1,1,118,0,2.685317," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{a \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a \cos\left(6 \, d x + 6 \, c\right)}{128 \, d} - \frac{7 \, a \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{7 \, a \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} + \frac{a \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{7 \, a \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{7 \, a \sin\left(3 \, d x + 3 \, c\right)}{64 \, d} + \frac{35 \, a \sin\left(d x + c\right)}{64 \, d}"," ",0,"-1/1024*a*cos(8*d*x + 8*c)/d - 1/128*a*cos(6*d*x + 6*c)/d - 7/256*a*cos(4*d*x + 4*c)/d - 7/128*a*cos(2*d*x + 2*c)/d + 1/448*a*sin(7*d*x + 7*c)/d + 7/320*a*sin(5*d*x + 5*c)/d + 7/64*a*sin(3*d*x + 3*c)/d + 35/64*a*sin(d*x + c)/d","A",0
2,1,107,0,1.291873," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{5}{16} \, a x - \frac{a \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{a \cos\left(5 \, d x + 5 \, c\right)}{64 \, d} - \frac{3 \, a \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{5 \, a \cos\left(d x + c\right)}{64 \, d} + \frac{a \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{3 \, a \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{15 \, a \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"5/16*a*x - 1/448*a*cos(7*d*x + 7*c)/d - 1/64*a*cos(5*d*x + 5*c)/d - 3/64*a*cos(3*d*x + 3*c)/d - 5/64*a*cos(d*x + c)/d + 1/192*a*sin(6*d*x + 6*c)/d + 3/64*a*sin(4*d*x + 4*c)/d + 15/64*a*sin(2*d*x + 2*c)/d","A",0
3,1,88,0,0.749888," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{a \cos\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{a \cos\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{5 \, a \cos\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{a \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{5 \, a \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{5 \, a \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/192*a*cos(6*d*x + 6*c)/d - 1/32*a*cos(4*d*x + 4*c)/d - 5/64*a*cos(2*d*x + 2*c)/d + 1/80*a*sin(5*d*x + 5*c)/d + 5/48*a*sin(3*d*x + 3*c)/d + 5/8*a*sin(d*x + c)/d","A",0
4,1,77,0,0.694285," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3}{8} \, a x - \frac{a \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{a \cos\left(3 \, d x + 3 \, c\right)}{16 \, d} - \frac{a \cos\left(d x + c\right)}{8 \, d} + \frac{a \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{a \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"3/8*a*x - 1/80*a*cos(5*d*x + 5*c)/d - 1/16*a*cos(3*d*x + 3*c)/d - 1/8*a*cos(d*x + c)/d + 1/32*a*sin(4*d*x + 4*c)/d + 1/4*a*sin(2*d*x + 2*c)/d","A",0
5,1,48,0,0.596215," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, a \sin\left(d x + c\right)^{4} + 4 \, a \sin\left(d x + c\right)^{3} - 6 \, a \sin\left(d x + c\right)^{2} - 12 \, a \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(3*a*sin(d*x + c)^4 + 4*a*sin(d*x + c)^3 - 6*a*sin(d*x + c)^2 - 12*a*sin(d*x + c))/d","A",0
6,1,47,0,0.804829," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{1}{2} \, a x - \frac{a \cos\left(3 \, d x + 3 \, c\right)}{12 \, d} - \frac{a \cos\left(d x + c\right)}{4 \, d} + \frac{a \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"1/2*a*x - 1/12*a*cos(3*d*x + 3*c)/d - 1/4*a*cos(d*x + c)/d + 1/4*a*sin(2*d*x + 2*c)/d","A",0
7,1,25,0,0.496118," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \sin\left(d x + c\right)^{2} + 2 \, a \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(a*sin(d*x + c)^2 + 2*a*sin(d*x + c))/d","A",0
8,1,37,0,0.935170," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 2 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{d}"," ",0,"(a*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 2*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)))/d","B",0
9,1,19,0,0.470002," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, a}{d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}"," ",0,"-2*a/(d*(tan(1/2*d*x + 1/2*c) - 1))","A",0
10,1,54,0,0.543849," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - a \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + \frac{a \sin\left(d x + c\right) - 3 \, a}{\sin\left(d x + c\right) - 1}}{4 \, d}"," ",0,"1/4*(a*log(abs(sin(d*x + c) + 1)) - a*log(abs(sin(d*x + c) - 1)) + (a*sin(d*x + c) - 3*a)/(sin(d*x + c) - 1))/d","A",0
11,1,66,0,0.363984," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} + \frac{9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, a}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(3*a/(tan(1/2*d*x + 1/2*c) + 1) + (9*a*tan(1/2*d*x + 1/2*c)^2 - 12*a*tan(1/2*d*x + 1/2*c) + 7*a)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
12,1,92,0,0.514520," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{6 \, a \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 6 \, a \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, a \sin\left(d x + c\right) + 5 \, a\right)}}{\sin\left(d x + c\right) + 1} + \frac{9 \, a \sin\left(d x + c\right)^{2} - 26 \, a \sin\left(d x + c\right) + 21 \, a}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{32 \, d}"," ",0,"1/32*(6*a*log(abs(sin(d*x + c) + 1)) - 6*a*log(abs(sin(d*x + c) - 1)) - 2*(3*a*sin(d*x + c) + 5*a)/(sin(d*x + c) + 1) + (9*a*sin(d*x + c)^2 - 26*a*sin(d*x + c) + 21*a)/(sin(d*x + c) - 1)^2)/d","A",0
13,1,123,0,0.521936," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{45}{128} \, a^{2} x - \frac{a^{2} \cos\left(7 \, d x + 7 \, c\right)}{224 \, d} - \frac{a^{2} \cos\left(5 \, d x + 5 \, c\right)}{32 \, d} - \frac{3 \, a^{2} \cos\left(3 \, d x + 3 \, c\right)}{32 \, d} - \frac{5 \, a^{2} \cos\left(d x + c\right)}{32 \, d} - \frac{a^{2} \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{5 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{a^{2} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"45/128*a^2*x - 1/224*a^2*cos(7*d*x + 7*c)/d - 1/32*a^2*cos(5*d*x + 5*c)/d - 3/32*a^2*cos(3*d*x + 3*c)/d - 5/32*a^2*cos(d*x + c)/d - 1/1024*a^2*sin(8*d*x + 8*c)/d + 5/128*a^2*sin(4*d*x + 4*c)/d + 1/4*a^2*sin(2*d*x + 2*c)/d","A",0
14,1,117,0,2.271439," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{a^{2} \cos\left(6 \, d x + 6 \, c\right)}{96 \, d} - \frac{a^{2} \cos\left(4 \, d x + 4 \, c\right)}{16 \, d} - \frac{5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)}{32 \, d} - \frac{a^{2} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{a^{2} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{19 \, a^{2} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{45 \, a^{2} \sin\left(d x + c\right)}{64 \, d}"," ",0,"-1/96*a^2*cos(6*d*x + 6*c)/d - 1/16*a^2*cos(4*d*x + 4*c)/d - 5/32*a^2*cos(2*d*x + 2*c)/d - 1/448*a^2*sin(7*d*x + 7*c)/d + 1/320*a^2*sin(5*d*x + 5*c)/d + 19/192*a^2*sin(3*d*x + 3*c)/d + 45/64*a^2*sin(d*x + c)/d","A",0
15,1,106,0,0.611671," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{7}{16} \, a^{2} x - \frac{a^{2} \cos\left(5 \, d x + 5 \, c\right)}{40 \, d} - \frac{a^{2} \cos\left(3 \, d x + 3 \, c\right)}{8 \, d} - \frac{a^{2} \cos\left(d x + c\right)}{4 \, d} - \frac{a^{2} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{a^{2} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{17 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"7/16*a^2*x - 1/40*a^2*cos(5*d*x + 5*c)/d - 1/8*a^2*cos(3*d*x + 3*c)/d - 1/4*a^2*cos(d*x + c)/d - 1/192*a^2*sin(6*d*x + 6*c)/d + 1/64*a^2*sin(4*d*x + 4*c)/d + 17/64*a^2*sin(2*d*x + 2*c)/d","A",0
16,1,56,0,0.886480," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, a^{2} \sin\left(d x + c\right)^{5} + 5 \, a^{2} \sin\left(d x + c\right)^{4} - 10 \, a^{2} \sin\left(d x + c\right)^{2} - 10 \, a^{2} \sin\left(d x + c\right)}{10 \, d}"," ",0,"-1/10*(2*a^2*sin(d*x + c)^5 + 5*a^2*sin(d*x + c)^4 - 10*a^2*sin(d*x + c)^2 - 10*a^2*sin(d*x + c))/d","A",0
17,1,72,0,0.442919," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{5}{8} \, a^{2} x - \frac{a^{2} \cos\left(3 \, d x + 3 \, c\right)}{6 \, d} - \frac{a^{2} \cos\left(d x + c\right)}{2 \, d} - \frac{a^{2} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{a^{2} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"5/8*a^2*x - 1/6*a^2*cos(3*d*x + 3*c)/d - 1/2*a^2*cos(d*x + c)/d - 1/32*a^2*sin(4*d*x + 4*c)/d + 1/4*a^2*sin(2*d*x + 2*c)/d","A",0
18,1,20,0,0.742638," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}{3 \, a d}"," ",0,"1/3*(a*sin(d*x + c) + a)^3/(a*d)","A",0
19,1,91,0,0.874116," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 2 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}\right)}}{d}"," ",0,"2*(a^2*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 2*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - (a^2*tan(1/2*d*x + 1/2*c)^2 + a^2*tan(1/2*d*x + 1/2*c) + a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","B",0
20,1,33,0,0.554859," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} a^{2} + \frac{4 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}}{d}"," ",0,"-((d*x + c)*a^2 + 4*a^2/(tan(1/2*d*x + 1/2*c) - 1))/d","A",0
21,1,30,0,0.739501," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{2}}"," ",0,"2*a^2*tan(1/2*d*x + 1/2*c)/(d*(tan(1/2*d*x + 1/2*c) - 1)^2)","A",0
22,1,54,0,1.686637," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2}\right)}}{3 \, d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}"," ",0,"-2/3*(3*a^2*tan(1/2*d*x + 1/2*c)^2 - 3*a^2*tan(1/2*d*x + 1/2*c) + 2*a^2)/(d*(tan(1/2*d*x + 1/2*c) - 1)^3)","A",0
23,1,77,0,0.622877," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, a^{2} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 2 \, a^{2} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2} - 10 \, a^{2} \sin\left(d x + c\right) + 11 \, a^{2}}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(2*a^2*log(abs(sin(d*x + c) + 1)) - 2*a^2*log(abs(sin(d*x + c) - 1)) + (3*a^2*sin(d*x + c)^2 - 10*a^2*sin(d*x + c) + 11*a^2)/(sin(d*x + c) - 1)^2)/d","A",0
24,1,106,0,0.649059," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{5 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} + \frac{35 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 90 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 70 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, a^{2}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{5}}}{20 \, d}"," ",0,"-1/20*(5*a^2/(tan(1/2*d*x + 1/2*c) + 1) + (35*a^2*tan(1/2*d*x + 1/2*c)^4 - 90*a^2*tan(1/2*d*x + 1/2*c)^3 + 120*a^2*tan(1/2*d*x + 1/2*c)^2 - 70*a^2*tan(1/2*d*x + 1/2*c) + 21*a^2)/(tan(1/2*d*x + 1/2*c) - 1)^5)/d","A",0
25,1,119,0,0.500584," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{6 \, a^{2} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 6 \, a^{2} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{3 \, {\left(2 \, a^{2} \sin\left(d x + c\right) + 3 \, a^{2}\right)}}{\sin\left(d x + c\right) + 1} + \frac{11 \, a^{2} \sin\left(d x + c\right)^{3} - 42 \, a^{2} \sin\left(d x + c\right)^{2} + 57 \, a^{2} \sin\left(d x + c\right) - 30 \, a^{2}}{{\left(\sin\left(d x + c\right) - 1\right)}^{3}}}{48 \, d}"," ",0,"1/48*(6*a^2*log(abs(sin(d*x + c) + 1)) - 6*a^2*log(abs(sin(d*x + c) - 1)) - 3*(2*a^2*sin(d*x + c) + 3*a^2)/(sin(d*x + c) + 1) + (11*a^2*sin(d*x + c)^3 - 42*a^2*sin(d*x + c)^2 + 57*a^2*sin(d*x + c) - 30*a^2)/(sin(d*x + c) - 1)^3)/d","A",0
26,1,171,0,0.650229," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{7 \, {\left(9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}} + \frac{273 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1155 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2450 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2870 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2037 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 791 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 152 \, a^{2}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{7}}}{168 \, d}"," ",0,"-1/168*(7*(9*a^2*tan(1/2*d*x + 1/2*c)^2 + 15*a^2*tan(1/2*d*x + 1/2*c) + 8*a^2)/(tan(1/2*d*x + 1/2*c) + 1)^3 + (273*a^2*tan(1/2*d*x + 1/2*c)^6 - 1155*a^2*tan(1/2*d*x + 1/2*c)^5 + 2450*a^2*tan(1/2*d*x + 1/2*c)^4 - 2870*a^2*tan(1/2*d*x + 1/2*c)^3 + 2037*a^2*tan(1/2*d*x + 1/2*c)^2 - 791*a^2*tan(1/2*d*x + 1/2*c) + 152*a^2)/(tan(1/2*d*x + 1/2*c) - 1)^7)/d","B",0
27,1,157,0,0.861637," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{55}{128} \, a^{3} x + \frac{a^{3} \cos\left(9 \, d x + 9 \, c\right)}{2304 \, d} - \frac{9 \, a^{3} \cos\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{3 \, a^{3} \cos\left(5 \, d x + 5 \, c\right)}{64 \, d} - \frac{29 \, a^{3} \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{33 \, a^{3} \cos\left(d x + c\right)}{128 \, d} - \frac{3 \, a^{3} \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a^{3} \sin\left(6 \, d x + 6 \, c\right)}{96 \, d} + \frac{3 \, a^{3} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{9 \, a^{3} \sin\left(2 \, d x + 2 \, c\right)}{32 \, d}"," ",0,"55/128*a^3*x + 1/2304*a^3*cos(9*d*x + 9*c)/d - 9/1792*a^3*cos(7*d*x + 7*c)/d - 3/64*a^3*cos(5*d*x + 5*c)/d - 29/192*a^3*cos(3*d*x + 3*c)/d - 33/128*a^3*cos(d*x + c)/d - 3/1024*a^3*sin(8*d*x + 8*c)/d - 1/96*a^3*sin(6*d*x + 6*c)/d + 3/128*a^3*sin(4*d*x + 4*c)/d + 9/32*a^3*sin(2*d*x + 2*c)/d","A",0
28,1,134,0,0.984787," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{5 \, a^{3} \cos\left(6 \, d x + 6 \, c\right)}{384 \, d} - \frac{25 \, a^{3} \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{33 \, a^{3} \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} - \frac{3 \, a^{3} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{a^{3} \sin\left(5 \, d x + 5 \, c\right)}{64 \, d} + \frac{17 \, a^{3} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{55 \, a^{3} \sin\left(d x + c\right)}{64 \, d}"," ",0,"1/1024*a^3*cos(8*d*x + 8*c)/d - 5/384*a^3*cos(6*d*x + 6*c)/d - 25/256*a^3*cos(4*d*x + 4*c)/d - 33/128*a^3*cos(2*d*x + 2*c)/d - 3/448*a^3*sin(7*d*x + 7*c)/d - 1/64*a^3*sin(5*d*x + 5*c)/d + 17/192*a^3*sin(3*d*x + 3*c)/d + 55/64*a^3*sin(d*x + c)/d","B",0
29,1,123,0,0.843434," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{9}{16} \, a^{3} x + \frac{a^{3} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{11 \, a^{3} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{13 \, a^{3} \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{27 \, a^{3} \cos\left(d x + c\right)}{64 \, d} - \frac{a^{3} \sin\left(6 \, d x + 6 \, c\right)}{64 \, d} - \frac{a^{3} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{19 \, a^{3} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"9/16*a^3*x + 1/448*a^3*cos(7*d*x + 7*c)/d - 11/320*a^3*cos(5*d*x + 5*c)/d - 13/64*a^3*cos(3*d*x + 3*c)/d - 27/64*a^3*cos(d*x + c)/d - 1/64*a^3*sin(6*d*x + 6*c)/d - 1/64*a^3*sin(4*d*x + 4*c)/d + 19/64*a^3*sin(2*d*x + 2*c)/d","A",0
30,1,82,0,0.712948," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{5 \, a^{3} \sin\left(d x + c\right)^{6} + 18 \, a^{3} \sin\left(d x + c\right)^{5} + 15 \, a^{3} \sin\left(d x + c\right)^{4} - 20 \, a^{3} \sin\left(d x + c\right)^{3} - 45 \, a^{3} \sin\left(d x + c\right)^{2} - 30 \, a^{3} \sin\left(d x + c\right)}{30 \, d}"," ",0,"-1/30*(5*a^3*sin(d*x + c)^6 + 18*a^3*sin(d*x + c)^5 + 15*a^3*sin(d*x + c)^4 - 20*a^3*sin(d*x + c)^3 - 45*a^3*sin(d*x + c)^2 - 30*a^3*sin(d*x + c))/d","A",0
31,1,89,0,1.067828," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{7}{8} \, a^{3} x + \frac{a^{3} \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{13 \, a^{3} \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{7 \, a^{3} \cos\left(d x + c\right)}{8 \, d} - \frac{3 \, a^{3} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{a^{3} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"7/8*a^3*x + 1/80*a^3*cos(5*d*x + 5*c)/d - 13/48*a^3*cos(3*d*x + 3*c)/d - 7/8*a^3*cos(d*x + c)/d - 3/32*a^3*sin(4*d*x + 4*c)/d + 1/4*a^3*sin(2*d*x + 2*c)/d","A",0
32,1,20,0,0.827760," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}{4 \, a d}"," ",0,"1/4*(a*sin(d*x + c) + a)^4/(a*d)","A",0
33,1,128,0,0.900198," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, {\left(2 \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 4 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}\right)}}{d}"," ",0,"2*(2*a^3*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 4*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - (3*a^3*tan(1/2*d*x + 1/2*c)^4 + 3*a^3*tan(1/2*d*x + 1/2*c)^3 + 7*a^3*tan(1/2*d*x + 1/2*c)^2 + 3*a^3*tan(1/2*d*x + 1/2*c) + 3*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
34,1,91,0,0.544786," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{3 \, {\left(d x + c\right)} a^{3} + \frac{2 \, {\left(4 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}}{d}"," ",0,"-(3*(d*x + c)*a^3 + 2*(4*a^3*tan(1/2*d*x + 1/2*c)^2 - a^3*tan(1/2*d*x + 1/2*c) + 5*a^3)/(tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) - 1))/d","A",0
35,1,92,0,0.499402," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 2 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{2}}}{d}"," ",0,"-(a^3*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 2*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (3*a^3*tan(1/2*d*x + 1/2*c)^2 - 10*a^3*tan(1/2*d*x + 1/2*c) + 3*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^2)/d","B",0
36,1,38,0,1.517574," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{3}\right)}}{3 \, d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}"," ",0,"-2/3*(3*a^3*tan(1/2*d*x + 1/2*c)^2 + a^3)/(d*(tan(1/2*d*x + 1/2*c) - 1)^3)","A",0
37,1,63,0,0.702315," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{4}}"," ",0,"2*(a^3*tan(1/2*d*x + 1/2*c)^3 - a^3*tan(1/2*d*x + 1/2*c)^2 + a^3*tan(1/2*d*x + 1/2*c))/(d*(tan(1/2*d*x + 1/2*c) - 1)^4)","B",0
38,1,86,0,0.821170," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 30 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 20 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, a^{3}\right)}}{15 \, d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{5}}"," ",0,"-2/15*(15*a^3*tan(1/2*d*x + 1/2*c)^4 - 30*a^3*tan(1/2*d*x + 1/2*c)^3 + 40*a^3*tan(1/2*d*x + 1/2*c)^2 - 20*a^3*tan(1/2*d*x + 1/2*c) + 7*a^3)/(d*(tan(1/2*d*x + 1/2*c) - 1)^5)","A",0
39,1,90,0,0.556742," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{6 \, a^{3} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 6 \, a^{3} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + \frac{11 \, a^{3} \sin\left(d x + c\right)^{3} - 45 \, a^{3} \sin\left(d x + c\right)^{2} + 69 \, a^{3} \sin\left(d x + c\right) - 51 \, a^{3}}{{\left(\sin\left(d x + c\right) - 1\right)}^{3}}}{96 \, d}"," ",0,"1/96*(6*a^3*log(abs(sin(d*x + c) + 1)) - 6*a^3*log(abs(sin(d*x + c) - 1)) + (11*a^3*sin(d*x + c)^3 - 45*a^3*sin(d*x + c)^2 + 69*a^3*sin(d*x + c) - 51*a^3)/(sin(d*x + c) - 1)^3)/d","A",0
40,1,138,0,0.519314," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{35 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} + \frac{525 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1960 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4025 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 4480 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3143 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1176 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 243 \, a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{7}}}{280 \, d}"," ",0,"-1/280*(35*a^3/(tan(1/2*d*x + 1/2*c) + 1) + (525*a^3*tan(1/2*d*x + 1/2*c)^6 - 1960*a^3*tan(1/2*d*x + 1/2*c)^5 + 4025*a^3*tan(1/2*d*x + 1/2*c)^4 - 4480*a^3*tan(1/2*d*x + 1/2*c)^3 + 3143*a^3*tan(1/2*d*x + 1/2*c)^2 - 1176*a^3*tan(1/2*d*x + 1/2*c) + 243*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^7)/d","A",0
41,1,219,0,1.958917," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{a^{8} \cos\left(12 \, d x + 12 \, c\right)}{3072 \, d} - \frac{3 \, a^{8} \cos\left(10 \, d x + 10 \, c\right)}{256 \, d} + \frac{27 \, a^{8} \cos\left(8 \, d x + 8 \, c\right)}{512 \, d} + \frac{155 \, a^{8} \cos\left(6 \, d x + 6 \, c\right)}{768 \, d} - \frac{475 \, a^{8} \cos\left(4 \, d x + 4 \, c\right)}{1024 \, d} - \frac{323 \, a^{8} \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} + \frac{a^{8} \sin\left(13 \, d x + 13 \, c\right)}{53248 \, d} - \frac{115 \, a^{8} \sin\left(11 \, d x + 11 \, c\right)}{45056 \, d} + \frac{205 \, a^{8} \sin\left(9 \, d x + 9 \, c\right)}{6144 \, d} - \frac{7 \, a^{8} \sin\left(7 \, d x + 7 \, c\right)}{2048 \, d} - \frac{2033 \, a^{8} \sin\left(5 \, d x + 5 \, c\right)}{4096 \, d} - \frac{6137 \, a^{8} \sin\left(3 \, d x + 3 \, c\right)}{12288 \, d} + \frac{4845 \, a^{8} \sin\left(d x + c\right)}{1024 \, d}"," ",0,"1/3072*a^8*cos(12*d*x + 12*c)/d - 3/256*a^8*cos(10*d*x + 10*c)/d + 27/512*a^8*cos(8*d*x + 8*c)/d + 155/768*a^8*cos(6*d*x + 6*c)/d - 475/1024*a^8*cos(4*d*x + 4*c)/d - 323/128*a^8*cos(2*d*x + 2*c)/d + 1/53248*a^8*sin(13*d*x + 13*c)/d - 115/45056*a^8*sin(11*d*x + 11*c)/d + 205/6144*a^8*sin(9*d*x + 9*c)/d - 7/2048*a^8*sin(7*d*x + 7*c)/d - 2033/4096*a^8*sin(5*d*x + 5*c)/d - 6137/12288*a^8*sin(3*d*x + 3*c)/d + 4845/1024*a^8*sin(d*x + c)/d","B",0
42,1,208,0,1.971052," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{4199}{1024} \, a^{8} x + \frac{a^{8} \cos\left(11 \, d x + 11 \, c\right)}{1408 \, d} - \frac{31 \, a^{8} \cos\left(9 \, d x + 9 \, c\right)}{1152 \, d} + \frac{139 \, a^{8} \cos\left(7 \, d x + 7 \, c\right)}{896 \, d} + \frac{171 \, a^{8} \cos\left(5 \, d x + 5 \, c\right)}{640 \, d} - \frac{323 \, a^{8} \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{323 \, a^{8} \cos\left(d x + c\right)}{64 \, d} + \frac{a^{8} \sin\left(12 \, d x + 12 \, c\right)}{24576 \, d} - \frac{29 \, a^{8} \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{673 \, a^{8} \sin\left(8 \, d x + 8 \, c\right)}{8192 \, d} - \frac{361 \, a^{8} \sin\left(6 \, d x + 6 \, c\right)}{3072 \, d} - \frac{8721 \, a^{8} \sin\left(4 \, d x + 4 \, c\right)}{8192 \, d} + \frac{323 \, a^{8} \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"4199/1024*a^8*x + 1/1408*a^8*cos(11*d*x + 11*c)/d - 31/1152*a^8*cos(9*d*x + 9*c)/d + 139/896*a^8*cos(7*d*x + 7*c)/d + 171/640*a^8*cos(5*d*x + 5*c)/d - 323/192*a^8*cos(3*d*x + 3*c)/d - 323/64*a^8*cos(d*x + c)/d + 1/24576*a^8*sin(12*d*x + 12*c)/d - 29/5120*a^8*sin(10*d*x + 10*c)/d + 673/8192*a^8*sin(8*d*x + 8*c)/d - 361/3072*a^8*sin(6*d*x + 6*c)/d - 8721/8192*a^8*sin(4*d*x + 4*c)/d + 323/512*a^8*sin(2*d*x + 2*c)/d","A",0
43,1,134,0,1.569279," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{5 \, a^{8} \sin\left(d x + c\right)^{11} + 44 \, a^{8} \sin\left(d x + c\right)^{10} + 165 \, a^{8} \sin\left(d x + c\right)^{9} + 330 \, a^{8} \sin\left(d x + c\right)^{8} + 330 \, a^{8} \sin\left(d x + c\right)^{7} - 462 \, a^{8} \sin\left(d x + c\right)^{5} - 660 \, a^{8} \sin\left(d x + c\right)^{4} - 495 \, a^{8} \sin\left(d x + c\right)^{3} - 220 \, a^{8} \sin\left(d x + c\right)^{2} - 55 \, a^{8} \sin\left(d x + c\right)}{55 \, d}"," ",0,"-1/55*(5*a^8*sin(d*x + c)^11 + 44*a^8*sin(d*x + c)^10 + 165*a^8*sin(d*x + c)^9 + 330*a^8*sin(d*x + c)^8 + 330*a^8*sin(d*x + c)^7 - 462*a^8*sin(d*x + c)^5 - 660*a^8*sin(d*x + c)^4 - 495*a^8*sin(d*x + c)^3 - 220*a^8*sin(d*x + c)^2 - 55*a^8*sin(d*x + c))/d","B",0
44,1,174,0,1.503269," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{2431}{256} \, a^{8} x + \frac{a^{8} \cos\left(9 \, d x + 9 \, c\right)}{288 \, d} - \frac{33 \, a^{8} \cos\left(7 \, d x + 7 \, c\right)}{224 \, d} + \frac{51 \, a^{8} \cos\left(5 \, d x + 5 \, c\right)}{40 \, d} - \frac{17 \, a^{8} \cos\left(3 \, d x + 3 \, c\right)}{8 \, d} - \frac{221 \, a^{8} \cos\left(d x + c\right)}{16 \, d} + \frac{a^{8} \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} - \frac{59 \, a^{8} \sin\left(8 \, d x + 8 \, c\right)}{2048 \, d} + \frac{527 \, a^{8} \sin\left(6 \, d x + 6 \, c\right)}{1024 \, d} - \frac{561 \, a^{8} \sin\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{663 \, a^{8} \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"2431/256*a^8*x + 1/288*a^8*cos(9*d*x + 9*c)/d - 33/224*a^8*cos(7*d*x + 7*c)/d + 51/40*a^8*cos(5*d*x + 5*c)/d - 17/8*a^8*cos(3*d*x + 3*c)/d - 221/16*a^8*cos(d*x + c)/d + 1/5120*a^8*sin(10*d*x + 10*c)/d - 59/2048*a^8*sin(8*d*x + 8*c)/d + 527/1024*a^8*sin(6*d*x + 6*c)/d - 561/256*a^8*sin(4*d*x + 4*c)/d - 663/512*a^8*sin(2*d*x + 2*c)/d","A",0
45,1,20,0,0.901342," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{9}}{9 \, a d}"," ",0,"1/9*(a*sin(d*x + c) + a)^9/(a*d)","A",0
46,1,288,0,0.954011," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{2 \, {\left(6720 \, a^{8} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 13440 \, a^{8} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{17424 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} + 13335 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 134568 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 93870 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 442344 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 265209 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 780640 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 370308 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 780640 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 265209 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 442344 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 93870 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 134568 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 13335 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17424 \, a^{8}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7}}\right)}}{105 \, d}"," ",0,"2/105*(6720*a^8*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 13440*a^8*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - (17424*a^8*tan(1/2*d*x + 1/2*c)^14 + 13335*a^8*tan(1/2*d*x + 1/2*c)^13 + 134568*a^8*tan(1/2*d*x + 1/2*c)^12 + 93870*a^8*tan(1/2*d*x + 1/2*c)^11 + 442344*a^8*tan(1/2*d*x + 1/2*c)^10 + 265209*a^8*tan(1/2*d*x + 1/2*c)^9 + 780640*a^8*tan(1/2*d*x + 1/2*c)^8 + 370308*a^8*tan(1/2*d*x + 1/2*c)^7 + 780640*a^8*tan(1/2*d*x + 1/2*c)^6 + 265209*a^8*tan(1/2*d*x + 1/2*c)^5 + 442344*a^8*tan(1/2*d*x + 1/2*c)^4 + 93870*a^8*tan(1/2*d*x + 1/2*c)^3 + 134568*a^8*tan(1/2*d*x + 1/2*c)^2 + 13335*a^8*tan(1/2*d*x + 1/2*c) + 17424*a^8)/(tan(1/2*d*x + 1/2*c)^2 + 1)^7)/d","A",0
47,1,231,0,1.901379," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{45045 \, {\left(d x + c\right)} a^{8} + \frac{61440 \, a^{8}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1} + \frac{2 \, {\left(14565 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 28800 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 50855 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 174720 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 36930 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 400640 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 36930 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 426240 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 50855 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 211584 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 14565 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 40064 \, a^{8}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"-1/240*(45045*(d*x + c)*a^8 + 61440*a^8/(tan(1/2*d*x + 1/2*c) - 1) + 2*(14565*a^8*tan(1/2*d*x + 1/2*c)^11 - 28800*a^8*tan(1/2*d*x + 1/2*c)^10 + 50855*a^8*tan(1/2*d*x + 1/2*c)^9 - 174720*a^8*tan(1/2*d*x + 1/2*c)^8 + 36930*a^8*tan(1/2*d*x + 1/2*c)^7 - 400640*a^8*tan(1/2*d*x + 1/2*c)^6 - 36930*a^8*tan(1/2*d*x + 1/2*c)^5 - 426240*a^8*tan(1/2*d*x + 1/2*c)^4 - 50855*a^8*tan(1/2*d*x + 1/2*c)^3 - 211584*a^8*tan(1/2*d*x + 1/2*c)^2 - 14565*a^8*tan(1/2*d*x + 1/2*c) - 40064*a^8)/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
48,1,275,0,0.938349," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{2 \, {\left(480 \, a^{8} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 960 \, a^{8} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{160 \, {\left(9 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 20 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, a^{8}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{2}} - \frac{1096 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 645 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 5840 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 2780 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12120 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 4286 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12120 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2780 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5840 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 645 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1096 \, a^{8}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}\right)}}{5 \, d}"," ",0,"-2/5*(480*a^8*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 960*a^8*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 160*(9*a^8*tan(1/2*d*x + 1/2*c)^2 - 20*a^8*tan(1/2*d*x + 1/2*c) + 9*a^8)/(tan(1/2*d*x + 1/2*c) - 1)^2 - (1096*a^8*tan(1/2*d*x + 1/2*c)^10 + 645*a^8*tan(1/2*d*x + 1/2*c)^9 + 5840*a^8*tan(1/2*d*x + 1/2*c)^8 + 2780*a^8*tan(1/2*d*x + 1/2*c)^7 + 12120*a^8*tan(1/2*d*x + 1/2*c)^6 + 4286*a^8*tan(1/2*d*x + 1/2*c)^5 + 12120*a^8*tan(1/2*d*x + 1/2*c)^4 + 2780*a^8*tan(1/2*d*x + 1/2*c)^3 + 5840*a^8*tan(1/2*d*x + 1/2*c)^2 + 645*a^8*tan(1/2*d*x + 1/2*c) + 1096*a^8)/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
49,1,200,0,0.889695," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{3465 \, {\left(d x + c\right)} a^{8} + \frac{1024 \, {\left(6 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, a^{8}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{2 \, {\left(369 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1728 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 393 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5568 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 393 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5696 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 369 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1856 \, a^{8}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3465*(d*x + c)*a^8 + 1024*(6*a^8*tan(1/2*d*x + 1/2*c)^2 - 15*a^8*tan(1/2*d*x + 1/2*c) + 7*a^8)/(tan(1/2*d*x + 1/2*c) - 1)^3 + 2*(369*a^8*tan(1/2*d*x + 1/2*c)^7 - 1728*a^8*tan(1/2*d*x + 1/2*c)^6 + 393*a^8*tan(1/2*d*x + 1/2*c)^5 - 5568*a^8*tan(1/2*d*x + 1/2*c)^4 - 393*a^8*tan(1/2*d*x + 1/2*c)^3 - 5696*a^8*tan(1/2*d*x + 1/2*c)^2 - 369*a^8*tan(1/2*d*x + 1/2*c) - 1856*a^8)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
50,1,243,0,0.814542," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{2 \, {\left(120 \, a^{8} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 240 \, a^{8} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{220 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 93 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 684 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 190 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 684 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 93 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 220 \, a^{8}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}} + \frac{4 \, {\left(125 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 536 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 846 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 536 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 125 \, a^{8}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{4}}\right)}}{3 \, d}"," ",0,"2/3*(120*a^8*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 240*a^8*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - (220*a^8*tan(1/2*d*x + 1/2*c)^6 + 93*a^8*tan(1/2*d*x + 1/2*c)^5 + 684*a^8*tan(1/2*d*x + 1/2*c)^4 + 190*a^8*tan(1/2*d*x + 1/2*c)^3 + 684*a^8*tan(1/2*d*x + 1/2*c)^2 + 93*a^8*tan(1/2*d*x + 1/2*c) + 220*a^8)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3 + 4*(125*a^8*tan(1/2*d*x + 1/2*c)^4 - 536*a^8*tan(1/2*d*x + 1/2*c)^3 + 846*a^8*tan(1/2*d*x + 1/2*c)^2 - 536*a^8*tan(1/2*d*x + 1/2*c) + 125*a^8)/(tan(1/2*d*x + 1/2*c) - 1)^4)/d","B",0
51,1,114,0,0.607598," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{15 \, {\left(d x + c\right)}}{a} - \frac{2 \, {\left(25 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 40 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 80 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5} a}}{40 \, d}"," ",0,"1/40*(15*(d*x + c)/a - 2*(25*tan(1/2*d*x + 1/2*c)^9 - 40*tan(1/2*d*x + 1/2*c)^8 + 10*tan(1/2*d*x + 1/2*c)^7 - 80*tan(1/2*d*x + 1/2*c)^4 - 10*tan(1/2*d*x + 1/2*c)^3 - 25*tan(1/2*d*x + 1/2*c) - 8)/((tan(1/2*d*x + 1/2*c)^2 + 1)^5*a))/d","A",0
52,1,47,0,0.348904," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{3} - 6 \, \sin\left(d x + c\right)^{2} + 12 \, \sin\left(d x + c\right)}{12 \, a d}"," ",0,"1/12*(3*sin(d*x + c)^4 - 4*sin(d*x + c)^3 - 6*sin(d*x + c)^2 + 12*sin(d*x + c))/(a*d)","A",0
53,1,75,0,0.855831," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(d x + c\right)}}{a} - \frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a}}{6 \, d}"," ",0,"1/6*(3*(d*x + c)/a - 2*(3*tan(1/2*d*x + 1/2*c)^5 - 6*tan(1/2*d*x + 1/2*c)^4 - 3*tan(1/2*d*x + 1/2*c) - 2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a))/d","A",0
54,1,25,0,0.401182," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)}{2 \, a d}"," ",0,"-1/2*(sin(d*x + c)^2 - 2*sin(d*x + c))/(a*d)","A",0
55,1,34,0,0.593863," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{d x + c}{a} + \frac{2}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a}}{d}"," ",0,"((d*x + c)/a + 2/((tan(1/2*d*x + 1/2*c)^2 + 1)*a))/d","A",0
56,1,19,0,0.399389," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\log\left({\left| a \sin\left(d x + c\right) + a \right|}\right)}{a d}"," ",0,"log(abs(a*sin(d*x + c) + a))/(a*d)","A",0
