{{\left(\cos\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + 4 \, \cos\left(x\right) + 2}{\cos\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1}"," ",0,"-((cos(x)^2 + 2*cos(x) + 1)*log(1/2*cos(x) + 1/2) + 4*cos(x) + 2)/(cos(x)^2 + 2*cos(x) + 1)","A",0
303,1,51,0,2.053837," ","integrate((csc(x)-sin(x))^4,x, algorithm=""fricas"")","-\frac{6 \, \cos\left(x\right)^{7} + 21 \, \cos\left(x\right)^{5} - 140 \, \cos\left(x\right)^{3} - 105 \, {\left(x \cos\left(x\right)^{2} - x\right)} \sin\left(x\right) + 105 \, \cos\left(x\right)}{24 \, {\left(\cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}"," ",0,"-1/24*(6*cos(x)^7 + 21*cos(x)^5 - 140*cos(x)^3 - 105*(x*cos(x)^2 - x)*sin(x) + 105*cos(x))/((cos(x)^2 - 1)*sin(x))","A",0
304,1,57,0,1.771136," ","integrate((csc(x)-sin(x))^3,x, algorithm=""fricas"")","-\frac{4 \, \cos\left(x\right)^{5} + 20 \, \cos\left(x\right)^{3} - 15 \, {\left(\cos\left(x\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + 15 \, {\left(\cos\left(x\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - 30 \, \cos\left(x\right)}{12 \, {\left(\cos\left(x\right)^{2} - 1\right)}}"," ",0,"-1/12*(4*cos(x)^5 + 20*cos(x)^3 - 15*(cos(x)^2 - 1)*log(1/2*cos(x) + 1/2) + 15*(cos(x)^2 - 1)*log(-1/2*cos(x) + 1/2) - 30*cos(x))/(cos(x)^2 - 1)","B",0
305,1,20,0,1.330306," ","integrate((csc(x)-sin(x))^2,x, algorithm=""fricas"")","\frac{\cos\left(x\right)^{3} - 3 \, x \sin\left(x\right) - 3 \, \cos\left(x\right)}{2 \, \sin\left(x\right)}"," ",0,"1/2*(cos(x)^3 - 3*x*sin(x) - 3*cos(x))/sin(x)","A",0
306,1,21,0,0.943840," ","integrate(csc(x)-sin(x),x, algorithm=""fricas"")","\cos\left(x\right) - \frac{1}{2} \, \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{2} \, \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"cos(x) - 1/2*log(1/2*cos(x) + 1/2) + 1/2*log(-1/2*cos(x) + 1/2)","B",0
307,1,4,0,2.197258," ","integrate(1/(csc(x)-sin(x)),x, algorithm=""fricas"")","\frac{1}{\cos\left(x\right)}"," ",0,"1/cos(x)","A",0
308,1,14,0,1.696484," ","integrate(1/(csc(x)-sin(x))^2,x, algorithm=""fricas"")","-\frac{{\left(\cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}{3 \, \cos\left(x\right)^{3}}"," ",0,"-1/3*(cos(x)^2 - 1)*sin(x)/cos(x)^3","B",0
309,1,14,0,1.202528," ","integrate(1/(csc(x)-sin(x))^3,x, algorithm=""fricas"")","-\frac{5 \, \cos\left(x\right)^{2} - 3}{15 \, \cos\left(x\right)^{5}}"," ",0,"-1/15*(5*cos(x)^2 - 3)/cos(x)^5","A",0
310,1,26,0,1.540784," ","integrate(1/(csc(x)-sin(x))^4,x, algorithm=""fricas"")","\frac{{\left(2 \, \cos\left(x\right)^{6} + \cos\left(x\right)^{4} - 8 \, \cos\left(x\right)^{2} + 5\right)} \sin\left(x\right)}{35 \, \cos\left(x\right)^{7}}"," ",0,"1/35*(2*cos(x)^6 + cos(x)^4 - 8*cos(x)^2 + 5)*sin(x)/cos(x)^7","A",0
311,1,20,0,0.969372," ","integrate(1/(csc(x)-sin(x))^5,x, algorithm=""fricas"")","\frac{63 \, \cos\left(x\right)^{4} - 90 \, \cos\left(x\right)^{2} + 35}{315 \, \cos\left(x\right)^{9}}"," ",0,"1/315*(63*cos(x)^4 - 90*cos(x)^2 + 35)/cos(x)^9","A",0
312,1,40,0,0.858787," ","integrate(1/(csc(x)-sin(x))^6,x, algorithm=""fricas"")","-\frac{{\left(8 \, \cos\left(x\right)^{10} + 4 \, \cos\left(x\right)^{8} + 3 \, \cos\left(x\right)^{6} - 113 \, \cos\left(x\right)^{4} + 161 \, \cos\left(x\right)^{2} - 63\right)} \sin\left(x\right)}{693 \, \cos\left(x\right)^{11}}"," ",0,"-1/693*(8*cos(x)^10 + 4*cos(x)^8 + 3*cos(x)^6 - 113*cos(x)^4 + 161*cos(x)^2 - 63)*sin(x)/cos(x)^11","B",0
313,1,26,0,0.652120," ","integrate(1/(csc(x)-sin(x))^7,x, algorithm=""fricas"")","-\frac{429 \, \cos\left(x\right)^{6} - 1001 \, \cos\left(x\right)^{4} + 819 \, \cos\left(x\right)^{2} - 231}{3003 \, \cos\left(x\right)^{13}}"," ",0,"-1/3003*(429*cos(x)^6 - 1001*cos(x)^4 + 819*cos(x)^2 - 231)/cos(x)^13","A",0
314,1,44,0,0.998373," ","integrate((csc(x)-sin(x))^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, \cos\left(x\right)^{6} + 20 \, \cos\left(x\right)^{4} - 160 \, \cos\left(x\right)^{2} + 128\right)} \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}}}{35 \, {\left(\cos\left(x\right)^{3} - \cos\left(x\right)\right)}}"," ",0,"-2/35*(5*cos(x)^6 + 20*cos(x)^4 - 160*cos(x)^2 + 128)*sqrt(cos(x)^2/sin(x))/(cos(x)^3 - cos(x))","A",0
315,1,35,0,1.719104," ","integrate((csc(x)-sin(x))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, \cos\left(x\right)^{4} + 24 \, \cos\left(x\right)^{2} - 32\right)} \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}}}{15 \, \cos\left(x\right) \sin\left(x\right)}"," ",0,"2/15*(3*cos(x)^4 + 24*cos(x)^2 - 32)*sqrt(cos(x)^2/sin(x))/(cos(x)*sin(x))","A",0
316,1,23,0,0.911377," ","integrate((csc(x)-sin(x))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\cos\left(x\right)^{2} - 4\right)} \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}}}{3 \, \cos\left(x\right)}"," ",0,"2/3*(cos(x)^2 - 4)*sqrt(cos(x)^2/sin(x))/cos(x)","A",0
317,1,19,0,0.769972," ","integrate((csc(x)-sin(x))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}} \sin\left(x\right)}{\cos\left(x\right)}"," ",0,"2*sqrt(cos(x)^2/sin(x))*sin(x)/cos(x)","A",0
318,1,124,0,1.057523," ","integrate(1/(csc(x)-sin(x))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \arctan\left(\frac{2 \, \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}} \sin\left(x\right)}{\cos\left(x\right) \sin\left(x\right) - \cos\left(x\right)}\right) + \frac{1}{4} \, \log\left(\frac{\cos\left(x\right)^{3} - 5 \, \cos\left(x\right)^{2} - {\left(\cos\left(x\right)^{2} + 6 \, \cos\left(x\right) + 4\right)} \sin\left(x\right) + 4 \, {\left(\cos\left(x\right)^{2} - {\left(\cos\left(x\right) + 1\right)} \sin\left(x\right) - 1\right)} \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}} - 2 \, \cos\left(x\right) + 4}{\cos\left(x\right)^{3} + 3 \, \cos\left(x\right)^{2} - {\left(\cos\left(x\right)^{2} - 2 \, \cos\left(x\right) - 4\right)} \sin\left(x\right) - 2 \, \cos\left(x\right) - 4}\right)"," ",0,"1/2*arctan(2*sqrt(cos(x)^2/sin(x))*sin(x)/(cos(x)*sin(x) - cos(x))) + 1/4*log((cos(x)^3 - 5*cos(x)^2 - (cos(x)^2 + 6*cos(x) + 4)*sin(x) + 4*(cos(x)^2 - (cos(x) + 1)*sin(x) - 1)*sqrt(cos(x)^2/sin(x)) - 2*cos(x) + 4)/(cos(x)^3 + 3*cos(x)^2 - (cos(x)^2 - 2*cos(x) - 4)*sin(x) - 2*cos(x) - 4))","B",0
319,1,152,0,1.801597," ","integrate(1/(csc(x)-sin(x))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \arctan\left(\frac{2 \, \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}} \sin\left(x\right)}{\cos\left(x\right) \sin\left(x\right) - \cos\left(x\right)}\right) \cos\left(x\right)^{3} + \cos\left(x\right)^{3} \log\left(\frac{\cos\left(x\right)^{3} - 5 \, \cos\left(x\right)^{2} - {\left(\cos\left(x\right)^{2} + 6 \, \cos\left(x\right) + 4\right)} \sin\left(x\right) - 4 \, {\left(\cos\left(x\right)^{2} - {\left(\cos\left(x\right) + 1\right)} \sin\left(x\right) - 1\right)} \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}} - 2 \, \cos\left(x\right) + 4}{\cos\left(x\right)^{3} + 3 \, \cos\left(x\right)^{2} - {\left(\cos\left(x\right)^{2} - 2 \, \cos\left(x\right) - 4\right)} \sin\left(x\right) - 2 \, \cos\left(x\right) - 4}\right) + 8 \, \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}} \sin\left(x\right)}{16 \, \cos\left(x\right)^{3}}"," ",0,"1/16*(2*arctan(2*sqrt(cos(x)^2/sin(x))*sin(x)/(cos(x)*sin(x) - cos(x)))*cos(x)^3 + cos(x)^3*log((cos(x)^3 - 5*cos(x)^2 - (cos(x)^2 + 6*cos(x) + 4)*sin(x) - 4*(cos(x)^2 - (cos(x) + 1)*sin(x) - 1)*sqrt(cos(x)^2/sin(x)) - 2*cos(x) + 4)/(cos(x)^3 + 3*cos(x)^2 - (cos(x)^2 - 2*cos(x) - 4)*sin(x) - 2*cos(x) - 4)) + 8*sqrt(cos(x)^2/sin(x))*sin(x))/cos(x)^3","B",0
320,1,165,0,1.954586," ","integrate(1/(csc(x)-sin(x))^(5/2),x, algorithm=""fricas"")","-\frac{6 \, \arctan\left(\frac{2 \, \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}} \sin\left(x\right)}{\cos\left(x\right) \sin\left(x\right) - \cos\left(x\right)}\right) \cos\left(x\right)^{5} - 3 \, \cos\left(x\right)^{5} \log\left(\frac{\cos\left(x\right)^{3} - 5 \, \cos\left(x\right)^{2} - {\left(\cos\left(x\right)^{2} + 6 \, \cos\left(x\right) + 4\right)} \sin\left(x\right) - 4 \, {\left(\cos\left(x\right)^{2} - {\left(\cos\left(x\right) + 1\right)} \sin\left(x\right) - 1\right)} \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}} - 2 \, \cos\left(x\right) + 4}{\cos\left(x\right)^{3} + 3 \, \cos\left(x\right)^{2} - {\left(\cos\left(x\right)^{2} - 2 \, \cos\left(x\right) - 4\right)} \sin\left(x\right) - 2 \, \cos\left(x\right) - 4}\right) - 8 \, {\left(3 \, \cos\left(x\right)^{4} - 7 \, \cos\left(x\right)^{2} + 4\right)} \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}}}{128 \, \cos\left(x\right)^{5}}"," ",0,"-1/128*(6*arctan(2*sqrt(cos(x)^2/sin(x))*sin(x)/(cos(x)*sin(x) - cos(x)))*cos(x)^5 - 3*cos(x)^5*log((cos(x)^3 - 5*cos(x)^2 - (cos(x)^2 + 6*cos(x) + 4)*sin(x) - 4*(cos(x)^2 - (cos(x) + 1)*sin(x) - 1)*sqrt(cos(x)^2/sin(x)) - 2*cos(x) + 4)/(cos(x)^3 + 3*cos(x)^2 - (cos(x)^2 - 2*cos(x) - 4)*sin(x) - 2*cos(x) - 4)) - 8*(3*cos(x)^4 - 7*cos(x)^2 + 4)*sqrt(cos(x)^2/sin(x)))/cos(x)^5","B",0
321,1,167,0,1.124387," ","integrate(1/(csc(x)-sin(x))^(7/2),x, algorithm=""fricas"")","-\frac{30 \, \arctan\left(\frac{2 \, \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}} \sin\left(x\right)}{\cos\left(x\right) \sin\left(x\right) - \cos\left(x\right)}\right) \cos\left(x\right)^{7} - 15 \, \cos\left(x\right)^{7} \log\left(\frac{\cos\left(x\right)^{3} - 5 \, \cos\left(x\right)^{2} - {\left(\cos\left(x\right)^{2} + 6 \, \cos\left(x\right) + 4\right)} \sin\left(x\right) + 4 \, {\left(\cos\left(x\right)^{2} - {\left(\cos\left(x\right) + 1\right)} \sin\left(x\right) - 1\right)} \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}} - 2 \, \cos\left(x\right) + 4}{\cos\left(x\right)^{3} + 3 \, \cos\left(x\right)^{2} - {\left(\cos\left(x\right)^{2} - 2 \, \cos\left(x\right) - 4\right)} \sin\left(x\right) - 2 \, \cos\left(x\right) - 4}\right) - 8 \, {\left(5 \, \cos\left(x\right)^{4} - 52 \, \cos\left(x\right)^{2} + 32\right)} \sqrt{\frac{\cos\left(x\right)^{2}}{\sin\left(x\right)}} \sin\left(x\right)}{1536 \, \cos\left(x\right)^{7}}"," ",0,"-1/1536*(30*arctan(2*sqrt(cos(x)^2/sin(x))*sin(x)/(cos(x)*sin(x) - cos(x)))*cos(x)^7 - 15*cos(x)^7*log((cos(x)^3 - 5*cos(x)^2 - (cos(x)^2 + 6*cos(x) + 4)*sin(x) + 4*(cos(x)^2 - (cos(x) + 1)*sin(x) - 1)*sqrt(cos(x)^2/sin(x)) - 2*cos(x) + 4)/(cos(x)^3 + 3*cos(x)^2 - (cos(x)^2 - 2*cos(x) - 4)*sin(x) - 2*cos(x) - 4)) - 8*(5*cos(x)^4 - 52*cos(x)^2 + 32)*sqrt(cos(x)^2/sin(x))*sin(x))/cos(x)^7","A",0
322,1,37,0,1.853912," ","integrate((-cos(x)+sec(x))^4,x, algorithm=""fricas"")","\frac{105 \, x \cos\left(x\right)^{3} + {\left(6 \, \cos\left(x\right)^{6} - 39 \, \cos\left(x\right)^{4} - 80 \, \cos\left(x\right)^{2} + 8\right)} \sin\left(x\right)}{24 \, \cos\left(x\right)^{3}}"," ",0,"1/24*(105*x*cos(x)^3 + (6*cos(x)^6 - 39*cos(x)^4 - 80*cos(x)^2 + 8)*sin(x))/cos(x)^3","A",0
323,1,49,0,0.941561," ","integrate((-cos(x)+sec(x))^3,x, algorithm=""fricas"")","-\frac{15 \, \cos\left(x\right)^{2} \log\left(\sin\left(x\right) + 1\right) - 15 \, \cos\left(x\right)^{2} \log\left(-\sin\left(x\right) + 1\right) + 2 \, {\left(2 \, \cos\left(x\right)^{4} - 14 \, \cos\left(x\right)^{2} - 3\right)} \sin\left(x\right)}{12 \, \cos\left(x\right)^{2}}"," ",0,"-1/12*(15*cos(x)^2*log(sin(x) + 1) - 15*cos(x)^2*log(-sin(x) + 1) + 2*(2*cos(x)^4 - 14*cos(x)^2 - 3)*sin(x))/cos(x)^2","A",0
324,1,22,0,0.952364," ","integrate((-cos(x)+sec(x))^2,x, algorithm=""fricas"")","-\frac{3 \, x \cos\left(x\right) - {\left(\cos\left(x\right)^{2} + 2\right)} \sin\left(x\right)}{2 \, \cos\left(x\right)}"," ",0,"-1/2*(3*x*cos(x) - (cos(x)^2 + 2)*sin(x))/cos(x)","A",0
325,1,21,0,0.945194," ","integrate(-cos(x)+sec(x),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(\sin\left(x\right) + 1\right) - \frac{1}{2} \, \log\left(-\sin\left(x\right) + 1\right) - \sin\left(x\right)"," ",0,"1/2*log(sin(x) + 1) - 1/2*log(-sin(x) + 1) - sin(x)","B",0
326,1,6,0,0.829865," ","integrate(1/(-cos(x)+sec(x)),x, algorithm=""fricas"")","-\frac{1}{\sin\left(x\right)}"," ",0,"-1/sin(x)","A",0
327,1,18,0,0.900520," ","integrate(1/(-cos(x)+sec(x))^2,x, algorithm=""fricas"")","\frac{\cos\left(x\right)^{3}}{3 \, {\left(\cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}"," ",0,"1/3*cos(x)^3/((cos(x)^2 - 1)*sin(x))","B",0
328,1,28,0,1.017537," ","integrate(1/(-cos(x)+sec(x))^3,x, algorithm=""fricas"")","-\frac{5 \, \cos\left(x\right)^{2} - 2}{15 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)} \sin\left(x\right)}"," ",0,"-1/15*(5*cos(x)^2 - 2)/((cos(x)^4 - 2*cos(x)^2 + 1)*sin(x))","B",0
329,1,39,0,0.648493," ","integrate(1/(-cos(x)+sec(x))^4,x, algorithm=""fricas"")","-\frac{2 \, \cos\left(x\right)^{7} - 7 \, \cos\left(x\right)^{5}}{35 \, {\left(\cos\left(x\right)^{6} - 3 \, \cos\left(x\right)^{4} + 3 \, \cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}"," ",0,"-1/35*(2*cos(x)^7 - 7*cos(x)^5)/((cos(x)^6 - 3*cos(x)^4 + 3*cos(x)^2 - 1)*sin(x))","B",0
330,1,46,0,1.383844," ","integrate(1/(-cos(x)+sec(x))^5,x, algorithm=""fricas"")","-\frac{63 \, \cos\left(x\right)^{4} - 36 \, \cos\left(x\right)^{2} + 8}{315 \, {\left(\cos\left(x\right)^{8} - 4 \, \cos\left(x\right)^{6} + 6 \, \cos\left(x\right)^{4} - 4 \, \cos\left(x\right)^{2} + 1\right)} \sin\left(x\right)}"," ",0,"-1/315*(63*cos(x)^4 - 36*cos(x)^2 + 8)/((cos(x)^8 - 4*cos(x)^6 + 6*cos(x)^4 - 4*cos(x)^2 + 1)*sin(x))","B",0
331,1,57,0,1.470721," ","integrate(1/(-cos(x)+sec(x))^6,x, algorithm=""fricas"")","\frac{8 \, \cos\left(x\right)^{11} - 44 \, \cos\left(x\right)^{9} + 99 \, \cos\left(x\right)^{7}}{693 \, {\left(\cos\left(x\right)^{10} - 5 \, \cos\left(x\right)^{8} + 10 \, \cos\left(x\right)^{6} - 10 \, \cos\left(x\right)^{4} + 5 \, \cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}"," ",0,"1/693*(8*cos(x)^11 - 44*cos(x)^9 + 99*cos(x)^7)/((cos(x)^10 - 5*cos(x)^8 + 10*cos(x)^6 - 10*cos(x)^4 + 5*cos(x)^2 - 1)*sin(x))","B",0
332,1,64,0,2.268044," ","integrate(1/(-cos(x)+sec(x))^7,x, algorithm=""fricas"")","-\frac{429 \, \cos\left(x\right)^{6} - 286 \, \cos\left(x\right)^{4} + 104 \, \cos\left(x\right)^{2} - 16}{3003 \, {\left(\cos\left(x\right)^{12} - 6 \, \cos\left(x\right)^{10} + 15 \, \cos\left(x\right)^{8} - 20 \, \cos\left(x\right)^{6} + 15 \, \cos\left(x\right)^{4} - 6 \, \cos\left(x\right)^{2} + 1\right)} \sin\left(x\right)}"," ",0,"-1/3003*(429*cos(x)^6 - 286*cos(x)^4 + 104*cos(x)^2 - 16)/((cos(x)^12 - 6*cos(x)^10 + 15*cos(x)^8 - 20*cos(x)^6 + 15*cos(x)^4 - 6*cos(x)^2 + 1)*sin(x))","B",0
333,1,44,0,0.989648," ","integrate((-cos(x)+sec(x))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, \cos\left(x\right)^{6} - 35 \, \cos\left(x\right)^{4} - 105 \, \cos\left(x\right)^{2} + 7\right)} \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}}}{35 \, \cos\left(x\right)^{2} \sin\left(x\right)}"," ",0,"2/35*(5*cos(x)^6 - 35*cos(x)^4 - 105*cos(x)^2 + 7)*sqrt(-(cos(x)^2 - 1)/cos(x))/(cos(x)^2*sin(x))","A",0
334,1,38,0,0.862822," ","integrate((-cos(x)+sec(x))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, \cos\left(x\right)^{4} - 30 \, \cos\left(x\right)^{2} - 5\right)} \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}}}{15 \, \cos\left(x\right) \sin\left(x\right)}"," ",0,"-2/15*(3*cos(x)^4 - 30*cos(x)^2 - 5)*sqrt(-(cos(x)^2 - 1)/cos(x))/(cos(x)*sin(x))","A",0
335,1,26,0,1.248641," ","integrate((-cos(x)+sec(x))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\cos\left(x\right)^{2} + 3\right)} \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}}}{3 \, \sin\left(x\right)}"," ",0,"2/3*(cos(x)^2 + 3)*sqrt(-(cos(x)^2 - 1)/cos(x))/sin(x)","A",0
336,1,22,0,1.259920," ","integrate((-cos(x)+sec(x))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}} \cos\left(x\right)}{\sin\left(x\right)}"," ",0,"-2*sqrt(-(cos(x)^2 - 1)/cos(x))*cos(x)/sin(x)","A",0
337,1,72,0,1.004896," ","integrate(1/(-cos(x)+sec(x))^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \arctan\left(\frac{2 \, \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}} \cos\left(x\right)}{{\left(\cos\left(x\right) - 1\right)} \sin\left(x\right)}\right) + \frac{1}{2} \, \log\left(\frac{{\left(\cos\left(x\right) + 1\right)} \sin\left(x\right) - 2 \, \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}} \cos\left(x\right)}{{\left(\cos\left(x\right) - 1\right)} \sin\left(x\right)}\right)"," ",0,"-1/2*arctan(2*sqrt(-(cos(x)^2 - 1)/cos(x))*cos(x)/((cos(x) - 1)*sin(x))) + 1/2*log(((cos(x) + 1)*sin(x) - 2*sqrt(-(cos(x)^2 - 1)/cos(x))*cos(x))/((cos(x) - 1)*sin(x)))","A",0
338,1,119,0,0.974293," ","integrate(1/(-cos(x)+sec(x))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(\cos\left(x\right)^{2} - 1\right)} \arctan\left(\frac{2 \, \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}} \cos\left(x\right)}{{\left(\cos\left(x\right) - 1\right)} \sin\left(x\right)}\right) \sin\left(x\right) - {\left(\cos\left(x\right)^{2} - 1\right)} \log\left(\frac{{\left(\cos\left(x\right) + 1\right)} \sin\left(x\right) + 2 \, \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}} \cos\left(x\right)}{{\left(\cos\left(x\right) - 1\right)} \sin\left(x\right)}\right) \sin\left(x\right) - 4 \, \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}} \cos\left(x\right)}{8 \, {\left(\cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}"," ",0,"-1/8*((cos(x)^2 - 1)*arctan(2*sqrt(-(cos(x)^2 - 1)/cos(x))*cos(x)/((cos(x) - 1)*sin(x)))*sin(x) - (cos(x)^2 - 1)*log(((cos(x) + 1)*sin(x) + 2*sqrt(-(cos(x)^2 - 1)/cos(x))*cos(x))/((cos(x) - 1)*sin(x)))*sin(x) - 4*sqrt(-(cos(x)^2 - 1)/cos(x))*cos(x))/((cos(x)^2 - 1)*sin(x))","B",0
339,1,147,0,1.023849," ","integrate(1/(-cos(x)+sec(x))^(5/2),x, algorithm=""fricas"")","\frac{3 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)} \arctan\left(\frac{2 \, \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}} \cos\left(x\right)}{{\left(\cos\left(x\right) - 1\right)} \sin\left(x\right)}\right) \sin\left(x\right) + 3 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)} \log\left(\frac{{\left(\cos\left(x\right) + 1\right)} \sin\left(x\right) + 2 \, \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}} \cos\left(x\right)}{{\left(\cos\left(x\right) - 1\right)} \sin\left(x\right)}\right) \sin\left(x\right) - 4 \, {\left(3 \, \cos\left(x\right)^{4} + \cos\left(x\right)^{2}\right)} \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}}}{64 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)} \sin\left(x\right)}"," ",0,"1/64*(3*(cos(x)^4 - 2*cos(x)^2 + 1)*arctan(2*sqrt(-(cos(x)^2 - 1)/cos(x))*cos(x)/((cos(x) - 1)*sin(x)))*sin(x) + 3*(cos(x)^4 - 2*cos(x)^2 + 1)*log(((cos(x) + 1)*sin(x) + 2*sqrt(-(cos(x)^2 - 1)/cos(x))*cos(x))/((cos(x) - 1)*sin(x)))*sin(x) - 4*(3*cos(x)^4 + cos(x)^2)*sqrt(-(cos(x)^2 - 1)/cos(x)))/((cos(x)^4 - 2*cos(x)^2 + 1)*sin(x))","B",0
340,1,171,0,1.629818," ","integrate(1/(-cos(x)+sec(x))^(7/2),x, algorithm=""fricas"")","\frac{15 \, {\left(\cos\left(x\right)^{6} - 3 \, \cos\left(x\right)^{4} + 3 \, \cos\left(x\right)^{2} - 1\right)} \arctan\left(\frac{2 \, \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}} \cos\left(x\right)}{{\left(\cos\left(x\right) - 1\right)} \sin\left(x\right)}\right) \sin\left(x\right) + 15 \, {\left(\cos\left(x\right)^{6} - 3 \, \cos\left(x\right)^{4} + 3 \, \cos\left(x\right)^{2} - 1\right)} \log\left(\frac{{\left(\cos\left(x\right) + 1\right)} \sin\left(x\right) - 2 \, \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}} \cos\left(x\right)}{{\left(\cos\left(x\right) - 1\right)} \sin\left(x\right)}\right) \sin\left(x\right) + 4 \, {\left(5 \, \cos\left(x\right)^{5} + 42 \, \cos\left(x\right)^{3} - 15 \, \cos\left(x\right)\right)} \sqrt{-\frac{\cos\left(x\right)^{2} - 1}{\cos\left(x\right)}}}{768 \, {\left(\cos\left(x\right)^{6} - 3 \, \cos\left(x\right)^{4} + 3 \, \cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}"," ",0,"1/768*(15*(cos(x)^6 - 3*cos(x)^4 + 3*cos(x)^2 - 1)*arctan(2*sqrt(-(cos(x)^2 - 1)/cos(x))*cos(x)/((cos(x) - 1)*sin(x)))*sin(x) + 15*(cos(x)^6 - 3*cos(x)^4 + 3*cos(x)^2 - 1)*log(((cos(x) + 1)*sin(x) - 2*sqrt(-(cos(x)^2 - 1)/cos(x))*cos(x))/((cos(x) - 1)*sin(x)))*sin(x) + 4*(5*cos(x)^5 + 42*cos(x)^3 - 15*cos(x))*sqrt(-(cos(x)^2 - 1)/cos(x)))/((cos(x)^6 - 3*cos(x)^4 + 3*cos(x)^2 - 1)*sin(x))","B",0
341,1,78,0,1.740963," ","integrate((sin(x)+tan(x))^4,x, algorithm=""fricas"")","-\frac{183 \, x \cos\left(x\right)^{3} + 24 \, \cos\left(x\right)^{3} \log\left(\sin\left(x\right) + 1\right) - 24 \, \cos\left(x\right)^{3} \log\left(-\sin\left(x\right) + 1\right) - {\left(6 \, \cos\left(x\right)^{6} + 32 \, \cos\left(x\right)^{5} + 57 \, \cos\left(x\right)^{4} - 32 \, \cos\left(x\right)^{3} + 112 \, \cos\left(x\right)^{2} + 48 \, \cos\left(x\right) + 8\right)} \sin\left(x\right)}{24 \, \cos\left(x\right)^{3}}"," ",0,"-1/24*(183*x*cos(x)^3 + 24*cos(x)^3*log(sin(x) + 1) - 24*cos(x)^3*log(-sin(x) + 1) - (6*cos(x)^6 + 32*cos(x)^5 + 57*cos(x)^4 - 32*cos(x)^3 + 112*cos(x)^2 + 48*cos(x) + 8)*sin(x))/cos(x)^3","A",0
342,1,47,0,2.015747," ","integrate((sin(x)+tan(x))^3,x, algorithm=""fricas"")","\frac{4 \, \cos\left(x\right)^{5} + 18 \, \cos\left(x\right)^{4} + 24 \, \cos\left(x\right)^{3} - 24 \, \cos\left(x\right)^{2} \log\left(-\cos\left(x\right)\right) - 9 \, \cos\left(x\right)^{2} + 36 \, \cos\left(x\right) + 6}{12 \, \cos\left(x\right)^{2}}"," ",0,"1/12*(4*cos(x)^5 + 18*cos(x)^4 + 24*cos(x)^3 - 24*cos(x)^2*log(-cos(x)) - 9*cos(x)^2 + 36*cos(x) + 6)/cos(x)^2","A",0
343,1,44,0,0.971074," ","integrate((sin(x)+tan(x))^2,x, algorithm=""fricas"")","-\frac{x \cos\left(x\right) - 2 \, \cos\left(x\right) \log\left(\sin\left(x\right) + 1\right) + 2 \, \cos\left(x\right) \log\left(-\sin\left(x\right) + 1\right) + {\left(\cos\left(x\right)^{2} + 4 \, \cos\left(x\right) - 2\right)} \sin\left(x\right)}{2 \, \cos\left(x\right)}"," ",0,"-1/2*(x*cos(x) - 2*cos(x)*log(sin(x) + 1) + 2*cos(x)*log(-sin(x) + 1) + (cos(x)^2 + 4*cos(x) - 2)*sin(x))/cos(x)","B",0
344,1,12,0,1.434845," ","integrate(sin(x)+tan(x),x, algorithm=""fricas"")","-\cos\left(x\right) - \log\left(-\cos\left(x\right)\right)"," ",0,"-cos(x) - log(-cos(x))","A",0
345,1,35,0,1.897067," ","integrate(1/(sin(x)+tan(x)),x, algorithm=""fricas"")","-\frac{{\left(\cos\left(x\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - {\left(\cos\left(x\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + 2}{4 \, {\left(\cos\left(x\right) + 1\right)}}"," ",0,"-1/4*((cos(x) + 1)*log(1/2*cos(x) + 1/2) - (cos(x) + 1)*log(-1/2*cos(x) + 1/2) + 2)/(cos(x) + 1)","A",0
346,1,34,0,1.447759," ","integrate(1/(sin(x)+tan(x))^2,x, algorithm=""fricas"")","-\frac{\cos\left(x\right)^{3} + 2 \, \cos\left(x\right)^{2} + 8 \, \cos\left(x\right) + 4}{15 \, {\left(\cos\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)} \sin\left(x\right)}"," ",0,"-1/15*(cos(x)^3 + 2*cos(x)^2 + 8*cos(x) + 4)/((cos(x)^2 + 2*cos(x) + 1)*sin(x))","A",0
347,1,130,0,1.821229," ","integrate(1/(sin(x)+tan(x))^3,x, algorithm=""fricas"")","-\frac{6 \, \cos\left(x\right)^{4} + 18 \, \cos\left(x\right)^{3} - 50 \, \cos\left(x\right)^{2} - 3 \, {\left(\cos\left(x\right)^{5} + 3 \, \cos\left(x\right)^{4} + 2 \, \cos\left(x\right)^{3} - 2 \, \cos\left(x\right)^{2} - 3 \, \cos\left(x\right) - 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + 3 \, {\left(\cos\left(x\right)^{5} + 3 \, \cos\left(x\right)^{4} + 2 \, \cos\left(x\right)^{3} - 2 \, \cos\left(x\right)^{2} - 3 \, \cos\left(x\right) - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - 54 \, \cos\left(x\right) - 16}{192 \, {\left(\cos\left(x\right)^{5} + 3 \, \cos\left(x\right)^{4} + 2 \, \cos\left(x\right)^{3} - 2 \, \cos\left(x\right)^{2} - 3 \, \cos\left(x\right) - 1\right)}}"," ",0,"-1/192*(6*cos(x)^4 + 18*cos(x)^3 - 50*cos(x)^2 - 3*(cos(x)^5 + 3*cos(x)^4 + 2*cos(x)^3 - 2*cos(x)^2 - 3*cos(x) - 1)*log(1/2*cos(x) + 1/2) + 3*(cos(x)^5 + 3*cos(x)^4 + 2*cos(x)^3 - 2*cos(x)^2 - 3*cos(x) - 1)*log(-1/2*cos(x) + 1/2) - 54*cos(x) - 16)/(cos(x)^5 + 3*cos(x)^4 + 2*cos(x)^3 - 2*cos(x)^2 - 3*cos(x) - 1)","B",0
348,1,78,0,1.064318," ","integrate(1/(sin(x)+tan(x))^4,x, algorithm=""fricas"")","\frac{122 \, \cos\left(x\right)^{7} + 488 \, \cos\left(x\right)^{6} + 549 \, \cos\left(x\right)^{5} - 244 \, \cos\left(x\right)^{4} - 64 \, \cos\left(x\right)^{3} + 144 \, \cos\left(x\right)^{2} + 128 \, \cos\left(x\right) + 32}{3465 \, {\left(\cos\left(x\right)^{6} + 4 \, \cos\left(x\right)^{5} + 5 \, \cos\left(x\right)^{4} - 5 \, \cos\left(x\right)^{2} - 4 \, \cos\left(x\right) - 1\right)} \sin\left(x\right)}"," ",0,"1/3465*(122*cos(x)^7 + 488*cos(x)^6 + 549*cos(x)^5 - 244*cos(x)^4 - 64*cos(x)^3 + 144*cos(x)^2 + 128*cos(x) + 32)/((cos(x)^6 + 4*cos(x)^5 + 5*cos(x)^4 - 5*cos(x)^2 - 4*cos(x) - 1)*sin(x))","A",0
349,1,144,0,0.930236," ","integrate((A+C*sin(x))/(b*cos(x)+c*sin(x)),x, algorithm=""fricas"")","\frac{2 \, C c x - C b \log\left(2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + c^{2}\right) + \sqrt{b^{2} + c^{2}} A \log\left(-\frac{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} - 2 \, b^{2} - c^{2} + 2 \, \sqrt{b^{2} + c^{2}} {\left(c \cos\left(x\right) - b \sin\left(x\right)\right)}}{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + c^{2}}\right)}{2 \, {\left(b^{2} + c^{2}\right)}}"," ",0,"1/2*(2*C*c*x - C*b*log(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 + c^2) + sqrt(b^2 + c^2)*A*log(-(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 - 2*b^2 - c^2 + 2*sqrt(b^2 + c^2)*(c*cos(x) - b*sin(x)))/(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 + c^2)))/(b^2 + c^2)","B",0
350,1,200,0,1.970386," ","integrate((A+C*sin(x))/(b*cos(x)+c*sin(x))^2,x, algorithm=""fricas"")","\frac{2 \, C b^{3} + 2 \, C b c^{2} + {\left(C b c \cos\left(x\right) + C c^{2} \sin\left(x\right)\right)} \sqrt{b^{2} + c^{2}} \log\left(-\frac{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} - 2 \, b^{2} - c^{2} + 2 \, \sqrt{b^{2} + c^{2}} {\left(c \cos\left(x\right) - b \sin\left(x\right)\right)}}{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + c^{2}}\right) - 2 \, {\left(A b^{2} c + A c^{3}\right)} \cos\left(x\right) + 2 \, {\left(A b^{3} + A b c^{2}\right)} \sin\left(x\right)}{2 \, {\left({\left(b^{5} + 2 \, b^{3} c^{2} + b c^{4}\right)} \cos\left(x\right) + {\left(b^{4} c + 2 \, b^{2} c^{3} + c^{5}\right)} \sin\left(x\right)\right)}}"," ",0,"1/2*(2*C*b^3 + 2*C*b*c^2 + (C*b*c*cos(x) + C*c^2*sin(x))*sqrt(b^2 + c^2)*log(-(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 - 2*b^2 - c^2 + 2*sqrt(b^2 + c^2)*(c*cos(x) - b*sin(x)))/(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 + c^2)) - 2*(A*b^2*c + A*c^3)*cos(x) + 2*(A*b^3 + A*b*c^2)*sin(x))/((b^5 + 2*b^3*c^2 + b*c^4)*cos(x) + (b^4*c + 2*b^2*c^3 + c^5)*sin(x))","B",0
351,1,279,0,0.919727," ","integrate((A+C*sin(x))/(b*cos(x)+c*sin(x))^3,x, algorithm=""fricas"")","-\frac{8 \, C b c^{2} \cos\left(x\right)^{2} - 2 \, C b^{3} - 6 \, C b c^{2} - {\left(2 \, A b c \cos\left(x\right) \sin\left(x\right) + A c^{2} + {\left(A b^{2} - A c^{2}\right)} \cos\left(x\right)^{2}\right)} \sqrt{b^{2} + c^{2}} \log\left(-\frac{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} - 2 \, b^{2} - c^{2} + 2 \, \sqrt{b^{2} + c^{2}} {\left(c \cos\left(x\right) - b \sin\left(x\right)\right)}}{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + c^{2}}\right) + 2 \, {\left(A b^{2} c + A c^{3}\right)} \cos\left(x\right) - 2 \, {\left(A b^{3} + A b c^{2} + 2 \, {\left(C b^{2} c - C c^{3}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{4 \, {\left(b^{4} c^{2} + 2 \, b^{2} c^{4} + c^{6} + {\left(b^{6} + b^{4} c^{2} - b^{2} c^{4} - c^{6}\right)} \cos\left(x\right)^{2} + 2 \, {\left(b^{5} c + 2 \, b^{3} c^{3} + b c^{5}\right)} \cos\left(x\right) \sin\left(x\right)\right)}}"," ",0,"-1/4*(8*C*b*c^2*cos(x)^2 - 2*C*b^3 - 6*C*b*c^2 - (2*A*b*c*cos(x)*sin(x) + A*c^2 + (A*b^2 - A*c^2)*cos(x)^2)*sqrt(b^2 + c^2)*log(-(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 - 2*b^2 - c^2 + 2*sqrt(b^2 + c^2)*(c*cos(x) - b*sin(x)))/(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 + c^2)) + 2*(A*b^2*c + A*c^3)*cos(x) - 2*(A*b^3 + A*b*c^2 + 2*(C*b^2*c - C*c^3)*cos(x))*sin(x))/(b^4*c^2 + 2*b^2*c^4 + c^6 + (b^6 + b^4*c^2 - b^2*c^4 - c^6)*cos(x)^2 + 2*(b^5*c + 2*b^3*c^3 + b*c^5)*cos(x)*sin(x))","B",0
352,1,143,0,1.662612," ","integrate((A+B*cos(x))/(b*cos(x)+c*sin(x)),x, algorithm=""fricas"")","\frac{2 \, B b x + B c \log\left(2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + c^{2}\right) + \sqrt{b^{2} + c^{2}} A \log\left(-\frac{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} - 2 \, b^{2} - c^{2} + 2 \, \sqrt{b^{2} + c^{2}} {\left(c \cos\left(x\right) - b \sin\left(x\right)\right)}}{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + c^{2}}\right)}{2 \, {\left(b^{2} + c^{2}\right)}}"," ",0,"1/2*(2*B*b*x + B*c*log(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 + c^2) + sqrt(b^2 + c^2)*A*log(-(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 - 2*b^2 - c^2 + 2*sqrt(b^2 + c^2)*(c*cos(x) - b*sin(x)))/(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 + c^2)))/(b^2 + c^2)","B",0
353,1,201,0,0.679536," ","integrate((A+B*cos(x))/(b*cos(x)+c*sin(x))^2,x, algorithm=""fricas"")","-\frac{2 \, B b^{2} c + 2 \, B c^{3} - {\left(B b^{2} \cos\left(x\right) + B b c \sin\left(x\right)\right)} \sqrt{b^{2} + c^{2}} \log\left(-\frac{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} - 2 \, b^{2} - c^{2} + 2 \, \sqrt{b^{2} + c^{2}} {\left(c \cos\left(x\right) - b \sin\left(x\right)\right)}}{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + c^{2}}\right) + 2 \, {\left(A b^{2} c + A c^{3}\right)} \cos\left(x\right) - 2 \, {\left(A b^{3} + A b c^{2}\right)} \sin\left(x\right)}{2 \, {\left({\left(b^{5} + 2 \, b^{3} c^{2} + b c^{4}\right)} \cos\left(x\right) + {\left(b^{4} c + 2 \, b^{2} c^{3} + c^{5}\right)} \sin\left(x\right)\right)}}"," ",0,"-1/2*(2*B*b^2*c + 2*B*c^3 - (B*b^2*cos(x) + B*b*c*sin(x))*sqrt(b^2 + c^2)*log(-(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 - 2*b^2 - c^2 + 2*sqrt(b^2 + c^2)*(c*cos(x) - b*sin(x)))/(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 + c^2)) + 2*(A*b^2*c + A*c^3)*cos(x) - 2*(A*b^3 + A*b*c^2)*sin(x))/((b^5 + 2*b^3*c^2 + b*c^4)*cos(x) + (b^4*c + 2*b^2*c^3 + c^5)*sin(x))","B",0
354,1,279,0,0.931912," ","integrate((A+B*cos(x))/(b*cos(x)+c*sin(x))^3,x, algorithm=""fricas"")","-\frac{8 \, B b^{2} c \cos\left(x\right)^{2} - 2 \, B b^{2} c + 2 \, B c^{3} - {\left(2 \, A b c \cos\left(x\right) \sin\left(x\right) + A c^{2} + {\left(A b^{2} - A c^{2}\right)} \cos\left(x\right)^{2}\right)} \sqrt{b^{2} + c^{2}} \log\left(-\frac{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} - 2 \, b^{2} - c^{2} + 2 \, \sqrt{b^{2} + c^{2}} {\left(c \cos\left(x\right) - b \sin\left(x\right)\right)}}{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + c^{2}}\right) + 2 \, {\left(A b^{2} c + A c^{3}\right)} \cos\left(x\right) - 2 \, {\left(A b^{3} + A b c^{2} + 2 \, {\left(B b^{3} - B b c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{4 \, {\left(b^{4} c^{2} + 2 \, b^{2} c^{4} + c^{6} + {\left(b^{6} + b^{4} c^{2} - b^{2} c^{4} - c^{6}\right)} \cos\left(x\right)^{2} + 2 \, {\left(b^{5} c + 2 \, b^{3} c^{3} + b c^{5}\right)} \cos\left(x\right) \sin\left(x\right)\right)}}"," ",0,"-1/4*(8*B*b^2*c*cos(x)^2 - 2*B*b^2*c + 2*B*c^3 - (2*A*b*c*cos(x)*sin(x) + A*c^2 + (A*b^2 - A*c^2)*cos(x)^2)*sqrt(b^2 + c^2)*log(-(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 - 2*b^2 - c^2 + 2*sqrt(b^2 + c^2)*(c*cos(x) - b*sin(x)))/(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 + c^2)) + 2*(A*b^2*c + A*c^3)*cos(x) - 2*(A*b^3 + A*b*c^2 + 2*(B*b^3 - B*b*c^2)*cos(x))*sin(x))/(b^4*c^2 + 2*b^2*c^4 + c^6 + (b^6 + b^4*c^2 - b^2*c^4 - c^6)*cos(x)^2 + 2*(b^5*c + 2*b^3*c^3 + b*c^5)*cos(x)*sin(x))","B",0
355,1,221,0,1.063864," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^4,x, algorithm=""fricas"")","-\frac{24 \, {\left(b^{3} c - b c^{3}\right)} \cos\left(e x + d\right)^{4} - 105 \, {\left(b^{4} + 2 \, b^{2} c^{2} + c^{4}\right)} e x + 48 \, {\left(3 \, b^{3} c + 4 \, b c^{3}\right)} \cos\left(e x + d\right)^{2} - 3 \, {\left(2 \, {\left(b^{4} - 6 \, b^{2} c^{2} + c^{4}\right)} \cos\left(e x + d\right)^{3} + {\left(27 \, b^{4} + 6 \, b^{2} c^{2} - 29 \, c^{4}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right) + 32 \, {\left({\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{3} + 3 \, {\left(b^{2} c + 2 \, c^{3}\right)} \cos\left(e x + d\right) - {\left(5 \, b^{3} + 6 \, b c^{2} + {\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right)\right)} \sqrt{b^{2} + c^{2}}}{24 \, e}"," ",0,"-1/24*(24*(b^3*c - b*c^3)*cos(e*x + d)^4 - 105*(b^4 + 2*b^2*c^2 + c^4)*e*x + 48*(3*b^3*c + 4*b*c^3)*cos(e*x + d)^2 - 3*(2*(b^4 - 6*b^2*c^2 + c^4)*cos(e*x + d)^3 + (27*b^4 + 6*b^2*c^2 - 29*c^4)*cos(e*x + d))*sin(e*x + d) + 32*((3*b^2*c - c^3)*cos(e*x + d)^3 + 3*(b^2*c + 2*c^3)*cos(e*x + d) - (5*b^3 + 6*b*c^2 + (b^3 - 3*b*c^2)*cos(e*x + d)^2)*sin(e*x + d))*sqrt(b^2 + c^2))/e","A",0
356,1,145,0,0.847945," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, c^{3}\right)} \cos\left(e x + d\right) - 2 \, {\left(11 \, b^{3} + 12 \, b c^{2} + {\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right) + 3 \, {\left(6 \, b c \cos\left(e x + d\right)^{2} - 5 \, {\left(b^{2} + c^{2}\right)} e x - 3 \, {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right) \sin\left(e x + d\right)\right)} \sqrt{b^{2} + c^{2}}}{6 \, e}"," ",0,"-1/6*(2*(3*b^2*c - c^3)*cos(e*x + d)^3 + 6*(3*b^2*c + 4*c^3)*cos(e*x + d) - 2*(11*b^3 + 12*b*c^2 + (b^3 - 3*b*c^2)*cos(e*x + d)^2)*sin(e*x + d) + 3*(6*b*c*cos(e*x + d)^2 - 5*(b^2 + c^2)*e*x - 3*(b^2 - c^2)*cos(e*x + d)*sin(e*x + d))*sqrt(b^2 + c^2))/e","A",0
357,1,81,0,0.944984," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^2,x, algorithm=""fricas"")","-\frac{2 \, b c \cos\left(e x + d\right)^{2} - 3 \, {\left(b^{2} + c^{2}\right)} e x - {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right) \sin\left(e x + d\right) + 4 \, \sqrt{b^{2} + c^{2}} {\left(c \cos\left(e x + d\right) - b \sin\left(e x + d\right)\right)}}{2 \, e}"," ",0,"-1/2*(2*b*c*cos(e*x + d)^2 - 3*(b^2 + c^2)*e*x - (b^2 - c^2)*cos(e*x + d)*sin(e*x + d) + 4*sqrt(b^2 + c^2)*(c*cos(e*x + d) - b*sin(e*x + d)))/e","A",0
358,1,34,0,0.920007," ","integrate(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b^{2} + c^{2}} e x - c \cos\left(e x + d\right) + b \sin\left(e x + d\right)}{e}"," ",0,"(sqrt(b^2 + c^2)*e*x - c*cos(e*x + d) + b*sin(e*x + d))/e","A",0
359,1,75,0,1.639555," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2)),x, algorithm=""fricas"")","-\frac{b^{2} + c^{2} - \sqrt{b^{2} + c^{2}} {\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right)\right)}}{{\left(b^{2} c + c^{3}\right)} e \cos\left(e x + d\right) - {\left(b^{3} + b c^{2}\right)} e \sin\left(e x + d\right)}"," ",0,"-(b^2 + c^2 - sqrt(b^2 + c^2)*(b*cos(e*x + d) + c*sin(e*x + d)))/((b^2*c + c^3)*e*cos(e*x + d) - (b^3 + b*c^2)*e*sin(e*x + d))","A",0
360,1,192,0,1.735833," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^2,x, algorithm=""fricas"")","-\frac{3 \, b^{3} \cos\left(e x + d\right) - {\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{3} + {\left(3 \, b^{2} c + 2 \, c^{3} - {\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right) - 2 \, {\left(b^{2} + c^{2}\right)}^{\frac{3}{2}}}{3 \, {\left({\left(3 \, b^{4} c + 2 \, b^{2} c^{3} - c^{5}\right)} e \cos\left(e x + d\right)^{3} - 3 \, {\left(b^{4} c + b^{2} c^{3}\right)} e \cos\left(e x + d\right) - {\left({\left(b^{5} - 2 \, b^{3} c^{2} - 3 \, b c^{4}\right)} e \cos\left(e x + d\right)^{2} - {\left(b^{5} + b^{3} c^{2}\right)} e\right)} \sin\left(e x + d\right)\right)}}"," ",0,"-1/3*(3*b^3*cos(e*x + d) - (b^3 - 3*b*c^2)*cos(e*x + d)^3 + (3*b^2*c + 2*c^3 - (3*b^2*c - c^3)*cos(e*x + d)^2)*sin(e*x + d) - 2*(b^2 + c^2)^(3/2))/((3*b^4*c + 2*b^2*c^3 - c^5)*e*cos(e*x + d)^3 - 3*(b^4*c + b^2*c^3)*e*cos(e*x + d) - ((b^5 - 2*b^3*c^2 - 3*b*c^4)*e*cos(e*x + d)^2 - (b^5 + b^3*c^2)*e)*sin(e*x + d))","A",0
361,1,490,0,0.964234," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^3,x, algorithm=""fricas"")","-\frac{7 \, b^{6} + 26 \, b^{4} c^{2} + 31 \, b^{2} c^{4} + 12 \, c^{6} + 5 \, {\left(b^{6} + b^{4} c^{2} - b^{2} c^{4} - c^{6}\right)} \cos\left(e x + d\right)^{2} + 10 \, {\left(b^{5} c + 2 \, b^{3} c^{3} + b c^{5}\right)} \cos\left(e x + d\right) \sin\left(e x + d\right) - {\left(2 \, {\left(b^{5} - 10 \, b^{3} c^{2} + 5 \, b c^{4}\right)} \cos\left(e x + d\right)^{5} - 5 \, {\left(b^{5} - 6 \, b^{3} c^{2} + b c^{4}\right)} \cos\left(e x + d\right)^{3} + 5 \, {\left(3 \, b^{5} + 3 \, b^{3} c^{2} + 2 \, b c^{4}\right)} \cos\left(e x + d\right) + {\left(15 \, b^{4} c + 25 \, b^{2} c^{3} + 12 \, c^{5} + 2 \, {\left(5 \, b^{4} c - 10 \, b^{2} c^{3} + c^{5}\right)} \cos\left(e x + d\right)^{4} - {\left(15 \, b^{4} c - 10 \, b^{2} c^{3} - c^{5}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right)\right)} \sqrt{b^{2} + c^{2}}}{15 \, {\left({\left(5 \, b^{8} c - 14 \, b^{4} c^{5} - 8 \, b^{2} c^{7} + c^{9}\right)} e \cos\left(e x + d\right)^{5} - 10 \, {\left(b^{8} c + b^{6} c^{3} - b^{4} c^{5} - b^{2} c^{7}\right)} e \cos\left(e x + d\right)^{3} + 5 \, {\left(b^{8} c + 2 \, b^{6} c^{3} + b^{4} c^{5}\right)} e \cos\left(e x + d\right) - {\left({\left(b^{9} - 8 \, b^{7} c^{2} - 14 \, b^{5} c^{4} + 5 \, b c^{8}\right)} e \cos\left(e x + d\right)^{4} - 2 \, {\left(b^{9} - 3 \, b^{7} c^{2} - 9 \, b^{5} c^{4} - 5 \, b^{3} c^{6}\right)} e \cos\left(e x + d\right)^{2} + {\left(b^{9} + 2 \, b^{7} c^{2} + b^{5} c^{4}\right)} e\right)} \sin\left(e x + d\right)\right)}}"," ",0,"-1/15*(7*b^6 + 26*b^4*c^2 + 31*b^2*c^4 + 12*c^6 + 5*(b^6 + b^4*c^2 - b^2*c^4 - c^6)*cos(e*x + d)^2 + 10*(b^5*c + 2*b^3*c^3 + b*c^5)*cos(e*x + d)*sin(e*x + d) - (2*(b^5 - 10*b^3*c^2 + 5*b*c^4)*cos(e*x + d)^5 - 5*(b^5 - 6*b^3*c^2 + b*c^4)*cos(e*x + d)^3 + 5*(3*b^5 + 3*b^3*c^2 + 2*b*c^4)*cos(e*x + d) + (15*b^4*c + 25*b^2*c^3 + 12*c^5 + 2*(5*b^4*c - 10*b^2*c^3 + c^5)*cos(e*x + d)^4 - (15*b^4*c - 10*b^2*c^3 - c^5)*cos(e*x + d)^2)*sin(e*x + d))*sqrt(b^2 + c^2))/((5*b^8*c - 14*b^4*c^5 - 8*b^2*c^7 + c^9)*e*cos(e*x + d)^5 - 10*(b^8*c + b^6*c^3 - b^4*c^5 - b^2*c^7)*e*cos(e*x + d)^3 + 5*(b^8*c + 2*b^6*c^3 + b^4*c^5)*e*cos(e*x + d) - ((b^9 - 8*b^7*c^2 - 14*b^5*c^4 + 5*b*c^8)*e*cos(e*x + d)^4 - 2*(b^9 - 3*b^7*c^2 - 9*b^5*c^4 - 5*b^3*c^6)*e*cos(e*x + d)^2 + (b^9 + 2*b^7*c^2 + b^5*c^4)*e)*sin(e*x + d))","B",0
362,1,739,0,1.850375," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^4,x, algorithm=""fricas"")","\frac{2 \, {\left(b^{7} - 21 \, b^{5} c^{2} + 35 \, b^{3} c^{4} - 7 \, b c^{6}\right)} \cos\left(e x + d\right)^{7} - 7 \, {\left(b^{7} - 15 \, b^{5} c^{2} + 15 \, b^{3} c^{4} - b c^{6}\right)} \cos\left(e x + d\right)^{5} - 14 \, {\left(5 \, b^{5} c^{2} - 5 \, b^{3} c^{4} - 2 \, b c^{6}\right)} \cos\left(e x + d\right)^{3} - 7 \, {\left(5 \, b^{7} + 15 \, b^{5} c^{2} + 20 \, b^{3} c^{4} + 8 \, b c^{6}\right)} \cos\left(e x + d\right) - {\left(35 \, b^{6} c + 105 \, b^{4} c^{3} + 112 \, b^{2} c^{5} + 40 \, c^{7} - 2 \, {\left(7 \, b^{6} c - 35 \, b^{4} c^{3} + 21 \, b^{2} c^{5} - c^{7}\right)} \cos\left(e x + d\right)^{6} + {\left(35 \, b^{6} c - 105 \, b^{4} c^{3} + 21 \, b^{2} c^{5} + c^{7}\right)} \cos\left(e x + d\right)^{4} + 2 \, {\left(35 \, b^{4} c^{3} + 7 \, b^{2} c^{5} - 4 \, c^{7}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right) + 4 \, {\left(3 \, b^{6} + 16 \, b^{4} c^{2} + 23 \, b^{2} c^{4} + 10 \, c^{6} + 7 \, {\left(b^{6} + b^{4} c^{2} - b^{2} c^{4} - c^{6}\right)} \cos\left(e x + d\right)^{2} + 14 \, {\left(b^{5} c + 2 \, b^{3} c^{3} + b c^{5}\right)} \cos\left(e x + d\right) \sin\left(e x + d\right)\right)} \sqrt{b^{2} + c^{2}}}{35 \, {\left({\left(7 \, b^{10} c - 21 \, b^{8} c^{3} - 42 \, b^{6} c^{5} + 6 \, b^{4} c^{7} + 19 \, b^{2} c^{9} - c^{11}\right)} e \cos\left(e x + d\right)^{7} - 7 \, {\left(3 \, b^{10} c - 4 \, b^{8} c^{3} - 14 \, b^{6} c^{5} - 4 \, b^{4} c^{7} + 3 \, b^{2} c^{9}\right)} e \cos\left(e x + d\right)^{5} + 7 \, {\left(3 \, b^{10} c + b^{8} c^{3} - 7 \, b^{6} c^{5} - 5 \, b^{4} c^{7}\right)} e \cos\left(e x + d\right)^{3} - 7 \, {\left(b^{10} c + 2 \, b^{8} c^{3} + b^{6} c^{5}\right)} e \cos\left(e x + d\right) - {\left({\left(b^{11} - 19 \, b^{9} c^{2} - 6 \, b^{7} c^{4} + 42 \, b^{5} c^{6} + 21 \, b^{3} c^{8} - 7 \, b c^{10}\right)} e \cos\left(e x + d\right)^{6} - {\left(3 \, b^{11} - 36 \, b^{9} c^{2} - 46 \, b^{7} c^{4} + 28 \, b^{5} c^{6} + 35 \, b^{3} c^{8}\right)} e \cos\left(e x + d\right)^{4} + 3 \, {\left(b^{11} - 5 \, b^{9} c^{2} - 13 \, b^{7} c^{4} - 7 \, b^{5} c^{6}\right)} e \cos\left(e x + d\right)^{2} - {\left(b^{11} + 2 \, b^{9} c^{2} + b^{7} c^{4}\right)} e\right)} \sin\left(e x + d\right)\right)}}"," ",0,"1/35*(2*(b^7 - 21*b^5*c^2 + 35*b^3*c^4 - 7*b*c^6)*cos(e*x + d)^7 - 7*(b^7 - 15*b^5*c^2 + 15*b^3*c^4 - b*c^6)*cos(e*x + d)^5 - 14*(5*b^5*c^2 - 5*b^3*c^4 - 2*b*c^6)*cos(e*x + d)^3 - 7*(5*b^7 + 15*b^5*c^2 + 20*b^3*c^4 + 8*b*c^6)*cos(e*x + d) - (35*b^6*c + 105*b^4*c^3 + 112*b^2*c^5 + 40*c^7 - 2*(7*b^6*c - 35*b^4*c^3 + 21*b^2*c^5 - c^7)*cos(e*x + d)^6 + (35*b^6*c - 105*b^4*c^3 + 21*b^2*c^5 + c^7)*cos(e*x + d)^4 + 2*(35*b^4*c^3 + 7*b^2*c^5 - 4*c^7)*cos(e*x + d)^2)*sin(e*x + d) + 4*(3*b^6 + 16*b^4*c^2 + 23*b^2*c^4 + 10*c^6 + 7*(b^6 + b^4*c^2 - b^2*c^4 - c^6)*cos(e*x + d)^2 + 14*(b^5*c + 2*b^3*c^3 + b*c^5)*cos(e*x + d)*sin(e*x + d))*sqrt(b^2 + c^2))/((7*b^10*c - 21*b^8*c^3 - 42*b^6*c^5 + 6*b^4*c^7 + 19*b^2*c^9 - c^11)*e*cos(e*x + d)^7 - 7*(3*b^10*c - 4*b^8*c^3 - 14*b^6*c^5 - 4*b^4*c^7 + 3*b^2*c^9)*e*cos(e*x + d)^5 + 7*(3*b^10*c + b^8*c^3 - 7*b^6*c^5 - 5*b^4*c^7)*e*cos(e*x + d)^3 - 7*(b^10*c + 2*b^8*c^3 + b^6*c^5)*e*cos(e*x + d) - ((b^11 - 19*b^9*c^2 - 6*b^7*c^4 + 42*b^5*c^6 + 21*b^3*c^8 - 7*b*c^10)*e*cos(e*x + d)^6 - (3*b^11 - 36*b^9*c^2 - 46*b^7*c^4 + 28*b^5*c^6 + 35*b^3*c^8)*e*cos(e*x + d)^4 + 3*(b^11 - 5*b^9*c^2 - 13*b^7*c^4 - 7*b^5*c^6)*e*cos(e*x + d)^2 - (b^11 + 2*b^9*c^2 + b^7*c^4)*e)*sin(e*x + d))","B",0
363,1,134,0,1.990317," ","integrate((2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^3,x, algorithm=""fricas"")","-\frac{4 \, {\left(18 \, a^{2} c \cos\left(e x + d\right)^{2} + 2 \, {\left(3 \, a^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{3} - 3 \, {\left(5 \, a^{3} + 3 \, a c^{2}\right)} e x + 6 \, {\left(3 \, a^{2} c + c^{3}\right)} \cos\left(e x + d\right) - {\left(22 \, a^{3} + 6 \, a c^{2} + 2 \, {\left(a^{3} - 3 \, a c^{2}\right)} \cos\left(e x + d\right)^{2} + 9 \, {\left(a^{3} - a c^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)}}{3 \, e}"," ",0,"-4/3*(18*a^2*c*cos(e*x + d)^2 + 2*(3*a^2*c - c^3)*cos(e*x + d)^3 - 3*(5*a^3 + 3*a*c^2)*e*x + 6*(3*a^2*c + c^3)*cos(e*x + d) - (22*a^3 + 6*a*c^2 + 2*(a^3 - 3*a*c^2)*cos(e*x + d)^2 + 9*(a^3 - a*c^2)*cos(e*x + d))*sin(e*x + d))/e","A",0
364,1,71,0,1.423486," ","integrate((2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, a c \cos\left(e x + d\right)^{2} - {\left(3 \, a^{2} + c^{2}\right)} e x + 4 \, a c \cos\left(e x + d\right) - {\left(4 \, a^{2} + {\left(a^{2} - c^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)}}{e}"," ",0,"-2*(2*a*c*cos(e*x + d)^2 - (3*a^2 + c^2)*e*x + 4*a*c*cos(e*x + d) - (4*a^2 + (a^2 - c^2)*cos(e*x + d))*sin(e*x + d))/e","A",0
365,1,27,0,0.882878," ","integrate(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d),x, algorithm=""fricas"")","\frac{2 \, {\left(a e x - c \cos\left(e x + d\right) + a \sin\left(e x + d\right)\right)}}{e}"," ",0,"2*(a*e*x - c*cos(e*x + d) + a*sin(e*x + d))/e","A",0
366,1,60,0,1.340085," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d)),x, algorithm=""fricas"")","\frac{\log\left(a c \sin\left(e x + d\right) + \frac{1}{2} \, a^{2} + \frac{1}{2} \, c^{2} + \frac{1}{2} \, {\left(a^{2} - c^{2}\right)} \cos\left(e x + d\right)\right) - \log\left(\frac{1}{2} \, \cos\left(e x + d\right) + \frac{1}{2}\right)}{4 \, c e}"," ",0,"1/4*(log(a*c*sin(e*x + d) + 1/2*a^2 + 1/2*c^2 + 1/2*(a^2 - c^2)*cos(e*x + d)) - log(1/2*cos(e*x + d) + 1/2))/(c*e)","B",0
367,1,154,0,0.990891," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^2,x, algorithm=""fricas"")","-\frac{2 \, c^{2} \cos\left(e x + d\right) - 2 \, a c \sin\left(e x + d\right) + {\left(a^{2} \cos\left(e x + d\right) + a c \sin\left(e x + d\right) + a^{2}\right)} \log\left(a c \sin\left(e x + d\right) + \frac{1}{2} \, a^{2} + \frac{1}{2} \, c^{2} + \frac{1}{2} \, {\left(a^{2} - c^{2}\right)} \cos\left(e x + d\right)\right) - {\left(a^{2} \cos\left(e x + d\right) + a c \sin\left(e x + d\right) + a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(e x + d\right) + \frac{1}{2}\right)}{8 \, {\left(a c^{3} e \cos\left(e x + d\right) + c^{4} e \sin\left(e x + d\right) + a c^{3} e\right)}}"," ",0,"-1/8*(2*c^2*cos(e*x + d) - 2*a*c*sin(e*x + d) + (a^2*cos(e*x + d) + a*c*sin(e*x + d) + a^2)*log(a*c*sin(e*x + d) + 1/2*a^2 + 1/2*c^2 + 1/2*(a^2 - c^2)*cos(e*x + d)) - (a^2*cos(e*x + d) + a*c*sin(e*x + d) + a^2)*log(1/2*cos(e*x + d) + 1/2))/(a*c^3*e*cos(e*x + d) + c^4*e*sin(e*x + d) + a*c^3*e)","B",0
368,1,433,0,0.947147," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^3,x, algorithm=""fricas"")","\frac{12 \, a^{2} c^{2} \cos\left(e x + d\right)^{2} - 6 \, a^{2} c^{2} + 2 \, {\left(3 \, a^{2} c^{2} - c^{4}\right)} \cos\left(e x + d\right) + {\left(3 \, a^{4} + 4 \, a^{2} c^{2} + c^{4} + {\left(3 \, a^{4} - 2 \, a^{2} c^{2} - c^{4}\right)} \cos\left(e x + d\right)^{2} + 2 \, {\left(3 \, a^{4} + a^{2} c^{2}\right)} \cos\left(e x + d\right) + 2 \, {\left(3 \, a^{3} c + a c^{3} + {\left(3 \, a^{3} c + a c^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \log\left(a c \sin\left(e x + d\right) + \frac{1}{2} \, a^{2} + \frac{1}{2} \, c^{2} + \frac{1}{2} \, {\left(a^{2} - c^{2}\right)} \cos\left(e x + d\right)\right) - {\left(3 \, a^{4} + 4 \, a^{2} c^{2} + c^{4} + {\left(3 \, a^{4} - 2 \, a^{2} c^{2} - c^{4}\right)} \cos\left(e x + d\right)^{2} + 2 \, {\left(3 \, a^{4} + a^{2} c^{2}\right)} \cos\left(e x + d\right) + 2 \, {\left(3 \, a^{3} c + a c^{3} + {\left(3 \, a^{3} c + a c^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \log\left(\frac{1}{2} \, \cos\left(e x + d\right) + \frac{1}{2}\right) - 2 \, {\left(3 \, a^{3} c - a c^{3} + 3 \, {\left(a^{3} c - a c^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{32 \, {\left(2 \, a^{2} c^{5} e \cos\left(e x + d\right) + {\left(a^{2} c^{5} - c^{7}\right)} e \cos\left(e x + d\right)^{2} + {\left(a^{2} c^{5} + c^{7}\right)} e + 2 \, {\left(a c^{6} e \cos\left(e x + d\right) + a c^{6} e\right)} \sin\left(e x + d\right)\right)}}"," ",0,"1/32*(12*a^2*c^2*cos(e*x + d)^2 - 6*a^2*c^2 + 2*(3*a^2*c^2 - c^4)*cos(e*x + d) + (3*a^4 + 4*a^2*c^2 + c^4 + (3*a^4 - 2*a^2*c^2 - c^4)*cos(e*x + d)^2 + 2*(3*a^4 + a^2*c^2)*cos(e*x + d) + 2*(3*a^3*c + a*c^3 + (3*a^3*c + a*c^3)*cos(e*x + d))*sin(e*x + d))*log(a*c*sin(e*x + d) + 1/2*a^2 + 1/2*c^2 + 1/2*(a^2 - c^2)*cos(e*x + d)) - (3*a^4 + 4*a^2*c^2 + c^4 + (3*a^4 - 2*a^2*c^2 - c^4)*cos(e*x + d)^2 + 2*(3*a^4 + a^2*c^2)*cos(e*x + d) + 2*(3*a^3*c + a*c^3 + (3*a^3*c + a*c^3)*cos(e*x + d))*sin(e*x + d))*log(1/2*cos(e*x + d) + 1/2) - 2*(3*a^3*c - a*c^3 + 3*(a^3*c - a*c^3)*cos(e*x + d))*sin(e*x + d))/(2*a^2*c^5*e*cos(e*x + d) + (a^2*c^5 - c^7)*e*cos(e*x + d)^2 + (a^2*c^5 + c^7)*e + 2*(a*c^6*e*cos(e*x + d) + a*c^6*e)*sin(e*x + d))","B",0
369,1,791,0,1.051429," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^4,x, algorithm=""fricas"")","\frac{60 \, a^{4} c^{2} + 6 \, a^{2} c^{4} - 2 \, {\left(45 \, a^{4} c^{2} - 3 \, a^{2} c^{4} - 4 \, c^{6}\right)} \cos\left(e x + d\right)^{3} - 12 \, {\left(10 \, a^{4} c^{2} + a^{2} c^{4}\right)} \cos\left(e x + d\right)^{2} + 6 \, {\left(5 \, a^{4} c^{2} - 2 \, a^{2} c^{4} - 2 \, c^{6}\right)} \cos\left(e x + d\right) - 3 \, {\left(5 \, a^{6} + 18 \, a^{4} c^{2} + 9 \, a^{2} c^{4} + {\left(5 \, a^{6} - 12 \, a^{4} c^{2} - 9 \, a^{2} c^{4}\right)} \cos\left(e x + d\right)^{3} + 3 \, {\left(5 \, a^{6} - 2 \, a^{4} c^{2} - 3 \, a^{2} c^{4}\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(5 \, a^{6} + 8 \, a^{4} c^{2} + 3 \, a^{2} c^{4}\right)} \cos\left(e x + d\right) + {\left(15 \, a^{5} c + 14 \, a^{3} c^{3} + 3 \, a c^{5} + {\left(15 \, a^{5} c + 4 \, a^{3} c^{3} - 3 \, a c^{5}\right)} \cos\left(e x + d\right)^{2} + 6 \, {\left(5 \, a^{5} c + 3 \, a^{3} c^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \log\left(a c \sin\left(e x + d\right) + \frac{1}{2} \, a^{2} + \frac{1}{2} \, c^{2} + \frac{1}{2} \, {\left(a^{2} - c^{2}\right)} \cos\left(e x + d\right)\right) + 3 \, {\left(5 \, a^{6} + 18 \, a^{4} c^{2} + 9 \, a^{2} c^{4} + {\left(5 \, a^{6} - 12 \, a^{4} c^{2} - 9 \, a^{2} c^{4}\right)} \cos\left(e x + d\right)^{3} + 3 \, {\left(5 \, a^{6} - 2 \, a^{4} c^{2} - 3 \, a^{2} c^{4}\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(5 \, a^{6} + 8 \, a^{4} c^{2} + 3 \, a^{2} c^{4}\right)} \cos\left(e x + d\right) + {\left(15 \, a^{5} c + 14 \, a^{3} c^{3} + 3 \, a c^{5} + {\left(15 \, a^{5} c + 4 \, a^{3} c^{3} - 3 \, a c^{5}\right)} \cos\left(e x + d\right)^{2} + 6 \, {\left(5 \, a^{5} c + 3 \, a^{3} c^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \log\left(\frac{1}{2} \, \cos\left(e x + d\right) + \frac{1}{2}\right) + 2 \, {\left(15 \, a^{5} c + 14 \, a^{3} c^{3} + 6 \, a c^{5} + {\left(15 \, a^{5} c - 41 \, a^{3} c^{3} - 12 \, a c^{5}\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(10 \, a^{5} c - 9 \, a^{3} c^{3} - a c^{5}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{192 \, {\left({\left(a^{3} c^{7} - 3 \, a c^{9}\right)} e \cos\left(e x + d\right)^{3} + 3 \, {\left(a^{3} c^{7} - a c^{9}\right)} e \cos\left(e x + d\right)^{2} + 3 \, {\left(a^{3} c^{7} + a c^{9}\right)} e \cos\left(e x + d\right) + {\left(a^{3} c^{7} + 3 \, a c^{9}\right)} e + {\left(6 \, a^{2} c^{8} e \cos\left(e x + d\right) + {\left(3 \, a^{2} c^{8} - c^{10}\right)} e \cos\left(e x + d\right)^{2} + {\left(3 \, a^{2} c^{8} + c^{10}\right)} e\right)} \sin\left(e x + d\right)\right)}}"," ",0,"1/192*(60*a^4*c^2 + 6*a^2*c^4 - 2*(45*a^4*c^2 - 3*a^2*c^4 - 4*c^6)*cos(e*x + d)^3 - 12*(10*a^4*c^2 + a^2*c^4)*cos(e*x + d)^2 + 6*(5*a^4*c^2 - 2*a^2*c^4 - 2*c^6)*cos(e*x + d) - 3*(5*a^6 + 18*a^4*c^2 + 9*a^2*c^4 + (5*a^6 - 12*a^4*c^2 - 9*a^2*c^4)*cos(e*x + d)^3 + 3*(5*a^6 - 2*a^4*c^2 - 3*a^2*c^4)*cos(e*x + d)^2 + 3*(5*a^6 + 8*a^4*c^2 + 3*a^2*c^4)*cos(e*x + d) + (15*a^5*c + 14*a^3*c^3 + 3*a*c^5 + (15*a^5*c + 4*a^3*c^3 - 3*a*c^5)*cos(e*x + d)^2 + 6*(5*a^5*c + 3*a^3*c^3)*cos(e*x + d))*sin(e*x + d))*log(a*c*sin(e*x + d) + 1/2*a^2 + 1/2*c^2 + 1/2*(a^2 - c^2)*cos(e*x + d)) + 3*(5*a^6 + 18*a^4*c^2 + 9*a^2*c^4 + (5*a^6 - 12*a^4*c^2 - 9*a^2*c^4)*cos(e*x + d)^3 + 3*(5*a^6 - 2*a^4*c^2 - 3*a^2*c^4)*cos(e*x + d)^2 + 3*(5*a^6 + 8*a^4*c^2 + 3*a^2*c^4)*cos(e*x + d) + (15*a^5*c + 14*a^3*c^3 + 3*a*c^5 + (15*a^5*c + 4*a^3*c^3 - 3*a*c^5)*cos(e*x + d)^2 + 6*(5*a^5*c + 3*a^3*c^3)*cos(e*x + d))*sin(e*x + d))*log(1/2*cos(e*x + d) + 1/2) + 2*(15*a^5*c + 14*a^3*c^3 + 6*a*c^5 + (15*a^5*c - 41*a^3*c^3 - 12*a*c^5)*cos(e*x + d)^2 + 3*(10*a^5*c - 9*a^3*c^3 - a*c^5)*cos(e*x + d))*sin(e*x + d))/((a^3*c^7 - 3*a*c^9)*e*cos(e*x + d)^3 + 3*(a^3*c^7 - a*c^9)*e*cos(e*x + d)^2 + 3*(a^3*c^7 + a*c^9)*e*cos(e*x + d) + (a^3*c^7 + 3*a*c^9)*e + (6*a^2*c^8*e*cos(e*x + d) + (3*a^2*c^8 - c^10)*e*cos(e*x + d)^2 + (3*a^2*c^8 + c^10)*e)*sin(e*x + d))","B",0
370,1,31,0,1.169912," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d)),x, algorithm=""fricas"")","-\frac{\log\left(\frac{1}{2} \, \cos\left(e x + d\right) + \frac{1}{2}\right) - \log\left(\sin\left(e x + d\right) + 1\right)}{4 \, a e}"," ",0,"-1/4*(log(1/2*cos(e*x + d) + 1/2) - log(sin(e*x + d) + 1))/(a*e)","A",0
371,1,100,0,1.211540," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d))^2,x, algorithm=""fricas"")","\frac{{\left(\cos\left(e x + d\right) + \sin\left(e x + d\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(e x + d\right) + \frac{1}{2}\right) - {\left(\cos\left(e x + d\right) + \sin\left(e x + d\right) + 1\right)} \log\left(\sin\left(e x + d\right) + 1\right) - 2 \, \cos\left(e x + d\right) + 2 \, \sin\left(e x + d\right)}{8 \, {\left(a^{2} e \cos\left(e x + d\right) + a^{2} e \sin\left(e x + d\right) + a^{2} e\right)}}"," ",0,"1/8*((cos(e*x + d) + sin(e*x + d) + 1)*log(1/2*cos(e*x + d) + 1/2) - (cos(e*x + d) + sin(e*x + d) + 1)*log(sin(e*x + d) + 1) - 2*cos(e*x + d) + 2*sin(e*x + d))/(a^2*e*cos(e*x + d) + a^2*e*sin(e*x + d) + a^2*e)","A",0
372,1,143,0,1.763841," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d))^3,x, algorithm=""fricas"")","\frac{6 \, \cos\left(e x + d\right)^{2} - 4 \, {\left({\left(\cos\left(e x + d\right) + 1\right)} \sin\left(e x + d\right) + \cos\left(e x + d\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(e x + d\right) + \frac{1}{2}\right) + 4 \, {\left({\left(\cos\left(e x + d\right) + 1\right)} \sin\left(e x + d\right) + \cos\left(e x + d\right) + 1\right)} \log\left(\sin\left(e x + d\right) + 1\right) + 2 \, \cos\left(e x + d\right) - 2 \, \sin\left(e x + d\right) - 3}{32 \, {\left(a^{3} e \cos\left(e x + d\right) + a^{3} e + {\left(a^{3} e \cos\left(e x + d\right) + a^{3} e\right)} \sin\left(e x + d\right)\right)}}"," ",0,"1/32*(6*cos(e*x + d)^2 - 4*((cos(e*x + d) + 1)*sin(e*x + d) + cos(e*x + d) + 1)*log(1/2*cos(e*x + d) + 1/2) + 4*((cos(e*x + d) + 1)*sin(e*x + d) + cos(e*x + d) + 1)*log(sin(e*x + d) + 1) + 2*cos(e*x + d) - 2*sin(e*x + d) - 3)/(a^3*e*cos(e*x + d) + a^3*e + (a^3*e*cos(e*x + d) + a^3*e)*sin(e*x + d))","A",0
373,1,237,0,0.952404," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d))^4,x, algorithm=""fricas"")","\frac{38 \, \cos\left(e x + d\right)^{3} + 66 \, \cos\left(e x + d\right)^{2} + 24 \, {\left(\cos\left(e x + d\right)^{3} - {\left(\cos\left(e x + d\right)^{2} + 3 \, \cos\left(e x + d\right) + 2\right)} \sin\left(e x + d\right) - 3 \, \cos\left(e x + d\right) - 2\right)} \log\left(\frac{1}{2} \, \cos\left(e x + d\right) + \frac{1}{2}\right) - 24 \, {\left(\cos\left(e x + d\right)^{3} - {\left(\cos\left(e x + d\right)^{2} + 3 \, \cos\left(e x + d\right) + 2\right)} \sin\left(e x + d\right) - 3 \, \cos\left(e x + d\right) - 2\right)} \log\left(\sin\left(e x + d\right) + 1\right) + {\left(38 \, \cos\left(e x + d\right)^{2} - 35\right)} \sin\left(e x + d\right) - 3 \, \cos\left(e x + d\right) - 33}{192 \, {\left(a^{4} e \cos\left(e x + d\right)^{3} - 3 \, a^{4} e \cos\left(e x + d\right) - 2 \, a^{4} e - {\left(a^{4} e \cos\left(e x + d\right)^{2} + 3 \, a^{4} e \cos\left(e x + d\right) + 2 \, a^{4} e\right)} \sin\left(e x + d\right)\right)}}"," ",0,"1/192*(38*cos(e*x + d)^3 + 66*cos(e*x + d)^2 + 24*(cos(e*x + d)^3 - (cos(e*x + d)^2 + 3*cos(e*x + d) + 2)*sin(e*x + d) - 3*cos(e*x + d) - 2)*log(1/2*cos(e*x + d) + 1/2) - 24*(cos(e*x + d)^3 - (cos(e*x + d)^2 + 3*cos(e*x + d) + 2)*sin(e*x + d) - 3*cos(e*x + d) - 2)*log(sin(e*x + d) + 1) + (38*cos(e*x + d)^2 - 35)*sin(e*x + d) - 3*cos(e*x + d) - 33)/(a^4*e*cos(e*x + d)^3 - 3*a^4*e*cos(e*x + d) - 2*a^4*e - (a^4*e*cos(e*x + d)^2 + 3*a^4*e*cos(e*x + d) + 2*a^4*e)*sin(e*x + d))","A",0
374,1,134,0,1.946899," ","integrate((2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^3,x, algorithm=""fricas"")","\frac{4 \, {\left(18 \, a^{2} c \cos\left(e x + d\right)^{2} - 2 \, {\left(3 \, a^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{3} + 3 \, {\left(5 \, a^{3} + 3 \, a c^{2}\right)} e x - 6 \, {\left(3 \, a^{2} c + c^{3}\right)} \cos\left(e x + d\right) - {\left(22 \, a^{3} + 6 \, a c^{2} + 2 \, {\left(a^{3} - 3 \, a c^{2}\right)} \cos\left(e x + d\right)^{2} - 9 \, {\left(a^{3} - a c^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)}}{3 \, e}"," ",0,"4/3*(18*a^2*c*cos(e*x + d)^2 - 2*(3*a^2*c - c^3)*cos(e*x + d)^3 + 3*(5*a^3 + 3*a*c^2)*e*x - 6*(3*a^2*c + c^3)*cos(e*x + d) - (22*a^3 + 6*a*c^2 + 2*(a^3 - 3*a*c^2)*cos(e*x + d)^2 - 9*(a^3 - a*c^2)*cos(e*x + d))*sin(e*x + d))/e","A",0
375,1,71,0,0.525344," ","integrate((2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a c \cos\left(e x + d\right)^{2} + {\left(3 \, a^{2} + c^{2}\right)} e x - 4 \, a c \cos\left(e x + d\right) - {\left(4 \, a^{2} - {\left(a^{2} - c^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)}}{e}"," ",0,"2*(2*a*c*cos(e*x + d)^2 + (3*a^2 + c^2)*e*x - 4*a*c*cos(e*x + d) - (4*a^2 - (a^2 - c^2)*cos(e*x + d))*sin(e*x + d))/e","A",0
376,1,28,0,0.842761," ","integrate(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d),x, algorithm=""fricas"")","\frac{2 \, {\left(a e x - c \cos\left(e x + d\right) - a \sin\left(e x + d\right)\right)}}{e}"," ",0,"2*(a*e*x - c*cos(e*x + d) - a*sin(e*x + d))/e","A",0
377,1,60,0,0.904732," ","integrate(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d)),x, algorithm=""fricas"")","-\frac{\log\left(a c \sin\left(e x + d\right) + \frac{1}{2} \, a^{2} + \frac{1}{2} \, c^{2} - \frac{1}{2} \, {\left(a^{2} - c^{2}\right)} \cos\left(e x + d\right)\right) - \log\left(-\frac{1}{2} \, \cos\left(e x + d\right) + \frac{1}{2}\right)}{4 \, c e}"," ",0,"-1/4*(log(a*c*sin(e*x + d) + 1/2*a^2 + 1/2*c^2 - 1/2*(a^2 - c^2)*cos(e*x + d)) - log(-1/2*cos(e*x + d) + 1/2))/(c*e)","B",0
378,1,162,0,0.955544," ","integrate(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^2,x, algorithm=""fricas"")","\frac{2 \, c^{2} \cos\left(e x + d\right) + 2 \, a c \sin\left(e x + d\right) + {\left(a^{2} \cos\left(e x + d\right) - a c \sin\left(e x + d\right) - a^{2}\right)} \log\left(a c \sin\left(e x + d\right) + \frac{1}{2} \, a^{2} + \frac{1}{2} \, c^{2} - \frac{1}{2} \, {\left(a^{2} - c^{2}\right)} \cos\left(e x + d\right)\right) - {\left(a^{2} \cos\left(e x + d\right) - a c \sin\left(e x + d\right) - a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(e x + d\right) + \frac{1}{2}\right)}{8 \, {\left(a c^{3} e \cos\left(e x + d\right) - c^{4} e \sin\left(e x + d\right) - a c^{3} e\right)}}"," ",0,"1/8*(2*c^2*cos(e*x + d) + 2*a*c*sin(e*x + d) + (a^2*cos(e*x + d) - a*c*sin(e*x + d) - a^2)*log(a*c*sin(e*x + d) + 1/2*a^2 + 1/2*c^2 - 1/2*(a^2 - c^2)*cos(e*x + d)) - (a^2*cos(e*x + d) - a*c*sin(e*x + d) - a^2)*log(-1/2*cos(e*x + d) + 1/2))/(a*c^3*e*cos(e*x + d) - c^4*e*sin(e*x + d) - a*c^3*e)","B",0
379,1,438,0,1.084906," ","integrate(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^3,x, algorithm=""fricas"")","\frac{12 \, a^{2} c^{2} \cos\left(e x + d\right)^{2} - 6 \, a^{2} c^{2} - 2 \, {\left(3 \, a^{2} c^{2} - c^{4}\right)} \cos\left(e x + d\right) + {\left(3 \, a^{4} + 4 \, a^{2} c^{2} + c^{4} + {\left(3 \, a^{4} - 2 \, a^{2} c^{2} - c^{4}\right)} \cos\left(e x + d\right)^{2} - 2 \, {\left(3 \, a^{4} + a^{2} c^{2}\right)} \cos\left(e x + d\right) + 2 \, {\left(3 \, a^{3} c + a c^{3} - {\left(3 \, a^{3} c + a c^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \log\left(a c \sin\left(e x + d\right) + \frac{1}{2} \, a^{2} + \frac{1}{2} \, c^{2} - \frac{1}{2} \, {\left(a^{2} - c^{2}\right)} \cos\left(e x + d\right)\right) - {\left(3 \, a^{4} + 4 \, a^{2} c^{2} + c^{4} + {\left(3 \, a^{4} - 2 \, a^{2} c^{2} - c^{4}\right)} \cos\left(e x + d\right)^{2} - 2 \, {\left(3 \, a^{4} + a^{2} c^{2}\right)} \cos\left(e x + d\right) + 2 \, {\left(3 \, a^{3} c + a c^{3} - {\left(3 \, a^{3} c + a c^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(e x + d\right) + \frac{1}{2}\right) - 2 \, {\left(3 \, a^{3} c - a c^{3} - 3 \, {\left(a^{3} c - a c^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{32 \, {\left(2 \, a^{2} c^{5} e \cos\left(e x + d\right) - {\left(a^{2} c^{5} - c^{7}\right)} e \cos\left(e x + d\right)^{2} - {\left(a^{2} c^{5} + c^{7}\right)} e + 2 \, {\left(a c^{6} e \cos\left(e x + d\right) - a c^{6} e\right)} \sin\left(e x + d\right)\right)}}"," ",0,"1/32*(12*a^2*c^2*cos(e*x + d)^2 - 6*a^2*c^2 - 2*(3*a^2*c^2 - c^4)*cos(e*x + d) + (3*a^4 + 4*a^2*c^2 + c^4 + (3*a^4 - 2*a^2*c^2 - c^4)*cos(e*x + d)^2 - 2*(3*a^4 + a^2*c^2)*cos(e*x + d) + 2*(3*a^3*c + a*c^3 - (3*a^3*c + a*c^3)*cos(e*x + d))*sin(e*x + d))*log(a*c*sin(e*x + d) + 1/2*a^2 + 1/2*c^2 - 1/2*(a^2 - c^2)*cos(e*x + d)) - (3*a^4 + 4*a^2*c^2 + c^4 + (3*a^4 - 2*a^2*c^2 - c^4)*cos(e*x + d)^2 - 2*(3*a^4 + a^2*c^2)*cos(e*x + d) + 2*(3*a^3*c + a*c^3 - (3*a^3*c + a*c^3)*cos(e*x + d))*sin(e*x + d))*log(-1/2*cos(e*x + d) + 1/2) - 2*(3*a^3*c - a*c^3 - 3*(a^3*c - a*c^3)*cos(e*x + d))*sin(e*x + d))/(2*a^2*c^5*e*cos(e*x + d) - (a^2*c^5 - c^7)*e*cos(e*x + d)^2 - (a^2*c^5 + c^7)*e + 2*(a*c^6*e*cos(e*x + d) - a*c^6*e)*sin(e*x + d))","B",0
380,1,796,0,2.474602," ","integrate(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^4,x, algorithm=""fricas"")","\frac{60 \, a^{4} c^{2} + 6 \, a^{2} c^{4} + 2 \, {\left(45 \, a^{4} c^{2} - 3 \, a^{2} c^{4} - 4 \, c^{6}\right)} \cos\left(e x + d\right)^{3} - 12 \, {\left(10 \, a^{4} c^{2} + a^{2} c^{4}\right)} \cos\left(e x + d\right)^{2} - 6 \, {\left(5 \, a^{4} c^{2} - 2 \, a^{2} c^{4} - 2 \, c^{6}\right)} \cos\left(e x + d\right) - 3 \, {\left(5 \, a^{6} + 18 \, a^{4} c^{2} + 9 \, a^{2} c^{4} - {\left(5 \, a^{6} - 12 \, a^{4} c^{2} - 9 \, a^{2} c^{4}\right)} \cos\left(e x + d\right)^{3} + 3 \, {\left(5 \, a^{6} - 2 \, a^{4} c^{2} - 3 \, a^{2} c^{4}\right)} \cos\left(e x + d\right)^{2} - 3 \, {\left(5 \, a^{6} + 8 \, a^{4} c^{2} + 3 \, a^{2} c^{4}\right)} \cos\left(e x + d\right) + {\left(15 \, a^{5} c + 14 \, a^{3} c^{3} + 3 \, a c^{5} + {\left(15 \, a^{5} c + 4 \, a^{3} c^{3} - 3 \, a c^{5}\right)} \cos\left(e x + d\right)^{2} - 6 \, {\left(5 \, a^{5} c + 3 \, a^{3} c^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \log\left(a c \sin\left(e x + d\right) + \frac{1}{2} \, a^{2} + \frac{1}{2} \, c^{2} - \frac{1}{2} \, {\left(a^{2} - c^{2}\right)} \cos\left(e x + d\right)\right) + 3 \, {\left(5 \, a^{6} + 18 \, a^{4} c^{2} + 9 \, a^{2} c^{4} - {\left(5 \, a^{6} - 12 \, a^{4} c^{2} - 9 \, a^{2} c^{4}\right)} \cos\left(e x + d\right)^{3} + 3 \, {\left(5 \, a^{6} - 2 \, a^{4} c^{2} - 3 \, a^{2} c^{4}\right)} \cos\left(e x + d\right)^{2} - 3 \, {\left(5 \, a^{6} + 8 \, a^{4} c^{2} + 3 \, a^{2} c^{4}\right)} \cos\left(e x + d\right) + {\left(15 \, a^{5} c + 14 \, a^{3} c^{3} + 3 \, a c^{5} + {\left(15 \, a^{5} c + 4 \, a^{3} c^{3} - 3 \, a c^{5}\right)} \cos\left(e x + d\right)^{2} - 6 \, {\left(5 \, a^{5} c + 3 \, a^{3} c^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(e x + d\right) + \frac{1}{2}\right) + 2 \, {\left(15 \, a^{5} c + 14 \, a^{3} c^{3} + 6 \, a c^{5} + {\left(15 \, a^{5} c - 41 \, a^{3} c^{3} - 12 \, a c^{5}\right)} \cos\left(e x + d\right)^{2} - 3 \, {\left(10 \, a^{5} c - 9 \, a^{3} c^{3} - a c^{5}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{192 \, {\left({\left(a^{3} c^{7} - 3 \, a c^{9}\right)} e \cos\left(e x + d\right)^{3} - 3 \, {\left(a^{3} c^{7} - a c^{9}\right)} e \cos\left(e x + d\right)^{2} + 3 \, {\left(a^{3} c^{7} + a c^{9}\right)} e \cos\left(e x + d\right) - {\left(a^{3} c^{7} + 3 \, a c^{9}\right)} e + {\left(6 \, a^{2} c^{8} e \cos\left(e x + d\right) - {\left(3 \, a^{2} c^{8} - c^{10}\right)} e \cos\left(e x + d\right)^{2} - {\left(3 \, a^{2} c^{8} + c^{10}\right)} e\right)} \sin\left(e x + d\right)\right)}}"," ",0,"1/192*(60*a^4*c^2 + 6*a^2*c^4 + 2*(45*a^4*c^2 - 3*a^2*c^4 - 4*c^6)*cos(e*x + d)^3 - 12*(10*a^4*c^2 + a^2*c^4)*cos(e*x + d)^2 - 6*(5*a^4*c^2 - 2*a^2*c^4 - 2*c^6)*cos(e*x + d) - 3*(5*a^6 + 18*a^4*c^2 + 9*a^2*c^4 - (5*a^6 - 12*a^4*c^2 - 9*a^2*c^4)*cos(e*x + d)^3 + 3*(5*a^6 - 2*a^4*c^2 - 3*a^2*c^4)*cos(e*x + d)^2 - 3*(5*a^6 + 8*a^4*c^2 + 3*a^2*c^4)*cos(e*x + d) + (15*a^5*c + 14*a^3*c^3 + 3*a*c^5 + (15*a^5*c + 4*a^3*c^3 - 3*a*c^5)*cos(e*x + d)^2 - 6*(5*a^5*c + 3*a^3*c^3)*cos(e*x + d))*sin(e*x + d))*log(a*c*sin(e*x + d) + 1/2*a^2 + 1/2*c^2 - 1/2*(a^2 - c^2)*cos(e*x + d)) + 3*(5*a^6 + 18*a^4*c^2 + 9*a^2*c^4 - (5*a^6 - 12*a^4*c^2 - 9*a^2*c^4)*cos(e*x + d)^3 + 3*(5*a^6 - 2*a^4*c^2 - 3*a^2*c^4)*cos(e*x + d)^2 - 3*(5*a^6 + 8*a^4*c^2 + 3*a^2*c^4)*cos(e*x + d) + (15*a^5*c + 14*a^3*c^3 + 3*a*c^5 + (15*a^5*c + 4*a^3*c^3 - 3*a*c^5)*cos(e*x + d)^2 - 6*(5*a^5*c + 3*a^3*c^3)*cos(e*x + d))*sin(e*x + d))*log(-1/2*cos(e*x + d) + 1/2) + 2*(15*a^5*c + 14*a^3*c^3 + 6*a*c^5 + (15*a^5*c - 41*a^3*c^3 - 12*a*c^5)*cos(e*x + d)^2 - 3*(10*a^5*c - 9*a^3*c^3 - a*c^5)*cos(e*x + d))*sin(e*x + d))/((a^3*c^7 - 3*a*c^9)*e*cos(e*x + d)^3 - 3*(a^3*c^7 - a*c^9)*e*cos(e*x + d)^2 + 3*(a^3*c^7 + a*c^9)*e*cos(e*x + d) - (a^3*c^7 + 3*a*c^9)*e + (6*a^2*c^8*e*cos(e*x + d) - (3*a^2*c^8 - c^10)*e*cos(e*x + d)^2 - (3*a^2*c^8 + c^10)*e)*sin(e*x + d))","B",0
381,1,127,0,0.768053," ","integrate((2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^3,x, algorithm=""fricas"")","-\frac{4 \, {\left(18 \, a^{2} b \cos\left(e x + d\right)^{2} + 24 \, a^{3} \cos\left(e x + d\right) - 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(e x + d\right)^{3} - 3 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} e x - {\left(24 \, a^{2} b + 4 \, b^{3} - 2 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(e x + d\right)^{2} - 9 \, {\left(a^{3} - a b^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)}}{3 \, e}"," ",0,"-4/3*(18*a^2*b*cos(e*x + d)^2 + 24*a^3*cos(e*x + d) - 2*(a^3 - 3*a*b^2)*cos(e*x + d)^3 - 3*(5*a^3 + 3*a*b^2)*e*x - (24*a^2*b + 4*b^3 - 2*(3*a^2*b - b^3)*cos(e*x + d)^2 - 9*(a^3 - a*b^2)*cos(e*x + d))*sin(e*x + d))/e","A",0
382,1,72,0,0.764816," ","integrate((2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, a b \cos\left(e x + d\right)^{2} - {\left(3 \, a^{2} + b^{2}\right)} e x + 4 \, a^{2} \cos\left(e x + d\right) - {\left(4 \, a b - {\left(a^{2} - b^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)}}{e}"," ",0,"-2*(2*a*b*cos(e*x + d)^2 - (3*a^2 + b^2)*e*x + 4*a^2*cos(e*x + d) - (4*a*b - (a^2 - b^2)*cos(e*x + d))*sin(e*x + d))/e","A",0
383,1,27,0,2.087468," ","integrate(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d),x, algorithm=""fricas"")","\frac{2 \, {\left(a e x - a \cos\left(e x + d\right) + b \sin\left(e x + d\right)\right)}}{e}"," ",0,"2*(a*e*x - a*cos(e*x + d) + b*sin(e*x + d))/e","A",0
384,1,54,0,1.752228," ","integrate(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d)),x, algorithm=""fricas"")","-\frac{\log\left(2 \, a b \cos\left(e x + d\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \sin\left(e x + d\right)\right) - \log\left(\sin\left(e x + d\right) + 1\right)}{4 \, b e}"," ",0,"-1/4*(log(2*a*b*cos(e*x + d) + a^2 + b^2 + (a^2 - b^2)*sin(e*x + d)) - log(sin(e*x + d) + 1))/(b*e)","B",0
385,1,148,0,1.250037," ","integrate(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^2,x, algorithm=""fricas"")","-\frac{2 \, a b \cos\left(e x + d\right) - 2 \, b^{2} \sin\left(e x + d\right) - {\left(a b \cos\left(e x + d\right) + a^{2} \sin\left(e x + d\right) + a^{2}\right)} \log\left(2 \, a b \cos\left(e x + d\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \sin\left(e x + d\right)\right) + {\left(a b \cos\left(e x + d\right) + a^{2} \sin\left(e x + d\right) + a^{2}\right)} \log\left(\sin\left(e x + d\right) + 1\right)}{8 \, {\left(b^{4} e \cos\left(e x + d\right) + a b^{3} e \sin\left(e x + d\right) + a b^{3} e\right)}}"," ",0,"-1/8*(2*a*b*cos(e*x + d) - 2*b^2*sin(e*x + d) - (a*b*cos(e*x + d) + a^2*sin(e*x + d) + a^2)*log(2*a*b*cos(e*x + d) + a^2 + b^2 + (a^2 - b^2)*sin(e*x + d)) + (a*b*cos(e*x + d) + a^2*sin(e*x + d) + a^2)*log(sin(e*x + d) + 1))/(b^4*e*cos(e*x + d) + a*b^3*e*sin(e*x + d) + a*b^3*e)","B",0
386,1,420,0,0.856870," ","integrate(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^3,x, algorithm=""fricas"")","\frac{12 \, a^{2} b^{2} \cos\left(e x + d\right)^{2} - 6 \, a^{2} b^{2} + 2 \, {\left(3 \, a^{3} b - a b^{3}\right)} \cos\left(e x + d\right) - {\left(6 \, a^{4} + 2 \, a^{2} b^{2} - {\left(3 \, a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(e x + d\right)^{2} + 2 \, {\left(3 \, a^{3} b + a b^{3}\right)} \cos\left(e x + d\right) + 2 \, {\left(3 \, a^{4} + a^{2} b^{2} + {\left(3 \, a^{3} b + a b^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \log\left(2 \, a b \cos\left(e x + d\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \sin\left(e x + d\right)\right) + {\left(6 \, a^{4} + 2 \, a^{2} b^{2} - {\left(3 \, a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(e x + d\right)^{2} + 2 \, {\left(3 \, a^{3} b + a b^{3}\right)} \cos\left(e x + d\right) + 2 \, {\left(3 \, a^{4} + a^{2} b^{2} + {\left(3 \, a^{3} b + a b^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \log\left(\sin\left(e x + d\right) + 1\right) - 2 \, {\left(3 \, a^{2} b^{2} - b^{4} - 3 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{32 \, {\left(2 \, a b^{6} e \cos\left(e x + d\right) + 2 \, a^{2} b^{5} e - {\left(a^{2} b^{5} - b^{7}\right)} e \cos\left(e x + d\right)^{2} + 2 \, {\left(a b^{6} e \cos\left(e x + d\right) + a^{2} b^{5} e\right)} \sin\left(e x + d\right)\right)}}"," ",0,"1/32*(12*a^2*b^2*cos(e*x + d)^2 - 6*a^2*b^2 + 2*(3*a^3*b - a*b^3)*cos(e*x + d) - (6*a^4 + 2*a^2*b^2 - (3*a^4 - 2*a^2*b^2 - b^4)*cos(e*x + d)^2 + 2*(3*a^3*b + a*b^3)*cos(e*x + d) + 2*(3*a^4 + a^2*b^2 + (3*a^3*b + a*b^3)*cos(e*x + d))*sin(e*x + d))*log(2*a*b*cos(e*x + d) + a^2 + b^2 + (a^2 - b^2)*sin(e*x + d)) + (6*a^4 + 2*a^2*b^2 - (3*a^4 - 2*a^2*b^2 - b^4)*cos(e*x + d)^2 + 2*(3*a^3*b + a*b^3)*cos(e*x + d) + 2*(3*a^4 + a^2*b^2 + (3*a^3*b + a*b^3)*cos(e*x + d))*sin(e*x + d))*log(sin(e*x + d) + 1) - 2*(3*a^2*b^2 - b^4 - 3*(a^3*b - a*b^3)*cos(e*x + d))*sin(e*x + d))/(2*a*b^6*e*cos(e*x + d) + 2*a^2*b^5*e - (a^2*b^5 - b^7)*e*cos(e*x + d)^2 + 2*(a*b^6*e*cos(e*x + d) + a^2*b^5*e)*sin(e*x + d))","B",0
387,1,729,0,1.089220," ","integrate(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^4,x, algorithm=""fricas"")","\frac{60 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + 2 \, {\left(15 \, a^{5} b - 41 \, a^{3} b^{3} - 12 \, a b^{5}\right)} \cos\left(e x + d\right)^{3} - 12 \, {\left(10 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(e x + d\right)^{2} - 6 \, {\left(10 \, a^{5} b - 9 \, a^{3} b^{3} - 2 \, a b^{5}\right)} \cos\left(e x + d\right) + 3 \, {\left(20 \, a^{6} + 12 \, a^{4} b^{2} - {\left(15 \, a^{5} b + 4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(e x + d\right)^{3} - 3 \, {\left(5 \, a^{6} - 2 \, a^{4} b^{2} - 3 \, a^{2} b^{4}\right)} \cos\left(e x + d\right)^{2} + 6 \, {\left(5 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(e x + d\right) + {\left(20 \, a^{6} + 12 \, a^{4} b^{2} - {\left(5 \, a^{6} - 12 \, a^{4} b^{2} - 9 \, a^{2} b^{4}\right)} \cos\left(e x + d\right)^{2} + 6 \, {\left(5 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \log\left(2 \, a b \cos\left(e x + d\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \sin\left(e x + d\right)\right) - 3 \, {\left(20 \, a^{6} + 12 \, a^{4} b^{2} - {\left(15 \, a^{5} b + 4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(e x + d\right)^{3} - 3 \, {\left(5 \, a^{6} - 2 \, a^{4} b^{2} - 3 \, a^{2} b^{4}\right)} \cos\left(e x + d\right)^{2} + 6 \, {\left(5 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(e x + d\right) + {\left(20 \, a^{6} + 12 \, a^{4} b^{2} - {\left(5 \, a^{6} - 12 \, a^{4} b^{2} - 9 \, a^{2} b^{4}\right)} \cos\left(e x + d\right)^{2} + 6 \, {\left(5 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \log\left(\sin\left(e x + d\right) + 1\right) + 2 \, {\left(30 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + 2 \, b^{6} - {\left(45 \, a^{4} b^{2} - 3 \, a^{2} b^{4} - 4 \, b^{6}\right)} \cos\left(e x + d\right)^{2} - 3 \, {\left(10 \, a^{5} b - 9 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{192 \, {\left(6 \, a^{2} b^{8} e \cos\left(e x + d\right) + 4 \, a^{3} b^{7} e - {\left(3 \, a^{2} b^{8} - b^{10}\right)} e \cos\left(e x + d\right)^{3} - 3 \, {\left(a^{3} b^{7} - a b^{9}\right)} e \cos\left(e x + d\right)^{2} + {\left(6 \, a^{2} b^{8} e \cos\left(e x + d\right) + 4 \, a^{3} b^{7} e - {\left(a^{3} b^{7} - 3 \, a b^{9}\right)} e \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right)\right)}}"," ",0,"1/192*(60*a^4*b^2 + 6*a^2*b^4 + 2*(15*a^5*b - 41*a^3*b^3 - 12*a*b^5)*cos(e*x + d)^3 - 12*(10*a^4*b^2 + a^2*b^4)*cos(e*x + d)^2 - 6*(10*a^5*b - 9*a^3*b^3 - 2*a*b^5)*cos(e*x + d) + 3*(20*a^6 + 12*a^4*b^2 - (15*a^5*b + 4*a^3*b^3 - 3*a*b^5)*cos(e*x + d)^3 - 3*(5*a^6 - 2*a^4*b^2 - 3*a^2*b^4)*cos(e*x + d)^2 + 6*(5*a^5*b + 3*a^3*b^3)*cos(e*x + d) + (20*a^6 + 12*a^4*b^2 - (5*a^6 - 12*a^4*b^2 - 9*a^2*b^4)*cos(e*x + d)^2 + 6*(5*a^5*b + 3*a^3*b^3)*cos(e*x + d))*sin(e*x + d))*log(2*a*b*cos(e*x + d) + a^2 + b^2 + (a^2 - b^2)*sin(e*x + d)) - 3*(20*a^6 + 12*a^4*b^2 - (15*a^5*b + 4*a^3*b^3 - 3*a*b^5)*cos(e*x + d)^3 - 3*(5*a^6 - 2*a^4*b^2 - 3*a^2*b^4)*cos(e*x + d)^2 + 6*(5*a^5*b + 3*a^3*b^3)*cos(e*x + d) + (20*a^6 + 12*a^4*b^2 - (5*a^6 - 12*a^4*b^2 - 9*a^2*b^4)*cos(e*x + d)^2 + 6*(5*a^5*b + 3*a^3*b^3)*cos(e*x + d))*sin(e*x + d))*log(sin(e*x + d) + 1) + 2*(30*a^4*b^2 + 3*a^2*b^4 + 2*b^6 - (45*a^4*b^2 - 3*a^2*b^4 - 4*b^6)*cos(e*x + d)^2 - 3*(10*a^5*b - 9*a^3*b^3 - a*b^5)*cos(e*x + d))*sin(e*x + d))/(6*a^2*b^8*e*cos(e*x + d) + 4*a^3*b^7*e - (3*a^2*b^8 - b^10)*e*cos(e*x + d)^3 - 3*(a^3*b^7 - a*b^9)*e*cos(e*x + d)^2 + (6*a^2*b^8*e*cos(e*x + d) + 4*a^3*b^7*e - (a^3*b^7 - 3*a*b^9)*e*cos(e*x + d)^2)*sin(e*x + d))","B",0
388,1,126,0,0.925218," ","integrate((2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^3,x, algorithm=""fricas"")","\frac{4 \, {\left(18 \, a^{2} b \cos\left(e x + d\right)^{2} + 24 \, a^{3} \cos\left(e x + d\right) - 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(e x + d\right)^{3} + 3 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} e x + {\left(24 \, a^{2} b + 4 \, b^{3} - 2 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(e x + d\right)^{2} - 9 \, {\left(a^{3} - a b^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)}}{3 \, e}"," ",0,"4/3*(18*a^2*b*cos(e*x + d)^2 + 24*a^3*cos(e*x + d) - 2*(a^3 - 3*a*b^2)*cos(e*x + d)^3 + 3*(5*a^3 + 3*a*b^2)*e*x + (24*a^2*b + 4*b^3 - 2*(3*a^2*b - b^3)*cos(e*x + d)^2 - 9*(a^3 - a*b^2)*cos(e*x + d))*sin(e*x + d))/e","A",0
389,1,70,0,0.901712," ","integrate((2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a b \cos\left(e x + d\right)^{2} + {\left(3 \, a^{2} + b^{2}\right)} e x + 4 \, a^{2} \cos\left(e x + d\right) + {\left(4 \, a b - {\left(a^{2} - b^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)}}{e}"," ",0,"2*(2*a*b*cos(e*x + d)^2 + (3*a^2 + b^2)*e*x + 4*a^2*cos(e*x + d) + (4*a*b - (a^2 - b^2)*cos(e*x + d))*sin(e*x + d))/e","A",0
390,1,26,0,2.898702," ","integrate(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d),x, algorithm=""fricas"")","\frac{2 \, {\left(a e x + a \cos\left(e x + d\right) + b \sin\left(e x + d\right)\right)}}{e}"," ",0,"2*(a*e*x + a*cos(e*x + d) + b*sin(e*x + d))/e","A",0
391,1,57,0,1.983556," ","integrate(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d)),x, algorithm=""fricas"")","\frac{\log\left(2 \, a b \cos\left(e x + d\right) + a^{2} + b^{2} - {\left(a^{2} - b^{2}\right)} \sin\left(e x + d\right)\right) - \log\left(-\sin\left(e x + d\right) + 1\right)}{4 \, b e}"," ",0,"1/4*(log(2*a*b*cos(e*x + d) + a^2 + b^2 - (a^2 - b^2)*sin(e*x + d)) - log(-sin(e*x + d) + 1))/(b*e)","B",0
392,1,154,0,0.840724," ","integrate(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^2,x, algorithm=""fricas"")","\frac{2 \, a b \cos\left(e x + d\right) + 2 \, b^{2} \sin\left(e x + d\right) - {\left(a b \cos\left(e x + d\right) - a^{2} \sin\left(e x + d\right) + a^{2}\right)} \log\left(2 \, a b \cos\left(e x + d\right) + a^{2} + b^{2} - {\left(a^{2} - b^{2}\right)} \sin\left(e x + d\right)\right) + {\left(a b \cos\left(e x + d\right) - a^{2} \sin\left(e x + d\right) + a^{2}\right)} \log\left(-\sin\left(e x + d\right) + 1\right)}{8 \, {\left(b^{4} e \cos\left(e x + d\right) - a b^{3} e \sin\left(e x + d\right) + a b^{3} e\right)}}"," ",0,"1/8*(2*a*b*cos(e*x + d) + 2*b^2*sin(e*x + d) - (a*b*cos(e*x + d) - a^2*sin(e*x + d) + a^2)*log(2*a*b*cos(e*x + d) + a^2 + b^2 - (a^2 - b^2)*sin(e*x + d)) + (a*b*cos(e*x + d) - a^2*sin(e*x + d) + a^2)*log(-sin(e*x + d) + 1))/(b^4*e*cos(e*x + d) - a*b^3*e*sin(e*x + d) + a*b^3*e)","B",0
393,1,423,0,1.511876," ","integrate(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^3,x, algorithm=""fricas"")","-\frac{12 \, a^{2} b^{2} \cos\left(e x + d\right)^{2} - 6 \, a^{2} b^{2} + 2 \, {\left(3 \, a^{3} b - a b^{3}\right)} \cos\left(e x + d\right) - {\left(6 \, a^{4} + 2 \, a^{2} b^{2} - {\left(3 \, a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(e x + d\right)^{2} + 2 \, {\left(3 \, a^{3} b + a b^{3}\right)} \cos\left(e x + d\right) - 2 \, {\left(3 \, a^{4} + a^{2} b^{2} + {\left(3 \, a^{3} b + a b^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \log\left(2 \, a b \cos\left(e x + d\right) + a^{2} + b^{2} - {\left(a^{2} - b^{2}\right)} \sin\left(e x + d\right)\right) + {\left(6 \, a^{4} + 2 \, a^{2} b^{2} - {\left(3 \, a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(e x + d\right)^{2} + 2 \, {\left(3 \, a^{3} b + a b^{3}\right)} \cos\left(e x + d\right) - 2 \, {\left(3 \, a^{4} + a^{2} b^{2} + {\left(3 \, a^{3} b + a b^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \log\left(-\sin\left(e x + d\right) + 1\right) + 2 \, {\left(3 \, a^{2} b^{2} - b^{4} - 3 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{32 \, {\left(2 \, a b^{6} e \cos\left(e x + d\right) + 2 \, a^{2} b^{5} e - {\left(a^{2} b^{5} - b^{7}\right)} e \cos\left(e x + d\right)^{2} - 2 \, {\left(a b^{6} e \cos\left(e x + d\right) + a^{2} b^{5} e\right)} \sin\left(e x + d\right)\right)}}"," ",0,"-1/32*(12*a^2*b^2*cos(e*x + d)^2 - 6*a^2*b^2 + 2*(3*a^3*b - a*b^3)*cos(e*x + d) - (6*a^4 + 2*a^2*b^2 - (3*a^4 - 2*a^2*b^2 - b^4)*cos(e*x + d)^2 + 2*(3*a^3*b + a*b^3)*cos(e*x + d) - 2*(3*a^4 + a^2*b^2 + (3*a^3*b + a*b^3)*cos(e*x + d))*sin(e*x + d))*log(2*a*b*cos(e*x + d) + a^2 + b^2 - (a^2 - b^2)*sin(e*x + d)) + (6*a^4 + 2*a^2*b^2 - (3*a^4 - 2*a^2*b^2 - b^4)*cos(e*x + d)^2 + 2*(3*a^3*b + a*b^3)*cos(e*x + d) - 2*(3*a^4 + a^2*b^2 + (3*a^3*b + a*b^3)*cos(e*x + d))*sin(e*x + d))*log(-sin(e*x + d) + 1) + 2*(3*a^2*b^2 - b^4 - 3*(a^3*b - a*b^3)*cos(e*x + d))*sin(e*x + d))/(2*a*b^6*e*cos(e*x + d) + 2*a^2*b^5*e - (a^2*b^5 - b^7)*e*cos(e*x + d)^2 - 2*(a*b^6*e*cos(e*x + d) + a^2*b^5*e)*sin(e*x + d))","B",0
394,1,735,0,1.998571," ","integrate(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^4,x, algorithm=""fricas"")","-\frac{60 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + 2 \, {\left(15 \, a^{5} b - 41 \, a^{3} b^{3} - 12 \, a b^{5}\right)} \cos\left(e x + d\right)^{3} - 12 \, {\left(10 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(e x + d\right)^{2} - 6 \, {\left(10 \, a^{5} b - 9 \, a^{3} b^{3} - 2 \, a b^{5}\right)} \cos\left(e x + d\right) + 3 \, {\left(20 \, a^{6} + 12 \, a^{4} b^{2} - {\left(15 \, a^{5} b + 4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(e x + d\right)^{3} - 3 \, {\left(5 \, a^{6} - 2 \, a^{4} b^{2} - 3 \, a^{2} b^{4}\right)} \cos\left(e x + d\right)^{2} + 6 \, {\left(5 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(e x + d\right) - {\left(20 \, a^{6} + 12 \, a^{4} b^{2} - {\left(5 \, a^{6} - 12 \, a^{4} b^{2} - 9 \, a^{2} b^{4}\right)} \cos\left(e x + d\right)^{2} + 6 \, {\left(5 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \log\left(2 \, a b \cos\left(e x + d\right) + a^{2} + b^{2} - {\left(a^{2} - b^{2}\right)} \sin\left(e x + d\right)\right) - 3 \, {\left(20 \, a^{6} + 12 \, a^{4} b^{2} - {\left(15 \, a^{5} b + 4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(e x + d\right)^{3} - 3 \, {\left(5 \, a^{6} - 2 \, a^{4} b^{2} - 3 \, a^{2} b^{4}\right)} \cos\left(e x + d\right)^{2} + 6 \, {\left(5 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(e x + d\right) - {\left(20 \, a^{6} + 12 \, a^{4} b^{2} - {\left(5 \, a^{6} - 12 \, a^{4} b^{2} - 9 \, a^{2} b^{4}\right)} \cos\left(e x + d\right)^{2} + 6 \, {\left(5 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \log\left(-\sin\left(e x + d\right) + 1\right) - 2 \, {\left(30 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + 2 \, b^{6} - {\left(45 \, a^{4} b^{2} - 3 \, a^{2} b^{4} - 4 \, b^{6}\right)} \cos\left(e x + d\right)^{2} - 3 \, {\left(10 \, a^{5} b - 9 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{192 \, {\left(6 \, a^{2} b^{8} e \cos\left(e x + d\right) + 4 \, a^{3} b^{7} e - {\left(3 \, a^{2} b^{8} - b^{10}\right)} e \cos\left(e x + d\right)^{3} - 3 \, {\left(a^{3} b^{7} - a b^{9}\right)} e \cos\left(e x + d\right)^{2} - {\left(6 \, a^{2} b^{8} e \cos\left(e x + d\right) + 4 \, a^{3} b^{7} e - {\left(a^{3} b^{7} - 3 \, a b^{9}\right)} e \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right)\right)}}"," ",0,"-1/192*(60*a^4*b^2 + 6*a^2*b^4 + 2*(15*a^5*b - 41*a^3*b^3 - 12*a*b^5)*cos(e*x + d)^3 - 12*(10*a^4*b^2 + a^2*b^4)*cos(e*x + d)^2 - 6*(10*a^5*b - 9*a^3*b^3 - 2*a*b^5)*cos(e*x + d) + 3*(20*a^6 + 12*a^4*b^2 - (15*a^5*b + 4*a^3*b^3 - 3*a*b^5)*cos(e*x + d)^3 - 3*(5*a^6 - 2*a^4*b^2 - 3*a^2*b^4)*cos(e*x + d)^2 + 6*(5*a^5*b + 3*a^3*b^3)*cos(e*x + d) - (20*a^6 + 12*a^4*b^2 - (5*a^6 - 12*a^4*b^2 - 9*a^2*b^4)*cos(e*x + d)^2 + 6*(5*a^5*b + 3*a^3*b^3)*cos(e*x + d))*sin(e*x + d))*log(2*a*b*cos(e*x + d) + a^2 + b^2 - (a^2 - b^2)*sin(e*x + d)) - 3*(20*a^6 + 12*a^4*b^2 - (15*a^5*b + 4*a^3*b^3 - 3*a*b^5)*cos(e*x + d)^3 - 3*(5*a^6 - 2*a^4*b^2 - 3*a^2*b^4)*cos(e*x + d)^2 + 6*(5*a^5*b + 3*a^3*b^3)*cos(e*x + d) - (20*a^6 + 12*a^4*b^2 - (5*a^6 - 12*a^4*b^2 - 9*a^2*b^4)*cos(e*x + d)^2 + 6*(5*a^5*b + 3*a^3*b^3)*cos(e*x + d))*sin(e*x + d))*log(-sin(e*x + d) + 1) - 2*(30*a^4*b^2 + 3*a^2*b^4 + 2*b^6 - (45*a^4*b^2 - 3*a^2*b^4 - 4*b^6)*cos(e*x + d)^2 - 3*(10*a^5*b - 9*a^3*b^3 - a*b^5)*cos(e*x + d))*sin(e*x + d))/(6*a^2*b^8*e*cos(e*x + d) + 4*a^3*b^7*e - (3*a^2*b^8 - b^10)*e*cos(e*x + d)^3 - 3*(a^3*b^7 - a*b^9)*e*cos(e*x + d)^2 - (6*a^2*b^8*e*cos(e*x + d) + 4*a^3*b^7*e - (a^3*b^7 - 3*a*b^9)*e*cos(e*x + d)^2)*sin(e*x + d))","B",0