57,1,58,0,0.449470," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{\log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} - \frac{\sin\left(d x + c\right) + 3}{a {\left(\sin\left(d x + c\right) + 1\right)}}}{4 \, d}"," ",0,"1/4*(log(abs(sin(d*x + c) + 1))/a - log(abs(sin(d*x + c) - 1))/a - (sin(d*x + c) + 3)/(a*(sin(d*x + c) + 1)))/d","A",0
58,1,67,0,0.646707," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} + \frac{9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(3/(a*(tan(1/2*d*x + 1/2*c) - 1)) + (9*tan(1/2*d*x + 1/2*c)^2 + 12*tan(1/2*d*x + 1/2*c) + 7)/(a*(tan(1/2*d*x + 1/2*c) + 1)^3))/d","A",0
59,1,96,0,0.852913," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{6 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{6 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{2 \, {\left(3 \, \sin\left(d x + c\right) - 5\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}} - \frac{9 \, \sin\left(d x + c\right)^{2} + 26 \, \sin\left(d x + c\right) + 21}{a {\left(\sin\left(d x + c\right) + 1\right)}^{2}}}{32 \, d}"," ",0,"1/32*(6*log(abs(sin(d*x + c) + 1))/a - 6*log(abs(sin(d*x + c) - 1))/a + 2*(3*sin(d*x + c) - 5)/(a*(sin(d*x + c) - 1)) - (9*sin(d*x + c)^2 + 26*sin(d*x + c) + 21)/(a*(sin(d*x + c) + 1)^2))/d","A",0
60,1,119,0,0.685416," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{5 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13\right)}}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{165 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 480 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 650 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 400 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 113}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{120 \, d}"," ",0,"-1/120*(5*(15*tan(1/2*d*x + 1/2*c)^2 - 24*tan(1/2*d*x + 1/2*c) + 13)/(a*(tan(1/2*d*x + 1/2*c) - 1)^3) + (165*tan(1/2*d*x + 1/2*c)^4 + 480*tan(1/2*d*x + 1/2*c)^3 + 650*tan(1/2*d*x + 1/2*c)^2 + 400*tan(1/2*d*x + 1/2*c) + 113)/(a*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","B",0
61,1,116,0,0.752671," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{30 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{30 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{3 \, {\left(15 \, \sin\left(d x + c\right)^{2} - 38 \, \sin\left(d x + c\right) + 25\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{2}} - \frac{55 \, \sin\left(d x + c\right)^{3} + 201 \, \sin\left(d x + c\right)^{2} + 255 \, \sin\left(d x + c\right) + 117}{a {\left(\sin\left(d x + c\right) + 1\right)}^{3}}}{192 \, d}"," ",0,"1/192*(30*log(abs(sin(d*x + c) + 1))/a - 30*log(abs(sin(d*x + c) - 1))/a + 3*(15*sin(d*x + c)^2 - 38*sin(d*x + c) + 25)/(a*(sin(d*x + c) - 1)^2) - (55*sin(d*x + c)^3 + 201*sin(d*x + c)^2 + 255*sin(d*x + c) + 117)/(a*(sin(d*x + c) + 1)^3))/d","A",0
62,1,179,0,0.801656," ","integrate(cos(d*x+c)^8/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{105 \, {\left(d x + c\right)}}{a^{2}} - \frac{2 \, {\left(135 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 480 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 445 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 480 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 330 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 330 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 960 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 445 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 96 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 135 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} a^{2}}}{240 \, d}"," ",0,"1/240*(105*(d*x + c)/a^2 - 2*(135*tan(1/2*d*x + 1/2*c)^11 - 480*tan(1/2*d*x + 1/2*c)^10 + 445*tan(1/2*d*x + 1/2*c)^9 - 480*tan(1/2*d*x + 1/2*c)^8 - 330*tan(1/2*d*x + 1/2*c)^7 - 960*tan(1/2*d*x + 1/2*c)^6 + 330*tan(1/2*d*x + 1/2*c)^5 - 960*tan(1/2*d*x + 1/2*c)^4 - 445*tan(1/2*d*x + 1/2*c)^3 - 96*tan(1/2*d*x + 1/2*c)^2 - 135*tan(1/2*d*x + 1/2*c) - 96)/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*a^2))/d","A",0
63,1,47,0,1.010840," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, \sin\left(d x + c\right)^{5} - 5 \, \sin\left(d x + c\right)^{4} + 10 \, \sin\left(d x + c\right)^{2} - 10 \, \sin\left(d x + c\right)}{10 \, a^{2} d}"," ",0,"-1/10*(2*sin(d*x + c)^5 - 5*sin(d*x + c)^4 + 10*sin(d*x + c)^2 - 10*sin(d*x + c))/(a^2*d)","A",0
64,1,127,0,0.647014," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(d x + c\right)}}{a^{2}} - \frac{2 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 33 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 33 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 16\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{2}}}{24 \, d}"," ",0,"1/24*(15*(d*x + c)/a^2 - 2*(9*tan(1/2*d*x + 1/2*c)^7 - 48*tan(1/2*d*x + 1/2*c)^6 + 33*tan(1/2*d*x + 1/2*c)^5 - 48*tan(1/2*d*x + 1/2*c)^4 - 33*tan(1/2*d*x + 1/2*c)^3 - 16*tan(1/2*d*x + 1/2*c)^2 - 9*tan(1/2*d*x + 1/2*c) - 16)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^2))/d","A",0
65,1,35,0,1.971316," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right)}{3 \, a^{2} d}"," ",0,"1/3*(sin(d*x + c)^3 - 3*sin(d*x + c)^2 + 3*sin(d*x + c))/(a^2*d)","A",0
66,1,73,0,0.361962," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}}}{2 \, d}"," ",0,"1/2*(3*(d*x + c)/a^2 + 2*(tan(1/2*d*x + 1/2*c)^3 + 4*tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c) + 4)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2))/d","A",0
67,1,54,0,0.425445," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, \log\left(\frac{{\left| a \sin\left(d x + c\right) + a \right|}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2} {\left| a \right|}}\right)}{a^{2}} + \frac{a \sin\left(d x + c\right) + a}{a^{3}}}{d}"," ",0,"-(2*log(abs(a*sin(d*x + c) + a)/((a*sin(d*x + c) + a)^2*abs(a)))/a^2 + (a*sin(d*x + c) + a)/a^3)/d","A",0
68,1,33,0,0.488354," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{d x + c}{a^{2}} + \frac{4}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}}{d}"," ",0,"-((d*x + c)/a^2 + 4/(a^2*(tan(1/2*d*x + 1/2*c) + 1)))/d","A",0
69,1,20,0,0.424725," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{1}{{\left(a \sin\left(d x + c\right) + a\right)} a d}"," ",0,"-1/((a*sin(d*x + c) + a)*a*d)","A",0
70,1,71,0,0.748414," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2}} - \frac{2 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2}} - \frac{3 \, \sin\left(d x + c\right)^{2} + 10 \, \sin\left(d x + c\right) + 11}{a^{2} {\left(\sin\left(d x + c\right) + 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(2*log(abs(sin(d*x + c) + 1))/a^2 - 2*log(abs(sin(d*x + c) - 1))/a^2 - (3*sin(d*x + c)^2 + 10*sin(d*x + c) + 11)/(a^2*(sin(d*x + c) + 1)^2))/d","A",0
71,1,93,0,0.380619," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{5}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} + \frac{35 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 90 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 70 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{20 \, d}"," ",0,"-1/20*(5/(a^2*(tan(1/2*d*x + 1/2*c) - 1)) + (35*tan(1/2*d*x + 1/2*c)^4 + 90*tan(1/2*d*x + 1/2*c)^3 + 120*tan(1/2*d*x + 1/2*c)^2 + 70*tan(1/2*d*x + 1/2*c) + 21)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
72,1,106,0,0.806018," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2}} + \frac{3 \, {\left(2 \, \sin\left(d x + c\right) - 3\right)}}{a^{2} {\left(\sin\left(d x + c\right) - 1\right)}} - \frac{11 \, \sin\left(d x + c\right)^{3} + 42 \, \sin\left(d x + c\right)^{2} + 57 \, \sin\left(d x + c\right) + 30}{a^{2} {\left(\sin\left(d x + c\right) + 1\right)}^{3}}}{48 \, d}"," ",0,"1/48*(6*log(abs(sin(d*x + c) + 1))/a^2 - 6*log(abs(sin(d*x + c) - 1))/a^2 + 3*(2*sin(d*x + c) - 3)/(a^2*(sin(d*x + c) - 1)) - (11*sin(d*x + c)^3 + 42*sin(d*x + c)^2 + 57*sin(d*x + c) + 30)/(a^2*(sin(d*x + c) + 1)^3))/d","A",0
73,1,145,0,0.783860," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{7 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{273 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1155 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2450 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2870 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2037 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 791 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 152}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{168 \, d}"," ",0,"-1/168*(7*(9*tan(1/2*d*x + 1/2*c)^2 - 15*tan(1/2*d*x + 1/2*c) + 8)/(a^2*(tan(1/2*d*x + 1/2*c) - 1)^3) + (273*tan(1/2*d*x + 1/2*c)^6 + 1155*tan(1/2*d*x + 1/2*c)^5 + 2450*tan(1/2*d*x + 1/2*c)^4 + 2870*tan(1/2*d*x + 1/2*c)^3 + 2037*tan(1/2*d*x + 1/2*c)^2 + 791*tan(1/2*d*x + 1/2*c) + 152)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
74,1,126,0,0.536132," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{60 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2}} - \frac{60 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2}} + \frac{2 \, {\left(45 \, \sin\left(d x + c\right)^{2} - 110 \, \sin\left(d x + c\right) + 69\right)}}{a^{2} {\left(\sin\left(d x + c\right) - 1\right)}^{2}} - \frac{125 \, \sin\left(d x + c\right)^{4} + 580 \, \sin\left(d x + c\right)^{3} + 1038 \, \sin\left(d x + c\right)^{2} + 868 \, \sin\left(d x + c\right) + 301}{a^{2} {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{512 \, d}"," ",0,"1/512*(60*log(abs(sin(d*x + c) + 1))/a^2 - 60*log(abs(sin(d*x + c) - 1))/a^2 + 2*(45*sin(d*x + c)^2 - 110*sin(d*x + c) + 69)/(a^2*(sin(d*x + c) - 1)^2) - (125*sin(d*x + c)^4 + 580*sin(d*x + c)^3 + 1038*sin(d*x + c)^2 + 868*sin(d*x + c) + 301)/(a^2*(sin(d*x + c) + 1)^4))/d","A",0
75,1,140,0,0.387996," ","integrate(cos(d*x+c)^8/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{105 \, {\left(d x + c\right)}}{a^{3}} - \frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 390 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 400 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 390 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 136\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5} a^{3}}}{120 \, d}"," ",0,"1/120*(105*(d*x + c)/a^3 - 2*(15*tan(1/2*d*x + 1/2*c)^9 - 360*tan(1/2*d*x + 1/2*c)^8 + 390*tan(1/2*d*x + 1/2*c)^7 - 960*tan(1/2*d*x + 1/2*c)^6 - 400*tan(1/2*d*x + 1/2*c)^4 - 390*tan(1/2*d*x + 1/2*c)^3 - 320*tan(1/2*d*x + 1/2*c)^2 - 15*tan(1/2*d*x + 1/2*c) - 136)/((tan(1/2*d*x + 1/2*c)^2 + 1)^5*a^3))/d","A",0
76,1,45,0,0.744596," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{3} + 6 \, \sin\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right)}{4 \, a^{3} d}"," ",0,"-1/4*(sin(d*x + c)^4 - 4*sin(d*x + c)^3 + 6*sin(d*x + c)^2 - 4*sin(d*x + c))/(a^3*d)","B",0
77,1,88,0,0.424352," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(d x + c\right)}}{a^{3}} + \frac{2 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 48 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 22\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{3}}}{6 \, d}"," ",0,"1/6*(15*(d*x + c)/a^3 + 2*(9*tan(1/2*d*x + 1/2*c)^5 + 18*tan(1/2*d*x + 1/2*c)^4 + 48*tan(1/2*d*x + 1/2*c)^2 - 9*tan(1/2*d*x + 1/2*c) + 22)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^3))/d","A",0
78,1,115,0,2.668722," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{2 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}{a^{3}} - \frac{4 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}}\right)}}{d}"," ",0,"-2*(2*log(tan(1/2*d*x + 1/2*c)^2 + 1)/a^3 - 4*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - (3*tan(1/2*d*x + 1/2*c)^4 - 3*tan(1/2*d*x + 1/2*c)^3 + 7*tan(1/2*d*x + 1/2*c)^2 - 3*tan(1/2*d*x + 1/2*c) + 3)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3))/d","B",0
79,1,80,0,2.084370," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)}}{a^{3}} + \frac{2 \, {\left(4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} a^{3}}}{d}"," ",0,"-(3*(d*x + c)/a^3 + 2*(4*tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) + 5)/((tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) + 1)*a^3))/d","A",0
80,1,35,0,1.251988," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3}} + \frac{2}{a^{3} {\left(\sin\left(d x + c\right) + 1\right)}}}{d}"," ",0,"-(log(abs(sin(d*x + c) + 1))/a^3 + 2/(a^3*(sin(d*x + c) + 1)))/d","A",0
81,1,36,0,0.553137," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}}{3 \, a^{3} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}}"," ",0,"-2/3*(3*tan(1/2*d*x + 1/2*c)^2 + 1)/(a^3*d*(tan(1/2*d*x + 1/2*c) + 1)^3)","A",0
82,1,20,0,2.911094," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{1}{2 \, {\left(a \sin\left(d x + c\right) + a\right)}^{2} a d}"," ",0,"-1/2/((a*sin(d*x + c) + a)^2*a*d)","A",0
83,1,81,0,1.442375," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{6 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3}} - \frac{6 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3}} - \frac{11 \, \sin\left(d x + c\right)^{3} + 45 \, \sin\left(d x + c\right)^{2} + 69 \, \sin\left(d x + c\right) + 51}{a^{3} {\left(\sin\left(d x + c\right) + 1\right)}^{3}}}{96 \, d}"," ",0,"1/96*(6*log(abs(sin(d*x + c) + 1))/a^3 - 6*log(abs(sin(d*x + c) - 1))/a^3 - (11*sin(d*x + c)^3 + 45*sin(d*x + c)^2 + 69*sin(d*x + c) + 51)/(a^3*(sin(d*x + c) + 1)^3))/d","A",0
84,1,119,0,0.475880," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{35}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} + \frac{525 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1960 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4025 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4480 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3143 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1176 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 243}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{280 \, d}"," ",0,"-1/280*(35/(a^3*(tan(1/2*d*x + 1/2*c) - 1)) + (525*tan(1/2*d*x + 1/2*c)^6 + 1960*tan(1/2*d*x + 1/2*c)^5 + 4025*tan(1/2*d*x + 1/2*c)^4 + 4480*tan(1/2*d*x + 1/2*c)^3 + 3143*tan(1/2*d*x + 1/2*c)^2 + 1176*tan(1/2*d*x + 1/2*c) + 243)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
85,1,116,0,0.743765," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3}} - \frac{60 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3}} + \frac{12 \, {\left(5 \, \sin\left(d x + c\right) - 7\right)}}{a^{3} {\left(\sin\left(d x + c\right) - 1\right)}} - \frac{125 \, \sin\left(d x + c\right)^{4} + 596 \, \sin\left(d x + c\right)^{3} + 1110 \, \sin\left(d x + c\right)^{2} + 996 \, \sin\left(d x + c\right) + 405}{a^{3} {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{768 \, d}"," ",0,"1/768*(60*log(abs(sin(d*x + c) + 1))/a^3 - 60*log(abs(sin(d*x + c) - 1))/a^3 + 12*(5*sin(d*x + c) - 7)/(a^3*(sin(d*x + c) - 1)) - (125*sin(d*x + c)^4 + 596*sin(d*x + c)^3 + 1110*sin(d*x + c)^2 + 996*sin(d*x + c) + 405)/(a^3*(sin(d*x + c) + 1)^4))/d","A",0
86,1,171,0,0.748776," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{21 \, {\left(21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{3591 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 19656 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 56196 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 95760 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 107730 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 79464 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 38484 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10944 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1615}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{9}}}{2016 \, d}"," ",0,"-1/2016*(21*(21*tan(1/2*d*x + 1/2*c)^2 - 36*tan(1/2*d*x + 1/2*c) + 19)/(a^3*(tan(1/2*d*x + 1/2*c) - 1)^3) + (3591*tan(1/2*d*x + 1/2*c)^8 + 19656*tan(1/2*d*x + 1/2*c)^7 + 56196*tan(1/2*d*x + 1/2*c)^6 + 95760*tan(1/2*d*x + 1/2*c)^5 + 107730*tan(1/2*d*x + 1/2*c)^4 + 79464*tan(1/2*d*x + 1/2*c)^3 + 38484*tan(1/2*d*x + 1/2*c)^2 + 10944*tan(1/2*d*x + 1/2*c) + 1615)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^9))/d","A",0
87,1,136,0,0.705012," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{420 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3}} - \frac{420 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3}} + \frac{10 \, {\left(63 \, \sin\left(d x + c\right)^{2} - 150 \, \sin\left(d x + c\right) + 91\right)}}{a^{3} {\left(\sin\left(d x + c\right) - 1\right)}^{2}} - \frac{959 \, \sin\left(d x + c\right)^{5} + 5395 \, \sin\left(d x + c\right)^{4} + 12390 \, \sin\left(d x + c\right)^{3} + 14710 \, \sin\left(d x + c\right)^{2} + 9275 \, \sin\left(d x + c\right) + 2647}{a^{3} {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{5120 \, d}"," ",0,"1/5120*(420*log(abs(sin(d*x + c) + 1))/a^3 - 420*log(abs(sin(d*x + c) - 1))/a^3 + 10*(63*sin(d*x + c)^2 - 150*sin(d*x + c) + 91)/(a^3*(sin(d*x + c) - 1)^2) - (959*sin(d*x + c)^5 + 5395*sin(d*x + c)^4 + 12390*sin(d*x + c)^3 + 14710*sin(d*x + c)^2 + 9275*sin(d*x + c) + 2647)/(a^3*(sin(d*x + c) + 1)^5))/d","A",0
88,1,99,0,1.178839," ","integrate(cos(d*x+c)^8/(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{\frac{105 \, {\left(d x + c\right)}}{a^{8}} + \frac{16 \, {\left(105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 175 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 490 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 294 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 133 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19\right)}}{a^{8} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{105 \, d}"," ",0,"1/105*(105*(d*x + c)/a^8 + 16*(105*tan(1/2*d*x + 1/2*c)^5 + 175*tan(1/2*d*x + 1/2*c)^4 + 490*tan(1/2*d*x + 1/2*c)^3 + 294*tan(1/2*d*x + 1/2*c)^2 + 133*tan(1/2*d*x + 1/2*c) + 19)/(a^8*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
89,1,68,0,1.398450," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{8} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{8}}"," ",0,"2*(tan(1/2*d*x + 1/2*c)^7 + 7*tan(1/2*d*x + 1/2*c)^5 + 7*tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))/(a^8*d*(tan(1/2*d*x + 1/2*c) + 1)^8)","A",0
90,1,125,0,0.610444," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{2 \, {\left(63 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 63 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 483 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 315 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 693 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 189 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 225 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8\right)}}{63 \, a^{8} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{9}}"," ",0,"-2/63*(63*tan(1/2*d*x + 1/2*c)^8 + 63*tan(1/2*d*x + 1/2*c)^7 + 483*tan(1/2*d*x + 1/2*c)^6 + 315*tan(1/2*d*x + 1/2*c)^5 + 693*tan(1/2*d*x + 1/2*c)^4 + 189*tan(1/2*d*x + 1/2*c)^3 + 225*tan(1/2*d*x + 1/2*c)^2 + 9*tan(1/2*d*x + 1/2*c) + 8)/(a^8*d*(tan(1/2*d*x + 1/2*c) + 1)^9)","B",0
91,1,137,0,1.443411," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 30 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 140 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 170 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 282 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 170 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 140 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{15 \, a^{8} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{10}}"," ",0,"2/15*(15*tan(1/2*d*x + 1/2*c)^9 + 30*tan(1/2*d*x + 1/2*c)^8 + 140*tan(1/2*d*x + 1/2*c)^7 + 170*tan(1/2*d*x + 1/2*c)^6 + 282*tan(1/2*d*x + 1/2*c)^5 + 170*tan(1/2*d*x + 1/2*c)^4 + 140*tan(1/2*d*x + 1/2*c)^3 + 30*tan(1/2*d*x + 1/2*c)^2 + 15*tan(1/2*d*x + 1/2*c))/(a^8*d*(tan(1/2*d*x + 1/2*c) + 1)^10)","B",0
92,1,151,0,0.595946," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{2 \, {\left(1155 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 3465 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 13860 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 23100 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 37422 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 32802 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27060 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 11220 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4895 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 517 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 152\right)}}{1155 \, a^{8} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{11}}"," ",0,"-2/1155*(1155*tan(1/2*d*x + 1/2*c)^10 + 3465*tan(1/2*d*x + 1/2*c)^9 + 13860*tan(1/2*d*x + 1/2*c)^8 + 23100*tan(1/2*d*x + 1/2*c)^7 + 37422*tan(1/2*d*x + 1/2*c)^6 + 32802*tan(1/2*d*x + 1/2*c)^5 + 27060*tan(1/2*d*x + 1/2*c)^4 + 11220*tan(1/2*d*x + 1/2*c)^3 + 4895*tan(1/2*d*x + 1/2*c)^2 + 517*tan(1/2*d*x + 1/2*c) + 152)/(a^8*d*(tan(1/2*d*x + 1/2*c) + 1)^11)","A",0
93,1,28,0,0.586230," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{3 \, \sin\left(d x + c\right) - 2}{15 \, a^{8} d {\left(\sin\left(d x + c\right) + 1\right)}^{6}}"," ",0,"1/15*(3*sin(d*x + c) - 2)/(a^8*d*(sin(d*x + c) + 1)^6)","A",0
94,1,177,0,0.782063," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{2 \, {\left(9009 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 45045 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 183183 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 435435 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 810810 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 1051050 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1076790 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 785070 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 451165 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 171457 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 51675 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7111 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1240\right)}}{9009 \, a^{8} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{13}}"," ",0,"-2/9009*(9009*tan(1/2*d*x + 1/2*c)^12 + 45045*tan(1/2*d*x + 1/2*c)^11 + 183183*tan(1/2*d*x + 1/2*c)^10 + 435435*tan(1/2*d*x + 1/2*c)^9 + 810810*tan(1/2*d*x + 1/2*c)^8 + 1051050*tan(1/2*d*x + 1/2*c)^7 + 1076790*tan(1/2*d*x + 1/2*c)^6 + 785070*tan(1/2*d*x + 1/2*c)^5 + 451165*tan(1/2*d*x + 1/2*c)^4 + 171457*tan(1/2*d*x + 1/2*c)^3 + 51675*tan(1/2*d*x + 1/2*c)^2 + 7111*tan(1/2*d*x + 1/2*c) + 1240)/(a^8*d*(tan(1/2*d*x + 1/2*c) + 1)^13)","A",0
95,1,20,0,0.491183," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{1}{7 \, {\left(a \sin\left(d x + c\right) + a\right)}^{7} a d}"," ",0,"-1/7/((a*sin(d*x + c) + a)^7*a*d)","A",0
96,1,131,0,0.469726," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{\frac{840 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{8}} - \frac{840 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{8}} - \frac{2283 \, \sin\left(d x + c\right)^{8} + 19944 \, \sin\left(d x + c\right)^{7} + 77364 \, \sin\left(d x + c\right)^{6} + 175448 \, \sin\left(d x + c\right)^{5} + 258370 \, \sin\left(d x + c\right)^{4} + 261464 \, \sin\left(d x + c\right)^{3} + 192052 \, \sin\left(d x + c\right)^{2} + 114152 \, \sin\left(d x + c\right) + 67819}{a^{8} {\left(\sin\left(d x + c\right) + 1\right)}^{8}}}{430080 \, d}"," ",0,"1/430080*(840*log(abs(sin(d*x + c) + 1))/a^8 - 840*log(abs(sin(d*x + c) - 1))/a^8 - (2283*sin(d*x + c)^8 + 19944*sin(d*x + c)^7 + 77364*sin(d*x + c)^6 + 175448*sin(d*x + c)^5 + 258370*sin(d*x + c)^4 + 261464*sin(d*x + c)^3 + 192052*sin(d*x + c)^2 + 114152*sin(d*x + c) + 67819)/(a^8*(sin(d*x + c) + 1)^8))/d","A",0
97,1,249,0,1.524046," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{\frac{12155}{a^{8} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} + \frac{6211205 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{16} + 55791450 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 303072770 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} + 1091397450 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2909561798 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 5901218466 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 9405145178 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 11877161010 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 12017308160 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 9710430158 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6263238566 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3172666718 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1247921210 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 365303990 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 77883902 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10498214 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 982907}{a^{8} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{17}}}{3111680 \, d}"," ",0,"-1/3111680*(12155/(a^8*(tan(1/2*d*x + 1/2*c) - 1)) + (6211205*tan(1/2*d*x + 1/2*c)^16 + 55791450*tan(1/2*d*x + 1/2*c)^15 + 303072770*tan(1/2*d*x + 1/2*c)^14 + 1091397450*tan(1/2*d*x + 1/2*c)^13 + 2909561798*tan(1/2*d*x + 1/2*c)^12 + 5901218466*tan(1/2*d*x + 1/2*c)^11 + 9405145178*tan(1/2*d*x + 1/2*c)^10 + 11877161010*tan(1/2*d*x + 1/2*c)^9 + 12017308160*tan(1/2*d*x + 1/2*c)^8 + 9710430158*tan(1/2*d*x + 1/2*c)^7 + 6263238566*tan(1/2*d*x + 1/2*c)^6 + 3172666718*tan(1/2*d*x + 1/2*c)^5 + 1247921210*tan(1/2*d*x + 1/2*c)^4 + 365303990*tan(1/2*d*x + 1/2*c)^3 + 77883902*tan(1/2*d*x + 1/2*c)^2 + 10498214*tan(1/2*d*x + 1/2*c) + 982907)/(a^8*(tan(1/2*d*x + 1/2*c) + 1)^17))/d","A",0
98,1,166,0,0.573524," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{\frac{2520 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{8}} - \frac{2520 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{8}} + \frac{504 \, {\left(5 \, \sin\left(d x + c\right) - 6\right)}}{a^{8} {\left(\sin\left(d x + c\right) - 1\right)}} - \frac{7129 \, \sin\left(d x + c\right)^{9} + 68697 \, \sin\left(d x + c\right)^{8} + 296964 \, \sin\left(d x + c\right)^{7} + 758772 \, \sin\left(d x + c\right)^{6} + 1271214 \, \sin\left(d x + c\right)^{5} + 1465758 \, \sin\left(d x + c\right)^{4} + 1191540 \, \sin\left(d x + c\right)^{3} + 693828 \, \sin\left(d x + c\right)^{2} + 295425 \, \sin\left(d x + c\right) + 89553}{a^{8} {\left(\sin\left(d x + c\right) + 1\right)}^{9}}}{516096 \, d}"," ",0,"1/516096*(2520*log(abs(sin(d*x + c) + 1))/a^8 - 2520*log(abs(sin(d*x + c) - 1))/a^8 + 504*(5*sin(d*x + c) - 6)/(a^8*(sin(d*x + c) - 1)) - (7129*sin(d*x + c)^9 + 68697*sin(d*x + c)^8 + 296964*sin(d*x + c)^7 + 758772*sin(d*x + c)^6 + 1271214*sin(d*x + c)^5 + 1465758*sin(d*x + c)^4 + 1191540*sin(d*x + c)^3 + 693828*sin(d*x + c)^2 + 295425*sin(d*x + c) + 89553)/(a^8*(sin(d*x + c) + 1)^9))/d","A",0
99,1,301,0,1.051153," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{\frac{4199 \, {\left(18 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 33 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17\right)}}{a^{8} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{12823746 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{18} + 140368371 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} + 879644311 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{16} + 3693272440 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 11467502592 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} + 27403194676 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 51919375300 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 79183835016 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 98304418212 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 99750226290 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 82860874122 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 56110430792 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30766700912 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 13462452660 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4616712644 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1197851960 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 226248618 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 27911475 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2143959}{a^{8} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{19}}}{6449664 \, d}"," ",0,"-1/6449664*(4199*(18*tan(1/2*d*x + 1/2*c)^2 - 33*tan(1/2*d*x + 1/2*c) + 17)/(a^8*(tan(1/2*d*x + 1/2*c) - 1)^3) + (12823746*tan(1/2*d*x + 1/2*c)^18 + 140368371*tan(1/2*d*x + 1/2*c)^17 + 879644311*tan(1/2*d*x + 1/2*c)^16 + 3693272440*tan(1/2*d*x + 1/2*c)^15 + 11467502592*tan(1/2*d*x + 1/2*c)^14 + 27403194676*tan(1/2*d*x + 1/2*c)^13 + 51919375300*tan(1/2*d*x + 1/2*c)^12 + 79183835016*tan(1/2*d*x + 1/2*c)^11 + 98304418212*tan(1/2*d*x + 1/2*c)^10 + 99750226290*tan(1/2*d*x + 1/2*c)^9 + 82860874122*tan(1/2*d*x + 1/2*c)^8 + 56110430792*tan(1/2*d*x + 1/2*c)^7 + 30766700912*tan(1/2*d*x + 1/2*c)^6 + 13462452660*tan(1/2*d*x + 1/2*c)^5 + 4616712644*tan(1/2*d*x + 1/2*c)^4 + 1197851960*tan(1/2*d*x + 1/2*c)^3 + 226248618*tan(1/2*d*x + 1/2*c)^2 + 27911475*tan(1/2*d*x + 1/2*c) + 2143959)/(a^8*(tan(1/2*d*x + 1/2*c) + 1)^19))/d","A",0
100,1,186,0,0.623763," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{\frac{27720 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{8}} - \frac{27720 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{8}} + \frac{420 \, {\left(99 \, \sin\left(d x + c\right)^{2} - 220 \, \sin\left(d x + c\right) + 123\right)}}{a^{8} {\left(\sin\left(d x + c\right) - 1\right)}^{2}} - \frac{81191 \, \sin\left(d x + c\right)^{10} + 858110 \, \sin\left(d x + c\right)^{9} + 4107195 \, \sin\left(d x + c\right)^{8} + 11748840 \, \sin\left(d x + c\right)^{7} + 22318590 \, \sin\left(d x + c\right)^{6} + 29583540 \, \sin\left(d x + c\right)^{5} + 27983550 \, \sin\left(d x + c\right)^{4} + 19002600 \, \sin\left(d x + c\right)^{3} + 9206235 \, \sin\left(d x + c\right)^{2} + 3108990 \, \sin\left(d x + c\right) + 648327}{a^{8} {\left(\sin\left(d x + c\right) + 1\right)}^{10}}}{3440640 \, d}"," ",0,"1/3440640*(27720*log(abs(sin(d*x + c) + 1))/a^8 - 27720*log(abs(sin(d*x + c) - 1))/a^8 + 420*(99*sin(d*x + c)^2 - 220*sin(d*x + c) + 123)/(a^8*(sin(d*x + c) - 1)^2) - (81191*sin(d*x + c)^10 + 858110*sin(d*x + c)^9 + 4107195*sin(d*x + c)^8 + 11748840*sin(d*x + c)^7 + 22318590*sin(d*x + c)^6 + 29583540*sin(d*x + c)^5 + 27983550*sin(d*x + c)^4 + 19002600*sin(d*x + c)^3 + 9206235*sin(d*x + c)^2 + 3108990*sin(d*x + c) + 648327)/(a^8*(sin(d*x + c) + 1)^10))/d","A",0
101,1,249,0,2.626877," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{1}{411840} \, \sqrt{2} \sqrt{a} {\left(\frac{495 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right)}{d} + \frac{5005 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{27027 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{225225 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{429 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{15}{2} \, d x + \frac{15}{2} \, c\right)}{d} + \frac{4095 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{19305 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{75075 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d}\right)}"," ",0,"1/411840*sqrt(2)*sqrt(a)*(495*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 13/2*d*x + 13/2*c)/d + 5005*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 9/2*d*x + 9/2*c)/d + 27027*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 5/2*d*x + 5/2*c)/d + 225225*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 1/2*d*x + 1/2*c)/d + 429*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 15/2*d*x + 15/2*c)/d + 4095*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 11/2*d*x + 11/2*c)/d + 19305*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 7/2*d*x + 7/2*c)/d + 75075*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 3/2*d*x + 3/2*c)/d)","B",0
102,1,219,0,1.119190," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{1}{96096} \, \sqrt{2} \sqrt{a} {\left(\frac{273 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{2574 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{15015 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{231 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right)}{d} + \frac{2002 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{9009 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{60060 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)}"," ",0,"1/96096*sqrt(2)*sqrt(a)*(273*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 11/2*d*x + 11/2*c)/d + 2574*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d + 15015*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d + 231*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 13/2*d*x + 13/2*c)/d + 2002*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d + 9009*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d + 60060*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)","A",0
103,1,189,0,1.695920," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{1}{11088} \, \sqrt{2} \sqrt{a} {\left(\frac{77 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{693 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{6930 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{63 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{495 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{2310 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d}\right)}"," ",0,"1/11088*sqrt(2)*sqrt(a)*(77*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 9/2*d*x + 9/2*c)/d + 693*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 5/2*d*x + 5/2*c)/d + 6930*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 1/2*d*x + 1/2*c)/d + 63*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 11/2*d*x + 11/2*c)/d + 495*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 7/2*d*x + 7/2*c)/d + 2310*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 3/2*d*x + 3/2*c)/d)","B",0