395,1,255,0,1.068787," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^4,x, algorithm=""fricas"")","-\frac{24 \, {\left(b^{3} c - b c^{3}\right)} \cos\left(e x + d\right)^{4} + 32 \, {\left(3 \, a b^{2} c - a c^{3}\right)} \cos\left(e x + d\right)^{3} - 3 \, {\left(8 \, a^{4} + 24 \, a^{2} b^{2} + 3 \, b^{4} + 3 \, c^{4} + 6 \, {\left(4 \, a^{2} + b^{2}\right)} c^{2}\right)} e x + 48 \, {\left(3 \, a^{2} b c + b c^{3}\right)} \cos\left(e x + d\right)^{2} + 96 \, {\left(a^{3} c + a c^{3}\right)} \cos\left(e x + d\right) - {\left(96 \, a^{3} b + 64 \, a b^{3} + 96 \, a b c^{2} + 6 \, {\left(b^{4} - 6 \, b^{2} c^{2} + c^{4}\right)} \cos\left(e x + d\right)^{3} + 32 \, {\left(a b^{3} - 3 \, a b c^{2}\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(24 \, a^{2} b^{2} + 3 \, b^{4} - 5 \, c^{4} - 6 \, {\left(4 \, a^{2} - b^{2}\right)} c^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{24 \, e}"," ",0,"-1/24*(24*(b^3*c - b*c^3)*cos(e*x + d)^4 + 32*(3*a*b^2*c - a*c^3)*cos(e*x + d)^3 - 3*(8*a^4 + 24*a^2*b^2 + 3*b^4 + 3*c^4 + 6*(4*a^2 + b^2)*c^2)*e*x + 48*(3*a^2*b*c + b*c^3)*cos(e*x + d)^2 + 96*(a^3*c + a*c^3)*cos(e*x + d) - (96*a^3*b + 64*a*b^3 + 96*a*b*c^2 + 6*(b^4 - 6*b^2*c^2 + c^4)*cos(e*x + d)^3 + 32*(a*b^3 - 3*a*b*c^2)*cos(e*x + d)^2 + 3*(24*a^2*b^2 + 3*b^4 - 5*c^4 - 6*(4*a^2 - b^2)*c^2)*cos(e*x + d))*sin(e*x + d))/e","A",0
396,1,147,0,2.941732," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^3,x, algorithm=""fricas"")","-\frac{18 \, a b c \cos\left(e x + d\right)^{2} + 2 \, {\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{3} - 3 \, {\left(2 \, a^{3} + 3 \, a b^{2} + 3 \, a c^{2}\right)} e x + 6 \, {\left(3 \, a^{2} c + c^{3}\right)} \cos\left(e x + d\right) - {\left(18 \, a^{2} b + 4 \, b^{3} + 6 \, b c^{2} + 2 \, {\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{2} + 9 \, {\left(a b^{2} - a c^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{6 \, e}"," ",0,"-1/6*(18*a*b*c*cos(e*x + d)^2 + 2*(3*b^2*c - c^3)*cos(e*x + d)^3 - 3*(2*a^3 + 3*a*b^2 + 3*a*c^2)*e*x + 6*(3*a^2*c + c^3)*cos(e*x + d) - (18*a^2*b + 4*b^3 + 6*b*c^2 + 2*(b^3 - 3*b*c^2)*cos(e*x + d)^2 + 9*(a*b^2 - a*c^2)*cos(e*x + d))*sin(e*x + d))/e","A",0
397,1,73,0,1.516078," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^2,x, algorithm=""fricas"")","-\frac{2 \, b c \cos\left(e x + d\right)^{2} - {\left(2 \, a^{2} + b^{2} + c^{2}\right)} e x + 4 \, a c \cos\left(e x + d\right) - {\left(4 \, a b + {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{2 \, e}"," ",0,"-1/2*(2*b*c*cos(e*x + d)^2 - (2*a^2 + b^2 + c^2)*e*x + 4*a*c*cos(e*x + d) - (4*a*b + (b^2 - c^2)*cos(e*x + d))*sin(e*x + d))/e","A",0
398,1,26,0,0.886739," ","integrate(a+b*cos(e*x+d)+c*sin(e*x+d),x, algorithm=""fricas"")","\frac{a e x - c \cos\left(e x + d\right) + b \sin\left(e x + d\right)}{e}"," ",0,"(a*e*x - c*cos(e*x + d) + b*sin(e*x + d))/e","A",0
399,1,434,0,1.705318," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2} + c^{2}} \log\left(-\frac{a^{2} b^{2} - 2 \, b^{4} - c^{4} - {\left(a^{2} + 3 \, b^{2}\right)} c^{2} - {\left(2 \, a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \cos\left(e x + d\right)^{2} - 2 \, {\left(a b^{3} + a b c^{2}\right)} \cos\left(e x + d\right) - 2 \, {\left(a b^{2} c + a c^{3} - {\left(b c^{3} - {\left(2 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right) + 2 \, {\left(2 \, a b c \cos\left(e x + d\right)^{2} - a b c + {\left(b^{2} c + c^{3}\right)} \cos\left(e x + d\right) - {\left(b^{3} + b c^{2} + {\left(a b^{2} - a c^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}}}{2 \, a b \cos\left(e x + d\right) + {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(e x + d\right) + a c\right)} \sin\left(e x + d\right)}\right)}{2 \, {\left(a^{2} - b^{2} - c^{2}\right)} e}, \frac{\arctan\left(-\frac{{\left(a b \cos\left(e x + d\right) + a c \sin\left(e x + d\right) + b^{2} + c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}}}{{\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(e x + d\right) + {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(e x + d\right)}\right)}{\sqrt{a^{2} - b^{2} - c^{2}} e}\right]"," ",0,"[-1/2*sqrt(-a^2 + b^2 + c^2)*log(-(a^2*b^2 - 2*b^4 - c^4 - (a^2 + 3*b^2)*c^2 - (2*a^2*b^2 - b^4 - 2*a^2*c^2 + c^4)*cos(e*x + d)^2 - 2*(a*b^3 + a*b*c^2)*cos(e*x + d) - 2*(a*b^2*c + a*c^3 - (b*c^3 - (2*a^2*b - b^3)*c)*cos(e*x + d))*sin(e*x + d) + 2*(2*a*b*c*cos(e*x + d)^2 - a*b*c + (b^2*c + c^3)*cos(e*x + d) - (b^3 + b*c^2 + (a*b^2 - a*c^2)*cos(e*x + d))*sin(e*x + d))*sqrt(-a^2 + b^2 + c^2))/(2*a*b*cos(e*x + d) + (b^2 - c^2)*cos(e*x + d)^2 + a^2 + c^2 + 2*(b*c*cos(e*x + d) + a*c)*sin(e*x + d)))/((a^2 - b^2 - c^2)*e), arctan(-(a*b*cos(e*x + d) + a*c*sin(e*x + d) + b^2 + c^2)*sqrt(a^2 - b^2 - c^2)/((c^3 - (a^2 - b^2)*c)*cos(e*x + d) + (a^2*b - b^3 - b*c^2)*sin(e*x + d)))/(sqrt(a^2 - b^2 - c^2)*e)]","B",0
400,1,819,0,1.037782," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^2,x, algorithm=""fricas"")","\left[\frac{{\left(a b \cos\left(e x + d\right) + a c \sin\left(e x + d\right) + a^{2}\right)} \sqrt{-a^{2} + b^{2} + c^{2}} \log\left(\frac{a^{2} b^{2} - 2 \, b^{4} - c^{4} - {\left(a^{2} + 3 \, b^{2}\right)} c^{2} - {\left(2 \, a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \cos\left(e x + d\right)^{2} - 2 \, {\left(a b^{3} + a b c^{2}\right)} \cos\left(e x + d\right) - 2 \, {\left(a b^{2} c + a c^{3} - {\left(b c^{3} - {\left(2 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right) - 2 \, {\left(2 \, a b c \cos\left(e x + d\right)^{2} - a b c + {\left(b^{2} c + c^{3}\right)} \cos\left(e x + d\right) - {\left(b^{3} + b c^{2} + {\left(a b^{2} - a c^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}}}{2 \, a b \cos\left(e x + d\right) + {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(e x + d\right) + a c\right)} \sin\left(e x + d\right)}\right) - 2 \, {\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(e x + d\right) - 2 \, {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(e x + d\right)}{2 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5} + b c^{4} - 2 \, {\left(a^{2} b - b^{3}\right)} c^{2}\right)} e \cos\left(e x + d\right) + {\left(c^{5} - 2 \, {\left(a^{2} - b^{2}\right)} c^{3} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c\right)} e \sin\left(e x + d\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4} + a c^{4} - 2 \, {\left(a^{3} - a b^{2}\right)} c^{2}\right)} e\right)}}, \frac{{\left(a b \cos\left(e x + d\right) + a c \sin\left(e x + d\right) + a^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}} \arctan\left(-\frac{{\left(a b \cos\left(e x + d\right) + a c \sin\left(e x + d\right) + b^{2} + c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}}}{{\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(e x + d\right) + {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(e x + d\right)}\right) - {\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(e x + d\right) - {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(e x + d\right)}{{\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5} + b c^{4} - 2 \, {\left(a^{2} b - b^{3}\right)} c^{2}\right)} e \cos\left(e x + d\right) + {\left(c^{5} - 2 \, {\left(a^{2} - b^{2}\right)} c^{3} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c\right)} e \sin\left(e x + d\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4} + a c^{4} - 2 \, {\left(a^{3} - a b^{2}\right)} c^{2}\right)} e}\right]"," ",0,"[1/2*((a*b*cos(e*x + d) + a*c*sin(e*x + d) + a^2)*sqrt(-a^2 + b^2 + c^2)*log((a^2*b^2 - 2*b^4 - c^4 - (a^2 + 3*b^2)*c^2 - (2*a^2*b^2 - b^4 - 2*a^2*c^2 + c^4)*cos(e*x + d)^2 - 2*(a*b^3 + a*b*c^2)*cos(e*x + d) - 2*(a*b^2*c + a*c^3 - (b*c^3 - (2*a^2*b - b^3)*c)*cos(e*x + d))*sin(e*x + d) - 2*(2*a*b*c*cos(e*x + d)^2 - a*b*c + (b^2*c + c^3)*cos(e*x + d) - (b^3 + b*c^2 + (a*b^2 - a*c^2)*cos(e*x + d))*sin(e*x + d))*sqrt(-a^2 + b^2 + c^2))/(2*a*b*cos(e*x + d) + (b^2 - c^2)*cos(e*x + d)^2 + a^2 + c^2 + 2*(b*c*cos(e*x + d) + a*c)*sin(e*x + d))) - 2*(c^3 - (a^2 - b^2)*c)*cos(e*x + d) - 2*(a^2*b - b^3 - b*c^2)*sin(e*x + d))/((a^4*b - 2*a^2*b^3 + b^5 + b*c^4 - 2*(a^2*b - b^3)*c^2)*e*cos(e*x + d) + (c^5 - 2*(a^2 - b^2)*c^3 + (a^4 - 2*a^2*b^2 + b^4)*c)*e*sin(e*x + d) + (a^5 - 2*a^3*b^2 + a*b^4 + a*c^4 - 2*(a^3 - a*b^2)*c^2)*e), ((a*b*cos(e*x + d) + a*c*sin(e*x + d) + a^2)*sqrt(a^2 - b^2 - c^2)*arctan(-(a*b*cos(e*x + d) + a*c*sin(e*x + d) + b^2 + c^2)*sqrt(a^2 - b^2 - c^2)/((c^3 - (a^2 - b^2)*c)*cos(e*x + d) + (a^2*b - b^3 - b*c^2)*sin(e*x + d))) - (c^3 - (a^2 - b^2)*c)*cos(e*x + d) - (a^2*b - b^3 - b*c^2)*sin(e*x + d))/((a^4*b - 2*a^2*b^3 + b^5 + b*c^4 - 2*(a^2*b - b^3)*c^2)*e*cos(e*x + d) + (c^5 - 2*(a^2 - b^2)*c^3 + (a^4 - 2*a^2*b^2 + b^4)*c)*e*sin(e*x + d) + (a^5 - 2*a^3*b^2 + a*b^4 + a*c^4 - 2*(a^3 - a*b^2)*c^2)*e)]","B",0
401,1,1947,0,2.013690," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^3,x, algorithm=""fricas"")","\left[\frac{6 \, a b c^{3} - 12 \, {\left(a b c^{3} - {\left(a^{3} b - a b^{3}\right)} c\right)} \cos\left(e x + d\right)^{2} - {\left(2 \, a^{4} + a^{2} b^{2} + c^{4} + {\left(3 \, a^{2} + b^{2}\right)} c^{2} + {\left(2 \, a^{2} b^{2} + b^{4} - 2 \, a^{2} c^{2} - c^{4}\right)} \cos\left(e x + d\right)^{2} + 2 \, {\left(2 \, a^{3} b + a b^{3} + a b c^{2}\right)} \cos\left(e x + d\right) + 2 \, {\left(a c^{3} + {\left(2 \, a^{3} + a b^{2}\right)} c + {\left(b c^{3} + {\left(2 \, a^{2} b + b^{3}\right)} c\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}} \log\left(-\frac{a^{2} b^{2} - 2 \, b^{4} - c^{4} - {\left(a^{2} + 3 \, b^{2}\right)} c^{2} - {\left(2 \, a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \cos\left(e x + d\right)^{2} - 2 \, {\left(a b^{3} + a b c^{2}\right)} \cos\left(e x + d\right) - 2 \, {\left(a b^{2} c + a c^{3} - {\left(b c^{3} - {\left(2 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right) + 2 \, {\left(2 \, a b c \cos\left(e x + d\right)^{2} - a b c + {\left(b^{2} c + c^{3}\right)} \cos\left(e x + d\right) - {\left(b^{3} + b c^{2} + {\left(a b^{2} - a c^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}}}{2 \, a b \cos\left(e x + d\right) + {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(e x + d\right) + a c\right)} \sin\left(e x + d\right)}\right) - 6 \, {\left(a^{3} b - a b^{3}\right)} c + 2 \, {\left(c^{5} - {\left(5 \, a^{2} - 2 \, b^{2}\right)} c^{3} + {\left(4 \, a^{4} - 5 \, a^{2} b^{2} + b^{4}\right)} c\right)} \cos\left(e x + d\right) - 2 \, {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} + b^{5} + b c^{4} - {\left(5 \, a^{2} b - 2 \, b^{3}\right)} c^{2} + 3 \, {\left(a^{3} b^{2} - a b^{4} - a^{3} c^{2} + a c^{4}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{4 \, {\left({\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8} + c^{8} - {\left(3 \, a^{2} - 2 \, b^{2}\right)} c^{6} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} c^{4} - {\left(a^{6} - 3 \, a^{2} b^{4} + 2 \, b^{6}\right)} c^{2}\right)} e \cos\left(e x + d\right)^{2} + 2 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7} - a b c^{6} + 3 \, {\left(a^{3} b - a b^{3}\right)} c^{4} - 3 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} c^{2}\right)} e \cos\left(e x + d\right) + {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6} - c^{8} + {\left(2 \, a^{2} - 3 \, b^{2}\right)} c^{6} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} c^{4} - {\left(2 \, a^{6} - 3 \, a^{4} b^{2} + b^{6}\right)} c^{2}\right)} e - 2 \, {\left({\left(b c^{7} - 3 \, {\left(a^{2} b - b^{3}\right)} c^{5} + 3 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} c^{3} - {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} c\right)} e \cos\left(e x + d\right) + {\left(a c^{7} - 3 \, {\left(a^{3} - a b^{2}\right)} c^{5} + 3 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} c^{3} - {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} c\right)} e\right)} \sin\left(e x + d\right)\right)}}, \frac{3 \, a b c^{3} - 6 \, {\left(a b c^{3} - {\left(a^{3} b - a b^{3}\right)} c\right)} \cos\left(e x + d\right)^{2} + {\left(2 \, a^{4} + a^{2} b^{2} + c^{4} + {\left(3 \, a^{2} + b^{2}\right)} c^{2} + {\left(2 \, a^{2} b^{2} + b^{4} - 2 \, a^{2} c^{2} - c^{4}\right)} \cos\left(e x + d\right)^{2} + 2 \, {\left(2 \, a^{3} b + a b^{3} + a b c^{2}\right)} \cos\left(e x + d\right) + 2 \, {\left(a c^{3} + {\left(2 \, a^{3} + a b^{2}\right)} c + {\left(b c^{3} + {\left(2 \, a^{2} b + b^{3}\right)} c\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \sqrt{a^{2} - b^{2} - c^{2}} \arctan\left(-\frac{{\left(a b \cos\left(e x + d\right) + a c \sin\left(e x + d\right) + b^{2} + c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}}}{{\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(e x + d\right) + {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(e x + d\right)}\right) - 3 \, {\left(a^{3} b - a b^{3}\right)} c + {\left(c^{5} - {\left(5 \, a^{2} - 2 \, b^{2}\right)} c^{3} + {\left(4 \, a^{4} - 5 \, a^{2} b^{2} + b^{4}\right)} c\right)} \cos\left(e x + d\right) - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} + b^{5} + b c^{4} - {\left(5 \, a^{2} b - 2 \, b^{3}\right)} c^{2} + 3 \, {\left(a^{3} b^{2} - a b^{4} - a^{3} c^{2} + a c^{4}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{2 \, {\left({\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8} + c^{8} - {\left(3 \, a^{2} - 2 \, b^{2}\right)} c^{6} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} c^{4} - {\left(a^{6} - 3 \, a^{2} b^{4} + 2 \, b^{6}\right)} c^{2}\right)} e \cos\left(e x + d\right)^{2} + 2 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7} - a b c^{6} + 3 \, {\left(a^{3} b - a b^{3}\right)} c^{4} - 3 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} c^{2}\right)} e \cos\left(e x + d\right) + {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6} - c^{8} + {\left(2 \, a^{2} - 3 \, b^{2}\right)} c^{6} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} c^{4} - {\left(2 \, a^{6} - 3 \, a^{4} b^{2} + b^{6}\right)} c^{2}\right)} e - 2 \, {\left({\left(b c^{7} - 3 \, {\left(a^{2} b - b^{3}\right)} c^{5} + 3 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} c^{3} - {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} c\right)} e \cos\left(e x + d\right) + {\left(a c^{7} - 3 \, {\left(a^{3} - a b^{2}\right)} c^{5} + 3 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} c^{3} - {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} c\right)} e\right)} \sin\left(e x + d\right)\right)}}\right]"," ",0,"[1/4*(6*a*b*c^3 - 12*(a*b*c^3 - (a^3*b - a*b^3)*c)*cos(e*x + d)^2 - (2*a^4 + a^2*b^2 + c^4 + (3*a^2 + b^2)*c^2 + (2*a^2*b^2 + b^4 - 2*a^2*c^2 - c^4)*cos(e*x + d)^2 + 2*(2*a^3*b + a*b^3 + a*b*c^2)*cos(e*x + d) + 2*(a*c^3 + (2*a^3 + a*b^2)*c + (b*c^3 + (2*a^2*b + b^3)*c)*cos(e*x + d))*sin(e*x + d))*sqrt(-a^2 + b^2 + c^2)*log(-(a^2*b^2 - 2*b^4 - c^4 - (a^2 + 3*b^2)*c^2 - (2*a^2*b^2 - b^4 - 2*a^2*c^2 + c^4)*cos(e*x + d)^2 - 2*(a*b^3 + a*b*c^2)*cos(e*x + d) - 2*(a*b^2*c + a*c^3 - (b*c^3 - (2*a^2*b - b^3)*c)*cos(e*x + d))*sin(e*x + d) + 2*(2*a*b*c*cos(e*x + d)^2 - a*b*c + (b^2*c + c^3)*cos(e*x + d) - (b^3 + b*c^2 + (a*b^2 - a*c^2)*cos(e*x + d))*sin(e*x + d))*sqrt(-a^2 + b^2 + c^2))/(2*a*b*cos(e*x + d) + (b^2 - c^2)*cos(e*x + d)^2 + a^2 + c^2 + 2*(b*c*cos(e*x + d) + a*c)*sin(e*x + d))) - 6*(a^3*b - a*b^3)*c + 2*(c^5 - (5*a^2 - 2*b^2)*c^3 + (4*a^4 - 5*a^2*b^2 + b^4)*c)*cos(e*x + d) - 2*(4*a^4*b - 5*a^2*b^3 + b^5 + b*c^4 - (5*a^2*b - 2*b^3)*c^2 + 3*(a^3*b^2 - a*b^4 - a^3*c^2 + a*c^4)*cos(e*x + d))*sin(e*x + d))/((a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + c^8 - (3*a^2 - 2*b^2)*c^6 + 3*(a^4 - a^2*b^2)*c^4 - (a^6 - 3*a^2*b^4 + 2*b^6)*c^2)*e*cos(e*x + d)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7 - a*b*c^6 + 3*(a^3*b - a*b^3)*c^4 - 3*(a^5*b - 2*a^3*b^3 + a*b^5)*c^2)*e*cos(e*x + d) + (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 - c^8 + (2*a^2 - 3*b^2)*c^6 + 3*(a^2*b^2 - b^4)*c^4 - (2*a^6 - 3*a^4*b^2 + b^6)*c^2)*e - 2*((b*c^7 - 3*(a^2*b - b^3)*c^5 + 3*(a^4*b - 2*a^2*b^3 + b^5)*c^3 - (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*c)*e*cos(e*x + d) + (a*c^7 - 3*(a^3 - a*b^2)*c^5 + 3*(a^5 - 2*a^3*b^2 + a*b^4)*c^3 - (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*c)*e)*sin(e*x + d)), 1/2*(3*a*b*c^3 - 6*(a*b*c^3 - (a^3*b - a*b^3)*c)*cos(e*x + d)^2 + (2*a^4 + a^2*b^2 + c^4 + (3*a^2 + b^2)*c^2 + (2*a^2*b^2 + b^4 - 2*a^2*c^2 - c^4)*cos(e*x + d)^2 + 2*(2*a^3*b + a*b^3 + a*b*c^2)*cos(e*x + d) + 2*(a*c^3 + (2*a^3 + a*b^2)*c + (b*c^3 + (2*a^2*b + b^3)*c)*cos(e*x + d))*sin(e*x + d))*sqrt(a^2 - b^2 - c^2)*arctan(-(a*b*cos(e*x + d) + a*c*sin(e*x + d) + b^2 + c^2)*sqrt(a^2 - b^2 - c^2)/((c^3 - (a^2 - b^2)*c)*cos(e*x + d) + (a^2*b - b^3 - b*c^2)*sin(e*x + d))) - 3*(a^3*b - a*b^3)*c + (c^5 - (5*a^2 - 2*b^2)*c^3 + (4*a^4 - 5*a^2*b^2 + b^4)*c)*cos(e*x + d) - (4*a^4*b - 5*a^2*b^3 + b^5 + b*c^4 - (5*a^2*b - 2*b^3)*c^2 + 3*(a^3*b^2 - a*b^4 - a^3*c^2 + a*c^4)*cos(e*x + d))*sin(e*x + d))/((a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + c^8 - (3*a^2 - 2*b^2)*c^6 + 3*(a^4 - a^2*b^2)*c^4 - (a^6 - 3*a^2*b^4 + 2*b^6)*c^2)*e*cos(e*x + d)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7 - a*b*c^6 + 3*(a^3*b - a*b^3)*c^4 - 3*(a^5*b - 2*a^3*b^3 + a*b^5)*c^2)*e*cos(e*x + d) + (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 - c^8 + (2*a^2 - 3*b^2)*c^6 + 3*(a^2*b^2 - b^4)*c^4 - (2*a^6 - 3*a^4*b^2 + b^6)*c^2)*e - 2*((b*c^7 - 3*(a^2*b - b^3)*c^5 + 3*(a^4*b - 2*a^2*b^3 + b^5)*c^3 - (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*c)*e*cos(e*x + d) + (a*c^7 - 3*(a^3 - a*b^2)*c^5 + 3*(a^5 - 2*a^3*b^2 + a*b^4)*c^3 - (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*c)*e)*sin(e*x + d))]","B",0
402,1,4069,0,1.632356," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^4,x, algorithm=""fricas"")","\left[\frac{6 \, a b c^{5} + 12 \, {\left(4 \, a^{3} b + a b^{3}\right)} c^{3} + 2 \, {\left(4 \, c^{7} + {\left(7 \, a^{2} - 4 \, b^{2}\right)} c^{5} - {\left(11 \, a^{4} + 14 \, a^{2} b^{2} + 20 \, b^{4}\right)} c^{3} + 3 \, {\left(11 \, a^{4} b^{2} - 7 \, a^{2} b^{4} - 4 \, b^{6}\right)} c\right)} \cos\left(e x + d\right)^{3} - 12 \, {\left(a b c^{5} + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} c^{3} - {\left(9 \, a^{5} b - 8 \, a^{3} b^{3} - a b^{5}\right)} c\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} + 9 \, a^{2} c^{4} + {\left(2 \, a^{3} b^{3} + 3 \, a b^{5} - 9 \, a b c^{4} - 6 \, {\left(a^{3} b + a b^{3}\right)} c^{2}\right)} \cos\left(e x + d\right)^{3} + 9 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} + 3 \, {\left(2 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - 2 \, a^{4} c^{2} - 3 \, a^{2} c^{4}\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(2 \, a^{5} b + 3 \, a^{3} b^{3} + 3 \, a b c^{4} + {\left(5 \, a^{3} b + 3 \, a b^{3}\right)} c^{2}\right)} \cos\left(e x + d\right) + {\left(3 \, a c^{5} + {\left(11 \, a^{3} + 3 \, a b^{2}\right)} c^{3} - {\left(3 \, a c^{5} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{3} - 3 \, {\left(2 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(2 \, a^{5} + 3 \, a^{3} b^{2}\right)} c + 6 \, {\left(3 \, a^{2} b c^{3} + {\left(2 \, a^{4} b + 3 \, a^{2} b^{3}\right)} c\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}} \log\left(\frac{a^{2} b^{2} - 2 \, b^{4} - c^{4} - {\left(a^{2} + 3 \, b^{2}\right)} c^{2} - {\left(2 \, a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \cos\left(e x + d\right)^{2} - 2 \, {\left(a b^{3} + a b c^{2}\right)} \cos\left(e x + d\right) - 2 \, {\left(a b^{2} c + a c^{3} - {\left(b c^{3} - {\left(2 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right) - 2 \, {\left(2 \, a b c \cos\left(e x + d\right)^{2} - a b c + {\left(b^{2} c + c^{3}\right)} \cos\left(e x + d\right) - {\left(b^{3} + b c^{2} + {\left(a b^{2} - a c^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}}}{2 \, a b \cos\left(e x + d\right) + {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(e x + d\right) + a c\right)} \sin\left(e x + d\right)}\right) - 6 \, {\left(9 \, a^{5} b - 8 \, a^{3} b^{3} - a b^{5}\right)} c - 6 \, {\left(2 \, b^{2} c^{5} + 2 \, c^{7} + {\left(4 \, a^{4} - 7 \, a^{2} b^{2} - 2 \, b^{4}\right)} c^{3} - {\left(6 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} + 2 \, b^{6}\right)} c\right)} \cos\left(e x + d\right) - 2 \, {\left(18 \, a^{6} b - 23 \, a^{4} b^{3} + 7 \, a^{2} b^{5} - 2 \, b^{7} - 14 \, b^{3} c^{4} - 6 \, b c^{6} - {\left(12 \, a^{4} b - 7 \, a^{2} b^{3} + 10 \, b^{5}\right)} c^{2} + {\left(11 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - 4 \, b^{7} + 12 \, b c^{6} + {\left(21 \, a^{2} b + 20 \, b^{3}\right)} c^{4} - {\left(33 \, a^{4} b - 14 \, a^{2} b^{3} - 4 \, b^{5}\right)} c^{2}\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(9 \, a^{5} b^{2} - 8 \, a^{3} b^{4} - a b^{6} + a c^{6} + {\left(8 \, a^{3} + a b^{2}\right)} c^{4} - {\left(9 \, a^{5} + a b^{4}\right)} c^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{12 \, {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11} - 3 \, b c^{10} + {\left(12 \, a^{2} b - 11 \, b^{3}\right)} c^{8} - 2 \, {\left(9 \, a^{4} b - 16 \, a^{2} b^{3} + 7 \, b^{5}\right)} c^{6} + 6 \, {\left(2 \, a^{6} b - 5 \, a^{4} b^{3} + 4 \, a^{2} b^{5} - b^{7}\right)} c^{4} - {\left(3 \, a^{8} b - 8 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - b^{9}\right)} c^{2}\right)} e \cos\left(e x + d\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10} - a c^{10} + {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{8} - 2 \, {\left(3 \, a^{5} - 4 \, a^{3} b^{2} + a b^{4}\right)} c^{6} + 2 \, {\left(2 \, a^{7} - 3 \, a^{5} b^{2} + a b^{6}\right)} c^{4} - {\left(a^{9} - 6 \, a^{5} b^{4} + 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} c^{2}\right)} e \cos\left(e x + d\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9} + b c^{10} - {\left(3 \, a^{2} b - 4 \, b^{3}\right)} c^{8} + 2 \, {\left(a^{4} b - 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} c^{6} + 2 \, {\left(a^{6} b - 3 \, a^{2} b^{5} + 2 \, b^{7}\right)} c^{4} - {\left(3 \, a^{8} b - 8 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - b^{9}\right)} c^{2}\right)} e \cos\left(e x + d\right) + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8} + 3 \, a c^{10} - {\left(11 \, a^{3} - 12 \, a b^{2}\right)} c^{8} + 2 \, {\left(7 \, a^{5} - 16 \, a^{3} b^{2} + 9 \, a b^{4}\right)} c^{6} - 6 \, {\left(a^{7} - 4 \, a^{5} b^{2} + 5 \, a^{3} b^{4} - 2 \, a b^{6}\right)} c^{4} - {\left(a^{9} - 6 \, a^{5} b^{4} + 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} c^{2}\right)} e - {\left({\left(c^{11} - {\left(4 \, a^{2} - b^{2}\right)} c^{9} + 6 \, {\left(a^{4} - b^{4}\right)} c^{7} - 2 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} - 12 \, a^{2} b^{4} + 7 \, b^{6}\right)} c^{5} + {\left(a^{8} + 8 \, a^{6} b^{2} - 30 \, a^{4} b^{4} + 32 \, a^{2} b^{6} - 11 \, b^{8}\right)} c^{3} - 3 \, {\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} c\right)} e \cos\left(e x + d\right)^{2} - 6 \, {\left(a b c^{9} - 4 \, {\left(a^{3} b - a b^{3}\right)} c^{7} + 6 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} c^{5} - 4 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} c^{3} + {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} c\right)} e \cos\left(e x + d\right) - {\left(c^{11} - {\left(a^{2} - 4 \, b^{2}\right)} c^{9} - 6 \, {\left(a^{4} - b^{4}\right)} c^{7} + 2 \, {\left(7 \, a^{6} - 12 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + 2 \, b^{6}\right)} c^{5} - {\left(11 \, a^{8} - 32 \, a^{6} b^{2} + 30 \, a^{4} b^{4} - 8 \, a^{2} b^{6} - b^{8}\right)} c^{3} + 3 \, {\left(a^{10} - 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} - 4 \, a^{4} b^{6} + a^{2} b^{8}\right)} c\right)} e\right)} \sin\left(e x + d\right)\right)}}, \frac{3 \, a b c^{5} + 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} c^{3} + {\left(4 \, c^{7} + {\left(7 \, a^{2} - 4 \, b^{2}\right)} c^{5} - {\left(11 \, a^{4} + 14 \, a^{2} b^{2} + 20 \, b^{4}\right)} c^{3} + 3 \, {\left(11 \, a^{4} b^{2} - 7 \, a^{2} b^{4} - 4 \, b^{6}\right)} c\right)} \cos\left(e x + d\right)^{3} - 6 \, {\left(a b c^{5} + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} c^{3} - {\left(9 \, a^{5} b - 8 \, a^{3} b^{3} - a b^{5}\right)} c\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} + 9 \, a^{2} c^{4} + {\left(2 \, a^{3} b^{3} + 3 \, a b^{5} - 9 \, a b c^{4} - 6 \, {\left(a^{3} b + a b^{3}\right)} c^{2}\right)} \cos\left(e x + d\right)^{3} + 9 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} + 3 \, {\left(2 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - 2 \, a^{4} c^{2} - 3 \, a^{2} c^{4}\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(2 \, a^{5} b + 3 \, a^{3} b^{3} + 3 \, a b c^{4} + {\left(5 \, a^{3} b + 3 \, a b^{3}\right)} c^{2}\right)} \cos\left(e x + d\right) + {\left(3 \, a c^{5} + {\left(11 \, a^{3} + 3 \, a b^{2}\right)} c^{3} - {\left(3 \, a c^{5} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{3} - 3 \, {\left(2 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(2 \, a^{5} + 3 \, a^{3} b^{2}\right)} c + 6 \, {\left(3 \, a^{2} b c^{3} + {\left(2 \, a^{4} b + 3 \, a^{2} b^{3}\right)} c\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)\right)} \sqrt{a^{2} - b^{2} - c^{2}} \arctan\left(-\frac{{\left(a b \cos\left(e x + d\right) + a c \sin\left(e x + d\right) + b^{2} + c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}}}{{\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(e x + d\right) + {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(e x + d\right)}\right) - 3 \, {\left(9 \, a^{5} b - 8 \, a^{3} b^{3} - a b^{5}\right)} c - 3 \, {\left(2 \, b^{2} c^{5} + 2 \, c^{7} + {\left(4 \, a^{4} - 7 \, a^{2} b^{2} - 2 \, b^{4}\right)} c^{3} - {\left(6 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} + 2 \, b^{6}\right)} c\right)} \cos\left(e x + d\right) - {\left(18 \, a^{6} b - 23 \, a^{4} b^{3} + 7 \, a^{2} b^{5} - 2 \, b^{7} - 14 \, b^{3} c^{4} - 6 \, b c^{6} - {\left(12 \, a^{4} b - 7 \, a^{2} b^{3} + 10 \, b^{5}\right)} c^{2} + {\left(11 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - 4 \, b^{7} + 12 \, b c^{6} + {\left(21 \, a^{2} b + 20 \, b^{3}\right)} c^{4} - {\left(33 \, a^{4} b - 14 \, a^{2} b^{3} - 4 \, b^{5}\right)} c^{2}\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(9 \, a^{5} b^{2} - 8 \, a^{3} b^{4} - a b^{6} + a c^{6} + {\left(8 \, a^{3} + a b^{2}\right)} c^{4} - {\left(9 \, a^{5} + a b^{4}\right)} c^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{6 \, {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11} - 3 \, b c^{10} + {\left(12 \, a^{2} b - 11 \, b^{3}\right)} c^{8} - 2 \, {\left(9 \, a^{4} b - 16 \, a^{2} b^{3} + 7 \, b^{5}\right)} c^{6} + 6 \, {\left(2 \, a^{6} b - 5 \, a^{4} b^{3} + 4 \, a^{2} b^{5} - b^{7}\right)} c^{4} - {\left(3 \, a^{8} b - 8 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - b^{9}\right)} c^{2}\right)} e \cos\left(e x + d\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10} - a c^{10} + {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{8} - 2 \, {\left(3 \, a^{5} - 4 \, a^{3} b^{2} + a b^{4}\right)} c^{6} + 2 \, {\left(2 \, a^{7} - 3 \, a^{5} b^{2} + a b^{6}\right)} c^{4} - {\left(a^{9} - 6 \, a^{5} b^{4} + 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} c^{2}\right)} e \cos\left(e x + d\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9} + b c^{10} - {\left(3 \, a^{2} b - 4 \, b^{3}\right)} c^{8} + 2 \, {\left(a^{4} b - 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} c^{6} + 2 \, {\left(a^{6} b - 3 \, a^{2} b^{5} + 2 \, b^{7}\right)} c^{4} - {\left(3 \, a^{8} b - 8 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - b^{9}\right)} c^{2}\right)} e \cos\left(e x + d\right) + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8} + 3 \, a c^{10} - {\left(11 \, a^{3} - 12 \, a b^{2}\right)} c^{8} + 2 \, {\left(7 \, a^{5} - 16 \, a^{3} b^{2} + 9 \, a b^{4}\right)} c^{6} - 6 \, {\left(a^{7} - 4 \, a^{5} b^{2} + 5 \, a^{3} b^{4} - 2 \, a b^{6}\right)} c^{4} - {\left(a^{9} - 6 \, a^{5} b^{4} + 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} c^{2}\right)} e - {\left({\left(c^{11} - {\left(4 \, a^{2} - b^{2}\right)} c^{9} + 6 \, {\left(a^{4} - b^{4}\right)} c^{7} - 2 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} - 12 \, a^{2} b^{4} + 7 \, b^{6}\right)} c^{5} + {\left(a^{8} + 8 \, a^{6} b^{2} - 30 \, a^{4} b^{4} + 32 \, a^{2} b^{6} - 11 \, b^{8}\right)} c^{3} - 3 \, {\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} c\right)} e \cos\left(e x + d\right)^{2} - 6 \, {\left(a b c^{9} - 4 \, {\left(a^{3} b - a b^{3}\right)} c^{7} + 6 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} c^{5} - 4 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} c^{3} + {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} c\right)} e \cos\left(e x + d\right) - {\left(c^{11} - {\left(a^{2} - 4 \, b^{2}\right)} c^{9} - 6 \, {\left(a^{4} - b^{4}\right)} c^{7} + 2 \, {\left(7 \, a^{6} - 12 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + 2 \, b^{6}\right)} c^{5} - {\left(11 \, a^{8} - 32 \, a^{6} b^{2} + 30 \, a^{4} b^{4} - 8 \, a^{2} b^{6} - b^{8}\right)} c^{3} + 3 \, {\left(a^{10} - 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} - 4 \, a^{4} b^{6} + a^{2} b^{8}\right)} c\right)} e\right)} \sin\left(e x + d\right)\right)}}\right]"," ",0,"[1/12*(6*a*b*c^5 + 12*(4*a^3*b + a*b^3)*c^3 + 2*(4*c^7 + (7*a^2 - 4*b^2)*c^5 - (11*a^4 + 14*a^2*b^2 + 20*b^4)*c^3 + 3*(11*a^4*b^2 - 7*a^2*b^4 - 4*b^6)*c)*cos(e*x + d)^3 - 12*(a*b*c^5 + 2*(4*a^3*b + a*b^3)*c^3 - (9*a^5*b - 8*a^3*b^3 - a*b^5)*c)*cos(e*x + d)^2 + 3*(2*a^6 + 3*a^4*b^2 + 9*a^2*c^4 + (2*a^3*b^3 + 3*a*b^5 - 9*a*b*c^4 - 6*(a^3*b + a*b^3)*c^2)*cos(e*x + d)^3 + 9*(a^4 + a^2*b^2)*c^2 + 3*(2*a^4*b^2 + 3*a^2*b^4 - 2*a^4*c^2 - 3*a^2*c^4)*cos(e*x + d)^2 + 3*(2*a^5*b + 3*a^3*b^3 + 3*a*b*c^4 + (5*a^3*b + 3*a*b^3)*c^2)*cos(e*x + d) + (3*a*c^5 + (11*a^3 + 3*a*b^2)*c^3 - (3*a*c^5 + 2*(a^3 - 3*a*b^2)*c^3 - 3*(2*a^3*b^2 + 3*a*b^4)*c)*cos(e*x + d)^2 + 3*(2*a^5 + 3*a^3*b^2)*c + 6*(3*a^2*b*c^3 + (2*a^4*b + 3*a^2*b^3)*c)*cos(e*x + d))*sin(e*x + d))*sqrt(-a^2 + b^2 + c^2)*log((a^2*b^2 - 2*b^4 - c^4 - (a^2 + 3*b^2)*c^2 - (2*a^2*b^2 - b^4 - 2*a^2*c^2 + c^4)*cos(e*x + d)^2 - 2*(a*b^3 + a*b*c^2)*cos(e*x + d) - 2*(a*b^2*c + a*c^3 - (b*c^3 - (2*a^2*b - b^3)*c)*cos(e*x + d))*sin(e*x + d) - 2*(2*a*b*c*cos(e*x + d)^2 - a*b*c + (b^2*c + c^3)*cos(e*x + d) - (b^3 + b*c^2 + (a*b^2 - a*c^2)*cos(e*x + d))*sin(e*x + d))*sqrt(-a^2 + b^2 + c^2))/(2*a*b*cos(e*x + d) + (b^2 - c^2)*cos(e*x + d)^2 + a^2 + c^2 + 2*(b*c*cos(e*x + d) + a*c)*sin(e*x + d))) - 6*(9*a^5*b - 8*a^3*b^3 - a*b^5)*c - 6*(2*b^2*c^5 + 2*c^7 + (4*a^4 - 7*a^2*b^2 - 2*b^4)*c^3 - (6*a^6 - 15*a^4*b^2 + 7*a^2*b^4 + 2*b^6)*c)*cos(e*x + d) - 2*(18*a^6*b - 23*a^4*b^3 + 7*a^2*b^5 - 2*b^7 - 14*b^3*c^4 - 6*b*c^6 - (12*a^4*b - 7*a^2*b^3 + 10*b^5)*c^2 + (11*a^4*b^3 - 7*a^2*b^5 - 4*b^7 + 12*b*c^6 + (21*a^2*b + 20*b^3)*c^4 - (33*a^4*b - 14*a^2*b^3 - 4*b^5)*c^2)*cos(e*x + d)^2 + 3*(9*a^5*b^2 - 8*a^3*b^4 - a*b^6 + a*c^6 + (8*a^3 + a*b^2)*c^4 - (9*a^5 + a*b^4)*c^2)*cos(e*x + d))*sin(e*x + d))/((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11 - 3*b*c^10 + (12*a^2*b - 11*b^3)*c^8 - 2*(9*a^4*b - 16*a^2*b^3 + 7*b^5)*c^6 + 6*(2*a^6*b - 5*a^4*b^3 + 4*a^2*b^5 - b^7)*c^4 - (3*a^8*b - 8*a^6*b^3 + 6*a^4*b^5 - b^9)*c^2)*e*cos(e*x + d)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10 - a*c^10 + (4*a^3 - 3*a*b^2)*c^8 - 2*(3*a^5 - 4*a^3*b^2 + a*b^4)*c^6 + 2*(2*a^7 - 3*a^5*b^2 + a*b^6)*c^4 - (a^9 - 6*a^5*b^4 + 8*a^3*b^6 - 3*a*b^8)*c^2)*e*cos(e*x + d)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9 + b*c^10 - (3*a^2*b - 4*b^3)*c^8 + 2*(a^4*b - 4*a^2*b^3 + 3*b^5)*c^6 + 2*(a^6*b - 3*a^2*b^5 + 2*b^7)*c^4 - (3*a^8*b - 8*a^6*b^3 + 6*a^4*b^5 - b^9)*c^2)*e*cos(e*x + d) + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8 + 3*a*c^10 - (11*a^3 - 12*a*b^2)*c^8 + 2*(7*a^5 - 16*a^3*b^2 + 9*a*b^4)*c^6 - 6*(a^7 - 4*a^5*b^2 + 5*a^3*b^4 - 2*a*b^6)*c^4 - (a^9 - 6*a^5*b^4 + 8*a^3*b^6 - 3*a*b^8)*c^2)*e - ((c^11 - (4*a^2 - b^2)*c^9 + 6*(a^4 - b^4)*c^7 - 2*(2*a^6 + 3*a^4*b^2 - 12*a^2*b^4 + 7*b^6)*c^5 + (a^8 + 8*a^6*b^2 - 30*a^4*b^4 + 32*a^2*b^6 - 11*b^8)*c^3 - 3*(a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*c)*e*cos(e*x + d)^2 - 6*(a*b*c^9 - 4*(a^3*b - a*b^3)*c^7 + 6*(a^5*b - 2*a^3*b^3 + a*b^5)*c^5 - 4*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*c^3 + (a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*c)*e*cos(e*x + d) - (c^11 - (a^2 - 4*b^2)*c^9 - 6*(a^4 - b^4)*c^7 + 2*(7*a^6 - 12*a^4*b^2 + 3*a^2*b^4 + 2*b^6)*c^5 - (11*a^8 - 32*a^6*b^2 + 30*a^4*b^4 - 8*a^2*b^6 - b^8)*c^3 + 3*(a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8)*c)*e)*sin(e*x + d)), 1/6*(3*a*b*c^5 + 6*(4*a^3*b + a*b^3)*c^3 + (4*c^7 + (7*a^2 - 4*b^2)*c^5 - (11*a^4 + 14*a^2*b^2 + 20*b^4)*c^3 + 3*(11*a^4*b^2 - 7*a^2*b^4 - 4*b^6)*c)*cos(e*x + d)^3 - 6*(a*b*c^5 + 2*(4*a^3*b + a*b^3)*c^3 - (9*a^5*b - 8*a^3*b^3 - a*b^5)*c)*cos(e*x + d)^2 + 3*(2*a^6 + 3*a^4*b^2 + 9*a^2*c^4 + (2*a^3*b^3 + 3*a*b^5 - 9*a*b*c^4 - 6*(a^3*b + a*b^3)*c^2)*cos(e*x + d)^3 + 9*(a^4 + a^2*b^2)*c^2 + 3*(2*a^4*b^2 + 3*a^2*b^4 - 2*a^4*c^2 - 3*a^2*c^4)*cos(e*x + d)^2 + 3*(2*a^5*b + 3*a^3*b^3 + 3*a*b*c^4 + (5*a^3*b + 3*a*b^3)*c^2)*cos(e*x + d) + (3*a*c^5 + (11*a^3 + 3*a*b^2)*c^3 - (3*a*c^5 + 2*(a^3 - 3*a*b^2)*c^3 - 3*(2*a^3*b^2 + 3*a*b^4)*c)*cos(e*x + d)^2 + 3*(2*a^5 + 3*a^3*b^2)*c + 6*(3*a^2*b*c^3 + (2*a^4*b + 3*a^2*b^3)*c)*cos(e*x + d))*sin(e*x + d))*sqrt(a^2 - b^2 - c^2)*arctan(-(a*b*cos(e*x + d) + a*c*sin(e*x + d) + b^2 + c^2)*sqrt(a^2 - b^2 - c^2)/((c^3 - (a^2 - b^2)*c)*cos(e*x + d) + (a^2*b - b^3 - b*c^2)*sin(e*x + d))) - 3*(9*a^5*b - 8*a^3*b^3 - a*b^5)*c - 3*(2*b^2*c^5 + 2*c^7 + (4*a^4 - 7*a^2*b^2 - 2*b^4)*c^3 - (6*a^6 - 15*a^4*b^2 + 7*a^2*b^4 + 2*b^6)*c)*cos(e*x + d) - (18*a^6*b - 23*a^4*b^3 + 7*a^2*b^5 - 2*b^7 - 14*b^3*c^4 - 6*b*c^6 - (12*a^4*b - 7*a^2*b^3 + 10*b^5)*c^2 + (11*a^4*b^3 - 7*a^2*b^5 - 4*b^7 + 12*b*c^6 + (21*a^2*b + 20*b^3)*c^4 - (33*a^4*b - 14*a^2*b^3 - 4*b^5)*c^2)*cos(e*x + d)^2 + 3*(9*a^5*b^2 - 8*a^3*b^4 - a*b^6 + a*c^6 + (8*a^3 + a*b^2)*c^4 - (9*a^5 + a*b^4)*c^2)*cos(e*x + d))*sin(e*x + d))/((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11 - 3*b*c^10 + (12*a^2*b - 11*b^3)*c^8 - 2*(9*a^4*b - 16*a^2*b^3 + 7*b^5)*c^6 + 6*(2*a^6*b - 5*a^4*b^3 + 4*a^2*b^5 - b^7)*c^4 - (3*a^8*b - 8*a^6*b^3 + 6*a^4*b^5 - b^9)*c^2)*e*cos(e*x + d)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10 - a*c^10 + (4*a^3 - 3*a*b^2)*c^8 - 2*(3*a^5 - 4*a^3*b^2 + a*b^4)*c^6 + 2*(2*a^7 - 3*a^5*b^2 + a*b^6)*c^4 - (a^9 - 6*a^5*b^4 + 8*a^3*b^6 - 3*a*b^8)*c^2)*e*cos(e*x + d)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9 + b*c^10 - (3*a^2*b - 4*b^3)*c^8 + 2*(a^4*b - 4*a^2*b^3 + 3*b^5)*c^6 + 2*(a^6*b - 3*a^2*b^5 + 2*b^7)*c^4 - (3*a^8*b - 8*a^6*b^3 + 6*a^4*b^5 - b^9)*c^2)*e*cos(e*x + d) + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8 + 3*a*c^10 - (11*a^3 - 12*a*b^2)*c^8 + 2*(7*a^5 - 16*a^3*b^2 + 9*a*b^4)*c^6 - 6*(a^7 - 4*a^5*b^2 + 5*a^3*b^4 - 2*a*b^6)*c^4 - (a^9 - 6*a^5*b^4 + 8*a^3*b^6 - 3*a*b^8)*c^2)*e - ((c^11 - (4*a^2 - b^2)*c^9 + 6*(a^4 - b^4)*c^7 - 2*(2*a^6 + 3*a^4*b^2 - 12*a^2*b^4 + 7*b^6)*c^5 + (a^8 + 8*a^6*b^2 - 30*a^4*b^4 + 32*a^2*b^6 - 11*b^8)*c^3 - 3*(a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*c)*e*cos(e*x + d)^2 - 6*(a*b*c^9 - 4*(a^3*b - a*b^3)*c^7 + 6*(a^5*b - 2*a^3*b^3 + a*b^5)*c^5 - 4*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*c^3 + (a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*c)*e*cos(e*x + d) - (c^11 - (a^2 - 4*b^2)*c^9 - 6*(a^4 - b^4)*c^7 + 2*(7*a^6 - 12*a^4*b^2 + 3*a^2*b^4 + 2*b^6)*c^5 - (11*a^8 - 32*a^6*b^2 + 30*a^4*b^4 - 8*a^2*b^6 - b^8)*c^3 + 3*(a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8)*c)*e)*sin(e*x + d))]","B",0
403,0,0,0,1.183765," ","integrate((2+3*cos(e*x+d)+5*sin(e*x+d))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(16 \, \cos\left(e x + d\right)^{2} - 10 \, {\left(3 \, \cos\left(e x + d\right) + 2\right)} \sin\left(e x + d\right) - 12 \, \cos\left(e x + d\right) - 29\right)} \sqrt{3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2}, x\right)"," ",0,"integral(-(16*cos(e*x + d)^2 - 10*(3*cos(e*x + d) + 2)*sin(e*x + d) - 12*cos(e*x + d) - 29)*sqrt(3*cos(e*x + d) + 5*sin(e*x + d) + 2), x)","F",0
404,0,0,0,0.868448," ","integrate((2+3*cos(e*x+d)+5*sin(e*x+d))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((3*cos(e*x + d) + 5*sin(e*x + d) + 2)^(3/2), x)","F",0
405,0,0,0,0.520687," ","integrate((2+3*cos(e*x+d)+5*sin(e*x+d))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2}, x\right)"," ",0,"integral(sqrt(3*cos(e*x + d) + 5*sin(e*x + d) + 2), x)","F",0
406,0,0,0,2.261160," ","integrate(1/(2+3*cos(e*x+d)+5*sin(e*x+d))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2}}, x\right)"," ",0,"integral(1/sqrt(3*cos(e*x + d) + 5*sin(e*x + d) + 2), x)","F",0
407,0,0,0,1.602140," ","integrate(1/(2+3*cos(e*x+d)+5*sin(e*x+d))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2}}{16 \, \cos\left(e x + d\right)^{2} - 10 \, {\left(3 \, \cos\left(e x + d\right) + 2\right)} \sin\left(e x + d\right) - 12 \, \cos\left(e x + d\right) - 29}, x\right)"," ",0,"integral(-sqrt(3*cos(e*x + d) + 5*sin(e*x + d) + 2)/(16*cos(e*x + d)^2 - 10*(3*cos(e*x + d) + 2)*sin(e*x + d) - 12*cos(e*x + d) - 29), x)","F",0
408,0,0,0,2.881851," ","integrate(1/(2+3*cos(e*x+d)+5*sin(e*x+d))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2}}{198 \, \cos\left(e x + d\right)^{3} + 96 \, \cos\left(e x + d\right)^{2} - 5 \, {\left(2 \, \cos\left(e x + d\right)^{2} + 36 \, \cos\left(e x + d\right) + 37\right)} \sin\left(e x + d\right) - 261 \, \cos\left(e x + d\right) - 158}, x\right)"," ",0,"integral(-sqrt(3*cos(e*x + d) + 5*sin(e*x + d) + 2)/(198*cos(e*x + d)^3 + 96*cos(e*x + d)^2 - 5*(2*cos(e*x + d)^2 + 36*cos(e*x + d) + 37)*sin(e*x + d) - 261*cos(e*x + d) - 158), x)","F",0
409,0,0,0,0.835186," ","integrate(1/(2+3*cos(e*x+d)+5*sin(e*x+d))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2}}{644 \, \cos\left(e x + d\right)^{4} + 1584 \, \cos\left(e x + d\right)^{3} + 284 \, \cos\left(e x + d\right)^{2} + 20 \, {\left(48 \, \cos\left(e x + d\right)^{3} - 4 \, \cos\left(e x + d\right)^{2} - 111 \, \cos\left(e x + d\right) - 58\right)} \sin\left(e x + d\right) - 1896 \, \cos\left(e x + d\right) - 1241}, x\right)"," ",0,"integral(-sqrt(3*cos(e*x + d) + 5*sin(e*x + d) + 2)/(644*cos(e*x + d)^4 + 1584*cos(e*x + d)^3 + 284*cos(e*x + d)^2 + 20*(48*cos(e*x + d)^3 - 4*cos(e*x + d)^2 - 111*cos(e*x + d) - 58)*sin(e*x + d) - 1896*cos(e*x + d) - 1241), x)","F",0
410,0,0,0,1.880345," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(2 \, a b \cos\left(e x + d\right) + {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(e x + d\right) + a c\right)} \sin\left(e x + d\right)\right)} \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a}, x\right)"," ",0,"integral((2*a*b*cos(e*x + d) + (b^2 - c^2)*cos(e*x + d)^2 + a^2 + c^2 + 2*(b*c*cos(e*x + d) + a*c)*sin(e*x + d))*sqrt(b*cos(e*x + d) + c*sin(e*x + d) + a), x)","F",0
411,0,0,0,0.855856," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((b*cos(e*x + d) + c*sin(e*x + d) + a)^(3/2), x)","F",0
412,0,0,0,0.750947," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a}, x\right)"," ",0,"integral(sqrt(b*cos(e*x + d) + c*sin(e*x + d) + a), x)","F",0
413,0,0,0,3.145125," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a}}, x\right)"," ",0,"integral(1/sqrt(b*cos(e*x + d) + c*sin(e*x + d) + a), x)","F",0
414,0,0,0,0.742492," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a}}{2 \, a b \cos\left(e x + d\right) + {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(e x + d\right) + a c\right)} \sin\left(e x + d\right)}, x\right)"," ",0,"integral(sqrt(b*cos(e*x + d) + c*sin(e*x + d) + a)/(2*a*b*cos(e*x + d) + (b^2 - c^2)*cos(e*x + d)^2 + a^2 + c^2 + 2*(b*c*cos(e*x + d) + a*c)*sin(e*x + d)), x)","F",0
415,0,0,0,2.964675," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a}}{{\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{3} + a^{3} + 3 \, a c^{2} + 3 \, {\left(a b^{2} - a c^{2}\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(a^{2} b + b c^{2}\right)} \cos\left(e x + d\right) + {\left(6 \, a b c \cos\left(e x + d\right) + 3 \, a^{2} c + c^{3} + {\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right)}, x\right)"," ",0,"integral(sqrt(b*cos(e*x + d) + c*sin(e*x + d) + a)/((b^3 - 3*b*c^2)*cos(e*x + d)^3 + a^3 + 3*a*c^2 + 3*(a*b^2 - a*c^2)*cos(e*x + d)^2 + 3*(a^2*b + b*c^2)*cos(e*x + d) + (6*a*b*c*cos(e*x + d) + 3*a^2*c + c^3 + (3*b^2*c - c^3)*cos(e*x + d)^2)*sin(e*x + d)), x)","F",0
416,0,0,0,1.123732," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a}}{{\left(b^{4} - 6 \, b^{2} c^{2} + c^{4}\right)} \cos\left(e x + d\right)^{4} + a^{4} + 6 \, a^{2} c^{2} + c^{4} + 4 \, {\left(a b^{3} - 3 \, a b c^{2}\right)} \cos\left(e x + d\right)^{3} + 2 \, {\left(3 \, a^{2} b^{2} - c^{4} - 3 \, {\left(a^{2} - b^{2}\right)} c^{2}\right)} \cos\left(e x + d\right)^{2} + 4 \, {\left(a^{3} b + 3 \, a b c^{2}\right)} \cos\left(e x + d\right) + 4 \, {\left(a^{3} c + a c^{3} + {\left(b^{3} c - b c^{3}\right)} \cos\left(e x + d\right)^{3} + {\left(3 \, a b^{2} c - a c^{3}\right)} \cos\left(e x + d\right)^{2} + {\left(3 \, a^{2} b c + b c^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}, x\right)"," ",0,"integral(sqrt(b*cos(e*x + d) + c*sin(e*x + d) + a)/((b^4 - 6*b^2*c^2 + c^4)*cos(e*x + d)^4 + a^4 + 6*a^2*c^2 + c^4 + 4*(a*b^3 - 3*a*b*c^2)*cos(e*x + d)^3 + 2*(3*a^2*b^2 - c^4 - 3*(a^2 - b^2)*c^2)*cos(e*x + d)^2 + 4*(a^3*b + 3*a*b*c^2)*cos(e*x + d) + 4*(a^3*c + a*c^3 + (b^3*c - b*c^3)*cos(e*x + d)^3 + (3*a*b^2*c - a*c^3)*cos(e*x + d)^2 + (3*a^2*b*c + b*c^3)*cos(e*x + d))*sin(e*x + d)), x)","F",0
417,1,101,0,1.085741," ","integrate((5+4*cos(e*x+d)+3*sin(e*x+d))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(237 \, \cos\left(e x + d\right)^{3} + 931 \, \cos\left(e x + d\right)^{2} + 9 \, {\left(\cos\left(e x + d\right)^{2} - 62 \, \cos\left(e x + d\right) - 344\right)} \sin\left(e x + d\right) + 1166 \, \cos\left(e x + d\right) + 472\right)} \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5}}{15 \, {\left(3 \, e \cos\left(e x + d\right) + e \sin\left(e x + d\right) + 3 \, e\right)}}"," ",0,"-2/15*(237*cos(e*x + d)^3 + 931*cos(e*x + d)^2 + 9*(cos(e*x + d)^2 - 62*cos(e*x + d) - 344)*sin(e*x + d) + 1166*cos(e*x + d) + 472)*sqrt(4*cos(e*x + d) + 3*sin(e*x + d) + 5)/(3*e*cos(e*x + d) + e*sin(e*x + d) + 3*e)","A",0
418,1,81,0,0.918381," ","integrate((5+4*cos(e*x+d)+3*sin(e*x+d))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(13 \, \cos\left(e x + d\right)^{2} - 9 \, {\left(\cos\left(e x + d\right) + 8\right)} \sin\left(e x + d\right) + 29 \, \cos\left(e x + d\right) + 16\right)} \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5}}{3 \, {\left(3 \, e \cos\left(e x + d\right) + e \sin\left(e x + d\right) + 3 \, e\right)}}"," ",0,"-2/3*(13*cos(e*x + d)^2 - 9*(cos(e*x + d) + 8)*sin(e*x + d) + 29*cos(e*x + d) + 16)*sqrt(4*cos(e*x + d) + 3*sin(e*x + d) + 5)/(3*e*cos(e*x + d) + e*sin(e*x + d) + 3*e)","A",0
419,1,61,0,1.838601," ","integrate((5+4*cos(e*x+d)+3*sin(e*x+d))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5} {\left(\cos\left(e x + d\right) - 3 \, \sin\left(e x + d\right) + 1\right)}}{3 \, e \cos\left(e x + d\right) + e \sin\left(e x + d\right) + 3 \, e}"," ",0,"-2*sqrt(4*cos(e*x + d) + 3*sin(e*x + d) + 5)*(cos(e*x + d) - 3*sin(e*x + d) + 1)/(3*e*cos(e*x + d) + e*sin(e*x + d) + 3*e)","A",0
420,1,147,0,1.170936," ","integrate(1/(5+4*cos(e*x+d)+3*sin(e*x+d))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{5} \sqrt{2} \log\left(-\frac{9 \, \cos\left(e x + d\right)^{2} + {\left(13 \, \cos\left(e x + d\right) - 6\right)} \sin\left(e x + d\right) + 2 \, {\left(\sqrt{5} \sqrt{2} \cos\left(e x + d\right) - 3 \, \sqrt{5} \sqrt{2} \sin\left(e x + d\right) + \sqrt{5} \sqrt{2}\right)} \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5} - 33 \, \cos\left(e x + d\right) - 42}{9 \, \cos\left(e x + d\right)^{2} + {\left(13 \, \cos\left(e x + d\right) + 14\right)} \sin\left(e x + d\right) + 27 \, \cos\left(e x + d\right) + 18}\right)}{10 \, e}"," ",0,"1/10*sqrt(5)*sqrt(2)*log(-(9*cos(e*x + d)^2 + (13*cos(e*x + d) - 6)*sin(e*x + d) + 2*(sqrt(5)*sqrt(2)*cos(e*x + d) - 3*sqrt(5)*sqrt(2)*sin(e*x + d) + sqrt(5)*sqrt(2))*sqrt(4*cos(e*x + d) + 3*sin(e*x + d) + 5) - 33*cos(e*x + d) - 42)/(9*cos(e*x + d)^2 + (13*cos(e*x + d) + 14)*sin(e*x + d) + 27*cos(e*x + d) + 18))/e","B",0
421,1,268,0,0.926040," ","integrate(1/(5+4*cos(e*x+d)+3*sin(e*x+d))^(3/2),x, algorithm=""fricas"")","\frac{{\left(9 \, \sqrt{10} \cos\left(e x + d\right)^{2} + {\left(13 \, \sqrt{10} \cos\left(e x + d\right) + 14 \, \sqrt{10}\right)} \sin\left(e x + d\right) + 27 \, \sqrt{10} \cos\left(e x + d\right) + 18 \, \sqrt{10}\right)} \log\left(-\frac{9 \, \cos\left(e x + d\right)^{2} + {\left(13 \, \cos\left(e x + d\right) - 6\right)} \sin\left(e x + d\right) + 2 \, {\left(\sqrt{10} \cos\left(e x + d\right) - 3 \, \sqrt{10} \sin\left(e x + d\right) + \sqrt{10}\right)} \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5} - 33 \, \cos\left(e x + d\right) - 42}{9 \, \cos\left(e x + d\right)^{2} + {\left(13 \, \cos\left(e x + d\right) + 14\right)} \sin\left(e x + d\right) + 27 \, \cos\left(e x + d\right) + 18}\right) - 20 \, \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5} {\left(\cos\left(e x + d\right) - 3 \, \sin\left(e x + d\right) + 1\right)}}{200 \, {\left(9 \, e \cos\left(e x + d\right)^{2} + 27 \, e \cos\left(e x + d\right) + {\left(13 \, e \cos\left(e x + d\right) + 14 \, e\right)} \sin\left(e x + d\right) + 18 \, e\right)}}"," ",0,"1/200*((9*sqrt(10)*cos(e*x + d)^2 + (13*sqrt(10)*cos(e*x + d) + 14*sqrt(10))*sin(e*x + d) + 27*sqrt(10)*cos(e*x + d) + 18*sqrt(10))*log(-(9*cos(e*x + d)^2 + (13*cos(e*x + d) - 6)*sin(e*x + d) + 2*(sqrt(10)*cos(e*x + d) - 3*sqrt(10)*sin(e*x + d) + sqrt(10))*sqrt(4*cos(e*x + d) + 3*sin(e*x + d) + 5) - 33*cos(e*x + d) - 42)/(9*cos(e*x + d)^2 + (13*cos(e*x + d) + 14)*sin(e*x + d) + 27*cos(e*x + d) + 18)) - 20*sqrt(4*cos(e*x + d) + 3*sin(e*x + d) + 5)*(cos(e*x + d) - 3*sin(e*x + d) + 1))/(9*e*cos(e*x + d)^2 + 27*e*cos(e*x + d) + (13*e*cos(e*x + d) + 14*e)*sin(e*x + d) + 18*e)","B",0
422,1,341,0,2.932637," ","integrate(1/(5+4*cos(e*x+d)+3*sin(e*x+d))^(5/2),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, \sqrt{10} \cos\left(e x + d\right)^{3} - 111 \, \sqrt{10} \cos\left(e x + d\right)^{2} - {\left(79 \, \sqrt{10} \cos\left(e x + d\right)^{2} + 202 \, \sqrt{10} \cos\left(e x + d\right) + 124 \, \sqrt{10}\right)} \sin\left(e x + d\right) - 246 \, \sqrt{10} \cos\left(e x + d\right) - 132 \, \sqrt{10}\right)} \log\left(-\frac{9 \, \cos\left(e x + d\right)^{2} + {\left(13 \, \cos\left(e x + d\right) - 6\right)} \sin\left(e x + d\right) + 2 \, {\left(\sqrt{10} \cos\left(e x + d\right) - 3 \, \sqrt{10} \sin\left(e x + d\right) + \sqrt{10}\right)} \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5} - 33 \, \cos\left(e x + d\right) - 42}{9 \, \cos\left(e x + d\right)^{2} + {\left(13 \, \cos\left(e x + d\right) + 14\right)} \sin\left(e x + d\right) + 27 \, \cos\left(e x + d\right) + 18}\right) + 20 \, {\left(39 \, \cos\left(e x + d\right)^{2} - 3 \, {\left(9 \, \cos\left(e x + d\right) + 32\right)} \sin\left(e x + d\right) + 47 \, \cos\left(e x + d\right) + 8\right)} \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5}}{8000 \, {\left(3 \, e \cos\left(e x + d\right)^{3} - 111 \, e \cos\left(e x + d\right)^{2} - 246 \, e \cos\left(e x + d\right) - {\left(79 \, e \cos\left(e x + d\right)^{2} + 202 \, e \cos\left(e x + d\right) + 124 \, e\right)} \sin\left(e x + d\right) - 132 \, e\right)}}"," ",0,"1/8000*(3*(3*sqrt(10)*cos(e*x + d)^3 - 111*sqrt(10)*cos(e*x + d)^2 - (79*sqrt(10)*cos(e*x + d)^2 + 202*sqrt(10)*cos(e*x + d) + 124*sqrt(10))*sin(e*x + d) - 246*sqrt(10)*cos(e*x + d) - 132*sqrt(10))*log(-(9*cos(e*x + d)^2 + (13*cos(e*x + d) - 6)*sin(e*x + d) + 2*(sqrt(10)*cos(e*x + d) - 3*sqrt(10)*sin(e*x + d) + sqrt(10))*sqrt(4*cos(e*x + d) + 3*sin(e*x + d) + 5) - 33*cos(e*x + d) - 42)/(9*cos(e*x + d)^2 + (13*cos(e*x + d) + 14)*sin(e*x + d) + 27*cos(e*x + d) + 18)) + 20*(39*cos(e*x + d)^2 - 3*(9*cos(e*x + d) + 32)*sin(e*x + d) + 47*cos(e*x + d) + 8)*sqrt(4*cos(e*x + d) + 3*sin(e*x + d) + 5))/(3*e*cos(e*x + d)^3 - 111*e*cos(e*x + d)^2 - 246*e*cos(e*x + d) - (79*e*cos(e*x + d)^2 + 202*e*cos(e*x + d) + 124*e)*sin(e*x + d) - 132*e)","B",0
423,1,121,0,0.845840," ","integrate((-5+4*cos(e*x+d)+3*sin(e*x+d))^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(249 \, \cos\left(e x + d\right)^{4} + 51 \, \cos\left(e x + d\right)^{3} - 3042 \, \cos\left(e x + d\right)^{2} - {\left(307 \, \cos\left(e x + d\right)^{3} - 1782 \, \cos\left(e x + d\right)^{2} + 2860 \, \cos\left(e x + d\right) - 1392\right)} \sin\left(e x + d\right) + 10068 \, \cos\left(e x + d\right) + 12912\right)} \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5}}{7 \, {\left(e \cos\left(e x + d\right) - 3 \, e \sin\left(e x + d\right) + e\right)}}"," ",0,"-2/7*(249*cos(e*x + d)^4 + 51*cos(e*x + d)^3 - 3042*cos(e*x + d)^2 - (307*cos(e*x + d)^3 - 1782*cos(e*x + d)^2 + 2860*cos(e*x + d) - 1392)*sin(e*x + d) + 10068*cos(e*x + d) + 12912)*sqrt(4*cos(e*x + d) + 3*sin(e*x + d) - 5)/(e*cos(e*x + d) - 3*e*sin(e*x + d) + e)","A",0
424,1,101,0,0.652383," ","integrate((-5+4*cos(e*x+d)+3*sin(e*x+d))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(9 \, \cos\left(e x + d\right)^{3} + 567 \, \cos\left(e x + d\right)^{2} - {\left(237 \, \cos\left(e x + d\right)^{2} - 694 \, \cos\left(e x + d\right) + 472\right)} \sin\left(e x + d\right) - 2538 \, \cos\left(e x + d\right) - 3096\right)} \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5}}{15 \, {\left(e \cos\left(e x + d\right) - 3 \, e \sin\left(e x + d\right) + e\right)}}"," ",0,"-2/15*(9*cos(e*x + d)^3 + 567*cos(e*x + d)^2 - (237*cos(e*x + d)^2 - 694*cos(e*x + d) + 472)*sin(e*x + d) - 2538*cos(e*x + d) - 3096)*sqrt(4*cos(e*x + d) + 3*sin(e*x + d) - 5)/(e*cos(e*x + d) - 3*e*sin(e*x + d) + e)","A",0
425,1,80,0,0.727809," ","integrate((-5+4*cos(e*x+d)+3*sin(e*x+d))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(9 \, \cos\left(e x + d\right)^{2} + {\left(13 \, \cos\left(e x + d\right) - 16\right)} \sin\left(e x + d\right) - 63 \, \cos\left(e x + d\right) - 72\right)} \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5}}{3 \, {\left(e \cos\left(e x + d\right) - 3 \, e \sin\left(e x + d\right) + e\right)}}"," ",0,"2/3*(9*cos(e*x + d)^2 + (13*cos(e*x + d) - 16)*sin(e*x + d) - 63*cos(e*x + d) - 72)*sqrt(4*cos(e*x + d) + 3*sin(e*x + d) - 5)/(e*cos(e*x + d) - 3*e*sin(e*x + d) + e)","A",0
426,1,59,0,0.645658," ","integrate((-5+4*cos(e*x+d)+3*sin(e*x+d))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5} {\left(3 \, \cos\left(e x + d\right) + \sin\left(e x + d\right) + 3\right)}}{e \cos\left(e x + d\right) - 3 \, e \sin\left(e x + d\right) + e}"," ",0,"2*sqrt(4*cos(e*x + d) + 3*sin(e*x + d) - 5)*(3*cos(e*x + d) + sin(e*x + d) + 3)/(e*cos(e*x + d) - 3*e*sin(e*x + d) + e)","A",0
427,1,88,0,2.112433," ","integrate(1/(-5+4*cos(e*x+d)+3*sin(e*x+d))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{5} \sqrt{2} \arctan\left(-\frac{{\left(3 \, \sqrt{5} \sqrt{2} \cos\left(e x + d\right) + \sqrt{5} \sqrt{2} \sin\left(e x + d\right) + 3 \, \sqrt{5} \sqrt{2}\right)} \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5}}{10 \, {\left(\cos\left(e x + d\right) - 3 \, \sin\left(e x + d\right) + 1\right)}}\right)}{5 \, e}"," ",0,"1/5*sqrt(5)*sqrt(2)*arctan(-1/10*(3*sqrt(5)*sqrt(2)*cos(e*x + d) + sqrt(5)*sqrt(2)*sin(e*x + d) + 3*sqrt(5)*sqrt(2))*sqrt(4*cos(e*x + d) + 3*sin(e*x + d) - 5)/(cos(e*x + d) - 3*sin(e*x + d) + 1))/e","B",0
428,1,210,0,1.034137," ","integrate(1/(-5+4*cos(e*x+d)+3*sin(e*x+d))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(13 \, \sqrt{10} \cos\left(e x + d\right)^{2} - 9 \, {\left(\sqrt{10} \cos\left(e x + d\right) - 2 \, \sqrt{10}\right)} \sin\left(e x + d\right) - \sqrt{10} \cos\left(e x + d\right) - 14 \, \sqrt{10}\right)} \arctan\left(-\frac{{\left(3 \, \sqrt{10} \cos\left(e x + d\right) + \sqrt{10} \sin\left(e x + d\right) + 3 \, \sqrt{10}\right)} \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5}}{10 \, {\left(\cos\left(e x + d\right) - 3 \, \sin\left(e x + d\right) + 1\right)}}\right) + 10 \, \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5} {\left(3 \, \cos\left(e x + d\right) + \sin\left(e x + d\right) + 3\right)}}{100 \, {\left(13 \, e \cos\left(e x + d\right)^{2} - e \cos\left(e x + d\right) - 9 \, {\left(e \cos\left(e x + d\right) - 2 \, e\right)} \sin\left(e x + d\right) - 14 \, e\right)}}"," ",0,"-1/100*((13*sqrt(10)*cos(e*x + d)^2 - 9*(sqrt(10)*cos(e*x + d) - 2*sqrt(10))*sin(e*x + d) - sqrt(10)*cos(e*x + d) - 14*sqrt(10))*arctan(-1/10*(3*sqrt(10)*cos(e*x + d) + sqrt(10)*sin(e*x + d) + 3*sqrt(10))*sqrt(4*cos(e*x + d) + 3*sin(e*x + d) - 5)/(cos(e*x + d) - 3*sin(e*x + d) + 1)) + 10*sqrt(4*cos(e*x + d) + 3*sin(e*x + d) - 5)*(3*cos(e*x + d) + sin(e*x + d) + 3))/(13*e*cos(e*x + d)^2 - e*cos(e*x + d) - 9*(e*cos(e*x + d) - 2*e)*sin(e*x + d) - 14*e)","B",0
429,1,280,0,0.893136," ","integrate(1/(-5+4*cos(e*x+d)+3*sin(e*x+d))^(5/2),x, algorithm=""fricas"")","\frac{3 \, {\left(79 \, \sqrt{10} \cos\left(e x + d\right)^{3} - 123 \, \sqrt{10} \cos\left(e x + d\right)^{2} + 3 \, {\left(\sqrt{10} \cos\left(e x + d\right)^{2} + 38 \, \sqrt{10} \cos\left(e x + d\right) - 44 \, \sqrt{10}\right)} \sin\left(e x + d\right) - 78 \, \sqrt{10} \cos\left(e x + d\right) + 124 \, \sqrt{10}\right)} \arctan\left(-\frac{{\left(3 \, \sqrt{10} \cos\left(e x + d\right) + \sqrt{10} \sin\left(e x + d\right) + 3 \, \sqrt{10}\right)} \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5}}{10 \, {\left(\cos\left(e x + d\right) - 3 \, \sin\left(e x + d\right) + 1\right)}}\right) + 10 \, {\left(27 \, \cos\left(e x + d\right)^{2} + {\left(39 \, \cos\left(e x + d\right) - 8\right)} \sin\left(e x + d\right) - 69 \, \cos\left(e x + d\right) - 96\right)} \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5}}{4000 \, {\left(79 \, e \cos\left(e x + d\right)^{3} - 123 \, e \cos\left(e x + d\right)^{2} - 78 \, e \cos\left(e x + d\right) + 3 \, {\left(e \cos\left(e x + d\right)^{2} + 38 \, e \cos\left(e x + d\right) - 44 \, e\right)} \sin\left(e x + d\right) + 124 \, e\right)}}"," ",0,"1/4000*(3*(79*sqrt(10)*cos(e*x + d)^3 - 123*sqrt(10)*cos(e*x + d)^2 + 3*(sqrt(10)*cos(e*x + d)^2 + 38*sqrt(10)*cos(e*x + d) - 44*sqrt(10))*sin(e*x + d) - 78*sqrt(10)*cos(e*x + d) + 124*sqrt(10))*arctan(-1/10*(3*sqrt(10)*cos(e*x + d) + sqrt(10)*sin(e*x + d) + 3*sqrt(10))*sqrt(4*cos(e*x + d) + 3*sin(e*x + d) - 5)/(cos(e*x + d) - 3*sin(e*x + d) + 1)) + 10*(27*cos(e*x + d)^2 + (39*cos(e*x + d) - 8)*sin(e*x + d) - 69*cos(e*x + d) - 96)*sqrt(4*cos(e*x + d) + 3*sin(e*x + d) - 5))/(79*e*cos(e*x + d)^3 - 123*e*cos(e*x + d)^2 - 78*e*cos(e*x + d) + 3*(e*cos(e*x + d)^2 + 38*e*cos(e*x + d) - 44*e)*sin(e*x + d) + 124*e)","B",0
430,1,268,0,1.521872," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, {\left(b^{4} - 6 \, b^{2} c^{2} + c^{4}\right)} \cos\left(e x + d\right)^{4} - 177 \, b^{4} - 310 \, b^{2} c^{2} - 128 \, c^{4} + 2 \, {\left(22 \, b^{4} + 15 \, b^{2} c^{2} - 27 \, c^{4}\right)} \cos\left(e x + d\right)^{2} + 4 \, {\left(5 \, {\left(b^{3} c - b c^{3}\right)} \cos\left(e x + d\right)^{3} + {\left(22 \, b^{3} c + 27 \, b c^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right) + 2 \, {\left(11 \, {\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{3} + {\left(53 \, b^{3} + 86 \, b c^{2}\right)} \cos\left(e x + d\right) + {\left(53 \, b^{2} c + 64 \, c^{3} + 11 \, {\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right)\right)} \sqrt{b^{2} + c^{2}}\right)} \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + \sqrt{b^{2} + c^{2}}}}{35 \, {\left(c e \cos\left(e x + d\right) - b e \sin\left(e x + d\right)\right)}}"," ",0,"2/35*(5*(b^4 - 6*b^2*c^2 + c^4)*cos(e*x + d)^4 - 177*b^4 - 310*b^2*c^2 - 128*c^4 + 2*(22*b^4 + 15*b^2*c^2 - 27*c^4)*cos(e*x + d)^2 + 4*(5*(b^3*c - b*c^3)*cos(e*x + d)^3 + (22*b^3*c + 27*b*c^3)*cos(e*x + d))*sin(e*x + d) + 2*(11*(b^3 - 3*b*c^2)*cos(e*x + d)^3 + (53*b^3 + 86*b*c^2)*cos(e*x + d) + (53*b^2*c + 64*c^3 + 11*(3*b^2*c - c^3)*cos(e*x + d)^2)*sin(e*x + d))*sqrt(b^2 + c^2))*sqrt(b*cos(e*x + d) + c*sin(e*x + d) + sqrt(b^2 + c^2))/(c*e*cos(e*x + d) - b*e*sin(e*x + d))","A",0
431,1,189,0,0.956321," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, {\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{3} + {\left(29 \, b^{3} + 38 \, b c^{2}\right)} \cos\left(e x + d\right) + {\left(29 \, b^{2} c + 32 \, c^{3} + 3 \, {\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right) + {\left(22 \, b c \cos\left(e x + d\right) \sin\left(e x + d\right) + 11 \, {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} - 43 \, b^{2} - 32 \, c^{2}\right)} \sqrt{b^{2} + c^{2}}\right)} \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + \sqrt{b^{2} + c^{2}}}}{15 \, {\left(c e \cos\left(e x + d\right) - b e \sin\left(e x + d\right)\right)}}"," ",0,"2/15*(3*(b^3 - 3*b*c^2)*cos(e*x + d)^3 + (29*b^3 + 38*b*c^2)*cos(e*x + d) + (29*b^2*c + 32*c^3 + 3*(3*b^2*c - c^3)*cos(e*x + d)^2)*sin(e*x + d) + (22*b*c*cos(e*x + d)*sin(e*x + d) + 11*(b^2 - c^2)*cos(e*x + d)^2 - 43*b^2 - 32*c^2)*sqrt(b^2 + c^2))*sqrt(b*cos(e*x + d) + c*sin(e*x + d) + sqrt(b^2 + c^2))/(c*e*cos(e*x + d) - b*e*sin(e*x + d))","A",0
432,1,125,0,0.680480," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, b c \cos\left(e x + d\right) \sin\left(e x + d\right) + {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} - 5 \, b^{2} - 4 \, c^{2} + 4 \, \sqrt{b^{2} + c^{2}} {\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right)\right)}\right)} \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + \sqrt{b^{2} + c^{2}}}}{3 \, {\left(c e \cos\left(e x + d\right) - b e \sin\left(e x + d\right)\right)}}"," ",0,"2/3*(2*b*c*cos(e*x + d)*sin(e*x + d) + (b^2 - c^2)*cos(e*x + d)^2 - 5*b^2 - 4*c^2 + 4*sqrt(b^2 + c^2)*(b*cos(e*x + d) + c*sin(e*x + d)))*sqrt(b*cos(e*x + d) + c*sin(e*x + d) + sqrt(b^2 + c^2))/(c*e*cos(e*x + d) - b*e*sin(e*x + d))","A",0
433,1,80,0,0.912268," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + \sqrt{b^{2} + c^{2}}} {\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right) - \sqrt{b^{2} + c^{2}}\right)}}{c e \cos\left(e x + d\right) - b e \sin\left(e x + d\right)}"," ",0,"2*sqrt(b*cos(e*x + d) + c*sin(e*x + d) + sqrt(b^2 + c^2))*(b*cos(e*x + d) + c*sin(e*x + d) - sqrt(b^2 + c^2))/(c*e*cos(e*x + d) - b*e*sin(e*x + d))","A",0
434,1,349,0,2.776425," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \log\left(\frac{{\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{3} + {\left(b^{2} c + 4 \, c^{3}\right)} \cos\left(e x + d\right) - {\left(3 \, b^{3} + 4 \, b c^{2} + {\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right) + \frac{2 \, \sqrt{2} {\left(2 \, {\left(b^{3} + b c^{2}\right)} \cos\left(e x + d\right) + 2 \, {\left(b^{2} c + c^{3}\right)} \sin\left(e x + d\right) - {\left(2 \, b c \cos\left(e x + d\right) \sin\left(e x + d\right) + {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} + b^{2} + 2 \, c^{2}\right)} \sqrt{b^{2} + c^{2}}\right)} \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + \sqrt{b^{2} + c^{2}}}}{{\left(b^{2} + c^{2}\right)}^{\frac{1}{4}}} - 4 \, {\left(2 \, b c \cos\left(e x + d\right)^{2} - {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right) \sin\left(e x + d\right) - b c\right)} \sqrt{b^{2} + c^{2}}}{3 \, b^{2} c \cos\left(e x + d\right) - {\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{3} - {\left(b^{3} - {\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right)}\right)}{2 \, {\left(b^{2} + c^{2}\right)}^{\frac{1}{4}} e}"," ",0,"1/2*sqrt(2)*log(((3*b^2*c - c^3)*cos(e*x + d)^3 + (b^2*c + 4*c^3)*cos(e*x + d) - (3*b^3 + 4*b*c^2 + (b^3 - 3*b*c^2)*cos(e*x + d)^2)*sin(e*x + d) + 2*sqrt(2)*(2*(b^3 + b*c^2)*cos(e*x + d) + 2*(b^2*c + c^3)*sin(e*x + d) - (2*b*c*cos(e*x + d)*sin(e*x + d) + (b^2 - c^2)*cos(e*x + d)^2 + b^2 + 2*c^2)*sqrt(b^2 + c^2))*sqrt(b*cos(e*x + d) + c*sin(e*x + d) + sqrt(b^2 + c^2))/(b^2 + c^2)^(1/4) - 4*(2*b*c*cos(e*x + d)^2 - (b^2 - c^2)*cos(e*x + d)*sin(e*x + d) - b*c)*sqrt(b^2 + c^2))/(3*b^2*c*cos(e*x + d) - (3*b^2*c - c^3)*cos(e*x + d)^3 - (b^3 - (b^3 - 3*b*c^2)*cos(e*x + d)^2)*sin(e*x + d)))/((b^2 + c^2)^(1/4)*e)","B",0
435,1,646,0,1.819440," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, \sqrt{2} b^{2} c \cos\left(e x + d\right) - \sqrt{2} {\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{3} - {\left(\sqrt{2} b^{3} - \sqrt{2} {\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right)\right)} {\left(b^{2} + c^{2}\right)}^{\frac{1}{4}} \log\left(\frac{{\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{3} + {\left(b^{2} c + 4 \, c^{3}\right)} \cos\left(e x + d\right) - {\left(3 \, b^{3} + 4 \, b c^{2} + {\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right) - 2 \, {\left(2 \, \sqrt{2} b c \cos\left(e x + d\right) \sin\left(e x + d\right) + \sqrt{2} {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} + \sqrt{2} {\left(b^{2} + 2 \, c^{2}\right)} - 2 \, {\left(\sqrt{2} b \cos\left(e x + d\right) + \sqrt{2} c \sin\left(e x + d\right)\right)} \sqrt{b^{2} + c^{2}}\right)} {\left(b^{2} + c^{2}\right)}^{\frac{1}{4}} \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + \sqrt{b^{2} + c^{2}}} - 4 \, {\left(2 \, b c \cos\left(e x + d\right)^{2} - {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right) \sin\left(e x + d\right) - b c\right)} \sqrt{b^{2} + c^{2}}}{3 \, b^{2} c \cos\left(e x + d\right) - {\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{3} - {\left(b^{3} - {\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right)}\right) + 4 \, {\left(2 \, {\left(b^{3} + b c^{2}\right)} \cos\left(e x + d\right) + 2 \, {\left(b^{2} c + c^{3}\right)} \sin\left(e x + d\right) - {\left(2 \, b c \cos\left(e x + d\right) \sin\left(e x + d\right) + {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} + b^{2} + 2 \, c^{2}\right)} \sqrt{b^{2} + c^{2}}\right)} \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + \sqrt{b^{2} + c^{2}}}}{8 \, {\left({\left(3 \, b^{4} c + 2 \, b^{2} c^{3} - c^{5}\right)} e \cos\left(e x + d\right)^{3} - 3 \, {\left(b^{4} c + b^{2} c^{3}\right)} e \cos\left(e x + d\right) - {\left({\left(b^{5} - 2 \, b^{3} c^{2} - 3 \, b c^{4}\right)} e \cos\left(e x + d\right)^{2} - {\left(b^{5} + b^{3} c^{2}\right)} e\right)} \sin\left(e x + d\right)\right)}}"," ",0,"-1/8*((3*sqrt(2)*b^2*c*cos(e*x + d) - sqrt(2)*(3*b^2*c - c^3)*cos(e*x + d)^3 - (sqrt(2)*b^3 - sqrt(2)*(b^3 - 3*b*c^2)*cos(e*x + d)^2)*sin(e*x + d))*(b^2 + c^2)^(1/4)*log(((3*b^2*c - c^3)*cos(e*x + d)^3 + (b^2*c + 4*c^3)*cos(e*x + d) - (3*b^3 + 4*b*c^2 + (b^3 - 3*b*c^2)*cos(e*x + d)^2)*sin(e*x + d) - 2*(2*sqrt(2)*b*c*cos(e*x + d)*sin(e*x + d) + sqrt(2)*(b^2 - c^2)*cos(e*x + d)^2 + sqrt(2)*(b^2 + 2*c^2) - 2*(sqrt(2)*b*cos(e*x + d) + sqrt(2)*c*sin(e*x + d))*sqrt(b^2 + c^2))*(b^2 + c^2)^(1/4)*sqrt(b*cos(e*x + d) + c*sin(e*x + d) + sqrt(b^2 + c^2)) - 4*(2*b*c*cos(e*x + d)^2 - (b^2 - c^2)*cos(e*x + d)*sin(e*x + d) - b*c)*sqrt(b^2 + c^2))/(3*b^2*c*cos(e*x + d) - (3*b^2*c - c^3)*cos(e*x + d)^3 - (b^3 - (b^3 - 3*b*c^2)*cos(e*x + d)^2)*sin(e*x + d))) + 4*(2*(b^3 + b*c^2)*cos(e*x + d) + 2*(b^2*c + c^3)*sin(e*x + d) - (2*b*c*cos(e*x + d)*sin(e*x + d) + (b^2 - c^2)*cos(e*x + d)^2 + b^2 + 2*c^2)*sqrt(b^2 + c^2))*sqrt(b*cos(e*x + d) + c*sin(e*x + d) + sqrt(b^2 + c^2)))/((3*b^4*c + 2*b^2*c^3 - c^5)*e*cos(e*x + d)^3 - 3*(b^4*c + b^2*c^3)*e*cos(e*x + d) - ((b^5 - 2*b^3*c^2 - 3*b*c^4)*e*cos(e*x + d)^2 - (b^5 + b^3*c^2)*e)*sin(e*x + d))","B",0
436,1,895,0,2.525858," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(5/2),x, algorithm=""fricas"")","\frac{\frac{3 \, \sqrt{\frac{1}{2}} {\left(5 \, b^{4} c \cos\left(e x + d\right) + {\left(5 \, b^{4} c - 10 \, b^{2} c^{3} + c^{5}\right)} \cos\left(e x + d\right)^{5} - 10 \, {\left(b^{4} c - b^{2} c^{3}\right)} \cos\left(e x + d\right)^{3} - {\left(b^{5} + {\left(b^{5} - 10 \, b^{3} c^{2} + 5 \, b c^{4}\right)} \cos\left(e x + d\right)^{4} - 2 \, {\left(b^{5} - 5 \, b^{3} c^{2}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right)\right)} \log\left(\frac{{\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{3} + {\left(b^{2} c + 4 \, c^{3}\right)} \cos\left(e x + d\right) - {\left(3 \, b^{3} + 4 \, b c^{2} + {\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right) + \frac{4 \, \sqrt{\frac{1}{2}} {\left(2 \, {\left(b^{3} + b c^{2}\right)} \cos\left(e x + d\right) + 2 \, {\left(b^{2} c + c^{3}\right)} \sin\left(e x + d\right) - {\left(2 \, b c \cos\left(e x + d\right) \sin\left(e x + d\right) + {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} + b^{2} + 2 \, c^{2}\right)} \sqrt{b^{2} + c^{2}}\right)} \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + \sqrt{b^{2} + c^{2}}}}{{\left(b^{2} + c^{2}\right)}^{\frac{1}{4}}} - 4 \, {\left(2 \, b c \cos\left(e x + d\right)^{2} - {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right) \sin\left(e x + d\right) - b c\right)} \sqrt{b^{2} + c^{2}}}{3 \, b^{2} c \cos\left(e x + d\right) - {\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{3} - {\left(b^{3} - {\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right)}\right)}{{\left(b^{2} + c^{2}\right)}^{\frac{1}{4}}} + 2 \, {\left(3 \, {\left(b^{4} - 6 \, b^{2} c^{2} + c^{4}\right)} \cos\left(e x + d\right)^{4} - 7 \, b^{4} - 26 \, b^{2} c^{2} - 16 \, c^{4} - 6 \, {\left(2 \, b^{4} - 3 \, b^{2} c^{2} - c^{4}\right)} \cos\left(e x + d\right)^{2} + 12 \, {\left({\left(b^{3} c - b c^{3}\right)} \cos\left(e x + d\right)^{3} - {\left(2 \, b^{3} c + b c^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right) - 2 \, {\left({\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{3} - 3 \, {\left(3 \, b^{3} + 2 \, b c^{2}\right)} \cos\left(e x + d\right) - {\left(9 \, b^{2} c + 8 \, c^{3} - {\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right)\right)} \sqrt{b^{2} + c^{2}}\right)} \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + \sqrt{b^{2} + c^{2}}}}{32 \, {\left({\left(5 \, b^{6} c - 5 \, b^{4} c^{3} - 9 \, b^{2} c^{5} + c^{7}\right)} e \cos\left(e x + d\right)^{5} - 10 \, {\left(b^{6} c - b^{2} c^{5}\right)} e \cos\left(e x + d\right)^{3} + 5 \, {\left(b^{6} c + b^{4} c^{3}\right)} e \cos\left(e x + d\right) - {\left({\left(b^{7} - 9 \, b^{5} c^{2} - 5 \, b^{3} c^{4} + 5 \, b c^{6}\right)} e \cos\left(e x + d\right)^{4} - 2 \, {\left(b^{7} - 4 \, b^{5} c^{2} - 5 \, b^{3} c^{4}\right)} e \cos\left(e x + d\right)^{2} + {\left(b^{7} + b^{5} c^{2}\right)} e\right)} \sin\left(e x + d\right)\right)}}"," ",0,"1/32*(3*sqrt(1/2)*(5*b^4*c*cos(e*x + d) + (5*b^4*c - 10*b^2*c^3 + c^5)*cos(e*x + d)^5 - 10*(b^4*c - b^2*c^3)*cos(e*x + d)^3 - (b^5 + (b^5 - 10*b^3*c^2 + 5*b*c^4)*cos(e*x + d)^4 - 2*(b^5 - 5*b^3*c^2)*cos(e*x + d)^2)*sin(e*x + d))*log(((3*b^2*c - c^3)*cos(e*x + d)^3 + (b^2*c + 4*c^3)*cos(e*x + d) - (3*b^3 + 4*b*c^2 + (b^3 - 3*b*c^2)*cos(e*x + d)^2)*sin(e*x + d) + 4*sqrt(1/2)*(2*(b^3 + b*c^2)*cos(e*x + d) + 2*(b^2*c + c^3)*sin(e*x + d) - (2*b*c*cos(e*x + d)*sin(e*x + d) + (b^2 - c^2)*cos(e*x + d)^2 + b^2 + 2*c^2)*sqrt(b^2 + c^2))*sqrt(b*cos(e*x + d) + c*sin(e*x + d) + sqrt(b^2 + c^2))/(b^2 + c^2)^(1/4) - 4*(2*b*c*cos(e*x + d)^2 - (b^2 - c^2)*cos(e*x + d)*sin(e*x + d) - b*c)*sqrt(b^2 + c^2))/(3*b^2*c*cos(e*x + d) - (3*b^2*c - c^3)*cos(e*x + d)^3 - (b^3 - (b^3 - 3*b*c^2)*cos(e*x + d)^2)*sin(e*x + d)))/(b^2 + c^2)^(1/4) + 2*(3*(b^4 - 6*b^2*c^2 + c^4)*cos(e*x + d)^4 - 7*b^4 - 26*b^2*c^2 - 16*c^4 - 6*(2*b^4 - 3*b^2*c^2 - c^4)*cos(e*x + d)^2 + 12*((b^3*c - b*c^3)*cos(e*x + d)^3 - (2*b^3*c + b*c^3)*cos(e*x + d))*sin(e*x + d) - 2*((b^3 - 3*b*c^2)*cos(e*x + d)^3 - 3*(3*b^3 + 2*b*c^2)*cos(e*x + d) - (9*b^2*c + 8*c^3 - (3*b^2*c - c^3)*cos(e*x + d)^2)*sin(e*x + d))*sqrt(b^2 + c^2))*sqrt(b*cos(e*x + d) + c*sin(e*x + d) + sqrt(b^2 + c^2)))/((5*b^6*c - 5*b^4*c^3 - 9*b^2*c^5 + c^7)*e*cos(e*x + d)^5 - 10*(b^6*c - b^2*c^5)*e*cos(e*x + d)^3 + 5*(b^6*c + b^4*c^3)*e*cos(e*x + d) - ((b^7 - 9*b^5*c^2 - 5*b^3*c^4 + 5*b*c^6)*e*cos(e*x + d)^4 - 2*(b^7 - 4*b^5*c^2 - 5*b^3*c^4)*e*cos(e*x + d)^2 + (b^7 + b^5*c^2)*e)*sin(e*x + d))","B",0
437,1,192,0,1.122005," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, {\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{3} + {\left(29 \, b^{3} + 38 \, b c^{2}\right)} \cos\left(e x + d\right) + {\left(29 \, b^{2} c + 32 \, c^{3} + 3 \, {\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right) - {\left(22 \, b c \cos\left(e x + d\right) \sin\left(e x + d\right) + 11 \, {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} - 43 \, b^{2} - 32 \, c^{2}\right)} \sqrt{b^{2} + c^{2}}\right)} \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) - \sqrt{b^{2} + c^{2}}}}{15 \, {\left(c e \cos\left(e x + d\right) - b e \sin\left(e x + d\right)\right)}}"," ",0,"2/15*(3*(b^3 - 3*b*c^2)*cos(e*x + d)^3 + (29*b^3 + 38*b*c^2)*cos(e*x + d) + (29*b^2*c + 32*c^3 + 3*(3*b^2*c - c^3)*cos(e*x + d)^2)*sin(e*x + d) - (22*b*c*cos(e*x + d)*sin(e*x + d) + 11*(b^2 - c^2)*cos(e*x + d)^2 - 43*b^2 - 32*c^2)*sqrt(b^2 + c^2))*sqrt(b*cos(e*x + d) + c*sin(e*x + d) - sqrt(b^2 + c^2))/(c*e*cos(e*x + d) - b*e*sin(e*x + d))","A",0
438,1,127,0,1.475989," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, b c \cos\left(e x + d\right) \sin\left(e x + d\right) + {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} - 5 \, b^{2} - 4 \, c^{2} - 4 \, \sqrt{b^{2} + c^{2}} {\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right)\right)}\right)} \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) - \sqrt{b^{2} + c^{2}}}}{3 \, {\left(c e \cos\left(e x + d\right) - b e \sin\left(e x + d\right)\right)}}"," ",0,"2/3*(2*b*c*cos(e*x + d)*sin(e*x + d) + (b^2 - c^2)*cos(e*x + d)^2 - 5*b^2 - 4*c^2 - 4*sqrt(b^2 + c^2)*(b*cos(e*x + d) + c*sin(e*x + d)))*sqrt(b*cos(e*x + d) + c*sin(e*x + d) - sqrt(b^2 + c^2))/(c*e*cos(e*x + d) - b*e*sin(e*x + d))","A",0
439,1,80,0,2.892287," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + \sqrt{b^{2} + c^{2}}\right)} \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) - \sqrt{b^{2} + c^{2}}}}{c e \cos\left(e x + d\right) - b e \sin\left(e x + d\right)}"," ",0,"2*(b*cos(e*x + d) + c*sin(e*x + d) + sqrt(b^2 + c^2))*sqrt(b*cos(e*x + d) + c*sin(e*x + d) - sqrt(b^2 + c^2))/(c*e*cos(e*x + d) - b*e*sin(e*x + d))","A",0
440,1,107,0,1.146341," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + \sqrt{b^{2} + c^{2}}\right)} \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) - \sqrt{b^{2} + c^{2}}}}{2 \, {\left(b^{2} + c^{2}\right)}^{\frac{1}{4}} {\left(c \cos\left(e x + d\right) - b \sin\left(e x + d\right)\right)}}\right)}{{\left(b^{2} + c^{2}\right)}^{\frac{1}{4}} e}"," ",0,"sqrt(2)*arctan(-1/2*sqrt(2)*(b*cos(e*x + d) + c*sin(e*x + d) + sqrt(b^2 + c^2))*sqrt(b*cos(e*x + d) + c*sin(e*x + d) - sqrt(b^2 + c^2))/((b^2 + c^2)^(1/4)*(c*cos(e*x + d) - b*sin(e*x + d))))/((b^2 + c^2)^(1/4)*e)","B",0
441,1,442,0,0.858518," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, \sqrt{2} b^{2} c \cos\left(e x + d\right) - \sqrt{2} {\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{3} - {\left(\sqrt{2} b^{3} - \sqrt{2} {\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right)\right)} {\left(b^{2} + c^{2}\right)}^{\frac{1}{4}} \arctan\left(-\frac{{\left(b^{2} + c^{2}\right)}^{\frac{1}{4}} \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) - \sqrt{b^{2} + c^{2}}} {\left({\left(\sqrt{2} b \cos\left(e x + d\right) + \sqrt{2} c \sin\left(e x + d\right)\right)} \sqrt{b^{2} + c^{2}} + \sqrt{2} {\left(b^{2} + c^{2}\right)}\right)}}{2 \, {\left({\left(b^{2} c + c^{3}\right)} \cos\left(e x + d\right) - {\left(b^{3} + b c^{2}\right)} \sin\left(e x + d\right)\right)}}\right) - 2 \, {\left(2 \, {\left(b^{3} + b c^{2}\right)} \cos\left(e x + d\right) + 2 \, {\left(b^{2} c + c^{3}\right)} \sin\left(e x + d\right) + {\left(2 \, b c \cos\left(e x + d\right) \sin\left(e x + d\right) + {\left(b^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} + b^{2} + 2 \, c^{2}\right)} \sqrt{b^{2} + c^{2}}\right)} \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) - \sqrt{b^{2} + c^{2}}}}{4 \, {\left({\left(3 \, b^{4} c + 2 \, b^{2} c^{3} - c^{5}\right)} e \cos\left(e x + d\right)^{3} - 3 \, {\left(b^{4} c + b^{2} c^{3}\right)} e \cos\left(e x + d\right) - {\left({\left(b^{5} - 2 \, b^{3} c^{2} - 3 \, b c^{4}\right)} e \cos\left(e x + d\right)^{2} - {\left(b^{5} + b^{3} c^{2}\right)} e\right)} \sin\left(e x + d\right)\right)}}"," ",0,"1/4*((3*sqrt(2)*b^2*c*cos(e*x + d) - sqrt(2)*(3*b^2*c - c^3)*cos(e*x + d)^3 - (sqrt(2)*b^3 - sqrt(2)*(b^3 - 3*b*c^2)*cos(e*x + d)^2)*sin(e*x + d))*(b^2 + c^2)^(1/4)*arctan(-1/2*(b^2 + c^2)^(1/4)*sqrt(b*cos(e*x + d) + c*sin(e*x + d) - sqrt(b^2 + c^2))*((sqrt(2)*b*cos(e*x + d) + sqrt(2)*c*sin(e*x + d))*sqrt(b^2 + c^2) + sqrt(2)*(b^2 + c^2))/((b^2*c + c^3)*cos(e*x + d) - (b^3 + b*c^2)*sin(e*x + d))) - 2*(2*(b^3 + b*c^2)*cos(e*x + d) + 2*(b^2*c + c^3)*sin(e*x + d) + (2*b*c*cos(e*x + d)*sin(e*x + d) + (b^2 - c^2)*cos(e*x + d)^2 + b^2 + 2*c^2)*sqrt(b^2 + c^2))*sqrt(b*cos(e*x + d) + c*sin(e*x + d) - sqrt(b^2 + c^2)))/((3*b^4*c + 2*b^2*c^3 - c^5)*e*cos(e*x + d)^3 - 3*(b^4*c + b^2*c^3)*e*cos(e*x + d) - ((b^5 - 2*b^3*c^2 - 3*b*c^4)*e*cos(e*x + d)^2 - (b^5 + b^3*c^2)*e)*sin(e*x + d))","B",0
442,1,655,0,1.197301," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(5/2),x, algorithm=""fricas"")","\frac{\frac{3 \, \sqrt{\frac{1}{2}} {\left(5 \, b^{4} c \cos\left(e x + d\right) + {\left(5 \, b^{4} c - 10 \, b^{2} c^{3} + c^{5}\right)} \cos\left(e x + d\right)^{5} - 10 \, {\left(b^{4} c - b^{2} c^{3}\right)} \cos\left(e x + d\right)^{3} - {\left(b^{5} + {\left(b^{5} - 10 \, b^{3} c^{2} + 5 \, b c^{4}\right)} \cos\left(e x + d\right)^{4} - 2 \, {\left(b^{5} - 5 \, b^{3} c^{2}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right)\right)} \arctan\left(-\frac{\sqrt{\frac{1}{2}} {\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + \sqrt{b^{2} + c^{2}}\right)} \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) - \sqrt{b^{2} + c^{2}}}}{{\left(b^{2} + c^{2}\right)}^{\frac{1}{4}} {\left(c \cos\left(e x + d\right) - b \sin\left(e x + d\right)\right)}}\right)}{{\left(b^{2} + c^{2}\right)}^{\frac{1}{4}}} + {\left(3 \, {\left(b^{4} - 6 \, b^{2} c^{2} + c^{4}\right)} \cos\left(e x + d\right)^{4} - 7 \, b^{4} - 26 \, b^{2} c^{2} - 16 \, c^{4} - 6 \, {\left(2 \, b^{4} - 3 \, b^{2} c^{2} - c^{4}\right)} \cos\left(e x + d\right)^{2} + 12 \, {\left({\left(b^{3} c - b c^{3}\right)} \cos\left(e x + d\right)^{3} - {\left(2 \, b^{3} c + b c^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right) + 2 \, {\left({\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(e x + d\right)^{3} - 3 \, {\left(3 \, b^{3} + 2 \, b c^{2}\right)} \cos\left(e x + d\right) - {\left(9 \, b^{2} c + 8 \, c^{3} - {\left(3 \, b^{2} c - c^{3}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right)\right)} \sqrt{b^{2} + c^{2}}\right)} \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) - \sqrt{b^{2} + c^{2}}}}{16 \, {\left({\left(5 \, b^{6} c - 5 \, b^{4} c^{3} - 9 \, b^{2} c^{5} + c^{7}\right)} e \cos\left(e x + d\right)^{5} - 10 \, {\left(b^{6} c - b^{2} c^{5}\right)} e \cos\left(e x + d\right)^{3} + 5 \, {\left(b^{6} c + b^{4} c^{3}\right)} e \cos\left(e x + d\right) - {\left({\left(b^{7} - 9 \, b^{5} c^{2} - 5 \, b^{3} c^{4} + 5 \, b c^{6}\right)} e \cos\left(e x + d\right)^{4} - 2 \, {\left(b^{7} - 4 \, b^{5} c^{2} - 5 \, b^{3} c^{4}\right)} e \cos\left(e x + d\right)^{2} + {\left(b^{7} + b^{5} c^{2}\right)} e\right)} \sin\left(e x + d\right)\right)}}"," ",0,"1/16*(3*sqrt(1/2)*(5*b^4*c*cos(e*x + d) + (5*b^4*c - 10*b^2*c^3 + c^5)*cos(e*x + d)^5 - 10*(b^4*c - b^2*c^3)*cos(e*x + d)^3 - (b^5 + (b^5 - 10*b^3*c^2 + 5*b*c^4)*cos(e*x + d)^4 - 2*(b^5 - 5*b^3*c^2)*cos(e*x + d)^2)*sin(e*x + d))*arctan(-sqrt(1/2)*(b*cos(e*x + d) + c*sin(e*x + d) + sqrt(b^2 + c^2))*sqrt(b*cos(e*x + d) + c*sin(e*x + d) - sqrt(b^2 + c^2))/((b^2 + c^2)^(1/4)*(c*cos(e*x + d) - b*sin(e*x + d))))/(b^2 + c^2)^(1/4) + (3*(b^4 - 6*b^2*c^2 + c^4)*cos(e*x + d)^4 - 7*b^4 - 26*b^2*c^2 - 16*c^4 - 6*(2*b^4 - 3*b^2*c^2 - c^4)*cos(e*x + d)^2 + 12*((b^3*c - b*c^3)*cos(e*x + d)^3 - (2*b^3*c + b*c^3)*cos(e*x + d))*sin(e*x + d) + 2*((b^3 - 3*b*c^2)*cos(e*x + d)^3 - 3*(3*b^3 + 2*b*c^2)*cos(e*x + d) - (9*b^2*c + 8*c^3 - (3*b^2*c - c^3)*cos(e*x + d)^2)*sin(e*x + d))*sqrt(b^2 + c^2))*sqrt(b*cos(e*x + d) + c*sin(e*x + d) - sqrt(b^2 + c^2)))/((5*b^6*c - 5*b^4*c^3 - 9*b^2*c^5 + c^7)*e*cos(e*x + d)^5 - 10*(b^6*c - b^2*c^5)*e*cos(e*x + d)^3 + 5*(b^6*c + b^4*c^3)*e*cos(e*x + d) - ((b^7 - 9*b^5*c^2 - 5*b^3*c^4 + 5*b*c^6)*e*cos(e*x + d)^4 - 2*(b^7 - 4*b^5*c^2 - 5*b^3*c^4)*e*cos(e*x + d)^2 + (b^7 + b^5*c^2)*e)*sin(e*x + d))","B",0
443,1,579,0,1.207336," ","integrate(sin(x)/(a+b*cos(x)+c*sin(x)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2} + c^{2}} a c \log\left(\frac{a^{2} b^{2} - 2 \, b^{4} - c^{4} - {\left(a^{2} + 3 \, b^{2}\right)} c^{2} - {\left(2 \, a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \cos\left(x\right)^{2} - 2 \, {\left(a b^{3} + a b c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a b^{2} c + a c^{3} - {\left(b c^{3} - {\left(2 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right) - 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(b^{2} c + c^{3}\right)} \cos\left(x\right) - {\left(b^{3} + b c^{2} + {\left(a b^{2} - a c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}}}{2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)}\right) + 2 \, {\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} x + {\left(a^{2} b - b^{3} - b c^{2}\right)} \log\left(2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)\right)}{2 \, {\left(a^{2} b^{2} - b^{4} - c^{4} + {\left(a^{2} - 2 \, b^{2}\right)} c^{2}\right)}}, -\frac{2 \, \sqrt{a^{2} - b^{2} - c^{2}} a c \arctan\left(-\frac{{\left(a b \cos\left(x\right) + a c \sin\left(x\right) + b^{2} + c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}}}{{\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(x\right) + {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(x\right)}\right) + 2 \, {\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} x + {\left(a^{2} b - b^{3} - b c^{2}\right)} \log\left(2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)\right)}{2 \, {\left(a^{2} b^{2} - b^{4} - c^{4} + {\left(a^{2} - 2 \, b^{2}\right)} c^{2}\right)}}\right]"," ",0,"[-1/2*(sqrt(-a^2 + b^2 + c^2)*a*c*log((a^2*b^2 - 2*b^4 - c^4 - (a^2 + 3*b^2)*c^2 - (2*a^2*b^2 - b^4 - 2*a^2*c^2 + c^4)*cos(x)^2 - 2*(a*b^3 + a*b*c^2)*cos(x) - 2*(a*b^2*c + a*c^3 - (b*c^3 - (2*a^2*b - b^3)*c)*cos(x))*sin(x) - 2*(2*a*b*c*cos(x)^2 - a*b*c + (b^2*c + c^3)*cos(x) - (b^3 + b*c^2 + (a*b^2 - a*c^2)*cos(x))*sin(x))*sqrt(-a^2 + b^2 + c^2))/(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x))) + 2*(c^3 - (a^2 - b^2)*c)*x + (a^2*b - b^3 - b*c^2)*log(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x)))/(a^2*b^2 - b^4 - c^4 + (a^2 - 2*b^2)*c^2), -1/2*(2*sqrt(a^2 - b^2 - c^2)*a*c*arctan(-(a*b*cos(x) + a*c*sin(x) + b^2 + c^2)*sqrt(a^2 - b^2 - c^2)/((c^3 - (a^2 - b^2)*c)*cos(x) + (a^2*b - b^3 - b*c^2)*sin(x))) + 2*(c^3 - (a^2 - b^2)*c)*x + (a^2*b - b^3 - b*c^2)*log(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x)))/(a^2*b^2 - b^4 - c^4 + (a^2 - 2*b^2)*c^2)]","B",0
444,1,11,0,2.116165," ","integrate(sin(x)/(1+cos(x)+sin(x)),x, algorithm=""fricas"")","\frac{1}{2} \, x - \frac{1}{2} \, \log\left(\sin\left(x\right) + 1\right)"," ",0,"1/2*x - 1/2*log(sin(x) + 1)","A",0