104,1,159,0,1.094443," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{1}{2520} \, \sqrt{2} \sqrt{a} {\left(\frac{45 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{420 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{35 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{252 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{1890 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)}"," ",0,"1/2520*sqrt(2)*sqrt(a)*(45*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d + 420*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d + 35*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d + 252*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d + 1890*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)","A",0
105,1,129,0,0.690173," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{1}{140} \, \sqrt{2} \sqrt{a} {\left(\frac{7 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{105 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{5 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{35 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d}\right)}"," ",0,"1/140*sqrt(2)*sqrt(a)*(7*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 5/2*d*x + 5/2*c)/d + 105*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 1/2*d*x + 1/2*c)/d + 5*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 7/2*d*x + 7/2*c)/d + 35*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 3/2*d*x + 3/2*c)/d)","B",0
106,1,99,0,0.397737," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{1}{30} \, \sqrt{2} \sqrt{a} {\left(\frac{5 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{3 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{30 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)}"," ",0,"1/30*sqrt(2)*sqrt(a)*(5*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d + 3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d + 30*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)","A",0
107,1,68,0,0.920134," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{2} \sqrt{a} {\left(\frac{3 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{\mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d}\right)}"," ",0,"1/3*sqrt(2)*sqrt(a)*(3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 1/2*d*x + 1/2*c)/d + sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 3/2*d*x + 3/2*c)/d)","B",0
108,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)-sqrt(2*a)*sign(cos(1/2*(d*x+c)-1/4*pi))*ln(abs(tan(1/2*(1/2*d*x+1/4*(2*c-pi)))))/d","F(-2)",0
109,1,102,0,0.523204," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\log\left({\left| \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - \log\left({\left| \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - \frac{2 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{\sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}\right)} \sqrt{a}}{4 \, d}"," ",0,"1/4*sqrt(2)*(log(abs(sin(-1/4*pi + 1/2*d*x + 1/2*c) + 1))*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)) - log(abs(sin(-1/4*pi + 1/2*d*x + 1/2*c) - 1))*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)) - 2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/sin(-1/4*pi + 1/2*d*x + 1/2*c))*sqrt(a)/d","A",0
110,1,282,0,0.871194," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(6 \, \log\left(\frac{{\left| -\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}}{{\left| \cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}}\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - \frac{{\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} + \frac{\frac{14 \, {\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} - \frac{3 \, {\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{{\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{2}} + \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{\frac{\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} + \frac{{\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{2}}{{\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{2}}}\right)} \sqrt{a}}{32 \, d}"," ",0,"-1/32*sqrt(2)*(6*log(abs(-cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1)/abs(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1))*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)) - (cos(-1/4*pi + 1/2*d*x + 1/2*c) - 1)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1) + (14*(cos(-1/4*pi + 1/2*d*x + 1/2*c) - 1)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1) - 3*(cos(-1/4*pi + 1/2*d*x + 1/2*c) - 1)^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1)^2 + sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)))/((cos(-1/4*pi + 1/2*d*x + 1/2*c) - 1)/(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1) + (cos(-1/4*pi + 1/2*d*x + 1/2*c) - 1)^2/(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1)^2))*sqrt(a)/d","B",0
111,1,178,0,0.773346," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(15 \, \log\left({\left| \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 15 \, \log\left({\left| \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - \frac{6 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - \frac{4 \, {\left(6 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)}}{\sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}\right)} \sqrt{a}}{96 \, d}"," ",0,"1/96*sqrt(2)*(15*log(abs(sin(-1/4*pi + 1/2*d*x + 1/2*c) + 1))*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)) - 15*log(abs(sin(-1/4*pi + 1/2*d*x + 1/2*c) - 1))*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)) - 6*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/(sin(-1/4*pi + 1/2*d*x + 1/2*c)^2 - 1) - 4*(6*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)^2 + sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)))/sin(-1/4*pi + 1/2*d*x + 1/2*c)^3)*sqrt(a)/d","A",0
112,1,442,0,2.746830," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(420 \, \log\left(\frac{{\left| -\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}}{{\left| \cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}}\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + \frac{3 \, {\left(\frac{24 \, {\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} - \frac{210 \, {\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{{\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{2}} - \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} {\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{2}}{{\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{2}} - \frac{72 \, {\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} + \frac{3 \, {\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{{\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{2}} + \frac{256 \, {\left(\frac{9 \, {\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} + \frac{6 \, {\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{{\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{2}} + 5 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)}}{{\left(\frac{\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} + 1\right)}^{3}}\right)} \sqrt{a}}{3072 \, d}"," ",0,"-1/3072*sqrt(2)*(420*log(abs(-cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1)/abs(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1))*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)) + 3*(24*(cos(-1/4*pi + 1/2*d*x + 1/2*c) - 1)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1) - 210*(cos(-1/4*pi + 1/2*d*x + 1/2*c) - 1)^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1)^2 - sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)))*(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1)^2/(cos(-1/4*pi + 1/2*d*x + 1/2*c) - 1)^2 - 72*(cos(-1/4*pi + 1/2*d*x + 1/2*c) - 1)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1) + 3*(cos(-1/4*pi + 1/2*d*x + 1/2*c) - 1)^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1)^2 + 256*(9*(cos(-1/4*pi + 1/2*d*x + 1/2*c) - 1)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1) + 6*(cos(-1/4*pi + 1/2*d*x + 1/2*c) - 1)^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1)^2 + 5*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)))/((cos(-1/4*pi + 1/2*d*x + 1/2*c) - 1)/(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1) + 1)^3)*sqrt(a)/d","B",0
113,1,239,0,2.531092," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(315 \, \log\left({\left| \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 315 \, \log\left({\left| \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - \frac{10 \, {\left(15 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 17 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} - \frac{16 \, {\left(30 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 5 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)}}{\sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}\right)} \sqrt{a}}{2560 \, d}"," ",0,"1/2560*sqrt(2)*(315*log(abs(sin(-1/4*pi + 1/2*d*x + 1/2*c) + 1))*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)) - 315*log(abs(sin(-1/4*pi + 1/2*d*x + 1/2*c) - 1))*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)) - 10*(15*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)^3 - 17*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c))/(sin(-1/4*pi + 1/2*d*x + 1/2*c)^2 - 1)^2 - 16*(30*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)^4 + 5*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)^2 + sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)))/sin(-1/4*pi + 1/2*d*x + 1/2*c)^5)*sqrt(a)/d","A",0
114,1,505,0,1.113586," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{1}{14002560} \, \sqrt{2} {\left(\frac{7293 \, a \cos\left(\frac{1}{4} \, \pi + \frac{15}{2} \, d x + \frac{15}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{59670 \, a \cos\left(\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{218790 \, a \cos\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{510510 \, a \cos\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{6435 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{17}{2} \, d x + \frac{17}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{50490 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{170170 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{306306 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{16830 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right)}{d} - \frac{170170 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} - \frac{918918 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} - \frac{7657650 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} - \frac{14586 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{15}{2} \, d x + \frac{15}{2} \, c\right)}{d} - \frac{139230 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} - \frac{656370 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} - \frac{2552550 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/14002560*sqrt(2)*(7293*a*cos(1/4*pi + 15/2*d*x + 15/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 59670*a*cos(1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 218790*a*cos(1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 510510*a*cos(1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 6435*a*cos(-1/4*pi + 17/2*d*x + 17/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 50490*a*cos(-1/4*pi + 13/2*d*x + 13/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 170170*a*cos(-1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 306306*a*cos(-1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 16830*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 13/2*d*x + 13/2*c)/d - 170170*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 9/2*d*x + 9/2*c)/d - 918918*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 5/2*d*x + 5/2*c)/d - 7657650*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 1/2*d*x + 1/2*c)/d - 14586*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 15/2*d*x + 15/2*c)/d - 139230*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 11/2*d*x + 11/2*c)/d - 656370*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 7/2*d*x + 7/2*c)/d - 2552550*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 3/2*d*x + 3/2*c)/d)*sqrt(a)","B",0
115,1,474,0,1.340194," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{1}{2882880} \, \sqrt{2} {\left(\frac{3465 \, a \cos\left(\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{25025 \, a \cos\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{81081 \, a \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{225225 \, a \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{3003 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{15}{2} \, d x + \frac{15}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{20475 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{57915 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{75075 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{8190 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} - \frac{77220 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} - \frac{450450 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} - \frac{6930 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right)}{d} - \frac{60060 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} - \frac{270270 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} - \frac{1801800 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/2882880*sqrt(2)*(3465*a*cos(1/4*pi + 13/2*d*x + 13/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 25025*a*cos(1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 81081*a*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 225225*a*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 3003*a*cos(-1/4*pi + 15/2*d*x + 15/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 20475*a*cos(-1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 57915*a*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 75075*a*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 8190*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 11/2*d*x + 11/2*c)/d - 77220*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d - 450450*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d - 6930*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 13/2*d*x + 13/2*c)/d - 60060*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d - 270270*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d - 1801800*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
116,1,381,0,1.025192," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{1}{288288} \, \sqrt{2} {\left(\frac{819 \, a \cos\left(\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{5148 \, a \cos\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{15015 \, a \cos\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{693 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{4004 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{9009 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{2002 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} - \frac{18018 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} - \frac{180180 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} - \frac{1638 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} - \frac{12870 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} - \frac{60060 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/288288*sqrt(2)*(819*a*cos(1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 5148*a*cos(1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 15015*a*cos(1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 693*a*cos(-1/4*pi + 13/2*d*x + 13/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 4004*a*cos(-1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 9009*a*cos(-1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 2002*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 9/2*d*x + 9/2*c)/d - 18018*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 5/2*d*x + 5/2*c)/d - 180180*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 1/2*d*x + 1/2*c)/d - 1638*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 11/2*d*x + 11/2*c)/d - 12870*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 7/2*d*x + 7/2*c)/d - 60060*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 3/2*d*x + 3/2*c)/d)*sqrt(a)","B",0
117,1,350,0,1.185201," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{1}{55440} \, \sqrt{2} {\left(\frac{385 \, a \cos\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{2079 \, a \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{6930 \, a \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{315 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{1485 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{2310 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{990 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} - \frac{9240 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} - \frac{770 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} - \frac{5544 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} - \frac{41580 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/55440*sqrt(2)*(385*a*cos(1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 2079*a*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 6930*a*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 315*a*cos(-1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 1485*a*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 2310*a*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 990*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d - 9240*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d - 770*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d - 5544*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d - 41580*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
118,1,257,0,0.703722," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{1}{2520} \, \sqrt{2} {\left(\frac{45 \, a \cos\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{210 \, a \cos\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{35 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{126 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{126 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} - \frac{1890 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} - \frac{90 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} - \frac{630 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/2520*sqrt(2)*(45*a*cos(1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 210*a*cos(1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 35*a*cos(-1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 126*a*cos(-1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 126*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 5/2*d*x + 5/2*c)/d - 1890*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 1/2*d*x + 1/2*c)/d - 90*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 7/2*d*x + 7/2*c)/d - 630*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 3/2*d*x + 3/2*c)/d)*sqrt(a)","B",0
119,1,226,0,0.635780," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{1}{420} \, \sqrt{2} {\left(\frac{21 \, a \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{105 \, a \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{15 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{35 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{70 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} - \frac{42 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} - \frac{420 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/420*sqrt(2)*(21*a*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 105*a*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 15*a*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 35*a*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 70*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d - 42*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d - 420*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
120,1,133,0,0.394774," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{1}{30} \, \sqrt{2} {\left(\frac{5 \, a \cos\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{3 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{30 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} - \frac{10 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/30*sqrt(2)*(5*a*cos(1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 3*a*cos(-1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 30*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 1/2*d*x + 1/2*c)/d - 10*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 3/2*d*x + 3/2*c)/d)*sqrt(a)","B",0
121,1,1021,0,12.200426," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \sqrt{a} {\left(\frac{\sqrt{2} {\left(6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} - 20 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} - 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{5} + \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right) - 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} + 60 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{3} - 15 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right) + 15 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} - \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \log\left(\frac{{\left| 2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} - 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) + 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{4} \, d x + c\right) + 6 \, \tan\left(\frac{1}{2} \, c\right) - 2 \right|}}{{\left| 2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} + 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} - 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) + 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{4} \, d x + c\right) + 6 \, \tan\left(\frac{1}{2} \, c\right) - 2 \right|}}\right)}{{\left(\tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}}} - \frac{4 \, {\left(a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{6} - 6 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{5} + a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{6} - 15 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{4} + 6 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{5} + 20 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{3} - 15 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{4} + 15 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{2} - 20 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{3} - 6 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right) + 15 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} - a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) + 6 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) - a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)}}{{\left(\sqrt{2} \tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \sqrt{2} \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \sqrt{2} \tan\left(\frac{1}{4} \, c\right)^{2} + \sqrt{2}\right)} {\left(\tan\left(\frac{1}{4} \, d x + c\right)^{2} + 1\right)}}\right)}}{d}"," ",0,"-sqrt(2)*sqrt(a)*(sqrt(2)*(6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^5 - 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^6 - 20*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^3 + 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^4 - 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^5 + sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^6 + 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c) - 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^2 + 60*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^3 - 15*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^4 + 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2 - 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c) + 15*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^2 - sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)))*log(abs(2*tan(1/4*d*x + c)*tan(1/2*c)^3 + 6*tan(1/4*d*x + c)*tan(1/2*c)^2 - 2*tan(1/2*c)^3 - 2*sqrt(2)*(tan(1/2*c)^2 + 1)^(3/2) - 6*tan(1/4*d*x + c)*tan(1/2*c) + 6*tan(1/2*c)^2 - 2*tan(1/4*d*x + c) + 6*tan(1/2*c) - 2)/abs(2*tan(1/4*d*x + c)*tan(1/2*c)^3 + 6*tan(1/4*d*x + c)*tan(1/2*c)^2 - 2*tan(1/2*c)^3 + 2*sqrt(2)*(tan(1/2*c)^2 + 1)^(3/2) - 6*tan(1/4*d*x + c)*tan(1/2*c) + 6*tan(1/2*c)^2 - 2*tan(1/4*d*x + c) + 6*tan(1/2*c) - 2))/((tan(1/4*c)^6 + 3*tan(1/4*c)^4 + 3*tan(1/4*c)^2 + 1)*(tan(1/2*c)^2 + 1)^(3/2)) - 4*(a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^6 - 6*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^5 + a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^6 - 15*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^4 + 6*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^5 + 20*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^3 - 15*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^4 + 15*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^2 - 20*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^3 - 6*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c) + 15*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^2 - a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c) + 6*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c) - a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)))/((sqrt(2)*tan(1/4*c)^6 + 3*sqrt(2)*tan(1/4*c)^4 + 3*sqrt(2)*tan(1/4*c)^2 + sqrt(2))*(tan(1/4*d*x + c)^2 + 1)))/d","B",0
122,1,3663,0,155.910357," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{2} \sqrt{a} {\left(\frac{\sqrt{2} {\left(\sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} - 15 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} + 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 15 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} - 60 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} - 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{5} - \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 20 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{3} + 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)\right)} \log\left(\frac{{\left| 2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} - 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) + 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{4} \, d x + c\right) + 6 \, \tan\left(\frac{1}{2} \, c\right) - 2 \right|}}{{\left| 2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} + 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} - 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) + 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{4} \, d x + c\right) + 6 \, \tan\left(\frac{1}{2} \, c\right) - 2 \right|}}\right)}{{\left(\tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}}} - \frac{4 \, {\left(6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{6} - 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{5} + 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{5} + 9 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{6} - 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{6} - 20 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{4} - 36 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{5} + 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{5} + 10 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} - 9 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{6} + 60 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{3} - 20 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{3} - 135 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{4} + 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{4} + 60 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{5} - 36 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{5} - 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} + 10 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} + 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right) - 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{2} + 120 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{3} - 60 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{3} - 150 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} + 135 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{4} + 54 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} - 60 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} - 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right) + 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right) + 135 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{2} - 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{2} - 200 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{3} + 120 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{3} + 90 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} - 150 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} - 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{5} + 54 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} + \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{6} - 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{5} - 36 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right) + 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right) + 150 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} - 135 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{2} - 180 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} + 200 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} - 90 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} + 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{5} - \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{6} - 9 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} + 60 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right) - 36 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right) - 90 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} + 150 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} + 60 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{3} - 180 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} - 15 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{4} + 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} - 10 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 9 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{4} + 54 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 60 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right) - 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 90 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} - 60 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{3} + 15 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{4} + 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 10 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right) + 54 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) + 15 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{2} - 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right) - 15 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} - \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) + 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) + \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 9 \, \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} - \tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} - 9 \, \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} + 9 \, \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{4} \, c\right)^{4} + \tan\left(\frac{1}{2} \, c\right)^{3} - 9 \, \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{4} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, c\right) - 1\right)} {\left(\tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{3} + 3 \, \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 3 \, \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{4} \, d x + c\right)^{2} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) - 3 \, \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{4} \, d x + c\right) + 3 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}\right)}}{2 \, d}"," ",0,"1/2*sqrt(2)*sqrt(a)*(sqrt(2)*(sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^6 - 15*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^4 + 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^5 - 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^6 + 15*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^2 - 60*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^3 + 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^4 - 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^5 - sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3 + 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c) - 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^2 + 20*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^3 + 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c) - 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c))*log(abs(2*tan(1/4*d*x + c)*tan(1/2*c)^3 + 6*tan(1/4*d*x + c)*tan(1/2*c)^2 - 2*tan(1/2*c)^3 - 2*sqrt(2)*(tan(1/2*c)^2 + 1)^(3/2) - 6*tan(1/4*d*x + c)*tan(1/2*c) + 6*tan(1/2*c)^2 - 2*tan(1/4*d*x + c) + 6*tan(1/2*c) - 2)/abs(2*tan(1/4*d*x + c)*tan(1/2*c)^3 + 6*tan(1/4*d*x + c)*tan(1/2*c)^2 - 2*tan(1/2*c)^3 + 2*sqrt(2)*(tan(1/2*c)^2 + 1)^(3/2) - 6*tan(1/4*d*x + c)*tan(1/2*c) + 6*tan(1/2*c)^2 - 2*tan(1/4*d*x + c) + 6*tan(1/2*c) - 2))/((tan(1/4*c)^6 + 3*tan(1/4*c)^4 + 3*tan(1/4*c)^2 + 1)*(tan(1/2*c)^2 + 1)^(3/2)) - 4*(6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^6*tan(1/4*c)^5 - 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^5*tan(1/4*c)^6 - 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^5*tan(1/4*c)^5 + 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^6*tan(1/4*c)^5 + 9*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4*tan(1/4*c)^6 - 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^5*tan(1/4*c)^6 - 20*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^6*tan(1/4*c)^3 + 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^5*tan(1/4*c)^4 - 36*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4*tan(1/4*c)^5 + 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^5*tan(1/4*c)^5 + 10*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^3*tan(1/4*c)^6 - 9*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^4*tan(1/4*c)^6 + 60*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^5*tan(1/4*c)^3 - 20*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^6*tan(1/4*c)^3 - 135*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4*tan(1/4*c)^4 + 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^5*tan(1/4*c)^4 + 60*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^3*tan(1/4*c)^5 - 36*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^4*tan(1/4*c)^5 - 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2*tan(1/4*c)^6 + 10*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^6 + 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^6*tan(1/4*c) - 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^5*tan(1/4*c)^2 + 120*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4*tan(1/4*c)^3 - 60*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^5*tan(1/4*c)^3 - 150*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^3*tan(1/4*c)^4 + 135*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^4*tan(1/4*c)^4 + 54*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2*tan(1/4*c)^5 - 60*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^5 - 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)*tan(1/4*c)^6 + 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^6 - 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^5*tan(1/4*c) + 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^6*tan(1/4*c) + 135*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4*tan(1/4*c)^2 - 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^5*tan(1/4*c)^2 - 200*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^3*tan(1/4*c)^3 + 120*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^4*tan(1/4*c)^3 + 90*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2*tan(1/4*c)^4 - 150*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^4 - 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)*tan(1/4*c)^5 + 54*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^5 + sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^6 - 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^6 + 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^5 - 36*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4*tan(1/4*c) + 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^5*tan(1/4*c) + 150*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^3*tan(1/4*c)^2 - 135*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^4*tan(1/4*c)^2 - 180*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2*tan(1/4*c)^3 + 200*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^3 + 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)*tan(1/4*c)^4 - 90*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^4 + 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^5 - sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^6 - 9*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4 + 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^5 + 60*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^3*tan(1/4*c) - 36*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^4*tan(1/4*c) - 90*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2*tan(1/4*c)^2 + 150*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^2 + 60*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)*tan(1/4*c)^3 - 180*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^3 - 15*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^4 + 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^4 - 10*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^3 + 9*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^4 + 54*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2*tan(1/4*c) - 60*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c) - 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)*tan(1/4*c)^2 + 90*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^2 - 60*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^3 + 15*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^4 + 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2 - 10*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3 - 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)*tan(1/4*c) + 54*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c) + 15*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^2 - 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^2 + 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c) - 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2 + 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c) - 15*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^2 - sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c) + 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c) + sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)))/((tan(1/2*c)^3*tan(1/4*c)^6 + 3*tan(1/2*c)^2*tan(1/4*c)^6 + 3*tan(1/2*c)^3*tan(1/4*c)^4 - 3*tan(1/2*c)*tan(1/4*c)^6 + 9*tan(1/2*c)^2*tan(1/4*c)^4 - tan(1/4*c)^6 + 3*tan(1/2*c)^3*tan(1/4*c)^2 - 9*tan(1/2*c)*tan(1/4*c)^4 + 9*tan(1/2*c)^2*tan(1/4*c)^2 - 3*tan(1/4*c)^4 + tan(1/2*c)^3 - 9*tan(1/2*c)*tan(1/4*c)^2 + 3*tan(1/2*c)^2 - 3*tan(1/4*c)^2 - 3*tan(1/2*c) - 1)*(tan(1/4*d*x + c)^2*tan(1/2*c)^3 + 3*tan(1/4*d*x + c)^2*tan(1/2*c)^2 - 2*tan(1/4*d*x + c)*tan(1/2*c)^3 - 3*tan(1/4*d*x + c)^2*tan(1/2*c) + 6*tan(1/4*d*x + c)*tan(1/2*c)^2 - tan(1/2*c)^3 - tan(1/4*d*x + c)^2 + 6*tan(1/4*d*x + c)*tan(1/2*c) - 3*tan(1/2*c)^2 - 2*tan(1/4*d*x + c) + 3*tan(1/2*c) + 1)))/d","B",0
123,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,-1,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,-1,0,0,0.000000," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
127,1,471,0,2.765030," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{1}{2882880} \, \sqrt{2} {\left(\frac{16380 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{102960 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{300300 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{13860 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{80080 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{180180 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{3465 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right)}{d} - \frac{5005 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} - \frac{171171 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} - \frac{2027025 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{3003 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{15}{2} \, d x + \frac{15}{2} \, c\right)}{d} - \frac{4095 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} - \frac{122265 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} - \frac{675675 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/2882880*sqrt(2)*(16380*a^2*cos(1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 102960*a^2*cos(1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 300300*a^2*cos(1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 13860*a^2*cos(-1/4*pi + 13/2*d*x + 13/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 80080*a^2*cos(-1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 180180*a^2*cos(-1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 3465*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 13/2*d*x + 13/2*c)/d - 5005*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 9/2*d*x + 9/2*c)/d - 171171*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 5/2*d*x + 5/2*c)/d - 2027025*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 1/2*d*x + 1/2*c)/d + 3003*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 15/2*d*x + 15/2*c)/d - 4095*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 11/2*d*x + 11/2*c)/d - 122265*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 7/2*d*x + 7/2*c)/d - 675675*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 3/2*d*x + 3/2*c)/d)*sqrt(a)","B",0
128,1,438,0,1.391520," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{1}{1441440} \, \sqrt{2} {\left(\frac{20020 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{108108 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{360360 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{16380 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{77220 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{120120 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{4095 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} - \frac{12870 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} - \frac{255255 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{3465 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right)}{d} - \frac{10010 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} - \frac{153153 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} - \frac{1261260 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/1441440*sqrt(2)*(20020*a^2*cos(1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 108108*a^2*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 360360*a^2*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 16380*a^2*cos(-1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 77220*a^2*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 120120*a^2*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 4095*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 11/2*d*x + 11/2*c)/d - 12870*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d - 255255*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d + 3465*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 13/2*d*x + 13/2*c)/d - 10010*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d - 153153*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d - 1261260*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
129,1,339,0,4.542266," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{1}{55440} \, \sqrt{2} {\left(\frac{1980 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{9240 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{1540 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{5544 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{385 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} - \frac{2079 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} - \frac{48510 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{315 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} - \frac{1485 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} - \frac{16170 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/55440*sqrt(2)*(1980*a^2*cos(1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 9240*a^2*cos(1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 1540*a^2*cos(-1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 5544*a^2*cos(-1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 385*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 9/2*d*x + 9/2*c)/d - 2079*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 5/2*d*x + 5/2*c)/d - 48510*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 1/2*d*x + 1/2*c)/d + 315*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 11/2*d*x + 11/2*c)/d - 1485*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 7/2*d*x + 7/2*c)/d - 16170*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 3/2*d*x + 3/2*c)/d)*sqrt(a)","B",0
130,1,306,0,1.367949," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{1}{2520} \, \sqrt{2} {\left(\frac{252 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{1260 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{180 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{420 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{45 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} - \frac{420 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{35 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} - \frac{252 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} - \frac{3150 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/2520*sqrt(2)*(252*a^2*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 1260*a^2*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 180*a^2*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 420*a^2*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 45*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d - 420*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d + 35*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d - 252*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d - 3150*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
131,1,207,0,0.555134," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{1}{420} \, \sqrt{2} {\left(\frac{140 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{84 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{21 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} - \frac{525 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{15 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} - \frac{175 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/420*sqrt(2)*(140*a^2*cos(1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 84*a^2*cos(-1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 21*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 5/2*d*x + 5/2*c)/d - 525*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 1/2*d*x + 1/2*c)/d + 15*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 7/2*d*x + 7/2*c)/d - 175*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 3/2*d*x + 3/2*c)/d)*sqrt(a)","B",0
132,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,1,6622,0,54.374321," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \sqrt{a} {\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} - 15 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} + 18 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 15 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} - 60 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} - 6 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{5} - \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 18 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 45 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 20 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{3} + 3 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)\right)} \log\left(\frac{{\left| -2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{4} \, d x + c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right) + 2 \right|}}{{\left| -2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} + 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{4} \, d x + c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right) + 2 \right|}}\right)}{{\left(\tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(\sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{6} - 6 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{5} + 12 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{6} - 3 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{6} - 15 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{4} + 72 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{5} - 18 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{5} - 15 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{6} + \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{6} + 20 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{3} - 180 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{4} + 45 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{4} + 90 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{5} - 30 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{5} - 40 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} + 45 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{6} + \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{6} + 15 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{2} - 240 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{3} + 60 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{3} + 225 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{4} - 15 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{4} - 240 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{5} + 270 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{5} - 18 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{5} + 15 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} - 51 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{6} + 12 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{6} - 6 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right) + 180 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{2} - 45 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{2} - 300 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{3} + 100 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{3} + 600 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} - 675 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{4} - 15 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{4} - 90 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} + 234 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{5} - 72 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{5} + 12 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} - 45 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} + 21 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{6} - \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{6} + 72 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right) - 18 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right) - 225 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{2} + 15 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{2} + 800 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{3} - 900 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{3} + 60 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{3} - 225 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} + 765 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{4} - 180 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{4} + 72 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{5} - 270 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} + 54 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{5} - \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} + 39 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} - 40 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} - 12 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{5} + 3 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} + 90 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right) - 30 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right) - 600 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} + 675 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{2} + 15 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{2} + 300 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} - 780 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{3} + 240 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{3} - 180 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} + 675 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} - 315 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{4} + 6 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{5} - 306 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} + 240 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{5} + 3 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} - 9 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} + 15 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} - \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{6} - 240 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right) + 270 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right) - 18 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right) + 225 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} - 765 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{2} + 180 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{2} - 240 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{3} + 900 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} - 180 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{3} + 15 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} - 585 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} + 600 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} + 18 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} - 126 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} - 5 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 12 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 40 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - 45 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} - \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{6} - 90 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) + 234 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right) - 72 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right) + 180 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} - 675 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} + 315 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{2} - 20 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{3} + 1020 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} - 800 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{3} - 45 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} + 135 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} + 6 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{5} - 72 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{5} + 3 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{6} - 15 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 51 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} - 12 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} + 72 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right) - 270 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) + 54 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right) - 15 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} + 585 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} - 600 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} - 60 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} + 420 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} + 75 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{4} - 180 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} - 6 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{5} - 12 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 45 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 21 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{4} + 6 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{4} \, c\right) - 306 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) + 240 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right) + 45 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} - 135 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} - 20 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{3} + 240 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{3} - 45 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{4} + \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} - 39 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 40 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 18 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 126 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 75 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 180 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 20 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{3} - 3 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} + 9 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 6 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right) - 72 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right) + 45 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 5 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) - 12 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) - 3 \, \sqrt{2} a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 9 \, \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} - \tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} - 9 \, \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} + 9 \, \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{4} \, c\right)^{4} + \tan\left(\frac{1}{2} \, c\right)^{3} - 9 \, \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{4} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, c\right) - 1\right)} {\left(\tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{3} + 3 \, \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - 3 \, \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 6 \, \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{4} \, d x + c\right)^{4} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, \tan\left(\frac{1}{4} \, d x + c\right)^{3} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, c\right)^{3} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) - 3 \, \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{4} \, d x + c\right) + 3 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}\right)}}{d}"," ",0,"-sqrt(2)*sqrt(a)*(sqrt(2)*(sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^6 - 15*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^4 + 18*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^5 - 3*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^6 + 15*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^2 - 60*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^3 + 45*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^4 - 6*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^5 - sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3 + 18*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c) - 45*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^2 + 20*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^3 + 3*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c) - 6*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c))*log(abs(-2*tan(1/4*d*x + c)*tan(1/2*c)^3 - 6*tan(1/4*d*x + c)*tan(1/2*c)^2 + 2*tan(1/2*c)^3 - 2*sqrt(2)*(tan(1/2*c)^2 + 1)^(3/2) + 6*tan(1/4*d*x + c)*tan(1/2*c) - 6*tan(1/2*c)^2 + 2*tan(1/4*d*x + c) - 6*tan(1/2*c) + 2)/abs(-2*tan(1/4*d*x + c)*tan(1/2*c)^3 - 6*tan(1/4*d*x + c)*tan(1/2*c)^2 + 2*tan(1/2*c)^3 + 2*sqrt(2)*(tan(1/2*c)^2 + 1)^(3/2) + 6*tan(1/4*d*x + c)*tan(1/2*c) - 6*tan(1/2*c)^2 + 2*tan(1/4*d*x + c) - 6*tan(1/2*c) + 2))/((tan(1/4*c)^6 + 3*tan(1/4*c)^4 + 3*tan(1/4*c)^2 + 1)*(tan(1/2*c)^2 + 1)^(3/2)) - 2*(sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^6*tan(1/4*c)^6 - 6*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^6*tan(1/4*c)^5 + 12*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^5*tan(1/4*c)^6 - 3*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^6*tan(1/4*c)^6 - 15*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^6*tan(1/4*c)^4 + 72*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^5*tan(1/4*c)^5 - 18*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^6*tan(1/4*c)^5 - 15*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^4*tan(1/4*c)^6 + sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^6*tan(1/4*c)^6 + 20*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^6*tan(1/4*c)^3 - 180*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^5*tan(1/4*c)^4 + 45*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^6*tan(1/4*c)^4 + 90*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^4*tan(1/4*c)^5 - 30*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^6*tan(1/4*c)^5 - 40*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^3*tan(1/4*c)^6 + 45*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^4*tan(1/4*c)^6 + sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^6*tan(1/4*c)^6 + 15*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^6*tan(1/4*c)^2 - 240*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^5*tan(1/4*c)^3 + 60*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^6*tan(1/4*c)^3 + 225*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^4*tan(1/4*c)^4 - 15*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^6*tan(1/4*c)^4 - 240*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^3*tan(1/4*c)^5 + 270*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^4*tan(1/4*c)^5 - 18*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^6*tan(1/4*c)^5 + 15*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^2*tan(1/4*c)^6 - 51*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4*tan(1/4*c)^6 + 12*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^5*tan(1/4*c)^6 - 6*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^6*tan(1/4*c) + 180*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^5*tan(1/4*c)^2 - 45*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^6*tan(1/4*c)^2 - 300*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^4*tan(1/4*c)^3 + 100*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^6*tan(1/4*c)^3 + 600*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^3*tan(1/4*c)^4 - 675*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^4*tan(1/4*c)^4 - 15*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^6*tan(1/4*c)^4 - 90*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^2*tan(1/4*c)^5 + 234*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4*tan(1/4*c)^5 - 72*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^5*tan(1/4*c)^5 + 12*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)*tan(1/4*c)^6 - 45*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^2*tan(1/4*c)^6 + 21*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^4*tan(1/4*c)^6 - sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^6 + 72*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^5*tan(1/4*c) - 18*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^6*tan(1/4*c) - 225*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^4*tan(1/4*c)^2 + 15*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^6*tan(1/4*c)^2 + 800*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^3*tan(1/4*c)^3 - 900*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^4*tan(1/4*c)^3 + 60*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^6*tan(1/4*c)^3 - 225*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^2*tan(1/4*c)^4 + 765*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4*tan(1/4*c)^4 - 180*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^5*tan(1/4*c)^4 + 72*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)*tan(1/4*c)^5 - 270*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^2*tan(1/4*c)^5 + 54*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^4*tan(1/4*c)^5 - sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/4*c)^6 + 39*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2*tan(1/4*c)^6 - 40*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^6 - 12*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^5 + 3*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^6 + 90*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^4*tan(1/4*c) - 30*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^6*tan(1/4*c) - 600*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^3*tan(1/4*c)^2 + 675*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^4*tan(1/4*c)^2 + 15*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^6*tan(1/4*c)^2 + 300*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^2*tan(1/4*c)^3 - 780*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4*tan(1/4*c)^3 + 240*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^5*tan(1/4*c)^3 - 180*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)*tan(1/4*c)^4 + 675*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^2*tan(1/4*c)^4 - 315*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^4*tan(1/4*c)^4 + 6*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/4*c)^5 - 306*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2*tan(1/4*c)^5 + 240*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^5 + 3*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/4*c)^6 - 9*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^6 + 15*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^4 - sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^6 - 240*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^3*tan(1/4*c) + 270*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^4*tan(1/4*c) - 18*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^6*tan(1/4*c) + 225*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^2*tan(1/4*c)^2 - 765*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4*tan(1/4*c)^2 + 180*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^5*tan(1/4*c)^2 - 240*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)*tan(1/4*c)^3 + 900*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^2*tan(1/4*c)^3 - 180*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^4*tan(1/4*c)^3 + 15*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/4*c)^4 - 585*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2*tan(1/4*c)^4 + 600*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^4 + 18*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/4*c)^5 - 126*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^5 - 5*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^6 + 12*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^6 + 40*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^3 - 45*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^4 - sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^6 - 90*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^2*tan(1/4*c) + 234*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4*tan(1/4*c) - 72*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^5*tan(1/4*c) + 180*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)*tan(1/4*c)^2 - 675*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^2*tan(1/4*c)^2 + 315*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^4*tan(1/4*c)^2 - 20*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/4*c)^3 + 1020*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2*tan(1/4*c)^3 - 800*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^3 - 45*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/4*c)^4 + 135*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^4 + 6*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^5 - 72*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^5 + 3*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^6 - 15*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^2 + 51*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4 - 12*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^5 + 72*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)*tan(1/4*c) - 270*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^2*tan(1/4*c) + 54*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^4*tan(1/4*c) - 15*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/4*c)^2 + 585*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2*tan(1/4*c)^2 - 600*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^2 - 60*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/4*c)^3 + 420*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^3 + 75*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^4 - 180*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^4 - 6*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^5 - 12*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c) + 45*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^2 - 21*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^4 + 6*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/4*c) - 306*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2*tan(1/4*c) + 240*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c) + 45*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/4*c)^2 - 135*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^2 - 20*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^3 + 240*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^3 - 45*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^4 + sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3 - 39*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2 + 40*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3 + 18*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/4*c) - 126*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c) - 75*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^2 + 180*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^2 + 20*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^3 - 3*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2 + 9*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2 + 6*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c) - 72*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c) + 45*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^2 + 5*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c) - 12*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c) - 6*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c) - 3*sqrt(2)*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)))/((tan(1/2*c)^3*tan(1/4*c)^6 + 3*tan(1/2*c)^2*tan(1/4*c)^6 + 3*tan(1/2*c)^3*tan(1/4*c)^4 - 3*tan(1/2*c)*tan(1/4*c)^6 + 9*tan(1/2*c)^2*tan(1/4*c)^4 - tan(1/4*c)^6 + 3*tan(1/2*c)^3*tan(1/4*c)^2 - 9*tan(1/2*c)*tan(1/4*c)^4 + 9*tan(1/2*c)^2*tan(1/4*c)^2 - 3*tan(1/4*c)^4 + tan(1/2*c)^3 - 9*tan(1/2*c)*tan(1/4*c)^2 + 3*tan(1/2*c)^2 - 3*tan(1/4*c)^2 - 3*tan(1/2*c) - 1)*(tan(1/4*d*x + c)^4*tan(1/2*c)^3 + 3*tan(1/4*d*x + c)^4*tan(1/2*c)^2 - 2*tan(1/4*d*x + c)^3*tan(1/2*c)^3 - 3*tan(1/4*d*x + c)^4*tan(1/2*c) + 6*tan(1/4*d*x + c)^3*tan(1/2*c)^2 - tan(1/4*d*x + c)^4 + 6*tan(1/4*d*x + c)^3*tan(1/2*c) - 2*tan(1/4*d*x + c)*tan(1/2*c)^3 - 2*tan(1/4*d*x + c)^3 + 6*tan(1/4*d*x + c)*tan(1/2*c)^2 - tan(1/2*c)^3 + 6*tan(1/4*d*x + c)*tan(1/2*c) - 3*tan(1/2*c)^2 - 2*tan(1/4*d*x + c) + 3*tan(1/2*c) + 1)))/d","B",0