445,1,553,0,1.760803," ","integrate(1/(a+c*sec(x)+b*tan(x)),x, algorithm=""fricas"")","\left[\frac{\sqrt{a^{2} + b^{2} - c^{2}} a c \log\left(\frac{2 \, a^{4} + 3 \, a^{2} b^{2} + b^{4} - {\left(a^{2} - b^{2}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c \cos\left(x\right) - {\left(a^{4} - b^{4} - 2 \, {\left(a^{2} - b^{2}\right)} c^{2}\right)} \cos\left(x\right)^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} c - {\left(a^{3} b + a b^{3} - 2 \, a b c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right) + 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(a^{2} b + b^{3}\right)} \cos\left(x\right) - {\left(a^{3} + a b^{2} + {\left(a^{2} - b^{2}\right)} c \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{a^{2} + b^{2} - c^{2}}}{2 \, a c \cos\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2} + c^{2} + 2 \, {\left(a b \cos\left(x\right) + b c\right)} \sin\left(x\right)}\right) + 2 \, {\left(a^{3} + a b^{2} - a c^{2}\right)} x + {\left(a^{2} b + b^{3} - b c^{2}\right)} \log\left(2 \, a c \cos\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2} + c^{2} + 2 \, {\left(a b \cos\left(x\right) + b c\right)} \sin\left(x\right)\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} - {\left(a^{2} + b^{2}\right)} c^{2}\right)}}, -\frac{2 \, \sqrt{-a^{2} - b^{2} + c^{2}} a c \arctan\left(\frac{{\left(a c \cos\left(x\right) + b c \sin\left(x\right) + a^{2} + b^{2}\right)} \sqrt{-a^{2} - b^{2} + c^{2}}}{{\left(a^{2} b + b^{3} - b c^{2}\right)} \cos\left(x\right) - {\left(a^{3} + a b^{2} - a c^{2}\right)} \sin\left(x\right)}\right) - 2 \, {\left(a^{3} + a b^{2} - a c^{2}\right)} x - {\left(a^{2} b + b^{3} - b c^{2}\right)} \log\left(2 \, a c \cos\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2} + c^{2} + 2 \, {\left(a b \cos\left(x\right) + b c\right)} \sin\left(x\right)\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} - {\left(a^{2} + b^{2}\right)} c^{2}\right)}}\right]"," ",0,"[1/2*(sqrt(a^2 + b^2 - c^2)*a*c*log((2*a^4 + 3*a^2*b^2 + b^4 - (a^2 - b^2)*c^2 + 2*(a^3 + a*b^2)*c*cos(x) - (a^4 - b^4 - 2*(a^2 - b^2)*c^2)*cos(x)^2 + 2*((a^2*b + b^3)*c - (a^3*b + a*b^3 - 2*a*b*c^2)*cos(x))*sin(x) + 2*(2*a*b*c*cos(x)^2 - a*b*c + (a^2*b + b^3)*cos(x) - (a^3 + a*b^2 + (a^2 - b^2)*c*cos(x))*sin(x))*sqrt(a^2 + b^2 - c^2))/(2*a*c*cos(x) + (a^2 - b^2)*cos(x)^2 + b^2 + c^2 + 2*(a*b*cos(x) + b*c)*sin(x))) + 2*(a^3 + a*b^2 - a*c^2)*x + (a^2*b + b^3 - b*c^2)*log(2*a*c*cos(x) + (a^2 - b^2)*cos(x)^2 + b^2 + c^2 + 2*(a*b*cos(x) + b*c)*sin(x)))/(a^4 + 2*a^2*b^2 + b^4 - (a^2 + b^2)*c^2), -1/2*(2*sqrt(-a^2 - b^2 + c^2)*a*c*arctan((a*c*cos(x) + b*c*sin(x) + a^2 + b^2)*sqrt(-a^2 - b^2 + c^2)/((a^2*b + b^3 - b*c^2)*cos(x) - (a^3 + a*b^2 - a*c^2)*sin(x))) - 2*(a^3 + a*b^2 - a*c^2)*x - (a^2*b + b^3 - b*c^2)*log(2*a*c*cos(x) + (a^2 - b^2)*cos(x)^2 + b^2 + c^2 + 2*(a*b*cos(x) + b*c)*sin(x)))/(a^4 + 2*a^2*b^2 + b^4 - (a^2 + b^2)*c^2)]","B",0
446,1,349,0,0.508614," ","integrate(sec(x)/(a+c*sec(x)+b*tan(x)),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{2 \, a^{4} + 3 \, a^{2} b^{2} + b^{4} - {\left(a^{2} - b^{2}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c \cos\left(x\right) - {\left(a^{4} - b^{4} - 2 \, {\left(a^{2} - b^{2}\right)} c^{2}\right)} \cos\left(x\right)^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} c - {\left(a^{3} b + a b^{3} - 2 \, a b c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right) - 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(a^{2} b + b^{3}\right)} \cos\left(x\right) - {\left(a^{3} + a b^{2} + {\left(a^{2} - b^{2}\right)} c \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{a^{2} + b^{2} - c^{2}}}{2 \, a c \cos\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2} + c^{2} + 2 \, {\left(a b \cos\left(x\right) + b c\right)} \sin\left(x\right)}\right)}{2 \, \sqrt{a^{2} + b^{2} - c^{2}}}, \frac{\sqrt{-a^{2} - b^{2} + c^{2}} \arctan\left(\frac{{\left(a c \cos\left(x\right) + b c \sin\left(x\right) + a^{2} + b^{2}\right)} \sqrt{-a^{2} - b^{2} + c^{2}}}{{\left(a^{2} b + b^{3} - b c^{2}\right)} \cos\left(x\right) - {\left(a^{3} + a b^{2} - a c^{2}\right)} \sin\left(x\right)}\right)}{a^{2} + b^{2} - c^{2}}\right]"," ",0,"[1/2*log(-(2*a^4 + 3*a^2*b^2 + b^4 - (a^2 - b^2)*c^2 + 2*(a^3 + a*b^2)*c*cos(x) - (a^4 - b^4 - 2*(a^2 - b^2)*c^2)*cos(x)^2 + 2*((a^2*b + b^3)*c - (a^3*b + a*b^3 - 2*a*b*c^2)*cos(x))*sin(x) - 2*(2*a*b*c*cos(x)^2 - a*b*c + (a^2*b + b^3)*cos(x) - (a^3 + a*b^2 + (a^2 - b^2)*c*cos(x))*sin(x))*sqrt(a^2 + b^2 - c^2))/(2*a*c*cos(x) + (a^2 - b^2)*cos(x)^2 + b^2 + c^2 + 2*(a*b*cos(x) + b*c)*sin(x)))/sqrt(a^2 + b^2 - c^2), sqrt(-a^2 - b^2 + c^2)*arctan((a*c*cos(x) + b*c*sin(x) + a^2 + b^2)*sqrt(-a^2 - b^2 + c^2)/((a^2*b + b^3 - b*c^2)*cos(x) - (a^3 + a*b^2 - a*c^2)*sin(x)))/(a^2 + b^2 - c^2)]","B",0
447,1,663,0,4.999482," ","integrate(sec(x)^2/(a+c*sec(x)+b*tan(x)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{a^{2} + b^{2} - c^{2}} a c \log\left(\frac{2 \, a^{4} + 3 \, a^{2} b^{2} + b^{4} - {\left(a^{2} - b^{2}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c \cos\left(x\right) - {\left(a^{4} - b^{4} - 2 \, {\left(a^{2} - b^{2}\right)} c^{2}\right)} \cos\left(x\right)^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} c - {\left(a^{3} b + a b^{3} - 2 \, a b c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right) + 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(a^{2} b + b^{3}\right)} \cos\left(x\right) - {\left(a^{3} + a b^{2} + {\left(a^{2} - b^{2}\right)} c \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{a^{2} + b^{2} - c^{2}}}{2 \, a c \cos\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2} + c^{2} + 2 \, {\left(a b \cos\left(x\right) + b c\right)} \sin\left(x\right)}\right) - {\left(a^{2} b + b^{3} - b c^{2}\right)} \log\left(2 \, a c \cos\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2} + c^{2} + 2 \, {\left(a b \cos\left(x\right) + b c\right)} \sin\left(x\right)\right) + {\left(a^{2} b + b^{3} - b c^{2} - c^{3} + {\left(a^{2} + b^{2}\right)} c\right)} \log\left(\sin\left(x\right) + 1\right) + {\left(a^{2} b + b^{3} - b c^{2} + c^{3} - {\left(a^{2} + b^{2}\right)} c\right)} \log\left(-\sin\left(x\right) + 1\right)}{2 \, {\left(a^{2} b^{2} + b^{4} + c^{4} - {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)}}, \frac{2 \, \sqrt{-a^{2} - b^{2} + c^{2}} a c \arctan\left(\frac{{\left(a c \cos\left(x\right) + b c \sin\left(x\right) + a^{2} + b^{2}\right)} \sqrt{-a^{2} - b^{2} + c^{2}}}{{\left(a^{2} b + b^{3} - b c^{2}\right)} \cos\left(x\right) - {\left(a^{3} + a b^{2} - a c^{2}\right)} \sin\left(x\right)}\right) + {\left(a^{2} b + b^{3} - b c^{2}\right)} \log\left(2 \, a c \cos\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2} + c^{2} + 2 \, {\left(a b \cos\left(x\right) + b c\right)} \sin\left(x\right)\right) - {\left(a^{2} b + b^{3} - b c^{2} - c^{3} + {\left(a^{2} + b^{2}\right)} c\right)} \log\left(\sin\left(x\right) + 1\right) - {\left(a^{2} b + b^{3} - b c^{2} + c^{3} - {\left(a^{2} + b^{2}\right)} c\right)} \log\left(-\sin\left(x\right) + 1\right)}{2 \, {\left(a^{2} b^{2} + b^{4} + c^{4} - {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)}}\right]"," ",0,"[-1/2*(sqrt(a^2 + b^2 - c^2)*a*c*log((2*a^4 + 3*a^2*b^2 + b^4 - (a^2 - b^2)*c^2 + 2*(a^3 + a*b^2)*c*cos(x) - (a^4 - b^4 - 2*(a^2 - b^2)*c^2)*cos(x)^2 + 2*((a^2*b + b^3)*c - (a^3*b + a*b^3 - 2*a*b*c^2)*cos(x))*sin(x) + 2*(2*a*b*c*cos(x)^2 - a*b*c + (a^2*b + b^3)*cos(x) - (a^3 + a*b^2 + (a^2 - b^2)*c*cos(x))*sin(x))*sqrt(a^2 + b^2 - c^2))/(2*a*c*cos(x) + (a^2 - b^2)*cos(x)^2 + b^2 + c^2 + 2*(a*b*cos(x) + b*c)*sin(x))) - (a^2*b + b^3 - b*c^2)*log(2*a*c*cos(x) + (a^2 - b^2)*cos(x)^2 + b^2 + c^2 + 2*(a*b*cos(x) + b*c)*sin(x)) + (a^2*b + b^3 - b*c^2 - c^3 + (a^2 + b^2)*c)*log(sin(x) + 1) + (a^2*b + b^3 - b*c^2 + c^3 - (a^2 + b^2)*c)*log(-sin(x) + 1))/(a^2*b^2 + b^4 + c^4 - (a^2 + 2*b^2)*c^2), 1/2*(2*sqrt(-a^2 - b^2 + c^2)*a*c*arctan((a*c*cos(x) + b*c*sin(x) + a^2 + b^2)*sqrt(-a^2 - b^2 + c^2)/((a^2*b + b^3 - b*c^2)*cos(x) - (a^3 + a*b^2 - a*c^2)*sin(x))) + (a^2*b + b^3 - b*c^2)*log(2*a*c*cos(x) + (a^2 - b^2)*cos(x)^2 + b^2 + c^2 + 2*(a*b*cos(x) + b*c)*sin(x)) - (a^2*b + b^3 - b*c^2 - c^3 + (a^2 + b^2)*c)*log(sin(x) + 1) - (a^2*b + b^3 - b*c^2 + c^3 - (a^2 + b^2)*c)*log(-sin(x) + 1))/(a^2*b^2 + b^4 + c^4 - (a^2 + 2*b^2)*c^2)]","A",0
448,0,0,0,0.878940," ","integrate((a+b*sec(e*x+d)+c*tan(e*x+d))^(3/2)/sec(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a\right)}^{\frac{3}{2}}}{\sec\left(e x + d\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b*sec(e*x + d) + c*tan(e*x + d) + a)^(3/2)/sec(e*x + d)^(3/2), x)","F",0
449,0,0,0,0.645110," ","integrate((a+b*sec(e*x+d)+c*tan(e*x+d))^(1/2)/sec(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a}}{\sqrt{\sec\left(e x + d\right)}}, x\right)"," ",0,"integral(sqrt(b*sec(e*x + d) + c*tan(e*x + d) + a)/sqrt(sec(e*x + d)), x)","F",0
450,0,0,0,2.896939," ","integrate(sec(e*x+d)^(1/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(e x + d\right)}}{\sqrt{b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a}}, x\right)"," ",0,"integral(sqrt(sec(e*x + d))/sqrt(b*sec(e*x + d) + c*tan(e*x + d) + a), x)","F",0
451,0,0,0,1.836704," ","integrate(sec(e*x+d)^(3/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a} \sec\left(e x + d\right)^{\frac{3}{2}}}{b^{2} \sec\left(e x + d\right)^{2} + c^{2} \tan\left(e x + d\right)^{2} + 2 \, a b \sec\left(e x + d\right) + a^{2} + 2 \, {\left(b c \sec\left(e x + d\right) + a c\right)} \tan\left(e x + d\right)}, x\right)"," ",0,"integral(sqrt(b*sec(e*x + d) + c*tan(e*x + d) + a)*sec(e*x + d)^(3/2)/(b^2*sec(e*x + d)^2 + c^2*tan(e*x + d)^2 + 2*a*b*sec(e*x + d) + a^2 + 2*(b*c*sec(e*x + d) + a*c)*tan(e*x + d)), x)","F",0
452,0,0,0,0.957104," ","integrate(sec(e*x+d)^(5/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a} \sec\left(e x + d\right)^{\frac{5}{2}}}{b^{3} \sec\left(e x + d\right)^{3} + c^{3} \tan\left(e x + d\right)^{3} + 3 \, a b^{2} \sec\left(e x + d\right)^{2} + 3 \, a^{2} b \sec\left(e x + d\right) + a^{3} + 3 \, {\left(b c^{2} \sec\left(e x + d\right) + a c^{2}\right)} \tan\left(e x + d\right)^{2} + 3 \, {\left(b^{2} c \sec\left(e x + d\right)^{2} + 2 \, a b c \sec\left(e x + d\right) + a^{2} c\right)} \tan\left(e x + d\right)}, x\right)"," ",0,"integral(sqrt(b*sec(e*x + d) + c*tan(e*x + d) + a)*sec(e*x + d)^(5/2)/(b^3*sec(e*x + d)^3 + c^3*tan(e*x + d)^3 + 3*a*b^2*sec(e*x + d)^2 + 3*a^2*b*sec(e*x + d) + a^3 + 3*(b*c^2*sec(e*x + d) + a*c^2)*tan(e*x + d)^2 + 3*(b^2*c*sec(e*x + d)^2 + 2*a*b*c*sec(e*x + d) + a^2*c)*tan(e*x + d)), x)","F",0
453,0,0,0,0.934434," ","integrate(cos(e*x+d)^(3/2)*(a+b*sec(e*x+d)+c*tan(e*x+d))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(e x + d\right) \sec\left(e x + d\right) + c \cos\left(e x + d\right) \tan\left(e x + d\right) + a \cos\left(e x + d\right)\right)} \sqrt{b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a} \sqrt{\cos\left(e x + d\right)}, x\right)"," ",0,"integral((b*cos(e*x + d)*sec(e*x + d) + c*cos(e*x + d)*tan(e*x + d) + a*cos(e*x + d))*sqrt(b*sec(e*x + d) + c*tan(e*x + d) + a)*sqrt(cos(e*x + d)), x)","F",0
454,0,0,0,1.117386," ","integrate(cos(e*x+d)^(1/2)*(a+b*sec(e*x+d)+c*tan(e*x+d))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a} \sqrt{\cos\left(e x + d\right)}, x\right)"," ",0,"integral(sqrt(b*sec(e*x + d) + c*tan(e*x + d) + a)*sqrt(cos(e*x + d)), x)","F",0
455,0,0,0,0.892052," ","integrate(1/cos(e*x+d)^(1/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a} \sqrt{\cos\left(e x + d\right)}}{b \cos\left(e x + d\right) \sec\left(e x + d\right) + c \cos\left(e x + d\right) \tan\left(e x + d\right) + a \cos\left(e x + d\right)}, x\right)"," ",0,"integral(sqrt(b*sec(e*x + d) + c*tan(e*x + d) + a)*sqrt(cos(e*x + d))/(b*cos(e*x + d)*sec(e*x + d) + c*cos(e*x + d)*tan(e*x + d) + a*cos(e*x + d)), x)","F",0
456,0,0,0,0.895029," ","integrate(1/cos(e*x+d)^(3/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a} \sqrt{\cos\left(e x + d\right)}}{b^{2} \cos\left(e x + d\right)^{2} \sec\left(e x + d\right)^{2} + c^{2} \cos\left(e x + d\right)^{2} \tan\left(e x + d\right)^{2} + 2 \, a b \cos\left(e x + d\right)^{2} \sec\left(e x + d\right) + a^{2} \cos\left(e x + d\right)^{2} + 2 \, {\left(b c \cos\left(e x + d\right)^{2} \sec\left(e x + d\right) + a c \cos\left(e x + d\right)^{2}\right)} \tan\left(e x + d\right)}, x\right)"," ",0,"integral(sqrt(b*sec(e*x + d) + c*tan(e*x + d) + a)*sqrt(cos(e*x + d))/(b^2*cos(e*x + d)^2*sec(e*x + d)^2 + c^2*cos(e*x + d)^2*tan(e*x + d)^2 + 2*a*b*cos(e*x + d)^2*sec(e*x + d) + a^2*cos(e*x + d)^2 + 2*(b*c*cos(e*x + d)^2*sec(e*x + d) + a*c*cos(e*x + d)^2)*tan(e*x + d)), x)","F",0
457,0,0,0,1.568237," ","integrate(1/cos(e*x+d)^(5/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a} \sqrt{\cos\left(e x + d\right)}}{b^{3} \cos\left(e x + d\right)^{3} \sec\left(e x + d\right)^{3} + c^{3} \cos\left(e x + d\right)^{3} \tan\left(e x + d\right)^{3} + 3 \, a b^{2} \cos\left(e x + d\right)^{3} \sec\left(e x + d\right)^{2} + 3 \, a^{2} b \cos\left(e x + d\right)^{3} \sec\left(e x + d\right) + a^{3} \cos\left(e x + d\right)^{3} + 3 \, {\left(b c^{2} \cos\left(e x + d\right)^{3} \sec\left(e x + d\right) + a c^{2} \cos\left(e x + d\right)^{3}\right)} \tan\left(e x + d\right)^{2} + 3 \, {\left(b^{2} c \cos\left(e x + d\right)^{3} \sec\left(e x + d\right)^{2} + 2 \, a b c \cos\left(e x + d\right)^{3} \sec\left(e x + d\right) + a^{2} c \cos\left(e x + d\right)^{3}\right)} \tan\left(e x + d\right)}, x\right)"," ",0,"integral(sqrt(b*sec(e*x + d) + c*tan(e*x + d) + a)*sqrt(cos(e*x + d))/(b^3*cos(e*x + d)^3*sec(e*x + d)^3 + c^3*cos(e*x + d)^3*tan(e*x + d)^3 + 3*a*b^2*cos(e*x + d)^3*sec(e*x + d)^2 + 3*a^2*b*cos(e*x + d)^3*sec(e*x + d) + a^3*cos(e*x + d)^3 + 3*(b*c^2*cos(e*x + d)^3*sec(e*x + d) + a*c^2*cos(e*x + d)^3)*tan(e*x + d)^2 + 3*(b^2*c*cos(e*x + d)^3*sec(e*x + d)^2 + 2*a*b*c*cos(e*x + d)^3*sec(e*x + d) + a^2*c*cos(e*x + d)^3)*tan(e*x + d)), x)","F",0
458,1,555,0,2.053429," ","integrate(1/(a+b*cot(x)+c*csc(x)),x, algorithm=""fricas"")","\left[\frac{\sqrt{a^{2} + b^{2} - c^{2}} a c \log\left(\frac{a^{4} + 3 \, a^{2} b^{2} + 2 \, b^{4} + {\left(a^{2} - b^{2}\right)} c^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} c \cos\left(x\right) + {\left(a^{4} - b^{4} - 2 \, {\left(a^{2} - b^{2}\right)} c^{2}\right)} \cos\left(x\right)^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} c - {\left(a^{3} b + a b^{3} - 2 \, a b c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right) + 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(a^{3} + a b^{2}\right)} \cos\left(x\right) - {\left(a^{2} b + b^{3} - {\left(a^{2} - b^{2}\right)} c \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{a^{2} + b^{2} - c^{2}}}{2 \, b c \cos\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(a b \cos\left(x\right) + a c\right)} \sin\left(x\right)}\right) + 2 \, {\left(a^{3} + a b^{2} - a c^{2}\right)} x - {\left(a^{2} b + b^{3} - b c^{2}\right)} \log\left(2 \, b c \cos\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(a b \cos\left(x\right) + a c\right)} \sin\left(x\right)\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} - {\left(a^{2} + b^{2}\right)} c^{2}\right)}}, -\frac{2 \, \sqrt{-a^{2} - b^{2} + c^{2}} a c \arctan\left(\frac{{\left(b c \cos\left(x\right) + a c \sin\left(x\right) + a^{2} + b^{2}\right)} \sqrt{-a^{2} - b^{2} + c^{2}}}{{\left(a^{3} + a b^{2} - a c^{2}\right)} \cos\left(x\right) - {\left(a^{2} b + b^{3} - b c^{2}\right)} \sin\left(x\right)}\right) - 2 \, {\left(a^{3} + a b^{2} - a c^{2}\right)} x + {\left(a^{2} b + b^{3} - b c^{2}\right)} \log\left(2 \, b c \cos\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(a b \cos\left(x\right) + a c\right)} \sin\left(x\right)\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} - {\left(a^{2} + b^{2}\right)} c^{2}\right)}}\right]"," ",0,"[1/2*(sqrt(a^2 + b^2 - c^2)*a*c*log((a^4 + 3*a^2*b^2 + 2*b^4 + (a^2 - b^2)*c^2 + 2*(a^2*b + b^3)*c*cos(x) + (a^4 - b^4 - 2*(a^2 - b^2)*c^2)*cos(x)^2 + 2*((a^3 + a*b^2)*c - (a^3*b + a*b^3 - 2*a*b*c^2)*cos(x))*sin(x) + 2*(2*a*b*c*cos(x)^2 - a*b*c + (a^3 + a*b^2)*cos(x) - (a^2*b + b^3 - (a^2 - b^2)*c*cos(x))*sin(x))*sqrt(a^2 + b^2 - c^2))/(2*b*c*cos(x) - (a^2 - b^2)*cos(x)^2 + a^2 + c^2 + 2*(a*b*cos(x) + a*c)*sin(x))) + 2*(a^3 + a*b^2 - a*c^2)*x - (a^2*b + b^3 - b*c^2)*log(2*b*c*cos(x) - (a^2 - b^2)*cos(x)^2 + a^2 + c^2 + 2*(a*b*cos(x) + a*c)*sin(x)))/(a^4 + 2*a^2*b^2 + b^4 - (a^2 + b^2)*c^2), -1/2*(2*sqrt(-a^2 - b^2 + c^2)*a*c*arctan((b*c*cos(x) + a*c*sin(x) + a^2 + b^2)*sqrt(-a^2 - b^2 + c^2)/((a^3 + a*b^2 - a*c^2)*cos(x) - (a^2*b + b^3 - b*c^2)*sin(x))) - 2*(a^3 + a*b^2 - a*c^2)*x + (a^2*b + b^3 - b*c^2)*log(2*b*c*cos(x) - (a^2 - b^2)*cos(x)^2 + a^2 + c^2 + 2*(a*b*cos(x) + a*c)*sin(x)))/(a^4 + 2*a^2*b^2 + b^4 - (a^2 + b^2)*c^2)]","B",0
459,1,349,0,0.808504," ","integrate(csc(x)/(a+b*cot(x)+c*csc(x)),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{a^{4} + 3 \, a^{2} b^{2} + 2 \, b^{4} + {\left(a^{2} - b^{2}\right)} c^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} c \cos\left(x\right) + {\left(a^{4} - b^{4} - 2 \, {\left(a^{2} - b^{2}\right)} c^{2}\right)} \cos\left(x\right)^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} c - {\left(a^{3} b + a b^{3} - 2 \, a b c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right) - 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(a^{3} + a b^{2}\right)} \cos\left(x\right) - {\left(a^{2} b + b^{3} - {\left(a^{2} - b^{2}\right)} c \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{a^{2} + b^{2} - c^{2}}}{2 \, b c \cos\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(a b \cos\left(x\right) + a c\right)} \sin\left(x\right)}\right)}{2 \, \sqrt{a^{2} + b^{2} - c^{2}}}, \frac{\sqrt{-a^{2} - b^{2} + c^{2}} \arctan\left(\frac{{\left(b c \cos\left(x\right) + a c \sin\left(x\right) + a^{2} + b^{2}\right)} \sqrt{-a^{2} - b^{2} + c^{2}}}{{\left(a^{3} + a b^{2} - a c^{2}\right)} \cos\left(x\right) - {\left(a^{2} b + b^{3} - b c^{2}\right)} \sin\left(x\right)}\right)}{a^{2} + b^{2} - c^{2}}\right]"," ",0,"[1/2*log(-(a^4 + 3*a^2*b^2 + 2*b^4 + (a^2 - b^2)*c^2 + 2*(a^2*b + b^3)*c*cos(x) + (a^4 - b^4 - 2*(a^2 - b^2)*c^2)*cos(x)^2 + 2*((a^3 + a*b^2)*c - (a^3*b + a*b^3 - 2*a*b*c^2)*cos(x))*sin(x) - 2*(2*a*b*c*cos(x)^2 - a*b*c + (a^3 + a*b^2)*cos(x) - (a^2*b + b^3 - (a^2 - b^2)*c*cos(x))*sin(x))*sqrt(a^2 + b^2 - c^2))/(2*b*c*cos(x) - (a^2 - b^2)*cos(x)^2 + a^2 + c^2 + 2*(a*b*cos(x) + a*c)*sin(x)))/sqrt(a^2 + b^2 - c^2), sqrt(-a^2 - b^2 + c^2)*arctan((b*c*cos(x) + a*c*sin(x) + a^2 + b^2)*sqrt(-a^2 - b^2 + c^2)/((a^3 + a*b^2 - a*c^2)*cos(x) - (a^2*b + b^3 - b*c^2)*sin(x)))/(a^2 + b^2 - c^2)]","B",0
460,1,669,0,6.046517," ","integrate(csc(x)^2/(a+b*cot(x)+c*csc(x)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{a^{2} + b^{2} - c^{2}} a c \log\left(\frac{a^{4} + 3 \, a^{2} b^{2} + 2 \, b^{4} + {\left(a^{2} - b^{2}\right)} c^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} c \cos\left(x\right) + {\left(a^{4} - b^{4} - 2 \, {\left(a^{2} - b^{2}\right)} c^{2}\right)} \cos\left(x\right)^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} c - {\left(a^{3} b + a b^{3} - 2 \, a b c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right) + 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(a^{3} + a b^{2}\right)} \cos\left(x\right) - {\left(a^{2} b + b^{3} - {\left(a^{2} - b^{2}\right)} c \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{a^{2} + b^{2} - c^{2}}}{2 \, b c \cos\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(a b \cos\left(x\right) + a c\right)} \sin\left(x\right)}\right) + {\left(a^{2} b + b^{3} - b c^{2}\right)} \log\left(2 \, b c \cos\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(a b \cos\left(x\right) + a c\right)} \sin\left(x\right)\right) - {\left(a^{2} b + b^{3} - b c^{2} - c^{3} + {\left(a^{2} + b^{2}\right)} c\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - {\left(a^{2} b + b^{3} - b c^{2} + c^{3} - {\left(a^{2} + b^{2}\right)} c\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{2 \, {\left(a^{2} b^{2} + b^{4} + c^{4} - {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)}}, \frac{2 \, \sqrt{-a^{2} - b^{2} + c^{2}} a c \arctan\left(\frac{{\left(b c \cos\left(x\right) + a c \sin\left(x\right) + a^{2} + b^{2}\right)} \sqrt{-a^{2} - b^{2} + c^{2}}}{{\left(a^{3} + a b^{2} - a c^{2}\right)} \cos\left(x\right) - {\left(a^{2} b + b^{3} - b c^{2}\right)} \sin\left(x\right)}\right) - {\left(a^{2} b + b^{3} - b c^{2}\right)} \log\left(2 \, b c \cos\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(a b \cos\left(x\right) + a c\right)} \sin\left(x\right)\right) + {\left(a^{2} b + b^{3} - b c^{2} - c^{3} + {\left(a^{2} + b^{2}\right)} c\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + {\left(a^{2} b + b^{3} - b c^{2} + c^{3} - {\left(a^{2} + b^{2}\right)} c\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{2 \, {\left(a^{2} b^{2} + b^{4} + c^{4} - {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)}}\right]"," ",0,"[-1/2*(sqrt(a^2 + b^2 - c^2)*a*c*log((a^4 + 3*a^2*b^2 + 2*b^4 + (a^2 - b^2)*c^2 + 2*(a^2*b + b^3)*c*cos(x) + (a^4 - b^4 - 2*(a^2 - b^2)*c^2)*cos(x)^2 + 2*((a^3 + a*b^2)*c - (a^3*b + a*b^3 - 2*a*b*c^2)*cos(x))*sin(x) + 2*(2*a*b*c*cos(x)^2 - a*b*c + (a^3 + a*b^2)*cos(x) - (a^2*b + b^3 - (a^2 - b^2)*c*cos(x))*sin(x))*sqrt(a^2 + b^2 - c^2))/(2*b*c*cos(x) - (a^2 - b^2)*cos(x)^2 + a^2 + c^2 + 2*(a*b*cos(x) + a*c)*sin(x))) + (a^2*b + b^3 - b*c^2)*log(2*b*c*cos(x) - (a^2 - b^2)*cos(x)^2 + a^2 + c^2 + 2*(a*b*cos(x) + a*c)*sin(x)) - (a^2*b + b^3 - b*c^2 - c^3 + (a^2 + b^2)*c)*log(1/2*cos(x) + 1/2) - (a^2*b + b^3 - b*c^2 + c^3 - (a^2 + b^2)*c)*log(-1/2*cos(x) + 1/2))/(a^2*b^2 + b^4 + c^4 - (a^2 + 2*b^2)*c^2), 1/2*(2*sqrt(-a^2 - b^2 + c^2)*a*c*arctan((b*c*cos(x) + a*c*sin(x) + a^2 + b^2)*sqrt(-a^2 - b^2 + c^2)/((a^3 + a*b^2 - a*c^2)*cos(x) - (a^2*b + b^3 - b*c^2)*sin(x))) - (a^2*b + b^3 - b*c^2)*log(2*b*c*cos(x) - (a^2 - b^2)*cos(x)^2 + a^2 + c^2 + 2*(a*b*cos(x) + a*c)*sin(x)) + (a^2*b + b^3 - b*c^2 - c^3 + (a^2 + b^2)*c)*log(1/2*cos(x) + 1/2) + (a^2*b + b^3 - b*c^2 + c^3 - (a^2 + b^2)*c)*log(-1/2*cos(x) + 1/2))/(a^2*b^2 + b^4 + c^4 - (a^2 + 2*b^2)*c^2)]","B",0
461,1,24,0,0.885708," ","integrate(csc(x)/(2+2*cot(x)+3*csc(x)),x, algorithm=""fricas"")","-\arctan\left(-\frac{3 \, \cos\left(x\right) + 3 \, \sin\left(x\right) + 4}{\cos\left(x\right) - \sin\left(x\right)}\right)"," ",0,"-arctan(-(3*cos(x) + 3*sin(x) + 4)/(cos(x) - sin(x)))","A",0
462,0,0,0,1.048614," ","integrate((a+c*cot(e*x+d)+b*csc(e*x+d))^(3/2)/csc(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a\right)}^{\frac{3}{2}}}{\csc\left(e x + d\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((c*cot(e*x + d) + b*csc(e*x + d) + a)^(3/2)/csc(e*x + d)^(3/2), x)","F",0
463,0,0,0,1.232384," ","integrate((a+c*cot(e*x+d)+b*csc(e*x+d))^(1/2)/csc(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a}}{\sqrt{\csc\left(e x + d\right)}}, x\right)"," ",0,"integral(sqrt(c*cot(e*x + d) + b*csc(e*x + d) + a)/sqrt(csc(e*x + d)), x)","F",0
464,0,0,0,0.665690," ","integrate(csc(e*x+d)^(1/2)/(a+c*cot(e*x+d)+b*csc(e*x+d))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\csc\left(e x + d\right)}}{\sqrt{c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a}}, x\right)"," ",0,"integral(sqrt(csc(e*x + d))/sqrt(c*cot(e*x + d) + b*csc(e*x + d) + a), x)","F",0
465,0,0,0,1.098142," ","integrate(csc(e*x+d)^(3/2)/(a+c*cot(e*x+d)+b*csc(e*x+d))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a} \csc\left(e x + d\right)^{\frac{3}{2}}}{c^{2} \cot\left(e x + d\right)^{2} + b^{2} \csc\left(e x + d\right)^{2} + 2 \, a c \cot\left(e x + d\right) + a^{2} + 2 \, {\left(b c \cot\left(e x + d\right) + a b\right)} \csc\left(e x + d\right)}, x\right)"," ",0,"integral(sqrt(c*cot(e*x + d) + b*csc(e*x + d) + a)*csc(e*x + d)^(3/2)/(c^2*cot(e*x + d)^2 + b^2*csc(e*x + d)^2 + 2*a*c*cot(e*x + d) + a^2 + 2*(b*c*cot(e*x + d) + a*b)*csc(e*x + d)), x)","F",0
466,0,0,0,0.677186," ","integrate(csc(e*x+d)^(5/2)/(a+c*cot(e*x+d)+b*csc(e*x+d))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a} \csc\left(e x + d\right)^{\frac{5}{2}}}{c^{3} \cot\left(e x + d\right)^{3} + b^{3} \csc\left(e x + d\right)^{3} + 3 \, a c^{2} \cot\left(e x + d\right)^{2} + 3 \, a^{2} c \cot\left(e x + d\right) + a^{3} + 3 \, {\left(b^{2} c \cot\left(e x + d\right) + a b^{2}\right)} \csc\left(e x + d\right)^{2} + 3 \, {\left(b c^{2} \cot\left(e x + d\right)^{2} + 2 \, a b c \cot\left(e x + d\right) + a^{2} b\right)} \csc\left(e x + d\right)}, x\right)"," ",0,"integral(sqrt(c*cot(e*x + d) + b*csc(e*x + d) + a)*csc(e*x + d)^(5/2)/(c^3*cot(e*x + d)^3 + b^3*csc(e*x + d)^3 + 3*a*c^2*cot(e*x + d)^2 + 3*a^2*c*cot(e*x + d) + a^3 + 3*(b^2*c*cot(e*x + d) + a*b^2)*csc(e*x + d)^2 + 3*(b*c^2*cot(e*x + d)^2 + 2*a*b*c*cot(e*x + d) + a^2*b)*csc(e*x + d)), x)","F",0
467,0,0,0,0.626784," ","integrate((a+c*cot(e*x+d)+b*csc(e*x+d))^(3/2)*sin(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a\right)}^{\frac{3}{2}} \sin\left(e x + d\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((c*cot(e*x + d) + b*csc(e*x + d) + a)^(3/2)*sin(e*x + d)^(3/2), x)","F",0
468,0,0,0,1.297221," ","integrate((a+c*cot(e*x+d)+b*csc(e*x+d))^(1/2)*sin(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a} \sqrt{\sin\left(e x + d\right)}, x\right)"," ",0,"integral(sqrt(c*cot(e*x + d) + b*csc(e*x + d) + a)*sqrt(sin(e*x + d)), x)","F",0
469,0,0,0,0.858503," ","integrate(1/(a+c*cot(e*x+d)+b*csc(e*x+d))^(1/2)/sin(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a} \sqrt{\sin\left(e x + d\right)}}, x\right)"," ",0,"integral(1/(sqrt(c*cot(e*x + d) + b*csc(e*x + d) + a)*sqrt(sin(e*x + d))), x)","F",0
470,0,0,0,1.196119," ","integrate(1/(a+c*cot(e*x+d)+b*csc(e*x+d))^(3/2)/sin(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a} \sqrt{\sin\left(e x + d\right)}}{a^{2} \cos\left(e x + d\right)^{2} + {\left(c^{2} \cos\left(e x + d\right)^{2} - c^{2}\right)} \cot\left(e x + d\right)^{2} + {\left(b^{2} \cos\left(e x + d\right)^{2} - b^{2}\right)} \csc\left(e x + d\right)^{2} - a^{2} + 2 \, {\left(a c \cos\left(e x + d\right)^{2} - a c\right)} \cot\left(e x + d\right) + 2 \, {\left(a b \cos\left(e x + d\right)^{2} - a b + {\left(b c \cos\left(e x + d\right)^{2} - b c\right)} \cot\left(e x + d\right)\right)} \csc\left(e x + d\right)}, x\right)"," ",0,"integral(-sqrt(c*cot(e*x + d) + b*csc(e*x + d) + a)*sqrt(sin(e*x + d))/(a^2*cos(e*x + d)^2 + (c^2*cos(e*x + d)^2 - c^2)*cot(e*x + d)^2 + (b^2*cos(e*x + d)^2 - b^2)*csc(e*x + d)^2 - a^2 + 2*(a*c*cos(e*x + d)^2 - a*c)*cot(e*x + d) + 2*(a*b*cos(e*x + d)^2 - a*b + (b*c*cos(e*x + d)^2 - b*c)*cot(e*x + d))*csc(e*x + d)), x)","F",0
471,0,0,0,1.943260," ","integrate(1/(a+c*cot(e*x+d)+b*csc(e*x+d))^(5/2)/sin(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a}}{{\left(a^{3} \cos\left(e x + d\right)^{2} + {\left(c^{3} \cos\left(e x + d\right)^{2} - c^{3}\right)} \cot\left(e x + d\right)^{3} + {\left(b^{3} \cos\left(e x + d\right)^{2} - b^{3}\right)} \csc\left(e x + d\right)^{3} - a^{3} + 3 \, {\left(a c^{2} \cos\left(e x + d\right)^{2} - a c^{2}\right)} \cot\left(e x + d\right)^{2} + 3 \, {\left(a b^{2} \cos\left(e x + d\right)^{2} - a b^{2} + {\left(b^{2} c \cos\left(e x + d\right)^{2} - b^{2} c\right)} \cot\left(e x + d\right)\right)} \csc\left(e x + d\right)^{2} + 3 \, {\left(a^{2} c \cos\left(e x + d\right)^{2} - a^{2} c\right)} \cot\left(e x + d\right) + 3 \, {\left(a^{2} b \cos\left(e x + d\right)^{2} - a^{2} b + {\left(b c^{2} \cos\left(e x + d\right)^{2} - b c^{2}\right)} \cot\left(e x + d\right)^{2} + 2 \, {\left(a b c \cos\left(e x + d\right)^{2} - a b c\right)} \cot\left(e x + d\right)\right)} \csc\left(e x + d\right)\right)} \sqrt{\sin\left(e x + d\right)}}, x\right)"," ",0,"integral(-sqrt(c*cot(e*x + d) + b*csc(e*x + d) + a)/((a^3*cos(e*x + d)^2 + (c^3*cos(e*x + d)^2 - c^3)*cot(e*x + d)^3 + (b^3*cos(e*x + d)^2 - b^3)*csc(e*x + d)^3 - a^3 + 3*(a*c^2*cos(e*x + d)^2 - a*c^2)*cot(e*x + d)^2 + 3*(a*b^2*cos(e*x + d)^2 - a*b^2 + (b^2*c*cos(e*x + d)^2 - b^2*c)*cot(e*x + d))*csc(e*x + d)^2 + 3*(a^2*c*cos(e*x + d)^2 - a^2*c)*cot(e*x + d) + 3*(a^2*b*cos(e*x + d)^2 - a^2*b + (b*c^2*cos(e*x + d)^2 - b*c^2)*cot(e*x + d)^2 + 2*(a*b*c*cos(e*x + d)^2 - a*b*c)*cot(e*x + d))*csc(e*x + d))*sqrt(sin(e*x + d))), x)","F",0
472,1,1,0,0.890718," ","integrate(1/(cos(x)^2+sin(x)^2),x, algorithm=""fricas"")","x"," ",0,"x","A",0
473,1,1,0,1.486941," ","integrate(1/(cos(x)^2+sin(x)^2)^2,x, algorithm=""fricas"")","x"," ",0,"x","A",0
474,1,1,0,0.986151," ","integrate(1/(cos(x)^2+sin(x)^2)^3,x, algorithm=""fricas"")","x"," ",0,"x","A",0
475,1,23,0,0.850289," ","integrate(1/(cos(x)^2-sin(x)^2),x, algorithm=""fricas"")","\frac{1}{4} \, \log\left(2 \, \cos\left(x\right) \sin\left(x\right) + 1\right) - \frac{1}{4} \, \log\left(-2 \, \cos\left(x\right) \sin\left(x\right) + 1\right)"," ",0,"1/4*log(2*cos(x)*sin(x) + 1) - 1/4*log(-2*cos(x)*sin(x) + 1)","B",0
476,1,15,0,1.306283," ","integrate(1/(cos(x)^2-sin(x)^2)^2,x, algorithm=""fricas"")","\frac{\cos\left(x\right) \sin\left(x\right)}{2 \, \cos\left(x\right)^{2} - 1}"," ",0,"cos(x)*sin(x)/(2*cos(x)^2 - 1)","A",0
477,1,74,0,0.763595," ","integrate(1/(cos(x)^2-sin(x)^2)^3,x, algorithm=""fricas"")","\frac{{\left(4 \, \cos\left(x\right)^{4} - 4 \, \cos\left(x\right)^{2} + 1\right)} \log\left(2 \, \cos\left(x\right) \sin\left(x\right) + 1\right) - {\left(4 \, \cos\left(x\right)^{4} - 4 \, \cos\left(x\right)^{2} + 1\right)} \log\left(-2 \, \cos\left(x\right) \sin\left(x\right) + 1\right) + 4 \, \cos\left(x\right) \sin\left(x\right)}{8 \, {\left(4 \, \cos\left(x\right)^{4} - 4 \, \cos\left(x\right)^{2} + 1\right)}}"," ",0,"1/8*((4*cos(x)^4 - 4*cos(x)^2 + 1)*log(2*cos(x)*sin(x) + 1) - (4*cos(x)^4 - 4*cos(x)^2 + 1)*log(-2*cos(x)*sin(x) + 1) + 4*cos(x)*sin(x))/(4*cos(x)^4 - 4*cos(x)^2 + 1)","B",0
478,1,35,0,0.686025," ","integrate(1/(cos(x)^2+a^2*sin(x)^2),x, algorithm=""fricas"")","-\frac{\arctan\left(\frac{{\left(a^{2} + 1\right)} \cos\left(x\right)^{2} - a^{2}}{2 \, a \cos\left(x\right) \sin\left(x\right)}\right)}{2 \, a}"," ",0,"-1/2*arctan(1/2*((a^2 + 1)*cos(x)^2 - a^2)/(a*cos(x)*sin(x)))/a","B",0
479,1,31,0,2.043881," ","integrate(1/(b^2*cos(x)^2+sin(x)^2),x, algorithm=""fricas"")","-\frac{\arctan\left(\frac{{\left(b^{2} + 1\right)} \cos\left(x\right)^{2} - 1}{2 \, b \cos\left(x\right) \sin\left(x\right)}\right)}{2 \, b}"," ",0,"-1/2*arctan(1/2*((b^2 + 1)*cos(x)^2 - 1)/(b*cos(x)*sin(x)))/b","B",0
480,1,43,0,2.387940," ","integrate(1/(b^2*cos(x)^2+a^2*sin(x)^2),x, algorithm=""fricas"")","-\frac{\arctan\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(x\right)^{2} - a^{2}}{2 \, a b \cos\left(x\right) \sin\left(x\right)}\right)}{2 \, a b}"," ",0,"-1/2*arctan(1/2*((a^2 + b^2)*cos(x)^2 - a^2)/(a*b*cos(x)*sin(x)))/(a*b)","B",0
481,1,43,0,0.986352," ","integrate(1/(4*cos(1+2*x)^2+3*sin(1+2*x)^2),x, algorithm=""fricas"")","-\frac{1}{24} \, \sqrt{3} \arctan\left(\frac{7 \, \sqrt{3} \cos\left(2 \, x + 1\right)^{2} - 3 \, \sqrt{3}}{12 \, \cos\left(2 \, x + 1\right) \sin\left(2 \, x + 1\right)}\right)"," ",0,"-1/24*sqrt(3)*arctan(1/12*(7*sqrt(3)*cos(2*x + 1)^2 - 3*sqrt(3))/(cos(2*x + 1)*sin(2*x + 1)))","A",0
482,1,182,0,0.703171," ","integrate(sin(x)^2/(a*cos(x)^2+b*sin(x)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-\frac{a}{b}} \log\left(\frac{{\left(a^{2} + 6 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(3 \, a b + b^{2}\right)} \cos\left(x\right)^{2} + 4 \, {\left({\left(a b + b^{2}\right)} \cos\left(x\right)^{3} - b^{2} \cos\left(x\right)\right)} \sqrt{-\frac{a}{b}} \sin\left(x\right) + b^{2}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} \cos\left(x\right)^{4} + 2 \, {\left(a b - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right) + 4 \, x}{4 \, {\left(a - b\right)}}, -\frac{\sqrt{\frac{a}{b}} \arctan\left(\frac{{\left({\left(a + b\right)} \cos\left(x\right)^{2} - b\right)} \sqrt{\frac{a}{b}}}{2 \, a \cos\left(x\right) \sin\left(x\right)}\right) + 2 \, x}{2 \, {\left(a - b\right)}}\right]"," ",0,"[-1/4*(sqrt(-a/b)*log(((a^2 + 6*a*b + b^2)*cos(x)^4 - 2*(3*a*b + b^2)*cos(x)^2 + 4*((a*b + b^2)*cos(x)^3 - b^2*cos(x))*sqrt(-a/b)*sin(x) + b^2)/((a^2 - 2*a*b + b^2)*cos(x)^4 + 2*(a*b - b^2)*cos(x)^2 + b^2)) + 4*x)/(a - b), -1/2*(sqrt(a/b)*arctan(1/2*((a + b)*cos(x)^2 - b)*sqrt(a/b)/(a*cos(x)*sin(x))) + 2*x)/(a - b)]","A",0
483,1,181,0,1.489722," ","integrate(cos(x)^2/(a*cos(x)^2+b*sin(x)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-\frac{b}{a}} \log\left(\frac{{\left(a^{2} + 6 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(3 \, a b + b^{2}\right)} \cos\left(x\right)^{2} - 4 \, {\left({\left(a^{2} + a b\right)} \cos\left(x\right)^{3} - a b \cos\left(x\right)\right)} \sqrt{-\frac{b}{a}} \sin\left(x\right) + b^{2}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} \cos\left(x\right)^{4} + 2 \, {\left(a b - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right) - 4 \, x}{4 \, {\left(a - b\right)}}, \frac{\sqrt{\frac{b}{a}} \arctan\left(\frac{{\left({\left(a + b\right)} \cos\left(x\right)^{2} - b\right)} \sqrt{\frac{b}{a}}}{2 \, b \cos\left(x\right) \sin\left(x\right)}\right) + 2 \, x}{2 \, {\left(a - b\right)}}\right]"," ",0,"[-1/4*(sqrt(-b/a)*log(((a^2 + 6*a*b + b^2)*cos(x)^4 - 2*(3*a*b + b^2)*cos(x)^2 - 4*((a^2 + a*b)*cos(x)^3 - a*b*cos(x))*sqrt(-b/a)*sin(x) + b^2)/((a^2 - 2*a*b + b^2)*cos(x)^4 + 2*(a*b - b^2)*cos(x)^2 + b^2)) - 4*x)/(a - b), 1/2*(sqrt(b/a)*arctan(1/2*((a + b)*cos(x)^2 - b)*sqrt(b/a)/(b*cos(x)*sin(x))) + 2*x)/(a - b)]","A",0
484,1,35,0,1.078741," ","integrate(1/(sec(x)^2+tan(x)^2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(x\right)^{2} - 2 \, \sqrt{2}}{4 \, \cos\left(x\right) \sin\left(x\right)}\right) - x"," ",0,"-1/2*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(x)^2 - 2*sqrt(2))/(cos(x)*sin(x))) - x","A",0
485,1,68,0,1.017306," ","integrate(1/(sec(x)^2+tan(x)^2)^2,x, algorithm=""fricas"")","\frac{4 \, x \cos\left(x\right)^{2} + {\left(\sqrt{2} \cos\left(x\right)^{2} - 2 \, \sqrt{2}\right)} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(x\right)^{2} - 2 \, \sqrt{2}}{4 \, \cos\left(x\right) \sin\left(x\right)}\right) - 4 \, \cos\left(x\right) \sin\left(x\right) - 8 \, x}{4 \, {\left(\cos\left(x\right)^{2} - 2\right)}}"," ",0,"1/4*(4*x*cos(x)^2 + (sqrt(2)*cos(x)^2 - 2*sqrt(2))*arctan(1/4*(3*sqrt(2)*cos(x)^2 - 2*sqrt(2))/(cos(x)*sin(x))) - 4*cos(x)*sin(x) - 8*x)/(cos(x)^2 - 2)","A",0
486,1,100,0,2.123175," ","integrate(1/(sec(x)^2+tan(x)^2)^3,x, algorithm=""fricas"")","-\frac{16 \, x \cos\left(x\right)^{4} - 64 \, x \cos\left(x\right)^{2} + 7 \, {\left(\sqrt{2} \cos\left(x\right)^{4} - 4 \, \sqrt{2} \cos\left(x\right)^{2} + 4 \, \sqrt{2}\right)} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(x\right)^{2} - 2 \, \sqrt{2}}{4 \, \cos\left(x\right) \sin\left(x\right)}\right) - 4 \, {\left(3 \, \cos\left(x\right)^{3} - 2 \, \cos\left(x\right)\right)} \sin\left(x\right) + 64 \, x}{16 \, {\left(\cos\left(x\right)^{4} - 4 \, \cos\left(x\right)^{2} + 4\right)}}"," ",0,"-1/16*(16*x*cos(x)^4 - 64*x*cos(x)^2 + 7*(sqrt(2)*cos(x)^4 - 4*sqrt(2)*cos(x)^2 + 4*sqrt(2))*arctan(1/4*(3*sqrt(2)*cos(x)^2 - 2*sqrt(2))/(cos(x)*sin(x))) - 4*(3*cos(x)^3 - 2*cos(x))*sin(x) + 64*x)/(cos(x)^4 - 4*cos(x)^2 + 4)","A",0
487,1,1,0,0.763895," ","integrate(1/(sec(x)^2-tan(x)^2),x, algorithm=""fricas"")","x"," ",0,"x","A",0
488,1,1,0,0.841868," ","integrate(1/(sec(x)^2-tan(x)^2)^2,x, algorithm=""fricas"")","x"," ",0,"x","A",0
489,1,1,0,1.528684," ","integrate(1/(sec(x)^2-tan(x)^2)^3,x, algorithm=""fricas"")","x"," ",0,"x","A",0
490,1,35,0,1.321120," ","integrate(1/(cot(x)^2+csc(x)^2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(x\right)^{2} - \sqrt{2}}{4 \, \cos\left(x\right) \sin\left(x\right)}\right) - x"," ",0,"-1/2*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(x)^2 - sqrt(2))/(cos(x)*sin(x))) - x","A",0
491,1,66,0,1.074272," ","integrate(1/(cot(x)^2+csc(x)^2)^2,x, algorithm=""fricas"")","\frac{4 \, x \cos\left(x\right)^{2} + {\left(\sqrt{2} \cos\left(x\right)^{2} + \sqrt{2}\right)} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(x\right)^{2} - \sqrt{2}}{4 \, \cos\left(x\right) \sin\left(x\right)}\right) - 4 \, \cos\left(x\right) \sin\left(x\right) + 4 \, x}{4 \, {\left(\cos\left(x\right)^{2} + 1\right)}}"," ",0,"1/4*(4*x*cos(x)^2 + (sqrt(2)*cos(x)^2 + sqrt(2))*arctan(1/4*(3*sqrt(2)*cos(x)^2 - sqrt(2))/(cos(x)*sin(x))) - 4*cos(x)*sin(x) + 4*x)/(cos(x)^2 + 1)","A",0
492,1,98,0,1.624706," ","integrate(1/(cot(x)^2+csc(x)^2)^3,x, algorithm=""fricas"")","-\frac{16 \, x \cos\left(x\right)^{4} + 32 \, x \cos\left(x\right)^{2} + 7 \, {\left(\sqrt{2} \cos\left(x\right)^{4} + 2 \, \sqrt{2} \cos\left(x\right)^{2} + \sqrt{2}\right)} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(x\right)^{2} - \sqrt{2}}{4 \, \cos\left(x\right) \sin\left(x\right)}\right) - 4 \, {\left(3 \, \cos\left(x\right)^{3} - \cos\left(x\right)\right)} \sin\left(x\right) + 16 \, x}{16 \, {\left(\cos\left(x\right)^{4} + 2 \, \cos\left(x\right)^{2} + 1\right)}}"," ",0,"-1/16*(16*x*cos(x)^4 + 32*x*cos(x)^2 + 7*(sqrt(2)*cos(x)^4 + 2*sqrt(2)*cos(x)^2 + sqrt(2))*arctan(1/4*(3*sqrt(2)*cos(x)^2 - sqrt(2))/(cos(x)*sin(x))) - 4*(3*cos(x)^3 - cos(x))*sin(x) + 16*x)/(cos(x)^4 + 2*cos(x)^2 + 1)","A",0
493,1,3,0,1.120530," ","integrate(1/(cot(x)^2-csc(x)^2),x, algorithm=""fricas"")","-x"," ",0,"-x","A",0
494,1,1,0,0.804994," ","integrate(1/(cot(x)^2-csc(x)^2)^2,x, algorithm=""fricas"")","x"," ",0,"x","A",0
495,1,3,0,0.496590," ","integrate(1/(cot(x)^2-csc(x)^2)^3,x, algorithm=""fricas"")","-x"," ",0,"-x","A",0
496,1,259,0,0.963387," ","integrate(1/(a+b*cos(x)^2+c*sin(x)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} - a b - {\left(a + b\right)} c} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2} + 2 \, {\left(4 \, a + 3 \, b\right)} c + c^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, a^{2} + 3 \, a b + {\left(5 \, a + 3 \, b\right)} c + c^{2}\right)} \cos\left(x\right)^{2} + 4 \, {\left({\left(2 \, a + b + c\right)} \cos\left(x\right)^{3} - {\left(a + c\right)} \cos\left(x\right)\right)} \sqrt{-a^{2} - a b - {\left(a + b\right)} c} \sin\left(x\right) + a^{2} + 2 \, a c + c^{2}}{{\left(b^{2} - 2 \, b c + c^{2}\right)} \cos\left(x\right)^{4} + 2 \, {\left(a b - {\left(a - b\right)} c - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + 2 \, a c + c^{2}}\right)}{4 \, {\left(a^{2} + a b + {\left(a + b\right)} c\right)}}, -\frac{\arctan\left(\frac{{\left(2 \, a + b + c\right)} \cos\left(x\right)^{2} - a - c}{2 \, \sqrt{a^{2} + a b + {\left(a + b\right)} c} \cos\left(x\right) \sin\left(x\right)}\right)}{2 \, \sqrt{a^{2} + a b + {\left(a + b\right)} c}}\right]"," ",0,"[-1/4*sqrt(-a^2 - a*b - (a + b)*c)*log(((8*a^2 + 8*a*b + b^2 + 2*(4*a + 3*b)*c + c^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b + (5*a + 3*b)*c + c^2)*cos(x)^2 + 4*((2*a + b + c)*cos(x)^3 - (a + c)*cos(x))*sqrt(-a^2 - a*b - (a + b)*c)*sin(x) + a^2 + 2*a*c + c^2)/((b^2 - 2*b*c + c^2)*cos(x)^4 + 2*(a*b - (a - b)*c - c^2)*cos(x)^2 + a^2 + 2*a*c + c^2))/(a^2 + a*b + (a + b)*c), -1/2*arctan(1/2*((2*a + b + c)*cos(x)^2 - a - c)/(sqrt(a^2 + a*b + (a + b)*c)*cos(x)*sin(x)))/sqrt(a^2 + a*b + (a + b)*c)]","B",0
497,1,2929,0,1.347366," ","integrate(x/(a+b*cos(x)^2+c*sin(x)^2),x, algorithm=""fricas"")","\frac{4 i \, {\left(b - c\right)} x \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} \log\left(-\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}} - 2 \, b + 2 \, c}{2 \, {\left(b - c\right)}}\right) - 4 i \, {\left(b - c\right)} x \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} \log\left(\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}} + 2 \, b - 2 \, c}{2 \, {\left(b - c\right)}}\right) - 4 i \, {\left(b - c\right)} x \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} \log\left(-\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}} - 2 \, b + 2 \, c}{2 \, {\left(b - c\right)}}\right) + 4 i \, {\left(b - c\right)} x \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} \log\left(\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}} + 2 \, b - 2 \, c}{2 \, {\left(b - c\right)}}\right) - 4 i \, {\left(b - c\right)} x \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} \log\left(-\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}} - 2 \, b + 2 \, c}{2 \, {\left(b - c\right)}}\right) + 4 i \, {\left(b - c\right)} x \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} \log\left(\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}} + 2 \, b - 2 \, c}{2 \, {\left(b - c\right)}}\right) + 4 i \, {\left(b - c\right)} x \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} \log\left(-\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}} - 2 \, b + 2 \, c}{2 \, {\left(b - c\right)}}\right) - 4 i \, {\left(b - c\right)} x \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} \log\left(\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}} + 2 \, b - 2 \, c}{2 \, {\left(b - c\right)}}\right) + 4 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}} - 2 \, b + 2 \, c}{2 \, {\left(b - c\right)}} + 1\right) + 4 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}} + 2 \, b - 2 \, c}{2 \, {\left(b - c\right)}} + 1\right) + 4 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}} - 2 \, b + 2 \, c}{2 \, {\left(b - c\right)}} + 1\right) + 4 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}} + 2 \, b - 2 \, c}{2 \, {\left(b - c\right)}} + 1\right) - 4 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}} - 2 \, b + 2 \, c}{2 \, {\left(b - c\right)}} + 1\right) - 4 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}} + 2 \, b - 2 \, c}{2 \, {\left(b - c\right)}} + 1\right) - 4 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}} - 2 \, b + 2 \, c}{2 \, {\left(b - c\right)}} + 1\right) - 4 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}} + 2 \, b - 2 \, c}{2 \, {\left(b - c\right)}} + 1\right)}{16 \, {\left(a^{2} + a b + {\left(a + b\right)} c\right)}}"," ",0,"1/16*(4*I*(b - c)*x*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*log(-1/2*((2*(2*a + b + c)*cos(x) + (4*I*a + 2*I*b + 2*I*c)*sin(x) - 4*((b - c)*cos(x) - (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c)) - 2*b + 2*c)/(b - c)) - 4*I*(b - c)*x*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*log(1/2*((2*(2*a + b + c)*cos(x) - (4*I*a + 2*I*b + 2*I*c)*sin(x) - 4*((b - c)*cos(x) + (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c)) + 2*b - 2*c)/(b - c)) - 4*I*(b - c)*x*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*log(-1/2*((2*(2*a + b + c)*cos(x) + (-4*I*a - 2*I*b - 2*I*c)*sin(x) - 4*((b - c)*cos(x) - (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c)) - 2*b + 2*c)/(b - c)) + 4*I*(b - c)*x*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*log(1/2*((2*(2*a + b + c)*cos(x) - (-4*I*a - 2*I*b - 2*I*c)*sin(x) - 4*((b - c)*cos(x) + (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c)) + 2*b - 2*c)/(b - c)) - 4*I*(b - c)*x*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*log(-1/2*((2*(2*a + b + c)*cos(x) + (4*I*a + 2*I*b + 2*I*c)*sin(x) + 4*((b - c)*cos(x) + (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c)) - 2*b + 2*c)/(b - c)) + 4*I*(b - c)*x*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*log(1/2*((2*(2*a + b + c)*cos(x) - (4*I*a + 2*I*b + 2*I*c)*sin(x) + 4*((b - c)*cos(x) - (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c)) + 2*b - 2*c)/(b - c)) + 4*I*(b - c)*x*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*log(-1/2*((2*(2*a + b + c)*cos(x) + (-4*I*a - 2*I*b - 2*I*c)*sin(x) + 4*((b - c)*cos(x) + (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c)) - 2*b + 2*c)/(b - c)) - 4*I*(b - c)*x*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*log(1/2*((2*(2*a + b + c)*cos(x) - (-4*I*a - 2*I*b - 2*I*c)*sin(x) + 4*((b - c)*cos(x) - (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c)) + 2*b - 2*c)/(b - c)) + 4*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*dilog(1/2*((2*(2*a + b + c)*cos(x) + (4*I*a + 2*I*b + 2*I*c)*sin(x) - 4*((b - c)*cos(x) - (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c)) - 2*b + 2*c)/(b - c) + 1) + 4*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*dilog(-1/2*((2*(2*a + b + c)*cos(x) - (4*I*a + 2*I*b + 2*I*c)*sin(x) - 4*((b - c)*cos(x) + (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c)) + 2*b - 2*c)/(b - c) + 1) + 4*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*dilog(1/2*((2*(2*a + b + c)*cos(x) + (-4*I*a - 2*I*b - 2*I*c)*sin(x) - 4*((b - c)*cos(x) - (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c)) - 2*b + 2*c)/(b - c) + 1) + 4*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*dilog(-1/2*((2*(2*a + b + c)*cos(x) - (-4*I*a - 2*I*b - 2*I*c)*sin(x) - 4*((b - c)*cos(x) + (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c)) + 2*b - 2*c)/(b - c) + 1) - 4*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*dilog(1/2*((2*(2*a + b + c)*cos(x) + (4*I*a + 2*I*b + 2*I*c)*sin(x) + 4*((b - c)*cos(x) + (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c)) - 2*b + 2*c)/(b - c) + 1) - 4*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*dilog(-1/2*((2*(2*a + b + c)*cos(x) - (4*I*a + 2*I*b + 2*I*c)*sin(x) + 4*((b - c)*cos(x) - (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c)) + 2*b - 2*c)/(b - c) + 1) - 4*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*dilog(1/2*((2*(2*a + b + c)*cos(x) + (-4*I*a - 2*I*b - 2*I*c)*sin(x) + 4*((b - c)*cos(x) + (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c)) - 2*b + 2*c)/(b - c) + 1) - 4*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*dilog(-1/2*((2*(2*a + b + c)*cos(x) - (-4*I*a - 2*I*b - 2*I*c)*sin(x) + 4*((b - c)*cos(x) - (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c)) + 2*b - 2*c)/(b - c) + 1))/(a^2 + a*b + (a + b)*c)","B",0
498,1,4357,0,2.221533," ","integrate(x^2/(a+b*cos(x)^2+c*sin(x)^2),x, algorithm=""fricas"")","\frac{4 i \, {\left(b - c\right)} x^{2} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} \log\left(-\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}} - 2 \, b + 2 \, c}{2 \, {\left(b - c\right)}}\right) - 4 i \, {\left(b - c\right)} x^{2} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} \log\left(\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}} + 2 \, b - 2 \, c}{2 \, {\left(b - c\right)}}\right) - 4 i \, {\left(b - c\right)} x^{2} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} \log\left(-\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}} - 2 \, b + 2 \, c}{2 \, {\left(b - c\right)}}\right) + 4 i \, {\left(b - c\right)} x^{2} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} \log\left(\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}} + 2 \, b - 2 \, c}{2 \, {\left(b - c\right)}}\right) - 4 i \, {\left(b - c\right)} x^{2} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} \log\left(-\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}} - 2 \, b + 2 \, c}{2 \, {\left(b - c\right)}}\right) + 4 i \, {\left(b - c\right)} x^{2} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} \log\left(\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}} + 2 \, b - 2 \, c}{2 \, {\left(b - c\right)}}\right) + 4 i \, {\left(b - c\right)} x^{2} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} \log\left(-\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}} - 2 \, b + 2 \, c}{2 \, {\left(b - c\right)}}\right) - 4 i \, {\left(b - c\right)} x^{2} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} \log\left(\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}} + 2 \, b - 2 \, c}{2 \, {\left(b - c\right)}}\right) + 8 \, {\left(b - c\right)} x \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}} - 2 \, b + 2 \, c}{2 \, {\left(b - c\right)}} + 1\right) + 8 \, {\left(b - c\right)} x \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}} + 2 \, b - 2 \, c}{2 \, {\left(b - c\right)}} + 1\right) + 8 \, {\left(b - c\right)} x \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}} - 2 \, b + 2 \, c}{2 \, {\left(b - c\right)}} + 1\right) + 8 \, {\left(b - c\right)} x \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}} + 2 \, b - 2 \, c}{2 \, {\left(b - c\right)}} + 1\right) - 8 \, {\left(b - c\right)} x \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}} - 2 \, b + 2 \, c}{2 \, {\left(b - c\right)}} + 1\right) - 8 \, {\left(b - c\right)} x \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}} + 2 \, b - 2 \, c}{2 \, {\left(b - c\right)}} + 1\right) - 8 \, {\left(b - c\right)} x \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm Li}_2\left(\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}} - 2 \, b + 2 \, c}{2 \, {\left(b - c\right)}} + 1\right) - 8 \, {\left(b - c\right)} x \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm Li}_2\left(-\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}} + 2 \, b - 2 \, c}{2 \, {\left(b - c\right)}} + 1\right) + 4 \, {\left(2 i \, b - 2 i \, c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm polylog}\left(3, -\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}}}{2 \, {\left(b - c\right)}}\right) + 4 \, {\left(-2 i \, b + 2 i \, c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm polylog}\left(3, \frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}}}{2 \, {\left(b - c\right)}}\right) + 4 \, {\left(-2 i \, b + 2 i \, c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm polylog}\left(3, -\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}}}{2 \, {\left(b - c\right)}}\right) + 4 \, {\left(2 i \, b - 2 i \, c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm polylog}\left(3, \frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) - 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{-\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} + 2 \, a + b + c}{b - c}}}{2 \, {\left(b - c\right)}}\right) + 4 \, {\left(-2 i \, b + 2 i \, c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm polylog}\left(3, -\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}}}{2 \, {\left(b - c\right)}}\right) + 4 \, {\left(2 i \, b - 2 i \, c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm polylog}\left(3, \frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(4 i \, a + 2 i \, b + 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(i \, b - i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}}}{2 \, {\left(b - c\right)}}\right) + 4 \, {\left(2 i \, b - 2 i \, c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm polylog}\left(3, -\frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) + {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) + {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}}}{2 \, {\left(b - c\right)}}\right) + 4 \, {\left(-2 i \, b + 2 i \, c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} {\rm polylog}\left(3, \frac{{\left(2 \, {\left(2 \, a + b + c\right)} \cos\left(x\right) - {\left(-4 i \, a - 2 i \, b - 2 i \, c\right)} \sin\left(x\right) + 4 \, {\left({\left(b - c\right)} \cos\left(x\right) - {\left(-i \, b + i \, c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}}\right)} \sqrt{\frac{2 \, {\left(b - c\right)} \sqrt{\frac{a^{2} + a b + {\left(a + b\right)} c}{b^{2} - 2 \, b c + c^{2}}} - 2 \, a - b - c}{b - c}}}{2 \, {\left(b - c\right)}}\right)}{16 \, {\left(a^{2} + a b + {\left(a + b\right)} c\right)}}"," ",0,"1/16*(4*I*(b - c)*x^2*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*log(-1/2*((2*(2*a + b + c)*cos(x) + (4*I*a + 2*I*b + 2*I*c)*sin(x) - 4*((b - c)*cos(x) - (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c)) - 2*b + 2*c)/(b - c)) - 4*I*(b - c)*x^2*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*log(1/2*((2*(2*a + b + c)*cos(x) - (4*I*a + 2*I*b + 2*I*c)*sin(x) - 4*((b - c)*cos(x) + (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c)) + 2*b - 2*c)/(b - c)) - 4*I*(b - c)*x^2*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*log(-1/2*((2*(2*a + b + c)*cos(x) + (-4*I*a - 2*I*b - 2*I*c)*sin(x) - 4*((b - c)*cos(x) - (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c)) - 2*b + 2*c)/(b - c)) + 4*I*(b - c)*x^2*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*log(1/2*((2*(2*a + b + c)*cos(x) - (-4*I*a - 2*I*b - 2*I*c)*sin(x) - 4*((b - c)*cos(x) + (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c)) + 2*b - 2*c)/(b - c)) - 4*I*(b - c)*x^2*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*log(-1/2*((2*(2*a + b + c)*cos(x) + (4*I*a + 2*I*b + 2*I*c)*sin(x) + 4*((b - c)*cos(x) + (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c)) - 2*b + 2*c)/(b - c)) + 4*I*(b - c)*x^2*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*log(1/2*((2*(2*a + b + c)*cos(x) - (4*I*a + 2*I*b + 2*I*c)*sin(x) + 4*((b - c)*cos(x) - (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c)) + 2*b - 2*c)/(b - c)) + 4*I*(b - c)*x^2*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*log(-1/2*((2*(2*a + b + c)*cos(x) + (-4*I*a - 2*I*b - 2*I*c)*sin(x) + 4*((b - c)*cos(x) + (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c)) - 2*b + 2*c)/(b - c)) - 4*I*(b - c)*x^2*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*log(1/2*((2*(2*a + b + c)*cos(x) - (-4*I*a - 2*I*b - 2*I*c)*sin(x) + 4*((b - c)*cos(x) - (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c)) + 2*b - 2*c)/(b - c)) + 8*(b - c)*x*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*dilog(1/2*((2*(2*a + b + c)*cos(x) + (4*I*a + 2*I*b + 2*I*c)*sin(x) - 4*((b - c)*cos(x) - (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c)) - 2*b + 2*c)/(b - c) + 1) + 8*(b - c)*x*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*dilog(-1/2*((2*(2*a + b + c)*cos(x) - (4*I*a + 2*I*b + 2*I*c)*sin(x) - 4*((b - c)*cos(x) + (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c)) + 2*b - 2*c)/(b - c) + 1) + 8*(b - c)*x*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*dilog(1/2*((2*(2*a + b + c)*cos(x) + (-4*I*a - 2*I*b - 2*I*c)*sin(x) - 4*((b - c)*cos(x) - (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c)) - 2*b + 2*c)/(b - c) + 1) + 8*(b - c)*x*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*dilog(-1/2*((2*(2*a + b + c)*cos(x) - (-4*I*a - 2*I*b - 2*I*c)*sin(x) - 4*((b - c)*cos(x) + (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c)) + 2*b - 2*c)/(b - c) + 1) - 8*(b - c)*x*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*dilog(1/2*((2*(2*a + b + c)*cos(x) + (4*I*a + 2*I*b + 2*I*c)*sin(x) + 4*((b - c)*cos(x) + (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c)) - 2*b + 2*c)/(b - c) + 1) - 8*(b - c)*x*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*dilog(-1/2*((2*(2*a + b + c)*cos(x) - (4*I*a + 2*I*b + 2*I*c)*sin(x) + 4*((b - c)*cos(x) - (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c)) + 2*b - 2*c)/(b - c) + 1) - 8*(b - c)*x*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*dilog(1/2*((2*(2*a + b + c)*cos(x) + (-4*I*a - 2*I*b - 2*I*c)*sin(x) + 4*((b - c)*cos(x) + (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c)) - 2*b + 2*c)/(b - c) + 1) - 8*(b - c)*x*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*dilog(-1/2*((2*(2*a + b + c)*cos(x) - (-4*I*a - 2*I*b - 2*I*c)*sin(x) + 4*((b - c)*cos(x) - (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c)) + 2*b - 2*c)/(b - c) + 1) + 4*(2*I*b - 2*I*c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*polylog(3, -1/2*(2*(2*a + b + c)*cos(x) + (4*I*a + 2*I*b + 2*I*c)*sin(x) - 4*((b - c)*cos(x) - (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c))/(b - c)) + 4*(-2*I*b + 2*I*c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*polylog(3, 1/2*(2*(2*a + b + c)*cos(x) - (4*I*a + 2*I*b + 2*I*c)*sin(x) - 4*((b - c)*cos(x) + (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c))/(b - c)) + 4*(-2*I*b + 2*I*c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*polylog(3, -1/2*(2*(2*a + b + c)*cos(x) + (-4*I*a - 2*I*b - 2*I*c)*sin(x) - 4*((b - c)*cos(x) - (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c))/(b - c)) + 4*(2*I*b - 2*I*c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*polylog(3, 1/2*(2*(2*a + b + c)*cos(x) - (-4*I*a - 2*I*b - 2*I*c)*sin(x) - 4*((b - c)*cos(x) + (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt(-(2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) + 2*a + b + c)/(b - c))/(b - c)) + 4*(-2*I*b + 2*I*c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*polylog(3, -1/2*(2*(2*a + b + c)*cos(x) + (4*I*a + 2*I*b + 2*I*c)*sin(x) + 4*((b - c)*cos(x) + (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c))/(b - c)) + 4*(2*I*b - 2*I*c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*polylog(3, 1/2*(2*(2*a + b + c)*cos(x) - (4*I*a + 2*I*b + 2*I*c)*sin(x) + 4*((b - c)*cos(x) - (I*b - I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c))/(b - c)) + 4*(2*I*b - 2*I*c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*polylog(3, -1/2*(2*(2*a + b + c)*cos(x) + (-4*I*a - 2*I*b - 2*I*c)*sin(x) + 4*((b - c)*cos(x) + (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c))/(b - c)) + 4*(-2*I*b + 2*I*c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2))*polylog(3, 1/2*(2*(2*a + b + c)*cos(x) - (-4*I*a - 2*I*b - 2*I*c)*sin(x) + 4*((b - c)*cos(x) - (-I*b + I*c)*sin(x))*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)))*sqrt((2*(b - c)*sqrt((a^2 + a*b + (a + b)*c)/(b^2 - 2*b*c + c^2)) - 2*a - b - c)/(b - c))/(b - c)))/(a^2 + a*b + (a + b)*c)","C",0
499,1,150,0,0.530043," ","integrate((a+b*sin(e*x+d))*(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^2,x, algorithm=""fricas"")","-\frac{8 \, a^{4} b \cos\left(e x + d\right)^{5} - 80 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cos\left(e x + d\right)^{3} - 15 \, {\left(a^{5} + 12 \, a^{3} b^{2} + 8 \, a b^{4}\right)} e x + 40 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(e x + d\right) - 5 \, {\left(2 \, {\left(a^{5} + 4 \, a^{3} b^{2}\right)} \cos\left(e x + d\right)^{3} - {\left(5 \, a^{5} + 44 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{40 \, e}"," ",0,"-1/40*(8*a^4*b*cos(e*x + d)^5 - 80*(a^4*b + a^2*b^3)*cos(e*x + d)^3 - 15*(a^5 + 12*a^3*b^2 + 8*a*b^4)*e*x + 40*(5*a^4*b + 10*a^2*b^3 + b^5)*cos(e*x + d) - 5*(2*(a^5 + 4*a^3*b^2)*cos(e*x + d)^3 - (5*a^5 + 44*a^3*b^2 + 16*a*b^4)*cos(e*x + d))*sin(e*x + d))/e","A",0
500,1,76,0,0.739548," ","integrate((a+b*sin(e*x+d))*(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2),x, algorithm=""fricas"")","\frac{2 \, a^{2} b \cos\left(e x + d\right)^{3} + 3 \, {\left(a^{3} + 4 \, a b^{2}\right)} e x - 3 \, {\left(a^{3} + 2 \, a b^{2}\right)} \cos\left(e x + d\right) \sin\left(e x + d\right) - 6 \, {\left(3 \, a^{2} b + b^{3}\right)} \cos\left(e x + d\right)}{6 \, e}"," ",0,"1/6*(2*a^2*b*cos(e*x + d)^3 + 3*(a^3 + 4*a*b^2)*e*x - 3*(a^3 + 2*a*b^2)*cos(e*x + d)*sin(e*x + d) - 6*(3*a^2*b + b^3)*cos(e*x + d))/e","A",0
501,1,23,0,0.830262," ","integrate((a+b*sin(e*x+d))/(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2),x, algorithm=""fricas"")","-\frac{\cos\left(e x + d\right)}{a e \sin\left(e x + d\right) + b e}"," ",0,"-cos(e*x + d)/(a*e*sin(e*x + d) + b*e)","A",0
502,1,795,0,1.980746," ","integrate((a+b*sin(e*x+d))/(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(2 \, a^{6} - a^{4} b^{2} - a^{2} b^{4}\right)} \cos\left(e x + d\right)^{3} - 6 \, {\left(a^{5} b - a b^{5}\right)} \cos\left(e x + d\right) \sin\left(e x + d\right) - 3 \, {\left(3 \, a^{3} b^{2} \cos\left(e x + d\right)^{2} - 3 \, a^{3} b^{2} - a b^{4} + {\left(a^{4} b \cos\left(e x + d\right)^{2} - a^{4} b - 3 \, a^{2} b^{3}\right)} \sin\left(e x + d\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{{\left(a^{2} - 2 \, b^{2}\right)} \cos\left(e x + d\right)^{2} + 2 \, a b \sin\left(e x + d\right) + a^{2} + b^{2} + 2 \, {\left(b \cos\left(e x + d\right) \sin\left(e x + d\right) + a \cos\left(e x + d\right)\right)} \sqrt{a^{2} - b^{2}}}{a^{2} \cos\left(e x + d\right)^{2} - 2 \, a b \sin\left(e x + d\right) - a^{2} - b^{2}}\right) - 6 \, {\left(a^{6} - a^{4} b^{2} + a^{2} b^{4} - b^{6}\right)} \cos\left(e x + d\right)}{6 \, {\left(3 \, {\left(a^{8} b - 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - a^{2} b^{7}\right)} e \cos\left(e x + d\right)^{2} - {\left(3 \, a^{8} b - 8 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - b^{9}\right)} e + {\left({\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} e \cos\left(e x + d\right)^{2} - {\left(a^{9} - 6 \, a^{5} b^{4} + 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} e\right)} \sin\left(e x + d\right)\right)}}, -\frac{{\left(2 \, a^{6} - a^{4} b^{2} - a^{2} b^{4}\right)} \cos\left(e x + d\right)^{3} - 3 \, {\left(a^{5} b - a b^{5}\right)} \cos\left(e x + d\right) \sin\left(e x + d\right) - 3 \, {\left(3 \, a^{3} b^{2} \cos\left(e x + d\right)^{2} - 3 \, a^{3} b^{2} - a b^{4} + {\left(a^{4} b \cos\left(e x + d\right)^{2} - a^{4} b - 3 \, a^{2} b^{3}\right)} \sin\left(e x + d\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \sin\left(e x + d\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \cos\left(e x + d\right)}\right) - 3 \, {\left(a^{6} - a^{4} b^{2} + a^{2} b^{4} - b^{6}\right)} \cos\left(e x + d\right)}{3 \, {\left(3 \, {\left(a^{8} b - 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - a^{2} b^{7}\right)} e \cos\left(e x + d\right)^{2} - {\left(3 \, a^{8} b - 8 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - b^{9}\right)} e + {\left({\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} e \cos\left(e x + d\right)^{2} - {\left(a^{9} - 6 \, a^{5} b^{4} + 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} e\right)} \sin\left(e x + d\right)\right)}}\right]"," ",0,"[-1/6*(2*(2*a^6 - a^4*b^2 - a^2*b^4)*cos(e*x + d)^3 - 6*(a^5*b - a*b^5)*cos(e*x + d)*sin(e*x + d) - 3*(3*a^3*b^2*cos(e*x + d)^2 - 3*a^3*b^2 - a*b^4 + (a^4*b*cos(e*x + d)^2 - a^4*b - 3*a^2*b^3)*sin(e*x + d))*sqrt(a^2 - b^2)*log(((a^2 - 2*b^2)*cos(e*x + d)^2 + 2*a*b*sin(e*x + d) + a^2 + b^2 + 2*(b*cos(e*x + d)*sin(e*x + d) + a*cos(e*x + d))*sqrt(a^2 - b^2))/(a^2*cos(e*x + d)^2 - 2*a*b*sin(e*x + d) - a^2 - b^2)) - 6*(a^6 - a^4*b^2 + a^2*b^4 - b^6)*cos(e*x + d))/(3*(a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*e*cos(e*x + d)^2 - (3*a^8*b - 8*a^6*b^3 + 6*a^4*b^5 - b^9)*e + ((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*e*cos(e*x + d)^2 - (a^9 - 6*a^5*b^4 + 8*a^3*b^6 - 3*a*b^8)*e)*sin(e*x + d)), -1/3*((2*a^6 - a^4*b^2 - a^2*b^4)*cos(e*x + d)^3 - 3*(a^5*b - a*b^5)*cos(e*x + d)*sin(e*x + d) - 3*(3*a^3*b^2*cos(e*x + d)^2 - 3*a^3*b^2 - a*b^4 + (a^4*b*cos(e*x + d)^2 - a^4*b - 3*a^2*b^3)*sin(e*x + d))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*sin(e*x + d) + a)/((a^2 - b^2)*cos(e*x + d))) - 3*(a^6 - a^4*b^2 + a^2*b^4 - b^6)*cos(e*x + d))/(3*(a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*e*cos(e*x + d)^2 - (3*a^8*b - 8*a^6*b^3 + 6*a^4*b^5 - b^9)*e + ((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*e*cos(e*x + d)^2 - (a^9 - 6*a^5*b^4 + 8*a^3*b^6 - 3*a*b^8)*e)*sin(e*x + d))]","B",0
503,1,6695,0,18.385000," ","integrate((d+e*sin(x))/(a+b*sin(x)+c*sin(x)^2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \sqrt{-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} d^{2} - 2 \, {\left(a b - b c\right)} d e + {\left(2 \, a^{2} - b^{2} + 2 \, a c\right)} e^{2} + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(4 \, b c^{2} d^{4} + 4 \, a b c e^{4} - 4 \, {\left(b^{2} c + 2 \, a c^{2} + 2 \, c^{3}\right)} d^{3} e + 12 \, {\left(a b c + b c^{2}\right)} d^{2} e^{2} - 4 \, {\left(2 \, a c^{2} + {\left(2 \, a^{2} + b^{2}\right)} c\right)} d e^{3} + 2 \, {\left({\left(4 \, a c^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c\right)} d^{2} + {\left(a^{2} b^{3} - b^{5} - 4 \, a b c^{3} - {\left(8 \, a^{2} b - b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} c\right)} d e - {\left(a^{3} b^{2} - a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} c\right)} e^{2}\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) + \sqrt{2} {\left({\left({\left(a^{2} b^{4} - b^{6} + 8 \, a c^{5} + 2 \, {\left(12 \, a^{2} - b^{2}\right)} c^{4} + 6 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{3} + {\left(8 \, a^{4} - 22 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c\right)} d - {\left(a^{3} b^{3} - a b^{5} + 4 \, a b c^{4} + {\left(4 \, a^{2} b - b^{3}\right)} c^{3} - {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} c^{2} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} - b^{5}\right)} c\right)} e\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) - {\left({\left(b^{4} - 4 \, a b^{2} c\right)} d^{3} - 3 \, {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} d^{2} e + {\left(2 \, a^{2} b^{2} + b^{4} - 8 \, a^{3} c - 8 \, a c^{3} - 2 \, {\left(8 \, a^{2} - b^{2}\right)} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} e^{3}\right)} \cos\left(x\right)\right)} \sqrt{-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} d^{2} - 2 \, {\left(a b - b c\right)} d e + {\left(2 \, a^{2} - b^{2} + 2 \, a c\right)} e^{2} + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} + 2 \, {\left(b^{2} c d^{4} + a b^{2} e^{4} - {\left(b^{3} + 2 \, a b c + 2 \, b c^{2}\right)} d^{3} e + 3 \, {\left(a b^{2} + b^{2} c\right)} d^{2} e^{2} - {\left(2 \, a^{2} b + b^{3} + 2 \, a b c\right)} d e^{3}\right)} \sin\left(x\right)\right) - \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} d^{2} - 2 \, {\left(a b - b c\right)} d e + {\left(2 \, a^{2} - b^{2} + 2 \, a c\right)} e^{2} - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(4 \, b c^{2} d^{4} + 4 \, a b c e^{4} - 4 \, {\left(b^{2} c + 2 \, a c^{2} + 2 \, c^{3}\right)} d^{3} e + 12 \, {\left(a b c + b c^{2}\right)} d^{2} e^{2} - 4 \, {\left(2 \, a c^{2} + {\left(2 \, a^{2} + b^{2}\right)} c\right)} d e^{3} - 2 \, {\left({\left(4 \, a c^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c\right)} d^{2} + {\left(a^{2} b^{3} - b^{5} - 4 \, a b c^{3} - {\left(8 \, a^{2} b - b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} c\right)} d e - {\left(a^{3} b^{2} - a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} c\right)} e^{2}\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) + \sqrt{2} {\left({\left({\left(a^{2} b^{4} - b^{6} + 8 \, a c^{5} + 2 \, {\left(12 \, a^{2} - b^{2}\right)} c^{4} + 6 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{3} + {\left(8 \, a^{4} - 22 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c\right)} d - {\left(a^{3} b^{3} - a b^{5} + 4 \, a b c^{4} + {\left(4 \, a^{2} b - b^{3}\right)} c^{3} - {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} c^{2} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} - b^{5}\right)} c\right)} e\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) + {\left({\left(b^{4} - 4 \, a b^{2} c\right)} d^{3} - 3 \, {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} d^{2} e + {\left(2 \, a^{2} b^{2} + b^{4} - 8 \, a^{3} c - 8 \, a c^{3} - 2 \, {\left(8 \, a^{2} - b^{2}\right)} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} e^{3}\right)} \cos\left(x\right)\right)} \sqrt{-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} d^{2} - 2 \, {\left(a b - b c\right)} d e + {\left(2 \, a^{2} - b^{2} + 2 \, a c\right)} e^{2} - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} + 2 \, {\left(b^{2} c d^{4} + a b^{2} e^{4} - {\left(b^{3} + 2 \, a b c + 2 \, b c^{2}\right)} d^{3} e + 3 \, {\left(a b^{2} + b^{2} c\right)} d^{2} e^{2} - {\left(2 \, a^{2} b + b^{3} + 2 \, a b c\right)} d e^{3}\right)} \sin\left(x\right)\right) + \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} d^{2} - 2 \, {\left(a b - b c\right)} d e + {\left(2 \, a^{2} - b^{2} + 2 \, a c\right)} e^{2} - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(-4 \, b c^{2} d^{4} - 4 \, a b c e^{4} + 4 \, {\left(b^{2} c + 2 \, a c^{2} + 2 \, c^{3}\right)} d^{3} e - 12 \, {\left(a b c + b c^{2}\right)} d^{2} e^{2} + 4 \, {\left(2 \, a c^{2} + {\left(2 \, a^{2} + b^{2}\right)} c\right)} d e^{3} + 2 \, {\left({\left(4 \, a c^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c\right)} d^{2} + {\left(a^{2} b^{3} - b^{5} - 4 \, a b c^{3} - {\left(8 \, a^{2} b - b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} c\right)} d e - {\left(a^{3} b^{2} - a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} c\right)} e^{2}\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) + \sqrt{2} {\left({\left({\left(a^{2} b^{4} - b^{6} + 8 \, a c^{5} + 2 \, {\left(12 \, a^{2} - b^{2}\right)} c^{4} + 6 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{3} + {\left(8 \, a^{4} - 22 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c\right)} d - {\left(a^{3} b^{3} - a b^{5} + 4 \, a b c^{4} + {\left(4 \, a^{2} b - b^{3}\right)} c^{3} - {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} c^{2} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} - b^{5}\right)} c\right)} e\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) + {\left({\left(b^{4} - 4 \, a b^{2} c\right)} d^{3} - 3 \, {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} d^{2} e + {\left(2 \, a^{2} b^{2} + b^{4} - 8 \, a^{3} c - 8 \, a c^{3} - 2 \, {\left(8 \, a^{2} - b^{2}\right)} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} e^{3}\right)} \cos\left(x\right)\right)} \sqrt{-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} d^{2} - 2 \, {\left(a b - b c\right)} d e + {\left(2 \, a^{2} - b^{2} + 2 \, a c\right)} e^{2} - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} - 2 \, {\left(b^{2} c d^{4} + a b^{2} e^{4} - {\left(b^{3} + 2 \, a b c + 2 \, b c^{2}\right)} d^{3} e + 3 \, {\left(a b^{2} + b^{2} c\right)} d^{2} e^{2} - {\left(2 \, a^{2} b + b^{3} + 2 \, a b c\right)} d e^{3}\right)} \sin\left(x\right)\right) - \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} d^{2} - 2 \, {\left(a b - b c\right)} d e + {\left(2 \, a^{2} - b^{2} + 2 \, a c\right)} e^{2} + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(-4 \, b c^{2} d^{4} - 4 \, a b c e^{4} + 4 \, {\left(b^{2} c + 2 \, a c^{2} + 2 \, c^{3}\right)} d^{3} e - 12 \, {\left(a b c + b c^{2}\right)} d^{2} e^{2} + 4 \, {\left(2 \, a c^{2} + {\left(2 \, a^{2} + b^{2}\right)} c\right)} d e^{3} - 2 \, {\left({\left(4 \, a c^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c\right)} d^{2} + {\left(a^{2} b^{3} - b^{5} - 4 \, a b c^{3} - {\left(8 \, a^{2} b - b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} c\right)} d e - {\left(a^{3} b^{2} - a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} c\right)} e^{2}\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) + \sqrt{2} {\left({\left({\left(a^{2} b^{4} - b^{6} + 8 \, a c^{5} + 2 \, {\left(12 \, a^{2} - b^{2}\right)} c^{4} + 6 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{3} + {\left(8 \, a^{4} - 22 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c\right)} d - {\left(a^{3} b^{3} - a b^{5} + 4 \, a b c^{4} + {\left(4 \, a^{2} b - b^{3}\right)} c^{3} - {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} c^{2} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} - b^{5}\right)} c\right)} e\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) - {\left({\left(b^{4} - 4 \, a b^{2} c\right)} d^{3} - 3 \, {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} d^{2} e + {\left(2 \, a^{2} b^{2} + b^{4} - 8 \, a^{3} c - 8 \, a c^{3} - 2 \, {\left(8 \, a^{2} - b^{2}\right)} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} e^{3}\right)} \cos\left(x\right)\right)} \sqrt{-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} d^{2} - 2 \, {\left(a b - b c\right)} d e + {\left(2 \, a^{2} - b^{2} + 2 \, a c\right)} e^{2} + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} - 2 \, {\left(b^{2} c d^{4} + a b^{2} e^{4} - {\left(b^{3} + 2 \, a b c + 2 \, b c^{2}\right)} d^{3} e + 3 \, {\left(a b^{2} + b^{2} c\right)} d^{2} e^{2} - {\left(2 \, a^{2} b + b^{3} + 2 \, a b c\right)} d e^{3}\right)} \sin\left(x\right)\right)"," ",0,"1/4*sqrt(2)*sqrt(-((b^2 - 2*a*c - 2*c^2)*d^2 - 2*(a*b - b*c)*d*e + (2*a^2 - b^2 + 2*a*c)*e^2 + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(4*b*c^2*d^4 + 4*a*b*c*e^4 - 4*(b^2*c + 2*a*c^2 + 2*c^3)*d^3*e + 12*(a*b*c + b*c^2)*d^2*e^2 - 4*(2*a*c^2 + (2*a^2 + b^2)*c)*d*e^3 + 2*((4*a*c^4 + (8*a^2 - b^2)*c^3 + 2*(2*a^3 - 3*a*b^2)*c^2 - (a^2*b^2 - b^4)*c)*d^2 + (a^2*b^3 - b^5 - 4*a*b*c^3 - (8*a^2*b - b^3)*c^2 - 2*(2*a^3*b - 3*a*b^3)*c)*d*e - (a^3*b^2 - a*b^4 - 4*a^2*c^3 - (8*a^3 - a*b^2)*c^2 - 2*(2*a^4 - 3*a^2*b^2)*c)*e^2)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) + sqrt(2)*(((a^2*b^4 - b^6 + 8*a*c^5 + 2*(12*a^2 - b^2)*c^4 + 6*(4*a^3 - 3*a*b^2)*c^3 + (8*a^4 - 22*a^2*b^2 + 3*b^4)*c^2 - 2*(3*a^3*b^2 - 4*a*b^4)*c)*d - (a^3*b^3 - a*b^5 + 4*a*b*c^4 + (4*a^2*b - b^3)*c^3 - (4*a^3*b + 5*a*b^3)*c^2 - (4*a^4*b - 5*a^2*b^3 - b^5)*c)*e)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) - ((b^4 - 4*a*b^2*c)*d^3 - 3*(a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*d^2*e + (2*a^2*b^2 + b^4 - 8*a^3*c - 8*a*c^3 - 2*(8*a^2 - b^2)*c^2)*d*e^2 - (a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*e^3)*cos(x))*sqrt(-((b^2 - 2*a*c - 2*c^2)*d^2 - 2*(a*b - b*c)*d*e + (2*a^2 - b^2 + 2*a*c)*e^2 + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)) + 2*(b^2*c*d^4 + a*b^2*e^4 - (b^3 + 2*a*b*c + 2*b*c^2)*d^3*e + 3*(a*b^2 + b^2*c)*d^2*e^2 - (2*a^2*b + b^3 + 2*a*b*c)*d*e^3)*sin(x)) - 1/4*sqrt(2)*sqrt(-((b^2 - 2*a*c - 2*c^2)*d^2 - 2*(a*b - b*c)*d*e + (2*a^2 - b^2 + 2*a*c)*e^2 - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(4*b*c^2*d^4 + 4*a*b*c*e^4 - 4*(b^2*c + 2*a*c^2 + 2*c^3)*d^3*e + 12*(a*b*c + b*c^2)*d^2*e^2 - 4*(2*a*c^2 + (2*a^2 + b^2)*c)*d*e^3 - 2*((4*a*c^4 + (8*a^2 - b^2)*c^3 + 2*(2*a^3 - 3*a*b^2)*c^2 - (a^2*b^2 - b^4)*c)*d^2 + (a^2*b^3 - b^5 - 4*a*b*c^3 - (8*a^2*b - b^3)*c^2 - 2*(2*a^3*b - 3*a*b^3)*c)*d*e - (a^3*b^2 - a*b^4 - 4*a^2*c^3 - (8*a^3 - a*b^2)*c^2 - 2*(2*a^4 - 3*a^2*b^2)*c)*e^2)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) + sqrt(2)*(((a^2*b^4 - b^6 + 8*a*c^5 + 2*(12*a^2 - b^2)*c^4 + 6*(4*a^3 - 3*a*b^2)*c^3 + (8*a^4 - 22*a^2*b^2 + 3*b^4)*c^2 - 2*(3*a^3*b^2 - 4*a*b^4)*c)*d - (a^3*b^3 - a*b^5 + 4*a*b*c^4 + (4*a^2*b - b^3)*c^3 - (4*a^3*b + 5*a*b^3)*c^2 - (4*a^4*b - 5*a^2*b^3 - b^5)*c)*e)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) + ((b^4 - 4*a*b^2*c)*d^3 - 3*(a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*d^2*e + (2*a^2*b^2 + b^4 - 8*a^3*c - 8*a*c^3 - 2*(8*a^2 - b^2)*c^2)*d*e^2 - (a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*e^3)*cos(x))*sqrt(-((b^2 - 2*a*c - 2*c^2)*d^2 - 2*(a*b - b*c)*d*e + (2*a^2 - b^2 + 2*a*c)*e^2 - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)) + 2*(b^2*c*d^4 + a*b^2*e^4 - (b^3 + 2*a*b*c + 2*b*c^2)*d^3*e + 3*(a*b^2 + b^2*c)*d^2*e^2 - (2*a^2*b + b^3 + 2*a*b*c)*d*e^3)*sin(x)) + 1/4*sqrt(2)*sqrt(-((b^2 - 2*a*c - 2*c^2)*d^2 - 2*(a*b - b*c)*d*e + (2*a^2 - b^2 + 2*a*c)*e^2 - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(-4*b*c^2*d^4 - 4*a*b*c*e^4 + 4*(b^2*c + 2*a*c^2 + 2*c^3)*d^3*e - 12*(a*b*c + b*c^2)*d^2*e^2 + 4*(2*a*c^2 + (2*a^2 + b^2)*c)*d*e^3 + 2*((4*a*c^4 + (8*a^2 - b^2)*c^3 + 2*(2*a^3 - 3*a*b^2)*c^2 - (a^2*b^2 - b^4)*c)*d^2 + (a^2*b^3 - b^5 - 4*a*b*c^3 - (8*a^2*b - b^3)*c^2 - 2*(2*a^3*b - 3*a*b^3)*c)*d*e - (a^3*b^2 - a*b^4 - 4*a^2*c^3 - (8*a^3 - a*b^2)*c^2 - 2*(2*a^4 - 3*a^2*b^2)*c)*e^2)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) + sqrt(2)*(((a^2*b^4 - b^6 + 8*a*c^5 + 2*(12*a^2 - b^2)*c^4 + 6*(4*a^3 - 3*a*b^2)*c^3 + (8*a^4 - 22*a^2*b^2 + 3*b^4)*c^2 - 2*(3*a^3*b^2 - 4*a*b^4)*c)*d - (a^3*b^3 - a*b^5 + 4*a*b*c^4 + (4*a^2*b - b^3)*c^3 - (4*a^3*b + 5*a*b^3)*c^2 - (4*a^4*b - 5*a^2*b^3 - b^5)*c)*e)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) + ((b^4 - 4*a*b^2*c)*d^3 - 3*(a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*d^2*e + (2*a^2*b^2 + b^4 - 8*a^3*c - 8*a*c^3 - 2*(8*a^2 - b^2)*c^2)*d*e^2 - (a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*e^3)*cos(x))*sqrt(-((b^2 - 2*a*c - 2*c^2)*d^2 - 2*(a*b - b*c)*d*e + (2*a^2 - b^2 + 2*a*c)*e^2 - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)) - 2*(b^2*c*d^4 + a*b^2*e^4 - (b^3 + 2*a*b*c + 2*b*c^2)*d^3*e + 3*(a*b^2 + b^2*c)*d^2*e^2 - (2*a^2*b + b^3 + 2*a*b*c)*d*e^3)*sin(x)) - 1/4*sqrt(2)*sqrt(-((b^2 - 2*a*c - 2*c^2)*d^2 - 2*(a*b - b*c)*d*e + (2*a^2 - b^2 + 2*a*c)*e^2 + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(-4*b*c^2*d^4 - 4*a*b*c*e^4 + 4*(b^2*c + 2*a*c^2 + 2*c^3)*d^3*e - 12*(a*b*c + b*c^2)*d^2*e^2 + 4*(2*a*c^2 + (2*a^2 + b^2)*c)*d*e^3 - 2*((4*a*c^4 + (8*a^2 - b^2)*c^3 + 2*(2*a^3 - 3*a*b^2)*c^2 - (a^2*b^2 - b^4)*c)*d^2 + (a^2*b^3 - b^5 - 4*a*b*c^3 - (8*a^2*b - b^3)*c^2 - 2*(2*a^3*b - 3*a*b^3)*c)*d*e - (a^3*b^2 - a*b^4 - 4*a^2*c^3 - (8*a^3 - a*b^2)*c^2 - 2*(2*a^4 - 3*a^2*b^2)*c)*e^2)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) + sqrt(2)*(((a^2*b^4 - b^6 + 8*a*c^5 + 2*(12*a^2 - b^2)*c^4 + 6*(4*a^3 - 3*a*b^2)*c^3 + (8*a^4 - 22*a^2*b^2 + 3*b^4)*c^2 - 2*(3*a^3*b^2 - 4*a*b^4)*c)*d - (a^3*b^3 - a*b^5 + 4*a*b*c^4 + (4*a^2*b - b^3)*c^3 - (4*a^3*b + 5*a*b^3)*c^2 - (4*a^4*b - 5*a^2*b^3 - b^5)*c)*e)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) - ((b^4 - 4*a*b^2*c)*d^3 - 3*(a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*d^2*e + (2*a^2*b^2 + b^4 - 8*a^3*c - 8*a*c^3 - 2*(8*a^2 - b^2)*c^2)*d*e^2 - (a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*e^3)*cos(x))*sqrt(-((b^2 - 2*a*c - 2*c^2)*d^2 - 2*(a*b - b*c)*d*e + (2*a^2 - b^2 + 2*a*c)*e^2 + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)) - 2*(b^2*c*d^4 + a*b^2*e^4 - (b^3 + 2*a*b*c + 2*b*c^2)*d^3*e + 3*(a*b^2 + b^2*c)*d^2*e^2 - (2*a^2*b + b^3 + 2*a*b*c)*d*e^3)*sin(x))","B",0
504,1,112,0,0.846244," ","integrate((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, algorithm=""fricas"")","\frac{8 \, {\left(a^{4} + 3 \, a^{2} b^{2}\right)} \cos\left(e x + d\right)^{3} + 15 \, {\left(3 \, a^{3} b + 4 \, a b^{3}\right)} e x - 24 \, {\left(a^{4} + 6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(e x + d\right) + 3 \, {\left(2 \, a^{3} b \cos\left(e x + d\right)^{3} - {\left(17 \, a^{3} b + 12 \, a b^{3}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{24 \, e}"," ",0,"1/24*(8*(a^4 + 3*a^2*b^2)*cos(e*x + d)^3 + 15*(3*a^3*b + 4*a*b^3)*e*x - 24*(a^4 + 6*a^2*b^2 + b^4)*cos(e*x + d) + 3*(2*a^3*b*cos(e*x + d)^3 - (17*a^3*b + 12*a*b^3)*cos(e*x + d))*sin(e*x + d))/e","A",0
505,1,43,0,0.870373," ","integrate((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, algorithm=""fricas"")","\frac{3 \, a b e x - a b \cos\left(e x + d\right) \sin\left(e x + d\right) - 2 \, {\left(a^{2} + b^{2}\right)} \cos\left(e x + d\right)}{2 \, e}"," ",0,"1/2*(3*a*b*e*x - a*b*cos(e*x + d)*sin(e*x + d) - 2*(a^2 + b^2)*cos(e*x + d))/e","A",0
506,1,204,0,0.924603," ","integrate((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, algorithm=""fricas"")","\left[\frac{2 \, b e x + \sqrt{a^{2} - b^{2}} \log\left(-\frac{{\left(a^{2} - 2 \, b^{2}\right)} \cos\left(e x + d\right)^{2} + 2 \, a b \sin\left(e x + d\right) + a^{2} + b^{2} - 2 \, {\left(b \cos\left(e x + d\right) \sin\left(e x + d\right) + a \cos\left(e x + d\right)\right)} \sqrt{a^{2} - b^{2}}}{a^{2} \cos\left(e x + d\right)^{2} - 2 \, a b \sin\left(e x + d\right) - a^{2} - b^{2}}\right)}{2 \, a e}, \frac{b e x - \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \sin\left(e x + d\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \cos\left(e x + d\right)}\right)}{a e}\right]"," ",0,"[1/2*(2*b*e*x + sqrt(a^2 - b^2)*log(-((a^2 - 2*b^2)*cos(e*x + d)^2 + 2*a*b*sin(e*x + d) + a^2 + b^2 - 2*(b*cos(e*x + d)*sin(e*x + d) + a*cos(e*x + d))*sqrt(a^2 - b^2))/(a^2*cos(e*x + d)^2 - 2*a*b*sin(e*x + d) - a^2 - b^2)))/(a*e), (b*e*x - sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*sin(e*x + d) + a)/((a^2 - b^2)*cos(e*x + d))))/(a*e)]","A",0
507,1,527,0,1.646263," ","integrate((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, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(e x + d\right) \sin\left(e x + d\right) + {\left(a^{3} \cos\left(e x + d\right)^{2} - 2 \, a^{2} b \sin\left(e x + d\right) - a^{3} - a b^{2}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{{\left(a^{2} - 2 \, b^{2}\right)} \cos\left(e x + d\right)^{2} + 2 \, a b \sin\left(e x + d\right) + a^{2} + b^{2} + 2 \, {\left(b \cos\left(e x + d\right) \sin\left(e x + d\right) + a \cos\left(e x + d\right)\right)} \sqrt{a^{2} - b^{2}}}{a^{2} \cos\left(e x + d\right)^{2} - 2 \, a b \sin\left(e x + d\right) - a^{2} - b^{2}}\right) - 2 \, {\left(a^{4} - 3 \, a^{2} b^{2} + 2 \, b^{4}\right)} \cos\left(e x + d\right)}{4 \, {\left({\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} e \cos\left(e x + d\right)^{2} - 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} e \sin\left(e x + d\right) - {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} e\right)}}, -\frac{{\left(a^{3} b - a b^{3}\right)} \cos\left(e x + d\right) \sin\left(e x + d\right) + {\left(a^{3} \cos\left(e x + d\right)^{2} - 2 \, a^{2} b \sin\left(e x + d\right) - a^{3} - a b^{2}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \sin\left(e x + d\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \cos\left(e x + d\right)}\right) - {\left(a^{4} - 3 \, a^{2} b^{2} + 2 \, b^{4}\right)} \cos\left(e x + d\right)}{2 \, {\left({\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} e \cos\left(e x + d\right)^{2} - 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} e \sin\left(e x + d\right) - {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} e\right)}}\right]"," ",0,"[-1/4*(2*(a^3*b - a*b^3)*cos(e*x + d)*sin(e*x + d) + (a^3*cos(e*x + d)^2 - 2*a^2*b*sin(e*x + d) - a^3 - a*b^2)*sqrt(a^2 - b^2)*log(((a^2 - 2*b^2)*cos(e*x + d)^2 + 2*a*b*sin(e*x + d) + a^2 + b^2 + 2*(b*cos(e*x + d)*sin(e*x + d) + a*cos(e*x + d))*sqrt(a^2 - b^2))/(a^2*cos(e*x + d)^2 - 2*a*b*sin(e*x + d) - a^2 - b^2)) - 2*(a^4 - 3*a^2*b^2 + 2*b^4)*cos(e*x + d))/((a^6 - 2*a^4*b^2 + a^2*b^4)*e*cos(e*x + d)^2 - 2*(a^5*b - 2*a^3*b^3 + a*b^5)*e*sin(e*x + d) - (a^6 - a^4*b^2 - a^2*b^4 + b^6)*e), -1/2*((a^3*b - a*b^3)*cos(e*x + d)*sin(e*x + d) + (a^3*cos(e*x + d)^2 - 2*a^2*b*sin(e*x + d) - a^3 - a*b^2)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*sin(e*x + d) + a)/((a^2 - b^2)*cos(e*x + d))) - (a^4 - 3*a^2*b^2 + 2*b^4)*cos(e*x + d))/((a^6 - 2*a^4*b^2 + a^2*b^4)*e*cos(e*x + d)^2 - 2*(a^5*b - 2*a^3*b^3 + a*b^5)*e*sin(e*x + d) - (a^6 - a^4*b^2 - a^2*b^4 + b^6)*e)]","A",0
508,1,11,0,0.777728," ","integrate((a+b*cos(x))/(b^2+2*a*b*cos(x)+a^2*cos(x)^2),x, algorithm=""fricas"")","\frac{\sin\left(x\right)}{a \cos\left(x\right) + b}"," ",0,"sin(x)/(a*cos(x) + b)","A",0
509,1,6697,0,16.183103," ","integrate((d+e*cos(x))/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \sqrt{-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} d^{2} - 2 \, {\left(a b - b c\right)} d e + {\left(2 \, a^{2} - b^{2} + 2 \, a c\right)} e^{2} - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(2 \, b c^{2} d^{4} + 2 \, a b c e^{4} - 2 \, {\left(b^{2} c + 2 \, a c^{2} + 2 \, c^{3}\right)} d^{3} e + 6 \, {\left(a b c + b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a c^{2} + {\left(2 \, a^{2} + b^{2}\right)} c\right)} d e^{3} - {\left({\left(4 \, a c^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c\right)} d^{2} + {\left(a^{2} b^{3} - b^{5} - 4 \, a b c^{3} - {\left(8 \, a^{2} b - b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} c\right)} d e - {\left(a^{3} b^{2} - a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} c\right)} e^{2}\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) + \frac{1}{2} \, \sqrt{2} {\left({\left({\left(a^{2} b^{4} - b^{6} + 8 \, a c^{5} + 2 \, {\left(12 \, a^{2} - b^{2}\right)} c^{4} + 6 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{3} + {\left(8 \, a^{4} - 22 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c\right)} d - {\left(a^{3} b^{3} - a b^{5} + 4 \, a b c^{4} + {\left(4 \, a^{2} b - b^{3}\right)} c^{3} - {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} c^{2} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} - b^{5}\right)} c\right)} e\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) + {\left({\left(b^{4} - 4 \, a b^{2} c\right)} d^{3} - 3 \, {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} d^{2} e + {\left(2 \, a^{2} b^{2} + b^{4} - 8 \, a^{3} c - 8 \, a c^{3} - 2 \, {\left(8 \, a^{2} - b^{2}\right)} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} e^{3}\right)} \sin\left(x\right)\right)} \sqrt{-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} d^{2} - 2 \, {\left(a b - b c\right)} d e + {\left(2 \, a^{2} - b^{2} + 2 \, a c\right)} e^{2} - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} + {\left(b^{2} c d^{4} + a b^{2} e^{4} - {\left(b^{3} + 2 \, a b c + 2 \, b c^{2}\right)} d^{3} e + 3 \, {\left(a b^{2} + b^{2} c\right)} d^{2} e^{2} - {\left(2 \, a^{2} b + b^{3} + 2 \, a b c\right)} d e^{3}\right)} \cos\left(x\right)\right) - \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} d^{2} - 2 \, {\left(a b - b c\right)} d e + {\left(2 \, a^{2} - b^{2} + 2 \, a c\right)} e^{2} - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(2 \, b c^{2} d^{4} + 2 \, a b c e^{4} - 2 \, {\left(b^{2} c + 2 \, a c^{2} + 2 \, c^{3}\right)} d^{3} e + 6 \, {\left(a b c + b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a c^{2} + {\left(2 \, a^{2} + b^{2}\right)} c\right)} d e^{3} - {\left({\left(4 \, a c^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c\right)} d^{2} + {\left(a^{2} b^{3} - b^{5} - 4 \, a b c^{3} - {\left(8 \, a^{2} b - b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} c\right)} d e - {\left(a^{3} b^{2} - a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} c\right)} e^{2}\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) - \frac{1}{2} \, \sqrt{2} {\left({\left({\left(a^{2} b^{4} - b^{6} + 8 \, a c^{5} + 2 \, {\left(12 \, a^{2} - b^{2}\right)} c^{4} + 6 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{3} + {\left(8 \, a^{4} - 22 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c\right)} d - {\left(a^{3} b^{3} - a b^{5} + 4 \, a b c^{4} + {\left(4 \, a^{2} b - b^{3}\right)} c^{3} - {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} c^{2} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} - b^{5}\right)} c\right)} e\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) + {\left({\left(b^{4} - 4 \, a b^{2} c\right)} d^{3} - 3 \, {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} d^{2} e + {\left(2 \, a^{2} b^{2} + b^{4} - 8 \, a^{3} c - 8 \, a c^{3} - 2 \, {\left(8 \, a^{2} - b^{2}\right)} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} e^{3}\right)} \sin\left(x\right)\right)} \sqrt{-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} d^{2} - 2 \, {\left(a b - b c\right)} d e + {\left(2 \, a^{2} - b^{2} + 2 \, a c\right)} e^{2} - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} + {\left(b^{2} c d^{4} + a b^{2} e^{4} - {\left(b^{3} + 2 \, a b c + 2 \, b c^{2}\right)} d^{3} e + 3 \, {\left(a b^{2} + b^{2} c\right)} d^{2} e^{2} - {\left(2 \, a^{2} b + b^{3} + 2 \, a b c\right)} d e^{3}\right)} \cos\left(x\right)\right) + \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} d^{2} - 2 \, {\left(a b - b c\right)} d e + {\left(2 \, a^{2} - b^{2} + 2 \, a c\right)} e^{2} + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(-2 \, b c^{2} d^{4} - 2 \, a b c e^{4} + 2 \, {\left(b^{2} c + 2 \, a c^{2} + 2 \, c^{3}\right)} d^{3} e - 6 \, {\left(a b c + b c^{2}\right)} d^{2} e^{2} + 2 \, {\left(2 \, a c^{2} + {\left(2 \, a^{2} + b^{2}\right)} c\right)} d e^{3} - {\left({\left(4 \, a c^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c\right)} d^{2} + {\left(a^{2} b^{3} - b^{5} - 4 \, a b c^{3} - {\left(8 \, a^{2} b - b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} c\right)} d e - {\left(a^{3} b^{2} - a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} c\right)} e^{2}\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) + \frac{1}{2} \, \sqrt{2} {\left({\left({\left(a^{2} b^{4} - b^{6} + 8 \, a c^{5} + 2 \, {\left(12 \, a^{2} - b^{2}\right)} c^{4} + 6 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{3} + {\left(8 \, a^{4} - 22 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c\right)} d - {\left(a^{3} b^{3} - a b^{5} + 4 \, a b c^{4} + {\left(4 \, a^{2} b - b^{3}\right)} c^{3} - {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} c^{2} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} - b^{5}\right)} c\right)} e\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) - {\left({\left(b^{4} - 4 \, a b^{2} c\right)} d^{3} - 3 \, {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} d^{2} e + {\left(2 \, a^{2} b^{2} + b^{4} - 8 \, a^{3} c - 8 \, a c^{3} - 2 \, {\left(8 \, a^{2} - b^{2}\right)} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} e^{3}\right)} \sin\left(x\right)\right)} \sqrt{-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} d^{2} - 2 \, {\left(a b - b c\right)} d e + {\left(2 \, a^{2} - b^{2} + 2 \, a c\right)} e^{2} + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} - {\left(b^{2} c d^{4} + a b^{2} e^{4} - {\left(b^{3} + 2 \, a b c + 2 \, b c^{2}\right)} d^{3} e + 3 \, {\left(a b^{2} + b^{2} c\right)} d^{2} e^{2} - {\left(2 \, a^{2} b + b^{3} + 2 \, a b c\right)} d e^{3}\right)} \cos\left(x\right)\right) - \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} d^{2} - 2 \, {\left(a b - b c\right)} d e + {\left(2 \, a^{2} - b^{2} + 2 \, a c\right)} e^{2} + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(-2 \, b c^{2} d^{4} - 2 \, a b c e^{4} + 2 \, {\left(b^{2} c + 2 \, a c^{2} + 2 \, c^{3}\right)} d^{3} e - 6 \, {\left(a b c + b c^{2}\right)} d^{2} e^{2} + 2 \, {\left(2 \, a c^{2} + {\left(2 \, a^{2} + b^{2}\right)} c\right)} d e^{3} - {\left({\left(4 \, a c^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c\right)} d^{2} + {\left(a^{2} b^{3} - b^{5} - 4 \, a b c^{3} - {\left(8 \, a^{2} b - b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} c\right)} d e - {\left(a^{3} b^{2} - a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} c\right)} e^{2}\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) - \frac{1}{2} \, \sqrt{2} {\left({\left({\left(a^{2} b^{4} - b^{6} + 8 \, a c^{5} + 2 \, {\left(12 \, a^{2} - b^{2}\right)} c^{4} + 6 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{3} + {\left(8 \, a^{4} - 22 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c\right)} d - {\left(a^{3} b^{3} - a b^{5} + 4 \, a b c^{4} + {\left(4 \, a^{2} b - b^{3}\right)} c^{3} - {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} c^{2} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} - b^{5}\right)} c\right)} e\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) - {\left({\left(b^{4} - 4 \, a b^{2} c\right)} d^{3} - 3 \, {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} d^{2} e + {\left(2 \, a^{2} b^{2} + b^{4} - 8 \, a^{3} c - 8 \, a c^{3} - 2 \, {\left(8 \, a^{2} - b^{2}\right)} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} e^{3}\right)} \sin\left(x\right)\right)} \sqrt{-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} d^{2} - 2 \, {\left(a b - b c\right)} d e + {\left(2 \, a^{2} - b^{2} + 2 \, a c\right)} e^{2} + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2} d^{4} + b^{2} e^{4} - 4 \, {\left(a b + b c\right)} d^{3} e + 2 \, {\left(2 \, a^{2} + b^{2} + 4 \, a c + 2 \, c^{2}\right)} d^{2} e^{2} - 4 \, {\left(a b + b c\right)} d e^{3}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} - {\left(b^{2} c d^{4} + a b^{2} e^{4} - {\left(b^{3} + 2 \, a b c + 2 \, b c^{2}\right)} d^{3} e + 3 \, {\left(a b^{2} + b^{2} c\right)} d^{2} e^{2} - {\left(2 \, a^{2} b + b^{3} + 2 \, a b c\right)} d e^{3}\right)} \cos\left(x\right)\right)"," ",0,"1/4*sqrt(2)*sqrt(-((b^2 - 2*a*c - 2*c^2)*d^2 - 2*(a*b - b*c)*d*e + (2*a^2 - b^2 + 2*a*c)*e^2 - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(2*b*c^2*d^4 + 2*a*b*c*e^4 - 2*(b^2*c + 2*a*c^2 + 2*c^3)*d^3*e + 6*(a*b*c + b*c^2)*d^2*e^2 - 2*(2*a*c^2 + (2*a^2 + b^2)*c)*d*e^3 - ((4*a*c^4 + (8*a^2 - b^2)*c^3 + 2*(2*a^3 - 3*a*b^2)*c^2 - (a^2*b^2 - b^4)*c)*d^2 + (a^2*b^3 - b^5 - 4*a*b*c^3 - (8*a^2*b - b^3)*c^2 - 2*(2*a^3*b - 3*a*b^3)*c)*d*e - (a^3*b^2 - a*b^4 - 4*a^2*c^3 - (8*a^3 - a*b^2)*c^2 - 2*(2*a^4 - 3*a^2*b^2)*c)*e^2)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) + 1/2*sqrt(2)*(((a^2*b^4 - b^6 + 8*a*c^5 + 2*(12*a^2 - b^2)*c^4 + 6*(4*a^3 - 3*a*b^2)*c^3 + (8*a^4 - 22*a^2*b^2 + 3*b^4)*c^2 - 2*(3*a^3*b^2 - 4*a*b^4)*c)*d - (a^3*b^3 - a*b^5 + 4*a*b*c^4 + (4*a^2*b - b^3)*c^3 - (4*a^3*b + 5*a*b^3)*c^2 - (4*a^4*b - 5*a^2*b^3 - b^5)*c)*e)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) + ((b^4 - 4*a*b^2*c)*d^3 - 3*(a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*d^2*e + (2*a^2*b^2 + b^4 - 8*a^3*c - 8*a*c^3 - 2*(8*a^2 - b^2)*c^2)*d*e^2 - (a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*e^3)*sin(x))*sqrt(-((b^2 - 2*a*c - 2*c^2)*d^2 - 2*(a*b - b*c)*d*e + (2*a^2 - b^2 + 2*a*c)*e^2 - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)) + (b^2*c*d^4 + a*b^2*e^4 - (b^3 + 2*a*b*c + 2*b*c^2)*d^3*e + 3*(a*b^2 + b^2*c)*d^2*e^2 - (2*a^2*b + b^3 + 2*a*b*c)*d*e^3)*cos(x)) - 1/4*sqrt(2)*sqrt(-((b^2 - 2*a*c - 2*c^2)*d^2 - 2*(a*b - b*c)*d*e + (2*a^2 - b^2 + 2*a*c)*e^2 - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(2*b*c^2*d^4 + 2*a*b*c*e^4 - 2*(b^2*c + 2*a*c^2 + 2*c^3)*d^3*e + 6*(a*b*c + b*c^2)*d^2*e^2 - 2*(2*a*c^2 + (2*a^2 + b^2)*c)*d*e^3 - ((4*a*c^4 + (8*a^2 - b^2)*c^3 + 2*(2*a^3 - 3*a*b^2)*c^2 - (a^2*b^2 - b^4)*c)*d^2 + (a^2*b^3 - b^5 - 4*a*b*c^3 - (8*a^2*b - b^3)*c^2 - 2*(2*a^3*b - 3*a*b^3)*c)*d*e - (a^3*b^2 - a*b^4 - 4*a^2*c^3 - (8*a^3 - a*b^2)*c^2 - 2*(2*a^4 - 3*a^2*b^2)*c)*e^2)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) - 1/2*sqrt(2)*(((a^2*b^4 - b^6 + 8*a*c^5 + 2*(12*a^2 - b^2)*c^4 + 6*(4*a^3 - 3*a*b^2)*c^3 + (8*a^4 - 22*a^2*b^2 + 3*b^4)*c^2 - 2*(3*a^3*b^2 - 4*a*b^4)*c)*d - (a^3*b^3 - a*b^5 + 4*a*b*c^4 + (4*a^2*b - b^3)*c^3 - (4*a^3*b + 5*a*b^3)*c^2 - (4*a^4*b - 5*a^2*b^3 - b^5)*c)*e)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) + ((b^4 - 4*a*b^2*c)*d^3 - 3*(a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*d^2*e + (2*a^2*b^2 + b^4 - 8*a^3*c - 8*a*c^3 - 2*(8*a^2 - b^2)*c^2)*d*e^2 - (a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*e^3)*sin(x))*sqrt(-((b^2 - 2*a*c - 2*c^2)*d^2 - 2*(a*b - b*c)*d*e + (2*a^2 - b^2 + 2*a*c)*e^2 - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)) + (b^2*c*d^4 + a*b^2*e^4 - (b^3 + 2*a*b*c + 2*b*c^2)*d^3*e + 3*(a*b^2 + b^2*c)*d^2*e^2 - (2*a^2*b + b^3 + 2*a*b*c)*d*e^3)*cos(x)) + 1/4*sqrt(2)*sqrt(-((b^2 - 2*a*c - 2*c^2)*d^2 - 2*(a*b - b*c)*d*e + (2*a^2 - b^2 + 2*a*c)*e^2 + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(-2*b*c^2*d^4 - 2*a*b*c*e^4 + 2*(b^2*c + 2*a*c^2 + 2*c^3)*d^3*e - 6*(a*b*c + b*c^2)*d^2*e^2 + 2*(2*a*c^2 + (2*a^2 + b^2)*c)*d*e^3 - ((4*a*c^4 + (8*a^2 - b^2)*c^3 + 2*(2*a^3 - 3*a*b^2)*c^2 - (a^2*b^2 - b^4)*c)*d^2 + (a^2*b^3 - b^5 - 4*a*b*c^3 - (8*a^2*b - b^3)*c^2 - 2*(2*a^3*b - 3*a*b^3)*c)*d*e - (a^3*b^2 - a*b^4 - 4*a^2*c^3 - (8*a^3 - a*b^2)*c^2 - 2*(2*a^4 - 3*a^2*b^2)*c)*e^2)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) + 1/2*sqrt(2)*(((a^2*b^4 - b^6 + 8*a*c^5 + 2*(12*a^2 - b^2)*c^4 + 6*(4*a^3 - 3*a*b^2)*c^3 + (8*a^4 - 22*a^2*b^2 + 3*b^4)*c^2 - 2*(3*a^3*b^2 - 4*a*b^4)*c)*d - (a^3*b^3 - a*b^5 + 4*a*b*c^4 + (4*a^2*b - b^3)*c^3 - (4*a^3*b + 5*a*b^3)*c^2 - (4*a^4*b - 5*a^2*b^3 - b^5)*c)*e)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) - ((b^4 - 4*a*b^2*c)*d^3 - 3*(a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*d^2*e + (2*a^2*b^2 + b^4 - 8*a^3*c - 8*a*c^3 - 2*(8*a^2 - b^2)*c^2)*d*e^2 - (a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*e^3)*sin(x))*sqrt(-((b^2 - 2*a*c - 2*c^2)*d^2 - 2*(a*b - b*c)*d*e + (2*a^2 - b^2 + 2*a*c)*e^2 + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)) - (b^2*c*d^4 + a*b^2*e^4 - (b^3 + 2*a*b*c + 2*b*c^2)*d^3*e + 3*(a*b^2 + b^2*c)*d^2*e^2 - (2*a^2*b + b^3 + 2*a*b*c)*d*e^3)*cos(x)) - 1/4*sqrt(2)*sqrt(-((b^2 - 2*a*c - 2*c^2)*d^2 - 2*(a*b - b*c)*d*e + (2*a^2 - b^2 + 2*a*c)*e^2 + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(-2*b*c^2*d^4 - 2*a*b*c*e^4 + 2*(b^2*c + 2*a*c^2 + 2*c^3)*d^3*e - 6*(a*b*c + b*c^2)*d^2*e^2 + 2*(2*a*c^2 + (2*a^2 + b^2)*c)*d*e^3 - ((4*a*c^4 + (8*a^2 - b^2)*c^3 + 2*(2*a^3 - 3*a*b^2)*c^2 - (a^2*b^2 - b^4)*c)*d^2 + (a^2*b^3 - b^5 - 4*a*b*c^3 - (8*a^2*b - b^3)*c^2 - 2*(2*a^3*b - 3*a*b^3)*c)*d*e - (a^3*b^2 - a*b^4 - 4*a^2*c^3 - (8*a^3 - a*b^2)*c^2 - 2*(2*a^4 - 3*a^2*b^2)*c)*e^2)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) - 1/2*sqrt(2)*(((a^2*b^4 - b^6 + 8*a*c^5 + 2*(12*a^2 - b^2)*c^4 + 6*(4*a^3 - 3*a*b^2)*c^3 + (8*a^4 - 22*a^2*b^2 + 3*b^4)*c^2 - 2*(3*a^3*b^2 - 4*a*b^4)*c)*d - (a^3*b^3 - a*b^5 + 4*a*b*c^4 + (4*a^2*b - b^3)*c^3 - (4*a^3*b + 5*a*b^3)*c^2 - (4*a^4*b - 5*a^2*b^3 - b^5)*c)*e)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) - ((b^4 - 4*a*b^2*c)*d^3 - 3*(a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*d^2*e + (2*a^2*b^2 + b^4 - 8*a^3*c - 8*a*c^3 - 2*(8*a^2 - b^2)*c^2)*d*e^2 - (a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*e^3)*sin(x))*sqrt(-((b^2 - 2*a*c - 2*c^2)*d^2 - 2*(a*b - b*c)*d*e + (2*a^2 - b^2 + 2*a*c)*e^2 + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt((b^2*d^4 + b^2*e^4 - 4*(a*b + b*c)*d^3*e + 2*(2*a^2 + b^2 + 4*a*c + 2*c^2)*d^2*e^2 - 4*(a*b + b*c)*d*e^3)/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)) - (b^2*c*d^4 + a*b^2*e^4 - (b^3 + 2*a*b*c + 2*b*c^2)*d^3*e + 3*(a*b^2 + b^2*c)*d^2*e^2 - (2*a^2*b + b^3 + 2*a*b*c)*d*e^3)*cos(x))","B",0
510,1,149,0,1.714829," ","integrate((a+b*tan(e*x+d))*(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^2,x, algorithm=""fricas"")","\frac{3 \, a^{4} b \tan\left(e x + d\right)^{4} + 4 \, {\left(a^{5} + 4 \, a^{3} b^{2}\right)} \tan\left(e x + d\right)^{3} + 12 \, {\left(a^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} e x + 18 \, {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \tan\left(e x + d\right)^{2} + 6 \, {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} \log\left(\frac{1}{\tan\left(e x + d\right)^{2} + 1}\right) - 12 \, {\left(a^{5} - 2 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \tan\left(e x + d\right)}{12 \, e}"," ",0,"1/12*(3*a^4*b*tan(e*x + d)^4 + 4*(a^5 + 4*a^3*b^2)*tan(e*x + d)^3 + 12*(a^5 - 2*a^3*b^2 - 3*a*b^4)*e*x + 18*(a^4*b + 2*a^2*b^3)*tan(e*x + d)^2 + 6*(3*a^4*b + 2*a^2*b^3 - b^5)*log(1/(tan(e*x + d)^2 + 1)) - 12*(a^5 - 2*a^3*b^2 - 4*a*b^4)*tan(e*x + d))/e","A",0
511,1,74,0,1.124517," ","integrate((a+b*tan(e*x+d))*(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2),x, algorithm=""fricas"")","\frac{a^{2} b \tan\left(e x + d\right)^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} e x - {\left(a^{2} b + b^{3}\right)} \log\left(\frac{1}{\tan\left(e x + d\right)^{2} + 1}\right) + 2 \, {\left(a^{3} + 2 \, a b^{2}\right)} \tan\left(e x + d\right)}{2 \, e}"," ",0,"1/2*(a^2*b*tan(e*x + d)^2 - 2*(a^3 + a*b^2)*e*x - (a^2*b + b^3)*log(1/(tan(e*x + d)^2 + 1)) + 2*(a^3 + 2*a*b^2)*tan(e*x + d))/e","A",0
512,1,191,0,0.721648," ","integrate((a+b*tan(e*x+d))/(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2),x, algorithm=""fricas"")","-\frac{2 \, a^{4} - 2 \, a^{2} b^{2} + 2 \, {\left(a^{3} b - 3 \, a b^{3}\right)} e x - {\left(3 \, a^{2} b^{2} - b^{4} + {\left(3 \, a^{3} b - a b^{3}\right)} \tan\left(e x + d\right)\right)} \log\left(\frac{a^{2} \tan\left(e x + d\right)^{2} + 2 \, a b \tan\left(e x + d\right) + b^{2}}{\tan\left(e x + d\right)^{2} + 1}\right) - 2 \, {\left(a^{3} b - a b^{3} - {\left(a^{4} - 3 \, a^{2} b^{2}\right)} e x\right)} \tan\left(e x + d\right)}{2 \, {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} e \tan\left(e x + d\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} e\right)}}"," ",0,"-1/2*(2*a^4 - 2*a^2*b^2 + 2*(a^3*b - 3*a*b^3)*e*x - (3*a^2*b^2 - b^4 + (3*a^3*b - a*b^3)*tan(e*x + d))*log((a^2*tan(e*x + d)^2 + 2*a*b*tan(e*x + d) + b^2)/(tan(e*x + d)^2 + 1)) - 2*(a^3*b - a*b^3 - (a^4 - 3*a^2*b^2)*e*x)*tan(e*x + d))/((a^5 + 2*a^3*b^2 + a*b^4)*e*tan(e*x + d) + (a^4*b + 2*a^2*b^3 + b^5)*e)","A",0
513,1,580,0,2.020596," ","integrate((a+b*tan(e*x+d))/(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^2,x, algorithm=""fricas"")","-\frac{2 \, a^{8} + 7 \, a^{6} b^{2} + 66 \, a^{4} b^{4} - 27 \, a^{2} b^{6} + {\left(21 \, a^{7} b - 56 \, a^{5} b^{3} + 11 \, a^{3} b^{5} - 6 \, {\left(a^{8} - 10 \, a^{6} b^{2} + 5 \, a^{4} b^{4}\right)} e x\right)} \tan\left(e x + d\right)^{3} - 6 \, {\left(a^{5} b^{3} - 10 \, a^{3} b^{5} + 5 \, a b^{7}\right)} e x - 3 \, {\left(2 \, a^{8} - 31 \, a^{6} b^{2} + 46 \, a^{4} b^{4} - 9 \, a^{2} b^{6} + 6 \, {\left(a^{7} b - 10 \, a^{5} b^{3} + 5 \, a^{3} b^{5}\right)} e x\right)} \tan\left(e x + d\right)^{2} + 3 \, {\left(5 \, a^{4} b^{4} - 10 \, a^{2} b^{6} + b^{8} + {\left(5 \, a^{7} b - 10 \, a^{5} b^{3} + a^{3} b^{5}\right)} \tan\left(e x + d\right)^{3} + 3 \, {\left(5 \, a^{6} b^{2} - 10 \, a^{4} b^{4} + a^{2} b^{6}\right)} \tan\left(e x + d\right)^{2} + 3 \, {\left(5 \, a^{5} b^{3} - 10 \, a^{3} b^{5} + a b^{7}\right)} \tan\left(e x + d\right)\right)} \log\left(\frac{a^{2} \tan\left(e x + d\right)^{2} + 2 \, a b \tan\left(e x + d\right) + b^{2}}{\tan\left(e x + d\right)^{2} + 1}\right) - 3 \, {\left(a^{7} b - 46 \, a^{5} b^{3} + 35 \, a^{3} b^{5} - 6 \, a b^{7} + 6 \, {\left(a^{6} b^{2} - 10 \, a^{4} b^{4} + 5 \, a^{2} b^{6}\right)} e x\right)} \tan\left(e x + d\right)}{6 \, {\left({\left(a^{11} + 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} + 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} e \tan\left(e x + d\right)^{3} + 3 \, {\left(a^{10} b + 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} + 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} e \tan\left(e x + d\right)^{2} + 3 \, {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} e \tan\left(e x + d\right) + {\left(a^{8} b^{3} + 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + 4 \, a^{2} b^{9} + b^{11}\right)} e\right)}}"," ",0,"-1/6*(2*a^8 + 7*a^6*b^2 + 66*a^4*b^4 - 27*a^2*b^6 + (21*a^7*b - 56*a^5*b^3 + 11*a^3*b^5 - 6*(a^8 - 10*a^6*b^2 + 5*a^4*b^4)*e*x)*tan(e*x + d)^3 - 6*(a^5*b^3 - 10*a^3*b^5 + 5*a*b^7)*e*x - 3*(2*a^8 - 31*a^6*b^2 + 46*a^4*b^4 - 9*a^2*b^6 + 6*(a^7*b - 10*a^5*b^3 + 5*a^3*b^5)*e*x)*tan(e*x + d)^2 + 3*(5*a^4*b^4 - 10*a^2*b^6 + b^8 + (5*a^7*b - 10*a^5*b^3 + a^3*b^5)*tan(e*x + d)^3 + 3*(5*a^6*b^2 - 10*a^4*b^4 + a^2*b^6)*tan(e*x + d)^2 + 3*(5*a^5*b^3 - 10*a^3*b^5 + a*b^7)*tan(e*x + d))*log((a^2*tan(e*x + d)^2 + 2*a*b*tan(e*x + d) + b^2)/(tan(e*x + d)^2 + 1)) - 3*(a^7*b - 46*a^5*b^3 + 35*a^3*b^5 - 6*a*b^7 + 6*(a^6*b^2 - 10*a^4*b^4 + 5*a^2*b^6)*e*x)*tan(e*x + d))/((a^11 + 4*a^9*b^2 + 6*a^7*b^4 + 4*a^5*b^6 + a^3*b^8)*e*tan(e*x + d)^3 + 3*(a^10*b + 4*a^8*b^3 + 6*a^6*b^5 + 4*a^4*b^7 + a^2*b^9)*e*tan(e*x + d)^2 + 3*(a^9*b^2 + 4*a^7*b^4 + 6*a^5*b^6 + 4*a^3*b^8 + a*b^10)*e*tan(e*x + d) + (a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*e)","B",0
514,1,102,0,2.830324," ","integrate((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, algorithm=""fricas"")","\frac{2 \, a^{3} b \tan\left(e x + d\right)^{3} - 12 \, {\left(a^{3} b + a b^{3}\right)} e x + 3 \, {\left(a^{4} + 3 \, a^{2} b^{2}\right)} \tan\left(e x + d\right)^{2} + 3 \, {\left(a^{4} - b^{4}\right)} \log\left(\frac{1}{\tan\left(e x + d\right)^{2} + 1}\right) + 6 \, {\left(2 \, a^{3} b + 3 \, a b^{3}\right)} \tan\left(e x + d\right)}{6 \, e}"," ",0,"1/6*(2*a^3*b*tan(e*x + d)^3 - 12*(a^3*b + a*b^3)*e*x + 3*(a^4 + 3*a^2*b^2)*tan(e*x + d)^2 + 3*(a^4 - b^4)*log(1/(tan(e*x + d)^2 + 1)) + 6*(2*a^3*b + 3*a*b^3)*tan(e*x + d))/e","A",0
515,1,38,0,2.630982," ","integrate((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, algorithm=""fricas"")","\frac{2 \, a b \tan\left(e x + d\right) - {\left(a^{2} + b^{2}\right)} \log\left(\frac{1}{\tan\left(e x + d\right)^{2} + 1}\right)}{2 \, e}"," ",0,"1/2*(2*a*b*tan(e*x + d) - (a^2 + b^2)*log(1/(tan(e*x + d)^2 + 1)))/e","A",0
516,1,71,0,0.724585," ","integrate((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, algorithm=""fricas"")","\frac{4 \, a b e x + {\left(a^{2} - b^{2}\right)} \log\left(\frac{a^{2} \tan\left(e x + d\right)^{2} + 2 \, a b \tan\left(e x + d\right) + b^{2}}{\tan\left(e x + d\right)^{2} + 1}\right)}{2 \, {\left(a^{2} + b^{2}\right)} e}"," ",0,"1/2*(4*a*b*e*x + (a^2 - b^2)*log((a^2*tan(e*x + d)^2 + 2*a*b*tan(e*x + d) + b^2)/(tan(e*x + d)^2 + 1)))/((a^2 + b^2)*e)","A",0
517,1,355,0,2.034397," ","integrate((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, algorithm=""fricas"")","-\frac{a^{6} + 8 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + 8 \, {\left(a^{3} b^{3} - a b^{5}\right)} e x + {\left(a^{6} - 8 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + 8 \, {\left(a^{5} b - a^{3} b^{3}\right)} e x\right)} \tan\left(e x + d\right)^{2} + {\left(a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6} + {\left(a^{6} - 6 \, a^{4} b^{2} + a^{2} b^{4}\right)} \tan\left(e x + d\right)^{2} + 2 \, {\left(a^{5} b - 6 \, a^{3} b^{3} + a b^{5}\right)} \tan\left(e x + d\right)\right)} \log\left(\frac{a^{2} \tan\left(e x + d\right)^{2} + 2 \, a b \tan\left(e x + d\right) + b^{2}}{\tan\left(e x + d\right)^{2} + 1}\right) + 4 \, {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5} + 4 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} e x\right)} \tan\left(e x + d\right)}{2 \, {\left({\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} e \tan\left(e x + d\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} e \tan\left(e x + d\right) + {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} e\right)}}"," ",0,"-1/2*(a^6 + 8*a^4*b^2 - 5*a^2*b^4 + 8*(a^3*b^3 - a*b^5)*e*x + (a^6 - 8*a^4*b^2 + 3*a^2*b^4 + 8*(a^5*b - a^3*b^3)*e*x)*tan(e*x + d)^2 + (a^4*b^2 - 6*a^2*b^4 + b^6 + (a^6 - 6*a^4*b^2 + a^2*b^4)*tan(e*x + d)^2 + 2*(a^5*b - 6*a^3*b^3 + a*b^5)*tan(e*x + d))*log((a^2*tan(e*x + d)^2 + 2*a*b*tan(e*x + d) + b^2)/(tan(e*x + d)^2 + 1)) + 4*(2*a^5*b - 3*a^3*b^3 + a*b^5 + 4*(a^4*b^2 - a^2*b^4)*e*x)*tan(e*x + d))/((a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*e*tan(e*x + d)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*e*tan(e*x + d) + (a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*e)","A",0
518,1,198,0,2.425869," ","integrate((a+b*sec(e*x+d))*(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^2,x, algorithm=""fricas"")","\frac{48 \, a b^{4} e x \cos\left(e x + d\right)^{4} + 3 \, {\left(19 \, a^{4} b + 56 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(e x + d\right)^{4} \log\left(\sin\left(e x + d\right) + 1\right) - 3 \, {\left(19 \, a^{4} b + 56 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(e x + d\right)^{4} \log\left(-\sin\left(e x + d\right) + 1\right) + 2 \, {\left(6 \, a^{4} b + 16 \, {\left(a^{5} + 13 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(e x + d\right)^{3} + 3 \, {\left(19 \, a^{4} b + 24 \, a^{2} b^{3}\right)} \cos\left(e x + d\right)^{2} + 8 \, {\left(a^{5} + 4 \, a^{3} b^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{48 \, e \cos\left(e x + d\right)^{4}}"," ",0,"1/48*(48*a*b^4*e*x*cos(e*x + d)^4 + 3*(19*a^4*b + 56*a^2*b^3 + 8*b^5)*cos(e*x + d)^4*log(sin(e*x + d) + 1) - 3*(19*a^4*b + 56*a^2*b^3 + 8*b^5)*cos(e*x + d)^4*log(-sin(e*x + d) + 1) + 2*(6*a^4*b + 16*(a^5 + 13*a^3*b^2 + 6*a*b^4)*cos(e*x + d)^3 + 3*(19*a^4*b + 24*a^2*b^3)*cos(e*x + d)^2 + 8*(a^5 + 4*a^3*b^2)*cos(e*x + d))*sin(e*x + d))/(e*cos(e*x + d)^4)","A",0
519,1,125,0,1.495878," ","integrate((a+b*sec(e*x+d))*(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2),x, algorithm=""fricas"")","\frac{4 \, a b^{2} e x \cos\left(e x + d\right)^{2} + {\left(5 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(e x + d\right)^{2} \log\left(\sin\left(e x + d\right) + 1\right) - {\left(5 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(e x + d\right)^{2} \log\left(-\sin\left(e x + d\right) + 1\right) + 2 \, {\left(a^{2} b + 2 \, {\left(a^{3} + 2 \, a b^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{4 \, e \cos\left(e x + d\right)^{2}}"," ",0,"1/4*(4*a*b^2*e*x*cos(e*x + d)^2 + (5*a^2*b + 2*b^3)*cos(e*x + d)^2*log(sin(e*x + d) + 1) - (5*a^2*b + 2*b^3)*cos(e*x + d)^2*log(-sin(e*x + d) + 1) + 2*(a^2*b + 2*(a^3 + 2*a*b^2)*cos(e*x + d))*sin(e*x + d))/(e*cos(e*x + d)^2)","A",0
520,1,279,0,0.846986," ","integrate((a+b*sec(e*x+d))/(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2),x, algorithm=""fricas"")","\left[\frac{2 \, a b e x \cos\left(e x + d\right) + 2 \, a^{2} e x - 2 \, a b \sin\left(e x + d\right) + \sqrt{-a^{2} + b^{2}} {\left(b \cos\left(e x + d\right) + a\right)} \log\left(\frac{2 \, a b \cos\left(e x + d\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(e x + d\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(e x + d\right) + b\right)} \sin\left(e x + d\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(e x + d\right)^{2} + 2 \, a b \cos\left(e x + d\right) + a^{2}}\right)}{2 \, {\left(b^{3} e \cos\left(e x + d\right) + a b^{2} e\right)}}, \frac{a b e x \cos\left(e x + d\right) + a^{2} e x - a b \sin\left(e x + d\right) - \sqrt{a^{2} - b^{2}} {\left(b \cos\left(e x + d\right) + a\right)} \arctan\left(-\frac{a \cos\left(e x + d\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(e x + d\right)}\right)}{b^{3} e \cos\left(e x + d\right) + a b^{2} e}\right]"," ",0,"[1/2*(2*a*b*e*x*cos(e*x + d) + 2*a^2*e*x - 2*a*b*sin(e*x + d) + sqrt(-a^2 + b^2)*(b*cos(e*x + d) + a)*log((2*a*b*cos(e*x + d) + (2*a^2 - b^2)*cos(e*x + d)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(e*x + d) + b)*sin(e*x + d) - a^2 + 2*b^2)/(b^2*cos(e*x + d)^2 + 2*a*b*cos(e*x + d) + a^2)))/(b^3*e*cos(e*x + d) + a*b^2*e), (a*b*e*x*cos(e*x + d) + a^2*e*x - a*b*sin(e*x + d) - sqrt(a^2 - b^2)*(b*cos(e*x + d) + a)*arctan(-(a*cos(e*x + d) + b)/(sqrt(a^2 - b^2)*sin(e*x + d))))/(b^3*e*cos(e*x + d) + a*b^2*e)]","A",0
521,1,1335,0,2.109532," ","integrate((a+b*sec(e*x+d))/(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^2,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a^{7} b^{3} - 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} - a b^{9}\right)} e x \cos\left(e x + d\right)^{3} + 36 \, {\left(a^{8} b^{2} - 3 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - a^{2} b^{8}\right)} e x \cos\left(e x + d\right)^{2} + 36 \, {\left(a^{9} b - 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - a^{3} b^{7}\right)} e x \cos\left(e x + d\right) + 12 \, {\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} e x + 3 \, {\left(2 \, a^{9} - 5 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - 2 \, a^{3} b^{6} + {\left(2 \, a^{6} b^{3} - 5 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - 2 \, b^{9}\right)} \cos\left(e x + d\right)^{3} + 3 \, {\left(2 \, a^{7} b^{2} - 5 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - 2 \, a b^{8}\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(2 \, a^{8} b - 5 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - 2 \, a^{2} b^{7}\right)} \cos\left(e x + d\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(e x + d\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(e x + d\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(e x + d\right) + b\right)} \sin\left(e x + d\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(e x + d\right)^{2} + 2 \, a b \cos\left(e x + d\right) + a^{2}}\right) - 2 \, {\left(6 \, a^{9} b - 17 \, a^{7} b^{3} + 22 \, a^{5} b^{5} - 11 \, a^{3} b^{7} + {\left(11 \, a^{7} b^{3} - 34 \, a^{5} b^{5} + 41 \, a^{3} b^{7} - 18 \, a b^{9}\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(5 \, a^{8} b^{2} - 15 \, a^{6} b^{4} + 19 \, a^{4} b^{6} - 9 \, a^{2} b^{8}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{12 \, {\left({\left(a^{6} b^{7} - 3 \, a^{4} b^{9} + 3 \, a^{2} b^{11} - b^{13}\right)} e \cos\left(e x + d\right)^{3} + 3 \, {\left(a^{7} b^{6} - 3 \, a^{5} b^{8} + 3 \, a^{3} b^{10} - a b^{12}\right)} e \cos\left(e x + d\right)^{2} + 3 \, {\left(a^{8} b^{5} - 3 \, a^{6} b^{7} + 3 \, a^{4} b^{9} - a^{2} b^{11}\right)} e \cos\left(e x + d\right) + {\left(a^{9} b^{4} - 3 \, a^{7} b^{6} + 3 \, a^{5} b^{8} - a^{3} b^{10}\right)} e\right)}}, \frac{6 \, {\left(a^{7} b^{3} - 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} - a b^{9}\right)} e x \cos\left(e x + d\right)^{3} + 18 \, {\left(a^{8} b^{2} - 3 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - a^{2} b^{8}\right)} e x \cos\left(e x + d\right)^{2} + 18 \, {\left(a^{9} b - 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - a^{3} b^{7}\right)} e x \cos\left(e x + d\right) + 6 \, {\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} e x - 3 \, {\left(2 \, a^{9} - 5 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - 2 \, a^{3} b^{6} + {\left(2 \, a^{6} b^{3} - 5 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - 2 \, b^{9}\right)} \cos\left(e x + d\right)^{3} + 3 \, {\left(2 \, a^{7} b^{2} - 5 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - 2 \, a b^{8}\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(2 \, a^{8} b - 5 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - 2 \, a^{2} b^{7}\right)} \cos\left(e x + d\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(e x + d\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(e x + d\right)}\right) - {\left(6 \, a^{9} b - 17 \, a^{7} b^{3} + 22 \, a^{5} b^{5} - 11 \, a^{3} b^{7} + {\left(11 \, a^{7} b^{3} - 34 \, a^{5} b^{5} + 41 \, a^{3} b^{7} - 18 \, a b^{9}\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(5 \, a^{8} b^{2} - 15 \, a^{6} b^{4} + 19 \, a^{4} b^{6} - 9 \, a^{2} b^{8}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{6 \, {\left({\left(a^{6} b^{7} - 3 \, a^{4} b^{9} + 3 \, a^{2} b^{11} - b^{13}\right)} e \cos\left(e x + d\right)^{3} + 3 \, {\left(a^{7} b^{6} - 3 \, a^{5} b^{8} + 3 \, a^{3} b^{10} - a b^{12}\right)} e \cos\left(e x + d\right)^{2} + 3 \, {\left(a^{8} b^{5} - 3 \, a^{6} b^{7} + 3 \, a^{4} b^{9} - a^{2} b^{11}\right)} e \cos\left(e x + d\right) + {\left(a^{9} b^{4} - 3 \, a^{7} b^{6} + 3 \, a^{5} b^{8} - a^{3} b^{10}\right)} e\right)}}\right]"," ",0,"[1/12*(12*(a^7*b^3 - 3*a^5*b^5 + 3*a^3*b^7 - a*b^9)*e*x*cos(e*x + d)^3 + 36*(a^8*b^2 - 3*a^6*b^4 + 3*a^4*b^6 - a^2*b^8)*e*x*cos(e*x + d)^2 + 36*(a^9*b - 3*a^7*b^3 + 3*a^5*b^5 - a^3*b^7)*e*x*cos(e*x + d) + 12*(a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*e*x + 3*(2*a^9 - 5*a^7*b^2 + 3*a^5*b^4 - 2*a^3*b^6 + (2*a^6*b^3 - 5*a^4*b^5 + 3*a^2*b^7 - 2*b^9)*cos(e*x + d)^3 + 3*(2*a^7*b^2 - 5*a^5*b^4 + 3*a^3*b^6 - 2*a*b^8)*cos(e*x + d)^2 + 3*(2*a^8*b - 5*a^6*b^3 + 3*a^4*b^5 - 2*a^2*b^7)*cos(e*x + d))*sqrt(-a^2 + b^2)*log((2*a*b*cos(e*x + d) + (2*a^2 - b^2)*cos(e*x + d)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(e*x + d) + b)*sin(e*x + d) - a^2 + 2*b^2)/(b^2*cos(e*x + d)^2 + 2*a*b*cos(e*x + d) + a^2)) - 2*(6*a^9*b - 17*a^7*b^3 + 22*a^5*b^5 - 11*a^3*b^7 + (11*a^7*b^3 - 34*a^5*b^5 + 41*a^3*b^7 - 18*a*b^9)*cos(e*x + d)^2 + 3*(5*a^8*b^2 - 15*a^6*b^4 + 19*a^4*b^6 - 9*a^2*b^8)*cos(e*x + d))*sin(e*x + d))/((a^6*b^7 - 3*a^4*b^9 + 3*a^2*b^11 - b^13)*e*cos(e*x + d)^3 + 3*(a^7*b^6 - 3*a^5*b^8 + 3*a^3*b^10 - a*b^12)*e*cos(e*x + d)^2 + 3*(a^8*b^5 - 3*a^6*b^7 + 3*a^4*b^9 - a^2*b^11)*e*cos(e*x + d) + (a^9*b^4 - 3*a^7*b^6 + 3*a^5*b^8 - a^3*b^10)*e), 1/6*(6*(a^7*b^3 - 3*a^5*b^5 + 3*a^3*b^7 - a*b^9)*e*x*cos(e*x + d)^3 + 18*(a^8*b^2 - 3*a^6*b^4 + 3*a^4*b^6 - a^2*b^8)*e*x*cos(e*x + d)^2 + 18*(a^9*b - 3*a^7*b^3 + 3*a^5*b^5 - a^3*b^7)*e*x*cos(e*x + d) + 6*(a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*e*x - 3*(2*a^9 - 5*a^7*b^2 + 3*a^5*b^4 - 2*a^3*b^6 + (2*a^6*b^3 - 5*a^4*b^5 + 3*a^2*b^7 - 2*b^9)*cos(e*x + d)^3 + 3*(2*a^7*b^2 - 5*a^5*b^4 + 3*a^3*b^6 - 2*a*b^8)*cos(e*x + d)^2 + 3*(2*a^8*b - 5*a^6*b^3 + 3*a^4*b^5 - 2*a^2*b^7)*cos(e*x + d))*sqrt(a^2 - b^2)*arctan(-(a*cos(e*x + d) + b)/(sqrt(a^2 - b^2)*sin(e*x + d))) - (6*a^9*b - 17*a^7*b^3 + 22*a^5*b^5 - 11*a^3*b^7 + (11*a^7*b^3 - 34*a^5*b^5 + 41*a^3*b^7 - 18*a*b^9)*cos(e*x + d)^2 + 3*(5*a^8*b^2 - 15*a^6*b^4 + 19*a^4*b^6 - 9*a^2*b^8)*cos(e*x + d))*sin(e*x + d))/((a^6*b^7 - 3*a^4*b^9 + 3*a^2*b^11 - b^13)*e*cos(e*x + d)^3 + 3*(a^7*b^6 - 3*a^5*b^8 + 3*a^3*b^10 - a*b^12)*e*cos(e*x + d)^2 + 3*(a^8*b^5 - 3*a^6*b^7 + 3*a^4*b^9 - a^2*b^11)*e*cos(e*x + d) + (a^9*b^4 - 3*a^7*b^6 + 3*a^5*b^8 - a^3*b^10)*e)]","B",0
522,1,162,0,1.580400," ","integrate((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, algorithm=""fricas"")","\frac{12 \, a b^{3} e x \cos\left(e x + d\right)^{3} + 3 \, {\left(a^{4} + 9 \, a^{2} b^{2} + 2 \, b^{4}\right)} \cos\left(e x + d\right)^{3} \log\left(\sin\left(e x + d\right) + 1\right) - 3 \, {\left(a^{4} + 9 \, a^{2} b^{2} + 2 \, b^{4}\right)} \cos\left(e x + d\right)^{3} \log\left(-\sin\left(e x + d\right) + 1\right) + 2 \, {\left(2 \, a^{3} b + 2 \, {\left(11 \, a^{3} b + 9 \, a b^{3}\right)} \cos\left(e x + d\right)^{2} + 3 \, {\left(a^{4} + 3 \, a^{2} b^{2}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{12 \, e \cos\left(e x + d\right)^{3}}"," ",0,"1/12*(12*a*b^3*e*x*cos(e*x + d)^3 + 3*(a^4 + 9*a^2*b^2 + 2*b^4)*cos(e*x + d)^3*log(sin(e*x + d) + 1) - 3*(a^4 + 9*a^2*b^2 + 2*b^4)*cos(e*x + d)^3*log(-sin(e*x + d) + 1) + 2*(2*a^3*b + 2*(11*a^3*b + 9*a*b^3)*cos(e*x + d)^2 + 3*(a^4 + 3*a^2*b^2)*cos(e*x + d))*sin(e*x + d))/(e*cos(e*x + d)^3)","A",0
523,1,85,0,0.960982," ","integrate((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, algorithm=""fricas"")","\frac{2 \, a b e x \cos\left(e x + d\right) + {\left(a^{2} + b^{2}\right)} \cos\left(e x + d\right) \log\left(\sin\left(e x + d\right) + 1\right) - {\left(a^{2} + b^{2}\right)} \cos\left(e x + d\right) \log\left(-\sin\left(e x + d\right) + 1\right) + 2 \, a b \sin\left(e x + d\right)}{2 \, e \cos\left(e x + d\right)}"," ",0,"1/2*(2*a*b*e*x*cos(e*x + d) + (a^2 + b^2)*cos(e*x + d)*log(sin(e*x + d) + 1) - (a^2 + b^2)*cos(e*x + d)*log(-sin(e*x + d) + 1) + 2*a*b*sin(e*x + d))/(e*cos(e*x + d))","A",0
524,1,184,0,1.064022," ","integrate((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, algorithm=""fricas"")","\left[\frac{2 \, a e x + \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(e x + d\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(e x + d\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(e x + d\right) + b\right)} \sin\left(e x + d\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(e x + d\right)^{2} + 2 \, a b \cos\left(e x + d\right) + a^{2}}\right)}{2 \, b e}, \frac{a e x - \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(e x + d\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(e x + d\right)}\right)}{b e}\right]"," ",0,"[1/2*(2*a*e*x + sqrt(-a^2 + b^2)*log((2*a*b*cos(e*x + d) + (2*a^2 - b^2)*cos(e*x + d)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(e*x + d) + b)*sin(e*x + d) - a^2 + 2*b^2)/(b^2*cos(e*x + d)^2 + 2*a*b*cos(e*x + d) + a^2)))/(b*e), (a*e*x - sqrt(a^2 - b^2)*arctan(-(a*cos(e*x + d) + b)/(sqrt(a^2 - b^2)*sin(e*x + d))))/(b*e)]","A",0
525,1,798,0,1.085983," ","integrate((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, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} e x \cos\left(e x + d\right)^{2} + 8 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} e x \cos\left(e x + d\right) + 4 \, {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} e x + {\left(2 \, a^{6} - 3 \, a^{4} b^{2} + 2 \, a^{2} b^{4} + {\left(2 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(e x + d\right)^{2} + 2 \, {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(e x + d\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(e x + d\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(e x + d\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(e x + d\right) + b\right)} \sin\left(e x + d\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(e x + d\right)^{2} + 2 \, a b \cos\left(e x + d\right) + a^{2}}\right) - 2 \, {\left(2 \, a^{6} b - 5 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + {\left(3 \, a^{5} b^{2} - 7 \, a^{3} b^{4} + 4 \, a b^{6}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{4 \, {\left({\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} e \cos\left(e x + d\right)^{2} + 2 \, {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)} e \cos\left(e x + d\right) + {\left(a^{6} b^{3} - 2 \, a^{4} b^{5} + a^{2} b^{7}\right)} e\right)}}, \frac{2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} e x \cos\left(e x + d\right)^{2} + 4 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} e x \cos\left(e x + d\right) + 2 \, {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} e x - {\left(2 \, a^{6} - 3 \, a^{4} b^{2} + 2 \, a^{2} b^{4} + {\left(2 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(e x + d\right)^{2} + 2 \, {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(e x + d\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(e x + d\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(e x + d\right)}\right) - {\left(2 \, a^{6} b - 5 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + {\left(3 \, a^{5} b^{2} - 7 \, a^{3} b^{4} + 4 \, a b^{6}\right)} \cos\left(e x + d\right)\right)} \sin\left(e x + d\right)}{2 \, {\left({\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} e \cos\left(e x + d\right)^{2} + 2 \, {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)} e \cos\left(e x + d\right) + {\left(a^{6} b^{3} - 2 \, a^{4} b^{5} + a^{2} b^{7}\right)} e\right)}}\right]"," ",0,"[1/4*(4*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*e*x*cos(e*x + d)^2 + 8*(a^6*b - 2*a^4*b^3 + a^2*b^5)*e*x*cos(e*x + d) + 4*(a^7 - 2*a^5*b^2 + a^3*b^4)*e*x + (2*a^6 - 3*a^4*b^2 + 2*a^2*b^4 + (2*a^4*b^2 - 3*a^2*b^4 + 2*b^6)*cos(e*x + d)^2 + 2*(2*a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(e*x + d))*sqrt(-a^2 + b^2)*log((2*a*b*cos(e*x + d) + (2*a^2 - b^2)*cos(e*x + d)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(e*x + d) + b)*sin(e*x + d) - a^2 + 2*b^2)/(b^2*cos(e*x + d)^2 + 2*a*b*cos(e*x + d) + a^2)) - 2*(2*a^6*b - 5*a^4*b^3 + 3*a^2*b^5 + (3*a^5*b^2 - 7*a^3*b^4 + 4*a*b^6)*cos(e*x + d))*sin(e*x + d))/((a^4*b^5 - 2*a^2*b^7 + b^9)*e*cos(e*x + d)^2 + 2*(a^5*b^4 - 2*a^3*b^6 + a*b^8)*e*cos(e*x + d) + (a^6*b^3 - 2*a^4*b^5 + a^2*b^7)*e), 1/2*(2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*e*x*cos(e*x + d)^2 + 4*(a^6*b - 2*a^4*b^3 + a^2*b^5)*e*x*cos(e*x + d) + 2*(a^7 - 2*a^5*b^2 + a^3*b^4)*e*x - (2*a^6 - 3*a^4*b^2 + 2*a^2*b^4 + (2*a^4*b^2 - 3*a^2*b^4 + 2*b^6)*cos(e*x + d)^2 + 2*(2*a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(e*x + d))*sqrt(a^2 - b^2)*arctan(-(a*cos(e*x + d) + b)/(sqrt(a^2 - b^2)*sin(e*x + d))) - (2*a^6*b - 5*a^4*b^3 + 3*a^2*b^5 + (3*a^5*b^2 - 7*a^3*b^4 + 4*a*b^6)*cos(e*x + d))*sin(e*x + d))/((a^4*b^5 - 2*a^2*b^7 + b^9)*e*cos(e*x + d)^2 + 2*(a^5*b^4 - 2*a^3*b^6 + a*b^8)*e*cos(e*x + d) + (a^6*b^3 - 2*a^4*b^5 + a^2*b^7)*e)]","A",0
526,1,6,0,0.703005," ","integrate((cos(x)-I*sin(x))/(cos(x)+I*sin(x)),x, algorithm=""fricas"")","\frac{1}{2} i \, e^{\left(-2 i \, x\right)}"," ",0,"1/2*I*e^(-2*I*x)","A",0
527,1,6,0,0.652378," ","integrate((cos(x)+I*sin(x))/(cos(x)-I*sin(x)),x, algorithm=""fricas"")","-\frac{1}{2} i \, e^{\left(2 i \, x\right)}"," ",0,"-1/2*I*e^(2*I*x)","A",0
528,1,11,0,0.824443," ","integrate((cos(x)-sin(x))/(cos(x)+sin(x)),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(2 \, \cos\left(x\right) \sin\left(x\right) + 1\right)"," ",0,"1/2*log(2*cos(x)*sin(x) + 1)","A",0
529,1,59,0,0.882280," ","integrate((B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x)),x, algorithm=""fricas"")","\frac{2 \, {\left(B b + C c\right)} x - {\left(C b - B c\right)} \log\left(2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + c^{2}\right)}{2 \, {\left(b^{2} + c^{2}\right)}}"," ",0,"1/2*(2*(B*b + C*c)*x - (C*b - B*c)*log(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 + c^2))/(b^2 + c^2)","A",0
530,1,194,0,1.626758," ","integrate((B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))^2,x, algorithm=""fricas"")","\frac{2 \, C b^{3} - 2 \, B b^{2} c + 2 \, C b c^{2} - 2 \, B c^{3} + \sqrt{b^{2} + c^{2}} {\left({\left(B b^{2} + C b c\right)} \cos\left(x\right) + {\left(B b c + C c^{2}\right)} \sin\left(x\right)\right)} \log\left(-\frac{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} - 2 \, b^{2} - c^{2} + 2 \, \sqrt{b^{2} + c^{2}} {\left(c \cos\left(x\right) - b \sin\left(x\right)\right)}}{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + c^{2}}\right)}{2 \, {\left({\left(b^{5} + 2 \, b^{3} c^{2} + b c^{4}\right)} \cos\left(x\right) + {\left(b^{4} c + 2 \, b^{2} c^{3} + c^{5}\right)} \sin\left(x\right)\right)}}"," ",0,"1/2*(2*C*b^3 - 2*B*b^2*c + 2*C*b*c^2 - 2*B*c^3 + sqrt(b^2 + c^2)*((B*b^2 + C*b*c)*cos(x) + (B*b*c + C*c^2)*sin(x))*log(-(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 - 2*b^2 - c^2 + 2*sqrt(b^2 + c^2)*(c*cos(x) - b*sin(x)))/(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 + c^2)))/((b^5 + 2*b^3*c^2 + b*c^4)*cos(x) + (b^4*c + 2*b^2*c^3 + c^5)*sin(x))","B",0
531,1,152,0,0.539794," ","integrate((B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))^3,x, algorithm=""fricas"")","\frac{C b^{3} + B b^{2} c + 3 \, C b c^{2} - B c^{3} - 4 \, {\left(B b^{2} c + C b c^{2}\right)} \cos\left(x\right)^{2} + 2 \, {\left(B b^{3} + C b^{2} c - B b c^{2} - C c^{3}\right)} \cos\left(x\right) \sin\left(x\right)}{2 \, {\left(b^{4} c^{2} + 2 \, b^{2} c^{4} + c^{6} + {\left(b^{6} + b^{4} c^{2} - b^{2} c^{4} - c^{6}\right)} \cos\left(x\right)^{2} + 2 \, {\left(b^{5} c + 2 \, b^{3} c^{3} + b c^{5}\right)} \cos\left(x\right) \sin\left(x\right)\right)}}"," ",0,"1/2*(C*b^3 + B*b^2*c + 3*C*b*c^2 - B*c^3 - 4*(B*b^2*c + C*b*c^2)*cos(x)^2 + 2*(B*b^3 + C*b^2*c - B*b*c^2 - C*c^3)*cos(x)*sin(x))/(b^4*c^2 + 2*b^2*c^4 + c^6 + (b^6 + b^4*c^2 - b^2*c^4 - c^6)*cos(x)^2 + 2*(b^5*c + 2*b^3*c^3 + b*c^5)*cos(x)*sin(x))","B",0
532,1,155,0,0.771684," ","integrate((A+B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x)),x, algorithm=""fricas"")","\frac{\sqrt{b^{2} + c^{2}} A \log\left(-\frac{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} - 2 \, b^{2} - c^{2} + 2 \, \sqrt{b^{2} + c^{2}} {\left(c \cos\left(x\right) - b \sin\left(x\right)\right)}}{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + c^{2}}\right) + 2 \, {\left(B b + C c\right)} x - {\left(C b - B c\right)} \log\left(2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + c^{2}\right)}{2 \, {\left(b^{2} + c^{2}\right)}}"," ",0,"1/2*(sqrt(b^2 + c^2)*A*log(-(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 - 2*b^2 - c^2 + 2*sqrt(b^2 + c^2)*(c*cos(x) - b*sin(x)))/(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 + c^2)) + 2*(B*b + C*c)*x - (C*b - B*c)*log(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 + c^2))/(b^2 + c^2)","A",0
533,1,226,0,3.023320," ","integrate((A+B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))^2,x, algorithm=""fricas"")","\frac{2 \, C b^{3} - 2 \, B b^{2} c + 2 \, C b c^{2} - 2 \, B c^{3} + \sqrt{b^{2} + c^{2}} {\left({\left(B b^{2} + C b c\right)} \cos\left(x\right) + {\left(B b c + C c^{2}\right)} \sin\left(x\right)\right)} \log\left(-\frac{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} - 2 \, b^{2} - c^{2} + 2 \, \sqrt{b^{2} + c^{2}} {\left(c \cos\left(x\right) - b \sin\left(x\right)\right)}}{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + c^{2}}\right) - 2 \, {\left(A b^{2} c + A c^{3}\right)} \cos\left(x\right) + 2 \, {\left(A b^{3} + A b c^{2}\right)} \sin\left(x\right)}{2 \, {\left({\left(b^{5} + 2 \, b^{3} c^{2} + b c^{4}\right)} \cos\left(x\right) + {\left(b^{4} c + 2 \, b^{2} c^{3} + c^{5}\right)} \sin\left(x\right)\right)}}"," ",0,"1/2*(2*C*b^3 - 2*B*b^2*c + 2*C*b*c^2 - 2*B*c^3 + sqrt(b^2 + c^2)*((B*b^2 + C*b*c)*cos(x) + (B*b*c + C*c^2)*sin(x))*log(-(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 - 2*b^2 - c^2 + 2*sqrt(b^2 + c^2)*(c*cos(x) - b*sin(x)))/(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 + c^2)) - 2*(A*b^2*c + A*c^3)*cos(x) + 2*(A*b^3 + A*b*c^2)*sin(x))/((b^5 + 2*b^3*c^2 + b*c^4)*cos(x) + (b^4*c + 2*b^2*c^3 + c^5)*sin(x))","B",0
534,1,311,0,1.690655," ","integrate((A+B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))^3,x, algorithm=""fricas"")","\frac{2 \, C b^{3} + 2 \, B b^{2} c + 6 \, C b c^{2} - 2 \, B c^{3} - 8 \, {\left(B b^{2} c + C b c^{2}\right)} \cos\left(x\right)^{2} + {\left(2 \, A b c \cos\left(x\right) \sin\left(x\right) + A c^{2} + {\left(A b^{2} - A c^{2}\right)} \cos\left(x\right)^{2}\right)} \sqrt{b^{2} + c^{2}} \log\left(-\frac{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} - 2 \, b^{2} - c^{2} + 2 \, \sqrt{b^{2} + c^{2}} {\left(c \cos\left(x\right) - b \sin\left(x\right)\right)}}{2 \, b c \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + c^{2}}\right) - 2 \, {\left(A b^{2} c + A c^{3}\right)} \cos\left(x\right) + 2 \, {\left(A b^{3} + A b c^{2} + 2 \, {\left(B b^{3} + C b^{2} c - B b c^{2} - C c^{3}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{4 \, {\left(b^{4} c^{2} + 2 \, b^{2} c^{4} + c^{6} + {\left(b^{6} + b^{4} c^{2} - b^{2} c^{4} - c^{6}\right)} \cos\left(x\right)^{2} + 2 \, {\left(b^{5} c + 2 \, b^{3} c^{3} + b c^{5}\right)} \cos\left(x\right) \sin\left(x\right)\right)}}"," ",0,"1/4*(2*C*b^3 + 2*B*b^2*c + 6*C*b*c^2 - 2*B*c^3 - 8*(B*b^2*c + C*b*c^2)*cos(x)^2 + (2*A*b*c*cos(x)*sin(x) + A*c^2 + (A*b^2 - A*c^2)*cos(x)^2)*sqrt(b^2 + c^2)*log(-(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 - 2*b^2 - c^2 + 2*sqrt(b^2 + c^2)*(c*cos(x) - b*sin(x)))/(2*b*c*cos(x)*sin(x) + (b^2 - c^2)*cos(x)^2 + c^2)) - 2*(A*b^2*c + A*c^3)*cos(x) + 2*(A*b^3 + A*b*c^2 + 2*(B*b^3 + C*b^2*c - B*b*c^2 - C*c^3)*cos(x))*sin(x))/(b^4*c^2 + 2*b^2*c^4 + c^6 + (b^6 + b^4*c^2 - b^2*c^4 - c^6)*cos(x)^2 + 2*(b^5*c + 2*b^3*c^3 + b*c^5)*cos(x)*sin(x))","B",0
535,1,625,0,1.784217," ","integrate((A+B*cos(x))/(a+b*cos(x)+c*sin(x)),x, algorithm=""fricas"")","\left[-\frac{{\left(B a b - A b^{2} - A c^{2}\right)} \sqrt{-a^{2} + b^{2} + c^{2}} \log\left(\frac{a^{2} b^{2} - 2 \, b^{4} - c^{4} - {\left(a^{2} + 3 \, b^{2}\right)} c^{2} - {\left(2 \, a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \cos\left(x\right)^{2} - 2 \, {\left(a b^{3} + a b c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a b^{2} c + a c^{3} - {\left(b c^{3} - {\left(2 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right) - 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(b^{2} c + c^{3}\right)} \cos\left(x\right) - {\left(b^{3} + b c^{2} + {\left(a b^{2} - a c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}}}{2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)}\right) - 2 \, {\left(B a^{2} b - B b^{3} - B b c^{2}\right)} x + {\left(B c^{3} - {\left(B a^{2} - B b^{2}\right)} c\right)} \log\left(2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)\right)}{2 \, {\left(a^{2} b^{2} - b^{4} - c^{4} + {\left(a^{2} - 2 \, b^{2}\right)} c^{2}\right)}}, -\frac{2 \, {\left(B a b - A b^{2} - A c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}} \arctan\left(-\frac{{\left(a b \cos\left(x\right) + a c \sin\left(x\right) + b^{2} + c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}}}{{\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(x\right) + {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(x\right)}\right) - 2 \, {\left(B a^{2} b - B b^{3} - B b c^{2}\right)} x + {\left(B c^{3} - {\left(B a^{2} - B b^{2}\right)} c\right)} \log\left(2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)\right)}{2 \, {\left(a^{2} b^{2} - b^{4} - c^{4} + {\left(a^{2} - 2 \, b^{2}\right)} c^{2}\right)}}\right]"," ",0,"[-1/2*((B*a*b - A*b^2 - A*c^2)*sqrt(-a^2 + b^2 + c^2)*log((a^2*b^2 - 2*b^4 - c^4 - (a^2 + 3*b^2)*c^2 - (2*a^2*b^2 - b^4 - 2*a^2*c^2 + c^4)*cos(x)^2 - 2*(a*b^3 + a*b*c^2)*cos(x) - 2*(a*b^2*c + a*c^3 - (b*c^3 - (2*a^2*b - b^3)*c)*cos(x))*sin(x) - 2*(2*a*b*c*cos(x)^2 - a*b*c + (b^2*c + c^3)*cos(x) - (b^3 + b*c^2 + (a*b^2 - a*c^2)*cos(x))*sin(x))*sqrt(-a^2 + b^2 + c^2))/(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x))) - 2*(B*a^2*b - B*b^3 - B*b*c^2)*x + (B*c^3 - (B*a^2 - B*b^2)*c)*log(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x)))/(a^2*b^2 - b^4 - c^4 + (a^2 - 2*b^2)*c^2), -1/2*(2*(B*a*b - A*b^2 - A*c^2)*sqrt(a^2 - b^2 - c^2)*arctan(-(a*b*cos(x) + a*c*sin(x) + b^2 + c^2)*sqrt(a^2 - b^2 - c^2)/((c^3 - (a^2 - b^2)*c)*cos(x) + (a^2*b - b^3 - b*c^2)*sin(x))) - 2*(B*a^2*b - B*b^3 - B*b*c^2)*x + (B*c^3 - (B*a^2 - B*b^2)*c)*log(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x)))/(a^2*b^2 - b^4 - c^4 + (a^2 - 2*b^2)*c^2)]","B",0
536,1,1277,0,1.690462," ","integrate((A+B*cos(x))/(a+b*cos(x)+c*sin(x))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, B c^{5} - 4 \, {\left(B a^{2} - B b^{2}\right)} c^{3} + {\left(A a^{2} b^{2} - B a b^{3} + {\left(A a^{2} - B a b\right)} c^{2} + {\left(A a b^{3} - B b^{4} + {\left(A a b - B b^{2}\right)} c^{2}\right)} \cos\left(x\right) + {\left({\left(A a - B b\right)} c^{3} + {\left(A a b^{2} - B b^{3}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}} \log\left(-\frac{a^{2} b^{2} - 2 \, b^{4} - c^{4} - {\left(a^{2} + 3 \, b^{2}\right)} c^{2} - {\left(2 \, a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \cos\left(x\right)^{2} - 2 \, {\left(a b^{3} + a b c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a b^{2} c + a c^{3} - {\left(b c^{3} - {\left(2 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right) + 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(b^{2} c + c^{3}\right)} \cos\left(x\right) - {\left(b^{3} + b c^{2} + {\left(a b^{2} - a c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}}}{2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)}\right) + 2 \, {\left(B a^{4} - 2 \, B a^{2} b^{2} + B b^{4}\right)} c + 2 \, {\left(A c^{5} - {\left(A a^{2} + B a b - 2 \, A b^{2}\right)} c^{3} + {\left(B a^{3} b - A a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c\right)} \cos\left(x\right) - 2 \, {\left(B a^{3} b^{2} - A a^{2} b^{3} - B a b^{4} + A b^{5} + A b c^{4} - {\left(A a^{2} b + B a b^{2} - 2 \, A b^{3}\right)} c^{2}\right)} \sin\left(x\right)}{2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6} + a c^{6} - {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{4} + {\left(a^{5} - 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c^{2} + {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7} + b c^{6} - {\left(2 \, a^{2} b - 3 \, b^{3}\right)} c^{4} + {\left(a^{4} b - 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} c^{2}\right)} \cos\left(x\right) + {\left(c^{7} - {\left(2 \, a^{2} - 3 \, b^{2}\right)} c^{5} + {\left(a^{4} - 4 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{3} + {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c\right)} \sin\left(x\right)\right)}}, -\frac{B c^{5} - 2 \, {\left(B a^{2} - B b^{2}\right)} c^{3} - {\left(A a^{2} b^{2} - B a b^{3} + {\left(A a^{2} - B a b\right)} c^{2} + {\left(A a b^{3} - B b^{4} + {\left(A a b - B b^{2}\right)} c^{2}\right)} \cos\left(x\right) + {\left({\left(A a - B b\right)} c^{3} + {\left(A a b^{2} - B b^{3}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{a^{2} - b^{2} - c^{2}} \arctan\left(-\frac{{\left(a b \cos\left(x\right) + a c \sin\left(x\right) + b^{2} + c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}}}{{\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(x\right) + {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(x\right)}\right) + {\left(B a^{4} - 2 \, B a^{2} b^{2} + B b^{4}\right)} c + {\left(A c^{5} - {\left(A a^{2} + B a b - 2 \, A b^{2}\right)} c^{3} + {\left(B a^{3} b - A a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c\right)} \cos\left(x\right) - {\left(B a^{3} b^{2} - A a^{2} b^{3} - B a b^{4} + A b^{5} + A b c^{4} - {\left(A a^{2} b + B a b^{2} - 2 \, A b^{3}\right)} c^{2}\right)} \sin\left(x\right)}{a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6} + a c^{6} - {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{4} + {\left(a^{5} - 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c^{2} + {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7} + b c^{6} - {\left(2 \, a^{2} b - 3 \, b^{3}\right)} c^{4} + {\left(a^{4} b - 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} c^{2}\right)} \cos\left(x\right) + {\left(c^{7} - {\left(2 \, a^{2} - 3 \, b^{2}\right)} c^{5} + {\left(a^{4} - 4 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{3} + {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c\right)} \sin\left(x\right)}\right]"," ",0,"[-1/2*(2*B*c^5 - 4*(B*a^2 - B*b^2)*c^3 + (A*a^2*b^2 - B*a*b^3 + (A*a^2 - B*a*b)*c^2 + (A*a*b^3 - B*b^4 + (A*a*b - B*b^2)*c^2)*cos(x) + ((A*a - B*b)*c^3 + (A*a*b^2 - B*b^3)*c)*sin(x))*sqrt(-a^2 + b^2 + c^2)*log(-(a^2*b^2 - 2*b^4 - c^4 - (a^2 + 3*b^2)*c^2 - (2*a^2*b^2 - b^4 - 2*a^2*c^2 + c^4)*cos(x)^2 - 2*(a*b^3 + a*b*c^2)*cos(x) - 2*(a*b^2*c + a*c^3 - (b*c^3 - (2*a^2*b - b^3)*c)*cos(x))*sin(x) + 2*(2*a*b*c*cos(x)^2 - a*b*c + (b^2*c + c^3)*cos(x) - (b^3 + b*c^2 + (a*b^2 - a*c^2)*cos(x))*sin(x))*sqrt(-a^2 + b^2 + c^2))/(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x))) + 2*(B*a^4 - 2*B*a^2*b^2 + B*b^4)*c + 2*(A*c^5 - (A*a^2 + B*a*b - 2*A*b^2)*c^3 + (B*a^3*b - A*a^2*b^2 - B*a*b^3 + A*b^4)*c)*cos(x) - 2*(B*a^3*b^2 - A*a^2*b^3 - B*a*b^4 + A*b^5 + A*b*c^4 - (A*a^2*b + B*a*b^2 - 2*A*b^3)*c^2)*sin(x))/(a^5*b^2 - 2*a^3*b^4 + a*b^6 + a*c^6 - (2*a^3 - 3*a*b^2)*c^4 + (a^5 - 4*a^3*b^2 + 3*a*b^4)*c^2 + (a^4*b^3 - 2*a^2*b^5 + b^7 + b*c^6 - (2*a^2*b - 3*b^3)*c^4 + (a^4*b - 4*a^2*b^3 + 3*b^5)*c^2)*cos(x) + (c^7 - (2*a^2 - 3*b^2)*c^5 + (a^4 - 4*a^2*b^2 + 3*b^4)*c^3 + (a^4*b^2 - 2*a^2*b^4 + b^6)*c)*sin(x)), -(B*c^5 - 2*(B*a^2 - B*b^2)*c^3 - (A*a^2*b^2 - B*a*b^3 + (A*a^2 - B*a*b)*c^2 + (A*a*b^3 - B*b^4 + (A*a*b - B*b^2)*c^2)*cos(x) + ((A*a - B*b)*c^3 + (A*a*b^2 - B*b^3)*c)*sin(x))*sqrt(a^2 - b^2 - c^2)*arctan(-(a*b*cos(x) + a*c*sin(x) + b^2 + c^2)*sqrt(a^2 - b^2 - c^2)/((c^3 - (a^2 - b^2)*c)*cos(x) + (a^2*b - b^3 - b*c^2)*sin(x))) + (B*a^4 - 2*B*a^2*b^2 + B*b^4)*c + (A*c^5 - (A*a^2 + B*a*b - 2*A*b^2)*c^3 + (B*a^3*b - A*a^2*b^2 - B*a*b^3 + A*b^4)*c)*cos(x) - (B*a^3*b^2 - A*a^2*b^3 - B*a*b^4 + A*b^5 + A*b*c^4 - (A*a^2*b + B*a*b^2 - 2*A*b^3)*c^2)*sin(x))/(a^5*b^2 - 2*a^3*b^4 + a*b^6 + a*c^6 - (2*a^3 - 3*a*b^2)*c^4 + (a^5 - 4*a^3*b^2 + 3*a*b^4)*c^2 + (a^4*b^3 - 2*a^2*b^5 + b^7 + b*c^6 - (2*a^2*b - 3*b^3)*c^4 + (a^4*b - 4*a^2*b^3 + 3*b^5)*c^2)*cos(x) + (c^7 - (2*a^2 - 3*b^2)*c^5 + (a^4 - 4*a^2*b^2 + 3*b^4)*c^3 + (a^4*b^2 - 2*a^2*b^4 + b^6)*c)*sin(x))]","B",0
537,1,3402,0,2.159158," ","integrate((A+B*cos(x))/(a+b*cos(x)+c*sin(x))^3,x, algorithm=""fricas"")","\left[\frac{2 \, B c^{7} - 2 \, {\left(3 \, B a^{2} - 3 \, A a b - B b^{2}\right)} c^{5} + 2 \, {\left(3 \, B a^{4} - 3 \, A a^{3} b - 5 \, B a^{2} b^{2} + 6 \, A a b^{3} - B b^{4}\right)} c^{3} - 4 \, {\left({\left(3 \, A a b - 2 \, B b^{2}\right)} c^{5} - {\left(3 \, A a^{3} b - B a^{2} b^{2} - 6 \, A a b^{3} + 4 \, B b^{4}\right)} c^{3} + {\left(B a^{4} b^{2} - 3 \, A a^{3} b^{3} + B a^{2} b^{4} + 3 \, A a b^{5} - 2 \, B b^{6}\right)} c\right)} \cos\left(x\right)^{2} - {\left(2 \, A a^{4} b^{2} - 3 \, B a^{3} b^{3} + A a^{2} b^{4} + A c^{6} + {\left(3 \, A a^{2} - 3 \, B a b + 2 \, A b^{2}\right)} c^{4} + {\left(2 \, A a^{4} - 3 \, B a^{3} b + 4 \, A a^{2} b^{2} - 3 \, B a b^{3} + A b^{4}\right)} c^{2} + {\left(2 \, A a^{2} b^{4} - 3 \, B a b^{5} + A b^{6} + A b^{4} c^{2} - A c^{6} - {\left(2 \, A a^{2} - 3 \, B a b + A b^{2}\right)} c^{4}\right)} \cos\left(x\right)^{2} + 2 \, {\left(2 \, A a^{3} b^{3} - 3 \, B a^{2} b^{4} + A a b^{5} + A a b c^{4} + {\left(2 \, A a^{3} b - 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} c^{2}\right)} \cos\left(x\right) + 2 \, {\left(A a c^{5} + {\left(2 \, A a^{3} - 3 \, B a^{2} b + 2 \, A a b^{2}\right)} c^{3} + {\left(2 \, A a^{3} b^{2} - 3 \, B a^{2} b^{3} + A a b^{4}\right)} c + {\left(A b c^{5} + {\left(2 \, A a^{2} b - 3 \, B a b^{2} + 2 \, A b^{3}\right)} c^{3} + {\left(2 \, A a^{2} b^{3} - 3 \, B a b^{4} + A b^{5}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}} \log\left(-\frac{a^{2} b^{2} - 2 \, b^{4} - c^{4} - {\left(a^{2} + 3 \, b^{2}\right)} c^{2} - {\left(2 \, a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \cos\left(x\right)^{2} - 2 \, {\left(a b^{3} + a b c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a b^{2} c + a c^{3} - {\left(b c^{3} - {\left(2 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right) + 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(b^{2} c + c^{3}\right)} \cos\left(x\right) - {\left(b^{3} + b c^{2} + {\left(a b^{2} - a c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}}}{2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)}\right) - 2 \, {\left(B a^{6} - 4 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3} + 2 \, B a^{2} b^{4} - 3 \, A a b^{5} + B b^{6}\right)} c + 2 \, {\left(A c^{7} - {\left(5 \, A a^{2} - B a b - 3 \, A b^{2}\right)} c^{5} + {\left(4 \, A a^{4} + B a^{3} b - 10 \, A a^{2} b^{2} + 2 \, B a b^{3} + 3 \, A b^{4}\right)} c^{3} - {\left(2 \, B a^{5} b - 4 \, A a^{4} b^{2} - B a^{3} b^{3} + 5 \, A a^{2} b^{4} - B a b^{5} - A b^{6}\right)} c\right)} \cos\left(x\right) + 2 \, {\left(2 \, B a^{5} b^{2} - 4 \, A a^{4} b^{3} - B a^{3} b^{4} + 5 \, A a^{2} b^{5} - B a b^{6} - A b^{7} - A b c^{6} + {\left(5 \, A a^{2} b - B a b^{2} - 3 \, A b^{3}\right)} c^{4} - {\left(4 \, A a^{4} b + B a^{3} b^{2} - 10 \, A a^{2} b^{3} + 2 \, B a b^{4} + 3 \, A b^{5}\right)} c^{2} + {\left(B a^{4} b^{3} - 3 \, A a^{3} b^{4} + B a^{2} b^{5} + 3 \, A a b^{6} - 2 \, B b^{7} - {\left(3 \, A a - 2 \, B b\right)} c^{6} + {\left(3 \, A a^{3} - B a^{2} b - 3 \, A a b^{2} + 2 \, B b^{3}\right)} c^{4} - {\left(B a^{4} b - 3 \, A a b^{4} + 2 \, B b^{5}\right)} c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{4 \, {\left(a^{8} b^{2} - 3 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - a^{2} b^{8} - c^{10} + 2 \, {\left(a^{2} - 2 \, b^{2}\right)} c^{8} + {\left(5 \, a^{2} b^{2} - 6 \, b^{4}\right)} c^{6} - {\left(2 \, a^{6} - 3 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + 4 \, b^{6}\right)} c^{4} + {\left(a^{8} - 5 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - a^{2} b^{6} - b^{8}\right)} c^{2} + {\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10} + c^{10} - 3 \, {\left(a^{2} - b^{2}\right)} c^{8} + {\left(3 \, a^{4} - 6 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{6} - {\left(a^{6} - 3 \, a^{4} b^{2} + 2 \, b^{6}\right)} c^{4} - 3 \, {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} c^{2}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{7} b^{3} - 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} - a b^{9} - a b c^{8} + {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} c^{6} - 3 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} c^{4} + {\left(a^{7} b - 6 \, a^{5} b^{3} + 9 \, a^{3} b^{5} - 4 \, a b^{7}\right)} c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a c^{9} - {\left(3 \, a^{3} - 4 \, a b^{2}\right)} c^{7} + 3 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{7} - 6 \, a^{5} b^{2} + 9 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c^{3} - {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} c + {\left(b c^{9} - {\left(3 \, a^{2} b - 4 \, b^{3}\right)} c^{7} + 3 \, {\left(a^{4} b - 3 \, a^{2} b^{3} + 2 \, b^{5}\right)} c^{5} - {\left(a^{6} b - 6 \, a^{4} b^{3} + 9 \, a^{2} b^{5} - 4 \, b^{7}\right)} c^{3} - {\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)}}, \frac{B c^{7} - {\left(3 \, B a^{2} - 3 \, A a b - B b^{2}\right)} c^{5} + {\left(3 \, B a^{4} - 3 \, A a^{3} b - 5 \, B a^{2} b^{2} + 6 \, A a b^{3} - B b^{4}\right)} c^{3} - 2 \, {\left({\left(3 \, A a b - 2 \, B b^{2}\right)} c^{5} - {\left(3 \, A a^{3} b - B a^{2} b^{2} - 6 \, A a b^{3} + 4 \, B b^{4}\right)} c^{3} + {\left(B a^{4} b^{2} - 3 \, A a^{3} b^{3} + B a^{2} b^{4} + 3 \, A a b^{5} - 2 \, B b^{6}\right)} c\right)} \cos\left(x\right)^{2} + {\left(2 \, A a^{4} b^{2} - 3 \, B a^{3} b^{3} + A a^{2} b^{4} + A c^{6} + {\left(3 \, A a^{2} - 3 \, B a b + 2 \, A b^{2}\right)} c^{4} + {\left(2 \, A a^{4} - 3 \, B a^{3} b + 4 \, A a^{2} b^{2} - 3 \, B a b^{3} + A b^{4}\right)} c^{2} + {\left(2 \, A a^{2} b^{4} - 3 \, B a b^{5} + A b^{6} + A b^{4} c^{2} - A c^{6} - {\left(2 \, A a^{2} - 3 \, B a b + A b^{2}\right)} c^{4}\right)} \cos\left(x\right)^{2} + 2 \, {\left(2 \, A a^{3} b^{3} - 3 \, B a^{2} b^{4} + A a b^{5} + A a b c^{4} + {\left(2 \, A a^{3} b - 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} c^{2}\right)} \cos\left(x\right) + 2 \, {\left(A a c^{5} + {\left(2 \, A a^{3} - 3 \, B a^{2} b + 2 \, A a b^{2}\right)} c^{3} + {\left(2 \, A a^{3} b^{2} - 3 \, B a^{2} b^{3} + A a b^{4}\right)} c + {\left(A b c^{5} + {\left(2 \, A a^{2} b - 3 \, B a b^{2} + 2 \, A b^{3}\right)} c^{3} + {\left(2 \, A a^{2} b^{3} - 3 \, B a b^{4} + A b^{5}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{a^{2} - b^{2} - c^{2}} \arctan\left(-\frac{{\left(a b \cos\left(x\right) + a c \sin\left(x\right) + b^{2} + c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}}}{{\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(x\right) + {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(x\right)}\right) - {\left(B a^{6} - 4 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3} + 2 \, B a^{2} b^{4} - 3 \, A a b^{5} + B b^{6}\right)} c + {\left(A c^{7} - {\left(5 \, A a^{2} - B a b - 3 \, A b^{2}\right)} c^{5} + {\left(4 \, A a^{4} + B a^{3} b - 10 \, A a^{2} b^{2} + 2 \, B a b^{3} + 3 \, A b^{4}\right)} c^{3} - {\left(2 \, B a^{5} b - 4 \, A a^{4} b^{2} - B a^{3} b^{3} + 5 \, A a^{2} b^{4} - B a b^{5} - A b^{6}\right)} c\right)} \cos\left(x\right) + {\left(2 \, B a^{5} b^{2} - 4 \, A a^{4} b^{3} - B a^{3} b^{4} + 5 \, A a^{2} b^{5} - B a b^{6} - A b^{7} - A b c^{6} + {\left(5 \, A a^{2} b - B a b^{2} - 3 \, A b^{3}\right)} c^{4} - {\left(4 \, A a^{4} b + B a^{3} b^{2} - 10 \, A a^{2} b^{3} + 2 \, B a b^{4} + 3 \, A b^{5}\right)} c^{2} + {\left(B a^{4} b^{3} - 3 \, A a^{3} b^{4} + B a^{2} b^{5} + 3 \, A a b^{6} - 2 \, B b^{7} - {\left(3 \, A a - 2 \, B b\right)} c^{6} + {\left(3 \, A a^{3} - B a^{2} b - 3 \, A a b^{2} + 2 \, B b^{3}\right)} c^{4} - {\left(B a^{4} b - 3 \, A a b^{4} + 2 \, B b^{5}\right)} c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{2 \, {\left(a^{8} b^{2} - 3 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - a^{2} b^{8} - c^{10} + 2 \, {\left(a^{2} - 2 \, b^{2}\right)} c^{8} + {\left(5 \, a^{2} b^{2} - 6 \, b^{4}\right)} c^{6} - {\left(2 \, a^{6} - 3 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + 4 \, b^{6}\right)} c^{4} + {\left(a^{8} - 5 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - a^{2} b^{6} - b^{8}\right)} c^{2} + {\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10} + c^{10} - 3 \, {\left(a^{2} - b^{2}\right)} c^{8} + {\left(3 \, a^{4} - 6 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{6} - {\left(a^{6} - 3 \, a^{4} b^{2} + 2 \, b^{6}\right)} c^{4} - 3 \, {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} c^{2}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{7} b^{3} - 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} - a b^{9} - a b c^{8} + {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} c^{6} - 3 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} c^{4} + {\left(a^{7} b - 6 \, a^{5} b^{3} + 9 \, a^{3} b^{5} - 4 \, a b^{7}\right)} c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a c^{9} - {\left(3 \, a^{3} - 4 \, a b^{2}\right)} c^{7} + 3 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{7} - 6 \, a^{5} b^{2} + 9 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c^{3} - {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} c + {\left(b c^{9} - {\left(3 \, a^{2} b - 4 \, b^{3}\right)} c^{7} + 3 \, {\left(a^{4} b - 3 \, a^{2} b^{3} + 2 \, b^{5}\right)} c^{5} - {\left(a^{6} b - 6 \, a^{4} b^{3} + 9 \, a^{2} b^{5} - 4 \, b^{7}\right)} c^{3} - {\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)}}\right]"," ",0,"[1/4*(2*B*c^7 - 2*(3*B*a^2 - 3*A*a*b - B*b^2)*c^5 + 2*(3*B*a^4 - 3*A*a^3*b - 5*B*a^2*b^2 + 6*A*a*b^3 - B*b^4)*c^3 - 4*((3*A*a*b - 2*B*b^2)*c^5 - (3*A*a^3*b - B*a^2*b^2 - 6*A*a*b^3 + 4*B*b^4)*c^3 + (B*a^4*b^2 - 3*A*a^3*b^3 + B*a^2*b^4 + 3*A*a*b^5 - 2*B*b^6)*c)*cos(x)^2 - (2*A*a^4*b^2 - 3*B*a^3*b^3 + A*a^2*b^4 + A*c^6 + (3*A*a^2 - 3*B*a*b + 2*A*b^2)*c^4 + (2*A*a^4 - 3*B*a^3*b + 4*A*a^2*b^2 - 3*B*a*b^3 + A*b^4)*c^2 + (2*A*a^2*b^4 - 3*B*a*b^5 + A*b^6 + A*b^4*c^2 - A*c^6 - (2*A*a^2 - 3*B*a*b + A*b^2)*c^4)*cos(x)^2 + 2*(2*A*a^3*b^3 - 3*B*a^2*b^4 + A*a*b^5 + A*a*b*c^4 + (2*A*a^3*b - 3*B*a^2*b^2 + 2*A*a*b^3)*c^2)*cos(x) + 2*(A*a*c^5 + (2*A*a^3 - 3*B*a^2*b + 2*A*a*b^2)*c^3 + (2*A*a^3*b^2 - 3*B*a^2*b^3 + A*a*b^4)*c + (A*b*c^5 + (2*A*a^2*b - 3*B*a*b^2 + 2*A*b^3)*c^3 + (2*A*a^2*b^3 - 3*B*a*b^4 + A*b^5)*c)*cos(x))*sin(x))*sqrt(-a^2 + b^2 + c^2)*log(-(a^2*b^2 - 2*b^4 - c^4 - (a^2 + 3*b^2)*c^2 - (2*a^2*b^2 - b^4 - 2*a^2*c^2 + c^4)*cos(x)^2 - 2*(a*b^3 + a*b*c^2)*cos(x) - 2*(a*b^2*c + a*c^3 - (b*c^3 - (2*a^2*b - b^3)*c)*cos(x))*sin(x) + 2*(2*a*b*c*cos(x)^2 - a*b*c + (b^2*c + c^3)*cos(x) - (b^3 + b*c^2 + (a*b^2 - a*c^2)*cos(x))*sin(x))*sqrt(-a^2 + b^2 + c^2))/(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x))) - 2*(B*a^6 - 4*B*a^4*b^2 + 3*A*a^3*b^3 + 2*B*a^2*b^4 - 3*A*a*b^5 + B*b^6)*c + 2*(A*c^7 - (5*A*a^2 - B*a*b - 3*A*b^2)*c^5 + (4*A*a^4 + B*a^3*b - 10*A*a^2*b^2 + 2*B*a*b^3 + 3*A*b^4)*c^3 - (2*B*a^5*b - 4*A*a^4*b^2 - B*a^3*b^3 + 5*A*a^2*b^4 - B*a*b^5 - A*b^6)*c)*cos(x) + 2*(2*B*a^5*b^2 - 4*A*a^4*b^3 - B*a^3*b^4 + 5*A*a^2*b^5 - B*a*b^6 - A*b^7 - A*b*c^6 + (5*A*a^2*b - B*a*b^2 - 3*A*b^3)*c^4 - (4*A*a^4*b + B*a^3*b^2 - 10*A*a^2*b^3 + 2*B*a*b^4 + 3*A*b^5)*c^2 + (B*a^4*b^3 - 3*A*a^3*b^4 + B*a^2*b^5 + 3*A*a*b^6 - 2*B*b^7 - (3*A*a - 2*B*b)*c^6 + (3*A*a^3 - B*a^2*b - 3*A*a*b^2 + 2*B*b^3)*c^4 - (B*a^4*b - 3*A*a*b^4 + 2*B*b^5)*c^2)*cos(x))*sin(x))/(a^8*b^2 - 3*a^6*b^4 + 3*a^4*b^6 - a^2*b^8 - c^10 + 2*(a^2 - 2*b^2)*c^8 + (5*a^2*b^2 - 6*b^4)*c^6 - (2*a^6 - 3*a^4*b^2 - 3*a^2*b^4 + 4*b^6)*c^4 + (a^8 - 5*a^6*b^2 + 6*a^4*b^4 - a^2*b^6 - b^8)*c^2 + (a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10 + c^10 - 3*(a^2 - b^2)*c^8 + (3*a^4 - 6*a^2*b^2 + 2*b^4)*c^6 - (a^6 - 3*a^4*b^2 + 2*b^6)*c^4 - 3*(a^4*b^4 - 2*a^2*b^6 + b^8)*c^2)*cos(x)^2 + 2*(a^7*b^3 - 3*a^5*b^5 + 3*a^3*b^7 - a*b^9 - a*b*c^8 + (3*a^3*b - 4*a*b^3)*c^6 - 3*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*c^4 + (a^7*b - 6*a^5*b^3 + 9*a^3*b^5 - 4*a*b^7)*c^2)*cos(x) - 2*(a*c^9 - (3*a^3 - 4*a*b^2)*c^7 + 3*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^7 - 6*a^5*b^2 + 9*a^3*b^4 - 4*a*b^6)*c^3 - (a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*c + (b*c^9 - (3*a^2*b - 4*b^3)*c^7 + 3*(a^4*b - 3*a^2*b^3 + 2*b^5)*c^5 - (a^6*b - 6*a^4*b^3 + 9*a^2*b^5 - 4*b^7)*c^3 - (a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*c)*cos(x))*sin(x)), 1/2*(B*c^7 - (3*B*a^2 - 3*A*a*b - B*b^2)*c^5 + (3*B*a^4 - 3*A*a^3*b - 5*B*a^2*b^2 + 6*A*a*b^3 - B*b^4)*c^3 - 2*((3*A*a*b - 2*B*b^2)*c^5 - (3*A*a^3*b - B*a^2*b^2 - 6*A*a*b^3 + 4*B*b^4)*c^3 + (B*a^4*b^2 - 3*A*a^3*b^3 + B*a^2*b^4 + 3*A*a*b^5 - 2*B*b^6)*c)*cos(x)^2 + (2*A*a^4*b^2 - 3*B*a^3*b^3 + A*a^2*b^4 + A*c^6 + (3*A*a^2 - 3*B*a*b + 2*A*b^2)*c^4 + (2*A*a^4 - 3*B*a^3*b + 4*A*a^2*b^2 - 3*B*a*b^3 + A*b^4)*c^2 + (2*A*a^2*b^4 - 3*B*a*b^5 + A*b^6 + A*b^4*c^2 - A*c^6 - (2*A*a^2 - 3*B*a*b + A*b^2)*c^4)*cos(x)^2 + 2*(2*A*a^3*b^3 - 3*B*a^2*b^4 + A*a*b^5 + A*a*b*c^4 + (2*A*a^3*b - 3*B*a^2*b^2 + 2*A*a*b^3)*c^2)*cos(x) + 2*(A*a*c^5 + (2*A*a^3 - 3*B*a^2*b + 2*A*a*b^2)*c^3 + (2*A*a^3*b^2 - 3*B*a^2*b^3 + A*a*b^4)*c + (A*b*c^5 + (2*A*a^2*b - 3*B*a*b^2 + 2*A*b^3)*c^3 + (2*A*a^2*b^3 - 3*B*a*b^4 + A*b^5)*c)*cos(x))*sin(x))*sqrt(a^2 - b^2 - c^2)*arctan(-(a*b*cos(x) + a*c*sin(x) + b^2 + c^2)*sqrt(a^2 - b^2 - c^2)/((c^3 - (a^2 - b^2)*c)*cos(x) + (a^2*b - b^3 - b*c^2)*sin(x))) - (B*a^6 - 4*B*a^4*b^2 + 3*A*a^3*b^3 + 2*B*a^2*b^4 - 3*A*a*b^5 + B*b^6)*c + (A*c^7 - (5*A*a^2 - B*a*b - 3*A*b^2)*c^5 + (4*A*a^4 + B*a^3*b - 10*A*a^2*b^2 + 2*B*a*b^3 + 3*A*b^4)*c^3 - (2*B*a^5*b - 4*A*a^4*b^2 - B*a^3*b^3 + 5*A*a^2*b^4 - B*a*b^5 - A*b^6)*c)*cos(x) + (2*B*a^5*b^2 - 4*A*a^4*b^3 - B*a^3*b^4 + 5*A*a^2*b^5 - B*a*b^6 - A*b^7 - A*b*c^6 + (5*A*a^2*b - B*a*b^2 - 3*A*b^3)*c^4 - (4*A*a^4*b + B*a^3*b^2 - 10*A*a^2*b^3 + 2*B*a*b^4 + 3*A*b^5)*c^2 + (B*a^4*b^3 - 3*A*a^3*b^4 + B*a^2*b^5 + 3*A*a*b^6 - 2*B*b^7 - (3*A*a - 2*B*b)*c^6 + (3*A*a^3 - B*a^2*b - 3*A*a*b^2 + 2*B*b^3)*c^4 - (B*a^4*b - 3*A*a*b^4 + 2*B*b^5)*c^2)*cos(x))*sin(x))/(a^8*b^2 - 3*a^6*b^4 + 3*a^4*b^6 - a^2*b^8 - c^10 + 2*(a^2 - 2*b^2)*c^8 + (5*a^2*b^2 - 6*b^4)*c^6 - (2*a^6 - 3*a^4*b^2 - 3*a^2*b^4 + 4*b^6)*c^4 + (a^8 - 5*a^6*b^2 + 6*a^4*b^4 - a^2*b^6 - b^8)*c^2 + (a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10 + c^10 - 3*(a^2 - b^2)*c^8 + (3*a^4 - 6*a^2*b^2 + 2*b^4)*c^6 - (a^6 - 3*a^4*b^2 + 2*b^6)*c^4 - 3*(a^4*b^4 - 2*a^2*b^6 + b^8)*c^2)*cos(x)^2 + 2*(a^7*b^3 - 3*a^5*b^5 + 3*a^3*b^7 - a*b^9 - a*b*c^8 + (3*a^3*b - 4*a*b^3)*c^6 - 3*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*c^4 + (a^7*b - 6*a^5*b^3 + 9*a^3*b^5 - 4*a*b^7)*c^2)*cos(x) - 2*(a*c^9 - (3*a^3 - 4*a*b^2)*c^7 + 3*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^7 - 6*a^5*b^2 + 9*a^3*b^4 - 4*a*b^6)*c^3 - (a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*c + (b*c^9 - (3*a^2*b - 4*b^3)*c^7 + 3*(a^4*b - 3*a^2*b^3 + 2*b^5)*c^5 - (a^6*b - 6*a^4*b^3 + 9*a^2*b^5 - 4*b^7)*c^3 - (a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*c)*cos(x))*sin(x))]","B",0
538,1,72,0,0.756471," ","integrate((A+B*cos(x))/(a+b*cos(x)+I*b*sin(x)),x, algorithm=""fricas"")","\frac{{\left(i \, B a b + {\left(2 \, A a b - B b^{2}\right)} x e^{\left(i \, x\right)} + {\left(-i \, B a^{2} + 2 i \, A a b - i \, B b^{2}\right)} e^{\left(i \, x\right)} \log\left(\frac{b e^{\left(i \, x\right)} + a}{b}\right)\right)} e^{\left(-i \, x\right)}}{2 \, a^{2} b}"," ",0,"1/2*(I*B*a*b + (2*A*a*b - B*b^2)*x*e^(I*x) + (-I*B*a^2 + 2*I*A*a*b - I*B*b^2)*e^(I*x)*log((b*e^(I*x) + a)/b))*e^(-I*x)/(a^2*b)","A",0
539,1,56,0,2.144081," ","integrate((A+B*cos(x))/(a+b*cos(x)-I*b*sin(x)),x, algorithm=""fricas"")","\frac{B a^{2} x - i \, B a b e^{\left(i \, x\right)} + {\left(i \, B a^{2} - 2 i \, A a b + i \, B b^{2}\right)} \log\left(\frac{a e^{\left(i \, x\right)} + b}{a}\right)}{2 \, a^{2} b}"," ",0,"1/2*(B*a^2*x - I*B*a*b*e^(I*x) + (I*B*a^2 - 2*I*A*a*b + I*B*b^2)*log((a*e^(I*x) + b)/a))/(a^2*b)","A",0
540,1,625,0,2.587280," ","integrate((A+C*sin(x))/(a+b*cos(x)+c*sin(x)),x, algorithm=""fricas"")","\left[\frac{{\left(A b^{2} - C a c + A c^{2}\right)} \sqrt{-a^{2} + b^{2} + c^{2}} \log\left(\frac{a^{2} b^{2} - 2 \, b^{4} - c^{4} - {\left(a^{2} + 3 \, b^{2}\right)} c^{2} - {\left(2 \, a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \cos\left(x\right)^{2} - 2 \, {\left(a b^{3} + a b c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a b^{2} c + a c^{3} - {\left(b c^{3} - {\left(2 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right) - 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(b^{2} c + c^{3}\right)} \cos\left(x\right) - {\left(b^{3} + b c^{2} + {\left(a b^{2} - a c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}}}{2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)}\right) - 2 \, {\left(C c^{3} - {\left(C a^{2} - C b^{2}\right)} c\right)} x - {\left(C a^{2} b - C b^{3} - C b c^{2}\right)} \log\left(2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)\right)}{2 \, {\left(a^{2} b^{2} - b^{4} - c^{4} + {\left(a^{2} - 2 \, b^{2}\right)} c^{2}\right)}}, \frac{2 \, {\left(A b^{2} - C a c + A c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}} \arctan\left(-\frac{{\left(a b \cos\left(x\right) + a c \sin\left(x\right) + b^{2} + c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}}}{{\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(x\right) + {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(x\right)}\right) - 2 \, {\left(C c^{3} - {\left(C a^{2} - C b^{2}\right)} c\right)} x - {\left(C a^{2} b - C b^{3} - C b c^{2}\right)} \log\left(2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)\right)}{2 \, {\left(a^{2} b^{2} - b^{4} - c^{4} + {\left(a^{2} - 2 \, b^{2}\right)} c^{2}\right)}}\right]"," ",0,"[1/2*((A*b^2 - C*a*c + A*c^2)*sqrt(-a^2 + b^2 + c^2)*log((a^2*b^2 - 2*b^4 - c^4 - (a^2 + 3*b^2)*c^2 - (2*a^2*b^2 - b^4 - 2*a^2*c^2 + c^4)*cos(x)^2 - 2*(a*b^3 + a*b*c^2)*cos(x) - 2*(a*b^2*c + a*c^3 - (b*c^3 - (2*a^2*b - b^3)*c)*cos(x))*sin(x) - 2*(2*a*b*c*cos(x)^2 - a*b*c + (b^2*c + c^3)*cos(x) - (b^3 + b*c^2 + (a*b^2 - a*c^2)*cos(x))*sin(x))*sqrt(-a^2 + b^2 + c^2))/(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x))) - 2*(C*c^3 - (C*a^2 - C*b^2)*c)*x - (C*a^2*b - C*b^3 - C*b*c^2)*log(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x)))/(a^2*b^2 - b^4 - c^4 + (a^2 - 2*b^2)*c^2), 1/2*(2*(A*b^2 - C*a*c + A*c^2)*sqrt(a^2 - b^2 - c^2)*arctan(-(a*b*cos(x) + a*c*sin(x) + b^2 + c^2)*sqrt(a^2 - b^2 - c^2)/((c^3 - (a^2 - b^2)*c)*cos(x) + (a^2*b - b^3 - b*c^2)*sin(x))) - 2*(C*c^3 - (C*a^2 - C*b^2)*c)*x - (C*a^2*b - C*b^3 - C*b*c^2)*log(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x)))/(a^2*b^2 - b^4 - c^4 + (a^2 - 2*b^2)*c^2)]","B",0
541,1,1301,0,1.240312," ","integrate((A+C*sin(x))/(a+b*cos(x)+c*sin(x))^2,x, algorithm=""fricas"")","\left[\frac{2 \, C a^{4} b - 4 \, C a^{2} b^{3} + 2 \, C b^{5} + 2 \, C b c^{4} - 4 \, {\left(C a^{2} b - C b^{3}\right)} c^{2} - {\left(A a^{2} b^{2} - C a b^{2} c + A a^{2} c^{2} - C a c^{3} + {\left(A a b^{3} - C b^{3} c + A a b c^{2} - C b c^{3}\right)} \cos\left(x\right) + {\left(A a b^{2} c - C b^{2} c^{2} + A a c^{3} - C c^{4}\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}} \log\left(-\frac{a^{2} b^{2} - 2 \, b^{4} - c^{4} - {\left(a^{2} + 3 \, b^{2}\right)} c^{2} - {\left(2 \, a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \cos\left(x\right)^{2} - 2 \, {\left(a b^{3} + a b c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a b^{2} c + a c^{3} - {\left(b c^{3} - {\left(2 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right) + 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(b^{2} c + c^{3}\right)} \cos\left(x\right) - {\left(b^{3} + b c^{2} + {\left(a b^{2} - a c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}}}{2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)}\right) + 2 \, {\left(C a c^{4} - A c^{5} + {\left(A a^{2} - 2 \, A b^{2}\right)} c^{3} - {\left(C a^{3} - C a b^{2}\right)} c^{2} + {\left(A a^{2} b^{2} - A b^{4}\right)} c\right)} \cos\left(x\right) - 2 \, {\left(A a^{2} b^{3} - A b^{5} + C a b c^{3} - A b c^{4} + {\left(A a^{2} b - 2 \, A b^{3}\right)} c^{2} - {\left(C a^{3} b - C a b^{3}\right)} c\right)} \sin\left(x\right)}{2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6} + a c^{6} - {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{4} + {\left(a^{5} - 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c^{2} + {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7} + b c^{6} - {\left(2 \, a^{2} b - 3 \, b^{3}\right)} c^{4} + {\left(a^{4} b - 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} c^{2}\right)} \cos\left(x\right) + {\left(c^{7} - {\left(2 \, a^{2} - 3 \, b^{2}\right)} c^{5} + {\left(a^{4} - 4 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{3} + {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c\right)} \sin\left(x\right)\right)}}, \frac{C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5} + C b c^{4} - 2 \, {\left(C a^{2} b - C b^{3}\right)} c^{2} + {\left(A a^{2} b^{2} - C a b^{2} c + A a^{2} c^{2} - C a c^{3} + {\left(A a b^{3} - C b^{3} c + A a b c^{2} - C b c^{3}\right)} \cos\left(x\right) + {\left(A a b^{2} c - C b^{2} c^{2} + A a c^{3} - C c^{4}\right)} \sin\left(x\right)\right)} \sqrt{a^{2} - b^{2} - c^{2}} \arctan\left(-\frac{{\left(a b \cos\left(x\right) + a c \sin\left(x\right) + b^{2} + c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}}}{{\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(x\right) + {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(x\right)}\right) + {\left(C a c^{4} - A c^{5} + {\left(A a^{2} - 2 \, A b^{2}\right)} c^{3} - {\left(C a^{3} - C a b^{2}\right)} c^{2} + {\left(A a^{2} b^{2} - A b^{4}\right)} c\right)} \cos\left(x\right) - {\left(A a^{2} b^{3} - A b^{5} + C a b c^{3} - A b c^{4} + {\left(A a^{2} b - 2 \, A b^{3}\right)} c^{2} - {\left(C a^{3} b - C a b^{3}\right)} c\right)} \sin\left(x\right)}{a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6} + a c^{6} - {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{4} + {\left(a^{5} - 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c^{2} + {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7} + b c^{6} - {\left(2 \, a^{2} b - 3 \, b^{3}\right)} c^{4} + {\left(a^{4} b - 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} c^{2}\right)} \cos\left(x\right) + {\left(c^{7} - {\left(2 \, a^{2} - 3 \, b^{2}\right)} c^{5} + {\left(a^{4} - 4 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{3} + {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c\right)} \sin\left(x\right)}\right]"," ",0,"[1/2*(2*C*a^4*b - 4*C*a^2*b^3 + 2*C*b^5 + 2*C*b*c^4 - 4*(C*a^2*b - C*b^3)*c^2 - (A*a^2*b^2 - C*a*b^2*c + A*a^2*c^2 - C*a*c^3 + (A*a*b^3 - C*b^3*c + A*a*b*c^2 - C*b*c^3)*cos(x) + (A*a*b^2*c - C*b^2*c^2 + A*a*c^3 - C*c^4)*sin(x))*sqrt(-a^2 + b^2 + c^2)*log(-(a^2*b^2 - 2*b^4 - c^4 - (a^2 + 3*b^2)*c^2 - (2*a^2*b^2 - b^4 - 2*a^2*c^2 + c^4)*cos(x)^2 - 2*(a*b^3 + a*b*c^2)*cos(x) - 2*(a*b^2*c + a*c^3 - (b*c^3 - (2*a^2*b - b^3)*c)*cos(x))*sin(x) + 2*(2*a*b*c*cos(x)^2 - a*b*c + (b^2*c + c^3)*cos(x) - (b^3 + b*c^2 + (a*b^2 - a*c^2)*cos(x))*sin(x))*sqrt(-a^2 + b^2 + c^2))/(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x))) + 2*(C*a*c^4 - A*c^5 + (A*a^2 - 2*A*b^2)*c^3 - (C*a^3 - C*a*b^2)*c^2 + (A*a^2*b^2 - A*b^4)*c)*cos(x) - 2*(A*a^2*b^3 - A*b^5 + C*a*b*c^3 - A*b*c^4 + (A*a^2*b - 2*A*b^3)*c^2 - (C*a^3*b - C*a*b^3)*c)*sin(x))/(a^5*b^2 - 2*a^3*b^4 + a*b^6 + a*c^6 - (2*a^3 - 3*a*b^2)*c^4 + (a^5 - 4*a^3*b^2 + 3*a*b^4)*c^2 + (a^4*b^3 - 2*a^2*b^5 + b^7 + b*c^6 - (2*a^2*b - 3*b^3)*c^4 + (a^4*b - 4*a^2*b^3 + 3*b^5)*c^2)*cos(x) + (c^7 - (2*a^2 - 3*b^2)*c^5 + (a^4 - 4*a^2*b^2 + 3*b^4)*c^3 + (a^4*b^2 - 2*a^2*b^4 + b^6)*c)*sin(x)), (C*a^4*b - 2*C*a^2*b^3 + C*b^5 + C*b*c^4 - 2*(C*a^2*b - C*b^3)*c^2 + (A*a^2*b^2 - C*a*b^2*c + A*a^2*c^2 - C*a*c^3 + (A*a*b^3 - C*b^3*c + A*a*b*c^2 - C*b*c^3)*cos(x) + (A*a*b^2*c - C*b^2*c^2 + A*a*c^3 - C*c^4)*sin(x))*sqrt(a^2 - b^2 - c^2)*arctan(-(a*b*cos(x) + a*c*sin(x) + b^2 + c^2)*sqrt(a^2 - b^2 - c^2)/((c^3 - (a^2 - b^2)*c)*cos(x) + (a^2*b - b^3 - b*c^2)*sin(x))) + (C*a*c^4 - A*c^5 + (A*a^2 - 2*A*b^2)*c^3 - (C*a^3 - C*a*b^2)*c^2 + (A*a^2*b^2 - A*b^4)*c)*cos(x) - (A*a^2*b^3 - A*b^5 + C*a*b*c^3 - A*b*c^4 + (A*a^2*b - 2*A*b^3)*c^2 - (C*a^3*b - C*a*b^3)*c)*sin(x))/(a^5*b^2 - 2*a^3*b^4 + a*b^6 + a*c^6 - (2*a^3 - 3*a*b^2)*c^4 + (a^5 - 4*a^3*b^2 + 3*a*b^4)*c^2 + (a^4*b^3 - 2*a^2*b^5 + b^7 + b*c^6 - (2*a^2*b - 3*b^3)*c^4 + (a^4*b - 4*a^2*b^3 + 3*b^5)*c^2)*cos(x) + (c^7 - (2*a^2 - 3*b^2)*c^5 + (a^4 - 4*a^2*b^2 + 3*b^4)*c^3 + (a^4*b^2 - 2*a^2*b^4 + b^6)*c)*sin(x))]","B",0