134,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
136,-1,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
137,-1,0,0,0.000000," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,-1,0,0,0.000000," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
139,1,669,0,6.140027," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\frac{1}{7449361920} \, \sqrt{2} {\left(\frac{765765 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{19}{2} \, d x + \frac{19}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{7759752 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{15}{2} \, d x + \frac{15}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{91265265 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{365816880 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{882671790 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{692835 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{21}{2} \, d x + \frac{21}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{6846840 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{17}{2} \, d x + \frac{17}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{77224455 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{284524240 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{529603074 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{5135130 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{17}{2} \, d x + \frac{17}{2} \, c\right)}{d} - \frac{24622290 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right)}{d} + \frac{12932920 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{488864376 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{5296030740 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} - \frac{4594590 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{19}{2} \, d x + \frac{19}{2} \, c\right)}{d} - \frac{21339318 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{15}{2} \, d x + \frac{15}{2} \, c\right)}{d} + \frac{10581480 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{349188840 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{1765343580 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/7449361920*sqrt(2)*(765765*a^3*cos(1/4*pi + 19/2*d*x + 19/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 7759752*a^3*cos(1/4*pi + 15/2*d*x + 15/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 91265265*a^3*cos(1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 365816880*a^3*cos(1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 882671790*a^3*cos(1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 692835*a^3*cos(-1/4*pi + 21/2*d*x + 21/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 6846840*a^3*cos(-1/4*pi + 17/2*d*x + 17/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 77224455*a^3*cos(-1/4*pi + 13/2*d*x + 13/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 284524240*a^3*cos(-1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 529603074*a^3*cos(-1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 5135130*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 17/2*d*x + 17/2*c)/d - 24622290*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 13/2*d*x + 13/2*c)/d + 12932920*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 9/2*d*x + 9/2*c)/d + 488864376*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 5/2*d*x + 5/2*c)/d + 5296030740*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 1/2*d*x + 1/2*c)/d - 4594590*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 19/2*d*x + 19/2*c)/d - 21339318*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 15/2*d*x + 15/2*c)/d + 10581480*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 11/2*d*x + 11/2*c)/d + 349188840*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 7/2*d*x + 7/2*c)/d + 1765343580*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 3/2*d*x + 3/2*c)/d)*sqrt(a)","B",0
140,1,636,0,8.967740," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\frac{1}{1241560320} \, \sqrt{2} {\left(\frac{285285 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{17}{2} \, d x + \frac{17}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{3357585 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{32332300 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{112516404 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{320089770 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{255255 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{19}{2} \, d x + \frac{19}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{2909907 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{15}{2} \, d x + \frac{15}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{26453700 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{80368860 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{106696590 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{1939938 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{15}{2} \, d x + \frac{15}{2} \, c\right)}{d} - \frac{7054320 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{16628040 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{232792560 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} - \frac{1711710 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{17}{2} \, d x + \frac{17}{2} \, c\right)}{d} - \frac{5969040 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right)}{d} + \frac{12932920 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{139675536 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{1066965900 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/1241560320*sqrt(2)*(285285*a^3*cos(1/4*pi + 17/2*d*x + 17/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 3357585*a^3*cos(1/4*pi + 13/2*d*x + 13/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 32332300*a^3*cos(1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 112516404*a^3*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 320089770*a^3*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 255255*a^3*cos(-1/4*pi + 19/2*d*x + 19/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 2909907*a^3*cos(-1/4*pi + 15/2*d*x + 15/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 26453700*a^3*cos(-1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 80368860*a^3*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 106696590*a^3*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 1939938*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 15/2*d*x + 15/2*c)/d - 7054320*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 11/2*d*x + 11/2*c)/d + 16628040*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d + 232792560*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d - 1711710*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 17/2*d*x + 17/2*c)/d - 5969040*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 13/2*d*x + 13/2*c)/d + 12932920*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d + 139675536*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d + 1066965900*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
141,1,537,0,3.130016," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\frac{1}{98017920} \, \sqrt{2} {\left(\frac{51051 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{15}{2} \, d x + \frac{15}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{696150 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{5469750 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{16846830 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{45045 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{17}{2} \, d x + \frac{17}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{589050 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{4254250 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{10108098 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{353430 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right)}{d} - \frac{850850 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{5207202 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{84234150 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} - \frac{306306 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{15}{2} \, d x + \frac{15}{2} \, c\right)}{d} - \frac{696150 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{3719430 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{28078050 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/98017920*sqrt(2)*(51051*a^3*cos(1/4*pi + 15/2*d*x + 15/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 696150*a^3*cos(1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 5469750*a^3*cos(1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 16846830*a^3*cos(1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 45045*a^3*cos(-1/4*pi + 17/2*d*x + 17/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 589050*a^3*cos(-1/4*pi + 13/2*d*x + 13/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 4254250*a^3*cos(-1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 10108098*a^3*cos(-1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 353430*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 13/2*d*x + 13/2*c)/d - 850850*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 9/2*d*x + 9/2*c)/d + 5207202*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 5/2*d*x + 5/2*c)/d + 84234150*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 1/2*d*x + 1/2*c)/d - 306306*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 15/2*d*x + 15/2*c)/d - 696150*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 11/2*d*x + 11/2*c)/d + 3719430*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 7/2*d*x + 7/2*c)/d + 28078050*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 3/2*d*x + 3/2*c)/d)*sqrt(a)","B",0
142,1,504,0,2.280743," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\frac{1}{2882880} \, \sqrt{2} {\left(\frac{3465 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{55055 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{351351 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{1216215 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{3003 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{15}{2} \, d x + \frac{15}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{45045 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{250965 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{405405 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{24570 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} - \frac{25740 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{570570 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} - \frac{20790 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right)}{d} - \frac{20020 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{342342 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{3243240 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/2882880*sqrt(2)*(3465*a^3*cos(1/4*pi + 13/2*d*x + 13/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 55055*a^3*cos(1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 351351*a^3*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 1216215*a^3*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 3003*a^3*cos(-1/4*pi + 15/2*d*x + 15/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 45045*a^3*cos(-1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 250965*a^3*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 405405*a^3*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 24570*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 11/2*d*x + 11/2*c)/d - 25740*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d + 570570*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d - 20790*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 13/2*d*x + 13/2*c)/d - 20020*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d + 342342*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d + 3243240*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
143,1,405,0,2.375127," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\frac{1}{480480} \, \sqrt{2} {\left(\frac{1365 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{25740 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{135135 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{1155 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{20020 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{81081 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{10010 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{6006 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{540540 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} - \frac{8190 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{4290 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{180180 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/480480*sqrt(2)*(1365*a^3*cos(1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 25740*a^3*cos(1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 135135*a^3*cos(1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 1155*a^3*cos(-1/4*pi + 13/2*d*x + 13/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 20020*a^3*cos(-1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 81081*a^3*cos(-1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 10010*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 9/2*d*x + 9/2*c)/d + 6006*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 5/2*d*x + 5/2*c)/d + 540540*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 1/2*d*x + 1/2*c)/d - 8190*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 11/2*d*x + 11/2*c)/d + 4290*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 7/2*d*x + 7/2*c)/d + 180180*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 3/2*d*x + 3/2*c)/d)*sqrt(a)","B",0
144,1,372,0,1.849579," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\frac{1}{55440} \, \sqrt{2} {\left(\frac{385 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{9009 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{48510 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{315 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{6435 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{16170 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{2970 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{9240 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} - \frac{2310 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{5544 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{97020 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/55440*sqrt(2)*(385*a^3*cos(1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 9009*a^3*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 48510*a^3*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 315*a^3*cos(-1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 6435*a^3*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 16170*a^3*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 2970*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d + 9240*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d - 2310*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d + 5544*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d + 97020*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
145,1,273,0,0.974241," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\frac{1}{2520} \, \sqrt{2} {\left(\frac{45 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{1470 \, a^{3} \cos\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{35 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{882 \, a^{3} \cos\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{378 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{4410 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} - \frac{270 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{1470 \, a^{3} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/2520*sqrt(2)*(45*a^3*cos(1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 1470*a^3*cos(1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 35*a^3*cos(-1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 882*a^3*cos(-1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 378*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 5/2*d*x + 5/2*c)/d + 4410*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 1/2*d*x + 1/2*c)/d - 270*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 7/2*d*x + 7/2*c)/d + 1470*a^3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 3/2*d*x + 3/2*c)/d)*sqrt(a)","B",0
146,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
150,-1,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,-1,0,0,0.000000," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
152,-1,0,0,0.000000," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,-1,0,0,0.000000," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,-1,0,0,0.000000," ","integrate(sec(d*x+c)^9*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,-1,0,0,0.000000," ","integrate(sec(d*x+c)^10*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,1,430,0,2.698885," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{835 \, a^{6}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{3003 \, a^{6}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{3926 \, a^{6}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{6006 \, a^{6}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{15301 \, a^{6}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{21021 \, a^{6}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{15444 \, a^{6}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{15444 \, a^{6}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{21021 \, a^{6}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{15301 \, a^{6}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{6006 \, a^{6}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{3926 \, a^{6}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{835 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{3003 \, a^{6}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{3003 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{13}{2}} d}"," ",0,"2/3003*(835*a^6/sgn(tan(1/2*d*x + 1/2*c) + 1) + (3003*a^6/sgn(tan(1/2*d*x + 1/2*c) + 1) + (3926*a^6/sgn(tan(1/2*d*x + 1/2*c) + 1) + (6006*a^6/sgn(tan(1/2*d*x + 1/2*c) + 1) + (15301*a^6/sgn(tan(1/2*d*x + 1/2*c) + 1) + (21021*a^6/sgn(tan(1/2*d*x + 1/2*c) + 1) + (15444*a^6/sgn(tan(1/2*d*x + 1/2*c) + 1) + (15444*a^6/sgn(tan(1/2*d*x + 1/2*c) + 1) + (21021*a^6/sgn(tan(1/2*d*x + 1/2*c) + 1) + (15301*a^6/sgn(tan(1/2*d*x + 1/2*c) + 1) + (6006*a^6/sgn(tan(1/2*d*x + 1/2*c) + 1) + (3926*a^6/sgn(tan(1/2*d*x + 1/2*c) + 1) + (835*a^6*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) + 3003*a^6/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^2 + a)^(13/2)*d)","B",0
157,1,402,0,4.622515," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{256 \, \sqrt{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{a}} - \frac{\frac{151 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{693 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{1177 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{1155 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{1782 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{3234 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{3234 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{1782 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{1155 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{1177 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{151 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{693 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{11}{2}}}\right)}}{693 \, d}"," ",0,"2/693*(256*sqrt(2)*sgn(tan(1/2*d*x + 1/2*c) + 1)/sqrt(a) - (151*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (693*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (1177*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (1155*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (1782*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (3234*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (3234*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (1782*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (1155*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (1177*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) + (151*a^5*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 693*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(11/2))/d","B",0
158,1,310,0,1.588268," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{107 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{315 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{324 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{420 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{882 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{882 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{420 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{324 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{107 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{315 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{315 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{9}{2}} d}"," ",0,"2/315*(107*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (315*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (324*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (420*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (882*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (882*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (420*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (324*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (107*a^4*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) + 315*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^2 + a)^(9/2)*d)","B",0
159,1,278,0,1.925120," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{16 \, \sqrt{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{a}} - \frac{\frac{9 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{35 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{49 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{35 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{35 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{49 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{35 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{7}{2}}}\right)}}{35 \, d}"," ",0,"2/35*(16*sqrt(2)*sgn(tan(1/2*d*x + 1/2*c) + 1)/sqrt(a) - (9*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (35*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (49*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (35*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (35*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (49*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) + (9*a^3*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 35*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(7/2))/d","B",0
160,1,75,0,1.164243," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(15 \, \sqrt{a \sin\left(d x + c\right) + a} - \frac{3 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 10 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{a \sin\left(d x + c\right) + a} a^{2}}{a^{2}}\right)}}{15 \, a d}"," ",0,"2/15*(15*sqrt(a*sin(d*x + c) + a) - (3*(a*sin(d*x + c) + a)^(5/2) - 10*(a*sin(d*x + c) + a)^(3/2)*a + 15*sqrt(a*sin(d*x + c) + a)*a^2)/a^2)/(a*d)","A",0
161,1,143,0,1.097959," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{2 \, \sqrt{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{a}} + \frac{{\left({\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{3 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{3 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}}}\right)}}{3 \, d}"," ",0,"2/3*(2*sqrt(2)*sgn(tan(1/2*d*x + 1/2*c) + 1)/sqrt(a) + (((a*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 3*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 3*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - a/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2))/d","B",0
162,1,20,0,0.844503," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{a \sin\left(d x + c\right) + a}}{a d}"," ",0,"2*sqrt(a*sin(d*x + c) + a)/(a*d)","A",0
163,1,211,0,1.437181," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} - \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} - \sqrt{a}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{d}"," ",0,"-(sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) - sqrt(a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) - sqrt(a))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
164,1,419,0,2.318956," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{3 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{4 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} + {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} - {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a + a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{4 \, d}"," ",0,"1/4*(3*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 4*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 + (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) - (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a + a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
165,1,587,0,2.812447," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{15 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} - \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{6 \, {\left(3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} - {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} - {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a - a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{16 \, {\left(3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} + 6 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{a} - 4 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a - 12 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{3}{2}} + 9 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{2} - 2 \, a^{\frac{5}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{24 \, d}"," ",0,"-1/24*(15*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) - sqrt(a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 6*(3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 - (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) - (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a - a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 16*(3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5 + 6*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(a) - 4*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a - 12*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(3/2) + 9*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^2 - 2*a^(5/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^3*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
166,1,745,0,4.085404," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{105 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{16 \, {\left(15 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} - 33 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{a} - 22 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a + 66 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{3}{2}} + 51 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{2} + 11 \, a^{\frac{5}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{6 \, {\left(53 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} + 179 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{a} + 127 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a - 195 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{3}{2}} + 7 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{2} + 121 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{5}{2}} - 67 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{3} + 15 \, a^{\frac{7}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{192 \, d}"," ",0,"1/192*(105*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 16*(15*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5 - 33*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(a) - 22*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a + 66*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(3/2) + 51*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^2 + 11*a^(5/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^3*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 6*(53*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7 + 179*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(a) + 127*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a - 195*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(3/2) + 7*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^2 + 121*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(5/2) - 67*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^3 + 15*a^(7/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^4*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
167,-2,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((d*t_nostep+c)/2-pi/4))]Discontinuities at zeroes of cos((d*t_nostep+c)/2-pi/4) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 0.46Not invertible Error: Bad Argument Value","F(-2)",0
168,-2,0,0,0.000000," ","integrate(sec(d*x+c)^6/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((d*t_nostep+c)/2-pi/4))]Discontinuities at zeroes of cos((d*t_nostep+c)/2-pi/4) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 0.47Not invertible Error: Bad Argument Value","F(-2)",0