542,1,3513,0,1.890630," ","integrate((A+C*sin(x))/(a+b*cos(x)+c*sin(x))^3,x, algorithm=""fricas"")","\left[\frac{2 \, C a^{6} b - 6 \, C a^{4} b^{3} + 6 \, C a^{2} b^{5} - 2 \, C b^{7} + 6 \, A a b c^{5} - 6 \, C b c^{6} + 2 \, {\left(4 \, C a^{2} b - 7 \, C b^{3}\right)} c^{4} - 6 \, {\left(A a^{3} b - 2 \, A a b^{3}\right)} c^{3} - 2 \, {\left(2 \, C a^{4} b - 7 \, C a^{2} b^{3} + 5 \, C b^{5}\right)} c^{2} - 4 \, {\left(3 \, A a b c^{5} - 2 \, C b c^{6} + {\left(C a^{2} b - 4 \, C b^{3}\right)} c^{4} - 3 \, {\left(A a^{3} b - 2 \, A a b^{3}\right)} c^{3} + {\left(C a^{4} b + C a^{2} b^{3} - 2 \, C b^{5}\right)} c^{2} - 3 \, {\left(A a^{3} b^{3} - A a b^{5}\right)} c\right)} \cos\left(x\right)^{2} - {\left(2 \, A a^{4} b^{2} + A a^{2} b^{4} - 3 \, C a^{3} b^{2} c - 3 \, C a c^{5} + A c^{6} + {\left(3 \, A a^{2} + 2 \, A b^{2}\right)} c^{4} - 3 \, {\left(C a^{3} + C a b^{2}\right)} c^{3} + {\left(2 \, A a^{4} + 4 \, A a^{2} b^{2} + A b^{4}\right)} c^{2} + {\left(2 \, A a^{2} b^{4} + A b^{6} - 3 \, C a b^{4} c + A b^{4} c^{2} + 3 \, C a c^{5} - A c^{6} - {\left(2 \, A a^{2} + A b^{2}\right)} c^{4}\right)} \cos\left(x\right)^{2} + 2 \, {\left(2 \, A a^{3} b^{3} + A a b^{5} - 3 \, C a^{2} b^{3} c - 3 \, C a^{2} b c^{3} + A a b c^{4} + 2 \, {\left(A a^{3} b + A a b^{3}\right)} c^{2}\right)} \cos\left(x\right) - 2 \, {\left(3 \, C a^{2} b^{2} c^{2} + 3 \, C a^{2} c^{4} - A a c^{5} - 2 \, {\left(A a^{3} + A a b^{2}\right)} c^{3} - {\left(2 \, A a^{3} b^{2} + A a b^{4}\right)} c + {\left(3 \, C a b^{3} c^{2} + 3 \, C a b c^{4} - A b c^{5} - 2 \, {\left(A a^{2} b + A b^{3}\right)} c^{3} - {\left(2 \, A a^{2} b^{3} + A b^{5}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}} \log\left(-\frac{a^{2} b^{2} - 2 \, b^{4} - c^{4} - {\left(a^{2} + 3 \, b^{2}\right)} c^{2} - {\left(2 \, a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \cos\left(x\right)^{2} - 2 \, {\left(a b^{3} + a b c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a b^{2} c + a c^{3} - {\left(b c^{3} - {\left(2 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right) + 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(b^{2} c + c^{3}\right)} \cos\left(x\right) - {\left(b^{3} + b c^{2} + {\left(a b^{2} - a c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}}}{2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)}\right) - 6 \, {\left(A a^{3} b^{3} - A a b^{5}\right)} c + 2 \, {\left(C a c^{6} + A c^{7} - {\left(5 \, A a^{2} - 3 \, A b^{2}\right)} c^{5} + {\left(C a^{3} + 2 \, C a b^{2}\right)} c^{4} + {\left(4 \, A a^{4} - 10 \, A a^{2} b^{2} + 3 \, A b^{4}\right)} c^{3} - {\left(2 \, C a^{5} - C a^{3} b^{2} - C a b^{4}\right)} c^{2} + {\left(4 \, A a^{4} b^{2} - 5 \, A a^{2} b^{4} + A b^{6}\right)} c\right)} \cos\left(x\right) - 2 \, {\left(4 \, A a^{4} b^{3} - 5 \, A a^{2} b^{5} + A b^{7} + C a b c^{5} + A b c^{6} - {\left(5 \, A a^{2} b - 3 \, A b^{3}\right)} c^{4} + {\left(C a^{3} b + 2 \, C a b^{3}\right)} c^{3} + {\left(4 \, A a^{4} b - 10 \, A a^{2} b^{3} + 3 \, A b^{5}\right)} c^{2} - {\left(2 \, C a^{5} b - C a^{3} b^{3} - C a b^{5}\right)} c + {\left(3 \, A a^{3} b^{4} - 3 \, A a b^{6} - 3 \, A a b^{4} c^{2} + 3 \, A a c^{6} - 2 \, C c^{7} + {\left(C a^{2} - 2 \, C b^{2}\right)} c^{5} - 3 \, {\left(A a^{3} - A a b^{2}\right)} c^{4} + {\left(C a^{4} + 2 \, C b^{4}\right)} c^{3} - {\left(C a^{4} b^{2} + C a^{2} b^{4} - 2 \, C b^{6}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{4 \, {\left(a^{8} b^{2} - 3 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - a^{2} b^{8} - c^{10} + 2 \, {\left(a^{2} - 2 \, b^{2}\right)} c^{8} + {\left(5 \, a^{2} b^{2} - 6 \, b^{4}\right)} c^{6} - {\left(2 \, a^{6} - 3 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + 4 \, b^{6}\right)} c^{4} + {\left(a^{8} - 5 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - a^{2} b^{6} - b^{8}\right)} c^{2} + {\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10} + c^{10} - 3 \, {\left(a^{2} - b^{2}\right)} c^{8} + {\left(3 \, a^{4} - 6 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{6} - {\left(a^{6} - 3 \, a^{4} b^{2} + 2 \, b^{6}\right)} c^{4} - 3 \, {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} c^{2}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{7} b^{3} - 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} - a b^{9} - a b c^{8} + {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} c^{6} - 3 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} c^{4} + {\left(a^{7} b - 6 \, a^{5} b^{3} + 9 \, a^{3} b^{5} - 4 \, a b^{7}\right)} c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a c^{9} - {\left(3 \, a^{3} - 4 \, a b^{2}\right)} c^{7} + 3 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{7} - 6 \, a^{5} b^{2} + 9 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c^{3} - {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} c + {\left(b c^{9} - {\left(3 \, a^{2} b - 4 \, b^{3}\right)} c^{7} + 3 \, {\left(a^{4} b - 3 \, a^{2} b^{3} + 2 \, b^{5}\right)} c^{5} - {\left(a^{6} b - 6 \, a^{4} b^{3} + 9 \, a^{2} b^{5} - 4 \, b^{7}\right)} c^{3} - {\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)}}, \frac{C a^{6} b - 3 \, C a^{4} b^{3} + 3 \, C a^{2} b^{5} - C b^{7} + 3 \, A a b c^{5} - 3 \, C b c^{6} + {\left(4 \, C a^{2} b - 7 \, C b^{3}\right)} c^{4} - 3 \, {\left(A a^{3} b - 2 \, A a b^{3}\right)} c^{3} - {\left(2 \, C a^{4} b - 7 \, C a^{2} b^{3} + 5 \, C b^{5}\right)} c^{2} - 2 \, {\left(3 \, A a b c^{5} - 2 \, C b c^{6} + {\left(C a^{2} b - 4 \, C b^{3}\right)} c^{4} - 3 \, {\left(A a^{3} b - 2 \, A a b^{3}\right)} c^{3} + {\left(C a^{4} b + C a^{2} b^{3} - 2 \, C b^{5}\right)} c^{2} - 3 \, {\left(A a^{3} b^{3} - A a b^{5}\right)} c\right)} \cos\left(x\right)^{2} + {\left(2 \, A a^{4} b^{2} + A a^{2} b^{4} - 3 \, C a^{3} b^{2} c - 3 \, C a c^{5} + A c^{6} + {\left(3 \, A a^{2} + 2 \, A b^{2}\right)} c^{4} - 3 \, {\left(C a^{3} + C a b^{2}\right)} c^{3} + {\left(2 \, A a^{4} + 4 \, A a^{2} b^{2} + A b^{4}\right)} c^{2} + {\left(2 \, A a^{2} b^{4} + A b^{6} - 3 \, C a b^{4} c + A b^{4} c^{2} + 3 \, C a c^{5} - A c^{6} - {\left(2 \, A a^{2} + A b^{2}\right)} c^{4}\right)} \cos\left(x\right)^{2} + 2 \, {\left(2 \, A a^{3} b^{3} + A a b^{5} - 3 \, C a^{2} b^{3} c - 3 \, C a^{2} b c^{3} + A a b c^{4} + 2 \, {\left(A a^{3} b + A a b^{3}\right)} c^{2}\right)} \cos\left(x\right) - 2 \, {\left(3 \, C a^{2} b^{2} c^{2} + 3 \, C a^{2} c^{4} - A a c^{5} - 2 \, {\left(A a^{3} + A a b^{2}\right)} c^{3} - {\left(2 \, A a^{3} b^{2} + A a b^{4}\right)} c + {\left(3 \, C a b^{3} c^{2} + 3 \, C a b c^{4} - A b c^{5} - 2 \, {\left(A a^{2} b + A b^{3}\right)} c^{3} - {\left(2 \, A a^{2} b^{3} + A b^{5}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{a^{2} - b^{2} - c^{2}} \arctan\left(-\frac{{\left(a b \cos\left(x\right) + a c \sin\left(x\right) + b^{2} + c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}}}{{\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(x\right) + {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(x\right)}\right) - 3 \, {\left(A a^{3} b^{3} - A a b^{5}\right)} c + {\left(C a c^{6} + A c^{7} - {\left(5 \, A a^{2} - 3 \, A b^{2}\right)} c^{5} + {\left(C a^{3} + 2 \, C a b^{2}\right)} c^{4} + {\left(4 \, A a^{4} - 10 \, A a^{2} b^{2} + 3 \, A b^{4}\right)} c^{3} - {\left(2 \, C a^{5} - C a^{3} b^{2} - C a b^{4}\right)} c^{2} + {\left(4 \, A a^{4} b^{2} - 5 \, A a^{2} b^{4} + A b^{6}\right)} c\right)} \cos\left(x\right) - {\left(4 \, A a^{4} b^{3} - 5 \, A a^{2} b^{5} + A b^{7} + C a b c^{5} + A b c^{6} - {\left(5 \, A a^{2} b - 3 \, A b^{3}\right)} c^{4} + {\left(C a^{3} b + 2 \, C a b^{3}\right)} c^{3} + {\left(4 \, A a^{4} b - 10 \, A a^{2} b^{3} + 3 \, A b^{5}\right)} c^{2} - {\left(2 \, C a^{5} b - C a^{3} b^{3} - C a b^{5}\right)} c + {\left(3 \, A a^{3} b^{4} - 3 \, A a b^{6} - 3 \, A a b^{4} c^{2} + 3 \, A a c^{6} - 2 \, C c^{7} + {\left(C a^{2} - 2 \, C b^{2}\right)} c^{5} - 3 \, {\left(A a^{3} - A a b^{2}\right)} c^{4} + {\left(C a^{4} + 2 \, C b^{4}\right)} c^{3} - {\left(C a^{4} b^{2} + C a^{2} b^{4} - 2 \, C b^{6}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{2 \, {\left(a^{8} b^{2} - 3 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - a^{2} b^{8} - c^{10} + 2 \, {\left(a^{2} - 2 \, b^{2}\right)} c^{8} + {\left(5 \, a^{2} b^{2} - 6 \, b^{4}\right)} c^{6} - {\left(2 \, a^{6} - 3 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + 4 \, b^{6}\right)} c^{4} + {\left(a^{8} - 5 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - a^{2} b^{6} - b^{8}\right)} c^{2} + {\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10} + c^{10} - 3 \, {\left(a^{2} - b^{2}\right)} c^{8} + {\left(3 \, a^{4} - 6 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{6} - {\left(a^{6} - 3 \, a^{4} b^{2} + 2 \, b^{6}\right)} c^{4} - 3 \, {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} c^{2}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{7} b^{3} - 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} - a b^{9} - a b c^{8} + {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} c^{6} - 3 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} c^{4} + {\left(a^{7} b - 6 \, a^{5} b^{3} + 9 \, a^{3} b^{5} - 4 \, a b^{7}\right)} c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a c^{9} - {\left(3 \, a^{3} - 4 \, a b^{2}\right)} c^{7} + 3 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{7} - 6 \, a^{5} b^{2} + 9 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c^{3} - {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} c + {\left(b c^{9} - {\left(3 \, a^{2} b - 4 \, b^{3}\right)} c^{7} + 3 \, {\left(a^{4} b - 3 \, a^{2} b^{3} + 2 \, b^{5}\right)} c^{5} - {\left(a^{6} b - 6 \, a^{4} b^{3} + 9 \, a^{2} b^{5} - 4 \, b^{7}\right)} c^{3} - {\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)}}\right]"," ",0,"[1/4*(2*C*a^6*b - 6*C*a^4*b^3 + 6*C*a^2*b^5 - 2*C*b^7 + 6*A*a*b*c^5 - 6*C*b*c^6 + 2*(4*C*a^2*b - 7*C*b^3)*c^4 - 6*(A*a^3*b - 2*A*a*b^3)*c^3 - 2*(2*C*a^4*b - 7*C*a^2*b^3 + 5*C*b^5)*c^2 - 4*(3*A*a*b*c^5 - 2*C*b*c^6 + (C*a^2*b - 4*C*b^3)*c^4 - 3*(A*a^3*b - 2*A*a*b^3)*c^3 + (C*a^4*b + C*a^2*b^3 - 2*C*b^5)*c^2 - 3*(A*a^3*b^3 - A*a*b^5)*c)*cos(x)^2 - (2*A*a^4*b^2 + A*a^2*b^4 - 3*C*a^3*b^2*c - 3*C*a*c^5 + A*c^6 + (3*A*a^2 + 2*A*b^2)*c^4 - 3*(C*a^3 + C*a*b^2)*c^3 + (2*A*a^4 + 4*A*a^2*b^2 + A*b^4)*c^2 + (2*A*a^2*b^4 + A*b^6 - 3*C*a*b^4*c + A*b^4*c^2 + 3*C*a*c^5 - A*c^6 - (2*A*a^2 + A*b^2)*c^4)*cos(x)^2 + 2*(2*A*a^3*b^3 + A*a*b^5 - 3*C*a^2*b^3*c - 3*C*a^2*b*c^3 + A*a*b*c^4 + 2*(A*a^3*b + A*a*b^3)*c^2)*cos(x) - 2*(3*C*a^2*b^2*c^2 + 3*C*a^2*c^4 - A*a*c^5 - 2*(A*a^3 + A*a*b^2)*c^3 - (2*A*a^3*b^2 + A*a*b^4)*c + (3*C*a*b^3*c^2 + 3*C*a*b*c^4 - A*b*c^5 - 2*(A*a^2*b + A*b^3)*c^3 - (2*A*a^2*b^3 + A*b^5)*c)*cos(x))*sin(x))*sqrt(-a^2 + b^2 + c^2)*log(-(a^2*b^2 - 2*b^4 - c^4 - (a^2 + 3*b^2)*c^2 - (2*a^2*b^2 - b^4 - 2*a^2*c^2 + c^4)*cos(x)^2 - 2*(a*b^3 + a*b*c^2)*cos(x) - 2*(a*b^2*c + a*c^3 - (b*c^3 - (2*a^2*b - b^3)*c)*cos(x))*sin(x) + 2*(2*a*b*c*cos(x)^2 - a*b*c + (b^2*c + c^3)*cos(x) - (b^3 + b*c^2 + (a*b^2 - a*c^2)*cos(x))*sin(x))*sqrt(-a^2 + b^2 + c^2))/(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x))) - 6*(A*a^3*b^3 - A*a*b^5)*c + 2*(C*a*c^6 + A*c^7 - (5*A*a^2 - 3*A*b^2)*c^5 + (C*a^3 + 2*C*a*b^2)*c^4 + (4*A*a^4 - 10*A*a^2*b^2 + 3*A*b^4)*c^3 - (2*C*a^5 - C*a^3*b^2 - C*a*b^4)*c^2 + (4*A*a^4*b^2 - 5*A*a^2*b^4 + A*b^6)*c)*cos(x) - 2*(4*A*a^4*b^3 - 5*A*a^2*b^5 + A*b^7 + C*a*b*c^5 + A*b*c^6 - (5*A*a^2*b - 3*A*b^3)*c^4 + (C*a^3*b + 2*C*a*b^3)*c^3 + (4*A*a^4*b - 10*A*a^2*b^3 + 3*A*b^5)*c^2 - (2*C*a^5*b - C*a^3*b^3 - C*a*b^5)*c + (3*A*a^3*b^4 - 3*A*a*b^6 - 3*A*a*b^4*c^2 + 3*A*a*c^6 - 2*C*c^7 + (C*a^2 - 2*C*b^2)*c^5 - 3*(A*a^3 - A*a*b^2)*c^4 + (C*a^4 + 2*C*b^4)*c^3 - (C*a^4*b^2 + C*a^2*b^4 - 2*C*b^6)*c)*cos(x))*sin(x))/(a^8*b^2 - 3*a^6*b^4 + 3*a^4*b^6 - a^2*b^8 - c^10 + 2*(a^2 - 2*b^2)*c^8 + (5*a^2*b^2 - 6*b^4)*c^6 - (2*a^6 - 3*a^4*b^2 - 3*a^2*b^4 + 4*b^6)*c^4 + (a^8 - 5*a^6*b^2 + 6*a^4*b^4 - a^2*b^6 - b^8)*c^2 + (a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10 + c^10 - 3*(a^2 - b^2)*c^8 + (3*a^4 - 6*a^2*b^2 + 2*b^4)*c^6 - (a^6 - 3*a^4*b^2 + 2*b^6)*c^4 - 3*(a^4*b^4 - 2*a^2*b^6 + b^8)*c^2)*cos(x)^2 + 2*(a^7*b^3 - 3*a^5*b^5 + 3*a^3*b^7 - a*b^9 - a*b*c^8 + (3*a^3*b - 4*a*b^3)*c^6 - 3*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*c^4 + (a^7*b - 6*a^5*b^3 + 9*a^3*b^5 - 4*a*b^7)*c^2)*cos(x) - 2*(a*c^9 - (3*a^3 - 4*a*b^2)*c^7 + 3*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^7 - 6*a^5*b^2 + 9*a^3*b^4 - 4*a*b^6)*c^3 - (a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*c + (b*c^9 - (3*a^2*b - 4*b^3)*c^7 + 3*(a^4*b - 3*a^2*b^3 + 2*b^5)*c^5 - (a^6*b - 6*a^4*b^3 + 9*a^2*b^5 - 4*b^7)*c^3 - (a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*c)*cos(x))*sin(x)), 1/2*(C*a^6*b - 3*C*a^4*b^3 + 3*C*a^2*b^5 - C*b^7 + 3*A*a*b*c^5 - 3*C*b*c^6 + (4*C*a^2*b - 7*C*b^3)*c^4 - 3*(A*a^3*b - 2*A*a*b^3)*c^3 - (2*C*a^4*b - 7*C*a^2*b^3 + 5*C*b^5)*c^2 - 2*(3*A*a*b*c^5 - 2*C*b*c^6 + (C*a^2*b - 4*C*b^3)*c^4 - 3*(A*a^3*b - 2*A*a*b^3)*c^3 + (C*a^4*b + C*a^2*b^3 - 2*C*b^5)*c^2 - 3*(A*a^3*b^3 - A*a*b^5)*c)*cos(x)^2 + (2*A*a^4*b^2 + A*a^2*b^4 - 3*C*a^3*b^2*c - 3*C*a*c^5 + A*c^6 + (3*A*a^2 + 2*A*b^2)*c^4 - 3*(C*a^3 + C*a*b^2)*c^3 + (2*A*a^4 + 4*A*a^2*b^2 + A*b^4)*c^2 + (2*A*a^2*b^4 + A*b^6 - 3*C*a*b^4*c + A*b^4*c^2 + 3*C*a*c^5 - A*c^6 - (2*A*a^2 + A*b^2)*c^4)*cos(x)^2 + 2*(2*A*a^3*b^3 + A*a*b^5 - 3*C*a^2*b^3*c - 3*C*a^2*b*c^3 + A*a*b*c^4 + 2*(A*a^3*b + A*a*b^3)*c^2)*cos(x) - 2*(3*C*a^2*b^2*c^2 + 3*C*a^2*c^4 - A*a*c^5 - 2*(A*a^3 + A*a*b^2)*c^3 - (2*A*a^3*b^2 + A*a*b^4)*c + (3*C*a*b^3*c^2 + 3*C*a*b*c^4 - A*b*c^5 - 2*(A*a^2*b + A*b^3)*c^3 - (2*A*a^2*b^3 + A*b^5)*c)*cos(x))*sin(x))*sqrt(a^2 - b^2 - c^2)*arctan(-(a*b*cos(x) + a*c*sin(x) + b^2 + c^2)*sqrt(a^2 - b^2 - c^2)/((c^3 - (a^2 - b^2)*c)*cos(x) + (a^2*b - b^3 - b*c^2)*sin(x))) - 3*(A*a^3*b^3 - A*a*b^5)*c + (C*a*c^6 + A*c^7 - (5*A*a^2 - 3*A*b^2)*c^5 + (C*a^3 + 2*C*a*b^2)*c^4 + (4*A*a^4 - 10*A*a^2*b^2 + 3*A*b^4)*c^3 - (2*C*a^5 - C*a^3*b^2 - C*a*b^4)*c^2 + (4*A*a^4*b^2 - 5*A*a^2*b^4 + A*b^6)*c)*cos(x) - (4*A*a^4*b^3 - 5*A*a^2*b^5 + A*b^7 + C*a*b*c^5 + A*b*c^6 - (5*A*a^2*b - 3*A*b^3)*c^4 + (C*a^3*b + 2*C*a*b^3)*c^3 + (4*A*a^4*b - 10*A*a^2*b^3 + 3*A*b^5)*c^2 - (2*C*a^5*b - C*a^3*b^3 - C*a*b^5)*c + (3*A*a^3*b^4 - 3*A*a*b^6 - 3*A*a*b^4*c^2 + 3*A*a*c^6 - 2*C*c^7 + (C*a^2 - 2*C*b^2)*c^5 - 3*(A*a^3 - A*a*b^2)*c^4 + (C*a^4 + 2*C*b^4)*c^3 - (C*a^4*b^2 + C*a^2*b^4 - 2*C*b^6)*c)*cos(x))*sin(x))/(a^8*b^2 - 3*a^6*b^4 + 3*a^4*b^6 - a^2*b^8 - c^10 + 2*(a^2 - 2*b^2)*c^8 + (5*a^2*b^2 - 6*b^4)*c^6 - (2*a^6 - 3*a^4*b^2 - 3*a^2*b^4 + 4*b^6)*c^4 + (a^8 - 5*a^6*b^2 + 6*a^4*b^4 - a^2*b^6 - b^8)*c^2 + (a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10 + c^10 - 3*(a^2 - b^2)*c^8 + (3*a^4 - 6*a^2*b^2 + 2*b^4)*c^6 - (a^6 - 3*a^4*b^2 + 2*b^6)*c^4 - 3*(a^4*b^4 - 2*a^2*b^6 + b^8)*c^2)*cos(x)^2 + 2*(a^7*b^3 - 3*a^5*b^5 + 3*a^3*b^7 - a*b^9 - a*b*c^8 + (3*a^3*b - 4*a*b^3)*c^6 - 3*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*c^4 + (a^7*b - 6*a^5*b^3 + 9*a^3*b^5 - 4*a*b^7)*c^2)*cos(x) - 2*(a*c^9 - (3*a^3 - 4*a*b^2)*c^7 + 3*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^7 - 6*a^5*b^2 + 9*a^3*b^4 - 4*a*b^6)*c^3 - (a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*c + (b*c^9 - (3*a^2*b - 4*b^3)*c^7 + 3*(a^4*b - 3*a^2*b^3 + 2*b^5)*c^5 - (a^6*b - 6*a^4*b^3 + 9*a^2*b^5 - 4*b^7)*c^3 - (a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*c)*cos(x))*sin(x))]","B",0
543,1,71,0,0.967500," ","integrate((A+C*sin(x))/(a+b*cos(x)+I*b*sin(x)),x, algorithm=""fricas"")","-\frac{{\left(C a b - {\left(2 \, A a b - i \, C b^{2}\right)} x e^{\left(i \, x\right)} + {\left(C a^{2} - 2 i \, A a b - C b^{2}\right)} e^{\left(i \, x\right)} \log\left(\frac{b e^{\left(i \, x\right)} + a}{b}\right)\right)} e^{\left(-i \, x\right)}}{2 \, a^{2} b}"," ",0,"-1/2*(C*a*b - (2*A*a*b - I*C*b^2)*x*e^(I*x) + (C*a^2 - 2*I*A*a*b - C*b^2)*e^(I*x)*log((b*e^(I*x) + a)/b))*e^(-I*x)/(a^2*b)","A",0
544,1,57,0,0.550295," ","integrate((A+C*sin(x))/(a+b*cos(x)-I*b*sin(x)),x, algorithm=""fricas"")","\frac{i \, C a^{2} x - C a b e^{\left(i \, x\right)} - {\left(C a^{2} + 2 i \, A a b - C b^{2}\right)} \log\left(\frac{a e^{\left(i \, x\right)} + b}{a}\right)}{2 \, a^{2} b}"," ",0,"1/2*(I*C*a^2*x - C*a*b*e^(I*x) - (C*a^2 + 2*I*A*a*b - C*b^2)*log((a*e^(I*x) + b)/a))/(a^2*b)","A",0
545,1,687,0,5.063729," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x)),x, algorithm=""fricas"")","\left[-\frac{{\left(B a b + C a c\right)} \sqrt{-a^{2} + b^{2} + c^{2}} \log\left(\frac{a^{2} b^{2} - 2 \, b^{4} - c^{4} - {\left(a^{2} + 3 \, b^{2}\right)} c^{2} - {\left(2 \, a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \cos\left(x\right)^{2} - 2 \, {\left(a b^{3} + a b c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a b^{2} c + a c^{3} - {\left(b c^{3} - {\left(2 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right) - 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(b^{2} c + c^{3}\right)} \cos\left(x\right) - {\left(b^{3} + b c^{2} + {\left(a b^{2} - a c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}}}{2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)}\right) - 2 \, {\left(B a^{2} b - B b^{3} - B b c^{2} - C c^{3} + {\left(C a^{2} - C b^{2}\right)} c\right)} x + {\left(C a^{2} b - C b^{3} - C b c^{2} + B c^{3} - {\left(B a^{2} - B b^{2}\right)} c\right)} \log\left(2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)\right)}{2 \, {\left(a^{2} b^{2} - b^{4} - c^{4} + {\left(a^{2} - 2 \, b^{2}\right)} c^{2}\right)}}, -\frac{2 \, {\left(B a b + C a c\right)} \sqrt{a^{2} - b^{2} - c^{2}} \arctan\left(-\frac{{\left(a b \cos\left(x\right) + a c \sin\left(x\right) + b^{2} + c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}}}{{\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(x\right) + {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(x\right)}\right) - 2 \, {\left(B a^{2} b - B b^{3} - B b c^{2} - C c^{3} + {\left(C a^{2} - C b^{2}\right)} c\right)} x + {\left(C a^{2} b - C b^{3} - C b c^{2} + B c^{3} - {\left(B a^{2} - B b^{2}\right)} c\right)} \log\left(2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)\right)}{2 \, {\left(a^{2} b^{2} - b^{4} - c^{4} + {\left(a^{2} - 2 \, b^{2}\right)} c^{2}\right)}}\right]"," ",0,"[-1/2*((B*a*b + C*a*c)*sqrt(-a^2 + b^2 + c^2)*log((a^2*b^2 - 2*b^4 - c^4 - (a^2 + 3*b^2)*c^2 - (2*a^2*b^2 - b^4 - 2*a^2*c^2 + c^4)*cos(x)^2 - 2*(a*b^3 + a*b*c^2)*cos(x) - 2*(a*b^2*c + a*c^3 - (b*c^3 - (2*a^2*b - b^3)*c)*cos(x))*sin(x) - 2*(2*a*b*c*cos(x)^2 - a*b*c + (b^2*c + c^3)*cos(x) - (b^3 + b*c^2 + (a*b^2 - a*c^2)*cos(x))*sin(x))*sqrt(-a^2 + b^2 + c^2))/(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x))) - 2*(B*a^2*b - B*b^3 - B*b*c^2 - C*c^3 + (C*a^2 - C*b^2)*c)*x + (C*a^2*b - C*b^3 - C*b*c^2 + B*c^3 - (B*a^2 - B*b^2)*c)*log(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x)))/(a^2*b^2 - b^4 - c^4 + (a^2 - 2*b^2)*c^2), -1/2*(2*(B*a*b + C*a*c)*sqrt(a^2 - b^2 - c^2)*arctan(-(a*b*cos(x) + a*c*sin(x) + b^2 + c^2)*sqrt(a^2 - b^2 - c^2)/((c^3 - (a^2 - b^2)*c)*cos(x) + (a^2*b - b^3 - b*c^2)*sin(x))) - 2*(B*a^2*b - B*b^3 - B*b*c^2 - C*c^3 + (C*a^2 - C*b^2)*c)*x + (C*a^2*b - C*b^3 - C*b*c^2 + B*c^3 - (B*a^2 - B*b^2)*c)*log(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x)))/(a^2*b^2 - b^4 - c^4 + (a^2 - 2*b^2)*c^2)]","B",0
546,1,1316,0,1.023525," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^2,x, algorithm=""fricas"")","\left[\frac{2 \, C a^{4} b - 4 \, C a^{2} b^{3} + 2 \, C b^{5} + 2 \, C b c^{4} - 2 \, B c^{5} + 4 \, {\left(B a^{2} - B b^{2}\right)} c^{3} - 4 \, {\left(C a^{2} b - C b^{3}\right)} c^{2} + {\left(B a b^{3} + C a b^{2} c + B a b c^{2} + C a c^{3} + {\left(B b^{4} + C b^{3} c + B b^{2} c^{2} + C b c^{3}\right)} \cos\left(x\right) + {\left(B b^{3} c + C b^{2} c^{2} + B b c^{3} + C c^{4}\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}} \log\left(-\frac{a^{2} b^{2} - 2 \, b^{4} - c^{4} - {\left(a^{2} + 3 \, b^{2}\right)} c^{2} - {\left(2 \, a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \cos\left(x\right)^{2} - 2 \, {\left(a b^{3} + a b c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a b^{2} c + a c^{3} - {\left(b c^{3} - {\left(2 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right) + 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(b^{2} c + c^{3}\right)} \cos\left(x\right) - {\left(b^{3} + b c^{2} + {\left(a b^{2} - a c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}}}{2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)}\right) - 2 \, {\left(B a^{4} - 2 \, B a^{2} b^{2} + B b^{4}\right)} c + 2 \, {\left(B a b c^{3} + C a c^{4} - {\left(C a^{3} - C a b^{2}\right)} c^{2} - {\left(B a^{3} b - B a b^{3}\right)} c\right)} \cos\left(x\right) + 2 \, {\left(B a^{3} b^{2} - B a b^{4} - B a b^{2} c^{2} - C a b c^{3} + {\left(C a^{3} b - C a b^{3}\right)} c\right)} \sin\left(x\right)}{2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6} + a c^{6} - {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{4} + {\left(a^{5} - 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c^{2} + {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7} + b c^{6} - {\left(2 \, a^{2} b - 3 \, b^{3}\right)} c^{4} + {\left(a^{4} b - 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} c^{2}\right)} \cos\left(x\right) + {\left(c^{7} - {\left(2 \, a^{2} - 3 \, b^{2}\right)} c^{5} + {\left(a^{4} - 4 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{3} + {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c\right)} \sin\left(x\right)\right)}}, \frac{C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5} + C b c^{4} - B c^{5} + 2 \, {\left(B a^{2} - B b^{2}\right)} c^{3} - 2 \, {\left(C a^{2} b - C b^{3}\right)} c^{2} - {\left(B a b^{3} + C a b^{2} c + B a b c^{2} + C a c^{3} + {\left(B b^{4} + C b^{3} c + B b^{2} c^{2} + C b c^{3}\right)} \cos\left(x\right) + {\left(B b^{3} c + C b^{2} c^{2} + B b c^{3} + C c^{4}\right)} \sin\left(x\right)\right)} \sqrt{a^{2} - b^{2} - c^{2}} \arctan\left(-\frac{{\left(a b \cos\left(x\right) + a c \sin\left(x\right) + b^{2} + c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}}}{{\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(x\right) + {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(x\right)}\right) - {\left(B a^{4} - 2 \, B a^{2} b^{2} + B b^{4}\right)} c + {\left(B a b c^{3} + C a c^{4} - {\left(C a^{3} - C a b^{2}\right)} c^{2} - {\left(B a^{3} b - B a b^{3}\right)} c\right)} \cos\left(x\right) + {\left(B a^{3} b^{2} - B a b^{4} - B a b^{2} c^{2} - C a b c^{3} + {\left(C a^{3} b - C a b^{3}\right)} c\right)} \sin\left(x\right)}{a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6} + a c^{6} - {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{4} + {\left(a^{5} - 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c^{2} + {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7} + b c^{6} - {\left(2 \, a^{2} b - 3 \, b^{3}\right)} c^{4} + {\left(a^{4} b - 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} c^{2}\right)} \cos\left(x\right) + {\left(c^{7} - {\left(2 \, a^{2} - 3 \, b^{2}\right)} c^{5} + {\left(a^{4} - 4 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{3} + {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c\right)} \sin\left(x\right)}\right]"," ",0,"[1/2*(2*C*a^4*b - 4*C*a^2*b^3 + 2*C*b^5 + 2*C*b*c^4 - 2*B*c^5 + 4*(B*a^2 - B*b^2)*c^3 - 4*(C*a^2*b - C*b^3)*c^2 + (B*a*b^3 + C*a*b^2*c + B*a*b*c^2 + C*a*c^3 + (B*b^4 + C*b^3*c + B*b^2*c^2 + C*b*c^3)*cos(x) + (B*b^3*c + C*b^2*c^2 + B*b*c^3 + C*c^4)*sin(x))*sqrt(-a^2 + b^2 + c^2)*log(-(a^2*b^2 - 2*b^4 - c^4 - (a^2 + 3*b^2)*c^2 - (2*a^2*b^2 - b^4 - 2*a^2*c^2 + c^4)*cos(x)^2 - 2*(a*b^3 + a*b*c^2)*cos(x) - 2*(a*b^2*c + a*c^3 - (b*c^3 - (2*a^2*b - b^3)*c)*cos(x))*sin(x) + 2*(2*a*b*c*cos(x)^2 - a*b*c + (b^2*c + c^3)*cos(x) - (b^3 + b*c^2 + (a*b^2 - a*c^2)*cos(x))*sin(x))*sqrt(-a^2 + b^2 + c^2))/(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x))) - 2*(B*a^4 - 2*B*a^2*b^2 + B*b^4)*c + 2*(B*a*b*c^3 + C*a*c^4 - (C*a^3 - C*a*b^2)*c^2 - (B*a^3*b - B*a*b^3)*c)*cos(x) + 2*(B*a^3*b^2 - B*a*b^4 - B*a*b^2*c^2 - C*a*b*c^3 + (C*a^3*b - C*a*b^3)*c)*sin(x))/(a^5*b^2 - 2*a^3*b^4 + a*b^6 + a*c^6 - (2*a^3 - 3*a*b^2)*c^4 + (a^5 - 4*a^3*b^2 + 3*a*b^4)*c^2 + (a^4*b^3 - 2*a^2*b^5 + b^7 + b*c^6 - (2*a^2*b - 3*b^3)*c^4 + (a^4*b - 4*a^2*b^3 + 3*b^5)*c^2)*cos(x) + (c^7 - (2*a^2 - 3*b^2)*c^5 + (a^4 - 4*a^2*b^2 + 3*b^4)*c^3 + (a^4*b^2 - 2*a^2*b^4 + b^6)*c)*sin(x)), (C*a^4*b - 2*C*a^2*b^3 + C*b^5 + C*b*c^4 - B*c^5 + 2*(B*a^2 - B*b^2)*c^3 - 2*(C*a^2*b - C*b^3)*c^2 - (B*a*b^3 + C*a*b^2*c + B*a*b*c^2 + C*a*c^3 + (B*b^4 + C*b^3*c + B*b^2*c^2 + C*b*c^3)*cos(x) + (B*b^3*c + C*b^2*c^2 + B*b*c^3 + C*c^4)*sin(x))*sqrt(a^2 - b^2 - c^2)*arctan(-(a*b*cos(x) + a*c*sin(x) + b^2 + c^2)*sqrt(a^2 - b^2 - c^2)/((c^3 - (a^2 - b^2)*c)*cos(x) + (a^2*b - b^3 - b*c^2)*sin(x))) - (B*a^4 - 2*B*a^2*b^2 + B*b^4)*c + (B*a*b*c^3 + C*a*c^4 - (C*a^3 - C*a*b^2)*c^2 - (B*a^3*b - B*a*b^3)*c)*cos(x) + (B*a^3*b^2 - B*a*b^4 - B*a*b^2*c^2 - C*a*b*c^3 + (C*a^3*b - C*a*b^3)*c)*sin(x))/(a^5*b^2 - 2*a^3*b^4 + a*b^6 + a*c^6 - (2*a^3 - 3*a*b^2)*c^4 + (a^5 - 4*a^3*b^2 + 3*a*b^4)*c^2 + (a^4*b^3 - 2*a^2*b^5 + b^7 + b*c^6 - (2*a^2*b - 3*b^3)*c^4 + (a^4*b - 4*a^2*b^3 + 3*b^5)*c^2)*cos(x) + (c^7 - (2*a^2 - 3*b^2)*c^5 + (a^4 - 4*a^2*b^2 + 3*b^4)*c^3 + (a^4*b^2 - 2*a^2*b^4 + b^6)*c)*sin(x))]","B",0
547,1,3264,0,2.203080," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^3,x, algorithm=""fricas"")","\left[\frac{2 \, C a^{6} b - 6 \, C a^{4} b^{3} + 6 \, C a^{2} b^{5} - 2 \, C b^{7} - 6 \, C b c^{6} + 2 \, B c^{7} - 2 \, {\left(3 \, B a^{2} - B b^{2}\right)} c^{5} + 2 \, {\left(4 \, C a^{2} b - 7 \, C b^{3}\right)} c^{4} + 2 \, {\left(3 \, B a^{4} - 5 \, B a^{2} b^{2} - B b^{4}\right)} c^{3} - 2 \, {\left(2 \, C a^{4} b - 7 \, C a^{2} b^{3} + 5 \, C b^{5}\right)} c^{2} + 4 \, {\left(2 \, B b^{2} c^{5} + 2 \, C b c^{6} - {\left(C a^{2} b - 4 \, C b^{3}\right)} c^{4} - {\left(B a^{2} b^{2} - 4 \, B b^{4}\right)} c^{3} - {\left(C a^{4} b + C a^{2} b^{3} - 2 \, C b^{5}\right)} c^{2} - {\left(B a^{4} b^{2} + B a^{2} b^{4} - 2 \, B b^{6}\right)} c\right)} \cos\left(x\right)^{2} - 3 \, {\left(B a^{3} b^{3} + C a^{3} b^{2} c + B a b c^{4} + C a c^{5} + {\left(C a^{3} + C a b^{2}\right)} c^{3} + {\left(B a^{3} b + B a b^{3}\right)} c^{2} + {\left(B a b^{5} + C a b^{4} c - B a b c^{4} - C a c^{5}\right)} \cos\left(x\right)^{2} + 2 \, {\left(B a^{2} b^{4} + C a^{2} b^{3} c + B a^{2} b^{2} c^{2} + C a^{2} b c^{3}\right)} \cos\left(x\right) + 2 \, {\left(B a^{2} b^{3} c + C a^{2} b^{2} c^{2} + B a^{2} b c^{3} + C a^{2} c^{4} + {\left(B a b^{4} c + C a b^{3} c^{2} + B a b^{2} c^{3} + C a b c^{4}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}} \log\left(\frac{a^{2} b^{2} - 2 \, b^{4} - c^{4} - {\left(a^{2} + 3 \, b^{2}\right)} c^{2} - {\left(2 \, a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \cos\left(x\right)^{2} - 2 \, {\left(a b^{3} + a b c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a b^{2} c + a c^{3} - {\left(b c^{3} - {\left(2 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right) - 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(b^{2} c + c^{3}\right)} \cos\left(x\right) - {\left(b^{3} + b c^{2} + {\left(a b^{2} - a c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}}}{2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)}\right) - 2 \, {\left(B a^{6} - 4 \, B a^{4} b^{2} + 2 \, B a^{2} b^{4} + B b^{6}\right)} c + 2 \, {\left(B a b c^{5} + C a c^{6} + {\left(C a^{3} + 2 \, C a b^{2}\right)} c^{4} + {\left(B a^{3} b + 2 \, B a b^{3}\right)} c^{3} - {\left(2 \, C a^{5} - C a^{3} b^{2} - C a b^{4}\right)} c^{2} - {\left(2 \, B a^{5} b - B a^{3} b^{3} - B a b^{5}\right)} c\right)} \cos\left(x\right) + 2 \, {\left(2 \, B a^{5} b^{2} - B a^{3} b^{4} - B a b^{6} - B a b^{2} c^{4} - C a b c^{5} - {\left(C a^{3} b + 2 \, C a b^{3}\right)} c^{3} - {\left(B a^{3} b^{2} + 2 \, B a b^{4}\right)} c^{2} + {\left(2 \, C a^{5} b - C a^{3} b^{3} - C a b^{5}\right)} c + {\left(B a^{4} b^{3} + B a^{2} b^{5} - 2 \, B b^{7} + 2 \, B b c^{6} + 2 \, C c^{7} - {\left(C a^{2} - 2 \, C b^{2}\right)} c^{5} - {\left(B a^{2} b - 2 \, B b^{3}\right)} c^{4} - {\left(C a^{4} + 2 \, C b^{4}\right)} c^{3} - {\left(B a^{4} b + 2 \, B b^{5}\right)} c^{2} + {\left(C a^{4} b^{2} + C a^{2} b^{4} - 2 \, C b^{6}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{4 \, {\left(a^{8} b^{2} - 3 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - a^{2} b^{8} - c^{10} + 2 \, {\left(a^{2} - 2 \, b^{2}\right)} c^{8} + {\left(5 \, a^{2} b^{2} - 6 \, b^{4}\right)} c^{6} - {\left(2 \, a^{6} - 3 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + 4 \, b^{6}\right)} c^{4} + {\left(a^{8} - 5 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - a^{2} b^{6} - b^{8}\right)} c^{2} + {\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10} + c^{10} - 3 \, {\left(a^{2} - b^{2}\right)} c^{8} + {\left(3 \, a^{4} - 6 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{6} - {\left(a^{6} - 3 \, a^{4} b^{2} + 2 \, b^{6}\right)} c^{4} - 3 \, {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} c^{2}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{7} b^{3} - 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} - a b^{9} - a b c^{8} + {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} c^{6} - 3 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} c^{4} + {\left(a^{7} b - 6 \, a^{5} b^{3} + 9 \, a^{3} b^{5} - 4 \, a b^{7}\right)} c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a c^{9} - {\left(3 \, a^{3} - 4 \, a b^{2}\right)} c^{7} + 3 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{7} - 6 \, a^{5} b^{2} + 9 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c^{3} - {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} c + {\left(b c^{9} - {\left(3 \, a^{2} b - 4 \, b^{3}\right)} c^{7} + 3 \, {\left(a^{4} b - 3 \, a^{2} b^{3} + 2 \, b^{5}\right)} c^{5} - {\left(a^{6} b - 6 \, a^{4} b^{3} + 9 \, a^{2} b^{5} - 4 \, b^{7}\right)} c^{3} - {\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)}}, \frac{C a^{6} b - 3 \, C a^{4} b^{3} + 3 \, C a^{2} b^{5} - C b^{7} - 3 \, C b c^{6} + B c^{7} - {\left(3 \, B a^{2} - B b^{2}\right)} c^{5} + {\left(4 \, C a^{2} b - 7 \, C b^{3}\right)} c^{4} + {\left(3 \, B a^{4} - 5 \, B a^{2} b^{2} - B b^{4}\right)} c^{3} - {\left(2 \, C a^{4} b - 7 \, C a^{2} b^{3} + 5 \, C b^{5}\right)} c^{2} + 2 \, {\left(2 \, B b^{2} c^{5} + 2 \, C b c^{6} - {\left(C a^{2} b - 4 \, C b^{3}\right)} c^{4} - {\left(B a^{2} b^{2} - 4 \, B b^{4}\right)} c^{3} - {\left(C a^{4} b + C a^{2} b^{3} - 2 \, C b^{5}\right)} c^{2} - {\left(B a^{4} b^{2} + B a^{2} b^{4} - 2 \, B b^{6}\right)} c\right)} \cos\left(x\right)^{2} - 3 \, {\left(B a^{3} b^{3} + C a^{3} b^{2} c + B a b c^{4} + C a c^{5} + {\left(C a^{3} + C a b^{2}\right)} c^{3} + {\left(B a^{3} b + B a b^{3}\right)} c^{2} + {\left(B a b^{5} + C a b^{4} c - B a b c^{4} - C a c^{5}\right)} \cos\left(x\right)^{2} + 2 \, {\left(B a^{2} b^{4} + C a^{2} b^{3} c + B a^{2} b^{2} c^{2} + C a^{2} b c^{3}\right)} \cos\left(x\right) + 2 \, {\left(B a^{2} b^{3} c + C a^{2} b^{2} c^{2} + B a^{2} b c^{3} + C a^{2} c^{4} + {\left(B a b^{4} c + C a b^{3} c^{2} + B a b^{2} c^{3} + C a b c^{4}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{a^{2} - b^{2} - c^{2}} \arctan\left(-\frac{{\left(a b \cos\left(x\right) + a c \sin\left(x\right) + b^{2} + c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}}}{{\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(x\right) + {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(x\right)}\right) - {\left(B a^{6} - 4 \, B a^{4} b^{2} + 2 \, B a^{2} b^{4} + B b^{6}\right)} c + {\left(B a b c^{5} + C a c^{6} + {\left(C a^{3} + 2 \, C a b^{2}\right)} c^{4} + {\left(B a^{3} b + 2 \, B a b^{3}\right)} c^{3} - {\left(2 \, C a^{5} - C a^{3} b^{2} - C a b^{4}\right)} c^{2} - {\left(2 \, B a^{5} b - B a^{3} b^{3} - B a b^{5}\right)} c\right)} \cos\left(x\right) + {\left(2 \, B a^{5} b^{2} - B a^{3} b^{4} - B a b^{6} - B a b^{2} c^{4} - C a b c^{5} - {\left(C a^{3} b + 2 \, C a b^{3}\right)} c^{3} - {\left(B a^{3} b^{2} + 2 \, B a b^{4}\right)} c^{2} + {\left(2 \, C a^{5} b - C a^{3} b^{3} - C a b^{5}\right)} c + {\left(B a^{4} b^{3} + B a^{2} b^{5} - 2 \, B b^{7} + 2 \, B b c^{6} + 2 \, C c^{7} - {\left(C a^{2} - 2 \, C b^{2}\right)} c^{5} - {\left(B a^{2} b - 2 \, B b^{3}\right)} c^{4} - {\left(C a^{4} + 2 \, C b^{4}\right)} c^{3} - {\left(B a^{4} b + 2 \, B b^{5}\right)} c^{2} + {\left(C a^{4} b^{2} + C a^{2} b^{4} - 2 \, C b^{6}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{2 \, {\left(a^{8} b^{2} - 3 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - a^{2} b^{8} - c^{10} + 2 \, {\left(a^{2} - 2 \, b^{2}\right)} c^{8} + {\left(5 \, a^{2} b^{2} - 6 \, b^{4}\right)} c^{6} - {\left(2 \, a^{6} - 3 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + 4 \, b^{6}\right)} c^{4} + {\left(a^{8} - 5 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - a^{2} b^{6} - b^{8}\right)} c^{2} + {\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10} + c^{10} - 3 \, {\left(a^{2} - b^{2}\right)} c^{8} + {\left(3 \, a^{4} - 6 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{6} - {\left(a^{6} - 3 \, a^{4} b^{2} + 2 \, b^{6}\right)} c^{4} - 3 \, {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} c^{2}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{7} b^{3} - 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} - a b^{9} - a b c^{8} + {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} c^{6} - 3 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} c^{4} + {\left(a^{7} b - 6 \, a^{5} b^{3} + 9 \, a^{3} b^{5} - 4 \, a b^{7}\right)} c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a c^{9} - {\left(3 \, a^{3} - 4 \, a b^{2}\right)} c^{7} + 3 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{7} - 6 \, a^{5} b^{2} + 9 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c^{3} - {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} c + {\left(b c^{9} - {\left(3 \, a^{2} b - 4 \, b^{3}\right)} c^{7} + 3 \, {\left(a^{4} b - 3 \, a^{2} b^{3} + 2 \, b^{5}\right)} c^{5} - {\left(a^{6} b - 6 \, a^{4} b^{3} + 9 \, a^{2} b^{5} - 4 \, b^{7}\right)} c^{3} - {\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)}}\right]"," ",0,"[1/4*(2*C*a^6*b - 6*C*a^4*b^3 + 6*C*a^2*b^5 - 2*C*b^7 - 6*C*b*c^6 + 2*B*c^7 - 2*(3*B*a^2 - B*b^2)*c^5 + 2*(4*C*a^2*b - 7*C*b^3)*c^4 + 2*(3*B*a^4 - 5*B*a^2*b^2 - B*b^4)*c^3 - 2*(2*C*a^4*b - 7*C*a^2*b^3 + 5*C*b^5)*c^2 + 4*(2*B*b^2*c^5 + 2*C*b*c^6 - (C*a^2*b - 4*C*b^3)*c^4 - (B*a^2*b^2 - 4*B*b^4)*c^3 - (C*a^4*b + C*a^2*b^3 - 2*C*b^5)*c^2 - (B*a^4*b^2 + B*a^2*b^4 - 2*B*b^6)*c)*cos(x)^2 - 3*(B*a^3*b^3 + C*a^3*b^2*c + B*a*b*c^4 + C*a*c^5 + (C*a^3 + C*a*b^2)*c^3 + (B*a^3*b + B*a*b^3)*c^2 + (B*a*b^5 + C*a*b^4*c - B*a*b*c^4 - C*a*c^5)*cos(x)^2 + 2*(B*a^2*b^4 + C*a^2*b^3*c + B*a^2*b^2*c^2 + C*a^2*b*c^3)*cos(x) + 2*(B*a^2*b^3*c + C*a^2*b^2*c^2 + B*a^2*b*c^3 + C*a^2*c^4 + (B*a*b^4*c + C*a*b^3*c^2 + B*a*b^2*c^3 + C*a*b*c^4)*cos(x))*sin(x))*sqrt(-a^2 + b^2 + c^2)*log((a^2*b^2 - 2*b^4 - c^4 - (a^2 + 3*b^2)*c^2 - (2*a^2*b^2 - b^4 - 2*a^2*c^2 + c^4)*cos(x)^2 - 2*(a*b^3 + a*b*c^2)*cos(x) - 2*(a*b^2*c + a*c^3 - (b*c^3 - (2*a^2*b - b^3)*c)*cos(x))*sin(x) - 2*(2*a*b*c*cos(x)^2 - a*b*c + (b^2*c + c^3)*cos(x) - (b^3 + b*c^2 + (a*b^2 - a*c^2)*cos(x))*sin(x))*sqrt(-a^2 + b^2 + c^2))/(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x))) - 2*(B*a^6 - 4*B*a^4*b^2 + 2*B*a^2*b^4 + B*b^6)*c + 2*(B*a*b*c^5 + C*a*c^6 + (C*a^3 + 2*C*a*b^2)*c^4 + (B*a^3*b + 2*B*a*b^3)*c^3 - (2*C*a^5 - C*a^3*b^2 - C*a*b^4)*c^2 - (2*B*a^5*b - B*a^3*b^3 - B*a*b^5)*c)*cos(x) + 2*(2*B*a^5*b^2 - B*a^3*b^4 - B*a*b^6 - B*a*b^2*c^4 - C*a*b*c^5 - (C*a^3*b + 2*C*a*b^3)*c^3 - (B*a^3*b^2 + 2*B*a*b^4)*c^2 + (2*C*a^5*b - C*a^3*b^3 - C*a*b^5)*c + (B*a^4*b^3 + B*a^2*b^5 - 2*B*b^7 + 2*B*b*c^6 + 2*C*c^7 - (C*a^2 - 2*C*b^2)*c^5 - (B*a^2*b - 2*B*b^3)*c^4 - (C*a^4 + 2*C*b^4)*c^3 - (B*a^4*b + 2*B*b^5)*c^2 + (C*a^4*b^2 + C*a^2*b^4 - 2*C*b^6)*c)*cos(x))*sin(x))/(a^8*b^2 - 3*a^6*b^4 + 3*a^4*b^6 - a^2*b^8 - c^10 + 2*(a^2 - 2*b^2)*c^8 + (5*a^2*b^2 - 6*b^4)*c^6 - (2*a^6 - 3*a^4*b^2 - 3*a^2*b^4 + 4*b^6)*c^4 + (a^8 - 5*a^6*b^2 + 6*a^4*b^4 - a^2*b^6 - b^8)*c^2 + (a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10 + c^10 - 3*(a^2 - b^2)*c^8 + (3*a^4 - 6*a^2*b^2 + 2*b^4)*c^6 - (a^6 - 3*a^4*b^2 + 2*b^6)*c^4 - 3*(a^4*b^4 - 2*a^2*b^6 + b^8)*c^2)*cos(x)^2 + 2*(a^7*b^3 - 3*a^5*b^5 + 3*a^3*b^7 - a*b^9 - a*b*c^8 + (3*a^3*b - 4*a*b^3)*c^6 - 3*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*c^4 + (a^7*b - 6*a^5*b^3 + 9*a^3*b^5 - 4*a*b^7)*c^2)*cos(x) - 2*(a*c^9 - (3*a^3 - 4*a*b^2)*c^7 + 3*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^7 - 6*a^5*b^2 + 9*a^3*b^4 - 4*a*b^6)*c^3 - (a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*c + (b*c^9 - (3*a^2*b - 4*b^3)*c^7 + 3*(a^4*b - 3*a^2*b^3 + 2*b^5)*c^5 - (a^6*b - 6*a^4*b^3 + 9*a^2*b^5 - 4*b^7)*c^3 - (a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*c)*cos(x))*sin(x)), 1/2*(C*a^6*b - 3*C*a^4*b^3 + 3*C*a^2*b^5 - C*b^7 - 3*C*b*c^6 + B*c^7 - (3*B*a^2 - B*b^2)*c^5 + (4*C*a^2*b - 7*C*b^3)*c^4 + (3*B*a^4 - 5*B*a^2*b^2 - B*b^4)*c^3 - (2*C*a^4*b - 7*C*a^2*b^3 + 5*C*b^5)*c^2 + 2*(2*B*b^2*c^5 + 2*C*b*c^6 - (C*a^2*b - 4*C*b^3)*c^4 - (B*a^2*b^2 - 4*B*b^4)*c^3 - (C*a^4*b + C*a^2*b^3 - 2*C*b^5)*c^2 - (B*a^4*b^2 + B*a^2*b^4 - 2*B*b^6)*c)*cos(x)^2 - 3*(B*a^3*b^3 + C*a^3*b^2*c + B*a*b*c^4 + C*a*c^5 + (C*a^3 + C*a*b^2)*c^3 + (B*a^3*b + B*a*b^3)*c^2 + (B*a*b^5 + C*a*b^4*c - B*a*b*c^4 - C*a*c^5)*cos(x)^2 + 2*(B*a^2*b^4 + C*a^2*b^3*c + B*a^2*b^2*c^2 + C*a^2*b*c^3)*cos(x) + 2*(B*a^2*b^3*c + C*a^2*b^2*c^2 + B*a^2*b*c^3 + C*a^2*c^4 + (B*a*b^4*c + C*a*b^3*c^2 + B*a*b^2*c^3 + C*a*b*c^4)*cos(x))*sin(x))*sqrt(a^2 - b^2 - c^2)*arctan(-(a*b*cos(x) + a*c*sin(x) + b^2 + c^2)*sqrt(a^2 - b^2 - c^2)/((c^3 - (a^2 - b^2)*c)*cos(x) + (a^2*b - b^3 - b*c^2)*sin(x))) - (B*a^6 - 4*B*a^4*b^2 + 2*B*a^2*b^4 + B*b^6)*c + (B*a*b*c^5 + C*a*c^6 + (C*a^3 + 2*C*a*b^2)*c^4 + (B*a^3*b + 2*B*a*b^3)*c^3 - (2*C*a^5 - C*a^3*b^2 - C*a*b^4)*c^2 - (2*B*a^5*b - B*a^3*b^3 - B*a*b^5)*c)*cos(x) + (2*B*a^5*b^2 - B*a^3*b^4 - B*a*b^6 - B*a*b^2*c^4 - C*a*b*c^5 - (C*a^3*b + 2*C*a*b^3)*c^3 - (B*a^3*b^2 + 2*B*a*b^4)*c^2 + (2*C*a^5*b - C*a^3*b^3 - C*a*b^5)*c + (B*a^4*b^3 + B*a^2*b^5 - 2*B*b^7 + 2*B*b*c^6 + 2*C*c^7 - (C*a^2 - 2*C*b^2)*c^5 - (B*a^2*b - 2*B*b^3)*c^4 - (C*a^4 + 2*C*b^4)*c^3 - (B*a^4*b + 2*B*b^5)*c^2 + (C*a^4*b^2 + C*a^2*b^4 - 2*C*b^6)*c)*cos(x))*sin(x))/(a^8*b^2 - 3*a^6*b^4 + 3*a^4*b^6 - a^2*b^8 - c^10 + 2*(a^2 - 2*b^2)*c^8 + (5*a^2*b^2 - 6*b^4)*c^6 - (2*a^6 - 3*a^4*b^2 - 3*a^2*b^4 + 4*b^6)*c^4 + (a^8 - 5*a^6*b^2 + 6*a^4*b^4 - a^2*b^6 - b^8)*c^2 + (a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10 + c^10 - 3*(a^2 - b^2)*c^8 + (3*a^4 - 6*a^2*b^2 + 2*b^4)*c^6 - (a^6 - 3*a^4*b^2 + 2*b^6)*c^4 - 3*(a^4*b^4 - 2*a^2*b^6 + b^8)*c^2)*cos(x)^2 + 2*(a^7*b^3 - 3*a^5*b^5 + 3*a^3*b^7 - a*b^9 - a*b*c^8 + (3*a^3*b - 4*a*b^3)*c^6 - 3*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*c^4 + (a^7*b - 6*a^5*b^3 + 9*a^3*b^5 - 4*a*b^7)*c^2)*cos(x) - 2*(a*c^9 - (3*a^3 - 4*a*b^2)*c^7 + 3*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^7 - 6*a^5*b^2 + 9*a^3*b^4 - 4*a*b^6)*c^3 - (a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*c + (b*c^9 - (3*a^2*b - 4*b^3)*c^7 + 3*(a^4*b - 3*a^2*b^3 + 2*b^5)*c^5 - (a^6*b - 6*a^4*b^3 + 9*a^2*b^5 - 4*b^7)*c^3 - (a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*c)*cos(x))*sin(x))]","B",0
548,1,78,0,1.053023," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)+I*b*sin(x)),x, algorithm=""fricas"")","-\frac{{\left({\left(B + i \, C\right)} b^{2} x e^{\left(i \, x\right)} - {\left(i \, B - C\right)} a b - {\left({\left(-i \, B - C\right)} a^{2} + {\left(-i \, B + C\right)} b^{2}\right)} e^{\left(i \, x\right)} \log\left(\frac{b e^{\left(i \, x\right)} + a}{b}\right)\right)} e^{\left(-i \, x\right)}}{2 \, a^{2} b}"," ",0,"-1/2*((B + I*C)*b^2*x*e^(I*x) - (I*B - C)*a*b - ((-I*B - C)*a^2 + (-I*B + C)*b^2)*e^(I*x)*log((b*e^(I*x) + a)/b))*e^(-I*x)/(a^2*b)","A",0
549,1,68,0,0.959157," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)-I*b*sin(x)),x, algorithm=""fricas"")","\frac{{\left(B + i \, C\right)} a^{2} x + {\left(-i \, B - C\right)} a b e^{\left(i \, x\right)} + {\left({\left(i \, B - C\right)} a^{2} + {\left(i \, B + C\right)} b^{2}\right)} \log\left(\frac{a e^{\left(i \, x\right)} + b}{a}\right)}{2 \, a^{2} b}"," ",0,"1/2*((B + I*C)*a^2*x + (-I*B - C)*a*b*e^(I*x) + ((I*B - C)*a^2 + (I*B + C)*b^2)*log((a*e^(I*x) + b)/a))/(a^2*b)","A",0
550,1,711,0,1.845064," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x)),x, algorithm=""fricas"")","\left[-\frac{{\left(B a b - A b^{2} + C a c - A c^{2}\right)} \sqrt{-a^{2} + b^{2} + c^{2}} \log\left(\frac{a^{2} b^{2} - 2 \, b^{4} - c^{4} - {\left(a^{2} + 3 \, b^{2}\right)} c^{2} - {\left(2 \, a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \cos\left(x\right)^{2} - 2 \, {\left(a b^{3} + a b c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a b^{2} c + a c^{3} - {\left(b c^{3} - {\left(2 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right) - 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(b^{2} c + c^{3}\right)} \cos\left(x\right) - {\left(b^{3} + b c^{2} + {\left(a b^{2} - a c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}}}{2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)}\right) - 2 \, {\left(B a^{2} b - B b^{3} - B b c^{2} - C c^{3} + {\left(C a^{2} - C b^{2}\right)} c\right)} x + {\left(C a^{2} b - C b^{3} - C b c^{2} + B c^{3} - {\left(B a^{2} - B b^{2}\right)} c\right)} \log\left(2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)\right)}{2 \, {\left(a^{2} b^{2} - b^{4} - c^{4} + {\left(a^{2} - 2 \, b^{2}\right)} c^{2}\right)}}, -\frac{2 \, {\left(B a b - A b^{2} + C a c - A c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}} \arctan\left(-\frac{{\left(a b \cos\left(x\right) + a c \sin\left(x\right) + b^{2} + c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}}}{{\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(x\right) + {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(x\right)}\right) - 2 \, {\left(B a^{2} b - B b^{3} - B b c^{2} - C c^{3} + {\left(C a^{2} - C b^{2}\right)} c\right)} x + {\left(C a^{2} b - C b^{3} - C b c^{2} + B c^{3} - {\left(B a^{2} - B b^{2}\right)} c\right)} \log\left(2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)\right)}{2 \, {\left(a^{2} b^{2} - b^{4} - c^{4} + {\left(a^{2} - 2 \, b^{2}\right)} c^{2}\right)}}\right]"," ",0,"[-1/2*((B*a*b - A*b^2 + C*a*c - A*c^2)*sqrt(-a^2 + b^2 + c^2)*log((a^2*b^2 - 2*b^4 - c^4 - (a^2 + 3*b^2)*c^2 - (2*a^2*b^2 - b^4 - 2*a^2*c^2 + c^4)*cos(x)^2 - 2*(a*b^3 + a*b*c^2)*cos(x) - 2*(a*b^2*c + a*c^3 - (b*c^3 - (2*a^2*b - b^3)*c)*cos(x))*sin(x) - 2*(2*a*b*c*cos(x)^2 - a*b*c + (b^2*c + c^3)*cos(x) - (b^3 + b*c^2 + (a*b^2 - a*c^2)*cos(x))*sin(x))*sqrt(-a^2 + b^2 + c^2))/(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x))) - 2*(B*a^2*b - B*b^3 - B*b*c^2 - C*c^3 + (C*a^2 - C*b^2)*c)*x + (C*a^2*b - C*b^3 - C*b*c^2 + B*c^3 - (B*a^2 - B*b^2)*c)*log(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x)))/(a^2*b^2 - b^4 - c^4 + (a^2 - 2*b^2)*c^2), -1/2*(2*(B*a*b - A*b^2 + C*a*c - A*c^2)*sqrt(a^2 - b^2 - c^2)*arctan(-(a*b*cos(x) + a*c*sin(x) + b^2 + c^2)*sqrt(a^2 - b^2 - c^2)/((c^3 - (a^2 - b^2)*c)*cos(x) + (a^2*b - b^3 - b*c^2)*sin(x))) - 2*(B*a^2*b - B*b^3 - B*b*c^2 - C*c^3 + (C*a^2 - C*b^2)*c)*x + (C*a^2*b - C*b^3 - C*b*c^2 + B*c^3 - (B*a^2 - B*b^2)*c)*log(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x)))/(a^2*b^2 - b^4 - c^4 + (a^2 - 2*b^2)*c^2)]","B",0
551,1,1556,0,2.176761," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^2,x, algorithm=""fricas"")","\left[\frac{2 \, C a^{4} b - 4 \, C a^{2} b^{3} + 2 \, C b^{5} + 2 \, C b c^{4} - 2 \, B c^{5} + 4 \, {\left(B a^{2} - B b^{2}\right)} c^{3} - 4 \, {\left(C a^{2} b - C b^{3}\right)} c^{2} - {\left(A a^{2} b^{2} - B a b^{3} - C a b^{2} c - C a c^{3} + {\left(A a^{2} - B a b\right)} c^{2} + {\left(A a b^{3} - B b^{4} - C b^{3} c - C b c^{3} + {\left(A a b - B b^{2}\right)} c^{2}\right)} \cos\left(x\right) - {\left(C b^{2} c^{2} + C c^{4} - {\left(A a - B b\right)} c^{3} - {\left(A a b^{2} - B b^{3}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}} \log\left(-\frac{a^{2} b^{2} - 2 \, b^{4} - c^{4} - {\left(a^{2} + 3 \, b^{2}\right)} c^{2} - {\left(2 \, a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \cos\left(x\right)^{2} - 2 \, {\left(a b^{3} + a b c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a b^{2} c + a c^{3} - {\left(b c^{3} - {\left(2 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right) + 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(b^{2} c + c^{3}\right)} \cos\left(x\right) - {\left(b^{3} + b c^{2} + {\left(a b^{2} - a c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}}}{2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)}\right) - 2 \, {\left(B a^{4} - 2 \, B a^{2} b^{2} + B b^{4}\right)} c + 2 \, {\left(C a c^{4} - A c^{5} + {\left(A a^{2} + B a b - 2 \, A b^{2}\right)} c^{3} - {\left(C a^{3} - C a b^{2}\right)} c^{2} - {\left(B a^{3} b - A a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c\right)} \cos\left(x\right) + 2 \, {\left(B a^{3} b^{2} - A a^{2} b^{3} - B a b^{4} + A b^{5} - C a b c^{3} + A b c^{4} - {\left(A a^{2} b + B a b^{2} - 2 \, A b^{3}\right)} c^{2} + {\left(C a^{3} b - C a b^{3}\right)} c\right)} \sin\left(x\right)}{2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6} + a c^{6} - {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{4} + {\left(a^{5} - 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c^{2} + {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7} + b c^{6} - {\left(2 \, a^{2} b - 3 \, b^{3}\right)} c^{4} + {\left(a^{4} b - 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} c^{2}\right)} \cos\left(x\right) + {\left(c^{7} - {\left(2 \, a^{2} - 3 \, b^{2}\right)} c^{5} + {\left(a^{4} - 4 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{3} + {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c\right)} \sin\left(x\right)\right)}}, \frac{C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5} + C b c^{4} - B c^{5} + 2 \, {\left(B a^{2} - B b^{2}\right)} c^{3} - 2 \, {\left(C a^{2} b - C b^{3}\right)} c^{2} + {\left(A a^{2} b^{2} - B a b^{3} - C a b^{2} c - C a c^{3} + {\left(A a^{2} - B a b\right)} c^{2} + {\left(A a b^{3} - B b^{4} - C b^{3} c - C b c^{3} + {\left(A a b - B b^{2}\right)} c^{2}\right)} \cos\left(x\right) - {\left(C b^{2} c^{2} + C c^{4} - {\left(A a - B b\right)} c^{3} - {\left(A a b^{2} - B b^{3}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{a^{2} - b^{2} - c^{2}} \arctan\left(-\frac{{\left(a b \cos\left(x\right) + a c \sin\left(x\right) + b^{2} + c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}}}{{\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(x\right) + {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(x\right)}\right) - {\left(B a^{4} - 2 \, B a^{2} b^{2} + B b^{4}\right)} c + {\left(C a c^{4} - A c^{5} + {\left(A a^{2} + B a b - 2 \, A b^{2}\right)} c^{3} - {\left(C a^{3} - C a b^{2}\right)} c^{2} - {\left(B a^{3} b - A a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c\right)} \cos\left(x\right) + {\left(B a^{3} b^{2} - A a^{2} b^{3} - B a b^{4} + A b^{5} - C a b c^{3} + A b c^{4} - {\left(A a^{2} b + B a b^{2} - 2 \, A b^{3}\right)} c^{2} + {\left(C a^{3} b - C a b^{3}\right)} c\right)} \sin\left(x\right)}{a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6} + a c^{6} - {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{4} + {\left(a^{5} - 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c^{2} + {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7} + b c^{6} - {\left(2 \, a^{2} b - 3 \, b^{3}\right)} c^{4} + {\left(a^{4} b - 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} c^{2}\right)} \cos\left(x\right) + {\left(c^{7} - {\left(2 \, a^{2} - 3 \, b^{2}\right)} c^{5} + {\left(a^{4} - 4 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{3} + {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c\right)} \sin\left(x\right)}\right]"," ",0,"[1/2*(2*C*a^4*b - 4*C*a^2*b^3 + 2*C*b^5 + 2*C*b*c^4 - 2*B*c^5 + 4*(B*a^2 - B*b^2)*c^3 - 4*(C*a^2*b - C*b^3)*c^2 - (A*a^2*b^2 - B*a*b^3 - C*a*b^2*c - C*a*c^3 + (A*a^2 - B*a*b)*c^2 + (A*a*b^3 - B*b^4 - C*b^3*c - C*b*c^3 + (A*a*b - B*b^2)*c^2)*cos(x) - (C*b^2*c^2 + C*c^4 - (A*a - B*b)*c^3 - (A*a*b^2 - B*b^3)*c)*sin(x))*sqrt(-a^2 + b^2 + c^2)*log(-(a^2*b^2 - 2*b^4 - c^4 - (a^2 + 3*b^2)*c^2 - (2*a^2*b^2 - b^4 - 2*a^2*c^2 + c^4)*cos(x)^2 - 2*(a*b^3 + a*b*c^2)*cos(x) - 2*(a*b^2*c + a*c^3 - (b*c^3 - (2*a^2*b - b^3)*c)*cos(x))*sin(x) + 2*(2*a*b*c*cos(x)^2 - a*b*c + (b^2*c + c^3)*cos(x) - (b^3 + b*c^2 + (a*b^2 - a*c^2)*cos(x))*sin(x))*sqrt(-a^2 + b^2 + c^2))/(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x))) - 2*(B*a^4 - 2*B*a^2*b^2 + B*b^4)*c + 2*(C*a*c^4 - A*c^5 + (A*a^2 + B*a*b - 2*A*b^2)*c^3 - (C*a^3 - C*a*b^2)*c^2 - (B*a^3*b - A*a^2*b^2 - B*a*b^3 + A*b^4)*c)*cos(x) + 2*(B*a^3*b^2 - A*a^2*b^3 - B*a*b^4 + A*b^5 - C*a*b*c^3 + A*b*c^4 - (A*a^2*b + B*a*b^2 - 2*A*b^3)*c^2 + (C*a^3*b - C*a*b^3)*c)*sin(x))/(a^5*b^2 - 2*a^3*b^4 + a*b^6 + a*c^6 - (2*a^3 - 3*a*b^2)*c^4 + (a^5 - 4*a^3*b^2 + 3*a*b^4)*c^2 + (a^4*b^3 - 2*a^2*b^5 + b^7 + b*c^6 - (2*a^2*b - 3*b^3)*c^4 + (a^4*b - 4*a^2*b^3 + 3*b^5)*c^2)*cos(x) + (c^7 - (2*a^2 - 3*b^2)*c^5 + (a^4 - 4*a^2*b^2 + 3*b^4)*c^3 + (a^4*b^2 - 2*a^2*b^4 + b^6)*c)*sin(x)), (C*a^4*b - 2*C*a^2*b^3 + C*b^5 + C*b*c^4 - B*c^5 + 2*(B*a^2 - B*b^2)*c^3 - 2*(C*a^2*b - C*b^3)*c^2 + (A*a^2*b^2 - B*a*b^3 - C*a*b^2*c - C*a*c^3 + (A*a^2 - B*a*b)*c^2 + (A*a*b^3 - B*b^4 - C*b^3*c - C*b*c^3 + (A*a*b - B*b^2)*c^2)*cos(x) - (C*b^2*c^2 + C*c^4 - (A*a - B*b)*c^3 - (A*a*b^2 - B*b^3)*c)*sin(x))*sqrt(a^2 - b^2 - c^2)*arctan(-(a*b*cos(x) + a*c*sin(x) + b^2 + c^2)*sqrt(a^2 - b^2 - c^2)/((c^3 - (a^2 - b^2)*c)*cos(x) + (a^2*b - b^3 - b*c^2)*sin(x))) - (B*a^4 - 2*B*a^2*b^2 + B*b^4)*c + (C*a*c^4 - A*c^5 + (A*a^2 + B*a*b - 2*A*b^2)*c^3 - (C*a^3 - C*a*b^2)*c^2 - (B*a^3*b - A*a^2*b^2 - B*a*b^3 + A*b^4)*c)*cos(x) + (B*a^3*b^2 - A*a^2*b^3 - B*a*b^4 + A*b^5 - C*a*b*c^3 + A*b*c^4 - (A*a^2*b + B*a*b^2 - 2*A*b^3)*c^2 + (C*a^3*b - C*a*b^3)*c)*sin(x))/(a^5*b^2 - 2*a^3*b^4 + a*b^6 + a*c^6 - (2*a^3 - 3*a*b^2)*c^4 + (a^5 - 4*a^3*b^2 + 3*a*b^4)*c^2 + (a^4*b^3 - 2*a^2*b^5 + b^7 + b*c^6 - (2*a^2*b - 3*b^3)*c^4 + (a^4*b - 4*a^2*b^3 + 3*b^5)*c^2)*cos(x) + (c^7 - (2*a^2 - 3*b^2)*c^5 + (a^4 - 4*a^2*b^2 + 3*b^4)*c^3 + (a^4*b^2 - 2*a^2*b^4 + b^6)*c)*sin(x))]","B",0
552,1,4240,0,1.619749," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^3,x, algorithm=""fricas"")","\left[\frac{2 \, C a^{6} b - 6 \, C a^{4} b^{3} + 6 \, C a^{2} b^{5} - 2 \, C b^{7} - 6 \, C b c^{6} + 2 \, B c^{7} - 2 \, {\left(3 \, B a^{2} - 3 \, A a b - B b^{2}\right)} c^{5} + 2 \, {\left(4 \, C a^{2} b - 7 \, C b^{3}\right)} c^{4} + 2 \, {\left(3 \, B a^{4} - 3 \, A a^{3} b - 5 \, B a^{2} b^{2} + 6 \, A a b^{3} - B b^{4}\right)} c^{3} - 2 \, {\left(2 \, C a^{4} b - 7 \, C a^{2} b^{3} + 5 \, C b^{5}\right)} c^{2} + 4 \, {\left(2 \, C b c^{6} - {\left(3 \, A a b - 2 \, B b^{2}\right)} c^{5} - {\left(C a^{2} b - 4 \, C b^{3}\right)} c^{4} + {\left(3 \, A a^{3} b - B a^{2} b^{2} - 6 \, A a b^{3} + 4 \, B b^{4}\right)} c^{3} - {\left(C a^{4} b + C a^{2} b^{3} - 2 \, C b^{5}\right)} c^{2} - {\left(B a^{4} b^{2} - 3 \, A a^{3} b^{3} + B a^{2} b^{4} + 3 \, A a b^{5} - 2 \, B b^{6}\right)} c\right)} \cos\left(x\right)^{2} - {\left(2 \, A a^{4} b^{2} - 3 \, B a^{3} b^{3} + A a^{2} b^{4} - 3 \, C a^{3} b^{2} c - 3 \, C a c^{5} + A c^{6} + {\left(3 \, A a^{2} - 3 \, B a b + 2 \, A b^{2}\right)} c^{4} - 3 \, {\left(C a^{3} + C a b^{2}\right)} c^{3} + {\left(2 \, A a^{4} - 3 \, B a^{3} b + 4 \, A a^{2} b^{2} - 3 \, B a b^{3} + A b^{4}\right)} c^{2} + {\left(2 \, A a^{2} b^{4} - 3 \, B a b^{5} + A b^{6} - 3 \, C a b^{4} c + A b^{4} c^{2} + 3 \, C a c^{5} - A c^{6} - {\left(2 \, A a^{2} - 3 \, B a b + A b^{2}\right)} c^{4}\right)} \cos\left(x\right)^{2} + 2 \, {\left(2 \, A a^{3} b^{3} - 3 \, B a^{2} b^{4} + A a b^{5} - 3 \, C a^{2} b^{3} c - 3 \, C a^{2} b c^{3} + A a b c^{4} + {\left(2 \, A a^{3} b - 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} c^{2}\right)} \cos\left(x\right) - 2 \, {\left(3 \, C a^{2} b^{2} c^{2} + 3 \, C a^{2} c^{4} - A a c^{5} - {\left(2 \, A a^{3} - 3 \, B a^{2} b + 2 \, A a b^{2}\right)} c^{3} - {\left(2 \, A a^{3} b^{2} - 3 \, B a^{2} b^{3} + A a b^{4}\right)} c + {\left(3 \, C a b^{3} c^{2} + 3 \, C a b c^{4} - A b c^{5} - {\left(2 \, A a^{2} b - 3 \, B a b^{2} + 2 \, A b^{3}\right)} c^{3} - {\left(2 \, A a^{2} b^{3} - 3 \, B a b^{4} + A b^{5}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}} \log\left(-\frac{a^{2} b^{2} - 2 \, b^{4} - c^{4} - {\left(a^{2} + 3 \, b^{2}\right)} c^{2} - {\left(2 \, a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \cos\left(x\right)^{2} - 2 \, {\left(a b^{3} + a b c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a b^{2} c + a c^{3} - {\left(b c^{3} - {\left(2 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right) + 2 \, {\left(2 \, a b c \cos\left(x\right)^{2} - a b c + {\left(b^{2} c + c^{3}\right)} \cos\left(x\right) - {\left(b^{3} + b c^{2} + {\left(a b^{2} - a c^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-a^{2} + b^{2} + c^{2}}}{2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)}\right) - 2 \, {\left(B a^{6} - 4 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3} + 2 \, B a^{2} b^{4} - 3 \, A a b^{5} + B b^{6}\right)} c + 2 \, {\left(C a c^{6} + A c^{7} - {\left(5 \, A a^{2} - B a b - 3 \, A b^{2}\right)} c^{5} + {\left(C a^{3} + 2 \, C a b^{2}\right)} c^{4} + {\left(4 \, A a^{4} + B a^{3} b - 10 \, A a^{2} b^{2} + 2 \, B a b^{3} + 3 \, A b^{4}\right)} c^{3} - {\left(2 \, C a^{5} - C a^{3} b^{2} - C a b^{4}\right)} c^{2} - {\left(2 \, B a^{5} b - 4 \, A a^{4} b^{2} - B a^{3} b^{3} + 5 \, A a^{2} b^{4} - B a b^{5} - A b^{6}\right)} c\right)} \cos\left(x\right) + 2 \, {\left(2 \, B a^{5} b^{2} - 4 \, A a^{4} b^{3} - B a^{3} b^{4} + 5 \, A a^{2} b^{5} - B a b^{6} - A b^{7} - C a b c^{5} - A b c^{6} + {\left(5 \, A a^{2} b - B a b^{2} - 3 \, A b^{3}\right)} c^{4} - {\left(C a^{3} b + 2 \, C a b^{3}\right)} c^{3} - {\left(4 \, A a^{4} b + B a^{3} b^{2} - 10 \, A a^{2} b^{3} + 2 \, B a b^{4} + 3 \, A b^{5}\right)} c^{2} + {\left(2 \, C a^{5} b - C a^{3} b^{3} - C a b^{5}\right)} c + {\left(B a^{4} b^{3} - 3 \, A a^{3} b^{4} + B a^{2} b^{5} + 3 \, A a b^{6} - 2 \, B b^{7} + 2 \, C c^{7} - {\left(3 \, A a - 2 \, B b\right)} c^{6} - {\left(C a^{2} - 2 \, C b^{2}\right)} c^{5} + {\left(3 \, A a^{3} - B a^{2} b - 3 \, A a b^{2} + 2 \, B b^{3}\right)} c^{4} - {\left(C a^{4} + 2 \, C b^{4}\right)} c^{3} - {\left(B a^{4} b - 3 \, A a b^{4} + 2 \, B b^{5}\right)} c^{2} + {\left(C a^{4} b^{2} + C a^{2} b^{4} - 2 \, C b^{6}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{4 \, {\left(a^{8} b^{2} - 3 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - a^{2} b^{8} - c^{10} + 2 \, {\left(a^{2} - 2 \, b^{2}\right)} c^{8} + {\left(5 \, a^{2} b^{2} - 6 \, b^{4}\right)} c^{6} - {\left(2 \, a^{6} - 3 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + 4 \, b^{6}\right)} c^{4} + {\left(a^{8} - 5 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - a^{2} b^{6} - b^{8}\right)} c^{2} + {\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10} + c^{10} - 3 \, {\left(a^{2} - b^{2}\right)} c^{8} + {\left(3 \, a^{4} - 6 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{6} - {\left(a^{6} - 3 \, a^{4} b^{2} + 2 \, b^{6}\right)} c^{4} - 3 \, {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} c^{2}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{7} b^{3} - 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} - a b^{9} - a b c^{8} + {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} c^{6} - 3 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} c^{4} + {\left(a^{7} b - 6 \, a^{5} b^{3} + 9 \, a^{3} b^{5} - 4 \, a b^{7}\right)} c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a c^{9} - {\left(3 \, a^{3} - 4 \, a b^{2}\right)} c^{7} + 3 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{7} - 6 \, a^{5} b^{2} + 9 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c^{3} - {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} c + {\left(b c^{9} - {\left(3 \, a^{2} b - 4 \, b^{3}\right)} c^{7} + 3 \, {\left(a^{4} b - 3 \, a^{2} b^{3} + 2 \, b^{5}\right)} c^{5} - {\left(a^{6} b - 6 \, a^{4} b^{3} + 9 \, a^{2} b^{5} - 4 \, b^{7}\right)} c^{3} - {\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)}}, \frac{C a^{6} b - 3 \, C a^{4} b^{3} + 3 \, C a^{2} b^{5} - C b^{7} - 3 \, C b c^{6} + B c^{7} - {\left(3 \, B a^{2} - 3 \, A a b - B b^{2}\right)} c^{5} + {\left(4 \, C a^{2} b - 7 \, C b^{3}\right)} c^{4} + {\left(3 \, B a^{4} - 3 \, A a^{3} b - 5 \, B a^{2} b^{2} + 6 \, A a b^{3} - B b^{4}\right)} c^{3} - {\left(2 \, C a^{4} b - 7 \, C a^{2} b^{3} + 5 \, C b^{5}\right)} c^{2} + 2 \, {\left(2 \, C b c^{6} - {\left(3 \, A a b - 2 \, B b^{2}\right)} c^{5} - {\left(C a^{2} b - 4 \, C b^{3}\right)} c^{4} + {\left(3 \, A a^{3} b - B a^{2} b^{2} - 6 \, A a b^{3} + 4 \, B b^{4}\right)} c^{3} - {\left(C a^{4} b + C a^{2} b^{3} - 2 \, C b^{5}\right)} c^{2} - {\left(B a^{4} b^{2} - 3 \, A a^{3} b^{3} + B a^{2} b^{4} + 3 \, A a b^{5} - 2 \, B b^{6}\right)} c\right)} \cos\left(x\right)^{2} + {\left(2 \, A a^{4} b^{2} - 3 \, B a^{3} b^{3} + A a^{2} b^{4} - 3 \, C a^{3} b^{2} c - 3 \, C a c^{5} + A c^{6} + {\left(3 \, A a^{2} - 3 \, B a b + 2 \, A b^{2}\right)} c^{4} - 3 \, {\left(C a^{3} + C a b^{2}\right)} c^{3} + {\left(2 \, A a^{4} - 3 \, B a^{3} b + 4 \, A a^{2} b^{2} - 3 \, B a b^{3} + A b^{4}\right)} c^{2} + {\left(2 \, A a^{2} b^{4} - 3 \, B a b^{5} + A b^{6} - 3 \, C a b^{4} c + A b^{4} c^{2} + 3 \, C a c^{5} - A c^{6} - {\left(2 \, A a^{2} - 3 \, B a b + A b^{2}\right)} c^{4}\right)} \cos\left(x\right)^{2} + 2 \, {\left(2 \, A a^{3} b^{3} - 3 \, B a^{2} b^{4} + A a b^{5} - 3 \, C a^{2} b^{3} c - 3 \, C a^{2} b c^{3} + A a b c^{4} + {\left(2 \, A a^{3} b - 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} c^{2}\right)} \cos\left(x\right) - 2 \, {\left(3 \, C a^{2} b^{2} c^{2} + 3 \, C a^{2} c^{4} - A a c^{5} - {\left(2 \, A a^{3} - 3 \, B a^{2} b + 2 \, A a b^{2}\right)} c^{3} - {\left(2 \, A a^{3} b^{2} - 3 \, B a^{2} b^{3} + A a b^{4}\right)} c + {\left(3 \, C a b^{3} c^{2} + 3 \, C a b c^{4} - A b c^{5} - {\left(2 \, A a^{2} b - 3 \, B a b^{2} + 2 \, A b^{3}\right)} c^{3} - {\left(2 \, A a^{2} b^{3} - 3 \, B a b^{4} + A b^{5}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{a^{2} - b^{2} - c^{2}} \arctan\left(-\frac{{\left(a b \cos\left(x\right) + a c \sin\left(x\right) + b^{2} + c^{2}\right)} \sqrt{a^{2} - b^{2} - c^{2}}}{{\left(c^{3} - {\left(a^{2} - b^{2}\right)} c\right)} \cos\left(x\right) + {\left(a^{2} b - b^{3} - b c^{2}\right)} \sin\left(x\right)}\right) - {\left(B a^{6} - 4 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3} + 2 \, B a^{2} b^{4} - 3 \, A a b^{5} + B b^{6}\right)} c + {\left(C a c^{6} + A c^{7} - {\left(5 \, A a^{2} - B a b - 3 \, A b^{2}\right)} c^{5} + {\left(C a^{3} + 2 \, C a b^{2}\right)} c^{4} + {\left(4 \, A a^{4} + B a^{3} b - 10 \, A a^{2} b^{2} + 2 \, B a b^{3} + 3 \, A b^{4}\right)} c^{3} - {\left(2 \, C a^{5} - C a^{3} b^{2} - C a b^{4}\right)} c^{2} - {\left(2 \, B a^{5} b - 4 \, A a^{4} b^{2} - B a^{3} b^{3} + 5 \, A a^{2} b^{4} - B a b^{5} - A b^{6}\right)} c\right)} \cos\left(x\right) + {\left(2 \, B a^{5} b^{2} - 4 \, A a^{4} b^{3} - B a^{3} b^{4} + 5 \, A a^{2} b^{5} - B a b^{6} - A b^{7} - C a b c^{5} - A b c^{6} + {\left(5 \, A a^{2} b - B a b^{2} - 3 \, A b^{3}\right)} c^{4} - {\left(C a^{3} b + 2 \, C a b^{3}\right)} c^{3} - {\left(4 \, A a^{4} b + B a^{3} b^{2} - 10 \, A a^{2} b^{3} + 2 \, B a b^{4} + 3 \, A b^{5}\right)} c^{2} + {\left(2 \, C a^{5} b - C a^{3} b^{3} - C a b^{5}\right)} c + {\left(B a^{4} b^{3} - 3 \, A a^{3} b^{4} + B a^{2} b^{5} + 3 \, A a b^{6} - 2 \, B b^{7} + 2 \, C c^{7} - {\left(3 \, A a - 2 \, B b\right)} c^{6} - {\left(C a^{2} - 2 \, C b^{2}\right)} c^{5} + {\left(3 \, A a^{3} - B a^{2} b - 3 \, A a b^{2} + 2 \, B b^{3}\right)} c^{4} - {\left(C a^{4} + 2 \, C b^{4}\right)} c^{3} - {\left(B a^{4} b - 3 \, A a b^{4} + 2 \, B b^{5}\right)} c^{2} + {\left(C a^{4} b^{2} + C a^{2} b^{4} - 2 \, C b^{6}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{2 \, {\left(a^{8} b^{2} - 3 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - a^{2} b^{8} - c^{10} + 2 \, {\left(a^{2} - 2 \, b^{2}\right)} c^{8} + {\left(5 \, a^{2} b^{2} - 6 \, b^{4}\right)} c^{6} - {\left(2 \, a^{6} - 3 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + 4 \, b^{6}\right)} c^{4} + {\left(a^{8} - 5 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - a^{2} b^{6} - b^{8}\right)} c^{2} + {\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10} + c^{10} - 3 \, {\left(a^{2} - b^{2}\right)} c^{8} + {\left(3 \, a^{4} - 6 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{6} - {\left(a^{6} - 3 \, a^{4} b^{2} + 2 \, b^{6}\right)} c^{4} - 3 \, {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} c^{2}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{7} b^{3} - 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} - a b^{9} - a b c^{8} + {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} c^{6} - 3 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} c^{4} + {\left(a^{7} b - 6 \, a^{5} b^{3} + 9 \, a^{3} b^{5} - 4 \, a b^{7}\right)} c^{2}\right)} \cos\left(x\right) - 2 \, {\left(a c^{9} - {\left(3 \, a^{3} - 4 \, a b^{2}\right)} c^{7} + 3 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{7} - 6 \, a^{5} b^{2} + 9 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c^{3} - {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} c + {\left(b c^{9} - {\left(3 \, a^{2} b - 4 \, b^{3}\right)} c^{7} + 3 \, {\left(a^{4} b - 3 \, a^{2} b^{3} + 2 \, b^{5}\right)} c^{5} - {\left(a^{6} b - 6 \, a^{4} b^{3} + 9 \, a^{2} b^{5} - 4 \, b^{7}\right)} c^{3} - {\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} c\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)}}\right]"," ",0,"[1/4*(2*C*a^6*b - 6*C*a^4*b^3 + 6*C*a^2*b^5 - 2*C*b^7 - 6*C*b*c^6 + 2*B*c^7 - 2*(3*B*a^2 - 3*A*a*b - B*b^2)*c^5 + 2*(4*C*a^2*b - 7*C*b^3)*c^4 + 2*(3*B*a^4 - 3*A*a^3*b - 5*B*a^2*b^2 + 6*A*a*b^3 - B*b^4)*c^3 - 2*(2*C*a^4*b - 7*C*a^2*b^3 + 5*C*b^5)*c^2 + 4*(2*C*b*c^6 - (3*A*a*b - 2*B*b^2)*c^5 - (C*a^2*b - 4*C*b^3)*c^4 + (3*A*a^3*b - B*a^2*b^2 - 6*A*a*b^3 + 4*B*b^4)*c^3 - (C*a^4*b + C*a^2*b^3 - 2*C*b^5)*c^2 - (B*a^4*b^2 - 3*A*a^3*b^3 + B*a^2*b^4 + 3*A*a*b^5 - 2*B*b^6)*c)*cos(x)^2 - (2*A*a^4*b^2 - 3*B*a^3*b^3 + A*a^2*b^4 - 3*C*a^3*b^2*c - 3*C*a*c^5 + A*c^6 + (3*A*a^2 - 3*B*a*b + 2*A*b^2)*c^4 - 3*(C*a^3 + C*a*b^2)*c^3 + (2*A*a^4 - 3*B*a^3*b + 4*A*a^2*b^2 - 3*B*a*b^3 + A*b^4)*c^2 + (2*A*a^2*b^4 - 3*B*a*b^5 + A*b^6 - 3*C*a*b^4*c + A*b^4*c^2 + 3*C*a*c^5 - A*c^6 - (2*A*a^2 - 3*B*a*b + A*b^2)*c^4)*cos(x)^2 + 2*(2*A*a^3*b^3 - 3*B*a^2*b^4 + A*a*b^5 - 3*C*a^2*b^3*c - 3*C*a^2*b*c^3 + A*a*b*c^4 + (2*A*a^3*b - 3*B*a^2*b^2 + 2*A*a*b^3)*c^2)*cos(x) - 2*(3*C*a^2*b^2*c^2 + 3*C*a^2*c^4 - A*a*c^5 - (2*A*a^3 - 3*B*a^2*b + 2*A*a*b^2)*c^3 - (2*A*a^3*b^2 - 3*B*a^2*b^3 + A*a*b^4)*c + (3*C*a*b^3*c^2 + 3*C*a*b*c^4 - A*b*c^5 - (2*A*a^2*b - 3*B*a*b^2 + 2*A*b^3)*c^3 - (2*A*a^2*b^3 - 3*B*a*b^4 + A*b^5)*c)*cos(x))*sin(x))*sqrt(-a^2 + b^2 + c^2)*log(-(a^2*b^2 - 2*b^4 - c^4 - (a^2 + 3*b^2)*c^2 - (2*a^2*b^2 - b^4 - 2*a^2*c^2 + c^4)*cos(x)^2 - 2*(a*b^3 + a*b*c^2)*cos(x) - 2*(a*b^2*c + a*c^3 - (b*c^3 - (2*a^2*b - b^3)*c)*cos(x))*sin(x) + 2*(2*a*b*c*cos(x)^2 - a*b*c + (b^2*c + c^3)*cos(x) - (b^3 + b*c^2 + (a*b^2 - a*c^2)*cos(x))*sin(x))*sqrt(-a^2 + b^2 + c^2))/(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x))) - 2*(B*a^6 - 4*B*a^4*b^2 + 3*A*a^3*b^3 + 2*B*a^2*b^4 - 3*A*a*b^5 + B*b^6)*c + 2*(C*a*c^6 + A*c^7 - (5*A*a^2 - B*a*b - 3*A*b^2)*c^5 + (C*a^3 + 2*C*a*b^2)*c^4 + (4*A*a^4 + B*a^3*b - 10*A*a^2*b^2 + 2*B*a*b^3 + 3*A*b^4)*c^3 - (2*C*a^5 - C*a^3*b^2 - C*a*b^4)*c^2 - (2*B*a^5*b - 4*A*a^4*b^2 - B*a^3*b^3 + 5*A*a^2*b^4 - B*a*b^5 - A*b^6)*c)*cos(x) + 2*(2*B*a^5*b^2 - 4*A*a^4*b^3 - B*a^3*b^4 + 5*A*a^2*b^5 - B*a*b^6 - A*b^7 - C*a*b*c^5 - A*b*c^6 + (5*A*a^2*b - B*a*b^2 - 3*A*b^3)*c^4 - (C*a^3*b + 2*C*a*b^3)*c^3 - (4*A*a^4*b + B*a^3*b^2 - 10*A*a^2*b^3 + 2*B*a*b^4 + 3*A*b^5)*c^2 + (2*C*a^5*b - C*a^3*b^3 - C*a*b^5)*c + (B*a^4*b^3 - 3*A*a^3*b^4 + B*a^2*b^5 + 3*A*a*b^6 - 2*B*b^7 + 2*C*c^7 - (3*A*a - 2*B*b)*c^6 - (C*a^2 - 2*C*b^2)*c^5 + (3*A*a^3 - B*a^2*b - 3*A*a*b^2 + 2*B*b^3)*c^4 - (C*a^4 + 2*C*b^4)*c^3 - (B*a^4*b - 3*A*a*b^4 + 2*B*b^5)*c^2 + (C*a^4*b^2 + C*a^2*b^4 - 2*C*b^6)*c)*cos(x))*sin(x))/(a^8*b^2 - 3*a^6*b^4 + 3*a^4*b^6 - a^2*b^8 - c^10 + 2*(a^2 - 2*b^2)*c^8 + (5*a^2*b^2 - 6*b^4)*c^6 - (2*a^6 - 3*a^4*b^2 - 3*a^2*b^4 + 4*b^6)*c^4 + (a^8 - 5*a^6*b^2 + 6*a^4*b^4 - a^2*b^6 - b^8)*c^2 + (a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10 + c^10 - 3*(a^2 - b^2)*c^8 + (3*a^4 - 6*a^2*b^2 + 2*b^4)*c^6 - (a^6 - 3*a^4*b^2 + 2*b^6)*c^4 - 3*(a^4*b^4 - 2*a^2*b^6 + b^8)*c^2)*cos(x)^2 + 2*(a^7*b^3 - 3*a^5*b^5 + 3*a^3*b^7 - a*b^9 - a*b*c^8 + (3*a^3*b - 4*a*b^3)*c^6 - 3*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*c^4 + (a^7*b - 6*a^5*b^3 + 9*a^3*b^5 - 4*a*b^7)*c^2)*cos(x) - 2*(a*c^9 - (3*a^3 - 4*a*b^2)*c^7 + 3*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^7 - 6*a^5*b^2 + 9*a^3*b^4 - 4*a*b^6)*c^3 - (a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*c + (b*c^9 - (3*a^2*b - 4*b^3)*c^7 + 3*(a^4*b - 3*a^2*b^3 + 2*b^5)*c^5 - (a^6*b - 6*a^4*b^3 + 9*a^2*b^5 - 4*b^7)*c^3 - (a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*c)*cos(x))*sin(x)), 1/2*(C*a^6*b - 3*C*a^4*b^3 + 3*C*a^2*b^5 - C*b^7 - 3*C*b*c^6 + B*c^7 - (3*B*a^2 - 3*A*a*b - B*b^2)*c^5 + (4*C*a^2*b - 7*C*b^3)*c^4 + (3*B*a^4 - 3*A*a^3*b - 5*B*a^2*b^2 + 6*A*a*b^3 - B*b^4)*c^3 - (2*C*a^4*b - 7*C*a^2*b^3 + 5*C*b^5)*c^2 + 2*(2*C*b*c^6 - (3*A*a*b - 2*B*b^2)*c^5 - (C*a^2*b - 4*C*b^3)*c^4 + (3*A*a^3*b - B*a^2*b^2 - 6*A*a*b^3 + 4*B*b^4)*c^3 - (C*a^4*b + C*a^2*b^3 - 2*C*b^5)*c^2 - (B*a^4*b^2 - 3*A*a^3*b^3 + B*a^2*b^4 + 3*A*a*b^5 - 2*B*b^6)*c)*cos(x)^2 + (2*A*a^4*b^2 - 3*B*a^3*b^3 + A*a^2*b^4 - 3*C*a^3*b^2*c - 3*C*a*c^5 + A*c^6 + (3*A*a^2 - 3*B*a*b + 2*A*b^2)*c^4 - 3*(C*a^3 + C*a*b^2)*c^3 + (2*A*a^4 - 3*B*a^3*b + 4*A*a^2*b^2 - 3*B*a*b^3 + A*b^4)*c^2 + (2*A*a^2*b^4 - 3*B*a*b^5 + A*b^6 - 3*C*a*b^4*c + A*b^4*c^2 + 3*C*a*c^5 - A*c^6 - (2*A*a^2 - 3*B*a*b + A*b^2)*c^4)*cos(x)^2 + 2*(2*A*a^3*b^3 - 3*B*a^2*b^4 + A*a*b^5 - 3*C*a^2*b^3*c - 3*C*a^2*b*c^3 + A*a*b*c^4 + (2*A*a^3*b - 3*B*a^2*b^2 + 2*A*a*b^3)*c^2)*cos(x) - 2*(3*C*a^2*b^2*c^2 + 3*C*a^2*c^4 - A*a*c^5 - (2*A*a^3 - 3*B*a^2*b + 2*A*a*b^2)*c^3 - (2*A*a^3*b^2 - 3*B*a^2*b^3 + A*a*b^4)*c + (3*C*a*b^3*c^2 + 3*C*a*b*c^4 - A*b*c^5 - (2*A*a^2*b - 3*B*a*b^2 + 2*A*b^3)*c^3 - (2*A*a^2*b^3 - 3*B*a*b^4 + A*b^5)*c)*cos(x))*sin(x))*sqrt(a^2 - b^2 - c^2)*arctan(-(a*b*cos(x) + a*c*sin(x) + b^2 + c^2)*sqrt(a^2 - b^2 - c^2)/((c^3 - (a^2 - b^2)*c)*cos(x) + (a^2*b - b^3 - b*c^2)*sin(x))) - (B*a^6 - 4*B*a^4*b^2 + 3*A*a^3*b^3 + 2*B*a^2*b^4 - 3*A*a*b^5 + B*b^6)*c + (C*a*c^6 + A*c^7 - (5*A*a^2 - B*a*b - 3*A*b^2)*c^5 + (C*a^3 + 2*C*a*b^2)*c^4 + (4*A*a^4 + B*a^3*b - 10*A*a^2*b^2 + 2*B*a*b^3 + 3*A*b^4)*c^3 - (2*C*a^5 - C*a^3*b^2 - C*a*b^4)*c^2 - (2*B*a^5*b - 4*A*a^4*b^2 - B*a^3*b^3 + 5*A*a^2*b^4 - B*a*b^5 - A*b^6)*c)*cos(x) + (2*B*a^5*b^2 - 4*A*a^4*b^3 - B*a^3*b^4 + 5*A*a^2*b^5 - B*a*b^6 - A*b^7 - C*a*b*c^5 - A*b*c^6 + (5*A*a^2*b - B*a*b^2 - 3*A*b^3)*c^4 - (C*a^3*b + 2*C*a*b^3)*c^3 - (4*A*a^4*b + B*a^3*b^2 - 10*A*a^2*b^3 + 2*B*a*b^4 + 3*A*b^5)*c^2 + (2*C*a^5*b - C*a^3*b^3 - C*a*b^5)*c + (B*a^4*b^3 - 3*A*a^3*b^4 + B*a^2*b^5 + 3*A*a*b^6 - 2*B*b^7 + 2*C*c^7 - (3*A*a - 2*B*b)*c^6 - (C*a^2 - 2*C*b^2)*c^5 + (3*A*a^3 - B*a^2*b - 3*A*a*b^2 + 2*B*b^3)*c^4 - (C*a^4 + 2*C*b^4)*c^3 - (B*a^4*b - 3*A*a*b^4 + 2*B*b^5)*c^2 + (C*a^4*b^2 + C*a^2*b^4 - 2*C*b^6)*c)*cos(x))*sin(x))/(a^8*b^2 - 3*a^6*b^4 + 3*a^4*b^6 - a^2*b^8 - c^10 + 2*(a^2 - 2*b^2)*c^8 + (5*a^2*b^2 - 6*b^4)*c^6 - (2*a^6 - 3*a^4*b^2 - 3*a^2*b^4 + 4*b^6)*c^4 + (a^8 - 5*a^6*b^2 + 6*a^4*b^4 - a^2*b^6 - b^8)*c^2 + (a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10 + c^10 - 3*(a^2 - b^2)*c^8 + (3*a^4 - 6*a^2*b^2 + 2*b^4)*c^6 - (a^6 - 3*a^4*b^2 + 2*b^6)*c^4 - 3*(a^4*b^4 - 2*a^2*b^6 + b^8)*c^2)*cos(x)^2 + 2*(a^7*b^3 - 3*a^5*b^5 + 3*a^3*b^7 - a*b^9 - a*b*c^8 + (3*a^3*b - 4*a*b^3)*c^6 - 3*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*c^4 + (a^7*b - 6*a^5*b^3 + 9*a^3*b^5 - 4*a*b^7)*c^2)*cos(x) - 2*(a*c^9 - (3*a^3 - 4*a*b^2)*c^7 + 3*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^7 - 6*a^5*b^2 + 9*a^3*b^4 - 4*a*b^6)*c^3 - (a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*c + (b*c^9 - (3*a^2*b - 4*b^3)*c^7 + 3*(a^4*b - 3*a^2*b^3 + 2*b^5)*c^5 - (a^6*b - 6*a^4*b^3 + 9*a^2*b^5 - 4*b^7)*c^3 - (a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*c)*cos(x))*sin(x))]","B",0
553,1,89,0,1.459737," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+I*b*sin(x)),x, algorithm=""fricas"")","\frac{{\left({\left(i \, B - C\right)} a b + {\left(2 \, A a b - {\left(B + i \, C\right)} b^{2}\right)} x e^{\left(i \, x\right)} + {\left({\left(-i \, B - C\right)} a^{2} + 2 i \, A a b + {\left(-i \, B + C\right)} b^{2}\right)} e^{\left(i \, x\right)} \log\left(\frac{b e^{\left(i \, x\right)} + a}{b}\right)\right)} e^{\left(-i \, x\right)}}{2 \, a^{2} b}"," ",0,"1/2*((I*B - C)*a*b + (2*A*a*b - (B + I*C)*b^2)*x*e^(I*x) + ((-I*B - C)*a^2 + 2*I*A*a*b + (-I*B + C)*b^2)*e^(I*x)*log((b*e^(I*x) + a)/b))*e^(-I*x)/(a^2*b)","A",0
554,1,73,0,1.090967," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)-I*b*sin(x)),x, algorithm=""fricas"")","\frac{{\left(B + i \, C\right)} a^{2} x + {\left(-i \, B - C\right)} a b e^{\left(i \, x\right)} + {\left({\left(i \, B - C\right)} a^{2} - 2 i \, A a b + {\left(i \, B + C\right)} b^{2}\right)} \log\left(\frac{a e^{\left(i \, x\right)} + b}{a}\right)}{2 \, a^{2} b}"," ",0,"1/2*((B + I*C)*a^2*x + (-I*B - C)*a*b*e^(I*x) + ((I*B - C)*a^2 - 2*I*A*a*b + (I*B + C)*b^2)*log((a*e^(I*x) + b)/a))/(a^2*b)","A",0
555,1,24,0,0.892844," ","integrate((b^2+c^2+a*b*cos(x)+a*c*sin(x))/(a+b*cos(x)+c*sin(x))^2,x, algorithm=""fricas"")","-\frac{c \cos\left(x\right) - b \sin\left(x\right)}{b \cos\left(x\right) + c \sin\left(x\right) + a}"," ",0,"-(c*cos(x) - b*sin(x))/(b*cos(x) + c*sin(x) + a)","A",0
556,0,0,0,1.631214," ","integrate((a+b*cos(x)+c*sin(x))^(5/2)*(d+b*e*cos(x)+c*e*sin(x)),x, algorithm=""fricas"")","{\rm integral}\left({\left({\left(b^{3} - 3 \, b c^{2}\right)} e \cos\left(x\right)^{3} + 2 \, a c^{2} e + {\left({\left(b^{2} - c^{2}\right)} d + 2 \, {\left(a b^{2} - a c^{2}\right)} e\right)} \cos\left(x\right)^{2} + {\left(a^{2} + c^{2}\right)} d + {\left(2 \, a b d + {\left(a^{2} b + 3 \, b c^{2}\right)} e\right)} \cos\left(x\right) + {\left({\left(3 \, b^{2} c - c^{3}\right)} e \cos\left(x\right)^{2} + 2 \, a c d + {\left(a^{2} c + c^{3}\right)} e + 2 \, {\left(2 \, a b c e + b c d\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{b \cos\left(x\right) + c \sin\left(x\right) + a}, x\right)"," ",0,"integral(((b^3 - 3*b*c^2)*e*cos(x)^3 + 2*a*c^2*e + ((b^2 - c^2)*d + 2*(a*b^2 - a*c^2)*e)*cos(x)^2 + (a^2 + c^2)*d + (2*a*b*d + (a^2*b + 3*b*c^2)*e)*cos(x) + ((3*b^2*c - c^3)*e*cos(x)^2 + 2*a*c*d + (a^2*c + c^3)*e + 2*(2*a*b*c*e + b*c*d)*cos(x))*sin(x))*sqrt(b*cos(x) + c*sin(x) + a), x)","F",0
557,0,0,0,0.996363," ","integrate((a+b*cos(x)+c*sin(x))^(3/2)*(d+b*e*cos(x)+c*e*sin(x)),x, algorithm=""fricas"")","{\rm integral}\left({\left({\left(b^{2} - c^{2}\right)} e \cos\left(x\right)^{2} + c^{2} e + a d + {\left(a b e + b d\right)} \cos\left(x\right) + {\left(2 \, b c e \cos\left(x\right) + a c e + c d\right)} \sin\left(x\right)\right)} \sqrt{b \cos\left(x\right) + c \sin\left(x\right) + a}, x\right)"," ",0,"integral(((b^2 - c^2)*e*cos(x)^2 + c^2*e + a*d + (a*b*e + b*d)*cos(x) + (2*b*c*e*cos(x) + a*c*e + c*d)*sin(x))*sqrt(b*cos(x) + c*sin(x) + a), x)","F",0
558,0,0,0,1.178650," ","integrate((a+b*cos(x)+c*sin(x))^(1/2)*(d+b*e*cos(x)+c*e*sin(x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b e \cos\left(x\right) + c e \sin\left(x\right) + d\right)} \sqrt{b \cos\left(x\right) + c \sin\left(x\right) + a}, x\right)"," ",0,"integral((b*e*cos(x) + c*e*sin(x) + d)*sqrt(b*cos(x) + c*sin(x) + a), x)","F",0
559,0,0,0,0.960599," ","integrate((d+b*e*cos(x)+c*e*sin(x))/(a+b*cos(x)+c*sin(x))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b e \cos\left(x\right) + c e \sin\left(x\right) + d}{\sqrt{b \cos\left(x\right) + c \sin\left(x\right) + a}}, x\right)"," ",0,"integral((b*e*cos(x) + c*e*sin(x) + d)/sqrt(b*cos(x) + c*sin(x) + a), x)","F",0
560,0,0,0,2.936810," ","integrate((d+b*e*cos(x)+c*e*sin(x))/(a+b*cos(x)+c*sin(x))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b e \cos\left(x\right) + c e \sin\left(x\right) + d\right)} \sqrt{b \cos\left(x\right) + c \sin\left(x\right) + a}}{2 \, a b \cos\left(x\right) + {\left(b^{2} - c^{2}\right)} \cos\left(x\right)^{2} + a^{2} + c^{2} + 2 \, {\left(b c \cos\left(x\right) + a c\right)} \sin\left(x\right)}, x\right)"," ",0,"integral((b*e*cos(x) + c*e*sin(x) + d)*sqrt(b*cos(x) + c*sin(x) + a)/(2*a*b*cos(x) + (b^2 - c^2)*cos(x)^2 + a^2 + c^2 + 2*(b*c*cos(x) + a*c)*sin(x)), x)","F",0
561,0,0,0,0.953543," ","integrate((d+b*e*cos(x)+c*e*sin(x))/(a+b*cos(x)+c*sin(x))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b e \cos\left(x\right) + c e \sin\left(x\right) + d\right)} \sqrt{b \cos\left(x\right) + c \sin\left(x\right) + a}}{{\left(b^{3} - 3 \, b c^{2}\right)} \cos\left(x\right)^{3} + a^{3} + 3 \, a c^{2} + 3 \, {\left(a b^{2} - a c^{2}\right)} \cos\left(x\right)^{2} + 3 \, {\left(a^{2} b + b c^{2}\right)} \cos\left(x\right) + {\left(6 \, a b c \cos\left(x\right) + 3 \, a^{2} c + c^{3} + {\left(3 \, b^{2} c - c^{3}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}, x\right)"," ",0,"integral((b*e*cos(x) + c*e*sin(x) + d)*sqrt(b*cos(x) + c*sin(x) + a)/((b^3 - 3*b*c^2)*cos(x)^3 + a^3 + 3*a*c^2 + 3*(a*b^2 - a*c^2)*cos(x)^2 + 3*(a^2*b + b*c^2)*cos(x) + (6*a*b*c*cos(x) + 3*a^2*c + c^3 + (3*b^2*c - c^3)*cos(x)^2)*sin(x)), x)","F",0
562,1,346,0,0.995565," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(C a^{2} - C c^{2}\right)} e x + {\left(C a - A c\right)} \sqrt{-a^{2} + c^{2}} \log\left(\frac{{\left(2 \, a^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} - 2 \, a c \sin\left(e x + d\right) - a^{2} - c^{2} + 2 \, {\left(a \cos\left(e x + d\right) \sin\left(e x + d\right) + c \cos\left(e x + d\right)\right)} \sqrt{-a^{2} + c^{2}}}{c^{2} \cos\left(e x + d\right)^{2} - 2 \, a c \sin\left(e x + d\right) - a^{2} - c^{2}}\right) + {\left(B a^{2} - B c^{2}\right)} \log\left(-c^{2} \cos\left(e x + d\right)^{2} + 2 \, a c \sin\left(e x + d\right) + a^{2} + c^{2}\right)}{2 \, {\left(a^{2} c - c^{3}\right)} e}, \frac{2 \, {\left(C a^{2} - C c^{2}\right)} e x + 2 \, {\left(C a - A c\right)} \sqrt{a^{2} - c^{2}} \arctan\left(-\frac{a \sin\left(e x + d\right) + c}{\sqrt{a^{2} - c^{2}} \cos\left(e x + d\right)}\right) + {\left(B a^{2} - B c^{2}\right)} \log\left(-c^{2} \cos\left(e x + d\right)^{2} + 2 \, a c \sin\left(e x + d\right) + a^{2} + c^{2}\right)}{2 \, {\left(a^{2} c - c^{3}\right)} e}\right]"," ",0,"[1/2*(2*(C*a^2 - C*c^2)*e*x + (C*a - A*c)*sqrt(-a^2 + c^2)*log(((2*a^2 - c^2)*cos(e*x + d)^2 - 2*a*c*sin(e*x + d) - a^2 - c^2 + 2*(a*cos(e*x + d)*sin(e*x + d) + c*cos(e*x + d))*sqrt(-a^2 + c^2))/(c^2*cos(e*x + d)^2 - 2*a*c*sin(e*x + d) - a^2 - c^2)) + (B*a^2 - B*c^2)*log(-c^2*cos(e*x + d)^2 + 2*a*c*sin(e*x + d) + a^2 + c^2))/((a^2*c - c^3)*e), 1/2*(2*(C*a^2 - C*c^2)*e*x + 2*(C*a - A*c)*sqrt(a^2 - c^2)*arctan(-(a*sin(e*x + d) + c)/(sqrt(a^2 - c^2)*cos(e*x + d))) + (B*a^2 - B*c^2)*log(-c^2*cos(e*x + d)^2 + 2*a*c*sin(e*x + d) + a^2 + c^2))/((a^2*c - c^3)*e)]","A",0
563,1,458,0,1.363998," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, B a^{4} - 4 \, B a^{2} c^{2} + 2 \, B c^{4} + {\left(A a^{2} c - C a c^{2} + {\left(A a c^{2} - C c^{3}\right)} \sin\left(e x + d\right)\right)} \sqrt{-a^{2} + c^{2}} \log\left(\frac{{\left(2 \, a^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} - 2 \, a c \sin\left(e x + d\right) - a^{2} - c^{2} + 2 \, {\left(a \cos\left(e x + d\right) \sin\left(e x + d\right) + c \cos\left(e x + d\right)\right)} \sqrt{-a^{2} + c^{2}}}{c^{2} \cos\left(e x + d\right)^{2} - 2 \, a c \sin\left(e x + d\right) - a^{2} - c^{2}}\right) + 2 \, {\left(C a^{3} c - A a^{2} c^{2} - C a c^{3} + A c^{4}\right)} \cos\left(e x + d\right)}{2 \, {\left({\left(a^{4} c^{2} - 2 \, a^{2} c^{4} + c^{6}\right)} e \sin\left(e x + d\right) + {\left(a^{5} c - 2 \, a^{3} c^{3} + a c^{5}\right)} e\right)}}, -\frac{B a^{4} - 2 \, B a^{2} c^{2} + B c^{4} + {\left(A a^{2} c - C a c^{2} + {\left(A a c^{2} - C c^{3}\right)} \sin\left(e x + d\right)\right)} \sqrt{a^{2} - c^{2}} \arctan\left(-\frac{a \sin\left(e x + d\right) + c}{\sqrt{a^{2} - c^{2}} \cos\left(e x + d\right)}\right) + {\left(C a^{3} c - A a^{2} c^{2} - C a c^{3} + A c^{4}\right)} \cos\left(e x + d\right)}{{\left(a^{4} c^{2} - 2 \, a^{2} c^{4} + c^{6}\right)} e \sin\left(e x + d\right) + {\left(a^{5} c - 2 \, a^{3} c^{3} + a c^{5}\right)} e}\right]"," ",0,"[-1/2*(2*B*a^4 - 4*B*a^2*c^2 + 2*B*c^4 + (A*a^2*c - C*a*c^2 + (A*a*c^2 - C*c^3)*sin(e*x + d))*sqrt(-a^2 + c^2)*log(((2*a^2 - c^2)*cos(e*x + d)^2 - 2*a*c*sin(e*x + d) - a^2 - c^2 + 2*(a*cos(e*x + d)*sin(e*x + d) + c*cos(e*x + d))*sqrt(-a^2 + c^2))/(c^2*cos(e*x + d)^2 - 2*a*c*sin(e*x + d) - a^2 - c^2)) + 2*(C*a^3*c - A*a^2*c^2 - C*a*c^3 + A*c^4)*cos(e*x + d))/((a^4*c^2 - 2*a^2*c^4 + c^6)*e*sin(e*x + d) + (a^5*c - 2*a^3*c^3 + a*c^5)*e), -(B*a^4 - 2*B*a^2*c^2 + B*c^4 + (A*a^2*c - C*a*c^2 + (A*a*c^2 - C*c^3)*sin(e*x + d))*sqrt(a^2 - c^2)*arctan(-(a*sin(e*x + d) + c)/(sqrt(a^2 - c^2)*cos(e*x + d))) + (C*a^3*c - A*a^2*c^2 - C*a*c^3 + A*c^4)*cos(e*x + d))/((a^4*c^2 - 2*a^2*c^4 + c^6)*e*sin(e*x + d) + (a^5*c - 2*a^3*c^3 + a*c^5)*e)]","A",0
564,1,880,0,1.169932," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d))^3,x, algorithm=""fricas"")","\left[\frac{2 \, B a^{6} - 6 \, B a^{4} c^{2} + 6 \, B a^{2} c^{4} - 2 \, B c^{6} + 2 \, {\left(C a^{4} c^{2} - 3 \, A a^{3} c^{3} + C a^{2} c^{4} + 3 \, A a c^{5} - 2 \, C c^{6}\right)} \cos\left(e x + d\right) \sin\left(e x + d\right) + {\left(2 \, A a^{4} c - 3 \, C a^{3} c^{2} + 3 \, A a^{2} c^{3} - 3 \, C a c^{4} + A c^{5} - {\left(2 \, A a^{2} c^{3} - 3 \, C a c^{4} + A c^{5}\right)} \cos\left(e x + d\right)^{2} + 2 \, {\left(2 \, A a^{3} c^{2} - 3 \, C a^{2} c^{3} + A a c^{4}\right)} \sin\left(e x + d\right)\right)} \sqrt{-a^{2} + c^{2}} \log\left(\frac{{\left(2 \, a^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} - 2 \, a c \sin\left(e x + d\right) - a^{2} - c^{2} + 2 \, {\left(a \cos\left(e x + d\right) \sin\left(e x + d\right) + c \cos\left(e x + d\right)\right)} \sqrt{-a^{2} + c^{2}}}{c^{2} \cos\left(e x + d\right)^{2} - 2 \, a c \sin\left(e x + d\right) - a^{2} - c^{2}}\right) + 2 \, {\left(2 \, C a^{5} c - 4 \, A a^{4} c^{2} - C a^{3} c^{3} + 5 \, A a^{2} c^{4} - C a c^{5} - A c^{6}\right)} \cos\left(e x + d\right)}{4 \, {\left({\left(a^{6} c^{3} - 3 \, a^{4} c^{5} + 3 \, a^{2} c^{7} - c^{9}\right)} e \cos\left(e x + d\right)^{2} - 2 \, {\left(a^{7} c^{2} - 3 \, a^{5} c^{4} + 3 \, a^{3} c^{6} - a c^{8}\right)} e \sin\left(e x + d\right) - {\left(a^{8} c - 2 \, a^{6} c^{3} + 2 \, a^{2} c^{7} - c^{9}\right)} e\right)}}, \frac{B a^{6} - 3 \, B a^{4} c^{2} + 3 \, B a^{2} c^{4} - B c^{6} + {\left(C a^{4} c^{2} - 3 \, A a^{3} c^{3} + C a^{2} c^{4} + 3 \, A a c^{5} - 2 \, C c^{6}\right)} \cos\left(e x + d\right) \sin\left(e x + d\right) + {\left(2 \, A a^{4} c - 3 \, C a^{3} c^{2} + 3 \, A a^{2} c^{3} - 3 \, C a c^{4} + A c^{5} - {\left(2 \, A a^{2} c^{3} - 3 \, C a c^{4} + A c^{5}\right)} \cos\left(e x + d\right)^{2} + 2 \, {\left(2 \, A a^{3} c^{2} - 3 \, C a^{2} c^{3} + A a c^{4}\right)} \sin\left(e x + d\right)\right)} \sqrt{a^{2} - c^{2}} \arctan\left(-\frac{a \sin\left(e x + d\right) + c}{\sqrt{a^{2} - c^{2}} \cos\left(e x + d\right)}\right) + {\left(2 \, C a^{5} c - 4 \, A a^{4} c^{2} - C a^{3} c^{3} + 5 \, A a^{2} c^{4} - C a c^{5} - A c^{6}\right)} \cos\left(e x + d\right)}{2 \, {\left({\left(a^{6} c^{3} - 3 \, a^{4} c^{5} + 3 \, a^{2} c^{7} - c^{9}\right)} e \cos\left(e x + d\right)^{2} - 2 \, {\left(a^{7} c^{2} - 3 \, a^{5} c^{4} + 3 \, a^{3} c^{6} - a c^{8}\right)} e \sin\left(e x + d\right) - {\left(a^{8} c - 2 \, a^{6} c^{3} + 2 \, a^{2} c^{7} - c^{9}\right)} e\right)}}\right]"," ",0,"[1/4*(2*B*a^6 - 6*B*a^4*c^2 + 6*B*a^2*c^4 - 2*B*c^6 + 2*(C*a^4*c^2 - 3*A*a^3*c^3 + C*a^2*c^4 + 3*A*a*c^5 - 2*C*c^6)*cos(e*x + d)*sin(e*x + d) + (2*A*a^4*c - 3*C*a^3*c^2 + 3*A*a^2*c^3 - 3*C*a*c^4 + A*c^5 - (2*A*a^2*c^3 - 3*C*a*c^4 + A*c^5)*cos(e*x + d)^2 + 2*(2*A*a^3*c^2 - 3*C*a^2*c^3 + A*a*c^4)*sin(e*x + d))*sqrt(-a^2 + c^2)*log(((2*a^2 - c^2)*cos(e*x + d)^2 - 2*a*c*sin(e*x + d) - a^2 - c^2 + 2*(a*cos(e*x + d)*sin(e*x + d) + c*cos(e*x + d))*sqrt(-a^2 + c^2))/(c^2*cos(e*x + d)^2 - 2*a*c*sin(e*x + d) - a^2 - c^2)) + 2*(2*C*a^5*c - 4*A*a^4*c^2 - C*a^3*c^3 + 5*A*a^2*c^4 - C*a*c^5 - A*c^6)*cos(e*x + d))/((a^6*c^3 - 3*a^4*c^5 + 3*a^2*c^7 - c^9)*e*cos(e*x + d)^2 - 2*(a^7*c^2 - 3*a^5*c^4 + 3*a^3*c^6 - a*c^8)*e*sin(e*x + d) - (a^8*c - 2*a^6*c^3 + 2*a^2*c^7 - c^9)*e), 1/2*(B*a^6 - 3*B*a^4*c^2 + 3*B*a^2*c^4 - B*c^6 + (C*a^4*c^2 - 3*A*a^3*c^3 + C*a^2*c^4 + 3*A*a*c^5 - 2*C*c^6)*cos(e*x + d)*sin(e*x + d) + (2*A*a^4*c - 3*C*a^3*c^2 + 3*A*a^2*c^3 - 3*C*a*c^4 + A*c^5 - (2*A*a^2*c^3 - 3*C*a*c^4 + A*c^5)*cos(e*x + d)^2 + 2*(2*A*a^3*c^2 - 3*C*a^2*c^3 + A*a*c^4)*sin(e*x + d))*sqrt(a^2 - c^2)*arctan(-(a*sin(e*x + d) + c)/(sqrt(a^2 - c^2)*cos(e*x + d))) + (2*C*a^5*c - 4*A*a^4*c^2 - C*a^3*c^3 + 5*A*a^2*c^4 - C*a*c^5 - A*c^6)*cos(e*x + d))/((a^6*c^3 - 3*a^4*c^5 + 3*a^2*c^7 - c^9)*e*cos(e*x + d)^2 - 2*(a^7*c^2 - 3*a^5*c^4 + 3*a^3*c^6 - a*c^8)*e*sin(e*x + d) - (a^8*c - 2*a^6*c^3 + 2*a^2*c^7 - c^9)*e)]","B",0
565,1,1411,0,0.786831," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d))^4,x, algorithm=""fricas"")","\left[\frac{4 \, B a^{8} - 16 \, B a^{6} c^{2} + 24 \, B a^{4} c^{4} - 16 \, B a^{2} c^{6} + 4 \, B c^{8} - 2 \, {\left(2 \, C a^{5} c^{3} - 11 \, A a^{4} c^{4} + 11 \, C a^{3} c^{5} + 7 \, A a^{2} c^{6} - 13 \, C a c^{7} + 4 \, A c^{8}\right)} \cos\left(e x + d\right)^{3} + 6 \, {\left(2 \, C a^{6} c^{2} - 9 \, A a^{5} c^{3} + 7 \, C a^{4} c^{4} + 8 \, A a^{3} c^{5} - 10 \, C a^{2} c^{6} + A a c^{7} + C c^{8}\right)} \cos\left(e x + d\right) \sin\left(e x + d\right) + 3 \, {\left(2 \, A a^{6} c - 4 \, C a^{5} c^{2} + 9 \, A a^{4} c^{3} - 13 \, C a^{3} c^{4} + 9 \, A a^{2} c^{5} - 3 \, C a c^{6} - 3 \, {\left(2 \, A a^{4} c^{3} - 4 \, C a^{3} c^{4} + 3 \, A a^{2} c^{5} - C a c^{6}\right)} \cos\left(e x + d\right)^{2} + {\left(6 \, A a^{5} c^{2} - 12 \, C a^{4} c^{3} + 11 \, A a^{3} c^{4} - 7 \, C a^{2} c^{5} + 3 \, A a c^{6} - C c^{7} - {\left(2 \, A a^{3} c^{4} - 4 \, C a^{2} c^{5} + 3 \, A a c^{6} - C c^{7}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right)\right)} \sqrt{-a^{2} + c^{2}} \log\left(\frac{{\left(2 \, a^{2} - c^{2}\right)} \cos\left(e x + d\right)^{2} - 2 \, a c \sin\left(e x + d\right) - a^{2} - c^{2} + 2 \, {\left(a \cos\left(e x + d\right) \sin\left(e x + d\right) + c \cos\left(e x + d\right)\right)} \sqrt{-a^{2} + c^{2}}}{c^{2} \cos\left(e x + d\right)^{2} - 2 \, a c \sin\left(e x + d\right) - a^{2} - c^{2}}\right) + 12 \, {\left(C a^{7} c - 3 \, A a^{6} c^{2} + C a^{5} c^{3} + 2 \, A a^{4} c^{4} - 2 \, C a c^{7} + A c^{8}\right)} \cos\left(e x + d\right)}{12 \, {\left(3 \, {\left(a^{9} c^{3} - 4 \, a^{7} c^{5} + 6 \, a^{5} c^{7} - 4 \, a^{3} c^{9} + a c^{11}\right)} e \cos\left(e x + d\right)^{2} - {\left(a^{11} c - a^{9} c^{3} - 6 \, a^{7} c^{5} + 14 \, a^{5} c^{7} - 11 \, a^{3} c^{9} + 3 \, a c^{11}\right)} e + {\left({\left(a^{8} c^{4} - 4 \, a^{6} c^{6} + 6 \, a^{4} c^{8} - 4 \, a^{2} c^{10} + c^{12}\right)} e \cos\left(e x + d\right)^{2} - {\left(3 \, a^{10} c^{2} - 11 \, a^{8} c^{4} + 14 \, a^{6} c^{6} - 6 \, a^{4} c^{8} - a^{2} c^{10} + c^{12}\right)} e\right)} \sin\left(e x + d\right)\right)}}, \frac{2 \, B a^{8} - 8 \, B a^{6} c^{2} + 12 \, B a^{4} c^{4} - 8 \, B a^{2} c^{6} + 2 \, B c^{8} - {\left(2 \, C a^{5} c^{3} - 11 \, A a^{4} c^{4} + 11 \, C a^{3} c^{5} + 7 \, A a^{2} c^{6} - 13 \, C a c^{7} + 4 \, A c^{8}\right)} \cos\left(e x + d\right)^{3} + 3 \, {\left(2 \, C a^{6} c^{2} - 9 \, A a^{5} c^{3} + 7 \, C a^{4} c^{4} + 8 \, A a^{3} c^{5} - 10 \, C a^{2} c^{6} + A a c^{7} + C c^{8}\right)} \cos\left(e x + d\right) \sin\left(e x + d\right) + 3 \, {\left(2 \, A a^{6} c - 4 \, C a^{5} c^{2} + 9 \, A a^{4} c^{3} - 13 \, C a^{3} c^{4} + 9 \, A a^{2} c^{5} - 3 \, C a c^{6} - 3 \, {\left(2 \, A a^{4} c^{3} - 4 \, C a^{3} c^{4} + 3 \, A a^{2} c^{5} - C a c^{6}\right)} \cos\left(e x + d\right)^{2} + {\left(6 \, A a^{5} c^{2} - 12 \, C a^{4} c^{3} + 11 \, A a^{3} c^{4} - 7 \, C a^{2} c^{5} + 3 \, A a c^{6} - C c^{7} - {\left(2 \, A a^{3} c^{4} - 4 \, C a^{2} c^{5} + 3 \, A a c^{6} - C c^{7}\right)} \cos\left(e x + d\right)^{2}\right)} \sin\left(e x + d\right)\right)} \sqrt{a^{2} - c^{2}} \arctan\left(-\frac{a \sin\left(e x + d\right) + c}{\sqrt{a^{2} - c^{2}} \cos\left(e x + d\right)}\right) + 6 \, {\left(C a^{7} c - 3 \, A a^{6} c^{2} + C a^{5} c^{3} + 2 \, A a^{4} c^{4} - 2 \, C a c^{7} + A c^{8}\right)} \cos\left(e x + d\right)}{6 \, {\left(3 \, {\left(a^{9} c^{3} - 4 \, a^{7} c^{5} + 6 \, a^{5} c^{7} - 4 \, a^{3} c^{9} + a c^{11}\right)} e \cos\left(e x + d\right)^{2} - {\left(a^{11} c - a^{9} c^{3} - 6 \, a^{7} c^{5} + 14 \, a^{5} c^{7} - 11 \, a^{3} c^{9} + 3 \, a c^{11}\right)} e + {\left({\left(a^{8} c^{4} - 4 \, a^{6} c^{6} + 6 \, a^{4} c^{8} - 4 \, a^{2} c^{10} + c^{12}\right)} e \cos\left(e x + d\right)^{2} - {\left(3 \, a^{10} c^{2} - 11 \, a^{8} c^{4} + 14 \, a^{6} c^{6} - 6 \, a^{4} c^{8} - a^{2} c^{10} + c^{12}\right)} e\right)} \sin\left(e x + d\right)\right)}}\right]"," ",0,"[1/12*(4*B*a^8 - 16*B*a^6*c^2 + 24*B*a^4*c^4 - 16*B*a^2*c^6 + 4*B*c^8 - 2*(2*C*a^5*c^3 - 11*A*a^4*c^4 + 11*C*a^3*c^5 + 7*A*a^2*c^6 - 13*C*a*c^7 + 4*A*c^8)*cos(e*x + d)^3 + 6*(2*C*a^6*c^2 - 9*A*a^5*c^3 + 7*C*a^4*c^4 + 8*A*a^3*c^5 - 10*C*a^2*c^6 + A*a*c^7 + C*c^8)*cos(e*x + d)*sin(e*x + d) + 3*(2*A*a^6*c - 4*C*a^5*c^2 + 9*A*a^4*c^3 - 13*C*a^3*c^4 + 9*A*a^2*c^5 - 3*C*a*c^6 - 3*(2*A*a^4*c^3 - 4*C*a^3*c^4 + 3*A*a^2*c^5 - C*a*c^6)*cos(e*x + d)^2 + (6*A*a^5*c^2 - 12*C*a^4*c^3 + 11*A*a^3*c^4 - 7*C*a^2*c^5 + 3*A*a*c^6 - C*c^7 - (2*A*a^3*c^4 - 4*C*a^2*c^5 + 3*A*a*c^6 - C*c^7)*cos(e*x + d)^2)*sin(e*x + d))*sqrt(-a^2 + c^2)*log(((2*a^2 - c^2)*cos(e*x + d)^2 - 2*a*c*sin(e*x + d) - a^2 - c^2 + 2*(a*cos(e*x + d)*sin(e*x + d) + c*cos(e*x + d))*sqrt(-a^2 + c^2))/(c^2*cos(e*x + d)^2 - 2*a*c*sin(e*x + d) - a^2 - c^2)) + 12*(C*a^7*c - 3*A*a^6*c^2 + C*a^5*c^3 + 2*A*a^4*c^4 - 2*C*a*c^7 + A*c^8)*cos(e*x + d))/(3*(a^9*c^3 - 4*a^7*c^5 + 6*a^5*c^7 - 4*a^3*c^9 + a*c^11)*e*cos(e*x + d)^2 - (a^11*c - a^9*c^3 - 6*a^7*c^5 + 14*a^5*c^7 - 11*a^3*c^9 + 3*a*c^11)*e + ((a^8*c^4 - 4*a^6*c^6 + 6*a^4*c^8 - 4*a^2*c^10 + c^12)*e*cos(e*x + d)^2 - (3*a^10*c^2 - 11*a^8*c^4 + 14*a^6*c^6 - 6*a^4*c^8 - a^2*c^10 + c^12)*e)*sin(e*x + d)), 1/6*(2*B*a^8 - 8*B*a^6*c^2 + 12*B*a^4*c^4 - 8*B*a^2*c^6 + 2*B*c^8 - (2*C*a^5*c^3 - 11*A*a^4*c^4 + 11*C*a^3*c^5 + 7*A*a^2*c^6 - 13*C*a*c^7 + 4*A*c^8)*cos(e*x + d)^3 + 3*(2*C*a^6*c^2 - 9*A*a^5*c^3 + 7*C*a^4*c^4 + 8*A*a^3*c^5 - 10*C*a^2*c^6 + A*a*c^7 + C*c^8)*cos(e*x + d)*sin(e*x + d) + 3*(2*A*a^6*c - 4*C*a^5*c^2 + 9*A*a^4*c^3 - 13*C*a^3*c^4 + 9*A*a^2*c^5 - 3*C*a*c^6 - 3*(2*A*a^4*c^3 - 4*C*a^3*c^4 + 3*A*a^2*c^5 - C*a*c^6)*cos(e*x + d)^2 + (6*A*a^5*c^2 - 12*C*a^4*c^3 + 11*A*a^3*c^4 - 7*C*a^2*c^5 + 3*A*a*c^6 - C*c^7 - (2*A*a^3*c^4 - 4*C*a^2*c^5 + 3*A*a*c^6 - C*c^7)*cos(e*x + d)^2)*sin(e*x + d))*sqrt(a^2 - c^2)*arctan(-(a*sin(e*x + d) + c)/(sqrt(a^2 - c^2)*cos(e*x + d))) + 6*(C*a^7*c - 3*A*a^6*c^2 + C*a^5*c^3 + 2*A*a^4*c^4 - 2*C*a*c^7 + A*c^8)*cos(e*x + d))/(3*(a^9*c^3 - 4*a^7*c^5 + 6*a^5*c^7 - 4*a^3*c^9 + a*c^11)*e*cos(e*x + d)^2 - (a^11*c - a^9*c^3 - 6*a^7*c^5 + 14*a^5*c^7 - 11*a^3*c^9 + 3*a*c^11)*e + ((a^8*c^4 - 4*a^6*c^6 + 6*a^4*c^8 - 4*a^2*c^10 + c^12)*e*cos(e*x + d)^2 - (3*a^10*c^2 - 11*a^8*c^4 + 14*a^6*c^6 - 6*a^4*c^8 - a^2*c^10 + c^12)*e)*sin(e*x + d))]","B",0
566,0,0,0,0.909763," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right) \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((b*cos(d*x + c)*sin(d*x + c) + a)^m, x)","F",0
567,1,97,0,1.753361," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, b^{3} \cos\left(d x + c\right)^{6} - 6 \, b^{3} \cos\left(d x + c\right)^{4} - 36 \, a^{2} b \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, a^{3} + 3 \, a b^{2}\right)} d x - 9 \, {\left(2 \, a b^{2} \cos\left(d x + c\right)^{3} - a b^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(4*b^3*cos(d*x + c)^6 - 6*b^3*cos(d*x + c)^4 - 36*a^2*b*cos(d*x + c)^2 + 3*(8*a^3 + 3*a*b^2)*d*x - 9*(2*a*b^2*cos(d*x + c)^3 - a*b^2*cos(d*x + c))*sin(d*x + c))/d","A",0
568,1,63,0,2.400792," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{8 \, a b \cos\left(d x + c\right)^{2} - {\left(8 \, a^{2} + b^{2}\right)} d x + {\left(2 \, b^{2} \cos\left(d x + c\right)^{3} - b^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/8*(8*a*b*cos(d*x + c)^2 - (8*a^2 + b^2)*d*x + (2*b^2*cos(d*x + c)^3 - b^2*cos(d*x + c))*sin(d*x + c))/d","A",0
569,1,22,0,0.753819," ","integrate(a+b*cos(d*x+c)*sin(d*x+c),x, algorithm=""fricas"")","\frac{2 \, a d x - b \cos\left(d x + c\right)^{2}}{2 \, d}"," ",0,"1/2*(2*a*d*x - b*cos(d*x + c)^2)/d","A",0
570,1,290,0,0.835929," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-4 \, a^{2} + b^{2}} \log\left(-\frac{2 \, {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} - 4 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, a^{2} - b^{2} + {\left(2 \, b \cos\left(d x + c\right)^{2} + 4 \, {\left(2 \, a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - b\right)} \sqrt{-4 \, a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{4} - b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - a^{2}}\right)}{2 \, {\left(4 \, a^{2} - b^{2}\right)} d}, -\frac{\arctan\left(-\frac{{\left(4 \, a \cos\left(d x + c\right) \sin\left(d x + c\right) + b\right)} \sqrt{4 \, a^{2} - b^{2}}}{2 \, {\left(4 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 4 \, a^{2} + b^{2}}\right)}{\sqrt{4 \, a^{2} - b^{2}} d}\right]"," ",0,"[-1/2*sqrt(-4*a^2 + b^2)*log(-(2*(8*a^2 - b^2)*cos(d*x + c)^4 - 4*a*b*cos(d*x + c)*sin(d*x + c) - 2*(8*a^2 - b^2)*cos(d*x + c)^2 + 2*a^2 - b^2 + (2*b*cos(d*x + c)^2 + 4*(2*a*cos(d*x + c)^3 - a*cos(d*x + c))*sin(d*x + c) - b)*sqrt(-4*a^2 + b^2))/(b^2*cos(d*x + c)^4 - b^2*cos(d*x + c)^2 - 2*a*b*cos(d*x + c)*sin(d*x + c) - a^2))/((4*a^2 - b^2)*d), -arctan(-(4*a*cos(d*x + c)*sin(d*x + c) + b)*sqrt(4*a^2 - b^2)/(2*(4*a^2 - b^2)*cos(d*x + c)^2 - 4*a^2 + b^2))/(sqrt(4*a^2 - b^2)*d)]","A",0
571,1,493,0,1.446235," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{2} b - b^{3} - 2 \, {\left(4 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a b \cos\left(d x + c\right) \sin\left(d x + c\right) + a^{2}\right)} \sqrt{-4 \, a^{2} + b^{2}} \log\left(\frac{2 \, {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} - 4 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, a^{2} - b^{2} - {\left(2 \, b \cos\left(d x + c\right)^{2} + 4 \, {\left(2 \, a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - b\right)} \sqrt{-4 \, a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{4} - b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - a^{2}}\right)}{{\left(16 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(16 \, a^{5} - 8 \, a^{3} b^{2} + a b^{4}\right)} d}, -\frac{4 \, a^{2} b - b^{3} - 2 \, {\left(4 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(a b \cos\left(d x + c\right) \sin\left(d x + c\right) + a^{2}\right)} \sqrt{4 \, a^{2} - b^{2}} \arctan\left(-\frac{{\left(4 \, a \cos\left(d x + c\right) \sin\left(d x + c\right) + b\right)} \sqrt{4 \, a^{2} - b^{2}}}{2 \, {\left(4 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 4 \, a^{2} + b^{2}}\right)}{{\left(16 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(16 \, a^{5} - 8 \, a^{3} b^{2} + a b^{4}\right)} d}\right]"," ",0,"[-(4*a^2*b - b^3 - 2*(4*a^2*b - b^3)*cos(d*x + c)^2 - 2*(a*b*cos(d*x + c)*sin(d*x + c) + a^2)*sqrt(-4*a^2 + b^2)*log((2*(8*a^2 - b^2)*cos(d*x + c)^4 - 4*a*b*cos(d*x + c)*sin(d*x + c) - 2*(8*a^2 - b^2)*cos(d*x + c)^2 + 2*a^2 - b^2 - (2*b*cos(d*x + c)^2 + 4*(2*a*cos(d*x + c)^3 - a*cos(d*x + c))*sin(d*x + c) - b)*sqrt(-4*a^2 + b^2))/(b^2*cos(d*x + c)^4 - b^2*cos(d*x + c)^2 - 2*a*b*cos(d*x + c)*sin(d*x + c) - a^2)))/((16*a^4*b - 8*a^2*b^3 + b^5)*d*cos(d*x + c)*sin(d*x + c) + (16*a^5 - 8*a^3*b^2 + a*b^4)*d), -(4*a^2*b - b^3 - 2*(4*a^2*b - b^3)*cos(d*x + c)^2 + 4*(a*b*cos(d*x + c)*sin(d*x + c) + a^2)*sqrt(4*a^2 - b^2)*arctan(-(4*a*cos(d*x + c)*sin(d*x + c) + b)*sqrt(4*a^2 - b^2)/(2*(4*a^2 - b^2)*cos(d*x + c)^2 - 4*a^2 + b^2)))/((16*a^4*b - 8*a^2*b^3 + b^5)*d*cos(d*x + c)*sin(d*x + c) + (16*a^5 - 8*a^3*b^2 + a*b^4)*d)]","B",0
572,1,969,0,1.062970," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{64 \, a^{4} b - 20 \, a^{2} b^{3} + b^{5} - 2 \, {\left(64 \, a^{4} b - 20 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left({\left(8 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} - 8 \, a^{4} - a^{2} b^{2} - {\left(8 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(8 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-4 \, a^{2} + b^{2}} \log\left(-\frac{2 \, {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} - 4 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, a^{2} - b^{2} + {\left(2 \, b \cos\left(d x + c\right)^{2} + 4 \, {\left(2 \, a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - b\right)} \sqrt{-4 \, a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{4} - b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - a^{2}}\right) - 12 \, {\left(2 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(64 \, a^{6} b^{2} - 48 \, a^{4} b^{4} + 12 \, a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{4} - {\left(64 \, a^{6} b^{2} - 48 \, a^{4} b^{4} + 12 \, a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(64 \, a^{7} b - 48 \, a^{5} b^{3} + 12 \, a^{3} b^{5} - a b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(64 \, a^{8} - 48 \, a^{6} b^{2} + 12 \, a^{4} b^{4} - a^{2} b^{6}\right)} d\right)}}, \frac{64 \, a^{4} b - 20 \, a^{2} b^{3} + b^{5} - 2 \, {\left(64 \, a^{4} b - 20 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left({\left(8 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} - 8 \, a^{4} - a^{2} b^{2} - {\left(8 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(8 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{4 \, a^{2} - b^{2}} \arctan\left(-\frac{{\left(4 \, a \cos\left(d x + c\right) \sin\left(d x + c\right) + b\right)} \sqrt{4 \, a^{2} - b^{2}}}{2 \, {\left(4 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 4 \, a^{2} + b^{2}}\right) - 12 \, {\left(2 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(64 \, a^{6} b^{2} - 48 \, a^{4} b^{4} + 12 \, a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{4} - {\left(64 \, a^{6} b^{2} - 48 \, a^{4} b^{4} + 12 \, a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(64 \, a^{7} b - 48 \, a^{5} b^{3} + 12 \, a^{3} b^{5} - a b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(64 \, a^{8} - 48 \, a^{6} b^{2} + 12 \, a^{4} b^{4} - a^{2} b^{6}\right)} d\right)}}\right]"," ",0,"[1/2*(64*a^4*b - 20*a^2*b^3 + b^5 - 2*(64*a^4*b - 20*a^2*b^3 + b^5)*cos(d*x + c)^2 - 2*((8*a^2*b^2 + b^4)*cos(d*x + c)^4 - 8*a^4 - a^2*b^2 - (8*a^2*b^2 + b^4)*cos(d*x + c)^2 - 2*(8*a^3*b + a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(-4*a^2 + b^2)*log(-(2*(8*a^2 - b^2)*cos(d*x + c)^4 - 4*a*b*cos(d*x + c)*sin(d*x + c) - 2*(8*a^2 - b^2)*cos(d*x + c)^2 + 2*a^2 - b^2 + (2*b*cos(d*x + c)^2 + 4*(2*a*cos(d*x + c)^3 - a*cos(d*x + c))*sin(d*x + c) - b)*sqrt(-4*a^2 + b^2))/(b^2*cos(d*x + c)^4 - b^2*cos(d*x + c)^2 - 2*a*b*cos(d*x + c)*sin(d*x + c) - a^2)) - 12*(2*(4*a^3*b^2 - a*b^4)*cos(d*x + c)^3 - (4*a^3*b^2 - a*b^4)*cos(d*x + c))*sin(d*x + c))/((64*a^6*b^2 - 48*a^4*b^4 + 12*a^2*b^6 - b^8)*d*cos(d*x + c)^4 - (64*a^6*b^2 - 48*a^4*b^4 + 12*a^2*b^6 - b^8)*d*cos(d*x + c)^2 - 2*(64*a^7*b - 48*a^5*b^3 + 12*a^3*b^5 - a*b^7)*d*cos(d*x + c)*sin(d*x + c) - (64*a^8 - 48*a^6*b^2 + 12*a^4*b^4 - a^2*b^6)*d), 1/2*(64*a^4*b - 20*a^2*b^3 + b^5 - 2*(64*a^4*b - 20*a^2*b^3 + b^5)*cos(d*x + c)^2 - 4*((8*a^2*b^2 + b^4)*cos(d*x + c)^4 - 8*a^4 - a^2*b^2 - (8*a^2*b^2 + b^4)*cos(d*x + c)^2 - 2*(8*a^3*b + a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(4*a^2 - b^2)*arctan(-(4*a*cos(d*x + c)*sin(d*x + c) + b)*sqrt(4*a^2 - b^2)/(2*(4*a^2 - b^2)*cos(d*x + c)^2 - 4*a^2 + b^2)) - 12*(2*(4*a^3*b^2 - a*b^4)*cos(d*x + c)^3 - (4*a^3*b^2 - a*b^4)*cos(d*x + c))*sin(d*x + c))/((64*a^6*b^2 - 48*a^4*b^4 + 12*a^2*b^6 - b^8)*d*cos(d*x + c)^4 - (64*a^6*b^2 - 48*a^4*b^4 + 12*a^2*b^6 - b^8)*d*cos(d*x + c)^2 - 2*(64*a^7*b - 48*a^5*b^3 + 12*a^3*b^5 - a*b^7)*d*cos(d*x + c)*sin(d*x + c) - (64*a^8 - 48*a^6*b^2 + 12*a^4*b^4 - a^2*b^6)*d)]","B",0
573,0,0,0,2.713891," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{2} \cos\left(d x + c\right)^{4} - b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - a^{2}\right)} \sqrt{b \cos\left(d x + c\right) \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(-(b^2*cos(d*x + c)^4 - b^2*cos(d*x + c)^2 - 2*a*b*cos(d*x + c)*sin(d*x + c) - a^2)*sqrt(b*cos(d*x + c)*sin(d*x + c) + a), x)","F",0
574,0,0,0,2.977931," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right) \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((b*cos(d*x + c)*sin(d*x + c) + a)^(3/2), x)","F",0
575,0,0,0,2.013084," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \cos\left(d x + c\right) \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c)*sin(d*x + c) + a), x)","F",0
576,0,0,0,2.004592," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b \cos\left(d x + c\right) \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral(1/sqrt(b*cos(d*x + c)*sin(d*x + c) + a), x)","F",0
577,0,0,0,0.549075," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \cos\left(d x + c\right) \sin\left(d x + c\right) + a}}{b^{2} \cos\left(d x + c\right)^{4} - b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - a^{2}}, x\right)"," ",0,"integral(-sqrt(b*cos(d*x + c)*sin(d*x + c) + a)/(b^2*cos(d*x + c)^4 - b^2*cos(d*x + c)^2 - 2*a*b*cos(d*x + c)*sin(d*x + c) - a^2), x)","F",0
578,0,0,0,1.743373," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \cos\left(d x + c\right) \sin\left(d x + c\right) + a}}{3 \, a b^{2} \cos\left(d x + c\right)^{4} - 3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} + {\left(b^{3} \cos\left(d x + c\right)^{5} - b^{3} \cos\left(d x + c\right)^{3} - 3 \, a^{2} b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(b*cos(d*x + c)*sin(d*x + c) + a)/(3*a*b^2*cos(d*x + c)^4 - 3*a*b^2*cos(d*x + c)^2 - a^3 + (b^3*cos(d*x + c)^5 - b^3*cos(d*x + c)^3 - 3*a^2*b*cos(d*x + c))*sin(d*x + c)), x)","F",0
579,1,3324,0,1.294182," ","integrate(x^3/(a+b*cos(x)*sin(x)),x, algorithm=""fricas"")","-\frac{2 \, b x^{3} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(\frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} + 2 \, b}{2 \, b}\right) + 2 \, b x^{3} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(\frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} + 2 \, b}{2 \, b}\right) - 2 \, b x^{3} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} - b}{b}\right) - 2 \, b x^{3} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} - b}{b}\right) + 2 \, b x^{3} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} - b}{b}\right) + 2 \, b x^{3} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} - b}{b}\right) - 2 \, b x^{3} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(\frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} + 2 \, b}{2 \, b}\right) - 2 \, b x^{3} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(\frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} + 2 \, b}{2 \, b}\right) + 6 i \, b x^{2} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} + 2 \, b}{2 \, b} + 1\right) + 6 i \, b x^{2} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} + 2 \, b}{2 \, b} + 1\right) + 6 i \, b x^{2} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} - b}{b} + 1\right) + 6 i \, b x^{2} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} - b}{b} + 1\right) - 6 i \, b x^{2} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} - b}{b} + 1\right) - 6 i \, b x^{2} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} - b}{b} + 1\right) - 6 i \, b x^{2} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} + 2 \, b}{2 \, b} + 1\right) - 6 i \, b x^{2} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} + 2 \, b}{2 \, b} + 1\right) + 12 \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}}}{2 \, b}\right) + 12 \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}}}{2 \, b}\right) - 12 \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}}}{b}\right) - 12 \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}}}{b}\right) + 12 \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}}}{b}\right) + 12 \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}}}{b}\right) - 12 \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}}}{2 \, b}\right) - 12 \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}}}{2 \, b}\right) - 12 i \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}}}{2 \, b}\right) - 12 i \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}}}{2 \, b}\right) - 12 i \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}}}{b}\right) - 12 i \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}}}{b}\right) + 12 i \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}}}{b}\right) + 12 i \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}}}{b}\right) + 12 i \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}}}{2 \, b}\right) + 12 i \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}}}{2 \, b}\right)}{4 \, {\left(4 \, a^{2} - b^{2}\right)}}"," ",0,"-1/4*(2*b*x^3*sqrt(-(4*a^2 - b^2)/b^2)*log(1/2*((4*I*a*cos(x) + 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) + 2*b)/b) + 2*b*x^3*sqrt(-(4*a^2 - b^2)/b^2)*log(1/2*((-4*I*a*cos(x) - 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) + 2*b)/b) - 2*b*x^3*sqrt(-(4*a^2 - b^2)/b^2)*log(-((2*I*a*cos(x) - 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) - b)/b) - 2*b*x^3*sqrt(-(4*a^2 - b^2)/b^2)*log(-((-2*I*a*cos(x) + 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) - b)/b) + 2*b*x^3*sqrt(-(4*a^2 - b^2)/b^2)*log(-((2*I*a*cos(x) - 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) - b)/b) + 2*b*x^3*sqrt(-(4*a^2 - b^2)/b^2)*log(-((-2*I*a*cos(x) + 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) - b)/b) - 2*b*x^3*sqrt(-(4*a^2 - b^2)/b^2)*log(1/2*((4*I*a*cos(x) + 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) + 2*b)/b) - 2*b*x^3*sqrt(-(4*a^2 - b^2)/b^2)*log(1/2*((-4*I*a*cos(x) - 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) + 2*b)/b) + 6*I*b*x^2*sqrt(-(4*a^2 - b^2)/b^2)*dilog(-1/2*((4*I*a*cos(x) + 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) + 2*b)/b + 1) + 6*I*b*x^2*sqrt(-(4*a^2 - b^2)/b^2)*dilog(-1/2*((-4*I*a*cos(x) - 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) + 2*b)/b + 1) + 6*I*b*x^2*sqrt(-(4*a^2 - b^2)/b^2)*dilog(((2*I*a*cos(x) - 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) - b)/b + 1) + 6*I*b*x^2*sqrt(-(4*a^2 - b^2)/b^2)*dilog(((-2*I*a*cos(x) + 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) - b)/b + 1) - 6*I*b*x^2*sqrt(-(4*a^2 - b^2)/b^2)*dilog(((2*I*a*cos(x) - 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) - b)/b + 1) - 6*I*b*x^2*sqrt(-(4*a^2 - b^2)/b^2)*dilog(((-2*I*a*cos(x) + 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) - b)/b + 1) - 6*I*b*x^2*sqrt(-(4*a^2 - b^2)/b^2)*dilog(-1/2*((4*I*a*cos(x) + 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) + 2*b)/b + 1) - 6*I*b*x^2*sqrt(-(4*a^2 - b^2)/b^2)*dilog(-1/2*((-4*I*a*cos(x) - 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) + 2*b)/b + 1) + 12*b*x*sqrt(-(4*a^2 - b^2)/b^2)*polylog(3, 1/2*(4*I*a*cos(x) + 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b)/b) + 12*b*x*sqrt(-(4*a^2 - b^2)/b^2)*polylog(3, 1/2*(-4*I*a*cos(x) - 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b)/b) - 12*b*x*sqrt(-(4*a^2 - b^2)/b^2)*polylog(3, -(2*I*a*cos(x) - 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b)/b) - 12*b*x*sqrt(-(4*a^2 - b^2)/b^2)*polylog(3, -(-2*I*a*cos(x) + 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b)/b) + 12*b*x*sqrt(-(4*a^2 - b^2)/b^2)*polylog(3, -(2*I*a*cos(x) - 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b)/b) + 12*b*x*sqrt(-(4*a^2 - b^2)/b^2)*polylog(3, -(-2*I*a*cos(x) + 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b)/b) - 12*b*x*sqrt(-(4*a^2 - b^2)/b^2)*polylog(3, 1/2*(4*I*a*cos(x) + 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b)/b) - 12*b*x*sqrt(-(4*a^2 - b^2)/b^2)*polylog(3, 1/2*(-4*I*a*cos(x) - 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b)/b) - 12*I*b*sqrt(-(4*a^2 - b^2)/b^2)*polylog(4, 1/2*(4*I*a*cos(x) + 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b)/b) - 12*I*b*sqrt(-(4*a^2 - b^2)/b^2)*polylog(4, 1/2*(-4*I*a*cos(x) - 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b)/b) - 12*I*b*sqrt(-(4*a^2 - b^2)/b^2)*polylog(4, -(2*I*a*cos(x) - 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b)/b) - 12*I*b*sqrt(-(4*a^2 - b^2)/b^2)*polylog(4, -(-2*I*a*cos(x) + 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b)/b) + 12*I*b*sqrt(-(4*a^2 - b^2)/b^2)*polylog(4, -(2*I*a*cos(x) - 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b)/b) + 12*I*b*sqrt(-(4*a^2 - b^2)/b^2)*polylog(4, -(-2*I*a*cos(x) + 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b)/b) + 12*I*b*sqrt(-(4*a^2 - b^2)/b^2)*polylog(4, 1/2*(4*I*a*cos(x) + 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b)/b) + 12*I*b*sqrt(-(4*a^2 - b^2)/b^2)*polylog(4, 1/2*(-4*I*a*cos(x) - 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b)/b))/(4*a^2 - b^2)","C",0
580,1,2506,0,2.282269," ","integrate(x^2/(a+b*cos(x)*sin(x)),x, algorithm=""fricas"")","-\frac{2 \, b x^{2} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(\frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} + 2 \, b}{2 \, b}\right) + 2 \, b x^{2} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(\frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} + 2 \, b}{2 \, b}\right) - 2 \, b x^{2} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} - b}{b}\right) - 2 \, b x^{2} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} - b}{b}\right) + 2 \, b x^{2} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} - b}{b}\right) + 2 \, b x^{2} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} - b}{b}\right) - 2 \, b x^{2} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(\frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} + 2 \, b}{2 \, b}\right) - 2 \, b x^{2} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(\frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} + 2 \, b}{2 \, b}\right) + 4 i \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} + 2 \, b}{2 \, b} + 1\right) + 4 i \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} + 2 \, b}{2 \, b} + 1\right) + 4 i \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} - b}{b} + 1\right) + 4 i \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} - b}{b} + 1\right) - 4 i \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} - b}{b} + 1\right) - 4 i \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} - b}{b} + 1\right) - 4 i \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} + 2 \, b}{2 \, b} + 1\right) - 4 i \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} + 2 \, b}{2 \, b} + 1\right) + 4 \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}}}{2 \, b}\right) + 4 \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}}}{2 \, b}\right) - 4 \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}}}{b}\right) - 4 \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}}}{b}\right) + 4 \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}}}{b}\right) + 4 \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}}}{b}\right) - 4 \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}}}{2 \, b}\right) - 4 \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}}}{2 \, b}\right)}{4 \, {\left(4 \, a^{2} - b^{2}\right)}}"," ",0,"-1/4*(2*b*x^2*sqrt(-(4*a^2 - b^2)/b^2)*log(1/2*((4*I*a*cos(x) + 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) + 2*b)/b) + 2*b*x^2*sqrt(-(4*a^2 - b^2)/b^2)*log(1/2*((-4*I*a*cos(x) - 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) + 2*b)/b) - 2*b*x^2*sqrt(-(4*a^2 - b^2)/b^2)*log(-((2*I*a*cos(x) - 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) - b)/b) - 2*b*x^2*sqrt(-(4*a^2 - b^2)/b^2)*log(-((-2*I*a*cos(x) + 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) - b)/b) + 2*b*x^2*sqrt(-(4*a^2 - b^2)/b^2)*log(-((2*I*a*cos(x) - 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) - b)/b) + 2*b*x^2*sqrt(-(4*a^2 - b^2)/b^2)*log(-((-2*I*a*cos(x) + 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) - b)/b) - 2*b*x^2*sqrt(-(4*a^2 - b^2)/b^2)*log(1/2*((4*I*a*cos(x) + 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) + 2*b)/b) - 2*b*x^2*sqrt(-(4*a^2 - b^2)/b^2)*log(1/2*((-4*I*a*cos(x) - 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) + 2*b)/b) + 4*I*b*x*sqrt(-(4*a^2 - b^2)/b^2)*dilog(-1/2*((4*I*a*cos(x) + 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) + 2*b)/b + 1) + 4*I*b*x*sqrt(-(4*a^2 - b^2)/b^2)*dilog(-1/2*((-4*I*a*cos(x) - 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) + 2*b)/b + 1) + 4*I*b*x*sqrt(-(4*a^2 - b^2)/b^2)*dilog(((2*I*a*cos(x) - 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) - b)/b + 1) + 4*I*b*x*sqrt(-(4*a^2 - b^2)/b^2)*dilog(((-2*I*a*cos(x) + 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) - b)/b + 1) - 4*I*b*x*sqrt(-(4*a^2 - b^2)/b^2)*dilog(((2*I*a*cos(x) - 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) - b)/b + 1) - 4*I*b*x*sqrt(-(4*a^2 - b^2)/b^2)*dilog(((-2*I*a*cos(x) + 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) - b)/b + 1) - 4*I*b*x*sqrt(-(4*a^2 - b^2)/b^2)*dilog(-1/2*((4*I*a*cos(x) + 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) + 2*b)/b + 1) - 4*I*b*x*sqrt(-(4*a^2 - b^2)/b^2)*dilog(-1/2*((-4*I*a*cos(x) - 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) + 2*b)/b + 1) + 4*b*sqrt(-(4*a^2 - b^2)/b^2)*polylog(3, 1/2*(4*I*a*cos(x) + 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b)/b) + 4*b*sqrt(-(4*a^2 - b^2)/b^2)*polylog(3, 1/2*(-4*I*a*cos(x) - 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b)/b) - 4*b*sqrt(-(4*a^2 - b^2)/b^2)*polylog(3, -(2*I*a*cos(x) - 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b)/b) - 4*b*sqrt(-(4*a^2 - b^2)/b^2)*polylog(3, -(-2*I*a*cos(x) + 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b)/b) + 4*b*sqrt(-(4*a^2 - b^2)/b^2)*polylog(3, -(2*I*a*cos(x) - 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b)/b) + 4*b*sqrt(-(4*a^2 - b^2)/b^2)*polylog(3, -(-2*I*a*cos(x) + 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b)/b) - 4*b*sqrt(-(4*a^2 - b^2)/b^2)*polylog(3, 1/2*(4*I*a*cos(x) + 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b)/b) - 4*b*sqrt(-(4*a^2 - b^2)/b^2)*polylog(3, 1/2*(-4*I*a*cos(x) - 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b)/b))/(4*a^2 - b^2)","C",0
581,1,1688,0,2.254596," ","integrate(x/(a+b*cos(x)*sin(x)),x, algorithm=""fricas"")","-\frac{2 \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(\frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} + 2 \, b}{2 \, b}\right) + 2 \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(\frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} + 2 \, b}{2 \, b}\right) - 2 \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} - b}{b}\right) - 2 \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} - b}{b}\right) + 2 \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} - b}{b}\right) + 2 \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} - b}{b}\right) - 2 \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(\frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} + 2 \, b}{2 \, b}\right) - 2 \, b x \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} \log\left(\frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} + 2 \, b}{2 \, b}\right) + 2 i \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} + 2 \, b}{2 \, b} + 1\right) + 2 i \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} + 2 \, b}{2 \, b} + 1\right) + 2 i \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} - b}{b} + 1\right) + 2 i \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} + 2 i \, a}{b}} - b}{b} + 1\right) - 2 i \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{{\left(2 i \, a \cos\left(x\right) - 2 \, a \sin\left(x\right) + {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} - b}{b} + 1\right) - 2 i \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{{\left(-2 i \, a \cos\left(x\right) + 2 \, a \sin\left(x\right) - {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} - b}{b} + 1\right) - 2 i \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{{\left(4 i \, a \cos\left(x\right) + 4 \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} + 2 \, b}{2 \, b} + 1\right) - 2 i \, b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{{\left(-4 i \, a \cos\left(x\right) - 4 \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}}\right)} \sqrt{-\frac{b \sqrt{-\frac{4 \, a^{2} - b^{2}}{b^{2}}} - 2 i \, a}{b}} + 2 \, b}{2 \, b} + 1\right)}{4 \, {\left(4 \, a^{2} - b^{2}\right)}}"," ",0,"-1/4*(2*b*x*sqrt(-(4*a^2 - b^2)/b^2)*log(1/2*((4*I*a*cos(x) + 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) + 2*b)/b) + 2*b*x*sqrt(-(4*a^2 - b^2)/b^2)*log(1/2*((-4*I*a*cos(x) - 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) + 2*b)/b) - 2*b*x*sqrt(-(4*a^2 - b^2)/b^2)*log(-((2*I*a*cos(x) - 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) - b)/b) - 2*b*x*sqrt(-(4*a^2 - b^2)/b^2)*log(-((-2*I*a*cos(x) + 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) - b)/b) + 2*b*x*sqrt(-(4*a^2 - b^2)/b^2)*log(-((2*I*a*cos(x) - 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) - b)/b) + 2*b*x*sqrt(-(4*a^2 - b^2)/b^2)*log(-((-2*I*a*cos(x) + 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) - b)/b) - 2*b*x*sqrt(-(4*a^2 - b^2)/b^2)*log(1/2*((4*I*a*cos(x) + 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) + 2*b)/b) - 2*b*x*sqrt(-(4*a^2 - b^2)/b^2)*log(1/2*((-4*I*a*cos(x) - 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) + 2*b)/b) + 2*I*b*sqrt(-(4*a^2 - b^2)/b^2)*dilog(-1/2*((4*I*a*cos(x) + 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) + 2*b)/b + 1) + 2*I*b*sqrt(-(4*a^2 - b^2)/b^2)*dilog(-1/2*((-4*I*a*cos(x) - 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) + 2*b)/b + 1) + 2*I*b*sqrt(-(4*a^2 - b^2)/b^2)*dilog(((2*I*a*cos(x) - 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) - b)/b + 1) + 2*I*b*sqrt(-(4*a^2 - b^2)/b^2)*dilog(((-2*I*a*cos(x) + 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) + 2*I*a)/b) - b)/b + 1) - 2*I*b*sqrt(-(4*a^2 - b^2)/b^2)*dilog(((2*I*a*cos(x) - 2*a*sin(x) + (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) - b)/b + 1) - 2*I*b*sqrt(-(4*a^2 - b^2)/b^2)*dilog(((-2*I*a*cos(x) + 2*a*sin(x) - (b*cos(x) + I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt((b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) - b)/b + 1) - 2*I*b*sqrt(-(4*a^2 - b^2)/b^2)*dilog(-1/2*((4*I*a*cos(x) + 4*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) + 2*b)/b + 1) - 2*I*b*sqrt(-(4*a^2 - b^2)/b^2)*dilog(-1/2*((-4*I*a*cos(x) - 4*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt(-(4*a^2 - b^2)/b^2))*sqrt(-(b*sqrt(-(4*a^2 - b^2)/b^2) - 2*I*a)/b) + 2*b)/b + 1))/(4*a^2 - b^2)","B",0
582,0,0,0,0.689910," ","integrate(1/x/(a+b*cos(x)*sin(x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x \cos\left(x\right) \sin\left(x\right) + a x}, x\right)"," ",0,"integral(1/(b*x*cos(x)*sin(x) + a*x), x)","F",0
583,0,0,0,0.963999," ","integrate((b*x)^(2-n)*sin(a*x)^n/(a*c*x*cos(a*x)-c*sin(a*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(b x\right)^{-n + 2} \sin\left(a x\right)^{n}}{2 \, a c^{2} x \cos\left(a x\right) \sin\left(a x\right) - {\left(a^{2} c^{2} x^{2} - c^{2}\right)} \cos\left(a x\right)^{2} - c^{2}}, x\right)"," ",0,"integral(-(b*x)^(-n + 2)*sin(a*x)^n/(2*a*c^2*x*cos(a*x)*sin(a*x) - (a^2*c^2*x^2 - c^2)*cos(a*x)^2 - c^2), x)","F",0
584,0,0,0,0.911557," ","integrate((b*x)^(2-n)*cos(a*x)^n/(c*cos(a*x)+a*c*x*sin(a*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(b x\right)^{-n + 2} \cos\left(a x\right)^{n}}{a^{2} c^{2} x^{2} + 2 \, a c^{2} x \cos\left(a x\right) \sin\left(a x\right) - {\left(a^{2} c^{2} x^{2} - c^{2}\right)} \cos\left(a x\right)^{2}}, x\right)"," ",0,"integral((b*x)^(-n + 2)*cos(a*x)^n/(a^2*c^2*x^2 + 2*a*c^2*x*cos(a*x)*sin(a*x) - (a^2*c^2*x^2 - c^2)*cos(a*x)^2), x)","F",0
585,1,186,0,1.073954," ","integrate(sin(a*x)^6/x^4/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""fricas"")","\frac{4 \, {\left(8 \, a^{3} x^{3} + a x\right)} \cos\left(a x\right)^{5} - 2 \, {\left(17 \, a^{3} x^{3} + 4 \, a x\right)} \cos\left(a x\right)^{3} + {\left(16 \, a^{4} x^{4} \operatorname{Si}\left(4 \, a x\right) - 2 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) + 5 \, a^{3} x^{3} + 4 \, a x\right)} \cos\left(a x\right) - {\left(16 \, a^{3} x^{3} \operatorname{Si}\left(4 \, a x\right) - 2 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) + {\left(24 \, a^{2} x^{2} - 1\right)} \cos\left(a x\right)^{4} + 5 \, a^{2} x^{2} - {\left(29 \, a^{2} x^{2} - 2\right)} \cos\left(a x\right)^{2} - 1\right)} \sin\left(a x\right)}{3 \, {\left(a x^{4} \cos\left(a x\right) - x^{3} \sin\left(a x\right)\right)}}"," ",0,"1/3*(4*(8*a^3*x^3 + a*x)*cos(a*x)^5 - 2*(17*a^3*x^3 + 4*a*x)*cos(a*x)^3 + (16*a^4*x^4*sin_integral(4*a*x) - 2*a^4*x^4*sin_integral(2*a*x) + 5*a^3*x^3 + 4*a*x)*cos(a*x) - (16*a^3*x^3*sin_integral(4*a*x) - 2*a^3*x^3*sin_integral(2*a*x) + (24*a^2*x^2 - 1)*cos(a*x)^4 + 5*a^2*x^2 - (29*a^2*x^2 - 2)*cos(a*x)^2 - 1)*sin(a*x))/(a*x^4*cos(a*x) - x^3*sin(a*x))","A",0
586,1,142,0,1.035651," ","integrate(sin(a*x)^5/x^3/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""fricas"")","\frac{4 \, {\left(9 \, a^{2} x^{2} + 1\right)} \cos\left(a x\right)^{4} - 4 \, {\left(7 \, a^{2} x^{2} + 2\right)} \cos\left(a x\right)^{2} + {\left(27 \, a^{3} x^{3} \operatorname{Si}\left(3 \, a x\right) - a^{3} x^{3} \operatorname{Si}\left(a x\right)\right)} \cos\left(a x\right) - {\left(24 \, a x \cos\left(a x\right)^{3} + 27 \, a^{2} x^{2} \operatorname{Si}\left(3 \, a x\right) - a^{2} x^{2} \operatorname{Si}\left(a x\right) - 24 \, a x \cos\left(a x\right)\right)} \sin\left(a x\right) + 4}{8 \, {\left(a x^{3} \cos\left(a x\right) - x^{2} \sin\left(a x\right)\right)}}"," ",0,"1/8*(4*(9*a^2*x^2 + 1)*cos(a*x)^4 - 4*(7*a^2*x^2 + 2)*cos(a*x)^2 + (27*a^3*x^3*sin_integral(3*a*x) - a^3*x^3*sin_integral(a*x))*cos(a*x) - (24*a*x*cos(a*x)^3 + 27*a^2*x^2*sin_integral(3*a*x) - a^2*x^2*sin_integral(a*x) - 24*a*x*cos(a*x))*sin(a*x) + 4)/(a*x^3*cos(a*x) - x^2*sin(a*x))","A",0
587,1,77,0,1.033847," ","integrate(sin(a*x)^4/x^2/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""fricas"")","\frac{2 \, a x \cos\left(a x\right)^{3} + {\left(2 \, a^{2} x^{2} \operatorname{Si}\left(2 \, a x\right) - a x\right)} \cos\left(a x\right) - {\left(2 \, a x \operatorname{Si}\left(2 \, a x\right) + \cos\left(a x\right)^{2} - 1\right)} \sin\left(a x\right)}{a x^{2} \cos\left(a x\right) - x \sin\left(a x\right)}"," ",0,"(2*a*x*cos(a*x)^3 + (2*a^2*x^2*sin_integral(2*a*x) - a*x)*cos(a*x) - (2*a*x*sin_integral(2*a*x) + cos(a*x)^2 - 1)*sin(a*x))/(a*x^2*cos(a*x) - x*sin(a*x))","A",0
588,1,45,0,0.866963," ","integrate(sin(a*x)^3/x/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""fricas"")","\frac{a x \cos\left(a x\right) \operatorname{Si}\left(a x\right) + \cos\left(a x\right)^{2} - \sin\left(a x\right) \operatorname{Si}\left(a x\right)}{a x \cos\left(a x\right) - \sin\left(a x\right)}"," ",0,"(a*x*cos(a*x)*sin_integral(a*x) + cos(a*x)^2 - sin(a*x)*sin_integral(a*x))/(a*x*cos(a*x) - sin(a*x))","A",0
589,1,24,0,1.954960," ","integrate(sin(a*x)^2/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""fricas"")","\frac{\cos\left(a x\right)}{a^{2} x \cos\left(a x\right) - a \sin\left(a x\right)}"," ",0,"cos(a*x)/(a^2*x*cos(a*x) - a*sin(a*x))","A",0
590,1,21,0,1.745764," ","integrate(x*sin(a*x)/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""fricas"")","\frac{1}{a^{3} x \cos\left(a x\right) - a^{2} \sin\left(a x\right)}"," ",0,"1/(a^3*x*cos(a*x) - a^2*sin(a*x))","A",0
591,1,34,0,0.822818," ","integrate(x^2/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""fricas"")","\frac{a x \sin\left(a x\right) + \cos\left(a x\right)}{a^{4} x \cos\left(a x\right) - a^{3} \sin\left(a x\right)}"," ",0,"(a*x*sin(a*x) + cos(a*x))/(a^4*x*cos(a*x) - a^3*sin(a*x))","A",0
592,1,295,0,2.955250," ","integrate(x^3*csc(a*x)/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""fricas"")","\frac{2 \, a^{2} x^{2} - {\left(i \, a x \cos\left(a x\right) - i \, \sin\left(a x\right)\right)} {\rm Li}_2\left(\cos\left(a x\right) + i \, \sin\left(a x\right)\right) - {\left(-i \, a x \cos\left(a x\right) + i \, \sin\left(a x\right)\right)} {\rm Li}_2\left(\cos\left(a x\right) - i \, \sin\left(a x\right)\right) - {\left(i \, a x \cos\left(a x\right) - i \, \sin\left(a x\right)\right)} {\rm Li}_2\left(-\cos\left(a x\right) + i \, \sin\left(a x\right)\right) - {\left(-i \, a x \cos\left(a x\right) + i \, \sin\left(a x\right)\right)} {\rm Li}_2\left(-\cos\left(a x\right) - i \, \sin\left(a x\right)\right) - {\left(a^{2} x^{2} \cos\left(a x\right) - a x \sin\left(a x\right)\right)} \log\left(\cos\left(a x\right) + i \, \sin\left(a x\right) + 1\right) - {\left(a^{2} x^{2} \cos\left(a x\right) - a x \sin\left(a x\right)\right)} \log\left(\cos\left(a x\right) - i \, \sin\left(a x\right) + 1\right) + {\left(a^{2} x^{2} \cos\left(a x\right) - a x \sin\left(a x\right)\right)} \log\left(-\cos\left(a x\right) + i \, \sin\left(a x\right) + 1\right) + {\left(a^{2} x^{2} \cos\left(a x\right) - a x \sin\left(a x\right)\right)} \log\left(-\cos\left(a x\right) - i \, \sin\left(a x\right) + 1\right) + 2}{2 \, {\left(a^{5} x \cos\left(a x\right) - a^{4} \sin\left(a x\right)\right)}}"," ",0,"1/2*(2*a^2*x^2 - (I*a*x*cos(a*x) - I*sin(a*x))*dilog(cos(a*x) + I*sin(a*x)) - (-I*a*x*cos(a*x) + I*sin(a*x))*dilog(cos(a*x) - I*sin(a*x)) - (I*a*x*cos(a*x) - I*sin(a*x))*dilog(-cos(a*x) + I*sin(a*x)) - (-I*a*x*cos(a*x) + I*sin(a*x))*dilog(-cos(a*x) - I*sin(a*x)) - (a^2*x^2*cos(a*x) - a*x*sin(a*x))*log(cos(a*x) + I*sin(a*x) + 1) - (a^2*x^2*cos(a*x) - a*x*sin(a*x))*log(cos(a*x) - I*sin(a*x) + 1) + (a^2*x^2*cos(a*x) - a*x*sin(a*x))*log(-cos(a*x) + I*sin(a*x) + 1) + (a^2*x^2*cos(a*x) - a*x*sin(a*x))*log(-cos(a*x) - I*sin(a*x) + 1) + 2)/(a^5*x*cos(a*x) - a^4*sin(a*x))","B",0
593,1,406,0,0.997092," ","integrate(x^4*csc(a*x)^2/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""fricas"")","\frac{a^{3} x^{3} - {\left(2 \, a^{3} x^{3} + a x\right)} \cos\left(a x\right)^{2} + {\left(2 \, a^{2} x^{2} + 1\right)} \cos\left(a x\right) \sin\left(a x\right) + a x + {\left(-2 i \, a x \cos\left(a x\right) \sin\left(a x\right) - 2 i \, \cos\left(a x\right)^{2} + 2 i\right)} {\rm Li}_2\left(\cos\left(a x\right) + i \, \sin\left(a x\right)\right) + {\left(2 i \, a x \cos\left(a x\right) \sin\left(a x\right) + 2 i \, \cos\left(a x\right)^{2} - 2 i\right)} {\rm Li}_2\left(\cos\left(a x\right) - i \, \sin\left(a x\right)\right) + {\left(2 i \, a x \cos\left(a x\right) \sin\left(a x\right) + 2 i \, \cos\left(a x\right)^{2} - 2 i\right)} {\rm Li}_2\left(-\cos\left(a x\right) + i \, \sin\left(a x\right)\right) + {\left(-2 i \, a x \cos\left(a x\right) \sin\left(a x\right) - 2 i \, \cos\left(a x\right)^{2} + 2 i\right)} {\rm Li}_2\left(-\cos\left(a x\right) - i \, \sin\left(a x\right)\right) + 2 \, {\left(a^{2} x^{2} \cos\left(a x\right) \sin\left(a x\right) + a x \cos\left(a x\right)^{2} - a x\right)} \log\left(\cos\left(a x\right) + i \, \sin\left(a x\right) + 1\right) + 2 \, {\left(a^{2} x^{2} \cos\left(a x\right) \sin\left(a x\right) + a x \cos\left(a x\right)^{2} - a x\right)} \log\left(\cos\left(a x\right) - i \, \sin\left(a x\right) + 1\right) + 2 \, {\left(a^{2} x^{2} \cos\left(a x\right) \sin\left(a x\right) + a x \cos\left(a x\right)^{2} - a x\right)} \log\left(-\cos\left(a x\right) + i \, \sin\left(a x\right) + 1\right) + 2 \, {\left(a^{2} x^{2} \cos\left(a x\right) \sin\left(a x\right) + a x \cos\left(a x\right)^{2} - a x\right)} \log\left(-\cos\left(a x\right) - i \, \sin\left(a x\right) + 1\right)}{a^{6} x \cos\left(a x\right) \sin\left(a x\right) + a^{5} \cos\left(a x\right)^{2} - a^{5}}"," ",0,"(a^3*x^3 - (2*a^3*x^3 + a*x)*cos(a*x)^2 + (2*a^2*x^2 + 1)*cos(a*x)*sin(a*x) + a*x + (-2*I*a*x*cos(a*x)*sin(a*x) - 2*I*cos(a*x)^2 + 2*I)*dilog(cos(a*x) + I*sin(a*x)) + (2*I*a*x*cos(a*x)*sin(a*x) + 2*I*cos(a*x)^2 - 2*I)*dilog(cos(a*x) - I*sin(a*x)) + (2*I*a*x*cos(a*x)*sin(a*x) + 2*I*cos(a*x)^2 - 2*I)*dilog(-cos(a*x) + I*sin(a*x)) + (-2*I*a*x*cos(a*x)*sin(a*x) - 2*I*cos(a*x)^2 + 2*I)*dilog(-cos(a*x) - I*sin(a*x)) + 2*(a^2*x^2*cos(a*x)*sin(a*x) + a*x*cos(a*x)^2 - a*x)*log(cos(a*x) + I*sin(a*x) + 1) + 2*(a^2*x^2*cos(a*x)*sin(a*x) + a*x*cos(a*x)^2 - a*x)*log(cos(a*x) - I*sin(a*x) + 1) + 2*(a^2*x^2*cos(a*x)*sin(a*x) + a*x*cos(a*x)^2 - a*x)*log(-cos(a*x) + I*sin(a*x) + 1) + 2*(a^2*x^2*cos(a*x)*sin(a*x) + a*x*cos(a*x)^2 - a*x)*log(-cos(a*x) - I*sin(a*x) + 1))/(a^6*x*cos(a*x)*sin(a*x) + a^5*cos(a*x)^2 - a^5)","B",0
594,1,162,0,0.915154," ","integrate(cos(a*x)^6/x^4/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""fricas"")","-\frac{19 \, a^{2} x^{2} \cos\left(a x\right)^{3} - {\left(24 \, a^{2} x^{2} - 1\right)} \cos\left(a x\right)^{5} - 2 \, {\left(8 \, a^{3} x^{3} \operatorname{Si}\left(4 \, a x\right) + a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right)\right)} \cos\left(a x\right) - {\left(16 \, a^{4} x^{4} \operatorname{Si}\left(4 \, a x\right) + 2 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) - 30 \, a^{3} x^{3} \cos\left(a x\right)^{2} + 3 \, a^{3} x^{3} + 4 \, {\left(8 \, a^{3} x^{3} + a x\right)} \cos\left(a x\right)^{4}\right)} \sin\left(a x\right)}{3 \, {\left(a x^{4} \sin\left(a x\right) + x^{3} \cos\left(a x\right)\right)}}"," ",0,"-1/3*(19*a^2*x^2*cos(a*x)^3 - (24*a^2*x^2 - 1)*cos(a*x)^5 - 2*(8*a^3*x^3*sin_integral(4*a*x) + a^3*x^3*sin_integral(2*a*x))*cos(a*x) - (16*a^4*x^4*sin_integral(4*a*x) + 2*a^4*x^4*sin_integral(2*a*x) - 30*a^3*x^3*cos(a*x)^2 + 3*a^3*x^3 + 4*(8*a^3*x^3 + a*x)*cos(a*x)^4)*sin(a*x))/(a*x^4*sin(a*x) + x^3*cos(a*x))","A",0
595,1,185,0,0.921027," ","integrate(cos(a*x)^5/x^3/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""fricas"")","\frac{88 \, a^{2} x^{2} \cos\left(a x\right)^{2} - 8 \, {\left(9 \, a^{2} x^{2} + 1\right)} \cos\left(a x\right)^{4} - 16 \, a^{2} x^{2} - {\left(27 \, a^{2} x^{2} \operatorname{Ci}\left(3 \, a x\right) + a^{2} x^{2} \operatorname{Ci}\left(a x\right) + a^{2} x^{2} \operatorname{Ci}\left(-a x\right) + 27 \, a^{2} x^{2} \operatorname{Ci}\left(-3 \, a x\right)\right)} \cos\left(a x\right) - {\left(27 \, a^{3} x^{3} \operatorname{Ci}\left(3 \, a x\right) + a^{3} x^{3} \operatorname{Ci}\left(a x\right) + a^{3} x^{3} \operatorname{Ci}\left(-a x\right) + 27 \, a^{3} x^{3} \operatorname{Ci}\left(-3 \, a x\right) - 48 \, a x \cos\left(a x\right)^{3}\right)} \sin\left(a x\right)}{16 \, {\left(a x^{3} \sin\left(a x\right) + x^{2} \cos\left(a x\right)\right)}}"," ",0,"1/16*(88*a^2*x^2*cos(a*x)^2 - 8*(9*a^2*x^2 + 1)*cos(a*x)^4 - 16*a^2*x^2 - (27*a^2*x^2*cos_integral(3*a*x) + a^2*x^2*cos_integral(a*x) + a^2*x^2*cos_integral(-a*x) + 27*a^2*x^2*cos_integral(-3*a*x))*cos(a*x) - (27*a^3*x^3*cos_integral(3*a*x) + a^3*x^3*cos_integral(a*x) + a^3*x^3*cos_integral(-a*x) + 27*a^3*x^3*cos_integral(-3*a*x) - 48*a*x*cos(a*x)^3)*sin(a*x))/(a*x^3*sin(a*x) + x^2*cos(a*x))","A",0
596,1,73,0,0.900477," ","integrate(cos(a*x)^4/x^2/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""fricas"")","-\frac{2 \, a x \cos\left(a x\right) \operatorname{Si}\left(2 \, a x\right) + \cos\left(a x\right)^{3} + {\left(2 \, a^{2} x^{2} \operatorname{Si}\left(2 \, a x\right) + 2 \, a x \cos\left(a x\right)^{2} - a x\right)} \sin\left(a x\right)}{a x^{2} \sin\left(a x\right) + x \cos\left(a x\right)}"," ",0,"-(2*a*x*cos(a*x)*sin_integral(2*a*x) + cos(a*x)^3 + (2*a^2*x^2*sin_integral(2*a*x) + 2*a*x*cos(a*x)^2 - a*x)*sin(a*x))/(a*x^2*sin(a*x) + x*cos(a*x))","A",0
597,1,62,0,0.951333," ","integrate(cos(a*x)^3/x/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""fricas"")","\frac{{\left(\operatorname{Ci}\left(a x\right) + \operatorname{Ci}\left(-a x\right)\right)} \cos\left(a x\right) + 2 \, \cos\left(a x\right)^{2} + {\left(a x \operatorname{Ci}\left(a x\right) + a x \operatorname{Ci}\left(-a x\right)\right)} \sin\left(a x\right) - 2}{2 \, {\left(a x \sin\left(a x\right) + \cos\left(a x\right)\right)}}"," ",0,"1/2*((cos_integral(a*x) + cos_integral(-a*x))*cos(a*x) + 2*cos(a*x)^2 + (a*x*cos_integral(a*x) + a*x*cos_integral(-a*x))*sin(a*x) - 2)/(a*x*sin(a*x) + cos(a*x))","A",0
598,1,23,0,3.571856," ","integrate(cos(a*x)^2/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""fricas"")","\frac{\sin\left(a x\right)}{a^{2} x \sin\left(a x\right) + a \cos\left(a x\right)}"," ",0,"sin(a*x)/(a^2*x*sin(a*x) + a*cos(a*x))","A",0
599,1,22,0,0.860834," ","integrate(x*cos(a*x)/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""fricas"")","-\frac{1}{a^{3} x \sin\left(a x\right) + a^{2} \cos\left(a x\right)}"," ",0,"-1/(a^3*x*sin(a*x) + a^2*cos(a*x))","A",0
600,1,36,0,1.846295," ","integrate(x^2/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""fricas"")","-\frac{a x \cos\left(a x\right) - \sin\left(a x\right)}{a^{4} x \sin\left(a x\right) + a^{3} \cos\left(a x\right)}"," ",0,"-(a*x*cos(a*x) - sin(a*x))/(a^4*x*sin(a*x) + a^3*cos(a*x))","A",0
601,1,290,0,0.992931," ","integrate(x^3*sec(a*x)/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} x^{2} - {\left(-i \, a x \sin\left(a x\right) - i \, \cos\left(a x\right)\right)} {\rm Li}_2\left(i \, \cos\left(a x\right) + \sin\left(a x\right)\right) - {\left(-i \, a x \sin\left(a x\right) - i \, \cos\left(a x\right)\right)} {\rm Li}_2\left(i \, \cos\left(a x\right) - \sin\left(a x\right)\right) - {\left(i \, a x \sin\left(a x\right) + i \, \cos\left(a x\right)\right)} {\rm Li}_2\left(-i \, \cos\left(a x\right) + \sin\left(a x\right)\right) - {\left(i \, a x \sin\left(a x\right) + i \, \cos\left(a x\right)\right)} {\rm Li}_2\left(-i \, \cos\left(a x\right) - \sin\left(a x\right)\right) - {\left(a^{2} x^{2} \sin\left(a x\right) + a x \cos\left(a x\right)\right)} \log\left(i \, \cos\left(a x\right) + \sin\left(a x\right) + 1\right) + {\left(a^{2} x^{2} \sin\left(a x\right) + a x \cos\left(a x\right)\right)} \log\left(i \, \cos\left(a x\right) - \sin\left(a x\right) + 1\right) - {\left(a^{2} x^{2} \sin\left(a x\right) + a x \cos\left(a x\right)\right)} \log\left(-i \, \cos\left(a x\right) + \sin\left(a x\right) + 1\right) + {\left(a^{2} x^{2} \sin\left(a x\right) + a x \cos\left(a x\right)\right)} \log\left(-i \, \cos\left(a x\right) - \sin\left(a x\right) + 1\right) + 2}{2 \, {\left(a^{5} x \sin\left(a x\right) + a^{4} \cos\left(a x\right)\right)}}"," ",0,"-1/2*(2*a^2*x^2 - (-I*a*x*sin(a*x) - I*cos(a*x))*dilog(I*cos(a*x) + sin(a*x)) - (-I*a*x*sin(a*x) - I*cos(a*x))*dilog(I*cos(a*x) - sin(a*x)) - (I*a*x*sin(a*x) + I*cos(a*x))*dilog(-I*cos(a*x) + sin(a*x)) - (I*a*x*sin(a*x) + I*cos(a*x))*dilog(-I*cos(a*x) - sin(a*x)) - (a^2*x^2*sin(a*x) + a*x*cos(a*x))*log(I*cos(a*x) + sin(a*x) + 1) + (a^2*x^2*sin(a*x) + a*x*cos(a*x))*log(I*cos(a*x) - sin(a*x) + 1) - (a^2*x^2*sin(a*x) + a*x*cos(a*x))*log(-I*cos(a*x) + sin(a*x) + 1) + (a^2*x^2*sin(a*x) + a*x*cos(a*x))*log(-I*cos(a*x) - sin(a*x) + 1) + 2)/(a^5*x*sin(a*x) + a^4*cos(a*x))","B",0
602,1,378,0,1.882622," ","integrate(x^4*sec(a*x)^2/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""fricas"")","\frac{a^{3} x^{3} - {\left(2 \, a^{3} x^{3} + a x\right)} \cos\left(a x\right)^{2} + {\left(2 \, a^{2} x^{2} + 1\right)} \cos\left(a x\right) \sin\left(a x\right) + {\left(2 i \, a x \cos\left(a x\right) \sin\left(a x\right) + 2 i \, \cos\left(a x\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(a x\right) + \sin\left(a x\right)\right) + {\left(-2 i \, a x \cos\left(a x\right) \sin\left(a x\right) - 2 i \, \cos\left(a x\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(a x\right) - \sin\left(a x\right)\right) + {\left(-2 i \, a x \cos\left(a x\right) \sin\left(a x\right) - 2 i \, \cos\left(a x\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(a x\right) + \sin\left(a x\right)\right) + {\left(2 i \, a x \cos\left(a x\right) \sin\left(a x\right) + 2 i \, \cos\left(a x\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(a x\right) - \sin\left(a x\right)\right) + 2 \, {\left(a^{2} x^{2} \cos\left(a x\right) \sin\left(a x\right) + a x \cos\left(a x\right)^{2}\right)} \log\left(i \, \cos\left(a x\right) + \sin\left(a x\right) + 1\right) + 2 \, {\left(a^{2} x^{2} \cos\left(a x\right) \sin\left(a x\right) + a x \cos\left(a x\right)^{2}\right)} \log\left(i \, \cos\left(a x\right) - \sin\left(a x\right) + 1\right) + 2 \, {\left(a^{2} x^{2} \cos\left(a x\right) \sin\left(a x\right) + a x \cos\left(a x\right)^{2}\right)} \log\left(-i \, \cos\left(a x\right) + \sin\left(a x\right) + 1\right) + 2 \, {\left(a^{2} x^{2} \cos\left(a x\right) \sin\left(a x\right) + a x \cos\left(a x\right)^{2}\right)} \log\left(-i \, \cos\left(a x\right) - \sin\left(a x\right) + 1\right)}{a^{6} x \cos\left(a x\right) \sin\left(a x\right) + a^{5} \cos\left(a x\right)^{2}}"," ",0,"(a^3*x^3 - (2*a^3*x^3 + a*x)*cos(a*x)^2 + (2*a^2*x^2 + 1)*cos(a*x)*sin(a*x) + (2*I*a*x*cos(a*x)*sin(a*x) + 2*I*cos(a*x)^2)*dilog(I*cos(a*x) + sin(a*x)) + (-2*I*a*x*cos(a*x)*sin(a*x) - 2*I*cos(a*x)^2)*dilog(I*cos(a*x) - sin(a*x)) + (-2*I*a*x*cos(a*x)*sin(a*x) - 2*I*cos(a*x)^2)*dilog(-I*cos(a*x) + sin(a*x)) + (2*I*a*x*cos(a*x)*sin(a*x) + 2*I*cos(a*x)^2)*dilog(-I*cos(a*x) - sin(a*x)) + 2*(a^2*x^2*cos(a*x)*sin(a*x) + a*x*cos(a*x)^2)*log(I*cos(a*x) + sin(a*x) + 1) + 2*(a^2*x^2*cos(a*x)*sin(a*x) + a*x*cos(a*x)^2)*log(I*cos(a*x) - sin(a*x) + 1) + 2*(a^2*x^2*cos(a*x)*sin(a*x) + a*x*cos(a*x)^2)*log(-I*cos(a*x) + sin(a*x) + 1) + 2*(a^2*x^2*cos(a*x)*sin(a*x) + a*x*cos(a*x)^2)*log(-I*cos(a*x) - sin(a*x) + 1))/(a^6*x*cos(a*x)*sin(a*x) + a^5*cos(a*x)^2)","B",0
603,1,106,0,0.884677," ","integrate(sec(2*b*x+2*a)^4*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(35 \, \tan\left(b x + a\right)^{6} - 35 \, \tan\left(b x + a\right)^{4} + 49 \, \tan\left(b x + a\right)^{2} - 9\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{35 \, {\left(b \tan\left(b x + a\right)^{7} - 3 \, b \tan\left(b x + a\right)^{5} + 3 \, b \tan\left(b x + a\right)^{3} - b \tan\left(b x + a\right)\right)}}"," ",0,"-1/35*sqrt(2)*(35*tan(b*x + a)^6 - 35*tan(b*x + a)^4 + 49*tan(b*x + a)^2 - 9)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))/(b*tan(b*x + a)^7 - 3*b*tan(b*x + a)^5 + 3*b*tan(b*x + a)^3 - b*tan(b*x + a))","A",0
604,1,84,0,1.501214," ","integrate(sec(2*b*x+2*a)^3*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(15 \, \tan\left(b x + a\right)^{4} - 10 \, \tan\left(b x + a\right)^{2} + 7\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{15 \, {\left(b \tan\left(b x + a\right)^{5} - 2 \, b \tan\left(b x + a\right)^{3} + b \tan\left(b x + a\right)\right)}}"," ",0,"1/15*sqrt(2)*(15*tan(b*x + a)^4 - 10*tan(b*x + a)^2 + 7)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))/(b*tan(b*x + a)^5 - 2*b*tan(b*x + a)^3 + b*tan(b*x + a))","A",0
605,1,64,0,0.906256," ","integrate(sec(2*b*x+2*a)^2*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(3 \, \tan\left(b x + a\right)^{2} - 1\right)}}{3 \, {\left(b \tan\left(b x + a\right)^{3} - b \tan\left(b x + a\right)\right)}}"," ",0,"-1/3*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(3*tan(b*x + a)^2 - 1)/(b*tan(b*x + a)^3 - b*tan(b*x + a))","A",0
606,1,40,0,0.427329," ","integrate(sec(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{b \tan\left(b x + a\right)}"," ",0,"sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))/(b*tan(b*x + a))","A",0
607,1,201,0,1.464648," ","integrate((c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{c} \log\left(-\frac{c \tan\left(b x + a\right)^{5} - 14 \, c \tan\left(b x + a\right)^{3} - 4 \, \sqrt{2} {\left(\tan\left(b x + a\right)^{4} - 4 \, \tan\left(b x + a\right)^{2} + 3\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} \sqrt{c} + 17 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{5} + 2 \, \tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)}\right)}{4 \, b}, \frac{\sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)^{3} - 3 \, c \tan\left(b x + a\right)}\right)}{2 \, b}\right]"," ",0,"[1/4*sqrt(c)*log(-(c*tan(b*x + a)^5 - 14*c*tan(b*x + a)^3 - 4*sqrt(2)*(tan(b*x + a)^4 - 4*tan(b*x + a)^2 + 3)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*sqrt(c) + 17*c*tan(b*x + a))/(tan(b*x + a)^5 + 2*tan(b*x + a)^3 + tan(b*x + a)))/b, 1/2*sqrt(-c)*arctan(2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a)^3 - 3*c*tan(b*x + a)))/b]","A",0
608,1,351,0,2.277280," ","integrate(cos(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(\tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)\right)} \sqrt{c} \log\left(-\frac{c \tan\left(b x + a\right)^{5} - 14 \, c \tan\left(b x + a\right)^{3} + 4 \, \sqrt{2} {\left(\tan\left(b x + a\right)^{4} - 4 \, \tan\left(b x + a\right)^{2} + 3\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} \sqrt{c} + 17 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{5} + 2 \, \tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)}\right) + 4 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)}}{8 \, {\left(b \tan\left(b x + a\right)^{3} + b \tan\left(b x + a\right)\right)}}, -\frac{{\left(\tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)^{3} - 3 \, c \tan\left(b x + a\right)}\right) - 2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)}}{4 \, {\left(b \tan\left(b x + a\right)^{3} + b \tan\left(b x + a\right)\right)}}\right]"," ",0,"[1/8*((tan(b*x + a)^3 + tan(b*x + a))*sqrt(c)*log(-(c*tan(b*x + a)^5 - 14*c*tan(b*x + a)^3 + 4*sqrt(2)*(tan(b*x + a)^4 - 4*tan(b*x + a)^2 + 3)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*sqrt(c) + 17*c*tan(b*x + a))/(tan(b*x + a)^5 + 2*tan(b*x + a)^3 + tan(b*x + a))) + 4*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1))/(b*tan(b*x + a)^3 + b*tan(b*x + a)), -1/4*((tan(b*x + a)^3 + tan(b*x + a))*sqrt(-c)*arctan(2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a)^3 - 3*c*tan(b*x + a))) - 2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1))/(b*tan(b*x + a)^3 + b*tan(b*x + a))]","B",0
609,1,419,0,0.953395," ","integrate(cos(2*b*x+2*a)^2*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(\tan\left(b x + a\right)^{5} + 2 \, \tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)\right)} \sqrt{c} \log\left(-\frac{c \tan\left(b x + a\right)^{5} - 14 \, c \tan\left(b x + a\right)^{3} - 4 \, \sqrt{2} {\left(\tan\left(b x + a\right)^{4} - 4 \, \tan\left(b x + a\right)^{2} + 3\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} \sqrt{c} + 17 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{5} + 2 \, \tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)}\right) - 4 \, \sqrt{2} {\left(5 \, \tan\left(b x + a\right)^{4} - 4 \, \tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{32 \, {\left(b \tan\left(b x + a\right)^{5} + 2 \, b \tan\left(b x + a\right)^{3} + b \tan\left(b x + a\right)\right)}}, \frac{3 \, {\left(\tan\left(b x + a\right)^{5} + 2 \, \tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)^{3} - 3 \, c \tan\left(b x + a\right)}\right) - 2 \, \sqrt{2} {\left(5 \, \tan\left(b x + a\right)^{4} - 4 \, \tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{16 \, {\left(b \tan\left(b x + a\right)^{5} + 2 \, b \tan\left(b x + a\right)^{3} + b \tan\left(b x + a\right)\right)}}\right]"," ",0,"[1/32*(3*(tan(b*x + a)^5 + 2*tan(b*x + a)^3 + tan(b*x + a))*sqrt(c)*log(-(c*tan(b*x + a)^5 - 14*c*tan(b*x + a)^3 - 4*sqrt(2)*(tan(b*x + a)^4 - 4*tan(b*x + a)^2 + 3)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*sqrt(c) + 17*c*tan(b*x + a))/(tan(b*x + a)^5 + 2*tan(b*x + a)^3 + tan(b*x + a))) - 4*sqrt(2)*(5*tan(b*x + a)^4 - 4*tan(b*x + a)^2 - 1)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*tan(b*x + a)^5 + 2*b*tan(b*x + a)^3 + b*tan(b*x + a)), 1/16*(3*(tan(b*x + a)^5 + 2*tan(b*x + a)^3 + tan(b*x + a))*sqrt(-c)*arctan(2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a)^3 - 3*c*tan(b*x + a))) - 2*sqrt(2)*(5*tan(b*x + a)^4 - 4*tan(b*x + a)^2 - 1)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*tan(b*x + a)^5 + 2*b*tan(b*x + a)^3 + b*tan(b*x + a))]","A",0
610,1,481,0,2.224208," ","integrate(cos(2*b*x+2*a)^3*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(\tan\left(b x + a\right)^{7} + 3 \, \tan\left(b x + a\right)^{5} + 3 \, \tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)\right)} \sqrt{c} \log\left(-\frac{c \tan\left(b x + a\right)^{5} - 14 \, c \tan\left(b x + a\right)^{3} + 4 \, \sqrt{2} {\left(\tan\left(b x + a\right)^{4} - 4 \, \tan\left(b x + a\right)^{2} + 3\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} \sqrt{c} + 17 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{5} + 2 \, \tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)}\right) + 4 \, \sqrt{2} {\left(33 \, \tan\left(b x + a\right)^{6} - 19 \, \tan\left(b x + a\right)^{4} - \tan\left(b x + a\right)^{2} - 13\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{192 \, {\left(b \tan\left(b x + a\right)^{7} + 3 \, b \tan\left(b x + a\right)^{5} + 3 \, b \tan\left(b x + a\right)^{3} + b \tan\left(b x + a\right)\right)}}, -\frac{15 \, {\left(\tan\left(b x + a\right)^{7} + 3 \, \tan\left(b x + a\right)^{5} + 3 \, \tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)^{3} - 3 \, c \tan\left(b x + a\right)}\right) - 2 \, \sqrt{2} {\left(33 \, \tan\left(b x + a\right)^{6} - 19 \, \tan\left(b x + a\right)^{4} - \tan\left(b x + a\right)^{2} - 13\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{96 \, {\left(b \tan\left(b x + a\right)^{7} + 3 \, b \tan\left(b x + a\right)^{5} + 3 \, b \tan\left(b x + a\right)^{3} + b \tan\left(b x + a\right)\right)}}\right]"," ",0,"[1/192*(15*(tan(b*x + a)^7 + 3*tan(b*x + a)^5 + 3*tan(b*x + a)^3 + tan(b*x + a))*sqrt(c)*log(-(c*tan(b*x + a)^5 - 14*c*tan(b*x + a)^3 + 4*sqrt(2)*(tan(b*x + a)^4 - 4*tan(b*x + a)^2 + 3)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*sqrt(c) + 17*c*tan(b*x + a))/(tan(b*x + a)^5 + 2*tan(b*x + a)^3 + tan(b*x + a))) + 4*sqrt(2)*(33*tan(b*x + a)^6 - 19*tan(b*x + a)^4 - tan(b*x + a)^2 - 13)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*tan(b*x + a)^7 + 3*b*tan(b*x + a)^5 + 3*b*tan(b*x + a)^3 + b*tan(b*x + a)), -1/96*(15*(tan(b*x + a)^7 + 3*tan(b*x + a)^5 + 3*tan(b*x + a)^3 + tan(b*x + a))*sqrt(-c)*arctan(2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a)^3 - 3*c*tan(b*x + a))) - 2*sqrt(2)*(33*tan(b*x + a)^6 - 19*tan(b*x + a)^4 - tan(b*x + a)^2 - 13)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*tan(b*x + a)^7 + 3*b*tan(b*x + a)^5 + 3*b*tan(b*x + a)^3 + b*tan(b*x + a))]","A",0
611,1,132,0,1.047497," ","integrate(sec(2*b*x+2*a)^4*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left(315 \, c \tan\left(b x + a\right)^{8} - 525 \, c \tan\left(b x + a\right)^{6} + 819 \, c \tan\left(b x + a\right)^{4} - 423 \, c \tan\left(b x + a\right)^{2} + 94 \, c\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{315 \, {\left(b \tan\left(b x + a\right)^{9} - 4 \, b \tan\left(b x + a\right)^{7} + 6 \, b \tan\left(b x + a\right)^{5} - 4 \, b \tan\left(b x + a\right)^{3} + b \tan\left(b x + a\right)\right)}}"," ",0,"2/315*sqrt(2)*(315*c*tan(b*x + a)^8 - 525*c*tan(b*x + a)^6 + 819*c*tan(b*x + a)^4 - 423*c*tan(b*x + a)^2 + 94*c)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))/(b*tan(b*x + a)^9 - 4*b*tan(b*x + a)^7 + 6*b*tan(b*x + a)^5 - 4*b*tan(b*x + a)^3 + b*tan(b*x + a))","A",0
612,1,111,0,0.973994," ","integrate(sec(2*b*x+2*a)^3*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} {\left(105 \, c \tan\left(b x + a\right)^{6} - 140 \, c \tan\left(b x + a\right)^{4} + 133 \, c \tan\left(b x + a\right)^{2} - 38 \, c\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{105 \, {\left(b \tan\left(b x + a\right)^{7} - 3 \, b \tan\left(b x + a\right)^{5} + 3 \, b \tan\left(b x + a\right)^{3} - b \tan\left(b x + a\right)\right)}}"," ",0,"-2/105*sqrt(2)*(105*c*tan(b*x + a)^6 - 140*c*tan(b*x + a)^4 + 133*c*tan(b*x + a)^2 - 38*c)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))/(b*tan(b*x + a)^7 - 3*b*tan(b*x + a)^5 + 3*b*tan(b*x + a)^3 - b*tan(b*x + a))","A",0
613,1,88,0,0.901953," ","integrate(sec(2*b*x+2*a)^2*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left(5 \, c \tan\left(b x + a\right)^{4} - 5 \, c \tan\left(b x + a\right)^{2} + 2 \, c\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{5 \, {\left(b \tan\left(b x + a\right)^{5} - 2 \, b \tan\left(b x + a\right)^{3} + b \tan\left(b x + a\right)\right)}}"," ",0,"2/5*sqrt(2)*(5*c*tan(b*x + a)^4 - 5*c*tan(b*x + a)^2 + 2*c)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))/(b*tan(b*x + a)^5 - 2*b*tan(b*x + a)^3 + b*tan(b*x + a))","A",0
614,1,67,0,0.883687," ","integrate(sec(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} {\left(3 \, c \tan\left(b x + a\right)^{2} - 2 \, c\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{3 \, {\left(b \tan\left(b x + a\right)^{3} - b \tan\left(b x + a\right)\right)}}"," ",0,"-2/3*sqrt(2)*(3*c*tan(b*x + a)^2 - 2*c)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))/(b*tan(b*x + a)^3 - b*tan(b*x + a))","A",0
615,1,296,0,1.032939," ","integrate((c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""fricas"")","\left[\frac{c^{\frac{3}{2}} \log\left(-\frac{c \tan\left(b x + a\right)^{5} - 14 \, c \tan\left(b x + a\right)^{3} + 4 \, \sqrt{2} {\left(\tan\left(b x + a\right)^{4} - 4 \, \tan\left(b x + a\right)^{2} + 3\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} \sqrt{c} + 17 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{5} + 2 \, \tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)}\right) \tan\left(b x + a\right) + 4 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} c}{4 \, b \tan\left(b x + a\right)}, -\frac{\sqrt{-c} c \arctan\left(\frac{2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)^{3} - 3 \, c \tan\left(b x + a\right)}\right) \tan\left(b x + a\right) - 2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} c}{2 \, b \tan\left(b x + a\right)}\right]"," ",0,"[1/4*(c^(3/2)*log(-(c*tan(b*x + a)^5 - 14*c*tan(b*x + a)^3 + 4*sqrt(2)*(tan(b*x + a)^4 - 4*tan(b*x + a)^2 + 3)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*sqrt(c) + 17*c*tan(b*x + a))/(tan(b*x + a)^5 + 2*tan(b*x + a)^3 + tan(b*x + a)))*tan(b*x + a) + 4*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*c)/(b*tan(b*x + a)), -1/2*(sqrt(-c)*c*arctan(2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a)^3 - 3*c*tan(b*x + a)))*tan(b*x + a) - 2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*c)/(b*tan(b*x + a))]","A",0
616,1,369,0,2.090246," ","integrate(cos(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c \tan\left(b x + a\right)^{3} + c \tan\left(b x + a\right)\right)} \sqrt{c} \log\left(-\frac{c \tan\left(b x + a\right)^{5} - 14 \, c \tan\left(b x + a\right)^{3} - 4 \, \sqrt{2} {\left(\tan\left(b x + a\right)^{4} - 4 \, \tan\left(b x + a\right)^{2} + 3\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} \sqrt{c} + 17 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{5} + 2 \, \tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)}\right) - 4 \, \sqrt{2} {\left(c \tan\left(b x + a\right)^{2} - c\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{8 \, {\left(b \tan\left(b x + a\right)^{3} + b \tan\left(b x + a\right)\right)}}, \frac{3 \, {\left(c \tan\left(b x + a\right)^{3} + c \tan\left(b x + a\right)\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)^{3} - 3 \, c \tan\left(b x + a\right)}\right) - 2 \, \sqrt{2} {\left(c \tan\left(b x + a\right)^{2} - c\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{4 \, {\left(b \tan\left(b x + a\right)^{3} + b \tan\left(b x + a\right)\right)}}\right]"," ",0,"[1/8*(3*(c*tan(b*x + a)^3 + c*tan(b*x + a))*sqrt(c)*log(-(c*tan(b*x + a)^5 - 14*c*tan(b*x + a)^3 - 4*sqrt(2)*(tan(b*x + a)^4 - 4*tan(b*x + a)^2 + 3)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*sqrt(c) + 17*c*tan(b*x + a))/(tan(b*x + a)^5 + 2*tan(b*x + a)^3 + tan(b*x + a))) - 4*sqrt(2)*(c*tan(b*x + a)^2 - c)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*tan(b*x + a)^3 + b*tan(b*x + a)), 1/4*(3*(c*tan(b*x + a)^3 + c*tan(b*x + a))*sqrt(-c)*arctan(2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a)^3 - 3*c*tan(b*x + a))) - 2*sqrt(2)*(c*tan(b*x + a)^2 - c)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*tan(b*x + a)^3 + b*tan(b*x + a))]","B",0
617,1,437,0,1.040923," ","integrate(cos(2*b*x+2*a)^2*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""fricas"")","\left[\frac{7 \, {\left(c \tan\left(b x + a\right)^{5} + 2 \, c \tan\left(b x + a\right)^{3} + c \tan\left(b x + a\right)\right)} \sqrt{c} \log\left(-\frac{c \tan\left(b x + a\right)^{5} - 14 \, c \tan\left(b x + a\right)^{3} + 4 \, \sqrt{2} {\left(\tan\left(b x + a\right)^{4} - 4 \, \tan\left(b x + a\right)^{2} + 3\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} \sqrt{c} + 17 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{5} + 2 \, \tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)}\right) + 4 \, \sqrt{2} {\left(9 \, c \tan\left(b x + a\right)^{4} - 4 \, c \tan\left(b x + a\right)^{2} - 5 \, c\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{32 \, {\left(b \tan\left(b x + a\right)^{5} + 2 \, b \tan\left(b x + a\right)^{3} + b \tan\left(b x + a\right)\right)}}, -\frac{7 \, {\left(c \tan\left(b x + a\right)^{5} + 2 \, c \tan\left(b x + a\right)^{3} + c \tan\left(b x + a\right)\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)^{3} - 3 \, c \tan\left(b x + a\right)}\right) - 2 \, \sqrt{2} {\left(9 \, c \tan\left(b x + a\right)^{4} - 4 \, c \tan\left(b x + a\right)^{2} - 5 \, c\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{16 \, {\left(b \tan\left(b x + a\right)^{5} + 2 \, b \tan\left(b x + a\right)^{3} + b \tan\left(b x + a\right)\right)}}\right]"," ",0,"[1/32*(7*(c*tan(b*x + a)^5 + 2*c*tan(b*x + a)^3 + c*tan(b*x + a))*sqrt(c)*log(-(c*tan(b*x + a)^5 - 14*c*tan(b*x + a)^3 + 4*sqrt(2)*(tan(b*x + a)^4 - 4*tan(b*x + a)^2 + 3)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*sqrt(c) + 17*c*tan(b*x + a))/(tan(b*x + a)^5 + 2*tan(b*x + a)^3 + tan(b*x + a))) + 4*sqrt(2)*(9*c*tan(b*x + a)^4 - 4*c*tan(b*x + a)^2 - 5*c)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*tan(b*x + a)^5 + 2*b*tan(b*x + a)^3 + b*tan(b*x + a)), -1/16*(7*(c*tan(b*x + a)^5 + 2*c*tan(b*x + a)^3 + c*tan(b*x + a))*sqrt(-c)*arctan(2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a)^3 - 3*c*tan(b*x + a))) - 2*sqrt(2)*(9*c*tan(b*x + a)^4 - 4*c*tan(b*x + a)^2 - 5*c)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*tan(b*x + a)^5 + 2*b*tan(b*x + a)^3 + b*tan(b*x + a))]","A",0
618,1,503,0,0.728356," ","integrate(cos(2*b*x+2*a)^3*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""fricas"")","\left[\frac{33 \, {\left(c \tan\left(b x + a\right)^{7} + 3 \, c \tan\left(b x + a\right)^{5} + 3 \, c \tan\left(b x + a\right)^{3} + c \tan\left(b x + a\right)\right)} \sqrt{c} \log\left(-\frac{c \tan\left(b x + a\right)^{5} - 14 \, c \tan\left(b x + a\right)^{3} - 4 \, \sqrt{2} {\left(\tan\left(b x + a\right)^{4} - 4 \, \tan\left(b x + a\right)^{2} + 3\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} \sqrt{c} + 17 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{5} + 2 \, \tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)}\right) - 4 \, \sqrt{2} {\left(63 \, c \tan\left(b x + a\right)^{6} - 13 \, c \tan\left(b x + a\right)^{4} - 31 \, c \tan\left(b x + a\right)^{2} - 19 \, c\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{192 \, {\left(b \tan\left(b x + a\right)^{7} + 3 \, b \tan\left(b x + a\right)^{5} + 3 \, b \tan\left(b x + a\right)^{3} + b \tan\left(b x + a\right)\right)}}, \frac{33 \, {\left(c \tan\left(b x + a\right)^{7} + 3 \, c \tan\left(b x + a\right)^{5} + 3 \, c \tan\left(b x + a\right)^{3} + c \tan\left(b x + a\right)\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)^{3} - 3 \, c \tan\left(b x + a\right)}\right) - 2 \, \sqrt{2} {\left(63 \, c \tan\left(b x + a\right)^{6} - 13 \, c \tan\left(b x + a\right)^{4} - 31 \, c \tan\left(b x + a\right)^{2} - 19 \, c\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{96 \, {\left(b \tan\left(b x + a\right)^{7} + 3 \, b \tan\left(b x + a\right)^{5} + 3 \, b \tan\left(b x + a\right)^{3} + b \tan\left(b x + a\right)\right)}}\right]"," ",0,"[1/192*(33*(c*tan(b*x + a)^7 + 3*c*tan(b*x + a)^5 + 3*c*tan(b*x + a)^3 + c*tan(b*x + a))*sqrt(c)*log(-(c*tan(b*x + a)^5 - 14*c*tan(b*x + a)^3 - 4*sqrt(2)*(tan(b*x + a)^4 - 4*tan(b*x + a)^2 + 3)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*sqrt(c) + 17*c*tan(b*x + a))/(tan(b*x + a)^5 + 2*tan(b*x + a)^3 + tan(b*x + a))) - 4*sqrt(2)*(63*c*tan(b*x + a)^6 - 13*c*tan(b*x + a)^4 - 31*c*tan(b*x + a)^2 - 19*c)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*tan(b*x + a)^7 + 3*b*tan(b*x + a)^5 + 3*b*tan(b*x + a)^3 + b*tan(b*x + a)), 1/96*(33*(c*tan(b*x + a)^7 + 3*c*tan(b*x + a)^5 + 3*c*tan(b*x + a)^3 + c*tan(b*x + a))*sqrt(-c)*arctan(2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a)^3 - 3*c*tan(b*x + a))) - 2*sqrt(2)*(63*c*tan(b*x + a)^6 - 13*c*tan(b*x + a)^4 - 31*c*tan(b*x + a)^2 - 19*c)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*tan(b*x + a)^7 + 3*b*tan(b*x + a)^5 + 3*b*tan(b*x + a)^3 + b*tan(b*x + a))]","A",0
619,1,380,0,0.507759," ","integrate(sec(2*b*x+2*a)^4/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left(15 \, \tan\left(b x + a\right)^{4} - 20 \, \tan\left(b x + a\right)^{2} + 17\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} + \frac{15 \, \sqrt{2} {\left(c \tan\left(b x + a\right)^{5} - 2 \, c \tan\left(b x + a\right)^{3} + c \tan\left(b x + a\right)\right)} \log\left(\frac{\tan\left(b x + a\right)^{3} - \frac{2 \, \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)}}{\sqrt{c}} - 2 \, \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3}}\right)}{\sqrt{c}}}{60 \, {\left(b c \tan\left(b x + a\right)^{5} - 2 \, b c \tan\left(b x + a\right)^{3} + b c \tan\left(b x + a\right)\right)}}, -\frac{15 \, \sqrt{2} {\left(c \tan\left(b x + a\right)^{5} - 2 \, c \tan\left(b x + a\right)^{3} + c \tan\left(b x + a\right)\right)} \sqrt{-\frac{1}{c}} \arctan\left(\frac{\sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-\frac{1}{c}}}{\tan\left(b x + a\right)}\right) - 2 \, \sqrt{2} {\left(15 \, \tan\left(b x + a\right)^{4} - 20 \, \tan\left(b x + a\right)^{2} + 17\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{30 \, {\left(b c \tan\left(b x + a\right)^{5} - 2 \, b c \tan\left(b x + a\right)^{3} + b c \tan\left(b x + a\right)\right)}}\right]"," ",0,"[1/60*(4*sqrt(2)*(15*tan(b*x + a)^4 - 20*tan(b*x + a)^2 + 17)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)) + 15*sqrt(2)*(c*tan(b*x + a)^5 - 2*c*tan(b*x + a)^3 + c*tan(b*x + a))*log((tan(b*x + a)^3 - 2*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)/sqrt(c) - 2*tan(b*x + a))/tan(b*x + a)^3)/sqrt(c))/(b*c*tan(b*x + a)^5 - 2*b*c*tan(b*x + a)^3 + b*c*tan(b*x + a)), -1/30*(15*sqrt(2)*(c*tan(b*x + a)^5 - 2*c*tan(b*x + a)^3 + c*tan(b*x + a))*sqrt(-1/c)*arctan(sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-1/c)/tan(b*x + a)) - 2*sqrt(2)*(15*tan(b*x + a)^4 - 20*tan(b*x + a)^2 + 17)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*c*tan(b*x + a)^5 - 2*b*c*tan(b*x + a)^3 + b*c*tan(b*x + a))]","A",0
620,1,294,0,2.195125," ","integrate(sec(2*b*x+2*a)^3/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""fricas"")","\left[\frac{\frac{3 \, \sqrt{2} {\left(c \tan\left(b x + a\right)^{3} - c \tan\left(b x + a\right)\right)} \log\left(\frac{\tan\left(b x + a\right)^{3} - \frac{2 \, \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)}}{\sqrt{c}} - 2 \, \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3}}\right)}{\sqrt{c}} - 8 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{12 \, {\left(b c \tan\left(b x + a\right)^{3} - b c \tan\left(b x + a\right)\right)}}, -\frac{3 \, \sqrt{2} {\left(c \tan\left(b x + a\right)^{3} - c \tan\left(b x + a\right)\right)} \sqrt{-\frac{1}{c}} \arctan\left(\frac{\sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-\frac{1}{c}}}{\tan\left(b x + a\right)}\right) + 4 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{6 \, {\left(b c \tan\left(b x + a\right)^{3} - b c \tan\left(b x + a\right)\right)}}\right]"," ",0,"[1/12*(3*sqrt(2)*(c*tan(b*x + a)^3 - c*tan(b*x + a))*log((tan(b*x + a)^3 - 2*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)/sqrt(c) - 2*tan(b*x + a))/tan(b*x + a)^3)/sqrt(c) - 8*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*c*tan(b*x + a)^3 - b*c*tan(b*x + a)), -1/6*(3*sqrt(2)*(c*tan(b*x + a)^3 - c*tan(b*x + a))*sqrt(-1/c)*arctan(sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-1/c)/tan(b*x + a)) + 4*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*c*tan(b*x + a)^3 - b*c*tan(b*x + a))]","A",0
621,1,245,0,1.625058," ","integrate(sec(2*b*x+2*a)^2/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{c} \log\left(\frac{\tan\left(b x + a\right)^{3} - \frac{2 \, \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)}}{\sqrt{c}} - 2 \, \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3}}\right) \tan\left(b x + a\right) + 4 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{4 \, b c \tan\left(b x + a\right)}, -\frac{\sqrt{2} c \sqrt{-\frac{1}{c}} \arctan\left(\frac{\sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-\frac{1}{c}}}{\tan\left(b x + a\right)}\right) \tan\left(b x + a\right) - 2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{2 \, b c \tan\left(b x + a\right)}\right]"," ",0,"[1/4*(sqrt(2)*sqrt(c)*log((tan(b*x + a)^3 - 2*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)/sqrt(c) - 2*tan(b*x + a))/tan(b*x + a)^3)*tan(b*x + a) + 4*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*c*tan(b*x + a)), -1/2*(sqrt(2)*c*sqrt(-1/c)*arctan(sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-1/c)/tan(b*x + a))*tan(b*x + a) - 2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*c*tan(b*x + a))]","A",0
622,1,146,0,2.000709," ","integrate(sec(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \log\left(\frac{\tan\left(b x + a\right)^{3} - \frac{2 \, \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)}}{\sqrt{c}} - 2 \, \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3}}\right)}{4 \, b \sqrt{c}}, -\frac{\sqrt{2} \sqrt{-\frac{1}{c}} \arctan\left(\frac{\sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-\frac{1}{c}}}{\tan\left(b x + a\right)}\right)}{2 \, b}\right]"," ",0,"[1/4*sqrt(2)*log((tan(b*x + a)^3 - 2*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)/sqrt(c) - 2*tan(b*x + a))/tan(b*x + a)^3)/(b*sqrt(c)), -1/2*sqrt(2)*sqrt(-1/c)*arctan(sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-1/c)/tan(b*x + a))/b]","A",0
623,1,309,0,1.903738," ","integrate(1/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{c} \log\left(\frac{c \tan\left(b x + a\right)^{3} - 2 \, \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{c} - 2 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3}}\right) + 2 \, \sqrt{c} \log\left(\frac{c \tan\left(b x + a\right)^{3} + 2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{c} - 3 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)}\right)}{4 \, b c}, -\frac{\sqrt{2} \sqrt{-c} \arctan\left(\frac{\sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)}\right) - 2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{2 \, c \tan\left(b x + a\right)}\right)}{2 \, b c}\right]"," ",0,"[1/4*(sqrt(2)*sqrt(c)*log((c*tan(b*x + a)^3 - 2*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(c) - 2*c*tan(b*x + a))/tan(b*x + a)^3) + 2*sqrt(c)*log((c*tan(b*x + a)^3 + 2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(c) - 3*c*tan(b*x + a))/(tan(b*x + a)^3 + tan(b*x + a))))/(b*c), -1/2*(sqrt(2)*sqrt(-c)*arctan(sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a))) - 2*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a))))/(b*c)]","A",0
624,1,481,0,0.963470," ","integrate(cos(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left(\tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)\right)} \sqrt{c} \log\left(\frac{c \tan\left(b x + a\right)^{3} - 2 \, \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{c} - 2 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3}}\right) + {\left(\tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)\right)} \sqrt{c} \log\left(\frac{c \tan\left(b x + a\right)^{3} + 2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{c} - 3 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)}\right) - 2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)}}{4 \, {\left(b c \tan\left(b x + a\right)^{3} + b c \tan\left(b x + a\right)\right)}}, -\frac{\sqrt{2} {\left(\tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)}\right) - {\left(\tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{2 \, c \tan\left(b x + a\right)}\right) + \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)}}{2 \, {\left(b c \tan\left(b x + a\right)^{3} + b c \tan\left(b x + a\right)\right)}}\right]"," ",0,"[1/4*(sqrt(2)*(tan(b*x + a)^3 + tan(b*x + a))*sqrt(c)*log((c*tan(b*x + a)^3 - 2*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(c) - 2*c*tan(b*x + a))/tan(b*x + a)^3) + (tan(b*x + a)^3 + tan(b*x + a))*sqrt(c)*log((c*tan(b*x + a)^3 + 2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(c) - 3*c*tan(b*x + a))/(tan(b*x + a)^3 + tan(b*x + a))) - 2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1))/(b*c*tan(b*x + a)^3 + b*c*tan(b*x + a)), -1/2*(sqrt(2)*(tan(b*x + a)^3 + tan(b*x + a))*sqrt(-c)*arctan(sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a))) - (tan(b*x + a)^3 + tan(b*x + a))*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a))) + sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1))/(b*c*tan(b*x + a)^3 + b*c*tan(b*x + a))]","A",0