169,1,370,0,2.563518," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{533 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{1155 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{1199 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{3465 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{5874 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{4158 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{4158 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{5874 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{3465 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{1199 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{533 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{1155 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{1155 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{11}{2}} d}"," ",0,"2/1155*(533*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (1155*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (1199*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (3465*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (5874*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (4158*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (4158*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (5874*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (3465*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (1199*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (533*a^4*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) + 1155*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^2 + a)^(11/2)*d)","B",0
170,1,340,0,1.715670," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{32 \, \sqrt{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{\frac{3}{2}}} - \frac{\frac{11 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{63 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{144 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{168 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{126 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{126 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{168 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{144 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{11 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{63 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{9}{2}}}\right)}}{63 \, d}"," ",0,"2/63*(32*sqrt(2)*sgn(tan(1/2*d*x + 1/2*c) + 1)/a^(3/2) - (11*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (63*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (144*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (168*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (126*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (126*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (168*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (144*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) + (11*a^3*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 63*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(9/2))/d","B",0
171,1,250,0,2.209274," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left({\left({\left({\left({\left(\frac{71 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{105 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{91 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{245 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{245 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{91 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{105 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{71 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{105 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{7}{2}} d}"," ",0,"2/105*(((((((71*a^2*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) + 105*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 91*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 245*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 245*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 91*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 105*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 71*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))/((a*tan(1/2*d*x + 1/2*c)^2 + a)^(7/2)*d)","B",0
172,1,199,0,1.734716," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{4 \, \sqrt{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{\frac{3}{2}}} + \frac{{\left({\left({\left({\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{5 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{10 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{10 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{5 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{5}{2}}}\right)}}{5 \, d}"," ",0,"2/5*(4*sqrt(2)*sgn(tan(1/2*d*x + 1/2*c) + 1)/a^(3/2) + (((((a*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 5*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 10*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 10*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 5*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - a/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2))/d","B",0
173,1,56,0,1.678074," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, \sqrt{a \sin\left(d x + c\right) + a} - \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} - 3 \, \sqrt{a \sin\left(d x + c\right) + a} a}{a}\right)}}{3 \, a^{2} d}"," ",0,"2/3*(3*sqrt(a*sin(d*x + c) + a) - ((a*sin(d*x + c) + a)^(3/2) - 3*sqrt(a*sin(d*x + c) + a)*a)/a)/(a^2*d)","A",0
174,1,190,0,1.932727," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{1}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} + \frac{\sqrt{2} {\left(2 \, \sqrt{a} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) + \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{-a} a^{\frac{3}{2}}} - \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{d}"," ",0,"-2*((tan(1/2*d*x + 1/2*c)/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 1/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(2)*(2*sqrt(a)*arctan(sqrt(a)/sqrt(-a)) + sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(-a)*a^(3/2)) - 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
175,1,20,0,1.881723," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{2}{\sqrt{a \sin\left(d x + c\right) + a} a d}"," ",0,"-2/(sqrt(a*sin(d*x + c) + a)*a*d)","A",0
176,1,379,0,2.049394," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{3 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} - \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(9 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} + 15 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{a} - 10 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a - 30 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{3}{2}} + 21 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{2} - 5 \, a^{\frac{5}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{3} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{6 \, d}"," ",0,"-1/6*(3*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) - sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(9*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5 + 15*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(a) - 10*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a - 30*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(3/2) + 21*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^2 - 5*a^(5/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^3*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
177,1,591,0,2.654930," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{15 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{16 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(41 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} + 127 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{a} + 91 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a - 143 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{3}{2}} + 3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{2} + 93 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{5}{2}} - 47 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{3} + 11 \, a^{\frac{7}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{4} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{32 \, d}"," ",0,"1/32*(15*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 16*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(41*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7 + 127*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(a) + 91*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a - 143*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(3/2) + 3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^2 + 93*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(5/2) - 47*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^3 + 11*a^(7/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^4*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
178,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((d*t_nostep+c)/2-pi/4))]Discontinuities at zeroes of cos((d*t_nostep+c)/2-pi/4) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 0.56Not invertible Error: Bad Argument Value","F(-2)",0
179,1,914,0,9.618099," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{315 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{64 \, {\left(9 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} - 21 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{a} - 14 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a + 42 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{3}{2}} + 33 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{2} + 7 \, a^{\frac{5}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{3} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(933 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{11} + 5847 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} \sqrt{a} + 13605 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{9} a + 5595 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} a^{\frac{3}{2}} - 17214 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} a^{2} - 8474 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} a^{\frac{5}{2}} + 20250 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a^{3} - 2250 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{7}{2}} - 8695 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{4} + 6195 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{9}{2}} - 1743 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{5} + 223 \, a^{\frac{11}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{6} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{768 \, d}"," ",0,"1/768*(315*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 64*(9*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5 - 21*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(a) - 14*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a + 42*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(3/2) + 33*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^2 + 7*a^(5/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^3*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(933*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^11 + 5847*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^10*sqrt(a) + 13605*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^9*a + 5595*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^8*a^(3/2) - 17214*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7*a^2 - 8474*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*a^(5/2) + 20250*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a^3 - 2250*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(7/2) - 8695*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^4 + 6195*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(9/2) - 1743*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^5 + 223*a^(11/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^6*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
180,1,1076,0,7.406278," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{3465 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} - \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{70 \, {\left(77 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} - 283 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{a} + 199 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a + 299 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{3}{2}} + 15 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{2} - 177 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{5}{2}} - 107 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{3} - 23 \, a^{\frac{7}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{4} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{32 \, {\left(735 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{13} + 5985 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} \sqrt{a} + 18830 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{11} a + 16730 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} a^{\frac{3}{2}} - 32403 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{9} a^{2} - 61397 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} a^{\frac{5}{2}} + 28244 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} a^{3} + 69692 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} a^{\frac{7}{2}} - 40663 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a^{4} - 32697 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{9}{2}} + 41342 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{5} - 17654 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{11}{2}} + 3563 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{6} - 307 \, a^{\frac{13}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{7} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{8960 \, d}"," ",0,"-1/8960*(3465*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) - sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 70*(77*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7 - 283*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(a) + 199*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a + 299*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(3/2) + 15*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^2 - 177*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(5/2) - 107*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^3 - 23*a^(7/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^4*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 32*(735*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^13 + 5985*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^12*sqrt(a) + 18830*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^11*a + 16730*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^10*a^(3/2) - 32403*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^9*a^2 - 61397*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^8*a^(5/2) + 28244*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7*a^3 + 69692*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*a^(7/2) - 40663*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a^4 - 32697*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(9/2) + 41342*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^5 - 17654*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(11/2) + 3563*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^6 - 307*a^(13/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^7*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
181,-2,0,0,0.000000," ","integrate(sec(d*x+c)^6/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((d*t_nostep+c)/2-pi/4))]Discontinuities at zeroes of cos((d*t_nostep+c)/2-pi/4) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 0.71Not invertible Error: Bad Argument Value","F(-2)",0
182,1,526,0,2.360278," ","integrate(cos(d*x+c)^10/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{1024 \, \sqrt{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{\frac{5}{2}}} - \frac{\frac{263 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{2145 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{7335 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{13585 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{15795 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{17589 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{29315 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{45045 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{45045 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{29315 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{17589 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{15795 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{13585 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{7335 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{263 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{2145 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{15}{2}}}\right)}}{2145 \, d}"," ",0,"2/2145*(1024*sqrt(2)*sgn(tan(1/2*d*x + 1/2*c) + 1)/a^(5/2) - (263*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (2145*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (7335*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (13585*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (15795*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (17589*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (29315*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (45045*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (45045*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (29315*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (17589*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (15795*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (13585*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (7335*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) + (263*a^5*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 2145*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(15/2))/d","B",0
183,1,430,0,2.948833," ","integrate(cos(d*x+c)^9/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{9683 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{15015 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{25402 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{90090 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{107393 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{93093 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{183612 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{183612 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{93093 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{107393 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{90090 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{25402 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{9683 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{15015 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{15015 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{13}{2}} d}"," ",0,"2/15015*(9683*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (15015*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (25402*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (90090*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (107393*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (93093*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (183612*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (183612*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (93093*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (107393*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (90090*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (25402*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (9683*a^4*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) + 15015*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^2 + a)^(13/2)*d)","B",0
184,1,402,0,3.162052," ","integrate(cos(d*x+c)^8/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{64 \, \sqrt{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{\frac{5}{2}}} - \frac{\frac{13 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{99 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{319 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{561 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{594 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{462 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{462 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{594 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{561 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{319 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{13 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{99 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{11}{2}}}\right)}}{99 \, d}"," ",0,"2/99*(64*sqrt(2)*sgn(tan(1/2*d*x + 1/2*c) + 1)/a^(5/2) - (13*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (99*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (319*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (561*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (594*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (462*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (462*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (594*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (561*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (319*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) + (13*a^3*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 99*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(11/2))/d","B",0
185,1,310,0,10.721484," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left({\left({\left({\left({\left({\left({\left(\frac{319 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{315 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{648 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{1680 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{1134 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{1134 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{1680 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{648 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{315 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{319 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{315 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{9}{2}} d}"," ",0,"2/315*(((((((((319*a^2*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) + 315*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 648*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 1680*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 1134*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 1134*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 1680*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 648*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 315*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 319*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))/((a*tan(1/2*d*x + 1/2*c)^2 + a)^(9/2)*d)","B",0
186,1,255,0,5.636797," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{8 \, \sqrt{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{\frac{5}{2}}} + \frac{{\left({\left({\left({\left({\left({\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{7 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{21 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{35 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{35 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{21 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{7 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{7}{2}}}\right)}}{7 \, d}"," ",0,"2/7*(8*sqrt(2)*sgn(tan(1/2*d*x + 1/2*c) + 1)/a^(5/2) + (((((((a*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 7*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 21*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 35*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 35*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 21*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 7*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - a/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(7/2))/d","B",0
187,1,172,0,5.242854," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left({\left({\left(\frac{43 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{15}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{70}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{70}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{15}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{43}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{15 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{5}{2}} d}"," ",0,"2/15*(((((43*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) + 15/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 70/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 70/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 15/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 43/sgn(tan(1/2*d*x + 1/2*c) + 1))/((a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2)*d)","B",0
188,1,255,0,3.119246," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left({\left(\frac{7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{9}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{9}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{7}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}}} + \frac{4 \, \sqrt{2} {\left(3 \, a \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) + 2 \, \sqrt{-a} \sqrt{a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{-a} a^{3}} - \frac{12 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{3 \, d}"," ",0,"-2/3*((((7*tan(1/2*d*x + 1/2*c)/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 9/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) + 9/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) - 7/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2) + 4*sqrt(2)*(3*a*arctan(sqrt(a)/sqrt(-a)) + 2*sqrt(-a)*sqrt(a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(-a)*a^3) - 12*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
189,1,39,0,1.446134," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{\sqrt{a \sin\left(d x + c\right) + a}}{a^{3}} + \frac{2}{\sqrt{a \sin\left(d x + c\right) + a} a^{2}}\right)}}{d}"," ",0,"-2*(sqrt(a*sin(d*x + c) + a)/a^3 + 2/(sqrt(a*sin(d*x + c) + a)*a^2))/d","A",0
190,1,293,0,1.631937," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{2 \, {\left(3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} + {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} - {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a + a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{2} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{d}"," ",0,"-(sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 2*(3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 + (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) - (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a + a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^2*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
191,1,20,0,1.429212," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{2}{3 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a d}"," ",0,"-2/3/((a*sin(d*x + c) + a)^(3/2)*a*d)","A",0
192,-2,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((d*t_nostep+c)/2-pi/4))]Discontinuities at zeroes of cos((d*t_nostep+c)/2-pi/4) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 0.46Not invertible Error: Bad Argument Value","F(-2)",0
193,1,751,0,5.625957," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{105 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{96 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(615 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{11} + 3501 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} \sqrt{a} + 7911 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{9} a + 2841 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} a^{\frac{3}{2}} - 10122 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} a^{2} - 5054 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} a^{\frac{5}{2}} + 12222 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a^{3} - 846 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{7}{2}} - 5389 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{4} + 3681 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{9}{2}} - 981 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{5} + 133 \, a^{\frac{11}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{6} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{384 \, d}"," ",0,"1/384*(105*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 96*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(615*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^11 + 3501*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^10*sqrt(a) + 7911*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^9*a + 2841*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^8*a^(3/2) - 10122*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7*a^2 - 5054*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*a^(5/2) + 12222*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a^3 - 846*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(7/2) - 5389*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^4 + 3681*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(9/2) - 981*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^5 + 133*a^(11/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^6*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
194,1,916,0,11.917054," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{315 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} - \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{70 \, {\left(3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} - {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} - {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a - a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{2} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{8 \, {\left(455 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{13} + 3395 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} \sqrt{a} + 10290 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{11} a + 8750 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} a^{\frac{3}{2}} - 16807 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{9} a^{2} - 31423 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} a^{\frac{5}{2}} + 14076 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} a^{3} + 33908 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} a^{\frac{7}{2}} - 19607 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a^{4} - 15883 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{9}{2}} + 19698 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{5} - 8386 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{11}{2}} + 1687 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{6} - 153 \, a^{\frac{13}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{7} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{1120 \, d}"," ",0,"-1/1120*(315*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) - sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 70*(3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 - (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) - (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a - a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^2*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 8*(455*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^13 + 3395*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^12*sqrt(a) + 10290*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^11*a + 8750*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^10*a^(3/2) - 16807*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^9*a^2 - 31423*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^8*a^(5/2) + 14076*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7*a^3 + 33908*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*a^(7/2) - 19607*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a^4 - 15883*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(9/2) + 19698*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^5 - 8386*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(11/2) + 1687*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^6 - 153*a^(13/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^7*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
195,1,1074,0,9.341046," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{3465 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{256 \, {\left(21 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} - 51 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{a} - 34 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a + 102 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{3}{2}} + 81 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{2} + 17 \, a^{\frac{5}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{3} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(18423 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{15} + 165753 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} \sqrt{a} + 644313 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{13} a + 1072899 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} a^{\frac{3}{2}} + 94635 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{11} a^{2} - 1907635 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} a^{\frac{5}{2}} - 875803 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{9} a^{3} + 2261311 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} a^{\frac{7}{2}} + 723029 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} a^{4} - 2030229 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} a^{\frac{9}{2}} + 509147 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a^{5} + 688777 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{11}{2}} - 599223 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{6} + 219151 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{13}{2}} - 40793 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{7} + 3701 \, a^{\frac{15}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{8} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{12288 \, d}"," ",0,"1/12288*(3465*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 256*(21*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5 - 51*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(a) - 34*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a + 102*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(3/2) + 81*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^2 + 17*a^(5/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^3*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(18423*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^15 + 165753*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^14*sqrt(a) + 644313*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^13*a + 1072899*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^12*a^(3/2) + 94635*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^11*a^2 - 1907635*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^10*a^(5/2) - 875803*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^9*a^3 + 2261311*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^8*a^(7/2) + 723029*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7*a^4 - 2030229*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*a^(9/2) + 509147*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a^5 + 688777*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(11/2) - 599223*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^6 + 219151*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(13/2) - 40793*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^7 + 3701*a^(15/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^8*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
196,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(a \sin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)*(a*sin(d*x + c) + a), x)","F",0
197,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(a*sin(d*x + c) + a), x)","F",0
198,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a), x)","F",0
199,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))*(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a), x)","F",0
200,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{a \sin\left(d x + c\right) + a}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)/sqrt(e*cos(d*x + c)), x)","F",0
201,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))/(e*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{a \sin\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)/(e*cos(d*x + c))^(3/2), x)","F",0
202,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))/(e*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{a \sin\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)/(e*cos(d*x + c))^(5/2), x)","F",0
203,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))/(e*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{a \sin\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)/(e*cos(d*x + c))^(7/2), x)","F",0
204,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)*(a*sin(d*x + c) + a)^2, x)","F",0
205,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(a*sin(d*x + c) + a)^2, x)","F",0
206,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^2, x)","F",0
207,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2*(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^2, x)","F",0
208,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2/sqrt(e*cos(d*x + c)), x)","F",0
209,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2/(e*cos(d*x + c))^(3/2), x)","F",0
210,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2/(e*cos(d*x + c))^(5/2), x)","F",0
211,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2/(e*cos(d*x + c))^(7/2), x)","F",0
212,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(9/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2/(e*cos(d*x + c))^(9/2), x)","F",0
213,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(11/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}{\left(e \cos\left(d x + c\right)\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2/(e*cos(d*x + c))^(11/2), x)","F",0
214,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)*(a*sin(d*x + c) + a)^3, x)","F",0
215,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(a*sin(d*x + c) + a)^3, x)","F",0
216,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^3, x)","F",0
217,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3*(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^3, x)","F",0
218,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^3/sqrt(e*cos(d*x + c)), x)","F",0
219,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(3/2), x)","F",0
220,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(5/2), x)","F",0
221,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(7/2), x)","F",0
222,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(9/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(9/2), x)","F",0
223,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(11/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(11/2), x)","F",0
224,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{4}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^4, x)","F",0
225,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4*(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{4}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^4, x)","F",0
226,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^4/sqrt(e*cos(d*x + c)), x)","F",0
227,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(3/2), x)","F",0
228,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(5/2), x)","F",0
229,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(7/2), x)","F",0
230,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(9/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(9/2), x)","F",0
231,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(11/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(11/2), x)","F",0
232,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(13/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(13/2), x)","F",0
233,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
234,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
235,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)/(a*sin(d*x + c) + a), x)","F",0
236,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)/(a*sin(d*x + c) + a), x)","F",0
237,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)/(a*sin(d*x + c) + a), x)","F",0
238,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(a*sin(d*x + c) + a), x)","F",0
239,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)), x)","F",0
240,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)), x)","F",0
241,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(5/2)*(a*sin(d*x + c) + a)), x)","F",0
242,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(a \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(7/2)*(a*sin(d*x + c) + a)), x)","F",0
243,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
245,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
246,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)/(a*sin(d*x + c) + a)^2, x)","F",0
247,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)/(a*sin(d*x + c) + a)^2, x)","F",0
248,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(a*sin(d*x + c) + a)^2, x)","F",0
249,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^2), x)","F",0
250,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^2), x)","F",0
251,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(5/2)*(a*sin(d*x + c) + a)^2), x)","F",0
252,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(7/2)*(a*sin(d*x + c) + a)^2), x)","F",0
253,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(15/2)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
254,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(13/2)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
255,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
256,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
257,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)/(a*sin(d*x + c) + a)^3, x)","F",0
260,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(a*sin(d*x + c) + a)^3, x)","F",0
261,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^3), x)","F",0
262,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^3), x)","F",0
263,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(15/2)/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
264,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(13/2)/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
265,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
266,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
267,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
268,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
269,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
270,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(a*sin(d*x + c) + a)^4, x)","F",0
271,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^4), x)","F",0
272,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^4), x)","F",0
273,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} \sqrt{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*sqrt(a*sin(d*x + c) + a), x)","F",0
274,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a), x)","F",0
275,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)/sqrt(e*cos(d*x + c)), x)","F",0
276,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{a \sin\left(d x + c\right) + a}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)/(e*cos(d*x + c))^(3/2), x)","F",0
277,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
278,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
279,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
280,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(a*sin(d*x + c) + a)^(3/2), x)","F",0
281,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^(3/2), x)","F",0
282,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(3/2)*(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^(3/2), x)","F",0
283,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
284,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
285,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
286,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
287,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
288,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
289,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^(5/2), x)","F",0
290,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(5/2)*(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^(5/2), x)","F",0
291,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
294,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
295,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
296,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
297,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
300,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/sqrt(a*sin(d*x + c) + a), x)","F",0
301,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a)), x)","F",0
302,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} \sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(3/2)*sqrt(a*sin(d*x + c) + a)), x)","F",0
303,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} \sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(5/2)*sqrt(a*sin(d*x + c) + a)), x)","F",0
304,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} \sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(7/2)*sqrt(a*sin(d*x + c) + a)), x)","F",0
305,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
307,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
308,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(a*sin(d*x + c) + a)^(3/2), x)","F",0
309,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^(3/2)), x)","F",0
310,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^(3/2)), x)","F",0
311,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(5/2)*(a*sin(d*x + c) + a)^(3/2)), x)","F",0
312,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(7/2)*(a*sin(d*x + c) + a)^(3/2)), x)","F",0
313,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
314,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
315,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
316,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
317,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(a*sin(d*x + c) + a)^(5/2), x)","F",0
318,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^(5/2)), x)","F",0
319,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^(5/2)), x)","F",0
320,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(5/2)*(a*sin(d*x + c) + a)^(5/2)), x)","F",0
321,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
322,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(2/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
325,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(1/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(4/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{8} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^8*(e*cos(d*x + c))^p, x)","F",0
328,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{3} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^3*(e*cos(d*x + c))^p, x)","F",0
329,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{2} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2*(e*cos(d*x + c))^p, x)","F",0
330,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)*(e*cos(d*x + c))^p, x)","F",0
331,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(a*sin(d*x + c) + a), x)","F",0
332,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(a*sin(d*x + c) + a)^2, x)","F",0
333,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(a*sin(d*x + c) + a)^3, x)","F",0
334,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^8,x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(a \sin\left(d x + c\right) + a\right)}^{8}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(a*sin(d*x + c) + a)^8, x)","F",0
335,-2,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((d*x+c)/2-pi/4))]Simplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Evaluation time: 0.53Unable to divide, perhaps due to rounding error%%%{64*i,[0,2,0,2,2,1,3,1,1]%%%} / %%%{128*i,[0,2,0,2,2,0,0,0,0]%%%} Error: Bad Argument Value","F(-2)",0
336,-2,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((d*x+c)/2-pi/4))]Simplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to divide, perhaps due to rounding error%%%{-64,[0,2,0,2,2,1,2,1,1]%%%} / %%%{128*i,[0,2,0,2,2,0,0,0,0]%%%} Error: Bad Argument Value","F(-2)",0
337,-2,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((d*x+c)/2-pi/4))]Simplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to divide, perhaps due to rounding error%%%{-64*i,[0,2,0,2,2,1,1,1,1]%%%} / %%%{128*i,[0,2,0,2,2,0,0,0,0]%%%} Error: Bad Argument Value","F(-2)",0
338,-2,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((d*x+c)/2-pi/4))]Simplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to divide, perhaps due to rounding error%%%{64,[0,2,0,2,2,1,1,1]%%%} / %%%{128*i,[0,2,0,2,2,0,0,0]%%%} Error: Bad Argument Value","F(-2)",0
339,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/sqrt(a*sin(d*x + c) + a), x)","F",0
340,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(a*sin(d*x + c) + a)^(3/2), x)","F",0
341,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(a*sin(d*x + c) + a)^(5/2), x)","F",0
342,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{p} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p*(a*sin(d*x + c) + a)^m, x)","F",0
343,-1,0,0,0.000000," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
344,-1,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
345,1,152,0,1.470523," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","-\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m} m \sin\left(d x + c\right)^{3} + {\left(a \sin\left(d x + c\right) + a\right)}^{m} m \sin\left(d x + c\right)^{2} + 2 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sin\left(d x + c\right)^{3} - {\left(a \sin\left(d x + c\right) + a\right)}^{m} m \sin\left(d x + c\right) - {\left(a \sin\left(d x + c\right) + a\right)}^{m} m - 6 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sin\left(d x + c\right) - 4 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{{\left(m^{2} + 5 \, m + 6\right)} d}"," ",0,"-((a*sin(d*x + c) + a)^m*m*sin(d*x + c)^3 + (a*sin(d*x + c) + a)^m*m*sin(d*x + c)^2 + 2*(a*sin(d*x + c) + a)^m*sin(d*x + c)^3 - (a*sin(d*x + c) + a)^m*m*sin(d*x + c) - (a*sin(d*x + c) + a)^m*m - 6*(a*sin(d*x + c) + a)^m*sin(d*x + c) - 4*(a*sin(d*x + c) + a)^m)/((m^2 + 5*m + 6)*d)","B",0
346,1,26,0,0.921144," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m + 1}}{a d {\left(m + 1\right)}}"," ",0,"(a*sin(d*x + c) + a)^(m + 1)/(a*d*(m + 1))","A",0
347,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*sec(d*x + c), x)","F",0
348,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*sec(d*x + c)^3, x)","F",0
349,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*sec(d*x + c)^5, x)","F",0
350,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*cos(d*x + c)^4, x)","F",0
351,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*cos(d*x + c)^2, x)","F",0
352,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*sec(d*x + c)^2, x)","F",0
353,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*sec(d*x + c)^4, x)","F",0
354,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(a*sin(d*x + c) + a)^m, x)","F",0
355,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^m, x)","F",0
356,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^m, x)","F",0
357,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^m/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m/sqrt(e*cos(d*x + c)), x)","F",0
358,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^m/(e*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m/(e*cos(d*x + c))^(3/2), x)","F",0
359,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^m/(e*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m/(e*cos(d*x + c))^(5/2), x)","F",0
360,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-4-m)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-m - 4} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m - 4)*(a*sin(d*x + c) + a)^m, x)","F",0
361,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-3-m)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-m - 3} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m - 3)*(a*sin(d*x + c) + a)^m, x)","F",0
362,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-2-m)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-m - 2} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m - 2)*(a*sin(d*x + c) + a)^m, x)","F",0
363,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-1-m)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-m - 1} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m - 1)*(a*sin(d*x + c) + a)^m, x)","F",0
364,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^m/((e*cos(d*x+c))^m),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m}}{\left(e \cos\left(d x + c\right)\right)^{m}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m/(e*cos(d*x + c))^m, x)","F",0
365,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1-m)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-m + 1} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m + 1)*(a*sin(d*x + c) + a)^m, x)","F",0
366,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(2-m)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-m + 2} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m + 2)*(a*sin(d*x + c) + a)^m, x)","F",0
367,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-2 \, m + 5} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-2*m + 5)*(a*sin(d*x + c) + a)^m, x)","F",0
368,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-2 \, m + 3} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-2*m + 3)*(a*sin(d*x + c) + a)^m, x)","F",0
369,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-2 \, m + 1} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-2*m + 1)*(a*sin(d*x + c) + a)^m, x)","F",0
370,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-1-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-2 \, m - 1} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-2*m - 1)*(a*sin(d*x + c) + a)^m, x)","F",0
371,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-3-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-2 \, m - 3} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-2*m - 3)*(a*sin(d*x + c) + a)^m, x)","F",0
372,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(4-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-2 \, m + 4} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-2*m + 4)*(a*sin(d*x + c) + a)^m, x)","F",0
373,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(2-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-2 \, m + 2} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-2*m + 2)*(a*sin(d*x + c) + a)^m, x)","F",0
374,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^m/((e*cos(d*x+c))^(2*m)),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m}}{\left(e \cos\left(d x + c\right)\right)^{2 \, m}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m/(e*cos(d*x + c))^(2*m), x)","F",0
375,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-2-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-2 \, m - 2} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-2*m - 2)*(a*sin(d*x + c) + a)^m, x)","F",0
376,1,88,0,0.920331," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{b \cos\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{b \cos\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{5 \, b \cos\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{a \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{5 \, a \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{5 \, a \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/192*b*cos(6*d*x + 6*c)/d - 1/32*b*cos(4*d*x + 4*c)/d - 5/64*b*cos(2*d*x + 2*c)/d + 1/80*a*sin(5*d*x + 5*c)/d + 5/48*a*sin(3*d*x + 3*c)/d + 5/8*a*sin(d*x + c)/d","A",0
377,1,48,0,0.443657," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, b \sin\left(d x + c\right)^{4} + 4 \, a \sin\left(d x + c\right)^{3} - 6 \, b \sin\left(d x + c\right)^{2} - 12 \, a \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(3*b*sin(d*x + c)^4 + 4*a*sin(d*x + c)^3 - 6*b*sin(d*x + c)^2 - 12*a*sin(d*x + c))/d","A",0
378,1,25,0,0.404416," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{b \sin\left(d x + c\right)^{2} + 2 \, a \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(b*sin(d*x + c)^2 + 2*a*sin(d*x + c))/d","A",0
379,1,37,0,0.746443," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{{\left(a - b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - {\left(a + b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{2 \, d}"," ",0,"1/2*((a - b)*log(abs(sin(d*x + c) + 1)) - (a + b)*log(abs(sin(d*x + c) - 1)))/d","A",0
380,1,55,0,0.660555," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - a \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(a \sin\left(d x + c\right) + b\right)}}{\sin\left(d x + c\right)^{2} - 1}}{4 \, d}"," ",0,"1/4*(a*log(abs(sin(d*x + c) + 1)) - a*log(abs(sin(d*x + c) - 1)) - 2*(a*sin(d*x + c) + b)/(sin(d*x + c)^2 - 1))/d","A",0
381,1,70,0,0.579347," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 3 \, a \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, a \sin\left(d x + c\right)^{3} - 5 \, a \sin\left(d x + c\right) - 2 \, b\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(3*a*log(abs(sin(d*x + c) + 1)) - 3*a*log(abs(sin(d*x + c) - 1)) - 2*(3*a*sin(d*x + c)^3 - 5*a*sin(d*x + c) - 2*b)/(sin(d*x + c)^2 - 1)^2)/d","A",0
382,1,77,0,2.015300," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{3}{8} \, a x - \frac{b \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{b \cos\left(3 \, d x + 3 \, c\right)}{16 \, d} - \frac{b \cos\left(d x + c\right)}{8 \, d} + \frac{a \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{a \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"3/8*a*x - 1/80*b*cos(5*d*x + 5*c)/d - 1/16*b*cos(3*d*x + 3*c)/d - 1/8*b*cos(d*x + c)/d + 1/32*a*sin(4*d*x + 4*c)/d + 1/4*a*sin(2*d*x + 2*c)/d","A",0
383,1,47,0,0.347011," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{1}{2} \, a x - \frac{b \cos\left(3 \, d x + 3 \, c\right)}{12 \, d} - \frac{b \cos\left(d x + c\right)}{4 \, d} + \frac{a \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"1/2*a*x - 1/12*b*cos(3*d*x + 3*c)/d - 1/4*b*cos(d*x + c)/d + 1/4*a*sin(2*d*x + 2*c)/d","A",0
384,1,33,0,0.821374," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} d}"," ",0,"-2*(a*tan(1/2*d*x + 1/2*c) + b)/((tan(1/2*d*x + 1/2*c)^2 - 1)*d)","A",0
385,1,76,0,0.413027," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b\right)}}{3 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} d}"," ",0,"-2/3*(3*a*tan(1/2*d*x + 1/2*c)^5 + 3*b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^3 + 3*a*tan(1/2*d*x + 1/2*c) + b)/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*d)","A",0
386,1,120,0,1.274394," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 15 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 20 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 58 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 30 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 20 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, b\right)}}{15 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5} d}"," ",0,"-2/15*(15*a*tan(1/2*d*x + 1/2*c)^9 + 15*b*tan(1/2*d*x + 1/2*c)^8 - 20*a*tan(1/2*d*x + 1/2*c)^7 + 58*a*tan(1/2*d*x + 1/2*c)^5 + 30*b*tan(1/2*d*x + 1/2*c)^4 - 20*a*tan(1/2*d*x + 1/2*c)^3 + 15*a*tan(1/2*d*x + 1/2*c) + 3*b)/((tan(1/2*d*x + 1/2*c)^2 - 1)^5*d)","B",0
387,1,136,0,0.748046," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{a b \cos\left(6 \, d x + 6 \, c\right)}{96 \, d} - \frac{a b \cos\left(4 \, d x + 4 \, c\right)}{16 \, d} - \frac{5 \, a b \cos\left(2 \, d x + 2 \, c\right)}{32 \, d} - \frac{b^{2} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{{\left(4 \, a^{2} - 3 \, b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(20 \, a^{2} - b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{5 \, {\left(8 \, a^{2} + b^{2}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"-1/96*a*b*cos(6*d*x + 6*c)/d - 1/16*a*b*cos(4*d*x + 4*c)/d - 5/32*a*b*cos(2*d*x + 2*c)/d - 1/448*b^2*sin(7*d*x + 7*c)/d + 1/320*(4*a^2 - 3*b^2)*sin(5*d*x + 5*c)/d + 1/192*(20*a^2 - b^2)*sin(3*d*x + 3*c)/d + 5/64*(8*a^2 + b^2)*sin(d*x + c)/d","A",0
388,1,80,0,0.631352," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{6 \, b^{2} \sin\left(d x + c\right)^{5} + 15 \, a b \sin\left(d x + c\right)^{4} + 10 \, a^{2} \sin\left(d x + c\right)^{3} - 10 \, b^{2} \sin\left(d x + c\right)^{3} - 30 \, a b \sin\left(d x + c\right)^{2} - 30 \, a^{2} \sin\left(d x + c\right)}{30 \, d}"," ",0,"-1/30*(6*b^2*sin(d*x + c)^5 + 15*a*b*sin(d*x + c)^4 + 10*a^2*sin(d*x + c)^3 - 10*b^2*sin(d*x + c)^3 - 30*a*b*sin(d*x + c)^2 - 30*a^2*sin(d*x + c))/d","A",0
389,1,20,0,0.662733," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}{3 \, b d}"," ",0,"1/3*(b*sin(d*x + c) + a)^3/(b*d)","A",0
390,1,62,0,0.508860," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, b^{2} \sin\left(d x + c\right) - {\left(a^{2} - 2 \, a b + b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + {\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{2 \, d}"," ",0,"-1/2*(2*b^2*sin(d*x + c) - (a^2 - 2*a*b + b^2)*log(abs(sin(d*x + c) + 1)) + (a^2 + 2*a*b + b^2)*log(abs(sin(d*x + c) - 1)))/d","A",0
391,1,86,0,1.151879," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{{\left(a^{2} - b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - {\left(a^{2} - b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(a^{2} \sin\left(d x + c\right) + b^{2} \sin\left(d x + c\right) + 2 \, a b\right)}}{\sin\left(d x + c\right)^{2} - 1}}{4 \, d}"," ",0,"1/4*((a^2 - b^2)*log(abs(sin(d*x + c) + 1)) - (a^2 - b^2)*log(abs(sin(d*x + c) - 1)) - 2*(a^2*sin(d*x + c) + b^2*sin(d*x + c) + 2*a*b)/(sin(d*x + c)^2 - 1))/d","A",0
392,1,118,0,0.972736," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{{\left(3 \, a^{2} - b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - {\left(3 \, a^{2} - b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, a^{2} \sin\left(d x + c\right)^{3} - b^{2} \sin\left(d x + c\right)^{3} - 5 \, a^{2} \sin\left(d x + c\right) - b^{2} \sin\left(d x + c\right) - 4 \, a b\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*((3*a^2 - b^2)*log(abs(sin(d*x + c) + 1)) - (3*a^2 - b^2)*log(abs(sin(d*x + c) - 1)) - 2*(3*a^2*sin(d*x + c)^3 - b^2*sin(d*x + c)^3 - 5*a^2*sin(d*x + c) - b^2*sin(d*x + c) - 4*a*b)/(sin(d*x + c)^2 - 1)^2)/d","A",0
393,1,162,0,0.619997," ","integrate(cos(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{5}{128} \, {\left(8 \, a^{2} + b^{2}\right)} x - \frac{a b \cos\left(7 \, d x + 7 \, c\right)}{224 \, d} - \frac{a b \cos\left(5 \, d x + 5 \, c\right)}{32 \, d} - \frac{3 \, a b \cos\left(3 \, d x + 3 \, c\right)}{32 \, d} - \frac{5 \, a b \cos\left(d x + c\right)}{32 \, d} - \frac{b^{2} \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{{\left(a^{2} - b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{{\left(6 \, a^{2} - b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{{\left(15 \, a^{2} + b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"5/128*(8*a^2 + b^2)*x - 1/224*a*b*cos(7*d*x + 7*c)/d - 1/32*a*b*cos(5*d*x + 5*c)/d - 3/32*a*b*cos(3*d*x + 3*c)/d - 5/32*a*b*cos(d*x + c)/d - 1/1024*b^2*sin(8*d*x + 8*c)/d + 1/192*(a^2 - b^2)*sin(6*d*x + 6*c)/d + 1/128*(6*a^2 - b^2)*sin(4*d*x + 4*c)/d + 1/64*(15*a^2 + b^2)*sin(2*d*x + 2*c)/d","A",0
394,1,123,0,0.935445," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{16} \, {\left(6 \, a^{2} + b^{2}\right)} x - \frac{a b \cos\left(5 \, d x + 5 \, c\right)}{40 \, d} - \frac{a b \cos\left(3 \, d x + 3 \, c\right)}{8 \, d} - \frac{a b \cos\left(d x + c\right)}{4 \, d} - \frac{b^{2} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{{\left(2 \, a^{2} - b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(16 \, a^{2} + b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"1/16*(6*a^2 + b^2)*x - 1/40*a*b*cos(5*d*x + 5*c)/d - 1/8*a*b*cos(3*d*x + 3*c)/d - 1/4*a*b*cos(d*x + c)/d - 1/192*b^2*sin(6*d*x + 6*c)/d + 1/64*(2*a^2 - b^2)*sin(4*d*x + 4*c)/d + 1/64*(16*a^2 + b^2)*sin(2*d*x + 2*c)/d","A",0
395,1,76,0,1.006548," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, a^{2} + b^{2}\right)} x - \frac{a b \cos\left(3 \, d x + 3 \, c\right)}{6 \, d} - \frac{a b \cos\left(d x + c\right)}{2 \, d} - \frac{b^{2} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{a^{2} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"1/8*(4*a^2 + b^2)*x - 1/6*a*b*cos(3*d*x + 3*c)/d - 1/2*a*b*cos(d*x + c)/d - 1/32*b^2*sin(4*d*x + 4*c)/d + 1/4*a^2*sin(2*d*x + 2*c)/d","A",0
396,1,63,0,0.780428," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} b^{2} + \frac{2 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a b\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"-((d*x + c)*b^2 + 2*(a^2*tan(1/2*d*x + 1/2*c) + b^2*tan(1/2*d*x + 1/2*c) + 2*a*b)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","A",0
397,1,102,0,0.509546," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a b\right)}}{3 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} d}"," ",0,"-2/3*(3*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*a*b*tan(1/2*d*x + 1/2*c)^4 - 2*a^2*tan(1/2*d*x + 1/2*c)^3 + 4*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*a^2*tan(1/2*d*x + 1/2*c) + 2*a*b)/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*d)","A",0
398,1,181,0,0.544078," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 30 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 20 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 20 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 58 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 8 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 20 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a b\right)}}{15 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5} d}"," ",0,"-2/15*(15*a^2*tan(1/2*d*x + 1/2*c)^9 + 30*a*b*tan(1/2*d*x + 1/2*c)^8 - 20*a^2*tan(1/2*d*x + 1/2*c)^7 + 20*b^2*tan(1/2*d*x + 1/2*c)^7 + 58*a^2*tan(1/2*d*x + 1/2*c)^5 + 8*b^2*tan(1/2*d*x + 1/2*c)^5 + 60*a*b*tan(1/2*d*x + 1/2*c)^4 - 20*a^2*tan(1/2*d*x + 1/2*c)^3 + 20*b^2*tan(1/2*d*x + 1/2*c)^3 + 15*a^2*tan(1/2*d*x + 1/2*c) + 6*a*b)/((tan(1/2*d*x + 1/2*c)^2 - 1)^5*d)","A",0