625,1,569,0,1.946548," ","integrate(cos(2*b*x+2*a)^2/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left(\tan\left(b x + a\right)^{5} + 2 \, \tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)\right)} \sqrt{c} \log\left(\frac{c \tan\left(b x + a\right)^{3} - 2 \, \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{c} - 2 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3}}\right) + 7 \, {\left(\tan\left(b x + a\right)^{5} + 2 \, \tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)\right)} \sqrt{c} \log\left(\frac{c \tan\left(b x + a\right)^{3} + 2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{c} - 3 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)}\right) + 2 \, \sqrt{2} {\left(\tan\left(b x + a\right)^{4} - 4 \, \tan\left(b x + a\right)^{2} + 3\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{16 \, {\left(b c \tan\left(b x + a\right)^{5} + 2 \, b c \tan\left(b x + a\right)^{3} + b c \tan\left(b x + a\right)\right)}}, -\frac{4 \, \sqrt{2} {\left(\tan\left(b x + a\right)^{5} + 2 \, \tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)}\right) - 7 \, {\left(\tan\left(b x + a\right)^{5} + 2 \, \tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{2 \, c \tan\left(b x + a\right)}\right) - \sqrt{2} {\left(\tan\left(b x + a\right)^{4} - 4 \, \tan\left(b x + a\right)^{2} + 3\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{8 \, {\left(b c \tan\left(b x + a\right)^{5} + 2 \, b c \tan\left(b x + a\right)^{3} + b c \tan\left(b x + a\right)\right)}}\right]"," ",0,"[1/16*(4*sqrt(2)*(tan(b*x + a)^5 + 2*tan(b*x + a)^3 + tan(b*x + a))*sqrt(c)*log((c*tan(b*x + a)^3 - 2*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(c) - 2*c*tan(b*x + a))/tan(b*x + a)^3) + 7*(tan(b*x + a)^5 + 2*tan(b*x + a)^3 + tan(b*x + a))*sqrt(c)*log((c*tan(b*x + a)^3 + 2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(c) - 3*c*tan(b*x + a))/(tan(b*x + a)^3 + tan(b*x + a))) + 2*sqrt(2)*(tan(b*x + a)^4 - 4*tan(b*x + a)^2 + 3)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*c*tan(b*x + a)^5 + 2*b*c*tan(b*x + a)^3 + b*c*tan(b*x + a)), -1/8*(4*sqrt(2)*(tan(b*x + a)^5 + 2*tan(b*x + a)^3 + tan(b*x + a))*sqrt(-c)*arctan(sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a))) - 7*(tan(b*x + a)^5 + 2*tan(b*x + a)^3 + tan(b*x + a))*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a))) - sqrt(2)*(tan(b*x + a)^4 - 4*tan(b*x + a)^2 + 3)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*c*tan(b*x + a)^5 + 2*b*c*tan(b*x + a)^3 + b*c*tan(b*x + a))]","A",0
626,1,350,0,1.154552," ","integrate(sec(2*b*x+2*a)^4/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""fricas"")","\left[\frac{33 \, \sqrt{2} {\left(\tan\left(b x + a\right)^{5} - \tan\left(b x + a\right)^{3}\right)} \sqrt{c} \log\left(\frac{c \tan\left(b x + a\right)^{3} - 2 \, \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{c} - 2 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3}}\right) + 2 \, \sqrt{2} {\left(27 \, \tan\left(b x + a\right)^{4} - 46 \, \tan\left(b x + a\right)^{2} + 3\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{48 \, {\left(b c^{2} \tan\left(b x + a\right)^{5} - b c^{2} \tan\left(b x + a\right)^{3}\right)}}, -\frac{33 \, \sqrt{2} {\left(\tan\left(b x + a\right)^{5} - \tan\left(b x + a\right)^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)}\right) - \sqrt{2} {\left(27 \, \tan\left(b x + a\right)^{4} - 46 \, \tan\left(b x + a\right)^{2} + 3\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{24 \, {\left(b c^{2} \tan\left(b x + a\right)^{5} - b c^{2} \tan\left(b x + a\right)^{3}\right)}}\right]"," ",0,"[1/48*(33*sqrt(2)*(tan(b*x + a)^5 - tan(b*x + a)^3)*sqrt(c)*log((c*tan(b*x + a)^3 - 2*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(c) - 2*c*tan(b*x + a))/tan(b*x + a)^3) + 2*sqrt(2)*(27*tan(b*x + a)^4 - 46*tan(b*x + a)^2 + 3)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*c^2*tan(b*x + a)^5 - b*c^2*tan(b*x + a)^3), -1/24*(33*sqrt(2)*(tan(b*x + a)^5 - tan(b*x + a)^3)*sqrt(-c)*arctan(sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a))) - sqrt(2)*(27*tan(b*x + a)^4 - 46*tan(b*x + a)^2 + 3)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*c^2*tan(b*x + a)^5 - b*c^2*tan(b*x + a)^3)]","A",0
627,1,276,0,1.998082," ","integrate(sec(2*b*x+2*a)^3/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""fricas"")","\left[\frac{7 \, \sqrt{2} \sqrt{c} \log\left(\frac{c \tan\left(b x + a\right)^{3} - 2 \, \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{c} - 2 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3}}\right) \tan\left(b x + a\right)^{3} + 2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(9 \, \tan\left(b x + a\right)^{2} - 1\right)}}{16 \, b c^{2} \tan\left(b x + a\right)^{3}}, -\frac{7 \, \sqrt{2} \sqrt{-c} \arctan\left(\frac{\sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)}\right) \tan\left(b x + a\right)^{3} - \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(9 \, \tan\left(b x + a\right)^{2} - 1\right)}}{8 \, b c^{2} \tan\left(b x + a\right)^{3}}\right]"," ",0,"[1/16*(7*sqrt(2)*sqrt(c)*log((c*tan(b*x + a)^3 - 2*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(c) - 2*c*tan(b*x + a))/tan(b*x + a)^3)*tan(b*x + a)^3 + 2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(9*tan(b*x + a)^2 - 1))/(b*c^2*tan(b*x + a)^3), -1/8*(7*sqrt(2)*sqrt(-c)*arctan(sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a)))*tan(b*x + a)^3 - sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(9*tan(b*x + a)^2 - 1))/(b*c^2*tan(b*x + a)^3)]","A",0
628,1,272,0,1.026368," ","integrate(sec(2*b*x+2*a)^2/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} \sqrt{c} \log\left(\frac{c \tan\left(b x + a\right)^{3} - 2 \, \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{c} - 2 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3}}\right) \tan\left(b x + a\right)^{3} + 2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)}}{16 \, b c^{2} \tan\left(b x + a\right)^{3}}, -\frac{3 \, \sqrt{2} \sqrt{-c} \arctan\left(\frac{\sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)}\right) \tan\left(b x + a\right)^{3} - \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)}}{8 \, b c^{2} \tan\left(b x + a\right)^{3}}\right]"," ",0,"[1/16*(3*sqrt(2)*sqrt(c)*log((c*tan(b*x + a)^3 - 2*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(c) - 2*c*tan(b*x + a))/tan(b*x + a)^3)*tan(b*x + a)^3 + 2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1))/(b*c^2*tan(b*x + a)^3), -1/8*(3*sqrt(2)*sqrt(-c)*arctan(sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a)))*tan(b*x + a)^3 - sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1))/(b*c^2*tan(b*x + a)^3)]","A",0
629,1,269,0,1.210350," ","integrate(sec(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{c} \log\left(\frac{c \tan\left(b x + a\right)^{3} + 2 \, \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{c} - 2 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3}}\right) \tan\left(b x + a\right)^{3} + 2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)}}{16 \, b c^{2} \tan\left(b x + a\right)^{3}}, \frac{\sqrt{2} \sqrt{-c} \arctan\left(\frac{\sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)}\right) \tan\left(b x + a\right)^{3} + \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)}}{8 \, b c^{2} \tan\left(b x + a\right)^{3}}\right]"," ",0,"[1/16*(sqrt(2)*sqrt(c)*log((c*tan(b*x + a)^3 + 2*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(c) - 2*c*tan(b*x + a))/tan(b*x + a)^3)*tan(b*x + a)^3 + 2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1))/(b*c^2*tan(b*x + a)^3), 1/8*(sqrt(2)*sqrt(-c)*arctan(sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a)))*tan(b*x + a)^3 + sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1))/(b*c^2*tan(b*x + a)^3)]","A",0
630,1,438,0,0.665456," ","integrate(1/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""fricas"")","\left[\frac{5 \, \sqrt{2} \sqrt{c} \log\left(\frac{c \tan\left(b x + a\right)^{3} + 2 \, \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{c} - 2 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3}}\right) \tan\left(b x + a\right)^{3} + 8 \, \sqrt{c} \log\left(\frac{c \tan\left(b x + a\right)^{3} - 2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{c} - 3 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)}\right) \tan\left(b x + a\right)^{3} + 2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)}}{16 \, b c^{2} \tan\left(b x + a\right)^{3}}, \frac{5 \, \sqrt{2} \sqrt{-c} \arctan\left(\frac{\sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)}\right) \tan\left(b x + a\right)^{3} - 8 \, \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{2 \, c \tan\left(b x + a\right)}\right) \tan\left(b x + a\right)^{3} + \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)}}{8 \, b c^{2} \tan\left(b x + a\right)^{3}}\right]"," ",0,"[1/16*(5*sqrt(2)*sqrt(c)*log((c*tan(b*x + a)^3 + 2*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(c) - 2*c*tan(b*x + a))/tan(b*x + a)^3)*tan(b*x + a)^3 + 8*sqrt(c)*log((c*tan(b*x + a)^3 - 2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(c) - 3*c*tan(b*x + a))/(tan(b*x + a)^3 + tan(b*x + a)))*tan(b*x + a)^3 + 2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1))/(b*c^2*tan(b*x + a)^3), 1/8*(5*sqrt(2)*sqrt(-c)*arctan(sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a)))*tan(b*x + a)^3 - 8*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a)))*tan(b*x + a)^3 + sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1))/(b*c^2*tan(b*x + a)^3)]","A",0
631,1,528,0,1.050724," ","integrate(cos(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""fricas"")","\left[\frac{9 \, \sqrt{2} {\left(\tan\left(b x + a\right)^{5} + \tan\left(b x + a\right)^{3}\right)} \sqrt{c} \log\left(\frac{c \tan\left(b x + a\right)^{3} + 2 \, \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{c} - 2 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3}}\right) + 12 \, {\left(\tan\left(b x + a\right)^{5} + \tan\left(b x + a\right)^{3}\right)} \sqrt{c} \log\left(\frac{c \tan\left(b x + a\right)^{3} - 2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{c} - 3 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)}\right) + 2 \, \sqrt{2} {\left(5 \, \tan\left(b x + a\right)^{4} - 4 \, \tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{16 \, {\left(b c^{2} \tan\left(b x + a\right)^{5} + b c^{2} \tan\left(b x + a\right)^{3}\right)}}, \frac{9 \, \sqrt{2} {\left(\tan\left(b x + a\right)^{5} + \tan\left(b x + a\right)^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)}\right) - 12 \, {\left(\tan\left(b x + a\right)^{5} + \tan\left(b x + a\right)^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{2 \, c \tan\left(b x + a\right)}\right) + \sqrt{2} {\left(5 \, \tan\left(b x + a\right)^{4} - 4 \, \tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{8 \, {\left(b c^{2} \tan\left(b x + a\right)^{5} + b c^{2} \tan\left(b x + a\right)^{3}\right)}}\right]"," ",0,"[1/16*(9*sqrt(2)*(tan(b*x + a)^5 + tan(b*x + a)^3)*sqrt(c)*log((c*tan(b*x + a)^3 + 2*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(c) - 2*c*tan(b*x + a))/tan(b*x + a)^3) + 12*(tan(b*x + a)^5 + tan(b*x + a)^3)*sqrt(c)*log((c*tan(b*x + a)^3 - 2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(c) - 3*c*tan(b*x + a))/(tan(b*x + a)^3 + tan(b*x + a))) + 2*sqrt(2)*(5*tan(b*x + a)^4 - 4*tan(b*x + a)^2 - 1)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*c^2*tan(b*x + a)^5 + b*c^2*tan(b*x + a)^3), 1/8*(9*sqrt(2)*(tan(b*x + a)^5 + tan(b*x + a)^3)*sqrt(-c)*arctan(sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a))) - 12*(tan(b*x + a)^5 + tan(b*x + a)^3)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a))) + sqrt(2)*(5*tan(b*x + a)^4 - 4*tan(b*x + a)^2 - 1)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*c^2*tan(b*x + a)^5 + b*c^2*tan(b*x + a)^3)]","A",0
632,1,616,0,0.975429," ","integrate(cos(2*b*x+2*a)^2/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""fricas"")","\left[\frac{13 \, \sqrt{2} {\left(\tan\left(b x + a\right)^{7} + 2 \, \tan\left(b x + a\right)^{5} + \tan\left(b x + a\right)^{3}\right)} \sqrt{c} \log\left(\frac{c \tan\left(b x + a\right)^{3} + 2 \, \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{c} - 2 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3}}\right) + 19 \, {\left(\tan\left(b x + a\right)^{7} + 2 \, \tan\left(b x + a\right)^{5} + \tan\left(b x + a\right)^{3}\right)} \sqrt{c} \log\left(\frac{c \tan\left(b x + a\right)^{3} - 2 \, \sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{c} - 3 \, c \tan\left(b x + a\right)}{\tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)}\right) + 2 \, \sqrt{2} {\left(4 \, \tan\left(b x + a\right)^{6} + 5 \, \tan\left(b x + a\right)^{4} - 8 \, \tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{16 \, {\left(b c^{2} \tan\left(b x + a\right)^{7} + 2 \, b c^{2} \tan\left(b x + a\right)^{5} + b c^{2} \tan\left(b x + a\right)^{3}\right)}}, \frac{13 \, \sqrt{2} {\left(\tan\left(b x + a\right)^{7} + 2 \, \tan\left(b x + a\right)^{5} + \tan\left(b x + a\right)^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{c \tan\left(b x + a\right)}\right) - 19 \, {\left(\tan\left(b x + a\right)^{7} + 2 \, \tan\left(b x + a\right)^{5} + \tan\left(b x + a\right)^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}} {\left(\tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-c}}{2 \, c \tan\left(b x + a\right)}\right) + \sqrt{2} {\left(4 \, \tan\left(b x + a\right)^{6} + 5 \, \tan\left(b x + a\right)^{4} - 8 \, \tan\left(b x + a\right)^{2} - 1\right)} \sqrt{-\frac{c \tan\left(b x + a\right)^{2}}{\tan\left(b x + a\right)^{2} - 1}}}{8 \, {\left(b c^{2} \tan\left(b x + a\right)^{7} + 2 \, b c^{2} \tan\left(b x + a\right)^{5} + b c^{2} \tan\left(b x + a\right)^{3}\right)}}\right]"," ",0,"[1/16*(13*sqrt(2)*(tan(b*x + a)^7 + 2*tan(b*x + a)^5 + tan(b*x + a)^3)*sqrt(c)*log((c*tan(b*x + a)^3 + 2*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(c) - 2*c*tan(b*x + a))/tan(b*x + a)^3) + 19*(tan(b*x + a)^7 + 2*tan(b*x + a)^5 + tan(b*x + a)^3)*sqrt(c)*log((c*tan(b*x + a)^3 - 2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(c) - 3*c*tan(b*x + a))/(tan(b*x + a)^3 + tan(b*x + a))) + 2*sqrt(2)*(4*tan(b*x + a)^6 + 5*tan(b*x + a)^4 - 8*tan(b*x + a)^2 - 1)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*c^2*tan(b*x + a)^7 + 2*b*c^2*tan(b*x + a)^5 + b*c^2*tan(b*x + a)^3), 1/8*(13*sqrt(2)*(tan(b*x + a)^7 + 2*tan(b*x + a)^5 + tan(b*x + a)^3)*sqrt(-c)*arctan(sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a))) - 19*(tan(b*x + a)^7 + 2*tan(b*x + a)^5 + tan(b*x + a)^3)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1))*(tan(b*x + a)^2 - 1)*sqrt(-c)/(c*tan(b*x + a))) + sqrt(2)*(4*tan(b*x + a)^6 + 5*tan(b*x + a)^4 - 8*tan(b*x + a)^2 - 1)*sqrt(-c*tan(b*x + a)^2/(tan(b*x + a)^2 - 1)))/(b*c^2*tan(b*x + a)^7 + 2*b*c^2*tan(b*x + a)^5 + b*c^2*tan(b*x + a)^3)]","A",0
633,1,29,0,1.869253," ","integrate(cot(x)*csc(x)/sin(2*x)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\cos\left(x\right) \sin\left(x\right)} \cos\left(x\right) + \cos\left(x\right)^{2} - 1}{3 \, {\left(\cos\left(x\right)^{2} - 1\right)}}"," ",0,"1/3*(sqrt(2)*sqrt(cos(x)*sin(x))*cos(x) + cos(x)^2 - 1)/(cos(x)^2 - 1)","B",0
634,1,120,0,2.702082," ","integrate(csc(x)^2*sec(x)/sin(2*x)^(1/2)/(-2+tan(x)),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} \sqrt{\cos\left(x\right) \sin\left(x\right)} {\left(2 \, \cos\left(x\right) + 3 \, \sin\left(x\right)\right)} - 4 \, \cos\left(x\right)^{2} - 15 \, {\left(\cos\left(x\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \sqrt{2} \sqrt{\cos\left(x\right) \sin\left(x\right)} {\left(4 \, \cos\left(x\right) + 3 \, \sin\left(x\right)\right)} + \frac{1}{2} \, \cos\left(x\right)^{2} + \frac{7}{2} \, \cos\left(x\right) \sin\left(x\right) + \frac{1}{2}\right) + 15 \, {\left(\cos\left(x\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right)^{2} + \frac{1}{2} \, \sqrt{2} \sqrt{\cos\left(x\right) \sin\left(x\right)} \sin\left(x\right) - \frac{1}{2} \, \cos\left(x\right) \sin\left(x\right) + \frac{1}{2}\right) + 4}{48 \, {\left(\cos\left(x\right)^{2} - 1\right)}}"," ",0,"-1/48*(4*sqrt(2)*sqrt(cos(x)*sin(x))*(2*cos(x) + 3*sin(x)) - 4*cos(x)^2 - 15*(cos(x)^2 - 1)*log(-1/2*sqrt(2)*sqrt(cos(x)*sin(x))*(4*cos(x) + 3*sin(x)) + 1/2*cos(x)^2 + 7/2*cos(x)*sin(x) + 1/2) + 15*(cos(x)^2 - 1)*log(1/2*cos(x)^2 + 1/2*sqrt(2)*sqrt(cos(x)*sin(x))*sin(x) - 1/2*cos(x)*sin(x) + 1/2) + 4)/(cos(x)^2 - 1)","B",0
635,1,120,0,1.040101," ","integrate(cos(x)^2*sin(x)/(sin(x)^2-sin(2*x))/sin(2*x)^(5/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} \sqrt{\cos\left(x\right) \sin\left(x\right)} {\left(2 \, \cos\left(x\right) + 3 \, \sin\left(x\right)\right)} - 4 \, \cos\left(x\right)^{2} - 15 \, {\left(\cos\left(x\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \sqrt{2} \sqrt{\cos\left(x\right) \sin\left(x\right)} {\left(4 \, \cos\left(x\right) + 3 \, \sin\left(x\right)\right)} + \frac{1}{2} \, \cos\left(x\right)^{2} + \frac{7}{2} \, \cos\left(x\right) \sin\left(x\right) + \frac{1}{2}\right) + 15 \, {\left(\cos\left(x\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right)^{2} + \frac{1}{2} \, \sqrt{2} \sqrt{\cos\left(x\right) \sin\left(x\right)} \sin\left(x\right) - \frac{1}{2} \, \cos\left(x\right) \sin\left(x\right) + \frac{1}{2}\right) + 4}{192 \, {\left(\cos\left(x\right)^{2} - 1\right)}}"," ",0,"-1/192*(4*sqrt(2)*sqrt(cos(x)*sin(x))*(2*cos(x) + 3*sin(x)) - 4*cos(x)^2 - 15*(cos(x)^2 - 1)*log(-1/2*sqrt(2)*sqrt(cos(x)*sin(x))*(4*cos(x) + 3*sin(x)) + 1/2*cos(x)^2 + 7/2*cos(x)*sin(x) + 1/2) + 15*(cos(x)^2 - 1)*log(1/2*cos(x)^2 + 1/2*sqrt(2)*sqrt(cos(x)*sin(x))*sin(x) - 1/2*cos(x)*sin(x) + 1/2) + 4)/(cos(x)^2 - 1)","A",0
636,1,136,0,0.469261," ","integrate(cos(x)^3*cos(2*x)/(sin(x)^2-sin(2*x))/sin(2*x)^(5/2),x, algorithm=""fricas"")","-\frac{45 \, {\left(\cos\left(x\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \sqrt{2} \sqrt{\cos\left(x\right) \sin\left(x\right)} {\left(4 \, \cos\left(x\right) + 3 \, \sin\left(x\right)\right)} + \frac{1}{2} \, \cos\left(x\right)^{2} + \frac{7}{2} \, \cos\left(x\right) \sin\left(x\right) + \frac{1}{2}\right) \sin\left(x\right) - 45 \, {\left(\cos\left(x\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right)^{2} + \frac{1}{2} \, \sqrt{2} \sqrt{\cos\left(x\right) \sin\left(x\right)} \sin\left(x\right) - \frac{1}{2} \, \cos\left(x\right) \sin\left(x\right) + \frac{1}{2}\right) \sin\left(x\right) + 4 \, \sqrt{2} {\left(57 \, \cos\left(x\right)^{2} + 10 \, \cos\left(x\right) \sin\left(x\right) - 45\right)} \sqrt{\cos\left(x\right) \sin\left(x\right)} + 268 \, {\left(\cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}{1920 \, {\left(\cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}"," ",0,"-1/1920*(45*(cos(x)^2 - 1)*log(-1/2*sqrt(2)*sqrt(cos(x)*sin(x))*(4*cos(x) + 3*sin(x)) + 1/2*cos(x)^2 + 7/2*cos(x)*sin(x) + 1/2)*sin(x) - 45*(cos(x)^2 - 1)*log(1/2*cos(x)^2 + 1/2*sqrt(2)*sqrt(cos(x)*sin(x))*sin(x) - 1/2*cos(x)*sin(x) + 1/2)*sin(x) + 4*sqrt(2)*(57*cos(x)^2 + 10*cos(x)*sin(x) - 45)*sqrt(cos(x)*sin(x)) + 268*(cos(x)^2 - 1)*sin(x))/((cos(x)^2 - 1)*sin(x))","A",0
637,1,59,0,3.047650," ","integrate((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, algorithm=""fricas"")","\frac{{\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b\right)} \left(\frac{a \cos\left(d x + c\right) \sin\left(d x + c\right) + b}{\cos\left(d x + c\right)}\right)^{n}}{{\left(d n + d\right)} \cos\left(d x + c\right)}"," ",0,"(a*cos(d*x + c)*sin(d*x + c) + b)*((a*cos(d*x + c)*sin(d*x + c) + b)/cos(d*x + c))^n/((d*n + d)*cos(d*x + c))","A",0
638,1,122,0,0.685632," ","integrate((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, algorithm=""fricas"")","\frac{8 \, a^{4} \cos\left(d x + c\right)^{8} - 16 \, a^{4} \cos\left(d x + c\right)^{6} + 5 \, a^{4} \cos\left(d x + c\right)^{4} + 48 \, a^{2} b^{2} \cos\left(d x + c\right)^{2} + 8 \, b^{4} - 32 \, {\left(a^{3} b \cos\left(d x + c\right)^{5} - a^{3} b \cos\left(d x + c\right)^{3} - a b^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{32 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/32*(8*a^4*cos(d*x + c)^8 - 16*a^4*cos(d*x + c)^6 + 5*a^4*cos(d*x + c)^4 + 48*a^2*b^2*cos(d*x + c)^2 + 8*b^4 - 32*(a^3*b*cos(d*x + c)^5 - a^3*b*cos(d*x + c)^3 - a*b^3*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","B",0
639,1,92,0,0.981827," ","integrate((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, algorithm=""fricas"")","-\frac{3 \, a^{2} b \cos\left(d x + c\right)^{4} - 3 \, a^{2} b \cos\left(d x + c\right)^{2} - b^{3} + {\left(a^{3} \cos\left(d x + c\right)^{5} - a^{3} \cos\left(d x + c\right)^{3} - 3 \, a b^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3 \, d \cos\left(d x + c\right)^{3}}"," ",0,"-1/3*(3*a^2*b*cos(d*x + c)^4 - 3*a^2*b*cos(d*x + c)^2 - b^3 + (a^3*cos(d*x + c)^5 - a^3*cos(d*x + c)^3 - 3*a*b^2*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","B",0
640,1,61,0,0.976496," ","integrate((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, algorithm=""fricas"")","-\frac{2 \, a^{2} \cos\left(d x + c\right)^{4} - a^{2} \cos\left(d x + c\right)^{2} - 4 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, b^{2}}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"-1/4*(2*a^2*cos(d*x + c)^4 - a^2*cos(d*x + c)^2 - 4*a*b*cos(d*x + c)*sin(d*x + c) - 2*b^2)/(d*cos(d*x + c)^2)","B",0
641,1,33,0,1.133617," ","integrate((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, algorithm=""fricas"")","\frac{\log\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b\right) - \log\left(-\cos\left(d x + c\right)\right)}{d}"," ",0,"(log(a*cos(d*x + c)*sin(d*x + c) + b) - log(-cos(d*x + c)))/d","A",0
642,1,29,0,0.903340," ","integrate((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, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right)}{a d \cos\left(d x + c\right) \sin\left(d x + c\right) + b d}"," ",0,"-cos(d*x + c)/(a*d*cos(d*x + c)*sin(d*x + c) + b*d)","A",0
643,1,63,0,1.907757," ","integrate((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, algorithm=""fricas"")","\frac{\cos\left(d x + c\right)^{2}}{2 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} - a^{2} d \cos\left(d x + c\right)^{2} - 2 \, a b d \cos\left(d x + c\right) \sin\left(d x + c\right) - b^{2} d\right)}}"," ",0,"1/2*cos(d*x + c)^2/(a^2*d*cos(d*x + c)^4 - a^2*d*cos(d*x + c)^2 - 2*a*b*d*cos(d*x + c)*sin(d*x + c) - b^2*d)","B",0
644,0,0,0,0.858443," ","integrate(F(c,d,cos(b*x+a),r,s)*sin(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(F\left(c, d, \cos\left(b x + a\right), r, s\right) \sin\left(b x + a\right), x\right)"," ",0,"integral(F(c, d, cos(b*x + a), r, s)*sin(b*x + a), x)","F",0
645,0,0,0,0.902692," ","integrate(cos(b*x+a)*F(c,d,sin(b*x+a),r,s),x, algorithm=""fricas"")","{\rm integral}\left(F\left(c, d, \sin\left(b x + a\right), r, s\right) \cos\left(b x + a\right), x\right)"," ",0,"integral(F(c, d, sin(b*x + a), r, s)*cos(b*x + a), x)","F",0
646,0,0,0,0.864355," ","integrate(F(c,d,tan(b*x+a),r,s)*sec(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(F\left(c, d, \tan\left(b x + a\right), r, s\right) \sec\left(b x + a\right)^{2}, x\right)"," ",0,"integral(F(c, d, tan(b*x + a), r, s)*sec(b*x + a)^2, x)","F",0
647,0,0,0,1.973661," ","integrate(csc(b*x+a)^2*F(c,d,cot(b*x+a),r,s),x, algorithm=""fricas"")","{\rm integral}\left(F\left(c, d, \cot\left(b x + a\right), r, s\right) \csc\left(b x + a\right)^{2}, x\right)"," ",0,"integral(F(c, d, cot(b*x + a), r, s)*csc(b*x + a)^2, x)","F",0
648,1,15,0,0.733718," ","integrate(sin(x)/(a+b*cos(x)),x, algorithm=""fricas"")","-\frac{\log\left(-b \cos\left(x\right) - a\right)}{b}"," ",0,"-log(-b*cos(x) - a)/b","A",0
649,1,23,0,0.628014," ","integrate((a+b*cos(x))^n*sin(x),x, algorithm=""fricas"")","-\frac{{\left(b \cos\left(x\right) + a\right)} {\left(b \cos\left(x\right) + a\right)}^{n}}{b n + b}"," ",0,"-(b*cos(x) + a)*(b*cos(x) + a)^n/(b*n + b)","A",0
650,1,36,0,0.957675," ","integrate(sin(x)/(1+cos(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \log\left(8 \, \cos\left(x\right)^{4} + 8 \, \cos\left(x\right)^{2} - 4 \, {\left(2 \, \cos\left(x\right)^{3} + \cos\left(x\right)\right)} \sqrt{\cos\left(x\right)^{2} + 1} + 1\right)"," ",0,"1/4*log(8*cos(x)^4 + 8*cos(x)^2 - 4*(2*cos(x)^3 + cos(x))*sqrt(cos(x)^2 + 1) + 1)","B",0
651,1,20,0,0.788656," ","integrate(cos(cos(x))*sin(x),x, algorithm=""fricas"")","\sin\left(\frac{\tan\left(\frac{1}{2} \, x\right)^{2} - 1}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)"," ",0,"sin((tan(1/2*x)^2 - 1)/(tan(1/2*x)^2 + 1))","B",0
652,1,73,0,0.998619," ","integrate(cos(x)*cos(cos(x))*sin(x)*sin(cos(x)),x, algorithm=""fricas"")","\frac{1}{2} \, \cos\left(x\right) \cos\left(\frac{\tan\left(\frac{1}{2} \, x\right)^{2} - 1}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)^{2} + \frac{1}{4} \, \cos\left(\frac{\tan\left(\frac{1}{2} \, x\right)^{2} - 1}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \sin\left(\frac{\tan\left(\frac{1}{2} \, x\right)^{2} - 1}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) - \frac{1}{4} \, \cos\left(x\right)"," ",0,"1/2*cos(x)*cos((tan(1/2*x)^2 - 1)/(tan(1/2*x)^2 + 1))^2 + 1/4*cos((tan(1/2*x)^2 - 1)/(tan(1/2*x)^2 + 1))*sin((tan(1/2*x)^2 - 1)/(tan(1/2*x)^2 + 1)) - 1/4*cos(x)","B",0
653,1,168,0,1.920737," ","integrate(cos(cos(x))*sin(x)*sin(6*cos(x))^2,x, algorithm=""fricas"")","-\frac{4}{143} \, {\left(2816 \, \cos\left(\frac{\tan\left(\frac{1}{2} \, x\right)^{2} - 1}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)^{12} - 6912 \, \cos\left(\frac{\tan\left(\frac{1}{2} \, x\right)^{2} - 1}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)^{10} + 6048 \, \cos\left(\frac{\tan\left(\frac{1}{2} \, x\right)^{2} - 1}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)^{8} - 2240 \, \cos\left(\frac{\tan\left(\frac{1}{2} \, x\right)^{2} - 1}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)^{6} + 315 \, \cos\left(\frac{\tan\left(\frac{1}{2} \, x\right)^{2} - 1}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)^{4} - 9 \, \cos\left(\frac{\tan\left(\frac{1}{2} \, x\right)^{2} - 1}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)^{2} - 18\right)} \sin\left(\frac{\tan\left(\frac{1}{2} \, x\right)^{2} - 1}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)"," ",0,"-4/143*(2816*cos((tan(1/2*x)^2 - 1)/(tan(1/2*x)^2 + 1))^12 - 6912*cos((tan(1/2*x)^2 - 1)/(tan(1/2*x)^2 + 1))^10 + 6048*cos((tan(1/2*x)^2 - 1)/(tan(1/2*x)^2 + 1))^8 - 2240*cos((tan(1/2*x)^2 - 1)/(tan(1/2*x)^2 + 1))^6 + 315*cos((tan(1/2*x)^2 - 1)/(tan(1/2*x)^2 + 1))^4 - 9*cos((tan(1/2*x)^2 - 1)/(tan(1/2*x)^2 + 1))^2 - 18)*sin((tan(1/2*x)^2 - 1)/(tan(1/2*x)^2 + 1))","B",0
654,1,39,0,0.922926," ","integrate(cos(x)^3*(a+b*cos(x)^2)^3*sin(x),x, algorithm=""fricas"")","-\frac{1}{10} \, b^{3} \cos\left(x\right)^{10} - \frac{3}{8} \, a b^{2} \cos\left(x\right)^{8} - \frac{1}{2} \, a^{2} b \cos\left(x\right)^{6} - \frac{1}{4} \, a^{3} \cos\left(x\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",0
655,1,22,0,0.951013," ","integrate(sin(3*x)*sin(cos(3*x)),x, algorithm=""fricas"")","\frac{1}{3} \, \cos\left(\frac{\tan\left(\frac{3}{2} \, x\right)^{2} - 1}{\tan\left(\frac{3}{2} \, x\right)^{2} + 1}\right)"," ",0,"1/3*cos((tan(3/2*x)^2 - 1)/(tan(3/2*x)^2 + 1))","B",0
656,1,17,0,0.842234," ","integrate(exp(cos(1+3*x))*cos(1+3*x)*sin(1+3*x),x, algorithm=""fricas"")","-\frac{1}{3} \, {\left(\cos\left(3 \, x + 1\right) - 1\right)} e^{\left(\cos\left(3 \, x + 1\right)\right)}"," ",0,"-1/3*(cos(3*x + 1) - 1)*e^(cos(3*x + 1))","A",0
657,1,29,0,1.113852," ","integrate(cos(x)^2*sin(x)/(1-cos(x)^6)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \arctan\left(\frac{2 \, \sqrt{-\cos\left(x\right)^{6} + 1} \cos\left(x\right)^{3}}{2 \, \cos\left(x\right)^{6} - 1}\right)"," ",0,"1/6*arctan(2*sqrt(-cos(x)^6 + 1)*cos(x)^3/(2*cos(x)^6 - 1))","B",0
658,1,34,0,1.679032," ","integrate(sin(x)^5/(1-5*cos(x))^(1/2),x, algorithm=""fricas"")","\frac{2}{984375} \, {\left(21875 \, \cos\left(x\right)^{4} + 5000 \, \cos\left(x\right)^{3} - 77550 \, \cos\left(x\right)^{2} - 20680 \, \cos\left(x\right) + 188603\right)} \sqrt{-5 \, \cos\left(x\right) + 1}"," ",0,"2/984375*(21875*cos(x)^4 + 5000*cos(x)^3 - 77550*cos(x)^2 - 20680*cos(x) + 188603)*sqrt(-5*cos(x) + 1)","A",0
659,1,17,0,1.037744," ","integrate(exp(n*cos(b*x+a))*sin(b*x+a),x, algorithm=""fricas"")","-\frac{e^{\left(n \cos\left(b x + a\right)\right)}}{b n}"," ",0,"-e^(n*cos(b*x + a))/(b*n)","A",0
660,1,23,0,1.401810," ","integrate(exp(n*cos(b*c*x+a*c))*sin(c*(b*x+a)),x, algorithm=""fricas"")","-\frac{e^{\left(n \cos\left(b c x + a c\right)\right)}}{b c n}"," ",0,"-e^(n*cos(b*c*x + a*c))/(b*c*n)","A",0
661,1,23,0,0.896640," ","integrate(exp(n*cos(c*(b*x+a)))*sin(b*c*x+a*c),x, algorithm=""fricas"")","-\frac{e^{\left(n \cos\left(b c x + a c\right)\right)}}{b c n}"," ",0,"-e^(n*cos(b*c*x + a*c))/(b*c*n)","A",0
662,1,14,0,1.490283," ","integrate(exp(n*cos(b*x+a))*tan(b*x+a),x, algorithm=""fricas"")","-\frac{{\rm Ei}\left(n \cos\left(b x + a\right)\right)}{b}"," ",0,"-Ei(n*cos(b*x + a))/b","A",0
663,1,20,0,0.891694," ","integrate(exp(n*cos(b*c*x+a*c))*tan(c*(b*x+a)),x, algorithm=""fricas"")","-\frac{{\rm Ei}\left(n \cos\left(b c x + a c\right)\right)}{b c}"," ",0,"-Ei(n*cos(b*c*x + a*c))/(b*c)","A",0
664,1,20,0,0.768158," ","integrate(exp(n*cos(c*(b*x+a)))*tan(b*c*x+a*c),x, algorithm=""fricas"")","-\frac{{\rm Ei}\left(n \cos\left(b c x + a c\right)\right)}{b c}"," ",0,"-Ei(n*cos(b*c*x + a*c))/(b*c)","A",0
665,1,11,0,1.973986," ","integrate(cos(x)/(a+b*sin(x)),x, algorithm=""fricas"")","\frac{\log\left(b \sin\left(x\right) + a\right)}{b}"," ",0,"log(b*sin(x) + a)/b","A",0
666,1,22,0,0.571413," ","integrate(cos(x)*(a+b*sin(x))^n,x, algorithm=""fricas"")","\frac{{\left(b \sin\left(x\right) + a\right)} {\left(b \sin\left(x\right) + a\right)}^{n}}{b n + b}"," ",0,"(b*sin(x) + a)*(b*sin(x) + a)^n/(b*n + b)","A",0
667,1,39,0,1.189848," ","integrate(cos(x)/(1+sin(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \log\left(8 \, \cos\left(x\right)^{4} - 4 \, {\left(2 \, \cos\left(x\right)^{2} - 3\right)} \sqrt{-\cos\left(x\right)^{2} + 2} \sin\left(x\right) - 24 \, \cos\left(x\right)^{2} + 17\right)"," ",0,"1/4*log(8*cos(x)^4 - 4*(2*cos(x)^2 - 3)*sqrt(-cos(x)^2 + 2)*sin(x) - 24*cos(x)^2 + 17)","B",0
668,1,53,0,3.019431," ","integrate(cos(x)/(4-sin(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \arctan\left(\frac{\sqrt{\cos\left(x\right)^{2} + 3} {\left(\cos\left(x\right)^{2} + 1\right)} \sin\left(x\right) - 4 \, \cos\left(x\right) \sin\left(x\right)}{\cos\left(x\right)^{4} + 6 \, \cos\left(x\right)^{2} - 3}\right) + \frac{1}{2} \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)"," ",0,"1/2*arctan((sqrt(cos(x)^2 + 3)*(cos(x)^2 + 1)*sin(x) - 4*cos(x)*sin(x))/(cos(x)^4 + 6*cos(x)^2 - 3)) + 1/2*arctan(sin(x)/cos(x))","B",0
669,1,71,0,0.595935," ","integrate(cos(3*x)/(4-sin(3*x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \arctan\left(\frac{\sqrt{\cos\left(3 \, x\right)^{2} + 3} {\left(\cos\left(3 \, x\right)^{2} + 1\right)} \sin\left(3 \, x\right) - 4 \, \cos\left(3 \, x\right) \sin\left(3 \, x\right)}{\cos\left(3 \, x\right)^{4} + 6 \, \cos\left(3 \, x\right)^{2} - 3}\right) + \frac{1}{6} \, \arctan\left(\frac{\sin\left(3 \, x\right)}{\cos\left(3 \, x\right)}\right)"," ",0,"1/6*arctan((sqrt(cos(3*x)^2 + 3)*(cos(3*x)^2 + 1)*sin(3*x) - 4*cos(3*x)*sin(3*x))/(cos(3*x)^4 + 6*cos(3*x)^2 - 3)) + 1/6*arctan(sin(3*x)/cos(3*x))","B",0
670,1,79,0,0.987727," ","integrate(cos(x)*(1+csc(x))^(1/2),x, algorithm=""fricas"")","\sqrt{\frac{\sin\left(x\right) + 1}{\sin\left(x\right)}} \sin\left(x\right) + \frac{1}{2} \, \log\left(\frac{2 \, {\left(\sqrt{\frac{\sin\left(x\right) + 1}{\sin\left(x\right)}} \sin\left(x\right) + \sin\left(x\right) + 1\right)}}{\cos\left(x\right) + \sin\left(x\right) + 1}\right) - \frac{1}{2} \, \log\left(-\frac{2 \, {\left(\sqrt{\frac{\sin\left(x\right) + 1}{\sin\left(x\right)}} \sin\left(x\right) - \sin\left(x\right) - 1\right)}}{\cos\left(x\right) + \sin\left(x\right) + 1}\right)"," ",0,"sqrt((sin(x) + 1)/sin(x))*sin(x) + 1/2*log(2*(sqrt((sin(x) + 1)/sin(x))*sin(x) + sin(x) + 1)/(cos(x) + sin(x) + 1)) - 1/2*log(-2*(sqrt((sin(x) + 1)/sin(x))*sin(x) - sin(x) - 1)/(cos(x) + sin(x) + 1))","B",0
671,1,61,0,1.074916," ","integrate(cos(x)*(4-sin(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\cos\left(x\right)^{2} + 3} \sin\left(x\right) + \arctan\left(\frac{\sqrt{\cos\left(x\right)^{2} + 3} {\left(\cos\left(x\right)^{2} + 1\right)} \sin\left(x\right) - 4 \, \cos\left(x\right) \sin\left(x\right)}{\cos\left(x\right)^{4} + 6 \, \cos\left(x\right)^{2} - 3}\right) + \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)"," ",0,"1/2*sqrt(cos(x)^2 + 3)*sin(x) + arctan((sqrt(cos(x)^2 + 3)*(cos(x)^2 + 1)*sin(x) - 4*cos(x)*sin(x))/(cos(x)^4 + 6*cos(x)^2 - 3)) + arctan(sin(x)/cos(x))","B",0
672,1,12,0,0.880687," ","integrate(cos(x)*sin(x)*(1+sin(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(-\cos\left(x\right)^{2} + 2\right)}^{\frac{3}{2}}"," ",0,"1/3*(-cos(x)^2 + 2)^(3/2)","A",0
673,1,35,0,2.962462," ","integrate(cos(x)/(2*sin(x)+sin(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(-2 \, \cos\left(x\right)^{2} + 2 \, \sqrt{-\cos\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1} {\left(\sin\left(x\right) + 1\right)} + 4 \, \sin\left(x\right) + 3\right)"," ",0,"1/2*log(-2*cos(x)^2 + 2*sqrt(-cos(x)^2 + 2*sin(x) + 1)*(sin(x) + 1) + 4*sin(x) + 3)","B",0
674,1,17,0,1.642156," ","integrate(cos(x)*cos(sin(x)),x, algorithm=""fricas"")","\sin\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)"," ",0,"sin(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))","B",0
675,1,41,0,0.669046," ","integrate(cos(x)*cos(sin(x))*cos(sin(sin(x))),x, algorithm=""fricas"")","\sin\left(\frac{2 \, \tan\left(\frac{\tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)}{\tan\left(\frac{\tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)^{2} + 1}\right)"," ",0,"sin(2*tan(tan(1/2*x)/(tan(1/2*x)^2 + 1))/(tan(tan(1/2*x)/(tan(1/2*x)^2 + 1))^2 + 1))","B",0
676,1,47,0,0.877979," ","integrate(cos(x)*sec(sin(x)),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(\sin\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) + 1\right) - \frac{1}{2} \, \log\left(-\sin\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) + 1\right)"," ",0,"1/2*log(sin(2*tan(1/2*x)/(tan(1/2*x)^2 + 1)) + 1) - 1/2*log(-sin(2*tan(1/2*x)/(tan(1/2*x)^2 + 1)) + 1)","B",0
677,1,103,0,1.193369," ","integrate(cos(x)*sin(x)^3*(a+b*sin(x)^2)^3,x, algorithm=""fricas"")","-\frac{1}{10} \, b^{3} \cos\left(x\right)^{10} + \frac{1}{8} \, {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cos\left(x\right)^{8} - \frac{1}{2} \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \cos\left(x\right)^{6} + \frac{1}{4} \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cos\left(x\right)^{4} - \frac{1}{2} \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cos\left(x\right)^{2}"," ",0,"-1/10*b^3*cos(x)^10 + 1/8*(3*a*b^2 + 4*b^3)*cos(x)^8 - 1/2*(a^2*b + 3*a*b^2 + 2*b^3)*cos(x)^6 + 1/4*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cos(x)^4 - 1/2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cos(x)^2","B",0
678,1,8,0,0.861068," ","integrate(exp(sin(x))*cos(x)*sin(x),x, algorithm=""fricas"")","{\left(\sin\left(x\right) - 1\right)} e^{\sin\left(x\right)}"," ",0,"(sin(x) - 1)*e^sin(x)","A",0
679,1,28,0,0.892421," ","integrate(cos(x)^3/(sin(x)^3)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(\cos\left(x\right)^{2} - 4\right)} \sqrt{-{\left(\cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}}{3 \, {\left(\cos\left(x\right)^{2} - 1\right)}}"," ",0,"-2/3*(cos(x)^2 - 4)*sqrt(-(cos(x)^2 - 1)*sin(x))/(cos(x)^2 - 1)","A",0
680,1,7,0,1.184464," ","integrate(exp(sin(x)^(1/2))*cos(x)/sin(x)^(1/2),x, algorithm=""fricas"")","2 \, e^{\sqrt{\sin\left(x\right)}}"," ",0,"2*e^sqrt(sin(x))","A",0
681,1,5,0,0.939861," ","integrate(exp(4+sin(x))*cos(x),x, algorithm=""fricas"")","e^{\left(\sin\left(x\right) + 4\right)}"," ",0,"e^(sin(x) + 4)","A",0
682,1,6,0,0.787143," ","integrate(exp(cos(x)*sin(x))*cos(2*x),x, algorithm=""fricas"")","e^{\left(\cos\left(x\right) \sin\left(x\right)\right)}"," ",0,"e^(cos(x)*sin(x))","A",0
683,1,12,0,0.718233," ","integrate(exp(cos(1/2*x)*sin(1/2*x))*cos(x),x, algorithm=""fricas"")","2 \, e^{\left(\cos\left(\frac{1}{2} \, x\right) \sin\left(\frac{1}{2} \, x\right)\right)}"," ",0,"2*e^(cos(1/2*x)*sin(1/2*x))","A",0
684,1,16,0,0.777457," ","integrate(exp(n*sin(b*x+a))*cos(b*x+a),x, algorithm=""fricas"")","\frac{e^{\left(n \sin\left(b x + a\right)\right)}}{b n}"," ",0,"e^(n*sin(b*x + a))/(b*n)","A",0
685,1,22,0,1.046445," ","integrate(exp(n*sin(b*c*x+a*c))*cos(c*(b*x+a)),x, algorithm=""fricas"")","\frac{e^{\left(n \sin\left(b c x + a c\right)\right)}}{b c n}"," ",0,"e^(n*sin(b*c*x + a*c))/(b*c*n)","A",0
686,1,22,0,0.799906," ","integrate(exp(n*sin(c*(b*x+a)))*cos(b*c*x+a*c),x, algorithm=""fricas"")","\frac{e^{\left(n \sin\left(b c x + a c\right)\right)}}{b c n}"," ",0,"e^(n*sin(b*c*x + a*c))/(b*c*n)","A",0
687,1,13,0,0.996567," ","integrate(exp(n*sin(b*x+a))*cot(b*x+a),x, algorithm=""fricas"")","\frac{{\rm Ei}\left(n \sin\left(b x + a\right)\right)}{b}"," ",0,"Ei(n*sin(b*x + a))/b","A",0
688,1,19,0,0.667863," ","integrate(exp(n*sin(b*c*x+a*c))*cot(c*(b*x+a)),x, algorithm=""fricas"")","\frac{{\rm Ei}\left(n \sin\left(b c x + a c\right)\right)}{b c}"," ",0,"Ei(n*sin(b*c*x + a*c))/(b*c)","A",0
689,1,19,0,0.920740," ","integrate(exp(n*sin(c*(b*x+a)))*cot(b*c*x+a*c),x, algorithm=""fricas"")","\frac{{\rm Ei}\left(n \sin\left(b c x + a c\right)\right)}{b c}"," ",0,"Ei(n*sin(b*c*x + a*c))/(b*c)","A",0
690,1,40,0,1.824553," ","integrate(sec(x)^2/(a+b*tan(x)),x, algorithm=""fricas"")","\frac{\log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right) - \log\left(\cos\left(x\right)^{2}\right)}{2 \, b}"," ",0,"1/2*(log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2) - log(cos(x)^2))/b","B",0
691,1,23,0,0.568998," ","integrate(sec(x)^2/(1-tan(x)^2),x, algorithm=""fricas"")","\frac{1}{4} \, \log\left(2 \, \cos\left(x\right) \sin\left(x\right) + 1\right) - \frac{1}{4} \, \log\left(-2 \, \cos\left(x\right) \sin\left(x\right) + 1\right)"," ",0,"1/4*log(2*cos(x)*sin(x) + 1) - 1/4*log(-2*cos(x)*sin(x) + 1)","B",0
692,1,21,0,0.548463," ","integrate(sec(x)^2/(9+tan(x)^2),x, algorithm=""fricas"")","-\frac{1}{6} \, \arctan\left(\frac{10 \, \cos\left(x\right)^{2} - 1}{6 \, \cos\left(x\right) \sin\left(x\right)}\right)"," ",0,"-1/6*arctan(1/6*(10*cos(x)^2 - 1)/(cos(x)*sin(x)))","A",0
693,1,37,0,1.057964," ","integrate(sec(x)^2*(a+b*tan(x))^n,x, algorithm=""fricas"")","\frac{{\left(a \cos\left(x\right) + b \sin\left(x\right)\right)} \left(\frac{a \cos\left(x\right) + b \sin\left(x\right)}{\cos\left(x\right)}\right)^{n}}{{\left(b n + b\right)} \cos\left(x\right)}"," ",0,"(a*cos(x) + b*sin(x))*((a*cos(x) + b*sin(x))/cos(x))^n/((b*n + b)*cos(x))","A",0
694,1,12,0,0.890647," ","integrate(sec(x)^2*(1+1/(1+tan(x)^2)),x, algorithm=""fricas"")","\frac{x \cos\left(x\right) + \sin\left(x\right)}{\cos\left(x\right)}"," ",0,"(x*cos(x) + sin(x))/cos(x)","B",0
695,1,12,0,0.887674," ","integrate(sec(x)^2*(2+tan(x)^2)/(1+tan(x)^2),x, algorithm=""fricas"")","\frac{x \cos\left(x\right) + \sin\left(x\right)}{\cos\left(x\right)}"," ",0,"(x*cos(x) + sin(x))/cos(x)","B",0
696,1,35,0,0.859927," ","integrate(sec(x)^2/(2+2*tan(x)+tan(x)^2),x, algorithm=""fricas"")","-\frac{1}{2} \, \arctan\left(-\frac{3 \, \cos\left(x\right)^{2} + 6 \, \cos\left(x\right) \sin\left(x\right) + 1}{2 \, {\left(2 \, \cos\left(x\right)^{2} - \cos\left(x\right) \sin\left(x\right) - 1\right)}}\right)"," ",0,"-1/2*arctan(-1/2*(3*cos(x)^2 + 6*cos(x)*sin(x) + 1)/(2*cos(x)^2 - cos(x)*sin(x) - 1))","A",0
697,1,36,0,1.294421," ","integrate(sec(x)^2/(tan(x)^2+tan(x)^3),x, algorithm=""fricas"")","-\frac{\log\left(-\frac{1}{4} \, \cos\left(x\right)^{2} + \frac{1}{4}\right) \sin\left(x\right) - \log\left(2 \, \cos\left(x\right) \sin\left(x\right) + 1\right) \sin\left(x\right) + 2 \, \cos\left(x\right)}{2 \, \sin\left(x\right)}"," ",0,"-1/2*(log(-1/4*cos(x)^2 + 1/4)*sin(x) - log(2*cos(x)*sin(x) + 1)*sin(x) + 2*cos(x))/sin(x)","B",0
698,1,36,0,0.865611," ","integrate(sec(x)^2/(-tan(x)^2+tan(x)^3),x, algorithm=""fricas"")","-\frac{\log\left(-\frac{1}{4} \, \cos\left(x\right)^{2} + \frac{1}{4}\right) \sin\left(x\right) - \log\left(-2 \, \cos\left(x\right) \sin\left(x\right) + 1\right) \sin\left(x\right) - 2 \, \cos\left(x\right)}{2 \, \sin\left(x\right)}"," ",0,"-1/2*(log(-1/4*cos(x)^2 + 1/4)*sin(x) - log(-2*cos(x)*sin(x) + 1)*sin(x) - 2*cos(x))/sin(x)","B",0
699,1,441,0,1.104029," ","integrate(sec(x)^2/(3-4*tan(x)^3),x, algorithm=""fricas"")","-\frac{1}{36} \cdot 36^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} \arctan\left(-\frac{36^{\frac{1}{6}} {\left(28 \, {\left(36^{\frac{2}{3}} \sqrt{3} \left(-1\right)^{\frac{2}{3}} - 9 \, \sqrt{3} \left(-1\right)^{\frac{1}{3}}\right)} \cos\left(x\right)^{6} - 4 \, {\left(14 \cdot 36^{\frac{2}{3}} \sqrt{3} \left(-1\right)^{\frac{2}{3}} + 36 \cdot 36^{\frac{1}{3}} \sqrt{3} - 63 \, \sqrt{3} \left(-1\right)^{\frac{1}{3}}\right)} \cos\left(x\right)^{4} + {\left(37 \cdot 36^{\frac{2}{3}} \sqrt{3} \left(-1\right)^{\frac{2}{3}} + 144 \cdot 36^{\frac{1}{3}} \sqrt{3} + 144 \, \sqrt{3} \left(-1\right)^{\frac{1}{3}}\right)} \cos\left(x\right)^{2} - 6 \, {\left(16 \, {\left(36^{\frac{2}{3}} \sqrt{3} \left(-1\right)^{\frac{2}{3}} - 9 \, \sqrt{3} \left(-1\right)^{\frac{1}{3}}\right)} \cos\left(x\right)^{5} - {\left(24 \cdot 36^{\frac{2}{3}} \sqrt{3} \left(-1\right)^{\frac{2}{3}} - 7 \cdot 36^{\frac{1}{3}} \sqrt{3} - 72 \, \sqrt{3} \left(-1\right)^{\frac{1}{3}}\right)} \cos\left(x\right)^{3} + 4 \, {\left(36^{\frac{2}{3}} \sqrt{3} \left(-1\right)^{\frac{2}{3}} - 4 \cdot 36^{\frac{1}{3}} \sqrt{3} + 9 \, \sqrt{3} \left(-1\right)^{\frac{1}{3}}\right)} \cos\left(x\right)\right)} \sin\left(x\right) - 18 \cdot 36^{\frac{1}{3}} \sqrt{3} - 144 \, \sqrt{3} \left(-1\right)^{\frac{1}{3}}\right)}}{108 \, {\left(48 \, \cos\left(x\right)^{6} - 72 \, \cos\left(x\right)^{4} + 18 \, \cos\left(x\right)^{2} + 14 \, {\left(\cos\left(x\right)^{5} - \cos\left(x\right)^{3}\right)} \sin\left(x\right) + 3\right)}}\right) - \frac{1}{432} \cdot 36^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-3 \, {\left(2 \cdot 36^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} - 8 \cdot 36^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + 25\right)} \cos\left(x\right)^{4} + 3 \, {\left(3 \cdot 36^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} - 4 \cdot 36^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + 32\right)} \cos\left(x\right)^{2} - 2 \, {\left({\left(4 \cdot 36^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + 9 \cdot 36^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}}\right)} \cos\left(x\right)^{3} - 4 \, {\left(36^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} - 9\right)} \cos\left(x\right)\right)} \sin\left(x\right) - 12 \cdot 36^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} - 48\right) + \frac{1}{216} \cdot 36^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(3 \, {\left(2 \cdot 36^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + 8 \cdot 36^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} - 7\right)} \cos\left(x\right)^{2} + 2 \, {\left(4 \cdot 36^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} - 9 \cdot 36^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + 36\right)} \cos\left(x\right) \sin\left(x\right) - 3 \cdot 36^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} - 12 \cdot 36^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + 48\right)"," ",0,"-1/36*36^(1/6)*sqrt(3)*(-1)^(1/3)*arctan(-1/108*36^(1/6)*(28*(36^(2/3)*sqrt(3)*(-1)^(2/3) - 9*sqrt(3)*(-1)^(1/3))*cos(x)^6 - 4*(14*36^(2/3)*sqrt(3)*(-1)^(2/3) + 36*36^(1/3)*sqrt(3) - 63*sqrt(3)*(-1)^(1/3))*cos(x)^4 + (37*36^(2/3)*sqrt(3)*(-1)^(2/3) + 144*36^(1/3)*sqrt(3) + 144*sqrt(3)*(-1)^(1/3))*cos(x)^2 - 6*(16*(36^(2/3)*sqrt(3)*(-1)^(2/3) - 9*sqrt(3)*(-1)^(1/3))*cos(x)^5 - (24*36^(2/3)*sqrt(3)*(-1)^(2/3) - 7*36^(1/3)*sqrt(3) - 72*sqrt(3)*(-1)^(1/3))*cos(x)^3 + 4*(36^(2/3)*sqrt(3)*(-1)^(2/3) - 4*36^(1/3)*sqrt(3) + 9*sqrt(3)*(-1)^(1/3))*cos(x))*sin(x) - 18*36^(1/3)*sqrt(3) - 144*sqrt(3)*(-1)^(1/3))/(48*cos(x)^6 - 72*cos(x)^4 + 18*cos(x)^2 + 14*(cos(x)^5 - cos(x)^3)*sin(x) + 3)) - 1/432*36^(2/3)*(-1)^(1/3)*log(-3*(2*36^(2/3)*(-1)^(1/3) - 8*36^(1/3)*(-1)^(2/3) + 25)*cos(x)^4 + 3*(3*36^(2/3)*(-1)^(1/3) - 4*36^(1/3)*(-1)^(2/3) + 32)*cos(x)^2 - 2*((4*36^(2/3)*(-1)^(1/3) + 9*36^(1/3)*(-1)^(2/3))*cos(x)^3 - 4*(36^(2/3)*(-1)^(1/3) - 9)*cos(x))*sin(x) - 12*36^(1/3)*(-1)^(2/3) - 48) + 1/216*36^(2/3)*(-1)^(1/3)*log(3*(2*36^(2/3)*(-1)^(1/3) + 8*36^(1/3)*(-1)^(2/3) - 7)*cos(x)^2 + 2*(4*36^(2/3)*(-1)^(1/3) - 9*36^(1/3)*(-1)^(2/3) + 36)*cos(x)*sin(x) - 3*36^(2/3)*(-1)^(1/3) - 12*36^(1/3)*(-1)^(2/3) + 48)","B",0
700,1,48,0,0.981055," ","integrate(sec(x)^2/(11-5*tan(x)+5*tan(x)^2),x, algorithm=""fricas"")","\frac{1}{195} \, \sqrt{195} \arctan\left(-\frac{192 \, \sqrt{195} \cos\left(x\right)^{2} - 160 \, \sqrt{195} \cos\left(x\right) \sin\left(x\right) - 35 \, \sqrt{195}}{195 \, {\left(10 \, \cos\left(x\right)^{2} + 12 \, \cos\left(x\right) \sin\left(x\right) - 5\right)}}\right)"," ",0,"1/195*sqrt(195)*arctan(-1/195*(192*sqrt(195)*cos(x)^2 - 160*sqrt(195)*cos(x)*sin(x) - 35*sqrt(195))/(10*cos(x)^2 + 12*cos(x)*sin(x) - 5))","A",0
701,1,71,0,0.912263," ","integrate(sec(x)^2*(a+b*tan(x))/(c+d*tan(x)),x, algorithm=""fricas"")","-\frac{{\left(b c - a d\right)} \cos\left(x\right) \log\left(2 \, c d \cos\left(x\right) \sin\left(x\right) + {\left(c^{2} - d^{2}\right)} \cos\left(x\right)^{2} + d^{2}\right) - {\left(b c - a d\right)} \cos\left(x\right) \log\left(\cos\left(x\right)^{2}\right) - 2 \, b d \sin\left(x\right)}{2 \, d^{2} \cos\left(x\right)}"," ",0,"-1/2*((b*c - a*d)*cos(x)*log(2*c*d*cos(x)*sin(x) + (c^2 - d^2)*cos(x)^2 + d^2) - (b*c - a*d)*cos(x)*log(cos(x)^2) - 2*b*d*sin(x))/(d^2*cos(x))","B",0
702,1,122,0,1.626646," ","integrate(sec(x)^2*(a+b*tan(x))^2/(c+d*tan(x)),x, algorithm=""fricas"")","\frac{b^{2} d^{2} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \cos\left(x\right)^{2} \log\left(2 \, c d \cos\left(x\right) \sin\left(x\right) + {\left(c^{2} - d^{2}\right)} \cos\left(x\right)^{2} + d^{2}\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \cos\left(x\right)^{2} \log\left(\cos\left(x\right)^{2}\right) - 2 \, {\left(b^{2} c d - 2 \, a b d^{2}\right)} \cos\left(x\right) \sin\left(x\right)}{2 \, d^{3} \cos\left(x\right)^{2}}"," ",0,"1/2*(b^2*d^2 + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*cos(x)^2*log(2*c*d*cos(x)*sin(x) + (c^2 - d^2)*cos(x)^2 + d^2) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*cos(x)^2*log(cos(x)^2) - 2*(b^2*c*d - 2*a*b*d^2)*cos(x)*sin(x))/(d^3*cos(x)^2)","B",0
703,1,201,0,2.111343," ","integrate(sec(x)^2*(a+b*tan(x))^3/(c+d*tan(x)),x, algorithm=""fricas"")","-\frac{3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \cos\left(x\right)^{3} \log\left(2 \, c d \cos\left(x\right) \sin\left(x\right) + {\left(c^{2} - d^{2}\right)} \cos\left(x\right)^{2} + d^{2}\right) - 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \cos\left(x\right)^{3} \log\left(\cos\left(x\right)^{2}\right) + 3 \, {\left(b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} \cos\left(x\right) - 2 \, {\left(b^{3} d^{3} + {\left(3 \, b^{3} c^{2} d - 9 \, a b^{2} c d^{2} + {\left(9 \, a^{2} b - b^{3}\right)} d^{3}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{6 \, d^{4} \cos\left(x\right)^{3}}"," ",0,"-1/6*(3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*cos(x)^3*log(2*c*d*cos(x)*sin(x) + (c^2 - d^2)*cos(x)^2 + d^2) - 3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*cos(x)^3*log(cos(x)^2) + 3*(b^3*c*d^2 - 3*a*b^2*d^3)*cos(x) - 2*(b^3*d^3 + (3*b^3*c^2*d - 9*a*b^2*c*d^2 + (9*a^2*b - b^3)*d^3)*cos(x)^2)*sin(x))/(d^4*cos(x)^3)","B",0
704,1,36,0,0.850687," ","integrate(sec(x)^2*tan(x)^2/(2+tan(x)^3)^2,x, algorithm=""fricas"")","-\frac{\cos\left(x\right)^{3} + 2 \, {\left(\cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}{15 \, {\left(2 \, \cos\left(x\right)^{3} - {\left(\cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)\right)}}"," ",0,"-1/15*(cos(x)^3 + 2*(cos(x)^2 - 1)*sin(x))/(2*cos(x)^3 - (cos(x)^2 - 1)*sin(x))","B",0
705,1,46,0,0.861180," ","integrate(sec(x)^2*tan(x)^6*(1+tan(x)^2)^3,x, algorithm=""fricas"")","-\frac{{\left(16 \, \cos\left(x\right)^{12} + 8 \, \cos\left(x\right)^{10} + 6 \, \cos\left(x\right)^{8} + 5 \, \cos\left(x\right)^{6} - 371 \, \cos\left(x\right)^{4} + 567 \, \cos\left(x\right)^{2} - 231\right)} \sin\left(x\right)}{3003 \, \cos\left(x\right)^{13}}"," ",0,"-1/3003*(16*cos(x)^12 + 8*cos(x)^10 + 6*cos(x)^8 + 5*cos(x)^6 - 371*cos(x)^4 + 567*cos(x)^2 - 231)*sin(x)/cos(x)^13","A",0
706,1,52,0,2.512657," ","integrate(sec(x)^2*(2+tan(x)^2)/(1+tan(x)^3),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{4 \, \sqrt{3} \cos\left(x\right) \sin\left(x\right) - \sqrt{3}}{3 \, {\left(2 \, \cos\left(x\right)^{2} - 1\right)}}\right) - \frac{1}{2} \, \log\left(\cos\left(x\right)^{2}\right) + \frac{1}{2} \, \log\left(2 \, \cos\left(x\right) \sin\left(x\right) + 1\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*(4*sqrt(3)*cos(x)*sin(x) - sqrt(3))/(2*cos(x)^2 - 1)) - 1/2*log(cos(x)^2) + 1/2*log(2*cos(x)*sin(x) + 1)","A",0
707,1,12,0,0.408284," ","integrate((1+cos(x)^2)*sec(x)^2,x, algorithm=""fricas"")","\frac{x \cos\left(x\right) + \sin\left(x\right)}{\cos\left(x\right)}"," ",0,"(x*cos(x) + sin(x))/cos(x)","B",0
708,1,29,0,0.578122," ","integrate(sec(x)^2/(1+sec(x)^2-3*tan(x)),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(\frac{3}{4} \, \cos\left(x\right)^{2} - \cos\left(x\right) \sin\left(x\right) + \frac{1}{4}\right) - \frac{1}{2} \, \log\left(-2 \, \cos\left(x\right) \sin\left(x\right) + 1\right)"," ",0,"1/2*log(3/4*cos(x)^2 - cos(x)*sin(x) + 1/4) - 1/2*log(-2*cos(x)*sin(x) + 1)","A",0
709,1,25,0,0.832449," ","integrate(sec(x)^2/(4-sec(x)^2)^(1/2),x, algorithm=""fricas"")","-\arctan\left(\frac{\sqrt{\frac{4 \, \cos\left(x\right)^{2} - 1}{\cos\left(x\right)^{2}}} \cos\left(x\right)}{\sin\left(x\right)}\right)"," ",0,"-arctan(sqrt((4*cos(x)^2 - 1)/cos(x)^2)*cos(x)/sin(x))","B",0
710,1,45,0,0.832604," ","integrate(sec(x)^2/(1-4*tan(x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \arctan\left(\frac{{\left(9 \, \cos\left(x\right)^{3} - 8 \, \cos\left(x\right)\right)} \sqrt{\frac{5 \, \cos\left(x\right)^{2} - 4}{\cos\left(x\right)^{2}}}}{4 \, {\left(5 \, \cos\left(x\right)^{2} - 4\right)} \sin\left(x\right)}\right)"," ",0,"-1/4*arctan(1/4*(9*cos(x)^3 - 8*cos(x))*sqrt((5*cos(x)^2 - 4)/cos(x)^2)/((5*cos(x)^2 - 4)*sin(x)))","B",0
711,1,67,0,1.004810," ","integrate(sec(x)^2/(-4+tan(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \log\left(\frac{1}{2} \, \sqrt{-\frac{5 \, \cos\left(x\right)^{2} - 1}{\cos\left(x\right)^{2}}} \cos\left(x\right) \sin\left(x\right) - \frac{3}{2} \, \cos\left(x\right)^{2} + \frac{1}{2}\right) - \frac{1}{4} \, \log\left(-\frac{1}{2} \, \sqrt{-\frac{5 \, \cos\left(x\right)^{2} - 1}{\cos\left(x\right)^{2}}} \cos\left(x\right) \sin\left(x\right) - \frac{3}{2} \, \cos\left(x\right)^{2} + \frac{1}{2}\right)"," ",0,"1/4*log(1/2*sqrt(-(5*cos(x)^2 - 1)/cos(x)^2)*cos(x)*sin(x) - 3/2*cos(x)^2 + 1/2) - 1/4*log(-1/2*sqrt(-(5*cos(x)^2 - 1)/cos(x)^2)*cos(x)*sin(x) - 3/2*cos(x)^2 + 1/2)","B",0
712,1,78,0,0.968260," ","integrate(sec(x)^2*(1-cot(x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{\arctan\left(\frac{{\left(3 \, \cos\left(x\right)^{2} - 1\right)} \sqrt{\frac{2 \, \cos\left(x\right)^{2} - 1}{\cos\left(x\right)^{2} - 1}} \sin\left(x\right)}{2 \, {\left(2 \, \cos\left(x\right)^{3} - \cos\left(x\right)\right)}}\right) \cos\left(x\right) - 2 \, \sqrt{\frac{2 \, \cos\left(x\right)^{2} - 1}{\cos\left(x\right)^{2} - 1}} \sin\left(x\right)}{2 \, \cos\left(x\right)}"," ",0,"-1/2*(arctan(1/2*(3*cos(x)^2 - 1)*sqrt((2*cos(x)^2 - 1)/(cos(x)^2 - 1))*sin(x)/(2*cos(x)^3 - cos(x)))*cos(x) - 2*sqrt((2*cos(x)^2 - 1)/(cos(x)^2 - 1))*sin(x))/cos(x)","B",0
713,1,72,0,1.045391," ","integrate(sec(x)^2*(1-tan(x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{\arctan\left(\frac{{\left(3 \, \cos\left(x\right)^{3} - 2 \, \cos\left(x\right)\right)} \sqrt{\frac{2 \, \cos\left(x\right)^{2} - 1}{\cos\left(x\right)^{2}}}}{2 \, {\left(2 \, \cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}\right) \cos\left(x\right) - 2 \, \sqrt{\frac{2 \, \cos\left(x\right)^{2} - 1}{\cos\left(x\right)^{2}}} \sin\left(x\right)}{4 \, \cos\left(x\right)}"," ",0,"-1/4*(arctan(1/2*(3*cos(x)^3 - 2*cos(x))*sqrt((2*cos(x)^2 - 1)/cos(x)^2)/((2*cos(x)^2 - 1)*sin(x)))*cos(x) - 2*sqrt((2*cos(x)^2 - 1)/cos(x)^2)*sin(x))/cos(x)","B",0
714,1,8,0,0.518102," ","integrate(exp(tan(x))*sec(x)^2,x, algorithm=""fricas"")","e^{\frac{\sin\left(x\right)}{\cos\left(x\right)}}"," ",0,"e^(sin(x)/cos(x))","B",0
715,1,20,0,0.806394," ","integrate(sec(x)^4*(-1+sec(x)^2)^2*tan(x),x, algorithm=""fricas"")","\frac{6 \, \cos\left(x\right)^{4} - 8 \, \cos\left(x\right)^{2} + 3}{24 \, \cos\left(x\right)^{8}}"," ",0,"1/24*(6*cos(x)^4 - 8*cos(x)^2 + 3)/cos(x)^8","A",0
716,1,45,0,1.439127," ","integrate(csc(x)^2/(a+b*cot(x)),x, algorithm=""fricas"")","-\frac{\log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2}\right) - \log\left(-\frac{1}{4} \, \cos\left(x\right)^{2} + \frac{1}{4}\right)}{2 \, b}"," ",0,"-1/2*(log(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 + a^2) - log(-1/4*cos(x)^2 + 1/4))/b","B",0
717,1,38,0,0.652882," ","integrate((a+b*cot(x))^n*csc(x)^2,x, algorithm=""fricas"")","-\frac{{\left(b \cos\left(x\right) + a \sin\left(x\right)\right)} \left(\frac{b \cos\left(x\right) + a \sin\left(x\right)}{\sin\left(x\right)}\right)^{n}}{{\left(b n + b\right)} \sin\left(x\right)}"," ",0,"-(b*cos(x) + a*sin(x))*((b*cos(x) + a*sin(x))/sin(x))^n/((b*n + b)*sin(x))","A",0
718,1,14,0,0.672380," ","integrate(csc(x)^2*(1+sin(x)^2),x, algorithm=""fricas"")","\frac{x \sin\left(x\right) - \cos\left(x\right)}{\sin\left(x\right)}"," ",0,"(x*sin(x) - cos(x))/sin(x)","B",0
719,1,14,0,0.659715," ","integrate((1+1/(1+cot(x)^2))*csc(x)^2,x, algorithm=""fricas"")","\frac{x \sin\left(x\right) - \cos\left(x\right)}{\sin\left(x\right)}"," ",0,"(x*sin(x) - cos(x))/sin(x)","B",0
720,1,76,0,1.170181," ","integrate((a+b*cot(x))*csc(x)^2/(c+d*cot(x)),x, algorithm=""fricas"")","-\frac{2 \, b d \cos\left(x\right) - {\left(b c - a d\right)} \log\left(2 \, c d \cos\left(x\right) \sin\left(x\right) - {\left(c^{2} - d^{2}\right)} \cos\left(x\right)^{2} + c^{2}\right) \sin\left(x\right) + {\left(b c - a d\right)} \log\left(-\frac{1}{4} \, \cos\left(x\right)^{2} + \frac{1}{4}\right) \sin\left(x\right)}{2 \, d^{2} \sin\left(x\right)}"," ",0,"-1/2*(2*b*d*cos(x) - (b*c - a*d)*log(2*c*d*cos(x)*sin(x) - (c^2 - d^2)*cos(x)^2 + c^2)*sin(x) + (b*c - a*d)*log(-1/4*cos(x)^2 + 1/4)*sin(x))/(d^2*sin(x))","B",0
721,1,182,0,1.472874," ","integrate((a+b*cot(x))^2*csc(x)^2/(c+d*cot(x)),x, algorithm=""fricas"")","\frac{b^{2} d^{2} - 2 \, {\left(b^{2} c d - 2 \, a b d^{2}\right)} \cos\left(x\right) \sin\left(x\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \cos\left(x\right)^{2}\right)} \log\left(2 \, c d \cos\left(x\right) \sin\left(x\right) - {\left(c^{2} - d^{2}\right)} \cos\left(x\right)^{2} + c^{2}\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \cos\left(x\right)^{2}\right)} \log\left(-\frac{1}{4} \, \cos\left(x\right)^{2} + \frac{1}{4}\right)}{2 \, {\left(d^{3} \cos\left(x\right)^{2} - d^{3}\right)}}"," ",0,"1/2*(b^2*d^2 - 2*(b^2*c*d - 2*a*b*d^2)*cos(x)*sin(x) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2 - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*cos(x)^2)*log(2*c*d*cos(x)*sin(x) - (c^2 - d^2)*cos(x)^2 + c^2) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2 - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*cos(x)^2)*log(-1/4*cos(x)^2 + 1/4))/(d^3*cos(x)^2 - d^3)","B",0
722,1,320,0,1.624078," ","integrate((a+b*cot(x))^3*csc(x)^2/(c+d*cot(x)),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b^{3} c^{2} d - 9 \, a b^{2} c d^{2} + {\left(9 \, a^{2} b - b^{3}\right)} d^{3}\right)} \cos\left(x\right)^{3} + 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \cos\left(x\right)^{2}\right)} \log\left(2 \, c d \cos\left(x\right) \sin\left(x\right) - {\left(c^{2} - d^{2}\right)} \cos\left(x\right)^{2} + c^{2}\right) \sin\left(x\right) - 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \cos\left(x\right)^{2}\right)} \log\left(-\frac{1}{4} \, \cos\left(x\right)^{2} + \frac{1}{4}\right) \sin\left(x\right) - 6 \, {\left(b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} \cos\left(x\right) + 3 \, {\left(b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} \sin\left(x\right)}{6 \, {\left(d^{4} \cos\left(x\right)^{2} - d^{4}\right)} \sin\left(x\right)}"," ",0,"-1/6*(2*(3*b^3*c^2*d - 9*a*b^2*c*d^2 + (9*a^2*b - b^3)*d^3)*cos(x)^3 + 3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3 - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*cos(x)^2)*log(2*c*d*cos(x)*sin(x) - (c^2 - d^2)*cos(x)^2 + c^2)*sin(x) - 3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3 - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*cos(x)^2)*log(-1/4*cos(x)^2 + 1/4)*sin(x) - 6*(b^3*c^2*d - 3*a*b^2*c*d^2 + 3*a^2*b*d^3)*cos(x) + 3*(b^3*c*d^2 - 3*a*b^2*d^3)*sin(x))/((d^4*cos(x)^2 - d^4)*sin(x))","B",0
723,1,9,0,0.639518," ","integrate(csc(x)^2/exp(cot(x)),x, algorithm=""fricas"")","e^{\left(-\frac{\cos\left(x\right)}{\sin\left(x\right)}\right)}"," ",0,"e^(-cos(x)/sin(x))","A",0
724,1,19,0,0.671118," ","integrate(sec(x)*tan(x)/(a+b*sec(x)),x, algorithm=""fricas"")","\frac{\log\left(a \cos\left(x\right) + b\right) - \log\left(-\cos\left(x\right)\right)}{b}"," ",0,"(log(a*cos(x) + b) - log(-cos(x)))/b","A",0
725,1,5,0,4.939157," ","integrate(sec(x)*tan(x)/(1+sec(x)^2),x, algorithm=""fricas"")","-\arctan\left(\cos\left(x\right)\right)"," ",0,"-arctan(cos(x))","A",0
726,1,7,0,0.967323," ","integrate(sec(x)*tan(x)/(9+4*sec(x)^2),x, algorithm=""fricas"")","-\frac{1}{6} \, \arctan\left(\frac{3}{2} \, \cos\left(x\right)\right)"," ",0,"-1/6*arctan(3/2*cos(x))","A",0
727,1,9,0,0.844854," ","integrate(sec(x)*tan(x)/(sec(x)+sec(x)^2),x, algorithm=""fricas"")","-\log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"-log(1/2*cos(x) + 1/2)","A",0
728,1,27,0,0.945957," ","integrate(sec(x)*tan(x)/(4+sec(x)^2)^(1/2),x, algorithm=""fricas"")","\log\left(-\frac{\sqrt{\frac{4 \, \cos\left(x\right)^{2} + 1}{\cos\left(x\right)^{2}}} \cos\left(x\right) + 1}{\cos\left(x\right)}\right)"," ",0,"log(-(sqrt((4*cos(x)^2 + 1)/cos(x)^2)*cos(x) + 1)/cos(x))","B",0
729,1,16,0,0.668158," ","integrate(sec(x)*tan(x)/(1+cos(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{\cos\left(x\right)^{2} + 1} + \cos\left(x\right)}{\cos\left(x\right)}"," ",0,"(sqrt(cos(x)^2 + 1) + cos(x))/cos(x)","A",0
730,1,5,0,0.922035," ","integrate(exp(sec(x))*sec(x)*tan(x),x, algorithm=""fricas"")","e^{\frac{1}{\cos\left(x\right)}}"," ",0,"e^(1/cos(x))","A",0
731,1,11,0,0.473166," ","integrate(2^sec(x)*sec(x)*tan(x),x, algorithm=""fricas"")","\frac{2^{\left(\frac{1}{\cos\left(x\right)}\right)}}{\log\left(2\right)}"," ",0,"2^(1/cos(x))/log(2)","A",0
732,1,29,0,0.759761," ","integrate(sec(2*x)*tan(2*x)/(1+sec(2*x))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{\cos\left(2 \, x\right) + 1}{\cos\left(2 \, x\right)}} \cos\left(2 \, x\right)}{\cos\left(2 \, x\right) + 1}"," ",0,"-sqrt((cos(2*x) + 1)/cos(2*x))*cos(2*x)/(cos(2*x) + 1)","B",0
733,1,122,0,0.954261," ","integrate(sec(3*x)*(1+5*cos(3*x)^2)^(1/2)*tan(3*x),x, algorithm=""fricas"")","\frac{\sqrt{5} \cos\left(3 \, x\right) \log\left(80000 \, \cos\left(3 \, x\right)^{8} + 32000 \, \cos\left(3 \, x\right)^{6} + 4000 \, \cos\left(3 \, x\right)^{4} + 160 \, \cos\left(3 \, x\right)^{2} - 8 \, {\left(2000 \, \sqrt{5} \cos\left(3 \, x\right)^{7} + 600 \, \sqrt{5} \cos\left(3 \, x\right)^{5} + 50 \, \sqrt{5} \cos\left(3 \, x\right)^{3} + \sqrt{5} \cos\left(3 \, x\right)\right)} \sqrt{5 \, \cos\left(3 \, x\right)^{2} + 1} + 1\right) + 8 \, \sqrt{5 \, \cos\left(3 \, x\right)^{2} + 1}}{24 \, \cos\left(3 \, x\right)}"," ",0,"1/24*(sqrt(5)*cos(3*x)*log(80000*cos(3*x)^8 + 32000*cos(3*x)^6 + 4000*cos(3*x)^4 + 160*cos(3*x)^2 - 8*(2000*sqrt(5)*cos(3*x)^7 + 600*sqrt(5)*cos(3*x)^5 + 50*sqrt(5)*cos(3*x)^3 + sqrt(5)*cos(3*x))*sqrt(5*cos(3*x)^2 + 1) + 1) + 8*sqrt(5*cos(3*x)^2 + 1))/cos(3*x)","B",0
734,1,20,0,0.665933," ","integrate(sec(3*x)*tan(3*x)/(1+5*cos(3*x)^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{5 \, \cos\left(3 \, x\right)^{2} + 1}}{3 \, \cos\left(3 \, x\right)}"," ",0,"1/3*sqrt(5*cos(3*x)^2 + 1)/cos(3*x)","A",0
735,1,20,0,0.689436," ","integrate(cot(x)*csc(x)/(a+b*csc(x)),x, algorithm=""fricas"")","-\frac{\log\left(a \sin\left(x\right) + b\right) - \log\left(-\frac{1}{2} \, \sin\left(x\right)\right)}{b}"," ",0,"-(log(a*sin(x) + b) - log(-1/2*sin(x)))/b","A",0
736,1,14,0,1.139851," ","integrate(5^csc(3*x)*cot(3*x)*csc(3*x),x, algorithm=""fricas"")","-\frac{5^{\left(\frac{1}{\sin\left(3 \, x\right)}\right)}}{3 \, \log\left(5\right)}"," ",0,"-1/3*5^(1/sin(3*x))/log(5)","A",0
737,1,3,0,0.708590," ","integrate(cot(x)*csc(x)/(1+csc(x)^2),x, algorithm=""fricas"")","\arctan\left(\sin\left(x\right)\right)"," ",0,"arctan(sin(x))","A",0
738,1,73,0,0.640772," ","integrate(cot(6*x)*csc(6*x)/(5-11*csc(6*x)^2)^2,x, algorithm=""fricas"")","\frac{{\left(5 \, \sqrt{55} \cos\left(6 \, x\right)^{2} + 6 \, \sqrt{55}\right)} \log\left(-\frac{5 \, \cos\left(6 \, x\right)^{2} + 2 \, \sqrt{55} \sin\left(6 \, x\right) - 16}{5 \, \cos\left(6 \, x\right)^{2} + 6}\right) + 110 \, \sin\left(6 \, x\right)}{6600 \, {\left(5 \, \cos\left(6 \, x\right)^{2} + 6\right)}}"," ",0,"1/6600*((5*sqrt(55)*cos(6*x)^2 + 6*sqrt(55))*log(-(5*cos(6*x)^2 + 2*sqrt(55)*sin(6*x) - 16)/(5*cos(6*x)^2 + 6)) + 110*sin(6*x))/(5*cos(6*x)^2 + 6)","B",0
739,1,21,0,1.069323," ","integrate(cot(x)*csc(x)/(1+sin(x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-\cos\left(x\right)^{2} + 2} - \sin\left(x\right)}{\sin\left(x\right)}"," ",0,"-(sqrt(-cos(x)^2 + 2) - sin(x))/sin(x)","A",0
740,1,57,0,0.684341," ","integrate(cot(5*x)*csc(5*x)^3/(1+sin(5*x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(\cos\left(5 \, x\right)^{2} - 1\right)} \sin\left(5 \, x\right) - {\left(2 \, \cos\left(5 \, x\right)^{2} - 1\right)} \sqrt{-\cos\left(5 \, x\right)^{2} + 2}}{15 \, {\left(\cos\left(5 \, x\right)^{2} - 1\right)} \sin\left(5 \, x\right)}"," ",0,"-1/15*(2*(cos(5*x)^2 - 1)*sin(5*x) - (2*cos(5*x)^2 - 1)*sqrt(-cos(5*x)^2 + 2))/((cos(5*x)^2 - 1)*sin(5*x))","A",0
741,1,27,0,0.600267," ","integrate(exp(n*sin(b*x+a))*sin(2*b*x+2*a),x, algorithm=""fricas"")","\frac{2 \, {\left(n \sin\left(b x + a\right) - 1\right)} e^{\left(n \sin\left(b x + a\right)\right)}}{b n^{2}}"," ",0,"2*(n*sin(b*x + a) - 1)*e^(n*sin(b*x + a))/(b*n^2)","A",0
742,1,27,0,0.648630," ","integrate(exp(n*sin(b*x+a))*sin(2*b*x+2*a),x, algorithm=""fricas"")","\frac{2 \, {\left(n \sin\left(b x + a\right) - 1\right)} e^{\left(n \sin\left(b x + a\right)\right)}}{b n^{2}}"," ",0,"2*(n*sin(b*x + a) - 1)*e^(n*sin(b*x + a))/(b*n^2)","A",0
743,1,33,0,0.981505," ","integrate(exp(n*sin(1/2*a+1/2*b*x))*sin(b*x+a),x, algorithm=""fricas"")","\frac{4 \, {\left(n \sin\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) - 1\right)} e^{\left(n \sin\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right)\right)}}{b n^{2}}"," ",0,"4*(n*sin(1/2*b*x + 1/2*a) - 1)*e^(n*sin(1/2*b*x + 1/2*a))/(b*n^2)","A",0
744,1,33,0,0.691687," ","integrate(exp(n*sin(1/2*a+1/2*b*x))*sin(b*x+a),x, algorithm=""fricas"")","\frac{4 \, {\left(n \sin\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) - 1\right)} e^{\left(n \sin\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right)\right)}}{b n^{2}}"," ",0,"4*(n*sin(1/2*b*x + 1/2*a) - 1)*e^(n*sin(1/2*b*x + 1/2*a))/(b*n^2)","A",0
745,1,27,0,0.537298," ","integrate(exp(n*cos(b*x+a))*sin(2*b*x+2*a),x, algorithm=""fricas"")","-\frac{2 \, {\left(n \cos\left(b x + a\right) - 1\right)} e^{\left(n \cos\left(b x + a\right)\right)}}{b n^{2}}"," ",0,"-2*(n*cos(b*x + a) - 1)*e^(n*cos(b*x + a))/(b*n^2)","A",0
746,1,27,0,0.720237," ","integrate(exp(n*cos(b*x+a))*sin(2*b*x+2*a),x, algorithm=""fricas"")","-\frac{2 \, {\left(n \cos\left(b x + a\right) - 1\right)} e^{\left(n \cos\left(b x + a\right)\right)}}{b n^{2}}"," ",0,"-2*(n*cos(b*x + a) - 1)*e^(n*cos(b*x + a))/(b*n^2)","A",0
747,1,33,0,2.003746," ","integrate(exp(n*cos(1/2*a+1/2*b*x))*sin(b*x+a),x, algorithm=""fricas"")","-\frac{4 \, {\left(n \cos\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) - 1\right)} e^{\left(n \cos\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right)\right)}}{b n^{2}}"," ",0,"-4*(n*cos(1/2*b*x + 1/2*a) - 1)*e^(n*cos(1/2*b*x + 1/2*a))/(b*n^2)","A",0
748,1,33,0,0.503118," ","integrate(exp(n*cos(1/2*a+1/2*b*x))*sin(b*x+a),x, algorithm=""fricas"")","-\frac{4 \, {\left(n \cos\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) - 1\right)} e^{\left(n \cos\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right)\right)}}{b n^{2}}"," ",0,"-4*(n*cos(1/2*b*x + 1/2*a) - 1)*e^(n*cos(1/2*b*x + 1/2*a))/(b*n^2)","A",0
749,1,12,0,0.611570," ","integrate(csc(x)*log(tan(x))*sec(x),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)^{2}"," ",0,"1/2*log(sin(x)/cos(x))^2","A",0
750,1,7,0,0.510490," ","integrate(csc(2*x)*log(tan(x)),x, algorithm=""fricas"")","\frac{1}{4} \, \log\left(\tan\left(x\right)\right)^{2}"," ",0,"1/4*log(tan(x))^2","A",0
751,1,4,0,0.548584," ","integrate(exp(cos(x)^2+sin(x)^2),x, algorithm=""fricas"")","x e"," ",0,"x*e","C",0
752,1,18,0,0.527951," ","integrate(x*sec(x)^2,x, algorithm=""fricas"")","\frac{\cos\left(x\right) \log\left(-\cos\left(x\right)\right) + x \sin\left(x\right)}{\cos\left(x\right)}"," ",0,"(cos(x)*log(-cos(x)) + x*sin(x))/cos(x)","B",0
753,1,27,0,2.297638," ","integrate(x*cos(x^2)^4,x, algorithm=""fricas"")","\frac{3}{16} \, x^{2} + \frac{1}{16} \, {\left(2 \, \cos\left(x^{2}\right)^{3} + 3 \, \cos\left(x^{2}\right)\right)} \sin\left(x^{2}\right)"," ",0,"3/16*x^2 + 1/16*(2*cos(x^2)^3 + 3*cos(x^2))*sin(x^2)","A",0
754,1,6,0,0.588399," ","integrate(sin(x)*cos(x)^(1/2),x, algorithm=""fricas"")","-\frac{2}{3} \, \cos\left(x\right)^{\frac{3}{2}}"," ",0,"-2/3*cos(x)^(3/2)","A",0
755,1,14,0,1.375803," ","integrate(tan(exp(-2*x))/exp(2*x),x, algorithm=""fricas"")","\frac{1}{4} \, \log\left(\frac{1}{\tan\left(e^{\left(-2 \, x\right)}\right)^{2} + 1}\right)"," ",0,"1/4*log(1/(tan(e^(-2*x))^2 + 1))","A",0
756,1,9,0,0.709060," ","integrate(sec(x)*sin(2*x)/(1+cos(x)),x, algorithm=""fricas"")","-2 \, \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"-2*log(1/2*cos(x) + 1/2)","A",0
757,1,28,0,0.708120," ","integrate(x*sec(3*x)^2,x, algorithm=""fricas"")","\frac{\cos\left(3 \, x\right) \log\left(-\cos\left(3 \, x\right)\right) + 3 \, x \sin\left(3 \, x\right)}{9 \, \cos\left(3 \, x\right)}"," ",0,"1/9*(cos(3*x)*log(-cos(3*x)) + 3*x*sin(3*x))/cos(3*x)","A",0
758,1,29,0,0.702481," ","integrate(cos(2*pi*x)/exp(2*pi*x),x, algorithm=""fricas"")","-\frac{\cos\left(2 \, \pi x\right) e^{\left(-2 \, \pi x\right)} - e^{\left(-2 \, \pi x\right)} \sin\left(2 \, \pi x\right)}{4 \, \pi}"," ",0,"-1/4*(cos(2*pi*x)*e^(-2*pi*x) - e^(-2*pi*x)*sin(2*pi*x))/pi","A",0
759,1,39,0,1.533268," ","integrate(cos(x)^12*sin(x)^10-cos(x)^10*sin(x)^12,x, algorithm=""fricas"")","-\frac{1}{11} \, {\left(\cos\left(x\right)^{21} - 5 \, \cos\left(x\right)^{19} + 10 \, \cos\left(x\right)^{17} - 10 \, \cos\left(x\right)^{15} + 5 \, \cos\left(x\right)^{13} - \cos\left(x\right)^{11}\right)} \sin\left(x\right)"," ",0,"-1/11*(cos(x)^21 - 5*cos(x)^19 + 10*cos(x)^17 - 10*cos(x)^15 + 5*cos(x)^13 - cos(x)^11)*sin(x)","B",0
760,1,13,0,0.654397," ","integrate(x*cot(x^2),x, algorithm=""fricas"")","\frac{1}{4} \, \log\left(-\frac{1}{2} \, \cos\left(2 \, x^{2}\right) + \frac{1}{2}\right)"," ",0,"1/4*log(-1/2*cos(2*x^2) + 1/2)","A",0
761,1,12,0,1.040068," ","integrate(x*sec(x^2)^2,x, algorithm=""fricas"")","\frac{\sin\left(x^{2}\right)}{2 \, \cos\left(x^{2}\right)}"," ",0,"1/2*sin(x^2)/cos(x^2)","A",0
762,1,13,0,0.657446," ","integrate(sin(8*x)/(9+sin(4*x)^4),x, algorithm=""fricas"")","-\frac{1}{12} \, \arctan\left(\frac{1}{3} \, \cos\left(4 \, x\right)^{2} - \frac{1}{3}\right)"," ",0,"-1/12*arctan(1/3*cos(4*x)^2 - 1/3)","A",0
763,1,15,0,1.576862," ","integrate(cos(2*x)/(8+sin(2*x)^2),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{4} \, \sqrt{2} \sin\left(2 \, x\right)\right)"," ",0,"1/8*sqrt(2)*arctan(1/4*sqrt(2)*sin(2*x))","A",0
764,1,29,0,1.962635," ","integrate(x*(cos(x^2)^3-sin(x^2)^3),x, algorithm=""fricas"")","-\frac{1}{6} \, \cos\left(x^{2}\right)^{3} + \frac{1}{6} \, {\left(\cos\left(x^{2}\right)^{2} + 2\right)} \sin\left(x^{2}\right) + \frac{1}{2} \, \cos\left(x^{2}\right)"," ",0,"-1/6*cos(x^2)^3 + 1/6*(cos(x^2)^2 + 2)*sin(x^2) + 1/2*cos(x^2)","A",0
765,1,10,0,1.375393," ","integrate(cos(x)*sin(x)/(1-cos(x)),x, algorithm=""fricas"")","\cos\left(x\right) + \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"cos(x) + log(-1/2*cos(x) + 1/2)","A",0
766,1,6,0,0.530808," ","integrate(x*cos(x^2),x, algorithm=""fricas"")","\frac{1}{2} \, \sin\left(x^{2}\right)"," ",0,"1/2*sin(x^2)","A",0
767,1,8,0,0.765034," ","integrate(x^2*cos(4*x^3),x, algorithm=""fricas"")","\frac{1}{12} \, \sin\left(4 \, x^{3}\right)"," ",0,"1/12*sin(4*x^3)","A",0
768,1,6,0,0.674018," ","integrate(x^3*cos(x^4),x, algorithm=""fricas"")","\frac{1}{4} \, \sin\left(x^{4}\right)"," ",0,"1/4*sin(x^4)","A",0
769,1,8,0,0.486886," ","integrate(x*sin(1/2*x^2),x, algorithm=""fricas"")","-\cos\left(\frac{1}{2} \, x^{2}\right)"," ",0,"-cos(1/2*x^2)","A",0
770,1,8,0,0.767510," ","integrate(x*sec(x^2)*tan(x^2),x, algorithm=""fricas"")","\frac{1}{2 \, \cos\left(x^{2}\right)}"," ",0,"1/2/cos(x^2)","A",0
771,1,13,0,0.722018," ","integrate(tan(1/x)^2/x^2,x, algorithm=""fricas"")","-\frac{x \tan\left(\frac{1}{x}\right) - 1}{x}"," ",0,"-(x*tan(1/x) - 1)/x","A",0
772,1,15,0,0.791457," ","integrate(x*tan(x^2+1),x, algorithm=""fricas"")","-\frac{1}{4} \, \log\left(\frac{1}{\tan\left(x^{2} + 1\right)^{2} + 1}\right)"," ",0,"-1/4*log(1/(tan(x^2 + 1)^2 + 1))","A",0
773,1,12,0,0.565506," ","integrate(sin(pi*(1+2*x)),x, algorithm=""fricas"")","-\frac{\cos\left(\pi + 2 \, \pi x\right)}{2 \, \pi}"," ",0,"-1/2*cos(pi + 2*pi*x)/pi","A",0
774,1,29,0,0.674680," ","integrate((cot(x)+csc(x)^2)/(1-cos(x)^2),x, algorithm=""fricas"")","-\frac{4 \, \cos\left(x\right)^{3} - 6 \, \cos\left(x\right) - 3 \, \sin\left(x\right)}{6 \, {\left(\cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}"," ",0,"-1/6*(4*cos(x)^3 - 6*cos(x) - 3*sin(x))/((cos(x)^2 - 1)*sin(x))","A",0
775,1,40,0,0.502483," ","integrate(x^2*cos(4*x^3)*cos(5*x^3),x, algorithm=""fricas"")","\frac{1}{27} \, {\left(128 \, \cos\left(x^{3}\right)^{8} - 224 \, \cos\left(x^{3}\right)^{6} + 120 \, \cos\left(x^{3}\right)^{4} - 20 \, \cos\left(x^{3}\right)^{2} + 5\right)} \sin\left(x^{3}\right)"," ",0,"1/27*(128*cos(x^3)^8 - 224*cos(x^3)^6 + 120*cos(x^3)^4 - 20*cos(x^3)^2 + 5)*sin(x^3)","B",0
776,1,32,0,0.711371," ","integrate(x^14*sin(x^3),x, algorithm=""fricas"")","-\frac{1}{3} \, {\left(x^{12} - 12 \, x^{6} + 24\right)} \cos\left(x^{3}\right) + \frac{4}{3} \, {\left(x^{9} - 6 \, x^{3}\right)} \sin\left(x^{3}\right)"," ",0,"-1/3*(x^12 - 12*x^6 + 24)*cos(x^3) + 4/3*(x^9 - 6*x^3)*sin(x^3)","A",0
777,1,29,0,0.752865," ","integrate(x^2*sin(2*x^3)/exp(3*x^3),x, algorithm=""fricas"")","-\frac{2}{39} \, \cos\left(2 \, x^{3}\right) e^{\left(-3 \, x^{3}\right)} - \frac{1}{13} \, e^{\left(-3 \, x^{3}\right)} \sin\left(2 \, x^{3}\right)"," ",0,"-2/39*cos(2*x^3)*e^(-3*x^3) - 1/13*e^(-3*x^3)*sin(2*x^3)","A",0
778,1,4,0,0.786464," ","integrate(2*x*cos(x^2),x, algorithm=""fricas"")","\sin\left(x^{2}\right)"," ",0,"sin(x^2)","A",0
779,1,6,0,0.645816," ","integrate(3*x^2*cos(x^3+7),x, algorithm=""fricas"")","\sin\left(x^{3} + 7\right)"," ",0,"sin(x^3 + 7)","A",0
780,1,7,0,0.841014," ","integrate(1/(x^2+1)+sin(x),x, algorithm=""fricas"")","\arctan\left(x\right) - \cos\left(x\right)"," ",0,"arctan(x) - cos(x)","A",0
781,1,8,0,0.713196," ","integrate(x*sin(x^2+1),x, algorithm=""fricas"")","-\frac{1}{2} \, \cos\left(x^{2} + 1\right)"," ",0,"-1/2*cos(x^2 + 1)","A",0
782,1,8,0,0.579645," ","integrate(x*cos(x^2+1),x, algorithm=""fricas"")","\frac{1}{2} \, \sin\left(x^{2} + 1\right)"," ",0,"1/2*sin(x^2 + 1)","A",0
783,1,8,0,0.623003," ","integrate(1+x^2*cos(x^3),x, algorithm=""fricas"")","x + \frac{1}{3} \, \sin\left(x^{3}\right)"," ",0,"x + 1/3*sin(x^3)","A",0
784,1,8,0,0.957560," ","integrate(x^2*sin(x^3+1),x, algorithm=""fricas"")","-\frac{1}{3} \, \cos\left(x^{3} + 1\right)"," ",0,"-1/3*cos(x^3 + 1)","A",0
785,1,6,0,0.659081," ","integrate(12*x^2*cos(x^3),x, algorithm=""fricas"")","4 \, \sin\left(x^{3}\right)"," ",0,"4*sin(x^3)","A",0
786,1,14,0,0.526755," ","integrate((1+x)*sin(1+x),x, algorithm=""fricas"")","-{\left(x + 1\right)} \cos\left(x + 1\right) + \sin\left(x + 1\right)"," ",0,"-(x + 1)*cos(x + 1) + sin(x + 1)","A",0
787,1,16,0,0.587303," ","integrate(x^5*cos(x^3),x, algorithm=""fricas"")","\frac{1}{3} \, x^{3} \sin\left(x^{3}\right) + \frac{1}{3} \, \cos\left(x^{3}\right)"," ",0,"1/3*x^3*sin(x^3) + 1/3*cos(x^3)","A",0
788,1,17,0,0.692613," ","integrate(cos(x)/exp(3*x),x, algorithm=""fricas"")","-\frac{3}{10} \, \cos\left(x\right) e^{\left(-3 \, x\right)} + \frac{1}{10} \, e^{\left(-3 \, x\right)} \sin\left(x\right)"," ",0,"-3/10*cos(x)*e^(-3*x) + 1/10*e^(-3*x)*sin(x)","A",0
789,1,16,0,0.529083," ","integrate(x^3*sin(x^2),x, algorithm=""fricas"")","-\frac{1}{2} \, x^{2} \cos\left(x^{2}\right) + \frac{1}{2} \, \sin\left(x^{2}\right)"," ",0,"-1/2*x^2*cos(x^2) + 1/2*sin(x^2)","A",0
790,1,16,0,1.524080," ","integrate(x^3*cos(x^2),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} \sin\left(x^{2}\right) + \frac{1}{2} \, \cos\left(x^{2}\right)"," ",0,"1/2*x^2*sin(x^2) + 1/2*cos(x^2)","A",0
791,1,19,0,0.792784," ","integrate(cos(x)*cos(2*sin(x)),x, algorithm=""fricas"")","\frac{1}{2} \, \sin\left(\frac{4 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)"," ",0,"1/2*sin(4*tan(1/2*x)/(tan(1/2*x)^2 + 1))","B",0
792,1,11,0,0.685021," ","integrate(cos(x)*sin(x)/(1+cos(x)^2),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(\frac{1}{2} \, \cos\left(x\right)^{2} + \frac{1}{2}\right)"," ",0,"-1/2*log(1/2*cos(x)^2 + 1/2)","A",0
793,1,45,0,0.619711," ","integrate((1+cos(x))*(x+sin(x))^3,x, algorithm=""fricas"")","\frac{1}{4} \, x^{4} + \frac{1}{4} \, \cos\left(x\right)^{4} - \frac{1}{2} \, {\left(3 \, x^{2} + 1\right)} \cos\left(x\right)^{2} + \frac{3}{2} \, x^{2} + {\left(x^{3} - x \cos\left(x\right)^{2} + x\right)} \sin\left(x\right)"," ",0,"1/4*x^4 + 1/4*cos(x)^4 - 1/2*(3*x^2 + 1)*cos(x)^2 + 3/2*x^2 + (x^3 - x*cos(x)^2 + x)*sin(x)","B",0
794,1,10,0,0.625281," ","integrate((1+cos(x))*csc(x)^2,x, algorithm=""fricas"")","-\frac{\cos\left(x\right) + 1}{\sin\left(x\right)}"," ",0,"-(cos(x) + 1)/sin(x)","A",0
795,1,11,0,0.698816," ","integrate(sin(x)*tan(x)^2,x, algorithm=""fricas"")","\frac{\cos\left(x\right)^{2} + 1}{\cos\left(x\right)}"," ",0,"(cos(x)^2 + 1)/cos(x)","B",0
796,1,14,0,0.676543," ","integrate(exp(sin(x))*sec(x)^2*(x*cos(x)^3-sin(x)),x, algorithm=""fricas"")","\frac{{\left(x \cos\left(x\right) - 1\right)} e^{\sin\left(x\right)}}{\cos\left(x\right)}"," ",0,"(x*cos(x) - 1)*e^sin(x)/cos(x)","A",0
797,1,20,0,0.623658," ","integrate(x*csc(x)^2,x, algorithm=""fricas"")","-\frac{x \cos\left(x\right) - \log\left(\frac{1}{2} \, \sin\left(x\right)\right) \sin\left(x\right)}{\sin\left(x\right)}"," ",0,"-(x*cos(x) - log(1/2*sin(x))*sin(x))/sin(x)","B",0
798,1,31,0,1.736322," ","integrate(cos(x)*sin(1/6*pi+x),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{3} \cos\left(\frac{1}{6} \, \pi + x\right)^{2} - \frac{1}{4} \, \cos\left(\frac{1}{6} \, \pi + x\right) \sin\left(\frac{1}{6} \, \pi + x\right) + \frac{1}{4} \, x"," ",0,"-1/4*sqrt(3)*cos(1/6*pi + x)^2 - 1/4*cos(1/6*pi + x)*sin(1/6*pi + x) + 1/4*x","B",0
799,1,15,0,0.676016," ","integrate(x*sin(x^2)^3,x, algorithm=""fricas"")","\frac{1}{6} \, \cos\left(x^{2}\right)^{3} - \frac{1}{2} \, \cos\left(x^{2}\right)"," ",0,"1/6*cos(x^2)^3 - 1/2*cos(x^2)","A",0
800,1,14,0,0.799137," ","integrate(sin(x)^2*tan(x),x, algorithm=""fricas"")","\frac{1}{2} \, \cos\left(x\right)^{2} - \log\left(-\cos\left(x\right)\right)"," ",0,"1/2*cos(x)^2 - log(-cos(x))","A",0
801,1,37,0,0.602612," ","integrate(cos(x)^2*cot(x)^3,x, algorithm=""fricas"")","-\frac{2 \, \cos\left(x\right)^{4} - 3 \, \cos\left(x\right)^{2} + 8 \, {\left(\cos\left(x\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \sin\left(x\right)\right) - 1}{4 \, {\left(\cos\left(x\right)^{2} - 1\right)}}"," ",0,"-1/4*(2*cos(x)^4 - 3*cos(x)^2 + 8*(cos(x)^2 - 1)*log(1/2*sin(x)) - 1)/(cos(x)^2 - 1)","B",0
802,1,5,0,1.436838," ","integrate(sec(x)*(1-sin(x)),x, algorithm=""fricas"")","\log\left(\sin\left(x\right) + 1\right)"," ",0,"log(sin(x) + 1)","A",0
803,1,7,0,0.740814," ","integrate((1+cos(x))*csc(x),x, algorithm=""fricas"")","\log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"log(-1/2*cos(x) + 1/2)","A",0
804,1,5,0,0.530198," ","integrate(cos(x)^2*(1-tan(x)^2),x, algorithm=""fricas"")","\cos\left(x\right) \sin\left(x\right)"," ",0,"cos(x)*sin(x)","A",0
805,1,35,0,0.751529," ","integrate(csc(2*x)*(cos(x)+sin(x)),x, algorithm=""fricas"")","-\frac{1}{4} \, \log\left(-\frac{1}{2} \, {\left(\cos\left(x\right) + 1\right)} \sin\left(x\right) + \frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{4} \, \log\left(-\frac{1}{2} \, {\left(\cos\left(x\right) - 1\right)} \sin\left(x\right) - \frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"-1/4*log(-1/2*(cos(x) + 1)*sin(x) + 1/2*cos(x) + 1/2) + 1/4*log(-1/2*(cos(x) - 1)*sin(x) - 1/2*cos(x) + 1/2)","B",0
806,1,15,0,0.702115," ","integrate(cos(x)*(-3+2*sin(x))/(2-3*sin(x)+sin(x)^2),x, algorithm=""fricas"")","\log\left(-\frac{1}{2} \, \sin\left(x\right) + 1\right) + \log\left(-\sin\left(x\right) + 1\right)"," ",0,"log(-1/2*sin(x) + 1) + log(-sin(x) + 1)","A",0
807,1,17,0,0.619797," ","integrate(cos(x)^2*sin(x)/(5+cos(x)^2),x, algorithm=""fricas"")","\sqrt{5} \arctan\left(\frac{1}{5} \, \sqrt{5} \cos\left(x\right)\right) - \cos\left(x\right)"," ",0,"sqrt(5)*arctan(1/5*sqrt(5)*cos(x)) - cos(x)","A",0
808,1,13,0,0.601072," ","integrate(cos(x)/(sin(x)+sin(x)^2),x, algorithm=""fricas"")","\log\left(\frac{1}{2} \, \sin\left(x\right)\right) - \log\left(\sin\left(x\right) + 1\right)"," ",0,"log(1/2*sin(x)) - log(sin(x) + 1)","A",0
809,1,27,0,1.390319," ","integrate(cos(x)/(sin(x)+sin(x)^(2^(1/2))),x, algorithm=""fricas"")","-{\left(\sqrt{2} + 1\right)} \log\left(\sin\left(x\right)^{\left(\sqrt{2}\right)} + \sin\left(x\right)\right) + {\left(\sqrt{2} + 2\right)} \log\left(\sin\left(x\right)\right)"," ",0,"-(sqrt(2) + 1)*log(sin(x)^sqrt(2) + sin(x)) + (sqrt(2) + 2)*log(sin(x))","A",0
810,1,35,0,0.601650," ","integrate(1/(2*sin(x)+sin(2*x)),x, algorithm=""fricas"")","-\frac{{\left(\cos\left(x\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - {\left(\cos\left(x\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - 2}{8 \, {\left(\cos\left(x\right) + 1\right)}}"," ",0,"-1/8*((cos(x) + 1)*log(1/2*cos(x) + 1/2) - (cos(x) + 1)*log(-1/2*cos(x) + 1/2) - 2)/(cos(x) + 1)","B",0
811,1,26,0,0.553297," ","integrate((x^2+4*x-3)*sin(2*x),x, algorithm=""fricas"")","-\frac{1}{4} \, {\left(2 \, x^{2} + 8 \, x - 7\right)} \cos\left(2 \, x\right) + \frac{1}{2} \, {\left(x + 2\right)} \sin\left(2 \, x\right)"," ",0,"-1/4*(2*x^2 + 8*x - 7)*cos(2*x) + 1/2*(x + 2)*sin(2*x)","A",0
812,1,21,0,0.603392," ","integrate(cos(4*x)/exp(3*x),x, algorithm=""fricas"")","-\frac{3}{25} \, \cos\left(4 \, x\right) e^{\left(-3 \, x\right)} + \frac{4}{25} \, e^{\left(-3 \, x\right)} \sin\left(4 \, x\right)"," ",0,"-3/25*cos(4*x)*e^(-3*x) + 4/25*e^(-3*x)*sin(4*x)","A",0
813,1,12,0,0.710110," ","integrate(cos(x)*sin(x)/(1+sin(x))^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, \sqrt{\sin\left(x\right) + 1} {\left(\sin\left(x\right) - 2\right)}"," ",0,"2/3*sqrt(sin(x) + 1)*(sin(x) - 2)","A",0
814,1,36,0,0.586834," ","integrate(x+60*cos(x)^5*sin(x)^4,x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} + \frac{4}{21} \, {\left(35 \, \cos\left(x\right)^{8} - 50 \, \cos\left(x\right)^{6} + 3 \, \cos\left(x\right)^{4} + 4 \, \cos\left(x\right)^{2} + 8\right)} \sin\left(x\right)"," ",0,"1/2*x^2 + 4/21*(35*cos(x)^8 - 50*cos(x)^6 + 3*cos(x)^4 + 4*cos(x)^2 + 8)*sin(x)","A",0
815,1,6,0,0.533877," ","integrate(cos(x)*(sec(x)+tan(x)),x, algorithm=""fricas"")","x - \cos\left(x\right)"," ",0,"x - cos(x)","A",0
816,1,15,0,0.735672," ","integrate(cos(x)*(sec(x)^3+tan(x)),x, algorithm=""fricas"")","-\frac{\cos\left(x\right)^{2} - \sin\left(x\right)}{\cos\left(x\right)}"," ",0,"-(cos(x)^2 - sin(x))/cos(x)","B",0
817,1,10,0,1.082913," ","integrate(-1/2*cot(x)*csc(x)+1/2*csc(x)^2,x, algorithm=""fricas"")","\frac{\sin\left(x\right)}{2 \, {\left(\cos\left(x\right) + 1\right)}}"," ",0,"1/2*sin(x)/(cos(x) + 1)","A",0
818,1,22,0,0.587054," ","integrate(-csc(x)^2+sin(2*x),x, algorithm=""fricas"")","-\frac{{\left(2 \, \cos\left(x\right)^{2} - 1\right)} \sin\left(x\right) - 2 \, \cos\left(x\right)}{2 \, \sin\left(x\right)}"," ",0,"-1/2*((2*cos(x)^2 - 1)*sin(x) - 2*cos(x))/sin(x)","B",0
819,1,18,0,0.914883," ","integrate(2*cot(2*x)-3*sin(3*x),x, algorithm=""fricas"")","4 \, \cos\left(x\right)^{3} - 3 \, \cos\left(x\right) + \log\left(-\frac{1}{2} \, \cos\left(x\right) \sin\left(x\right)\right)"," ",0,"4*cos(x)^3 - 3*cos(x) + log(-1/2*cos(x)*sin(x))","A",0
820,1,8,0,0.697875," ","integrate(x*sin(2*x^2),x, algorithm=""fricas"")","-\frac{1}{4} \, \cos\left(2 \, x^{2}\right)"," ",0,"-1/4*cos(2*x^2)","A",0
821,1,14,0,0.625074," ","integrate(cos(-1+x)*sin(-1+x)*(1+sin(-1+x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(-\cos\left(x - 1\right)^{2} + 2\right)}^{\frac{3}{2}}"," ",0,"1/3*(-cos(x - 1)^2 + 2)^(3/2)","A",0
822,1,8,0,0.602436," ","integrate(cos(1/x)*sin(1/x)/x^2,x, algorithm=""fricas"")","\frac{1}{2} \, \cos\left(\frac{1}{x}\right)^{2}"," ",0,"1/2*cos(1/x)^2","A",0
823,1,21,0,0.750153," ","integrate(cos(1/2+3/2*x)*sin(1/2+3/2*x)^3,x, algorithm=""fricas"")","\frac{1}{6} \, \cos\left(\frac{3}{2} \, x + \frac{1}{2}\right)^{4} - \frac{1}{3} \, \cos\left(\frac{3}{2} \, x + \frac{1}{2}\right)^{2}"," ",0,"1/6*cos(3/2*x + 1/2)^4 - 1/3*cos(3/2*x + 1/2)^2","B",0
824,1,13,0,0.607156," ","integrate(4*x*tan(x^2),x, algorithm=""fricas"")","-\log\left(\frac{1}{\tan\left(x^{2}\right)^{2} + 1}\right)"," ",0,"-log(1/(tan(x^2)^2 + 1))","A",0
825,1,25,0,0.686333," ","integrate(x*sec(x^2-5),x, algorithm=""fricas"")","\frac{1}{4} \, \log\left(\sin\left(x^{2} - 5\right) + 1\right) - \frac{1}{4} \, \log\left(-\sin\left(x^{2} - 5\right) + 1\right)"," ",0,"1/4*log(sin(x^2 - 5) + 1) - 1/4*log(-sin(x^2 - 5) + 1)","B",0
826,1,23,0,0.646616," ","integrate(csc(1/x)/x^2,x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(\frac{1}{2} \, \cos\left(\frac{1}{x}\right) + \frac{1}{2}\right) - \frac{1}{2} \, \log\left(-\frac{1}{2} \, \cos\left(\frac{1}{x}\right) + \frac{1}{2}\right)"," ",0,"1/2*log(1/2*cos(1/x) + 1/2) - 1/2*log(-1/2*cos(1/x) + 1/2)","B",0
827,1,7,0,0.617108," ","integrate((csc(x)-sec(x))*(cos(x)+sin(x)),x, algorithm=""fricas"")","\log\left(-\frac{1}{2} \, \cos\left(x\right) \sin\left(x\right)\right)"," ",0,"log(-1/2*cos(x)*sin(x))","A",0
828,1,4,0,0.689568," ","integrate(-cos(3*x)*sin(2*x)+cos(2*x)*sin(3*x),x, algorithm=""fricas"")","-\cos\left(x\right)"," ",0,"-cos(x)","A",0
829,1,27,0,1.316979," ","integrate(4*x*sec(2*x)^2,x, algorithm=""fricas"")","\frac{\cos\left(2 \, x\right) \log\left(-\cos\left(2 \, x\right)\right) + 2 \, x \sin\left(2 \, x\right)}{\cos\left(2 \, x\right)}"," ",0,"(cos(2*x)*log(-cos(2*x)) + 2*x*sin(2*x))/cos(2*x)","B",0
830,1,22,0,0.592478," ","integrate(4*sin(x)^2*tan(x)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, x \cos\left(x\right) - {\left(\cos\left(x\right)^{2} + 2\right)} \sin\left(x\right)\right)}}{\cos\left(x\right)}"," ",0,"-2*(3*x*cos(x) - (cos(x)^2 + 2)*sin(x))/cos(x)","A",0
831,1,28,0,1.629437," ","integrate(cos(x)^4*cot(x)^2,x, algorithm=""fricas"")","\frac{2 \, \cos\left(x\right)^{5} + 5 \, \cos\left(x\right)^{3} - 15 \, x \sin\left(x\right) - 15 \, \cos\left(x\right)}{8 \, \sin\left(x\right)}"," ",0,"1/8*(2*cos(x)^5 + 5*cos(x)^3 - 15*x*sin(x) - 15*cos(x))/sin(x)","A",0
832,1,19,0,1.560493," ","integrate(16*cos(x)^2*sin(x)^2,x, algorithm=""fricas"")","-2 \, {\left(2 \, \cos\left(x\right)^{3} - \cos\left(x\right)\right)} \sin\left(x\right) + 2 \, x"," ",0,"-2*(2*cos(x)^3 - cos(x))*sin(x) + 2*x","A",0
833,1,25,0,2.391463," ","integrate(8*cos(x)^2*sin(x)^4,x, algorithm=""fricas"")","\frac{1}{6} \, {\left(8 \, \cos\left(x\right)^{5} - 14 \, \cos\left(x\right)^{3} + 3 \, \cos\left(x\right)\right)} \sin\left(x\right) + \frac{1}{2} \, x"," ",0,"1/6*(8*cos(x)^5 - 14*cos(x)^3 + 3*cos(x))*sin(x) + 1/2*x","A",0
834,1,21,0,0.468203," ","integrate(35*cos(x)^3*sin(x)^4,x, algorithm=""fricas"")","{\left(5 \, \cos\left(x\right)^{6} - 8 \, \cos\left(x\right)^{4} + \cos\left(x\right)^{2} + 2\right)} \sin\left(x\right)"," ",0,"(5*cos(x)^6 - 8*cos(x)^4 + cos(x)^2 + 2)*sin(x)","A",0
835,1,31,0,1.967484," ","integrate(4*cos(x)^4*sin(x)^4,x, algorithm=""fricas"")","\frac{1}{32} \, {\left(16 \, \cos\left(x\right)^{7} - 24 \, \cos\left(x\right)^{5} + 2 \, \cos\left(x\right)^{3} + 3 \, \cos\left(x\right)\right)} \sin\left(x\right) + \frac{3}{32} \, x"," ",0,"1/32*(16*cos(x)^7 - 24*cos(x)^5 + 2*cos(x)^3 + 3*cos(x))*sin(x) + 3/32*x","A",0
836,1,19,0,0.572997," ","integrate(cos(x)/(-sin(x)+sin(x)^3),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(\cos\left(x\right)^{2}\right) - \frac{1}{2} \, \log\left(-\frac{1}{4} \, \cos\left(x\right)^{2} + \frac{1}{4}\right)"," ",0,"1/2*log(cos(x)^2) - 1/2*log(-1/4*cos(x)^2 + 1/4)","B",0
837,1,12,0,0.712268," ","integrate(-1+2*cos(x)^2+cos(x)*sin(x),x, algorithm=""fricas"")","-\frac{1}{2} \, \cos\left(x\right)^{2} + \cos\left(x\right) \sin\left(x\right)"," ",0,"-1/2*cos(x)^2 + cos(x)*sin(x)","A",0
838,1,1,0,1.350851," ","integrate(cos(x)^2+sin(x)^2,x, algorithm=""fricas"")","x"," ",0,"x","A",0
839,1,6,0,0.411845," ","integrate(-cos(x)^2+sin(x)^2,x, algorithm=""fricas"")","-\cos\left(x\right) \sin\left(x\right)"," ",0,"-cos(x)*sin(x)","A",0
840,1,9,0,0.555277," ","integrate(2^sin(x)*cos(x),x, algorithm=""fricas"")","\frac{2^{\sin\left(x\right)}}{\log\left(2\right)}"," ",0,"2^sin(x)/log(2)","A",0
841,1,6,0,1.468586," ","integrate(tan(x)^3+tan(x)^5,x, algorithm=""fricas"")","\frac{1}{4} \, \tan\left(x\right)^{4}"," ",0,"1/4*tan(x)^4","A",0
842,1,8,0,2.142409," ","integrate(x*sec(x)*(2+x*tan(x)),x, algorithm=""fricas"")","\frac{x^{2}}{\cos\left(x\right)}"," ",0,"x^2/cos(x)","A",0
843,1,8,0,1.437284," ","integrate(cot(x^(1/2))*csc(x^(1/2))/x^(1/2),x, algorithm=""fricas"")","-\frac{2}{\sin\left(\sqrt{x}\right)}"," ",0,"-2/sin(sqrt(x))","A",0
844,1,8,0,0.733116," ","integrate(cos(x^(1/2))*sin(x^(1/2))/x^(1/2),x, algorithm=""fricas"")","-\cos\left(\sqrt{x}\right)^{2}"," ",0,"-cos(sqrt(x))^2","A",0
845,1,8,0,0.567044," ","integrate(sec(x^(1/2))*tan(x^(1/2))/x^(1/2),x, algorithm=""fricas"")","\frac{2}{\cos\left(\sqrt{x}\right)}"," ",0,"2/cos(sqrt(x))","A",0
846,1,320,0,1.906324," ","integrate(sin(x)^2/(a+b*sin(2*x)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} b \log\left(-\frac{4 \, {\left(2 \, a^{2} - b^{2}\right)} \cos\left(x\right)^{4} - 4 \, a b \cos\left(x\right) \sin\left(x\right) - 4 \, {\left(2 \, a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2} - 2 \, b^{2} + 2 \, {\left(2 \, b \cos\left(x\right)^{2} + 2 \, {\left(2 \, a \cos\left(x\right)^{3} - a \cos\left(x\right)\right)} \sin\left(x\right) - b\right)} \sqrt{-a^{2} + b^{2}}}{4 \, b^{2} \cos\left(x\right)^{4} - 4 \, b^{2} \cos\left(x\right)^{2} - 4 \, a b \cos\left(x\right) \sin\left(x\right) - a^{2}}\right) + {\left(a^{2} - b^{2}\right)} \log\left(-4 \, b^{2} \cos\left(x\right)^{4} + 4 \, b^{2} \cos\left(x\right)^{2} + 4 \, a b \cos\left(x\right) \sin\left(x\right) + a^{2}\right)}{8 \, {\left(a^{2} b - b^{3}\right)}}, -\frac{2 \, \sqrt{a^{2} - b^{2}} b \arctan\left(-\frac{{\left(2 \, a \cos\left(x\right) \sin\left(x\right) + b\right)} \sqrt{a^{2} - b^{2}}}{2 \, {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - a^{2} + b^{2}}\right) + {\left(a^{2} - b^{2}\right)} \log\left(-4 \, b^{2} \cos\left(x\right)^{4} + 4 \, b^{2} \cos\left(x\right)^{2} + 4 \, a b \cos\left(x\right) \sin\left(x\right) + a^{2}\right)}{8 \, {\left(a^{2} b - b^{3}\right)}}\right]"," ",0,"[-1/8*(sqrt(-a^2 + b^2)*b*log(-(4*(2*a^2 - b^2)*cos(x)^4 - 4*a*b*cos(x)*sin(x) - 4*(2*a^2 - b^2)*cos(x)^2 + a^2 - 2*b^2 + 2*(2*b*cos(x)^2 + 2*(2*a*cos(x)^3 - a*cos(x))*sin(x) - b)*sqrt(-a^2 + b^2))/(4*b^2*cos(x)^4 - 4*b^2*cos(x)^2 - 4*a*b*cos(x)*sin(x) - a^2)) + (a^2 - b^2)*log(-4*b^2*cos(x)^4 + 4*b^2*cos(x)^2 + 4*a*b*cos(x)*sin(x) + a^2))/(a^2*b - b^3), -1/8*(2*sqrt(a^2 - b^2)*b*arctan(-(2*a*cos(x)*sin(x) + b)*sqrt(a^2 - b^2)/(2*(a^2 - b^2)*cos(x)^2 - a^2 + b^2)) + (a^2 - b^2)*log(-4*b^2*cos(x)^4 + 4*b^2*cos(x)^2 + 4*a*b*cos(x)*sin(x) + a^2))/(a^2*b - b^3)]","B",0
847,1,322,0,1.277086," ","integrate(cos(x)^2/(a+b*sin(2*x)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} b \log\left(-\frac{4 \, {\left(2 \, a^{2} - b^{2}\right)} \cos\left(x\right)^{4} - 4 \, a b \cos\left(x\right) \sin\left(x\right) - 4 \, {\left(2 \, a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2} - 2 \, b^{2} + 2 \, {\left(2 \, b \cos\left(x\right)^{2} + 2 \, {\left(2 \, a \cos\left(x\right)^{3} - a \cos\left(x\right)\right)} \sin\left(x\right) - b\right)} \sqrt{-a^{2} + b^{2}}}{4 \, b^{2} \cos\left(x\right)^{4} - 4 \, b^{2} \cos\left(x\right)^{2} - 4 \, a b \cos\left(x\right) \sin\left(x\right) - a^{2}}\right) - {\left(a^{2} - b^{2}\right)} \log\left(-4 \, b^{2} \cos\left(x\right)^{4} + 4 \, b^{2} \cos\left(x\right)^{2} + 4 \, a b \cos\left(x\right) \sin\left(x\right) + a^{2}\right)}{8 \, {\left(a^{2} b - b^{3}\right)}}, -\frac{2 \, \sqrt{a^{2} - b^{2}} b \arctan\left(-\frac{{\left(2 \, a \cos\left(x\right) \sin\left(x\right) + b\right)} \sqrt{a^{2} - b^{2}}}{2 \, {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - a^{2} + b^{2}}\right) - {\left(a^{2} - b^{2}\right)} \log\left(-4 \, b^{2} \cos\left(x\right)^{4} + 4 \, b^{2} \cos\left(x\right)^{2} + 4 \, a b \cos\left(x\right) \sin\left(x\right) + a^{2}\right)}{8 \, {\left(a^{2} b - b^{3}\right)}}\right]"," ",0,"[-1/8*(sqrt(-a^2 + b^2)*b*log(-(4*(2*a^2 - b^2)*cos(x)^4 - 4*a*b*cos(x)*sin(x) - 4*(2*a^2 - b^2)*cos(x)^2 + a^2 - 2*b^2 + 2*(2*b*cos(x)^2 + 2*(2*a*cos(x)^3 - a*cos(x))*sin(x) - b)*sqrt(-a^2 + b^2))/(4*b^2*cos(x)^4 - 4*b^2*cos(x)^2 - 4*a*b*cos(x)*sin(x) - a^2)) - (a^2 - b^2)*log(-4*b^2*cos(x)^4 + 4*b^2*cos(x)^2 + 4*a*b*cos(x)*sin(x) + a^2))/(a^2*b - b^3), -1/8*(2*sqrt(a^2 - b^2)*b*arctan(-(2*a*cos(x)*sin(x) + b)*sqrt(a^2 - b^2)/(2*(a^2 - b^2)*cos(x)^2 - a^2 + b^2)) - (a^2 - b^2)*log(-4*b^2*cos(x)^4 + 4*b^2*cos(x)^2 + 4*a*b*cos(x)*sin(x) + a^2))/(a^2*b - b^3)]","B",0
848,1,225,0,1.219786," ","integrate(sin(x)^2/(a+b*cos(2*x)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{a + b}{a - b}} \log\left(\frac{4 \, {\left(2 \, a^{2} - b^{2}\right)} \cos\left(x\right)^{4} - 4 \, {\left(2 \, a^{2} - a b - b^{2}\right)} \cos\left(x\right)^{2} - 4 \, {\left(2 \, {\left(a^{2} - a b\right)} \cos\left(x\right)^{3} - {\left(a^{2} - 2 \, a b + b^{2}\right)} \cos\left(x\right)\right)} \sqrt{-\frac{a + b}{a - b}} \sin\left(x\right) + a^{2} - 2 \, a b + b^{2}}{4 \, b^{2} \cos\left(x\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cos\left(x\right)^{2} + a^{2} - 2 \, a b + b^{2}}\right) - 4 \, x}{8 \, b}, -\frac{\sqrt{\frac{a + b}{a - b}} \arctan\left(\frac{{\left(2 \, a \cos\left(x\right)^{2} - a + b\right)} \sqrt{\frac{a + b}{a - b}}}{2 \, {\left(a + b\right)} \cos\left(x\right) \sin\left(x\right)}\right) + 2 \, x}{4 \, b}\right]"," ",0,"[1/8*(sqrt(-(a + b)/(a - b))*log((4*(2*a^2 - b^2)*cos(x)^4 - 4*(2*a^2 - a*b - b^2)*cos(x)^2 - 4*(2*(a^2 - a*b)*cos(x)^3 - (a^2 - 2*a*b + b^2)*cos(x))*sqrt(-(a + b)/(a - b))*sin(x) + a^2 - 2*a*b + b^2)/(4*b^2*cos(x)^4 + 4*(a*b - b^2)*cos(x)^2 + a^2 - 2*a*b + b^2)) - 4*x)/b, -1/4*(sqrt((a + b)/(a - b))*arctan(1/2*(2*a*cos(x)^2 - a + b)*sqrt((a + b)/(a - b))/((a + b)*cos(x)*sin(x))) + 2*x)/b]","A",0
849,1,224,0,1.109760," ","integrate(cos(x)^2/(a+b*cos(2*x)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{a - b}{a + b}} \log\left(\frac{4 \, {\left(2 \, a^{2} - b^{2}\right)} \cos\left(x\right)^{4} - 4 \, {\left(2 \, a^{2} - a b - b^{2}\right)} \cos\left(x\right)^{2} + 4 \, {\left(2 \, {\left(a^{2} + a b\right)} \cos\left(x\right)^{3} - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)\right)} \sqrt{-\frac{a - b}{a + b}} \sin\left(x\right) + a^{2} - 2 \, a b + b^{2}}{4 \, b^{2} \cos\left(x\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cos\left(x\right)^{2} + a^{2} - 2 \, a b + b^{2}}\right) + 4 \, x}{8 \, b}, -\frac{\sqrt{\frac{a - b}{a + b}} \arctan\left(-\frac{{\left(2 \, a \cos\left(x\right)^{2} - a + b\right)} \sqrt{\frac{a - b}{a + b}}}{2 \, {\left(a - b\right)} \cos\left(x\right) \sin\left(x\right)}\right) - 2 \, x}{4 \, b}\right]"," ",0,"[1/8*(sqrt(-(a - b)/(a + b))*log((4*(2*a^2 - b^2)*cos(x)^4 - 4*(2*a^2 - a*b - b^2)*cos(x)^2 + 4*(2*(a^2 + a*b)*cos(x)^3 - (a^2 - b^2)*cos(x))*sqrt(-(a - b)/(a + b))*sin(x) + a^2 - 2*a*b + b^2)/(4*b^2*cos(x)^4 + 4*(a*b - b^2)*cos(x)^2 + a^2 - 2*a*b + b^2)) + 4*x)/b, -1/4*(sqrt((a - b)/(a + b))*arctan(-1/2*(2*a*cos(x)^2 - a + b)*sqrt((a - b)/(a + b))/((a - b)*cos(x)*sin(x))) - 2*x)/b]","A",0
850,1,91,0,0.893956," ","integrate(tan(d*x+c)/(a*sin(d*x+c)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a \cos\left(d x + c\right)^{2} + a} \log\left(-\frac{\sin\left(d x + c\right) + 1}{\sin\left(d x + c\right) - 1}\right)}{2 \, a d \sin\left(d x + c\right)}, -\frac{\sqrt{-a} \arctan\left(\frac{\sqrt{-a \cos\left(d x + c\right)^{2} + a} \sqrt{-a}}{a}\right)}{a d}\right]"," ",0,"[1/2*sqrt(-a*cos(d*x + c)^2 + a)*log(-(sin(d*x + c) + 1)/(sin(d*x + c) - 1))/(a*d*sin(d*x + c)), -sqrt(-a)*arctan(sqrt(-a*cos(d*x + c)^2 + a)*sqrt(-a)/a)/(a*d)]","A",0
851,1,84,0,1.213109," ","integrate(cot(d*x+c)/(a*cos(d*x+c)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{a \cos\left(d x + c\right)^{2}} \log\left(-\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right) - 1}\right)}{2 \, a d \cos\left(d x + c\right)}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right)^{2}} \sqrt{-a}}{a}\right)}{a d}\right]"," ",0,"[-1/2*sqrt(a*cos(d*x + c)^2)*log(-(cos(d*x + c) + 1)/(cos(d*x + c) - 1))/(a*d*cos(d*x + c)), sqrt(-a)*arctan(sqrt(a*cos(d*x + c)^2)*sqrt(-a)/a)/(a*d)]","A",0
852,1,6,0,2.081349," ","integrate(x*cos(x^2)/sin(x^2)^(1/2),x, algorithm=""fricas"")","\sqrt{\sin\left(x^{2}\right)}"," ",0,"sqrt(sin(x^2))","A",0
853,1,21,0,1.326349," ","integrate(cos(x)/(1-cos(2*x))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{-2 \, \cos\left(x\right)^{2} + 2} \log\left(\frac{1}{2} \, \sin\left(x\right)\right)}{2 \, \sin\left(x\right)}"," ",0,"1/2*sqrt(-2*cos(x)^2 + 2)*log(1/2*sin(x))/sin(x)","A",0
854,1,23,0,0.414668," ","integrate(cos(log(x))^2*sin(log(x))^2/x,x, algorithm=""fricas"")","-\frac{1}{8} \, {\left(2 \, \cos\left(\log\left(x\right)\right)^{3} - \cos\left(\log\left(x\right)\right)\right)} \sin\left(\log\left(x\right)\right) + \frac{1}{8} \, \log\left(x\right)"," ",0,"-1/8*(2*cos(log(x))^3 - cos(log(x)))*sin(log(x)) + 1/8*log(x)","A",0
855,1,26,0,2.014454," ","integrate(sin(x)^3/(cos(x)^3+sin(x)^3),x, algorithm=""fricas"")","\frac{1}{2} \, x - \frac{1}{12} \, \log\left(2 \, \cos\left(x\right) \sin\left(x\right) + 1\right) + \frac{1}{3} \, \log\left(-\cos\left(x\right) \sin\left(x\right) + 1\right)"," ",0,"1/2*x - 1/12*log(2*cos(x)*sin(x) + 1) + 1/3*log(-cos(x)*sin(x) + 1)","A",0
856,1,26,0,1.010113," ","integrate(cos(x)^3/(cos(x)^3+sin(x)^3),x, algorithm=""fricas"")","\frac{1}{2} \, x + \frac{1}{12} \, \log\left(2 \, \cos\left(x\right) \sin\left(x\right) + 1\right) - \frac{1}{3} \, \log\left(-\cos\left(x\right) \sin\left(x\right) + 1\right)"," ",0,"1/2*x + 1/12*log(2*cos(x)*sin(x) + 1) - 1/3*log(-cos(x)*sin(x) + 1)","A",0
857,1,46,0,1.167666," ","integrate(sec(x)/(-5+cos(x)^2+4*sin(x)),x, algorithm=""fricas"")","-\frac{{\left(\sin\left(x\right) - 2\right)} \log\left(\sin\left(x\right) + 1\right) + 8 \, {\left(\sin\left(x\right) - 2\right)} \log\left(-\frac{1}{2} \, \sin\left(x\right) + 1\right) - 9 \, {\left(\sin\left(x\right) - 2\right)} \log\left(-\sin\left(x\right) + 1\right) + 6}{18 \, {\left(\sin\left(x\right) - 2\right)}}"," ",0,"-1/18*((sin(x) - 2)*log(sin(x) + 1) + 8*(sin(x) - 2)*log(-1/2*sin(x) + 1) - 9*(sin(x) - 2)*log(-sin(x) + 1) + 6)/(sin(x) - 2)","A",0
858,1,15,0,0.874856," ","integrate(1/cos(x)^(3/2)/(3*cos(x)+sin(x))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3 \, \cos\left(x\right) + \sin\left(x\right)}}{\sqrt{\cos\left(x\right)}}"," ",0,"2*sqrt(3*cos(x) + sin(x))/sqrt(cos(x))","A",0
859,1,96,0,0.887132," ","integrate(csc(x)*(cos(x)+sin(x))^(1/2)/cos(x)^(3/2),x, algorithm=""fricas"")","-\frac{\cos\left(x\right) \log\left({\left(2 \, \cos\left(x\right) + \sin\left(x\right)\right)} \sqrt{\cos\left(x\right) + \sin\left(x\right)} \sqrt{\cos\left(x\right)} + \frac{7}{4} \, \cos\left(x\right)^{2} + 2 \, \cos\left(x\right) \sin\left(x\right) + \frac{1}{4}\right) - \cos\left(x\right) \log\left(-{\left(2 \, \cos\left(x\right) + \sin\left(x\right)\right)} \sqrt{\cos\left(x\right) + \sin\left(x\right)} \sqrt{\cos\left(x\right)} + \frac{7}{4} \, \cos\left(x\right)^{2} + 2 \, \cos\left(x\right) \sin\left(x\right) + \frac{1}{4}\right) - 8 \, \sqrt{\cos\left(x\right) + \sin\left(x\right)} \sqrt{\cos\left(x\right)}}{4 \, \cos\left(x\right)}"," ",0,"-1/4*(cos(x)*log((2*cos(x) + sin(x))*sqrt(cos(x) + sin(x))*sqrt(cos(x)) + 7/4*cos(x)^2 + 2*cos(x)*sin(x) + 1/4) - cos(x)*log(-(2*cos(x) + sin(x))*sqrt(cos(x) + sin(x))*sqrt(cos(x)) + 7/4*cos(x)^2 + 2*cos(x)*sin(x) + 1/4) - 8*sqrt(cos(x) + sin(x))*sqrt(cos(x)))/cos(x)","B",0
860,1,3,0,1.388789," ","integrate((cos(x)+sin(x))/(1+sin(2*x))^(1/2),x, algorithm=""fricas"")","-x"," ",0,"-x","A",0
861,1,21,0,0.892833," ","integrate(sec(x)*(sec(x)+tan(x))^(1/2),x, algorithm=""fricas"")","2 \, \sqrt{\frac{\cos\left(x\right) + \sin\left(x\right) + 1}{\cos\left(x\right) - \sin\left(x\right) + 1}}"," ",0,"2*sqrt((cos(x) + sin(x) + 1)/(cos(x) - sin(x) + 1))","A",0
862,1,25,0,1.256057," ","integrate(sec(x)*(4+3*sec(x))^(1/2)*tan(x),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\frac{4 \, \cos\left(x\right) + 3}{\cos\left(x\right)}} {\left(4 \, \cos\left(x\right) + 3\right)}}{9 \, \cos\left(x\right)}"," ",0,"2/9*sqrt((4*cos(x) + 3)/cos(x))*(4*cos(x) + 3)/cos(x)","B",0
863,1,35,0,0.867528," ","integrate(sec(x)*(1+sec(x))^(1/2)*tan(x)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(9 \, \cos\left(x\right)^{3} + 13 \, \cos\left(x\right)^{2} - \cos\left(x\right) - 5\right)} \sqrt{\frac{\cos\left(x\right) + 1}{\cos\left(x\right)}}}{35 \, \cos\left(x\right)^{3}}"," ",0,"-2/35*(9*cos(x)^3 + 13*cos(x)^2 - cos(x) - 5)*sqrt((cos(x) + 1)/cos(x))/cos(x)^3","B",0
864,1,44,0,0.405654," ","integrate(cot(x)^3*csc(x)*(1+csc(x))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(13 \, \cos\left(x\right)^{2} + {\left(9 \, \cos\left(x\right)^{2} - 8\right)} \sin\left(x\right) - 8\right)} \sqrt{\frac{\sin\left(x\right) + 1}{\sin\left(x\right)}}}{35 \, {\left(\cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}"," ",0,"2/35*(13*cos(x)^2 + (9*cos(x)^2 - 8)*sin(x) - 8)*sqrt((sin(x) + 1)/sin(x))/((cos(x)^2 - 1)*sin(x))","B",0
865,-2,0,0,0.000000," ","integrate(csc(x)^(1/2)*(x*cos(x)-4*sec(x)*tan(x)),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
866,1,34,0,1.922175," ","integrate(cot(x)*(1-sin(x)^2)^3*(-1+csc(x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{8 \, \cos\left(x\right)^{7} + 14 \, \cos\left(x\right)^{5} + 35 \, \cos\left(x\right)^{3} - 105 \, x \sin\left(x\right) - 105 \, \cos\left(x\right)}{48 \, \sin\left(x\right)}"," ",0,"-1/48*(8*cos(x)^7 + 14*cos(x)^5 + 35*cos(x)^3 - 105*x*sin(x) - 105*cos(x))/sin(x)","A",0
867,1,41,0,0.933949," ","integrate(cos(x)*(1-sin(x)^2)^3*(-1+csc(x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{7} \, \cos\left(x\right)^{7} - \frac{1}{5} \, \cos\left(x\right)^{5} - \frac{1}{3} \, \cos\left(x\right)^{3} - \cos\left(x\right) + \frac{1}{2} \, \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - \frac{1}{2} \, \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"-1/7*cos(x)^7 - 1/5*cos(x)^5 - 1/3*cos(x)^3 - cos(x) + 1/2*log(1/2*cos(x) + 1/2) - 1/2*log(-1/2*cos(x) + 1/2)","A",0
868,1,124,0,1.270724," ","integrate(x*csc(x)*sec(x)/(a*sec(x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(x \cos\left(x\right) \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x \cos\left(x\right) \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - x \cos\left(x\right) \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) - x \cos\left(x\right) \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) + i \, \cos\left(x\right) {\rm Li}_2\left(\cos\left(x\right) + i \, \sin\left(x\right)\right) - i \, \cos\left(x\right) {\rm Li}_2\left(\cos\left(x\right) - i \, \sin\left(x\right)\right) + i \, \cos\left(x\right) {\rm Li}_2\left(-\cos\left(x\right) + i \, \sin\left(x\right)\right) - i \, \cos\left(x\right) {\rm Li}_2\left(-\cos\left(x\right) - i \, \sin\left(x\right)\right)\right)} \sqrt{\frac{a}{\cos\left(x\right)^{2}}}}{2 \, a}"," ",0,"-1/2*(x*cos(x)*log(cos(x) + I*sin(x) + 1) + x*cos(x)*log(cos(x) - I*sin(x) + 1) - x*cos(x)*log(-cos(x) + I*sin(x) + 1) - x*cos(x)*log(-cos(x) - I*sin(x) + 1) + I*cos(x)*dilog(cos(x) + I*sin(x)) - I*cos(x)*dilog(cos(x) - I*sin(x)) + I*cos(x)*dilog(-cos(x) + I*sin(x)) - I*cos(x)*dilog(-cos(x) - I*sin(x)))*sqrt(a/cos(x)^2)/a","B",0
869,1,227,0,1.621971," ","integrate(x^2*csc(x)*sec(x)/(a*sec(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, \cos\left(x\right) + i \, \sin\left(x\right)\right) + 2 \, \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, \cos\left(x\right) - i \, \sin\left(x\right)\right) - 2 \, \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, -\cos\left(x\right) + i \, \sin\left(x\right)\right) - 2 \, \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, -\cos\left(x\right) - i \, \sin\left(x\right)\right) - {\left(x^{2} \cos\left(x\right) \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x^{2} \cos\left(x\right) \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - x^{2} \cos\left(x\right) \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) - x^{2} \cos\left(x\right) \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) + 2 i \, x \cos\left(x\right) {\rm Li}_2\left(\cos\left(x\right) + i \, \sin\left(x\right)\right) - 2 i \, x \cos\left(x\right) {\rm Li}_2\left(\cos\left(x\right) - i \, \sin\left(x\right)\right) + 2 i \, x \cos\left(x\right) {\rm Li}_2\left(-\cos\left(x\right) + i \, \sin\left(x\right)\right) - 2 i \, x \cos\left(x\right) {\rm Li}_2\left(-\cos\left(x\right) - i \, \sin\left(x\right)\right)\right)} \sqrt{\frac{a}{\cos\left(x\right)^{2}}}}{2 \, a}"," ",0,"1/2*(2*sqrt(a/cos(x)^2)*cos(x)*polylog(3, cos(x) + I*sin(x)) + 2*sqrt(a/cos(x)^2)*cos(x)*polylog(3, cos(x) - I*sin(x)) - 2*sqrt(a/cos(x)^2)*cos(x)*polylog(3, -cos(x) + I*sin(x)) - 2*sqrt(a/cos(x)^2)*cos(x)*polylog(3, -cos(x) - I*sin(x)) - (x^2*cos(x)*log(cos(x) + I*sin(x) + 1) + x^2*cos(x)*log(cos(x) - I*sin(x) + 1) - x^2*cos(x)*log(-cos(x) + I*sin(x) + 1) - x^2*cos(x)*log(-cos(x) - I*sin(x) + 1) + 2*I*x*cos(x)*dilog(cos(x) + I*sin(x)) - 2*I*x*cos(x)*dilog(cos(x) - I*sin(x)) + 2*I*x*cos(x)*dilog(-cos(x) + I*sin(x)) - 2*I*x*cos(x)*dilog(-cos(x) - I*sin(x)))*sqrt(a/cos(x)^2))/a","C",0
870,1,327,0,1.308664," ","integrate(x^3*csc(x)*sec(x)/(a*sec(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{6 \, x \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, \cos\left(x\right) + i \, \sin\left(x\right)\right) + 6 \, x \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, \cos\left(x\right) - i \, \sin\left(x\right)\right) - 6 \, x \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, -\cos\left(x\right) + i \, \sin\left(x\right)\right) - 6 \, x \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, -\cos\left(x\right) - i \, \sin\left(x\right)\right) + 6 i \, \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(4, \cos\left(x\right) + i \, \sin\left(x\right)\right) - 6 i \, \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(4, \cos\left(x\right) - i \, \sin\left(x\right)\right) + 6 i \, \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(4, -\cos\left(x\right) + i \, \sin\left(x\right)\right) - 6 i \, \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(4, -\cos\left(x\right) - i \, \sin\left(x\right)\right) - {\left(x^{3} \cos\left(x\right) \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x^{3} \cos\left(x\right) \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - x^{3} \cos\left(x\right) \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) - x^{3} \cos\left(x\right) \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) + 3 i \, x^{2} \cos\left(x\right) {\rm Li}_2\left(\cos\left(x\right) + i \, \sin\left(x\right)\right) - 3 i \, x^{2} \cos\left(x\right) {\rm Li}_2\left(\cos\left(x\right) - i \, \sin\left(x\right)\right) + 3 i \, x^{2} \cos\left(x\right) {\rm Li}_2\left(-\cos\left(x\right) + i \, \sin\left(x\right)\right) - 3 i \, x^{2} \cos\left(x\right) {\rm Li}_2\left(-\cos\left(x\right) - i \, \sin\left(x\right)\right)\right)} \sqrt{\frac{a}{\cos\left(x\right)^{2}}}}{2 \, a}"," ",0,"1/2*(6*x*sqrt(a/cos(x)^2)*cos(x)*polylog(3, cos(x) + I*sin(x)) + 6*x*sqrt(a/cos(x)^2)*cos(x)*polylog(3, cos(x) - I*sin(x)) - 6*x*sqrt(a/cos(x)^2)*cos(x)*polylog(3, -cos(x) + I*sin(x)) - 6*x*sqrt(a/cos(x)^2)*cos(x)*polylog(3, -cos(x) - I*sin(x)) + 6*I*sqrt(a/cos(x)^2)*cos(x)*polylog(4, cos(x) + I*sin(x)) - 6*I*sqrt(a/cos(x)^2)*cos(x)*polylog(4, cos(x) - I*sin(x)) + 6*I*sqrt(a/cos(x)^2)*cos(x)*polylog(4, -cos(x) + I*sin(x)) - 6*I*sqrt(a/cos(x)^2)*cos(x)*polylog(4, -cos(x) - I*sin(x)) - (x^3*cos(x)*log(cos(x) + I*sin(x) + 1) + x^3*cos(x)*log(cos(x) - I*sin(x) + 1) - x^3*cos(x)*log(-cos(x) + I*sin(x) + 1) - x^3*cos(x)*log(-cos(x) - I*sin(x) + 1) + 3*I*x^2*cos(x)*dilog(cos(x) + I*sin(x)) - 3*I*x^2*cos(x)*dilog(cos(x) - I*sin(x)) + 3*I*x^2*cos(x)*dilog(-cos(x) + I*sin(x)) - 3*I*x^2*cos(x)*dilog(-cos(x) - I*sin(x)))*sqrt(a/cos(x)^2))/a","C",0
871,1,138,0,2.099789," ","integrate(x*csc(x)*sec(x)/(a*sec(x)^4)^(1/2),x, algorithm=""fricas"")","\frac{{\left(x \cos\left(x\right)^{2} \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x \cos\left(x\right)^{2} \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) + x \cos\left(x\right)^{2} \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x \cos\left(x\right)^{2} \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - i \, \cos\left(x\right)^{2} {\rm Li}_2\left(\cos\left(x\right) + i \, \sin\left(x\right)\right) + i \, \cos\left(x\right)^{2} {\rm Li}_2\left(\cos\left(x\right) - i \, \sin\left(x\right)\right) + i \, \cos\left(x\right)^{2} {\rm Li}_2\left(-\cos\left(x\right) + i \, \sin\left(x\right)\right) - i \, \cos\left(x\right)^{2} {\rm Li}_2\left(-\cos\left(x\right) - i \, \sin\left(x\right)\right)\right)} \sqrt{\frac{a}{\cos\left(x\right)^{4}}}}{2 \, a}"," ",0,"1/2*(x*cos(x)^2*log(cos(x) + I*sin(x) + 1) + x*cos(x)^2*log(cos(x) - I*sin(x) + 1) + x*cos(x)^2*log(-cos(x) + I*sin(x) + 1) + x*cos(x)^2*log(-cos(x) - I*sin(x) + 1) - I*cos(x)^2*dilog(cos(x) + I*sin(x)) + I*cos(x)^2*dilog(cos(x) - I*sin(x)) + I*cos(x)^2*dilog(-cos(x) + I*sin(x)) - I*cos(x)^2*dilog(-cos(x) - I*sin(x)))*sqrt(a/cos(x)^4)/a","B",0
872,1,248,0,2.498362," ","integrate(x^2*csc(x)*sec(x)/(a*sec(x)^4)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, \cos\left(x\right) + i \, \sin\left(x\right)\right) + 2 \, \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, \cos\left(x\right) - i \, \sin\left(x\right)\right) + 2 \, \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, -\cos\left(x\right) + i \, \sin\left(x\right)\right) + 2 \, \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, -\cos\left(x\right) - i \, \sin\left(x\right)\right) + {\left(x^{2} \cos\left(x\right)^{2} \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x^{2} \cos\left(x\right)^{2} \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) + x^{2} \cos\left(x\right)^{2} \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x^{2} \cos\left(x\right)^{2} \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - 2 i \, x \cos\left(x\right)^{2} {\rm Li}_2\left(\cos\left(x\right) + i \, \sin\left(x\right)\right) + 2 i \, x \cos\left(x\right)^{2} {\rm Li}_2\left(\cos\left(x\right) - i \, \sin\left(x\right)\right) + 2 i \, x \cos\left(x\right)^{2} {\rm Li}_2\left(-\cos\left(x\right) + i \, \sin\left(x\right)\right) - 2 i \, x \cos\left(x\right)^{2} {\rm Li}_2\left(-\cos\left(x\right) - i \, \sin\left(x\right)\right)\right)} \sqrt{\frac{a}{\cos\left(x\right)^{4}}}}{2 \, a}"," ",0,"1/2*(2*sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, cos(x) + I*sin(x)) + 2*sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, cos(x) - I*sin(x)) + 2*sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, -cos(x) + I*sin(x)) + 2*sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, -cos(x) - I*sin(x)) + (x^2*cos(x)^2*log(cos(x) + I*sin(x) + 1) + x^2*cos(x)^2*log(cos(x) - I*sin(x) + 1) + x^2*cos(x)^2*log(-cos(x) + I*sin(x) + 1) + x^2*cos(x)^2*log(-cos(x) - I*sin(x) + 1) - 2*I*x*cos(x)^2*dilog(cos(x) + I*sin(x)) + 2*I*x*cos(x)^2*dilog(cos(x) - I*sin(x)) + 2*I*x*cos(x)^2*dilog(-cos(x) + I*sin(x)) - 2*I*x*cos(x)^2*dilog(-cos(x) - I*sin(x)))*sqrt(a/cos(x)^4))/a","C",0
873,1,356,0,2.051394," ","integrate(x^3*csc(x)*sec(x)/(a*sec(x)^4)^(1/2),x, algorithm=""fricas"")","\frac{6 \, x \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, \cos\left(x\right) + i \, \sin\left(x\right)\right) + 6 \, x \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, \cos\left(x\right) - i \, \sin\left(x\right)\right) + 6 \, x \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, -\cos\left(x\right) + i \, \sin\left(x\right)\right) + 6 \, x \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, -\cos\left(x\right) - i \, \sin\left(x\right)\right) + 6 i \, \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(4, \cos\left(x\right) + i \, \sin\left(x\right)\right) - 6 i \, \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(4, \cos\left(x\right) - i \, \sin\left(x\right)\right) - 6 i \, \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(4, -\cos\left(x\right) + i \, \sin\left(x\right)\right) + 6 i \, \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(4, -\cos\left(x\right) - i \, \sin\left(x\right)\right) + {\left(x^{3} \cos\left(x\right)^{2} \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x^{3} \cos\left(x\right)^{2} \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) + x^{3} \cos\left(x\right)^{2} \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x^{3} \cos\left(x\right)^{2} \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - 3 i \, x^{2} \cos\left(x\right)^{2} {\rm Li}_2\left(\cos\left(x\right) + i \, \sin\left(x\right)\right) + 3 i \, x^{2} \cos\left(x\right)^{2} {\rm Li}_2\left(\cos\left(x\right) - i \, \sin\left(x\right)\right) + 3 i \, x^{2} \cos\left(x\right)^{2} {\rm Li}_2\left(-\cos\left(x\right) + i \, \sin\left(x\right)\right) - 3 i \, x^{2} \cos\left(x\right)^{2} {\rm Li}_2\left(-\cos\left(x\right) - i \, \sin\left(x\right)\right)\right)} \sqrt{\frac{a}{\cos\left(x\right)^{4}}}}{2 \, a}"," ",0,"1/2*(6*x*sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, cos(x) + I*sin(x)) + 6*x*sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, cos(x) - I*sin(x)) + 6*x*sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, -cos(x) + I*sin(x)) + 6*x*sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, -cos(x) - I*sin(x)) + 6*I*sqrt(a/cos(x)^4)*cos(x)^2*polylog(4, cos(x) + I*sin(x)) - 6*I*sqrt(a/cos(x)^4)*cos(x)^2*polylog(4, cos(x) - I*sin(x)) - 6*I*sqrt(a/cos(x)^4)*cos(x)^2*polylog(4, -cos(x) + I*sin(x)) + 6*I*sqrt(a/cos(x)^4)*cos(x)^2*polylog(4, -cos(x) - I*sin(x)) + (x^3*cos(x)^2*log(cos(x) + I*sin(x) + 1) + x^3*cos(x)^2*log(cos(x) - I*sin(x) + 1) + x^3*cos(x)^2*log(-cos(x) + I*sin(x) + 1) + x^3*cos(x)^2*log(-cos(x) - I*sin(x) + 1) - 3*I*x^2*cos(x)^2*dilog(cos(x) + I*sin(x)) + 3*I*x^2*cos(x)^2*dilog(cos(x) - I*sin(x)) + 3*I*x^2*cos(x)^2*dilog(-cos(x) + I*sin(x)) - 3*I*x^2*cos(x)^2*dilog(-cos(x) - I*sin(x)))*sqrt(a/cos(x)^4))/a","C",0
874,1,140,0,0.853356," ","integrate(x*csc(x)*sec(x)*(a*sec(x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, {\left(x \cos\left(x\right) \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x \cos\left(x\right) \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - x \cos\left(x\right) \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) - x \cos\left(x\right) \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) + i \, \cos\left(x\right) {\rm Li}_2\left(\cos\left(x\right) + i \, \sin\left(x\right)\right) - i \, \cos\left(x\right) {\rm Li}_2\left(\cos\left(x\right) - i \, \sin\left(x\right)\right) + i \, \cos\left(x\right) {\rm Li}_2\left(-\cos\left(x\right) + i \, \sin\left(x\right)\right) - i \, \cos\left(x\right) {\rm Li}_2\left(-\cos\left(x\right) - i \, \sin\left(x\right)\right) + \cos\left(x\right) \log\left(-\frac{\sin\left(x\right) + 1}{\sin\left(x\right) - 1}\right) - 2 \, x\right)} \sqrt{\frac{a}{\cos\left(x\right)^{2}}}"," ",0,"-1/2*(x*cos(x)*log(cos(x) + I*sin(x) + 1) + x*cos(x)*log(cos(x) - I*sin(x) + 1) - x*cos(x)*log(-cos(x) + I*sin(x) + 1) - x*cos(x)*log(-cos(x) - I*sin(x) + 1) + I*cos(x)*dilog(cos(x) + I*sin(x)) - I*cos(x)*dilog(cos(x) - I*sin(x)) + I*cos(x)*dilog(-cos(x) + I*sin(x)) - I*cos(x)*dilog(-cos(x) - I*sin(x)) + cos(x)*log(-(sin(x) + 1)/(sin(x) - 1)) - 2*x)*sqrt(a/cos(x)^2)","A",0
875,1,337,0,0.807664," ","integrate(x^2*csc(x)*sec(x)*(a*sec(x)^2)^(1/2),x, algorithm=""fricas"")","\sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, \cos\left(x\right) + i \, \sin\left(x\right)\right) + \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, \cos\left(x\right) - i \, \sin\left(x\right)\right) - \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, -\cos\left(x\right) + i \, \sin\left(x\right)\right) - \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, -\cos\left(x\right) - i \, \sin\left(x\right)\right) - \frac{1}{2} \, {\left(x^{2} \cos\left(x\right) \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x^{2} \cos\left(x\right) \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - x^{2} \cos\left(x\right) \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) - x^{2} \cos\left(x\right) \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) + 2 i \, x \cos\left(x\right) {\rm Li}_2\left(\cos\left(x\right) + i \, \sin\left(x\right)\right) - 2 i \, x \cos\left(x\right) {\rm Li}_2\left(\cos\left(x\right) - i \, \sin\left(x\right)\right) + 2 i \, x \cos\left(x\right) {\rm Li}_2\left(-\cos\left(x\right) + i \, \sin\left(x\right)\right) - 2 i \, x \cos\left(x\right) {\rm Li}_2\left(-\cos\left(x\right) - i \, \sin\left(x\right)\right) + 2 \, x \cos\left(x\right) \log\left(i \, \cos\left(x\right) + \sin\left(x\right) + 1\right) - 2 \, x \cos\left(x\right) \log\left(i \, \cos\left(x\right) - \sin\left(x\right) + 1\right) + 2 \, x \cos\left(x\right) \log\left(-i \, \cos\left(x\right) + \sin\left(x\right) + 1\right) - 2 \, x \cos\left(x\right) \log\left(-i \, \cos\left(x\right) - \sin\left(x\right) + 1\right) - 2 \, x^{2} - 2 i \, \cos\left(x\right) {\rm Li}_2\left(i \, \cos\left(x\right) + \sin\left(x\right)\right) - 2 i \, \cos\left(x\right) {\rm Li}_2\left(i \, \cos\left(x\right) - \sin\left(x\right)\right) + 2 i \, \cos\left(x\right) {\rm Li}_2\left(-i \, \cos\left(x\right) + \sin\left(x\right)\right) + 2 i \, \cos\left(x\right) {\rm Li}_2\left(-i \, \cos\left(x\right) - \sin\left(x\right)\right)\right)} \sqrt{\frac{a}{\cos\left(x\right)^{2}}}"," ",0,"sqrt(a/cos(x)^2)*cos(x)*polylog(3, cos(x) + I*sin(x)) + sqrt(a/cos(x)^2)*cos(x)*polylog(3, cos(x) - I*sin(x)) - sqrt(a/cos(x)^2)*cos(x)*polylog(3, -cos(x) + I*sin(x)) - sqrt(a/cos(x)^2)*cos(x)*polylog(3, -cos(x) - I*sin(x)) - 1/2*(x^2*cos(x)*log(cos(x) + I*sin(x) + 1) + x^2*cos(x)*log(cos(x) - I*sin(x) + 1) - x^2*cos(x)*log(-cos(x) + I*sin(x) + 1) - x^2*cos(x)*log(-cos(x) - I*sin(x) + 1) + 2*I*x*cos(x)*dilog(cos(x) + I*sin(x)) - 2*I*x*cos(x)*dilog(cos(x) - I*sin(x)) + 2*I*x*cos(x)*dilog(-cos(x) + I*sin(x)) - 2*I*x*cos(x)*dilog(-cos(x) - I*sin(x)) + 2*x*cos(x)*log(I*cos(x) + sin(x) + 1) - 2*x*cos(x)*log(I*cos(x) - sin(x) + 1) + 2*x*cos(x)*log(-I*cos(x) + sin(x) + 1) - 2*x*cos(x)*log(-I*cos(x) - sin(x) + 1) - 2*x^2 - 2*I*cos(x)*dilog(I*cos(x) + sin(x)) - 2*I*cos(x)*dilog(I*cos(x) - sin(x)) + 2*I*cos(x)*dilog(-I*cos(x) + sin(x)) + 2*I*cos(x)*dilog(-I*cos(x) - sin(x)))*sqrt(a/cos(x)^2)","C",0
876,1,539,0,1.146778," ","integrate(x^3*csc(x)*sec(x)*(a*sec(x)^2)^(1/2),x, algorithm=""fricas"")","3 \, x \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, \cos\left(x\right) + i \, \sin\left(x\right)\right) + 3 \, x \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, \cos\left(x\right) - i \, \sin\left(x\right)\right) - 3 \, x \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, -\cos\left(x\right) + i \, \sin\left(x\right)\right) - 3 \, x \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, -\cos\left(x\right) - i \, \sin\left(x\right)\right) + 3 i \, \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(4, \cos\left(x\right) + i \, \sin\left(x\right)\right) - 3 i \, \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(4, \cos\left(x\right) - i \, \sin\left(x\right)\right) + 3 i \, \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(4, -\cos\left(x\right) + i \, \sin\left(x\right)\right) - 3 i \, \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(4, -\cos\left(x\right) - i \, \sin\left(x\right)\right) + 3 \, \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, i \, \cos\left(x\right) + \sin\left(x\right)\right) - 3 \, \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, i \, \cos\left(x\right) - \sin\left(x\right)\right) + 3 \, \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, -i \, \cos\left(x\right) + \sin\left(x\right)\right) - 3 \, \sqrt{\frac{a}{\cos\left(x\right)^{2}}} \cos\left(x\right) {\rm polylog}\left(3, -i \, \cos\left(x\right) - \sin\left(x\right)\right) - \frac{1}{2} \, {\left(x^{3} \cos\left(x\right) \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x^{3} \cos\left(x\right) \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - x^{3} \cos\left(x\right) \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) - x^{3} \cos\left(x\right) \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) + 3 i \, x^{2} \cos\left(x\right) {\rm Li}_2\left(\cos\left(x\right) + i \, \sin\left(x\right)\right) - 3 i \, x^{2} \cos\left(x\right) {\rm Li}_2\left(\cos\left(x\right) - i \, \sin\left(x\right)\right) + 3 i \, x^{2} \cos\left(x\right) {\rm Li}_2\left(-\cos\left(x\right) + i \, \sin\left(x\right)\right) - 3 i \, x^{2} \cos\left(x\right) {\rm Li}_2\left(-\cos\left(x\right) - i \, \sin\left(x\right)\right) + 3 \, x^{2} \cos\left(x\right) \log\left(i \, \cos\left(x\right) + \sin\left(x\right) + 1\right) - 3 \, x^{2} \cos\left(x\right) \log\left(i \, \cos\left(x\right) - \sin\left(x\right) + 1\right) + 3 \, x^{2} \cos\left(x\right) \log\left(-i \, \cos\left(x\right) + \sin\left(x\right) + 1\right) - 3 \, x^{2} \cos\left(x\right) \log\left(-i \, \cos\left(x\right) - \sin\left(x\right) + 1\right) - 2 \, x^{3} - 6 i \, x \cos\left(x\right) {\rm Li}_2\left(i \, \cos\left(x\right) + \sin\left(x\right)\right) - 6 i \, x \cos\left(x\right) {\rm Li}_2\left(i \, \cos\left(x\right) - \sin\left(x\right)\right) + 6 i \, x \cos\left(x\right) {\rm Li}_2\left(-i \, \cos\left(x\right) + \sin\left(x\right)\right) + 6 i \, x \cos\left(x\right) {\rm Li}_2\left(-i \, \cos\left(x\right) - \sin\left(x\right)\right)\right)} \sqrt{\frac{a}{\cos\left(x\right)^{2}}}"," ",0,"3*x*sqrt(a/cos(x)^2)*cos(x)*polylog(3, cos(x) + I*sin(x)) + 3*x*sqrt(a/cos(x)^2)*cos(x)*polylog(3, cos(x) - I*sin(x)) - 3*x*sqrt(a/cos(x)^2)*cos(x)*polylog(3, -cos(x) + I*sin(x)) - 3*x*sqrt(a/cos(x)^2)*cos(x)*polylog(3, -cos(x) - I*sin(x)) + 3*I*sqrt(a/cos(x)^2)*cos(x)*polylog(4, cos(x) + I*sin(x)) - 3*I*sqrt(a/cos(x)^2)*cos(x)*polylog(4, cos(x) - I*sin(x)) + 3*I*sqrt(a/cos(x)^2)*cos(x)*polylog(4, -cos(x) + I*sin(x)) - 3*I*sqrt(a/cos(x)^2)*cos(x)*polylog(4, -cos(x) - I*sin(x)) + 3*sqrt(a/cos(x)^2)*cos(x)*polylog(3, I*cos(x) + sin(x)) - 3*sqrt(a/cos(x)^2)*cos(x)*polylog(3, I*cos(x) - sin(x)) + 3*sqrt(a/cos(x)^2)*cos(x)*polylog(3, -I*cos(x) + sin(x)) - 3*sqrt(a/cos(x)^2)*cos(x)*polylog(3, -I*cos(x) - sin(x)) - 1/2*(x^3*cos(x)*log(cos(x) + I*sin(x) + 1) + x^3*cos(x)*log(cos(x) - I*sin(x) + 1) - x^3*cos(x)*log(-cos(x) + I*sin(x) + 1) - x^3*cos(x)*log(-cos(x) - I*sin(x) + 1) + 3*I*x^2*cos(x)*dilog(cos(x) + I*sin(x)) - 3*I*x^2*cos(x)*dilog(cos(x) - I*sin(x)) + 3*I*x^2*cos(x)*dilog(-cos(x) + I*sin(x)) - 3*I*x^2*cos(x)*dilog(-cos(x) - I*sin(x)) + 3*x^2*cos(x)*log(I*cos(x) + sin(x) + 1) - 3*x^2*cos(x)*log(I*cos(x) - sin(x) + 1) + 3*x^2*cos(x)*log(-I*cos(x) + sin(x) + 1) - 3*x^2*cos(x)*log(-I*cos(x) - sin(x) + 1) - 2*x^3 - 6*I*x*cos(x)*dilog(I*cos(x) + sin(x)) - 6*I*x*cos(x)*dilog(I*cos(x) - sin(x)) + 6*I*x*cos(x)*dilog(-I*cos(x) + sin(x)) + 6*I*x*cos(x)*dilog(-I*cos(x) - sin(x)))*sqrt(a/cos(x)^2)","C",0
877,1,270,0,0.760361," ","integrate(x*csc(x)*sec(x)*(a*sec(x)^4)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(x \cos\left(x\right)^{2} \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x \cos\left(x\right)^{2} \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - x \cos\left(x\right)^{2} \log\left(i \, \cos\left(x\right) + \sin\left(x\right) + 1\right) - x \cos\left(x\right)^{2} \log\left(i \, \cos\left(x\right) - \sin\left(x\right) + 1\right) - x \cos\left(x\right)^{2} \log\left(-i \, \cos\left(x\right) + \sin\left(x\right) + 1\right) - x \cos\left(x\right)^{2} \log\left(-i \, \cos\left(x\right) - \sin\left(x\right) + 1\right) + x \cos\left(x\right)^{2} \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x \cos\left(x\right)^{2} \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - i \, \cos\left(x\right)^{2} {\rm Li}_2\left(\cos\left(x\right) + i \, \sin\left(x\right)\right) + i \, \cos\left(x\right)^{2} {\rm Li}_2\left(\cos\left(x\right) - i \, \sin\left(x\right)\right) - i \, \cos\left(x\right)^{2} {\rm Li}_2\left(i \, \cos\left(x\right) + \sin\left(x\right)\right) + i \, \cos\left(x\right)^{2} {\rm Li}_2\left(i \, \cos\left(x\right) - \sin\left(x\right)\right) + i \, \cos\left(x\right)^{2} {\rm Li}_2\left(-i \, \cos\left(x\right) + \sin\left(x\right)\right) - i \, \cos\left(x\right)^{2} {\rm Li}_2\left(-i \, \cos\left(x\right) - \sin\left(x\right)\right) + i \, \cos\left(x\right)^{2} {\rm Li}_2\left(-\cos\left(x\right) + i \, \sin\left(x\right)\right) - i \, \cos\left(x\right)^{2} {\rm Li}_2\left(-\cos\left(x\right) - i \, \sin\left(x\right)\right) - \cos\left(x\right) \sin\left(x\right) + x\right)} \sqrt{\frac{a}{\cos\left(x\right)^{4}}}"," ",0,"1/2*(x*cos(x)^2*log(cos(x) + I*sin(x) + 1) + x*cos(x)^2*log(cos(x) - I*sin(x) + 1) - x*cos(x)^2*log(I*cos(x) + sin(x) + 1) - x*cos(x)^2*log(I*cos(x) - sin(x) + 1) - x*cos(x)^2*log(-I*cos(x) + sin(x) + 1) - x*cos(x)^2*log(-I*cos(x) - sin(x) + 1) + x*cos(x)^2*log(-cos(x) + I*sin(x) + 1) + x*cos(x)^2*log(-cos(x) - I*sin(x) + 1) - I*cos(x)^2*dilog(cos(x) + I*sin(x)) + I*cos(x)^2*dilog(cos(x) - I*sin(x)) - I*cos(x)^2*dilog(I*cos(x) + sin(x)) + I*cos(x)^2*dilog(I*cos(x) - sin(x)) + I*cos(x)^2*dilog(-I*cos(x) + sin(x)) - I*cos(x)^2*dilog(-I*cos(x) - sin(x)) + I*cos(x)^2*dilog(-cos(x) + I*sin(x)) - I*cos(x)^2*dilog(-cos(x) - I*sin(x)) - cos(x)*sin(x) + x)*sqrt(a/cos(x)^4)","B",0
878,1,550,0,2.048262," ","integrate(x^2*csc(x)*sec(x)*(a*sec(x)^4)^(1/2),x, algorithm=""fricas"")","\sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, \cos\left(x\right) + i \, \sin\left(x\right)\right) + \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, \cos\left(x\right) - i \, \sin\left(x\right)\right) - \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, i \, \cos\left(x\right) + \sin\left(x\right)\right) - \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, i \, \cos\left(x\right) - \sin\left(x\right)\right) - \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(x\right) + \sin\left(x\right)\right) - \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(x\right) - \sin\left(x\right)\right) + \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, -\cos\left(x\right) + i \, \sin\left(x\right)\right) + \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, -\cos\left(x\right) - i \, \sin\left(x\right)\right) + \frac{1}{2} \, {\left(x^{2} \cos\left(x\right)^{2} \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x^{2} \cos\left(x\right)^{2} \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - x^{2} \cos\left(x\right)^{2} \log\left(i \, \cos\left(x\right) + \sin\left(x\right) + 1\right) - x^{2} \cos\left(x\right)^{2} \log\left(i \, \cos\left(x\right) - \sin\left(x\right) + 1\right) - x^{2} \cos\left(x\right)^{2} \log\left(-i \, \cos\left(x\right) + \sin\left(x\right) + 1\right) - x^{2} \cos\left(x\right)^{2} \log\left(-i \, \cos\left(x\right) - \sin\left(x\right) + 1\right) + x^{2} \cos\left(x\right)^{2} \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x^{2} \cos\left(x\right)^{2} \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - 2 i \, x \cos\left(x\right)^{2} {\rm Li}_2\left(\cos\left(x\right) + i \, \sin\left(x\right)\right) + 2 i \, x \cos\left(x\right)^{2} {\rm Li}_2\left(\cos\left(x\right) - i \, \sin\left(x\right)\right) - 2 i \, x \cos\left(x\right)^{2} {\rm Li}_2\left(i \, \cos\left(x\right) + \sin\left(x\right)\right) + 2 i \, x \cos\left(x\right)^{2} {\rm Li}_2\left(i \, \cos\left(x\right) - \sin\left(x\right)\right) + 2 i \, x \cos\left(x\right)^{2} {\rm Li}_2\left(-i \, \cos\left(x\right) + \sin\left(x\right)\right) - 2 i \, x \cos\left(x\right)^{2} {\rm Li}_2\left(-i \, \cos\left(x\right) - \sin\left(x\right)\right) + 2 i \, x \cos\left(x\right)^{2} {\rm Li}_2\left(-\cos\left(x\right) + i \, \sin\left(x\right)\right) - 2 i \, x \cos\left(x\right)^{2} {\rm Li}_2\left(-\cos\left(x\right) - i \, \sin\left(x\right)\right) - \cos\left(x\right)^{2} \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + i\right) - \cos\left(x\right)^{2} \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + i\right) - \cos\left(x\right)^{2} \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + i\right) - \cos\left(x\right)^{2} \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + i\right) - 2 \, x \cos\left(x\right) \sin\left(x\right) + x^{2}\right)} \sqrt{\frac{a}{\cos\left(x\right)^{4}}}"," ",0,"sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, cos(x) + I*sin(x)) + sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, cos(x) - I*sin(x)) - sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, I*cos(x) + sin(x)) - sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, I*cos(x) - sin(x)) - sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, -I*cos(x) + sin(x)) - sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, -I*cos(x) - sin(x)) + sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, -cos(x) + I*sin(x)) + sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, -cos(x) - I*sin(x)) + 1/2*(x^2*cos(x)^2*log(cos(x) + I*sin(x) + 1) + x^2*cos(x)^2*log(cos(x) - I*sin(x) + 1) - x^2*cos(x)^2*log(I*cos(x) + sin(x) + 1) - x^2*cos(x)^2*log(I*cos(x) - sin(x) + 1) - x^2*cos(x)^2*log(-I*cos(x) + sin(x) + 1) - x^2*cos(x)^2*log(-I*cos(x) - sin(x) + 1) + x^2*cos(x)^2*log(-cos(x) + I*sin(x) + 1) + x^2*cos(x)^2*log(-cos(x) - I*sin(x) + 1) - 2*I*x*cos(x)^2*dilog(cos(x) + I*sin(x)) + 2*I*x*cos(x)^2*dilog(cos(x) - I*sin(x)) - 2*I*x*cos(x)^2*dilog(I*cos(x) + sin(x)) + 2*I*x*cos(x)^2*dilog(I*cos(x) - sin(x)) + 2*I*x*cos(x)^2*dilog(-I*cos(x) + sin(x)) - 2*I*x*cos(x)^2*dilog(-I*cos(x) - sin(x)) + 2*I*x*cos(x)^2*dilog(-cos(x) + I*sin(x)) - 2*I*x*cos(x)^2*dilog(-cos(x) - I*sin(x)) - cos(x)^2*log(cos(x) + I*sin(x) + I) - cos(x)^2*log(cos(x) - I*sin(x) + I) - cos(x)^2*log(-cos(x) + I*sin(x) + I) - cos(x)^2*log(-cos(x) - I*sin(x) + I) - 2*x*cos(x)*sin(x) + x^2)*sqrt(a/cos(x)^4)","C",0
879,1,736,0,1.079369," ","integrate(x^3*csc(x)*sec(x)*(a*sec(x)^4)^(1/2),x, algorithm=""fricas"")","3 \, x \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, \cos\left(x\right) + i \, \sin\left(x\right)\right) + 3 \, x \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, \cos\left(x\right) - i \, \sin\left(x\right)\right) - 3 \, x \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, i \, \cos\left(x\right) + \sin\left(x\right)\right) - 3 \, x \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, i \, \cos\left(x\right) - \sin\left(x\right)\right) - 3 \, x \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(x\right) + \sin\left(x\right)\right) - 3 \, x \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(x\right) - \sin\left(x\right)\right) + 3 \, x \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, -\cos\left(x\right) + i \, \sin\left(x\right)\right) + 3 \, x \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(3, -\cos\left(x\right) - i \, \sin\left(x\right)\right) + 3 i \, \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(4, \cos\left(x\right) + i \, \sin\left(x\right)\right) - 3 i \, \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(4, \cos\left(x\right) - i \, \sin\left(x\right)\right) + 3 i \, \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(4, i \, \cos\left(x\right) + \sin\left(x\right)\right) - 3 i \, \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(4, i \, \cos\left(x\right) - \sin\left(x\right)\right) - 3 i \, \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(4, -i \, \cos\left(x\right) + \sin\left(x\right)\right) + 3 i \, \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(4, -i \, \cos\left(x\right) - \sin\left(x\right)\right) - 3 i \, \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(4, -\cos\left(x\right) + i \, \sin\left(x\right)\right) + 3 i \, \sqrt{\frac{a}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} {\rm polylog}\left(4, -\cos\left(x\right) - i \, \sin\left(x\right)\right) + \frac{1}{2} \, {\left(x^{3} \cos\left(x\right)^{2} \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x^{3} \cos\left(x\right)^{2} \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) + x^{3} \cos\left(x\right)^{2} \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + x^{3} \cos\left(x\right)^{2} \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - 3 i \, x^{2} \cos\left(x\right)^{2} {\rm Li}_2\left(\cos\left(x\right) + i \, \sin\left(x\right)\right) + 3 i \, x^{2} \cos\left(x\right)^{2} {\rm Li}_2\left(\cos\left(x\right) - i \, \sin\left(x\right)\right) + 3 i \, x^{2} \cos\left(x\right)^{2} {\rm Li}_2\left(-\cos\left(x\right) + i \, \sin\left(x\right)\right) - 3 i \, x^{2} \cos\left(x\right)^{2} {\rm Li}_2\left(-\cos\left(x\right) - i \, \sin\left(x\right)\right) + {\left(-3 i \, x^{2} - 3 i\right)} \cos\left(x\right)^{2} {\rm Li}_2\left(i \, \cos\left(x\right) + \sin\left(x\right)\right) + {\left(3 i \, x^{2} + 3 i\right)} \cos\left(x\right)^{2} {\rm Li}_2\left(i \, \cos\left(x\right) - \sin\left(x\right)\right) + {\left(3 i \, x^{2} + 3 i\right)} \cos\left(x\right)^{2} {\rm Li}_2\left(-i \, \cos\left(x\right) + \sin\left(x\right)\right) + {\left(-3 i \, x^{2} - 3 i\right)} \cos\left(x\right)^{2} {\rm Li}_2\left(-i \, \cos\left(x\right) - \sin\left(x\right)\right) - {\left(x^{3} + 3 \, x\right)} \cos\left(x\right)^{2} \log\left(i \, \cos\left(x\right) + \sin\left(x\right) + 1\right) - {\left(x^{3} + 3 \, x\right)} \cos\left(x\right)^{2} \log\left(i \, \cos\left(x\right) - \sin\left(x\right) + 1\right) - {\left(x^{3} + 3 \, x\right)} \cos\left(x\right)^{2} \log\left(-i \, \cos\left(x\right) + \sin\left(x\right) + 1\right) - {\left(x^{3} + 3 \, x\right)} \cos\left(x\right)^{2} \log\left(-i \, \cos\left(x\right) - \sin\left(x\right) + 1\right) - 3 \, x^{2} \cos\left(x\right) \sin\left(x\right) + x^{3}\right)} \sqrt{\frac{a}{\cos\left(x\right)^{4}}}"," ",0,"3*x*sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, cos(x) + I*sin(x)) + 3*x*sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, cos(x) - I*sin(x)) - 3*x*sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, I*cos(x) + sin(x)) - 3*x*sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, I*cos(x) - sin(x)) - 3*x*sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, -I*cos(x) + sin(x)) - 3*x*sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, -I*cos(x) - sin(x)) + 3*x*sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, -cos(x) + I*sin(x)) + 3*x*sqrt(a/cos(x)^4)*cos(x)^2*polylog(3, -cos(x) - I*sin(x)) + 3*I*sqrt(a/cos(x)^4)*cos(x)^2*polylog(4, cos(x) + I*sin(x)) - 3*I*sqrt(a/cos(x)^4)*cos(x)^2*polylog(4, cos(x) - I*sin(x)) + 3*I*sqrt(a/cos(x)^4)*cos(x)^2*polylog(4, I*cos(x) + sin(x)) - 3*I*sqrt(a/cos(x)^4)*cos(x)^2*polylog(4, I*cos(x) - sin(x)) - 3*I*sqrt(a/cos(x)^4)*cos(x)^2*polylog(4, -I*cos(x) + sin(x)) + 3*I*sqrt(a/cos(x)^4)*cos(x)^2*polylog(4, -I*cos(x) - sin(x)) - 3*I*sqrt(a/cos(x)^4)*cos(x)^2*polylog(4, -cos(x) + I*sin(x)) + 3*I*sqrt(a/cos(x)^4)*cos(x)^2*polylog(4, -cos(x) - I*sin(x)) + 1/2*(x^3*cos(x)^2*log(cos(x) + I*sin(x) + 1) + x^3*cos(x)^2*log(cos(x) - I*sin(x) + 1) + x^3*cos(x)^2*log(-cos(x) + I*sin(x) + 1) + x^3*cos(x)^2*log(-cos(x) - I*sin(x) + 1) - 3*I*x^2*cos(x)^2*dilog(cos(x) + I*sin(x)) + 3*I*x^2*cos(x)^2*dilog(cos(x) - I*sin(x)) + 3*I*x^2*cos(x)^2*dilog(-cos(x) + I*sin(x)) - 3*I*x^2*cos(x)^2*dilog(-cos(x) - I*sin(x)) + (-3*I*x^2 - 3*I)*cos(x)^2*dilog(I*cos(x) + sin(x)) + (3*I*x^2 + 3*I)*cos(x)^2*dilog(I*cos(x) - sin(x)) + (3*I*x^2 + 3*I)*cos(x)^2*dilog(-I*cos(x) + sin(x)) + (-3*I*x^2 - 3*I)*cos(x)^2*dilog(-I*cos(x) - sin(x)) - (x^3 + 3*x)*cos(x)^2*log(I*cos(x) + sin(x) + 1) - (x^3 + 3*x)*cos(x)^2*log(I*cos(x) - sin(x) + 1) - (x^3 + 3*x)*cos(x)^2*log(-I*cos(x) + sin(x) + 1) - (x^3 + 3*x)*cos(x)^2*log(-I*cos(x) - sin(x) + 1) - 3*x^2*cos(x)*sin(x) + x^3)*sqrt(a/cos(x)^4)","C",0
880,1,17,0,0.913783," ","integrate(sin(x)*sin(2*x)*sin(3*x),x, algorithm=""fricas"")","\frac{4}{3} \, \cos\left(x\right)^{6} - \frac{5}{2} \, \cos\left(x\right)^{4} + \cos\left(x\right)^{2}"," ",0,"4/3*cos(x)^6 - 5/2*cos(x)^4 + cos(x)^2","A",0
881,1,25,0,0.868028," ","integrate(cos(x)*cos(2*x)*cos(3*x),x, algorithm=""fricas"")","\frac{1}{12} \, {\left(16 \, \cos\left(x\right)^{5} - 10 \, \cos\left(x\right)^{3} + 3 \, \cos\left(x\right)\right)} \sin\left(x\right) + \frac{1}{4} \, x"," ",0,"1/12*(16*cos(x)^5 - 10*cos(x)^3 + 3*cos(x))*sin(x) + 1/4*x","A",0
882,1,25,0,0.711333," ","integrate(cos(x)*sin(2*x)*sin(3*x),x, algorithm=""fricas"")","-\frac{1}{12} \, {\left(16 \, \cos\left(x\right)^{5} - 10 \, \cos\left(x\right)^{3} - 3 \, \cos\left(x\right)\right)} \sin\left(x\right) + \frac{1}{4} \, x"," ",0,"-1/12*(16*cos(x)^5 - 10*cos(x)^3 - 3*cos(x))*sin(x) + 1/4*x","A",0
883,1,19,0,0.880388," ","integrate(cos(2*x)*cos(3*x)*sin(x),x, algorithm=""fricas"")","-\frac{4}{3} \, \cos\left(x\right)^{6} + \frac{5}{2} \, \cos\left(x\right)^{4} - \frac{3}{2} \, \cos\left(x\right)^{2}"," ",0,"-4/3*cos(x)^6 + 5/2*cos(x)^4 - 3/2*cos(x)^2","A",0
884,1,6,0,0.830095," ","integrate(x*sin(x^2),x, algorithm=""fricas"")","-\frac{1}{2} \, \cos\left(x^{2}\right)"," ",0,"-1/2*cos(x^2)","A",0
885,1,34,0,0.634824," ","integrate((-cos(x)+sin(x))*(cos(x)+sin(x))^5,x, algorithm=""fricas"")","2 \, \cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + \frac{1}{3} \, {\left(4 \, \cos\left(x\right)^{5} - 4 \, \cos\left(x\right)^{3} - 3 \, \cos\left(x\right)\right)} \sin\left(x\right)"," ",0,"2*cos(x)^4 - 2*cos(x)^2 + 1/3*(4*cos(x)^5 - 4*cos(x)^3 - 3*cos(x))*sin(x)","B",0
886,1,15,0,0.806162," ","integrate(2*x*sec(x)^2*tan(x),x, algorithm=""fricas"")","-\frac{\cos\left(x\right) \sin\left(x\right) - x}{\cos\left(x\right)^{2}}"," ",0,"-(cos(x)*sin(x) - x)/cos(x)^2","A",0
887,1,13,0,1.092736," ","integrate((1+cos(x)^2)/(1+cos(2*x)),x, algorithm=""fricas"")","\frac{x \cos\left(x\right) + \sin\left(x\right)}{2 \, \cos\left(x\right)}"," ",0,"1/2*(x*cos(x) + sin(x))/cos(x)","A",0
888,1,33,0,0.930329," ","integrate(sin(x)/(cos(x)^3-cos(x)^5),x, algorithm=""fricas"")","-\frac{\cos\left(x\right)^{2} \log\left(\cos\left(x\right)^{2}\right) - \cos\left(x\right)^{2} \log\left(-\frac{1}{4} \, \cos\left(x\right)^{2} + \frac{1}{4}\right) - 1}{2 \, \cos\left(x\right)^{2}}"," ",0,"-1/2*(cos(x)^2*log(cos(x)^2) - cos(x)^2*log(-1/4*cos(x)^2 + 1/4) - 1)/cos(x)^2","B",0
889,1,20,0,1.066764," ","integrate(sec(x)*(5-11*sec(x)^5)^2*tan(x),x, algorithm=""fricas"")","\frac{75 \, \cos\left(x\right)^{10} - 55 \, \cos\left(x\right)^{5} + 33}{3 \, \cos\left(x\right)^{11}}"," ",0,"1/3*(75*cos(x)^10 - 55*cos(x)^5 + 33)/cos(x)^11","A",0
890,1,65,0,0.919843," ","integrate(sin(5*x)^3*tan(5*x)^3,x, algorithm=""fricas"")","-\frac{15 \, \cos\left(5 \, x\right)^{2} \log\left(\sin\left(5 \, x\right) + 1\right) - 15 \, \cos\left(5 \, x\right)^{2} \log\left(-\sin\left(5 \, x\right) + 1\right) + 2 \, {\left(2 \, \cos\left(5 \, x\right)^{4} - 14 \, \cos\left(5 \, x\right)^{2} - 3\right)} \sin\left(5 \, x\right)}{60 \, \cos\left(5 \, x\right)^{2}}"," ",0,"-1/60*(15*cos(5*x)^2*log(sin(5*x) + 1) - 15*cos(5*x)^2*log(-sin(5*x) + 1) + 2*(2*cos(5*x)^4 - 14*cos(5*x)^2 - 3)*sin(5*x))/cos(5*x)^2","A",0
891,1,32,0,1.847498," ","integrate(sin(5*x)^3*tan(5*x)^4,x, algorithm=""fricas"")","\frac{\cos\left(5 \, x\right)^{6} - 9 \, \cos\left(5 \, x\right)^{4} - 9 \, \cos\left(5 \, x\right)^{2} + 1}{15 \, \cos\left(5 \, x\right)^{3}}"," ",0,"1/15*(cos(5*x)^6 - 9*cos(5*x)^4 - 9*cos(5*x)^2 + 1)/cos(5*x)^3","A",0
892,1,73,0,0.932926," ","integrate(sin(6*x)^5*tan(6*x)^3,x, algorithm=""fricas"")","-\frac{105 \, \cos\left(6 \, x\right)^{2} \log\left(\sin\left(6 \, x\right) + 1\right) - 105 \, \cos\left(6 \, x\right)^{2} \log\left(-\sin\left(6 \, x\right) + 1\right) - 2 \, {\left(6 \, \cos\left(6 \, x\right)^{6} - 32 \, \cos\left(6 \, x\right)^{4} + 116 \, \cos\left(6 \, x\right)^{2} + 15\right)} \sin\left(6 \, x\right)}{360 \, \cos\left(6 \, x\right)^{2}}"," ",0,"-1/360*(105*cos(6*x)^2*log(sin(6*x) + 1) - 105*cos(6*x)^2*log(-sin(6*x) + 1) - 2*(6*cos(6*x)^6 - 32*cos(6*x)^4 + 116*cos(6*x)^2 + 15)*sin(6*x))/cos(6*x)^2","A",0
893,1,34,0,0.410239," ","integrate((-1+sec(2*x)^2)^3*sin(2*x),x, algorithm=""fricas"")","\frac{5 \, \cos\left(2 \, x\right)^{6} + 15 \, \cos\left(2 \, x\right)^{4} - 5 \, \cos\left(2 \, x\right)^{2} + 1}{10 \, \cos\left(2 \, x\right)^{5}}"," ",0,"1/10*(5*cos(2*x)^6 + 15*cos(2*x)^4 - 5*cos(2*x)^2 + 1)/cos(2*x)^5","A",0
894,1,49,0,0.970754," ","integrate(sin(x)*tan(x)^5,x, algorithm=""fricas"")","\frac{15 \, \cos\left(x\right)^{4} \log\left(\sin\left(x\right) + 1\right) - 15 \, \cos\left(x\right)^{4} \log\left(-\sin\left(x\right) + 1\right) - 2 \, {\left(8 \, \cos\left(x\right)^{4} + 9 \, \cos\left(x\right)^{2} - 2\right)} \sin\left(x\right)}{16 \, \cos\left(x\right)^{4}}"," ",0,"1/16*(15*cos(x)^4*log(sin(x) + 1) - 15*cos(x)^4*log(-sin(x) + 1) - 2*(8*cos(x)^4 + 9*cos(x)^2 - 2)*sin(x))/cos(x)^4","A",0
895,1,52,0,0.964030," ","integrate(cos(2*x)^5*cot(2*x)^4,x, algorithm=""fricas"")","-\frac{3 \, \cos\left(2 \, x\right)^{8} + 8 \, \cos\left(2 \, x\right)^{6} + 48 \, \cos\left(2 \, x\right)^{4} - 192 \, \cos\left(2 \, x\right)^{2} + 128}{30 \, {\left(\cos\left(2 \, x\right)^{2} - 1\right)} \sin\left(2 \, x\right)}"," ",0,"-1/30*(3*cos(2*x)^8 + 8*cos(2*x)^6 + 48*cos(2*x)^4 - 192*cos(2*x)^2 + 128)/((cos(2*x)^2 - 1)*sin(2*x))","A",0
896,1,92,0,1.046580," ","integrate(cos(3*x)*(-1+csc(3*x)^2)^3*(1-sin(3*x)^2)^5,x, algorithm=""fricas"")","\frac{45 \, \cos\left(3 \, x\right)^{16} + 80 \, \cos\left(3 \, x\right)^{14} + 160 \, \cos\left(3 \, x\right)^{12} + 384 \, \cos\left(3 \, x\right)^{10} + 1280 \, \cos\left(3 \, x\right)^{8} + 10240 \, \cos\left(3 \, x\right)^{6} - 61440 \, \cos\left(3 \, x\right)^{4} + 81920 \, \cos\left(3 \, x\right)^{2} - 32768}{1485 \, {\left(\cos\left(3 \, x\right)^{4} - 2 \, \cos\left(3 \, x\right)^{2} + 1\right)} \sin\left(3 \, x\right)}"," ",0,"1/1485*(45*cos(3*x)^16 + 80*cos(3*x)^14 + 160*cos(3*x)^12 + 384*cos(3*x)^10 + 1280*cos(3*x)^8 + 10240*cos(3*x)^6 - 61440*cos(3*x)^4 + 81920*cos(3*x)^2 - 32768)/((cos(3*x)^4 - 2*cos(3*x)^2 + 1)*sin(3*x))","A",0
897,1,79,0,0.898393," ","integrate(cot(2*x)*(-1+csc(2*x)^2)^2*(1-sin(2*x)^2)^2,x, algorithm=""fricas"")","\frac{8 \, \cos\left(2 \, x\right)^{8} + 32 \, \cos\left(2 \, x\right)^{6} - 115 \, \cos\left(2 \, x\right)^{4} + 38 \, \cos\left(2 \, x\right)^{2} + 192 \, {\left(\cos\left(2 \, x\right)^{4} - 2 \, \cos\left(2 \, x\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \sin\left(2 \, x\right)\right) + 29}{64 \, {\left(\cos\left(2 \, x\right)^{4} - 2 \, \cos\left(2 \, x\right)^{2} + 1\right)}}"," ",0,"1/64*(8*cos(2*x)^8 + 32*cos(2*x)^6 - 115*cos(2*x)^4 + 38*cos(2*x)^2 + 192*(cos(2*x)^4 - 2*cos(2*x)^2 + 1)*log(1/2*sin(2*x)) + 29)/(cos(2*x)^4 - 2*cos(2*x)^2 + 1)","B",0
898,1,84,0,2.933937," ","integrate(cos(2*x)*(-1+csc(2*x)^2)^4*(1-sin(2*x)^2)^2,x, algorithm=""fricas"")","-\frac{7 \, \cos\left(2 \, x\right)^{12} + 28 \, \cos\left(2 \, x\right)^{10} + 280 \, \cos\left(2 \, x\right)^{8} - 2240 \, \cos\left(2 \, x\right)^{6} + 4480 \, \cos\left(2 \, x\right)^{4} - 3584 \, \cos\left(2 \, x\right)^{2} + 1024}{70 \, {\left(\cos\left(2 \, x\right)^{6} - 3 \, \cos\left(2 \, x\right)^{4} + 3 \, \cos\left(2 \, x\right)^{2} - 1\right)} \sin\left(2 \, x\right)}"," ",0,"-1/70*(7*cos(2*x)^12 + 28*cos(2*x)^10 + 280*cos(2*x)^8 - 2240*cos(2*x)^6 + 4480*cos(2*x)^4 - 3584*cos(2*x)^2 + 1024)/((cos(2*x)^6 - 3*cos(2*x)^4 + 3*cos(2*x)^2 - 1)*sin(2*x))","A",0
899,1,103,0,0.836595," ","integrate(cot(3*x)*(-1+csc(3*x)^2)^3*(1-sin(3*x)^2)^2,x, algorithm=""fricas"")","-\frac{24 \, \cos\left(3 \, x\right)^{10} + 120 \, \cos\left(3 \, x\right)^{8} - 609 \, \cos\left(3 \, x\right)^{6} + 387 \, \cos\left(3 \, x\right)^{4} + 333 \, \cos\left(3 \, x\right)^{2} + 960 \, {\left(\cos\left(3 \, x\right)^{6} - 3 \, \cos\left(3 \, x\right)^{4} + 3 \, \cos\left(3 \, x\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \sin\left(3 \, x\right)\right) - 271}{288 \, {\left(\cos\left(3 \, x\right)^{6} - 3 \, \cos\left(3 \, x\right)^{4} + 3 \, \cos\left(3 \, x\right)^{2} - 1\right)}}"," ",0,"-1/288*(24*cos(3*x)^10 + 120*cos(3*x)^8 - 609*cos(3*x)^6 + 387*cos(3*x)^4 + 333*cos(3*x)^2 + 960*(cos(3*x)^6 - 3*cos(3*x)^4 + 3*cos(3*x)^2 - 1)*log(1/2*sin(3*x)) - 271)/(cos(3*x)^6 - 3*cos(3*x)^4 + 3*cos(3*x)^2 - 1)","B",0
900,1,42,0,0.625569," ","integrate((1+cot(9*x)^2)^2*(1+tan(9*x)^2)^3,x, algorithm=""fricas"")","\frac{3 \, \tan\left(9 \, x\right)^{8} + 20 \, \tan\left(9 \, x\right)^{6} + 90 \, \tan\left(9 \, x\right)^{4} - 60 \, \tan\left(9 \, x\right)^{2} - 5}{135 \, \tan\left(9 \, x\right)^{3}}"," ",0,"1/135*(3*tan(9*x)^8 + 20*tan(9*x)^6 + 90*tan(9*x)^4 - 60*tan(9*x)^2 - 5)/tan(9*x)^3","A",0
901,1,41,0,1.945787," ","integrate(cos(x)*(9-7*sin(x)^3)^2/(1-sin(x)^2),x, algorithm=""fricas"")","-63 \, \cos\left(x\right)^{2} - \frac{49}{15} \, {\left(3 \, \cos\left(x\right)^{4} - 11 \, \cos\left(x\right)^{2} + 23\right)} \sin\left(x\right) + 128 \, \log\left(\sin\left(x\right) + 1\right) - 2 \, \log\left(-\sin\left(x\right) + 1\right)"," ",0,"-63*cos(x)^2 - 49/15*(3*cos(x)^4 - 11*cos(x)^2 + 23)*sin(x) + 128*log(sin(x) + 1) - 2*log(-sin(x) + 1)","A",0
902,1,79,0,1.956364," ","integrate(cos(2*x)^4*cot(2*x)^5,x, algorithm=""fricas"")","\frac{8 \, \cos\left(2 \, x\right)^{8} + 32 \, \cos\left(2 \, x\right)^{6} - 115 \, \cos\left(2 \, x\right)^{4} + 38 \, \cos\left(2 \, x\right)^{2} + 192 \, {\left(\cos\left(2 \, x\right)^{4} - 2 \, \cos\left(2 \, x\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \sin\left(2 \, x\right)\right) + 29}{64 \, {\left(\cos\left(2 \, x\right)^{4} - 2 \, \cos\left(2 \, x\right)^{2} + 1\right)}}"," ",0,"1/64*(8*cos(2*x)^8 + 32*cos(2*x)^6 - 115*cos(2*x)^4 + 38*cos(2*x)^2 + 192*(cos(2*x)^4 - 2*cos(2*x)^2 + 1)*log(1/2*sin(2*x)) + 29)/(cos(2*x)^4 - 2*cos(2*x)^2 + 1)","B",0
903,1,82,0,0.833619," ","integrate(sec(x)*tan(x)^2/(4+3*sec(x)),x, algorithm=""fricas"")","\frac{\sqrt{7} \cos\left(x\right) \log\left(\frac{2 \, \cos\left(x\right)^{2} + 2 \, {\left(3 \, \sqrt{7} \cos\left(x\right) + 4 \, \sqrt{7}\right)} \sin\left(x\right) + 24 \, \cos\left(x\right) + 23}{16 \, \cos\left(x\right)^{2} + 24 \, \cos\left(x\right) + 9}\right) - 4 \, \cos\left(x\right) \log\left(\sin\left(x\right) + 1\right) + 4 \, \cos\left(x\right) \log\left(-\sin\left(x\right) + 1\right) + 6 \, \sin\left(x\right)}{18 \, \cos\left(x\right)}"," ",0,"1/18*(sqrt(7)*cos(x)*log((2*cos(x)^2 + 2*(3*sqrt(7)*cos(x) + 4*sqrt(7))*sin(x) + 24*cos(x) + 23)/(16*cos(x)^2 + 24*cos(x) + 9)) - 4*cos(x)*log(sin(x) + 1) + 4*cos(x)*log(-sin(x) + 1) + 6*sin(x))/cos(x)","A",0
904,1,39,0,0.673162," ","integrate(x*sec(1+x)*tan(1+x),x, algorithm=""fricas"")","-\frac{\cos\left(x + 1\right) \log\left(\sin\left(x + 1\right) + 1\right) - \cos\left(x + 1\right) \log\left(-\sin\left(x + 1\right) + 1\right) - 2 \, x}{2 \, \cos\left(x + 1\right)}"," ",0,"-1/2*(cos(x + 1)*log(sin(x + 1) + 1) - cos(x + 1)*log(-sin(x + 1) + 1) - 2*x)/cos(x + 1)","B",0
905,1,10,0,0.765221," ","integrate(sin(2*x)/(9-sin(x)^2)^(1/2),x, algorithm=""fricas"")","-2 \, \sqrt{\cos\left(x\right)^{2} + 8}"," ",0,"-2*sqrt(cos(x)^2 + 8)","A",0
906,1,24,0,1.312744," ","integrate(sin(2*x)/(9-cos(x)^4)^(1/2),x, algorithm=""fricas"")","\arctan\left(\frac{\sqrt{-\cos\left(x\right)^{4} + 9} \cos\left(x\right)^{2}}{\cos\left(x\right)^{4} - 9}\right)"," ",0,"arctan(sqrt(-cos(x)^4 + 9)*cos(x)^2/(cos(x)^4 - 9))","B",0
907,1,32,0,0.869668," ","integrate(cos(1/x)/x^5,x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, x^{3} - x\right)} \cos\left(\frac{1}{x}\right) + {\left(6 \, x^{2} - 1\right)} \sin\left(\frac{1}{x}\right)}{x^{3}}"," ",0,"(3*(2*x^3 - x)*cos(1/x) + (6*x^2 - 1)*sin(1/x))/x^3","A",0
908,1,17,0,0.816573," ","integrate(cos(1+x)^3*sin(1+x)^3,x, algorithm=""fricas"")","\frac{1}{6} \, \cos\left(x + 1\right)^{6} - \frac{1}{4} \, \cos\left(x + 1\right)^{4}"," ",0,"1/6*cos(x + 1)^6 - 1/4*cos(x + 1)^4","A",0
909,1,66,0,1.089658," ","integrate((1+2*x)^3*sin(1+2*x)^2,x, algorithm=""fricas"")","x^{4} + 2 \, x^{3} - \frac{3}{16} \, {\left(8 \, x^{2} + 8 \, x + 1\right)} \cos\left(2 \, x + 1\right)^{2} - \frac{1}{8} \, {\left(16 \, x^{3} + 24 \, x^{2} + 6 \, x - 1\right)} \cos\left(2 \, x + 1\right) \sin\left(2 \, x + 1\right) + \frac{9}{4} \, x^{2} + \frac{5}{4} \, x"," ",0,"x^4 + 2*x^3 - 3/16*(8*x^2 + 8*x + 1)*cos(2*x + 1)^2 - 1/8*(16*x^3 + 24*x^2 + 6*x - 1)*cos(2*x + 1)*sin(2*x + 1) + 9/4*x^2 + 5/4*x","A",0
910,1,51,0,1.409183," ","integrate((-1+sec(x))/(1-tan(x)),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{2 \, {\left(\sqrt{2} + \cos\left(x\right)\right)} \sin\left(x\right) + 2 \, \sqrt{2} \cos\left(x\right) + 3}{2 \, \cos\left(x\right) \sin\left(x\right) - 1}\right) - \frac{1}{2} \, x + \frac{1}{4} \, \log\left(-2 \, \cos\left(x\right) \sin\left(x\right) + 1\right)"," ",0,"1/4*sqrt(2)*log((2*(sqrt(2) + cos(x))*sin(x) + 2*sqrt(2)*cos(x) + 3)/(2*cos(x)*sin(x) - 1)) - 1/2*x + 1/4*log(-2*cos(x)*sin(x) + 1)","A",0
911,1,73,0,1.129699," ","integrate(x^2*cos(3*x)*cos(5*x),x, algorithm=""fricas"")","2 \, x \cos\left(x\right)^{8} - 4 \, x \cos\left(x\right)^{6} + \frac{5}{2} \, x \cos\left(x\right)^{4} + \frac{1}{64} \, {\left(16 \, {\left(32 \, x^{2} - 1\right)} \cos\left(x\right)^{7} - 24 \, {\left(32 \, x^{2} - 1\right)} \cos\left(x\right)^{5} + 10 \, {\left(32 \, x^{2} - 1\right)} \cos\left(x\right)^{3} - 15 \, \cos\left(x\right)\right)} \sin\left(x\right) - \frac{15}{64} \, x"," ",0,"2*x*cos(x)^8 - 4*x*cos(x)^6 + 5/2*x*cos(x)^4 + 1/64*(16*(32*x^2 - 1)*cos(x)^7 - 24*(32*x^2 - 1)*cos(x)^5 + 10*(32*x^2 - 1)*cos(x)^3 - 15*cos(x))*sin(x) - 15/64*x","A",0
912,1,85,0,0.982942," ","integrate((cos(x)+sin(x))/cos(x)^(1/2)/sin(x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \arctan\left(-\frac{{\left(32 \, \sqrt{2} \cos\left(x\right)^{4} - 32 \, \sqrt{2} \cos\left(x\right)^{2} + 16 \, \sqrt{2} \cos\left(x\right) \sin\left(x\right) - \sqrt{2}\right)} \sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)}}{8 \, {\left(4 \, \cos\left(x\right)^{5} - 3 \, \cos\left(x\right)^{3} - {\left(4 \, \cos\left(x\right)^{4} - 5 \, \cos\left(x\right)^{2}\right)} \sin\left(x\right) - \cos\left(x\right)\right)}}\right)"," ",0,"-1/4*sqrt(2)*arctan(-1/8*(32*sqrt(2)*cos(x)^4 - 32*sqrt(2)*cos(x)^2 + 16*sqrt(2)*cos(x)*sin(x) - sqrt(2))*sqrt(cos(x))*sqrt(sin(x))/(4*cos(x)^5 - 3*cos(x)^3 - (4*cos(x)^4 - 5*cos(x)^2)*sin(x) - cos(x)))","B",0
913,1,17,0,0.846852," ","integrate(sec(x)^2*(1+sin(x)),x, algorithm=""fricas"")","\frac{\cos\left(x\right) + \sin\left(x\right) + 1}{\cos\left(x\right) - \sin\left(x\right) + 1}"," ",0,"(cos(x) + sin(x) + 1)/(cos(x) - sin(x) + 1)","B",0
914,1,11,0,0.743653," ","integrate(10*x^9*cos(x^5*log(x))-x^10*(x^4+5*x^4*log(x))*sin(x^5*log(x)),x, algorithm=""fricas"")","x^{10} \cos\left(x^{5} \log\left(x\right)\right)"," ",0,"x^10*cos(x^5*log(x))","A",0
915,1,27,0,1.584700," ","integrate(cos(1/2*x)^2*tan(1/4*pi+1/2*x),x, algorithm=""fricas"")","-\cos\left(\frac{1}{2} \, x\right)^{2} + \frac{1}{2} \, x - \frac{1}{2} \, \log\left(-2 \, \cos\left(\frac{1}{2} \, x\right) \sin\left(\frac{1}{2} \, x\right) + 1\right)"," ",0,"-cos(1/2*x)^2 + 1/2*x - 1/2*log(-2*cos(1/2*x)*sin(1/2*x) + 1)","A",0
916,1,50,0,1.651476," ","integrate((2+3*x)^2*sin(x)^3,x, algorithm=""fricas"")","\frac{1}{3} \, {\left(9 \, x^{2} + 12 \, x + 2\right)} \cos\left(x\right)^{3} - {\left(9 \, x^{2} + 12 \, x - 10\right)} \cos\left(x\right) - \frac{2}{3} \, {\left({\left(3 \, x + 2\right)} \cos\left(x\right)^{2} - 21 \, x - 14\right)} \sin\left(x\right)"," ",0,"1/3*(9*x^2 + 12*x + 2)*cos(x)^3 - (9*x^2 + 12*x - 10)*cos(x) - 2/3*((3*x + 2)*cos(x)^2 - 21*x - 14)*sin(x)","A",0
917,1,14,0,0.916309," ","integrate(sec(x)^(1+m)*sin(x),x, algorithm=""fricas"")","\frac{\frac{1}{\cos\left(x\right)}^{m + 1} \cos\left(x\right)}{m}"," ",0,"(1/cos(x))^(m + 1)*cos(x)/m","A",0
918,1,41,0,0.953887," ","integrate(cos(b*x+a)^n*sin(b*x+a)^(-2-n),x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right)^{n} \sin\left(b x + a\right)^{-n - 2} \cos\left(b x + a\right) \sin\left(b x + a\right)}{b n + b}"," ",0,"-cos(b*x + a)^n*sin(b*x + a)^(-n - 2)*cos(b*x + a)*sin(b*x + a)/(b*n + b)","A",0
919,1,3,0,1.419215," ","integrate(1/(sec(x)+sin(x)*tan(x)),x, algorithm=""fricas"")","\arctan\left(\sin\left(x\right)\right)"," ",0,"arctan(sin(x))","A",0
920,1,27,0,0.587667," ","integrate((c*x^2+b*x+a)*sin(x),x, algorithm=""fricas"")","-{\left(c x^{2} + b x + a - 2 \, c\right)} \cos\left(x\right) + {\left(2 \, c x + b\right)} \sin\left(x\right)"," ",0,"-(c*x^2 + b*x + a - 2*c)*cos(x) + (2*c*x + b)*sin(x)","A",0
921,1,6,0,0.730894," ","integrate(sin(x^5)/x,x, algorithm=""fricas"")","\frac{1}{5} \, \operatorname{Si}\left(x^{5}\right)"," ",0,"1/5*sin_integral(x^5)","A",0
922,1,43,0,0.851010," ","integrate(sin(2^x)/(1+2^x),x, algorithm=""fricas"")","\frac{\operatorname{Ci}\left(2^{x} + 1\right) \sin\left(1\right) + \operatorname{Ci}\left(-2^{x} - 1\right) \sin\left(1\right) - 2 \, \cos\left(1\right) \operatorname{Si}\left(2^{x} + 1\right) + 2 \, \operatorname{Si}\left(2^{x}\right)}{2 \, \log\left(2\right)}"," ",0,"1/2*(cos_integral(2^x + 1)*sin(1) + cos_integral(-2^x - 1)*sin(1) - 2*cos(1)*sin_integral(2^x + 1) + 2*sin_integral(2^x))/log(2)","A",0
923,1,10,0,0.871642," ","integrate(x*cos(2*x^2)*sin(2*x^2)^(3/4),x, algorithm=""fricas"")","\frac{1}{7} \, \sin\left(2 \, x^{2}\right)^{\frac{7}{4}}"," ",0,"1/7*sin(2*x^2)^(7/4)","A",0
924,1,20,0,0.426204," ","integrate(x*sec(x^2)^2*tan(x^2)^2,x, algorithm=""fricas"")","-\frac{{\left(\cos\left(x^{2}\right)^{2} - 1\right)} \sin\left(x^{2}\right)}{6 \, \cos\left(x^{2}\right)^{3}}"," ",0,"-1/6*(cos(x^2)^2 - 1)*sin(x^2)/cos(x^2)^3","B",0
925,1,15,0,1.699728," ","integrate(x^2*cos(b*x^3+a)^7*sin(b*x^3+a),x, algorithm=""fricas"")","-\frac{\cos\left(b x^{3} + a\right)^{8}}{24 \, b}"," ",0,"-1/24*cos(b*x^3 + a)^8/b","A",0
926,1,85,0,1.090968," ","integrate(x^5*cos(b*x^3+a)^7*sin(b*x^3+a),x, algorithm=""fricas"")","-\frac{384 \, b x^{3} \cos\left(b x^{3} + a\right)^{8} - 105 \, b x^{3} - {\left(48 \, \cos\left(b x^{3} + a\right)^{7} + 56 \, \cos\left(b x^{3} + a\right)^{5} + 70 \, \cos\left(b x^{3} + a\right)^{3} + 105 \, \cos\left(b x^{3} + a\right)\right)} \sin\left(b x^{3} + a\right)}{9216 \, b^{2}}"," ",0,"-1/9216*(384*b*x^3*cos(b*x^3 + a)^8 - 105*b*x^3 - (48*cos(b*x^3 + a)^7 + 56*cos(b*x^3 + a)^5 + 70*cos(b*x^3 + a)^3 + 105*cos(b*x^3 + a))*sin(b*x^3 + a))/b^2","A",0
927,1,115,0,0.960487," ","integrate(x^5*sec(b*x^3+a)^7*tan(b*x^3+a),x, algorithm=""fricas"")","-\frac{15 \, \cos\left(b x^{3} + a\right)^{7} \log\left(\sin\left(b x^{3} + a\right) + 1\right) - 15 \, \cos\left(b x^{3} + a\right)^{7} \log\left(-\sin\left(b x^{3} + a\right) + 1\right) - 96 \, b x^{3} + 2 \, {\left(15 \, \cos\left(b x^{3} + a\right)^{5} + 10 \, \cos\left(b x^{3} + a\right)^{3} + 8 \, \cos\left(b x^{3} + a\right)\right)} \sin\left(b x^{3} + a\right)}{2016 \, b^{2} \cos\left(b x^{3} + a\right)^{7}}"," ",0,"-1/2016*(15*cos(b*x^3 + a)^7*log(sin(b*x^3 + a) + 1) - 15*cos(b*x^3 + a)^7*log(-sin(b*x^3 + a) + 1) - 96*b*x^3 + 2*(15*cos(b*x^3 + a)^5 + 10*cos(b*x^3 + a)^3 + 8*cos(b*x^3 + a))*sin(b*x^3 + a))/(b^2*cos(b*x^3 + a)^7)","A",0
928,1,12,0,1.041873," ","integrate(sec(1/x)^2/x^2,x, algorithm=""fricas"")","-\frac{\sin\left(\frac{1}{x}\right)}{\cos\left(\frac{1}{x}\right)}"," ",0,"-sin(1/x)/cos(1/x)","A",0
929,1,4,0,0.916311," ","integrate(3*x^2*cos(x^3),x, algorithm=""fricas"")","\sin\left(x^{3}\right)"," ",0,"sin(x^3)","A",0
930,1,39,0,0.826697," ","integrate((1+2*x)*sec(1+2*x)^2,x, algorithm=""fricas"")","\frac{\cos\left(2 \, x + 1\right) \log\left(-\cos\left(2 \, x + 1\right)\right) + {\left(2 \, x + 1\right)} \sin\left(2 \, x + 1\right)}{2 \, \cos\left(2 \, x + 1\right)}"," ",0,"1/2*(cos(2*x + 1)*log(-cos(2*x + 1)) + (2*x + 1)*sin(2*x + 1))/cos(2*x + 1)","A",0
931,-2,0,0,0.000000," ","integrate(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, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
932,-2,0,0,0.000000," ","integrate(x^2*cos(b*x+a)/(x^3+3*sin(b*x+a))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
933,1,10,0,0.881659," ","integrate((cos(x)+sin(x))/(exp(-x)+sin(x)),x, algorithm=""fricas"")","x + \log\left(e^{\left(-x\right)} + \sin\left(x\right)\right)"," ",0,"x + log(e^(-x) + sin(x))","A",0
934,1,60,0,1.131273," ","integrate(sin(d*x+c)*(a*sin(d*x+c)^2+b*sin(d*x+c)^3),x, algorithm=""fricas"")","\frac{8 \, a \cos\left(d x + c\right)^{3} + 9 \, b d x - 24 \, a \cos\left(d x + c\right) + 3 \, {\left(2 \, b \cos\left(d x + c\right)^{3} - 5 \, b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(8*a*cos(d*x + c)^3 + 9*b*d*x - 24*a*cos(d*x + c) + 3*(2*b*cos(d*x + c)^3 - 5*b*cos(d*x + c))*sin(d*x + c))/d","A",0
935,1,123,0,0.912342," ","integrate(sin(d*x+c)*(a*sin(d*x+c)^2+b*sin(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{120 \, b^{2} \cos\left(d x + c\right)^{7} - 168 \, {\left(a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{5} + 525 \, a b d x + 280 \, {\left(2 \, a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{3} - 840 \, {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right) - 35 \, {\left(8 \, a b \cos\left(d x + c\right)^{5} - 26 \, a b \cos\left(d x + c\right)^{3} + 33 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(120*b^2*cos(d*x + c)^7 - 168*(a^2 + 3*b^2)*cos(d*x + c)^5 + 525*a*b*d*x + 280*(2*a^2 + 3*b^2)*cos(d*x + c)^3 - 840*(a^2 + b^2)*cos(d*x + c) - 35*(8*a*b*cos(d*x + c)^5 - 26*a*b*cos(d*x + c)^3 + 33*a*b*cos(d*x + c))*sin(d*x + c))/d","A",0
936,1,72,0,0.878900," ","integrate(sin(d*x+c)*(a*sin(d*x+c)+b*sin(d*x+c)^2+c*sin(d*x+c)^3),x, algorithm=""fricas"")","\frac{8 \, b \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, a + 3 \, c\right)} d x - 24 \, b \cos\left(d x + c\right) + 3 \, {\left(2 \, c \cos\left(d x + c\right)^{3} - {\left(4 \, a + 5 \, c\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(8*b*cos(d*x + c)^3 + 3*(4*a + 3*c)*d*x - 24*b*cos(d*x + c) + 3*(2*c*cos(d*x + c)^3 - (4*a + 5*c)*cos(d*x + c))*sin(d*x + c))/d","A",0
937,1,162,0,1.962000," ","integrate(sin(d*x+c)*(a*sin(d*x+c)+b*sin(d*x+c)^2+c*sin(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{120 \, c^{2} \cos\left(d x + c\right)^{7} - 168 \, {\left(b^{2} + 2 \, a c + 3 \, c^{2}\right)} \cos\left(d x + c\right)^{5} + 280 \, {\left(a^{2} + 2 \, b^{2} + 4 \, a c + 3 \, c^{2}\right)} \cos\left(d x + c\right)^{3} + 105 \, {\left(6 \, a b + 5 \, b c\right)} d x - 840 \, {\left(a^{2} + b^{2} + 2 \, a c + c^{2}\right)} \cos\left(d x + c\right) - 35 \, {\left(8 \, b c \cos\left(d x + c\right)^{5} - 2 \, {\left(6 \, a b + 13 \, b c\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(10 \, a b + 11 \, b c\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(120*c^2*cos(d*x + c)^7 - 168*(b^2 + 2*a*c + 3*c^2)*cos(d*x + c)^5 + 280*(a^2 + 2*b^2 + 4*a*c + 3*c^2)*cos(d*x + c)^3 + 105*(6*a*b + 5*b*c)*d*x - 840*(a^2 + b^2 + 2*a*c + c^2)*cos(d*x + c) - 35*(8*b*c*cos(d*x + c)^5 - 2*(6*a*b + 13*b*c)*cos(d*x + c)^3 + 3*(10*a*b + 11*b*c)*cos(d*x + c))*sin(d*x + c))/d","A",0
938,0,0,0,1.779723," ","integrate(sin(d*x+c)*(a+c*sin(d*x+c)+b/sin(d*x+c)^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(-c \cos\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + b \sqrt{\sin\left(d x + c\right)} + c, x\right)"," ",0,"integral(-c*cos(d*x + c)^2 + a*sin(d*x + c) + b*sqrt(sin(d*x + c)) + c, x)","F",0
939,0,0,0,1.460189," ","integrate(sin(d*x+c)*(a+c*sin(d*x+c)+b/sin(d*x+c)^(1/2))^2,x, algorithm=""fricas"")","{\rm integral}\left(-2 \, a c \cos\left(d x + c\right)^{2} + b^{2} + 2 \, a c - {\left(c^{2} \cos\left(d x + c\right)^{2} - a^{2} - c^{2}\right)} \sin\left(d x + c\right) + 2 \, {\left(b c \sin\left(d x + c\right) + a b\right)} \sqrt{\sin\left(d x + c\right)}, x\right)"," ",0,"integral(-2*a*c*cos(d*x + c)^2 + b^2 + 2*a*c - (c^2*cos(d*x + c)^2 - a^2 - c^2)*sin(d*x + c) + 2*(b*c*sin(d*x + c) + a*b)*sqrt(sin(d*x + c)), x)","F",0
940,1,30,0,0.629854," ","integrate(f^(b*x+a)*(cos(d*x+c)+I*sin(d*x+c))^n,x, algorithm=""fricas"")","\frac{f^{b x + a} e^{\left(i \, d n x + i \, c n\right)}}{i \, d n + b \log\left(f\right)}"," ",0,"f^(b*x + a)*e^(I*d*n*x + I*c*n)/(I*d*n + b*log(f))","A",0
941,1,30,0,0.931649," ","integrate(f^(b*x+a)*(cos(d*x+c)-I*sin(d*x+c))^n,x, algorithm=""fricas"")","\frac{f^{b x + a} e^{\left(-i \, d n x - i \, c n\right)}}{-i \, d n + b \log\left(f\right)}"," ",0,"f^(b*x + a)*e^(-I*d*n*x - I*c*n)/(-I*d*n + b*log(f))","A",0
942,1,150,0,0.893939," ","integrate((cos(b*x+a)^5-sin(b*x+a)^5)/(cos(b*x+a)^5+sin(b*x+a)^5),x, algorithm=""fricas"")","\frac{2 \, \sqrt{5} \log\left(-\frac{2 \, \cos\left(b x + a\right)^{4} - 2 \, {\left(\sqrt{5} + 1\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, \cos\left(b x + a\right)^{2} - \sqrt{5} - 3}{\cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2} - \cos\left(b x + a\right) \sin\left(b x + a\right) + 1}\right) + 2 \, \log\left(\cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2} - \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right) + \log\left(2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{10 \, b}"," ",0,"1/10*(2*sqrt(5)*log(-(2*cos(b*x + a)^4 - 2*(sqrt(5) + 1)*cos(b*x + a)*sin(b*x + a) - 2*cos(b*x + a)^2 - sqrt(5) - 3)/(cos(b*x + a)^4 - cos(b*x + a)^2 - cos(b*x + a)*sin(b*x + a) + 1)) + 2*log(cos(b*x + a)^4 - cos(b*x + a)^2 - cos(b*x + a)*sin(b*x + a) + 1) + log(2*cos(b*x + a)*sin(b*x + a) + 1))/b","A",0
943,1,74,0,0.967620," ","integrate((cos(b*x+a)^4-sin(b*x+a)^4)/(cos(b*x+a)^4+sin(b*x+a)^4),x, algorithm=""fricas"")","\frac{\sqrt{2} \log\left(-\frac{2 \, \cos\left(b x + a\right)^{4} - 2 \, \sqrt{2} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, \cos\left(b x + a\right)^{2} - 1}{2 \, \cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1}\right)}{4 \, b}"," ",0,"1/4*sqrt(2)*log(-(2*cos(b*x + a)^4 - 2*sqrt(2)*cos(b*x + a)*sin(b*x + a) - 2*cos(b*x + a)^2 - 1)/(2*cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1))/b","A",0
944,1,42,0,0.895492," ","integrate((cos(b*x+a)^3-sin(b*x+a)^3)/(cos(b*x+a)^3+sin(b*x+a)^3),x, algorithm=""fricas"")","\frac{\log\left(2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right) - 4 \, \log\left(-\cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{6 \, b}"," ",0,"1/6*(log(2*cos(b*x + a)*sin(b*x + a) + 1) - 4*log(-cos(b*x + a)*sin(b*x + a) + 1))/b","A",0
945,1,16,0,0.546470," ","integrate((cos(b*x+a)^2-sin(b*x+a)^2)/(cos(b*x+a)^2+sin(b*x+a)^2),x, algorithm=""fricas"")","\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",0
946,1,22,0,1.164574," ","integrate((cos(b*x+a)-sin(b*x+a))/(cos(b*x+a)+sin(b*x+a)),x, algorithm=""fricas"")","\frac{\log\left(2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{2 \, b}"," ",0,"1/2*log(2*cos(b*x + a)*sin(b*x + a) + 1)/b","A",0
947,1,22,0,1.348375," ","integrate((-csc(b*x+a)+sec(b*x+a))/(csc(b*x+a)+sec(b*x+a)),x, algorithm=""fricas"")","-\frac{\log\left(2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{2 \, b}"," ",0,"-1/2*log(2*cos(b*x + a)*sin(b*x + a) + 1)/b","A",0
948,1,17,0,1.406525," ","integrate((-csc(b*x+a)^2+sec(b*x+a)^2)/(csc(b*x+a)^2+sec(b*x+a)^2),x, algorithm=""fricas"")","-\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",0
949,1,42,0,0.935016," ","integrate((-csc(b*x+a)^3+sec(b*x+a)^3)/(csc(b*x+a)^3+sec(b*x+a)^3),x, algorithm=""fricas"")","-\frac{\log\left(2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right) - 4 \, \log\left(-\cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{6 \, b}"," ",0,"-1/6*(log(2*cos(b*x + a)*sin(b*x + a) + 1) - 4*log(-cos(b*x + a)*sin(b*x + a) + 1))/b","A",0
950,1,74,0,1.154863," ","integrate((-csc(b*x+a)^4+sec(b*x+a)^4)/(csc(b*x+a)^4+sec(b*x+a)^4),x, algorithm=""fricas"")","\frac{\sqrt{2} \log\left(-\frac{2 \, \cos\left(b x + a\right)^{4} + 2 \, \sqrt{2} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, \cos\left(b x + a\right)^{2} - 1}{2 \, \cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1}\right)}{4 \, b}"," ",0,"1/4*sqrt(2)*log(-(2*cos(b*x + a)^4 + 2*sqrt(2)*cos(b*x + a)*sin(b*x + a) - 2*cos(b*x + a)^2 - 1)/(2*cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1))/b","A",0