399,1,260,0,0.404766," ","integrate(sec(d*x+c)^8*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(105 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 210 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 210 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 140 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 903 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 112 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1050 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 636 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 456 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 903 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 112 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 630 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 210 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 140 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 30 \, a b\right)}}{105 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{7} d}"," ",0,"-2/105*(105*a^2*tan(1/2*d*x + 1/2*c)^13 + 210*a*b*tan(1/2*d*x + 1/2*c)^12 - 210*a^2*tan(1/2*d*x + 1/2*c)^11 + 140*b^2*tan(1/2*d*x + 1/2*c)^11 + 903*a^2*tan(1/2*d*x + 1/2*c)^9 + 112*b^2*tan(1/2*d*x + 1/2*c)^9 + 1050*a*b*tan(1/2*d*x + 1/2*c)^8 - 636*a^2*tan(1/2*d*x + 1/2*c)^7 + 456*b^2*tan(1/2*d*x + 1/2*c)^7 + 903*a^2*tan(1/2*d*x + 1/2*c)^5 + 112*b^2*tan(1/2*d*x + 1/2*c)^5 + 630*a*b*tan(1/2*d*x + 1/2*c)^4 - 210*a^2*tan(1/2*d*x + 1/2*c)^3 + 140*b^2*tan(1/2*d*x + 1/2*c)^3 + 105*a^2*tan(1/2*d*x + 1/2*c) + 30*a*b)/((tan(1/2*d*x + 1/2*c)^2 - 1)^7*d)","B",0
400,1,185,0,0.996177," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{b^{3} \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{3 \, a b^{2} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{{\left(6 \, a^{2} b - b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)}{384 \, d} - \frac{{\left(24 \, a^{2} b + b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{3 \, {\left(10 \, a^{2} b + b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} + \frac{{\left(4 \, a^{3} - 9 \, a b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(20 \, a^{3} - 3 \, a b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{5 \, {\left(8 \, a^{3} + 3 \, a b^{2}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"1/1024*b^3*cos(8*d*x + 8*c)/d - 3/448*a*b^2*sin(7*d*x + 7*c)/d - 1/384*(6*a^2*b - b^3)*cos(6*d*x + 6*c)/d - 1/256*(24*a^2*b + b^3)*cos(4*d*x + 4*c)/d - 3/128*(10*a^2*b + b^3)*cos(2*d*x + 2*c)/d + 1/320*(4*a^3 - 9*a*b^2)*sin(5*d*x + 5*c)/d + 1/192*(20*a^3 - 3*a*b^2)*sin(3*d*x + 3*c)/d + 5/64*(8*a^3 + 3*a*b^2)*sin(d*x + c)/d","A",0
401,1,112,0,0.498942," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{10 \, b^{3} \sin\left(d x + c\right)^{6} + 36 \, a b^{2} \sin\left(d x + c\right)^{5} + 45 \, a^{2} b \sin\left(d x + c\right)^{4} - 15 \, b^{3} \sin\left(d x + c\right)^{4} + 20 \, a^{3} \sin\left(d x + c\right)^{3} - 60 \, a b^{2} \sin\left(d x + c\right)^{3} - 90 \, a^{2} b \sin\left(d x + c\right)^{2} - 60 \, a^{3} \sin\left(d x + c\right)}{60 \, d}"," ",0,"-1/60*(10*b^3*sin(d*x + c)^6 + 36*a*b^2*sin(d*x + c)^5 + 45*a^2*b*sin(d*x + c)^4 - 15*b^3*sin(d*x + c)^4 + 20*a^3*sin(d*x + c)^3 - 60*a*b^2*sin(d*x + c)^3 - 90*a^2*b*sin(d*x + c)^2 - 60*a^3*sin(d*x + c))/d","A",0
402,1,20,0,0.474445," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{{\left(b \sin\left(d x + c\right) + a\right)}^{4}}{4 \, b d}"," ",0,"1/4*(b*sin(d*x + c) + a)^4/(b*d)","A",0
403,1,93,0,0.526780," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{b^{3} \sin\left(d x + c\right)^{2} + 6 \, a b^{2} \sin\left(d x + c\right) - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{2 \, d}"," ",0,"-1/2*(b^3*sin(d*x + c)^2 + 6*a*b^2*sin(d*x + c) - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*log(abs(sin(d*x + c) + 1)) + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*log(abs(sin(d*x + c) - 1)))/d","A",0
404,1,114,0,1.134994," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{{\left(a^{3} - 3 \, a b^{2} + 2 \, b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(b^{3} \sin\left(d x + c\right)^{2} + a^{3} \sin\left(d x + c\right) + 3 \, a b^{2} \sin\left(d x + c\right) + 3 \, a^{2} b\right)}}{\sin\left(d x + c\right)^{2} - 1}}{4 \, d}"," ",0,"1/4*((a^3 - 3*a*b^2 + 2*b^3)*log(abs(sin(d*x + c) + 1)) - (a^3 - 3*a*b^2 - 2*b^3)*log(abs(sin(d*x + c) - 1)) - 2*(b^3*sin(d*x + c)^2 + a^3*sin(d*x + c) + 3*a*b^2*sin(d*x + c) + 3*a^2*b)/(sin(d*x + c)^2 - 1))/d","A",0
405,1,139,0,0.789155," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, {\left(a^{3} - a b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 3 \, {\left(a^{3} - a b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, a^{3} \sin\left(d x + c\right)^{3} - 3 \, a b^{2} \sin\left(d x + c\right)^{3} - 4 \, b^{3} \sin\left(d x + c\right)^{2} - 5 \, a^{3} \sin\left(d x + c\right) - 3 \, a b^{2} \sin\left(d x + c\right) - 6 \, a^{2} b + 2 \, b^{3}\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(3*(a^3 - a*b^2)*log(abs(sin(d*x + c) + 1)) - 3*(a^3 - a*b^2)*log(abs(sin(d*x + c) - 1)) - 2*(3*a^3*sin(d*x + c)^3 - 3*a*b^2*sin(d*x + c)^3 - 4*b^3*sin(d*x + c)^2 - 5*a^3*sin(d*x + c) - 3*a*b^2*sin(d*x + c) - 6*a^2*b + 2*b^3)/(sin(d*x + c)^2 - 1)^2)/d","A",0
406,1,173,0,1.261802," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{b^{3} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{a b^{2} \sin\left(6 \, d x + 6 \, c\right)}{64 \, d} + \frac{3}{16} \, {\left(2 \, a^{3} + a b^{2}\right)} x - \frac{{\left(12 \, a^{2} b - b^{3}\right)} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{{\left(12 \, a^{2} b + b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{3 \, {\left(8 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)}{64 \, d} + \frac{{\left(2 \, a^{3} - 3 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(16 \, a^{3} + 3 \, a b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"1/448*b^3*cos(7*d*x + 7*c)/d - 1/64*a*b^2*sin(6*d*x + 6*c)/d + 3/16*(2*a^3 + a*b^2)*x - 1/320*(12*a^2*b - b^3)*cos(5*d*x + 5*c)/d - 1/64*(12*a^2*b + b^3)*cos(3*d*x + 3*c)/d - 3/64*(8*a^2*b + b^3)*cos(d*x + c)/d + 1/64*(2*a^3 - 3*a*b^2)*sin(4*d*x + 4*c)/d + 1/64*(16*a^3 + 3*a*b^2)*sin(2*d*x + 2*c)/d","A",0
407,1,113,0,0.621973," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{b^{3} \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{3 \, a b^{2} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{a^{3} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{1}{8} \, {\left(4 \, a^{3} + 3 \, a b^{2}\right)} x - \frac{{\left(12 \, a^{2} b + b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{{\left(6 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)}{8 \, d}"," ",0,"1/80*b^3*cos(5*d*x + 5*c)/d - 3/32*a*b^2*sin(4*d*x + 4*c)/d + 1/4*a^3*sin(2*d*x + 2*c)/d + 1/8*(4*a^3 + 3*a*b^2)*x - 1/48*(12*a^2*b + b^3)*cos(3*d*x + 3*c)/d - 1/8*(6*a^2*b + b^3)*cos(d*x + c)/d","A",0
408,1,123,0,0.734683," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{3 \, {\left(d x + c\right)} a b^{2} + \frac{2 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2} b + 2 \, b^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"-(3*(d*x + c)*a*b^2 + 2*(a^3*tan(1/2*d*x + 1/2*c)^3 + 3*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*a^2*b*tan(1/2*d*x + 1/2*c)^2 + a^3*tan(1/2*d*x + 1/2*c) + 3*a*b^2*tan(1/2*d*x + 1/2*c) + 3*a^2*b + 2*b^3)/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","A",0
409,1,128,0,1.921371," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2} b - 2 \, b^{3}\right)}}{3 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} d}"," ",0,"-2/3*(3*a^3*tan(1/2*d*x + 1/2*c)^5 + 9*a^2*b*tan(1/2*d*x + 1/2*c)^4 - 2*a^3*tan(1/2*d*x + 1/2*c)^3 + 12*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*b^3*tan(1/2*d*x + 1/2*c)^2 + 3*a^3*tan(1/2*d*x + 1/2*c) + 3*a^2*b - 2*b^3)/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*d)","A",0
410,1,243,0,1.413829," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 45 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 20 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 58 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 90 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 10 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 20 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, a^{2} b - 2 \, b^{3}\right)}}{15 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5} d}"," ",0,"-2/15*(15*a^3*tan(1/2*d*x + 1/2*c)^9 + 45*a^2*b*tan(1/2*d*x + 1/2*c)^8 - 20*a^3*tan(1/2*d*x + 1/2*c)^7 + 60*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 30*b^3*tan(1/2*d*x + 1/2*c)^6 + 58*a^3*tan(1/2*d*x + 1/2*c)^5 + 24*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 90*a^2*b*tan(1/2*d*x + 1/2*c)^4 + 10*b^3*tan(1/2*d*x + 1/2*c)^4 - 20*a^3*tan(1/2*d*x + 1/2*c)^3 + 60*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 10*b^3*tan(1/2*d*x + 1/2*c)^2 + 15*a^3*tan(1/2*d*x + 1/2*c) + 9*a^2*b - 2*b^3)/((tan(1/2*d*x + 1/2*c)^2 - 1)^5*d)","A",0
411,1,358,0,1.884352," ","integrate(sec(d*x+c)^8*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(35 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 105 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 70 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 140 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 70 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 301 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 112 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 525 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 70 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 212 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 456 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 140 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 301 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 112 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 315 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 28 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 70 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 140 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 14 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, a^{2} b - 2 \, b^{3}\right)}}{35 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{7} d}"," ",0,"-2/35*(35*a^3*tan(1/2*d*x + 1/2*c)^13 + 105*a^2*b*tan(1/2*d*x + 1/2*c)^12 - 70*a^3*tan(1/2*d*x + 1/2*c)^11 + 140*a*b^2*tan(1/2*d*x + 1/2*c)^11 + 70*b^3*tan(1/2*d*x + 1/2*c)^10 + 301*a^3*tan(1/2*d*x + 1/2*c)^9 + 112*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 525*a^2*b*tan(1/2*d*x + 1/2*c)^8 + 70*b^3*tan(1/2*d*x + 1/2*c)^8 - 212*a^3*tan(1/2*d*x + 1/2*c)^7 + 456*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 140*b^3*tan(1/2*d*x + 1/2*c)^6 + 301*a^3*tan(1/2*d*x + 1/2*c)^5 + 112*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 315*a^2*b*tan(1/2*d*x + 1/2*c)^4 + 28*b^3*tan(1/2*d*x + 1/2*c)^4 - 70*a^3*tan(1/2*d*x + 1/2*c)^3 + 140*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 14*b^3*tan(1/2*d*x + 1/2*c)^2 + 35*a^3*tan(1/2*d*x + 1/2*c) + 15*a^2*b - 2*b^3)/((tan(1/2*d*x + 1/2*c)^2 - 1)^7*d)","B",0
412,1,473,0,1.595989," ","integrate(sec(d*x+c)^10*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(315 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} + 945 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{16} - 840 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 1260 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 630 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} + 4788 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1512 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 8820 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 1050 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 5112 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 8532 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3150 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 10658 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4272 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 13230 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 1890 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 5112 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 8532 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1890 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 4788 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1512 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3780 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 270 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 840 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1260 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 90 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 315 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, a^{2} b - 10 \, b^{3}\right)}}{315 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{9} d}"," ",0,"-2/315*(315*a^3*tan(1/2*d*x + 1/2*c)^17 + 945*a^2*b*tan(1/2*d*x + 1/2*c)^16 - 840*a^3*tan(1/2*d*x + 1/2*c)^15 + 1260*a*b^2*tan(1/2*d*x + 1/2*c)^15 + 630*b^3*tan(1/2*d*x + 1/2*c)^14 + 4788*a^3*tan(1/2*d*x + 1/2*c)^13 + 1512*a*b^2*tan(1/2*d*x + 1/2*c)^13 + 8820*a^2*b*tan(1/2*d*x + 1/2*c)^12 + 1050*b^3*tan(1/2*d*x + 1/2*c)^12 - 5112*a^3*tan(1/2*d*x + 1/2*c)^11 + 8532*a*b^2*tan(1/2*d*x + 1/2*c)^11 + 3150*b^3*tan(1/2*d*x + 1/2*c)^10 + 10658*a^3*tan(1/2*d*x + 1/2*c)^9 + 4272*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 13230*a^2*b*tan(1/2*d*x + 1/2*c)^8 + 1890*b^3*tan(1/2*d*x + 1/2*c)^8 - 5112*a^3*tan(1/2*d*x + 1/2*c)^7 + 8532*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 1890*b^3*tan(1/2*d*x + 1/2*c)^6 + 4788*a^3*tan(1/2*d*x + 1/2*c)^5 + 1512*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 3780*a^2*b*tan(1/2*d*x + 1/2*c)^4 + 270*b^3*tan(1/2*d*x + 1/2*c)^4 - 840*a^3*tan(1/2*d*x + 1/2*c)^3 + 1260*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 90*b^3*tan(1/2*d*x + 1/2*c)^2 + 315*a^3*tan(1/2*d*x + 1/2*c) + 105*a^2*b - 10*b^3)/((tan(1/2*d*x + 1/2*c)^2 - 1)^9*d)","B",0
413,1,464,0,3.939317," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{a b^{7} \cos\left(12 \, d x + 12 \, c\right)}{3072 \, d} + \frac{b^{8} \sin\left(13 \, d x + 13 \, c\right)}{53248 \, d} - \frac{{\left(14 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(10 \, d x + 10 \, c\right)}{1280 \, d} + \frac{{\left(28 \, a^{5} b^{3} - a b^{7}\right)} \cos\left(8 \, d x + 8 \, c\right)}{512 \, d} - \frac{{\left(32 \, a^{7} b - 112 \, a^{5} b^{3} - 70 \, a^{3} b^{5} - 5 \, a b^{7}\right)} \cos\left(6 \, d x + 6 \, c\right)}{768 \, d} - \frac{{\left(256 \, a^{7} b + 224 \, a^{5} b^{3} - 5 \, a b^{7}\right)} \cos\left(4 \, d x + 4 \, c\right)}{1024 \, d} - \frac{{\left(80 \, a^{7} b + 168 \, a^{5} b^{3} + 70 \, a^{3} b^{5} + 5 \, a b^{7}\right)} \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} - \frac{{\left(112 \, a^{2} b^{6} + 3 \, b^{8}\right)} \sin\left(11 \, d x + 11 \, c\right)}{45056 \, d} + \frac{{\left(560 \, a^{4} b^{4} + 56 \, a^{2} b^{6} - b^{8}\right)} \sin\left(9 \, d x + 9 \, c\right)}{18432 \, d} - \frac{{\left(128 \, a^{6} b^{2} - 80 \, a^{4} b^{4} - 40 \, a^{2} b^{6} - b^{8}\right)} \sin\left(7 \, d x + 7 \, c\right)}{2048 \, d} + \frac{{\left(256 \, a^{8} - 5376 \, a^{6} b^{2} - 4480 \, a^{4} b^{4} - 560 \, a^{2} b^{6} - 5 \, b^{8}\right)} \sin\left(5 \, d x + 5 \, c\right)}{20480 \, d} + \frac{{\left(1280 \, a^{8} - 1792 \, a^{6} b^{2} - 4480 \, a^{4} b^{4} - 1120 \, a^{2} b^{6} - 25 \, b^{8}\right)} \sin\left(3 \, d x + 3 \, c\right)}{12288 \, d} + \frac{5 \, {\left(128 \, a^{8} + 448 \, a^{6} b^{2} + 336 \, a^{4} b^{4} + 56 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{1024 \, d}"," ",0,"1/3072*a*b^7*cos(12*d*x + 12*c)/d + 1/53248*b^8*sin(13*d*x + 13*c)/d - 1/1280*(14*a^3*b^5 + a*b^7)*cos(10*d*x + 10*c)/d + 1/512*(28*a^5*b^3 - a*b^7)*cos(8*d*x + 8*c)/d - 1/768*(32*a^7*b - 112*a^5*b^3 - 70*a^3*b^5 - 5*a*b^7)*cos(6*d*x + 6*c)/d - 1/1024*(256*a^7*b + 224*a^5*b^3 - 5*a*b^7)*cos(4*d*x + 4*c)/d - 1/128*(80*a^7*b + 168*a^5*b^3 + 70*a^3*b^5 + 5*a*b^7)*cos(2*d*x + 2*c)/d - 1/45056*(112*a^2*b^6 + 3*b^8)*sin(11*d*x + 11*c)/d + 1/18432*(560*a^4*b^4 + 56*a^2*b^6 - b^8)*sin(9*d*x + 9*c)/d - 1/2048*(128*a^6*b^2 - 80*a^4*b^4 - 40*a^2*b^6 - b^8)*sin(7*d*x + 7*c)/d + 1/20480*(256*a^8 - 5376*a^6*b^2 - 4480*a^4*b^4 - 560*a^2*b^6 - 5*b^8)*sin(5*d*x + 5*c)/d + 1/12288*(1280*a^8 - 1792*a^6*b^2 - 4480*a^4*b^4 - 1120*a^2*b^6 - 25*b^8)*sin(3*d*x + 3*c)/d + 5/1024*(128*a^8 + 448*a^6*b^2 + 336*a^4*b^4 + 56*a^2*b^6 + b^8)*sin(d*x + c)/d","B",0
414,1,272,0,1.970851," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{45 \, b^{8} \sin\left(d x + c\right)^{11} + 396 \, a b^{7} \sin\left(d x + c\right)^{10} + 1540 \, a^{2} b^{6} \sin\left(d x + c\right)^{9} - 55 \, b^{8} \sin\left(d x + c\right)^{9} + 3465 \, a^{3} b^{5} \sin\left(d x + c\right)^{8} - 495 \, a b^{7} \sin\left(d x + c\right)^{8} + 4950 \, a^{4} b^{4} \sin\left(d x + c\right)^{7} - 1980 \, a^{2} b^{6} \sin\left(d x + c\right)^{7} + 4620 \, a^{5} b^{3} \sin\left(d x + c\right)^{6} - 4620 \, a^{3} b^{5} \sin\left(d x + c\right)^{6} + 2772 \, a^{6} b^{2} \sin\left(d x + c\right)^{5} - 6930 \, a^{4} b^{4} \sin\left(d x + c\right)^{5} + 990 \, a^{7} b \sin\left(d x + c\right)^{4} - 6930 \, a^{5} b^{3} \sin\left(d x + c\right)^{4} + 165 \, a^{8} \sin\left(d x + c\right)^{3} - 4620 \, a^{6} b^{2} \sin\left(d x + c\right)^{3} - 1980 \, a^{7} b \sin\left(d x + c\right)^{2} - 495 \, a^{8} \sin\left(d x + c\right)}{495 \, d}"," ",0,"-1/495*(45*b^8*sin(d*x + c)^11 + 396*a*b^7*sin(d*x + c)^10 + 1540*a^2*b^6*sin(d*x + c)^9 - 55*b^8*sin(d*x + c)^9 + 3465*a^3*b^5*sin(d*x + c)^8 - 495*a*b^7*sin(d*x + c)^8 + 4950*a^4*b^4*sin(d*x + c)^7 - 1980*a^2*b^6*sin(d*x + c)^7 + 4620*a^5*b^3*sin(d*x + c)^6 - 4620*a^3*b^5*sin(d*x + c)^6 + 2772*a^6*b^2*sin(d*x + c)^5 - 6930*a^4*b^4*sin(d*x + c)^5 + 990*a^7*b*sin(d*x + c)^4 - 6930*a^5*b^3*sin(d*x + c)^4 + 165*a^8*sin(d*x + c)^3 - 4620*a^6*b^2*sin(d*x + c)^3 - 1980*a^7*b*sin(d*x + c)^2 - 495*a^8*sin(d*x + c))/d","B",0
415,1,20,0,2.932443," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{{\left(b \sin\left(d x + c\right) + a\right)}^{9}}{9 \, b d}"," ",0,"1/9*(b*sin(d*x + c) + a)^9/(b*d)","A",0
416,1,378,0,1.992464," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{30 \, b^{8} \sin\left(d x + c\right)^{7} + 280 \, a b^{7} \sin\left(d x + c\right)^{6} + 1176 \, a^{2} b^{6} \sin\left(d x + c\right)^{5} + 42 \, b^{8} \sin\left(d x + c\right)^{5} + 2940 \, a^{3} b^{5} \sin\left(d x + c\right)^{4} + 420 \, a b^{7} \sin\left(d x + c\right)^{4} + 4900 \, a^{4} b^{4} \sin\left(d x + c\right)^{3} + 1960 \, a^{2} b^{6} \sin\left(d x + c\right)^{3} + 70 \, b^{8} \sin\left(d x + c\right)^{3} + 5880 \, a^{5} b^{3} \sin\left(d x + c\right)^{2} + 5880 \, a^{3} b^{5} \sin\left(d x + c\right)^{2} + 840 \, a b^{7} \sin\left(d x + c\right)^{2} + 5880 \, a^{6} b^{2} \sin\left(d x + c\right) + 14700 \, a^{4} b^{4} \sin\left(d x + c\right) + 5880 \, a^{2} b^{6} \sin\left(d x + c\right) + 210 \, b^{8} \sin\left(d x + c\right) - 105 \, {\left(a^{8} - 8 \, a^{7} b + 28 \, a^{6} b^{2} - 56 \, a^{5} b^{3} + 70 \, a^{4} b^{4} - 56 \, a^{3} b^{5} + 28 \, a^{2} b^{6} - 8 \, a b^{7} + b^{8}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 105 \, {\left(a^{8} + 8 \, a^{7} b + 28 \, a^{6} b^{2} + 56 \, a^{5} b^{3} + 70 \, a^{4} b^{4} + 56 \, a^{3} b^{5} + 28 \, a^{2} b^{6} + 8 \, a b^{7} + b^{8}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{210 \, d}"," ",0,"-1/210*(30*b^8*sin(d*x + c)^7 + 280*a*b^7*sin(d*x + c)^6 + 1176*a^2*b^6*sin(d*x + c)^5 + 42*b^8*sin(d*x + c)^5 + 2940*a^3*b^5*sin(d*x + c)^4 + 420*a*b^7*sin(d*x + c)^4 + 4900*a^4*b^4*sin(d*x + c)^3 + 1960*a^2*b^6*sin(d*x + c)^3 + 70*b^8*sin(d*x + c)^3 + 5880*a^5*b^3*sin(d*x + c)^2 + 5880*a^3*b^5*sin(d*x + c)^2 + 840*a*b^7*sin(d*x + c)^2 + 5880*a^6*b^2*sin(d*x + c) + 14700*a^4*b^4*sin(d*x + c) + 5880*a^2*b^6*sin(d*x + c) + 210*b^8*sin(d*x + c) - 105*(a^8 - 8*a^7*b + 28*a^6*b^2 - 56*a^5*b^3 + 70*a^4*b^4 - 56*a^3*b^5 + 28*a^2*b^6 - 8*a*b^7 + b^8)*log(abs(sin(d*x + c) + 1)) + 105*(a^8 + 8*a^7*b + 28*a^6*b^2 + 56*a^5*b^3 + 70*a^4*b^4 + 56*a^3*b^5 + 28*a^2*b^6 + 8*a*b^7 + b^8)*log(abs(sin(d*x + c) - 1)))/d","A",0
417,1,408,0,0.596167," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{12 \, b^{8} \sin\left(d x + c\right)^{5} + 120 \, a b^{7} \sin\left(d x + c\right)^{4} + 560 \, a^{2} b^{6} \sin\left(d x + c\right)^{3} + 40 \, b^{8} \sin\left(d x + c\right)^{3} + 1680 \, a^{3} b^{5} \sin\left(d x + c\right)^{2} + 480 \, a b^{7} \sin\left(d x + c\right)^{2} + 4200 \, a^{4} b^{4} \sin\left(d x + c\right) + 3360 \, a^{2} b^{6} \sin\left(d x + c\right) + 180 \, b^{8} \sin\left(d x + c\right) + 15 \, {\left(a^{8} - 28 \, a^{6} b^{2} + 112 \, a^{5} b^{3} - 210 \, a^{4} b^{4} + 224 \, a^{3} b^{5} - 140 \, a^{2} b^{6} + 48 \, a b^{7} - 7 \, b^{8}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 15 \, {\left(a^{8} - 28 \, a^{6} b^{2} - 112 \, a^{5} b^{3} - 210 \, a^{4} b^{4} - 224 \, a^{3} b^{5} - 140 \, a^{2} b^{6} - 48 \, a b^{7} - 7 \, b^{8}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{30 \, {\left(56 \, a^{5} b^{3} \sin\left(d x + c\right)^{2} + 112 \, a^{3} b^{5} \sin\left(d x + c\right)^{2} + 24 \, a b^{7} \sin\left(d x + c\right)^{2} + a^{8} \sin\left(d x + c\right) + 28 \, a^{6} b^{2} \sin\left(d x + c\right) + 70 \, a^{4} b^{4} \sin\left(d x + c\right) + 28 \, a^{2} b^{6} \sin\left(d x + c\right) + b^{8} \sin\left(d x + c\right) + 8 \, a^{7} b - 56 \, a^{3} b^{5} - 16 \, a b^{7}\right)}}{\sin\left(d x + c\right)^{2} - 1}}{60 \, d}"," ",0,"1/60*(12*b^8*sin(d*x + c)^5 + 120*a*b^7*sin(d*x + c)^4 + 560*a^2*b^6*sin(d*x + c)^3 + 40*b^8*sin(d*x + c)^3 + 1680*a^3*b^5*sin(d*x + c)^2 + 480*a*b^7*sin(d*x + c)^2 + 4200*a^4*b^4*sin(d*x + c) + 3360*a^2*b^6*sin(d*x + c) + 180*b^8*sin(d*x + c) + 15*(a^8 - 28*a^6*b^2 + 112*a^5*b^3 - 210*a^4*b^4 + 224*a^3*b^5 - 140*a^2*b^6 + 48*a*b^7 - 7*b^8)*log(abs(sin(d*x + c) + 1)) - 15*(a^8 - 28*a^6*b^2 - 112*a^5*b^3 - 210*a^4*b^4 - 224*a^3*b^5 - 140*a^2*b^6 - 48*a*b^7 - 7*b^8)*log(abs(sin(d*x + c) - 1)) - 30*(56*a^5*b^3*sin(d*x + c)^2 + 112*a^3*b^5*sin(d*x + c)^2 + 24*a*b^7*sin(d*x + c)^2 + a^8*sin(d*x + c) + 28*a^6*b^2*sin(d*x + c) + 70*a^4*b^4*sin(d*x + c) + 28*a^2*b^6*sin(d*x + c) + b^8*sin(d*x + c) + 8*a^7*b - 56*a^3*b^5 - 16*a*b^7)/(sin(d*x + c)^2 - 1))/d","A",0
418,1,429,0,0.998444," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{16 \, b^{8} \sin\left(d x + c\right)^{3} + 192 \, a b^{7} \sin\left(d x + c\right)^{2} + 1344 \, a^{2} b^{6} \sin\left(d x + c\right) + 144 \, b^{8} \sin\left(d x + c\right) - 3 \, {\left(3 \, a^{8} - 28 \, a^{6} b^{2} + 210 \, a^{4} b^{4} - 448 \, a^{3} b^{5} + 420 \, a^{2} b^{6} - 192 \, a b^{7} + 35 \, b^{8}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 3 \, {\left(3 \, a^{8} - 28 \, a^{6} b^{2} + 210 \, a^{4} b^{4} + 448 \, a^{3} b^{5} + 420 \, a^{2} b^{6} + 192 \, a b^{7} + 35 \, b^{8}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{6 \, {\left(336 \, a^{3} b^{5} \sin\left(d x + c\right)^{4} + 144 \, a b^{7} \sin\left(d x + c\right)^{4} - 3 \, a^{8} \sin\left(d x + c\right)^{3} + 28 \, a^{6} b^{2} \sin\left(d x + c\right)^{3} + 350 \, a^{4} b^{4} \sin\left(d x + c\right)^{3} + 252 \, a^{2} b^{6} \sin\left(d x + c\right)^{3} + 13 \, b^{8} \sin\left(d x + c\right)^{3} + 224 \, a^{5} b^{3} \sin\left(d x + c\right)^{2} - 224 \, a^{3} b^{5} \sin\left(d x + c\right)^{2} - 192 \, a b^{7} \sin\left(d x + c\right)^{2} + 5 \, a^{8} \sin\left(d x + c\right) + 28 \, a^{6} b^{2} \sin\left(d x + c\right) - 210 \, a^{4} b^{4} \sin\left(d x + c\right) - 196 \, a^{2} b^{6} \sin\left(d x + c\right) - 11 \, b^{8} \sin\left(d x + c\right) + 16 \, a^{7} b - 112 \, a^{5} b^{3} + 64 \, a b^{7}\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{48 \, d}"," ",0,"-1/48*(16*b^8*sin(d*x + c)^3 + 192*a*b^7*sin(d*x + c)^2 + 1344*a^2*b^6*sin(d*x + c) + 144*b^8*sin(d*x + c) - 3*(3*a^8 - 28*a^6*b^2 + 210*a^4*b^4 - 448*a^3*b^5 + 420*a^2*b^6 - 192*a*b^7 + 35*b^8)*log(abs(sin(d*x + c) + 1)) + 3*(3*a^8 - 28*a^6*b^2 + 210*a^4*b^4 + 448*a^3*b^5 + 420*a^2*b^6 + 192*a*b^7 + 35*b^8)*log(abs(sin(d*x + c) - 1)) - 6*(336*a^3*b^5*sin(d*x + c)^4 + 144*a*b^7*sin(d*x + c)^4 - 3*a^8*sin(d*x + c)^3 + 28*a^6*b^2*sin(d*x + c)^3 + 350*a^4*b^4*sin(d*x + c)^3 + 252*a^2*b^6*sin(d*x + c)^3 + 13*b^8*sin(d*x + c)^3 + 224*a^5*b^3*sin(d*x + c)^2 - 224*a^3*b^5*sin(d*x + c)^2 - 192*a*b^7*sin(d*x + c)^2 + 5*a^8*sin(d*x + c) + 28*a^6*b^2*sin(d*x + c) - 210*a^4*b^4*sin(d*x + c) - 196*a^2*b^6*sin(d*x + c) - 11*b^8*sin(d*x + c) + 16*a^7*b - 112*a^5*b^3 + 64*a*b^7)/(sin(d*x + c)^2 - 1)^2)/d","A",0
419,1,364,0,3.190056," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{a b^{7} \cos\left(9 \, d x + 9 \, c\right)}{288 \, d} + \frac{b^{8} \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{1}{256} \, {\left(128 \, a^{8} + 896 \, a^{6} b^{2} + 1120 \, a^{4} b^{4} + 280 \, a^{2} b^{6} + 7 \, b^{8}\right)} x - \frac{{\left(28 \, a^{3} b^{5} + 5 \, a b^{7}\right)} \cos\left(7 \, d x + 7 \, c\right)}{224 \, d} + \frac{{\left(28 \, a^{5} b^{3} + 21 \, a^{3} b^{5} + 2 \, a b^{7}\right)} \cos\left(5 \, d x + 5 \, c\right)}{40 \, d} - \frac{{\left(16 \, a^{7} b + 28 \, a^{5} b^{3} + 7 \, a^{3} b^{5}\right)} \cos\left(3 \, d x + 3 \, c\right)}{24 \, d} - \frac{{\left(32 \, a^{7} b + 112 \, a^{5} b^{3} + 70 \, a^{3} b^{5} + 7 \, a b^{7}\right)} \cos\left(d x + c\right)}{16 \, d} - \frac{{\left(56 \, a^{2} b^{6} + 3 \, b^{8}\right)} \sin\left(8 \, d x + 8 \, c\right)}{2048 \, d} + \frac{{\left(1120 \, a^{4} b^{4} + 448 \, a^{2} b^{6} + 13 \, b^{8}\right)} \sin\left(6 \, d x + 6 \, c\right)}{3072 \, d} - \frac{{\left(224 \, a^{6} b^{2} + 280 \, a^{4} b^{4} + 56 \, a^{2} b^{6} + b^{8}\right)} \sin\left(4 \, d x + 4 \, c\right)}{256 \, d} + \frac{{\left(128 \, a^{8} - 560 \, a^{4} b^{4} - 224 \, a^{2} b^{6} - 7 \, b^{8}\right)} \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"1/288*a*b^7*cos(9*d*x + 9*c)/d + 1/5120*b^8*sin(10*d*x + 10*c)/d + 1/256*(128*a^8 + 896*a^6*b^2 + 1120*a^4*b^4 + 280*a^2*b^6 + 7*b^8)*x - 1/224*(28*a^3*b^5 + 5*a*b^7)*cos(7*d*x + 7*c)/d + 1/40*(28*a^5*b^3 + 21*a^3*b^5 + 2*a*b^7)*cos(5*d*x + 5*c)/d - 1/24*(16*a^7*b + 28*a^5*b^3 + 7*a^3*b^5)*cos(3*d*x + 3*c)/d - 1/16*(32*a^7*b + 112*a^5*b^3 + 70*a^3*b^5 + 7*a*b^7)*cos(d*x + c)/d - 1/2048*(56*a^2*b^6 + 3*b^8)*sin(8*d*x + 8*c)/d + 1/3072*(1120*a^4*b^4 + 448*a^2*b^6 + 13*b^8)*sin(6*d*x + 6*c)/d - 1/256*(224*a^6*b^2 + 280*a^4*b^4 + 56*a^2*b^6 + b^8)*sin(4*d*x + 4*c)/d + 1/512*(128*a^8 - 560*a^4*b^4 - 224*a^2*b^6 - 7*b^8)*sin(2*d*x + 2*c)/d","A",0
420,1,799,0,0.782850," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{105 \, {\left(64 \, a^{6} b^{2} + 240 \, a^{4} b^{4} + 120 \, a^{2} b^{6} + 5 \, b^{8}\right)} {\left(d x + c\right)} + \frac{480 \, {\left(a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 28 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 70 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 28 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, a^{7} b + 56 \, a^{5} b^{3} + 56 \, a^{3} b^{5} + 8 \, a b^{7}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + \frac{2 \, {\left(8400 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 5880 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 285 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 13440 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 13440 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 1920 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 25200 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 24360 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1295 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 67200 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 94080 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 13440 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 16800 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 18480 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1650 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 134400 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 224000 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 42240 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 16800 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18480 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1650 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 134400 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 241920 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 49920 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 25200 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24360 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1295 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 67200 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 120960 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 23424 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8400 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5880 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 285 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 13440 \, a^{5} b^{3} - 22400 \, a^{3} b^{5} - 4224 \, a b^{7}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"-1/240*(105*(64*a^6*b^2 + 240*a^4*b^4 + 120*a^2*b^6 + 5*b^8)*(d*x + c) + 480*(a^8*tan(1/2*d*x + 1/2*c) + 28*a^6*b^2*tan(1/2*d*x + 1/2*c) + 70*a^4*b^4*tan(1/2*d*x + 1/2*c) + 28*a^2*b^6*tan(1/2*d*x + 1/2*c) + b^8*tan(1/2*d*x + 1/2*c) + 8*a^7*b + 56*a^5*b^3 + 56*a^3*b^5 + 8*a*b^7)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 2*(8400*a^4*b^4*tan(1/2*d*x + 1/2*c)^11 + 5880*a^2*b^6*tan(1/2*d*x + 1/2*c)^11 + 285*b^8*tan(1/2*d*x + 1/2*c)^11 - 13440*a^5*b^3*tan(1/2*d*x + 1/2*c)^10 - 13440*a^3*b^5*tan(1/2*d*x + 1/2*c)^10 - 1920*a*b^7*tan(1/2*d*x + 1/2*c)^10 + 25200*a^4*b^4*tan(1/2*d*x + 1/2*c)^9 + 24360*a^2*b^6*tan(1/2*d*x + 1/2*c)^9 + 1295*b^8*tan(1/2*d*x + 1/2*c)^9 - 67200*a^5*b^3*tan(1/2*d*x + 1/2*c)^8 - 94080*a^3*b^5*tan(1/2*d*x + 1/2*c)^8 - 13440*a*b^7*tan(1/2*d*x + 1/2*c)^8 + 16800*a^4*b^4*tan(1/2*d*x + 1/2*c)^7 + 18480*a^2*b^6*tan(1/2*d*x + 1/2*c)^7 + 1650*b^8*tan(1/2*d*x + 1/2*c)^7 - 134400*a^5*b^3*tan(1/2*d*x + 1/2*c)^6 - 224000*a^3*b^5*tan(1/2*d*x + 1/2*c)^6 - 42240*a*b^7*tan(1/2*d*x + 1/2*c)^6 - 16800*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 18480*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 - 1650*b^8*tan(1/2*d*x + 1/2*c)^5 - 134400*a^5*b^3*tan(1/2*d*x + 1/2*c)^4 - 241920*a^3*b^5*tan(1/2*d*x + 1/2*c)^4 - 49920*a*b^7*tan(1/2*d*x + 1/2*c)^4 - 25200*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 - 24360*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 - 1295*b^8*tan(1/2*d*x + 1/2*c)^3 - 67200*a^5*b^3*tan(1/2*d*x + 1/2*c)^2 - 120960*a^3*b^5*tan(1/2*d*x + 1/2*c)^2 - 23424*a*b^7*tan(1/2*d*x + 1/2*c)^2 - 8400*a^4*b^4*tan(1/2*d*x + 1/2*c) - 5880*a^2*b^6*tan(1/2*d*x + 1/2*c) - 285*b^8*tan(1/2*d*x + 1/2*c) - 13440*a^5*b^3 - 22400*a^3*b^5 - 4224*a*b^7)/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","B",0
421,1,684,0,0.758868," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{105 \, {\left(16 \, a^{4} b^{4} + 16 \, a^{2} b^{6} + b^{8}\right)} {\left(d x + c\right)} - \frac{16 \, {\left(3 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 210 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 168 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 168 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 48 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 112 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 700 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 448 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 22 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 336 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 672 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 144 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 210 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 168 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, a^{7} b - 112 \, a^{5} b^{3} - 280 \, a^{3} b^{5} - 64 \, a b^{7}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}} + \frac{2 \, {\left(336 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1344 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 384 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 336 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 57 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4032 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1536 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 336 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 57 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4032 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1664 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 336 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 33 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1344 \, a^{3} b^{5} - 512 \, a b^{7}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(105*(16*a^4*b^4 + 16*a^2*b^6 + b^8)*(d*x + c) - 16*(3*a^8*tan(1/2*d*x + 1/2*c)^5 - 210*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 168*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 - 9*b^8*tan(1/2*d*x + 1/2*c)^5 + 24*a^7*b*tan(1/2*d*x + 1/2*c)^4 - 168*a^3*b^5*tan(1/2*d*x + 1/2*c)^4 - 48*a*b^7*tan(1/2*d*x + 1/2*c)^4 - 2*a^8*tan(1/2*d*x + 1/2*c)^3 + 112*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 + 700*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 + 448*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 + 22*b^8*tan(1/2*d*x + 1/2*c)^3 + 336*a^5*b^3*tan(1/2*d*x + 1/2*c)^2 + 672*a^3*b^5*tan(1/2*d*x + 1/2*c)^2 + 144*a*b^7*tan(1/2*d*x + 1/2*c)^2 + 3*a^8*tan(1/2*d*x + 1/2*c) - 210*a^4*b^4*tan(1/2*d*x + 1/2*c) - 168*a^2*b^6*tan(1/2*d*x + 1/2*c) - 9*b^8*tan(1/2*d*x + 1/2*c) + 8*a^7*b - 112*a^5*b^3 - 280*a^3*b^5 - 64*a*b^7)/(tan(1/2*d*x + 1/2*c)^2 - 1)^3 + 2*(336*a^2*b^6*tan(1/2*d*x + 1/2*c)^7 + 33*b^8*tan(1/2*d*x + 1/2*c)^7 - 1344*a^3*b^5*tan(1/2*d*x + 1/2*c)^6 - 384*a*b^7*tan(1/2*d*x + 1/2*c)^6 + 336*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 + 57*b^8*tan(1/2*d*x + 1/2*c)^5 - 4032*a^3*b^5*tan(1/2*d*x + 1/2*c)^4 - 1536*a*b^7*tan(1/2*d*x + 1/2*c)^4 - 336*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 - 57*b^8*tan(1/2*d*x + 1/2*c)^3 - 4032*a^3*b^5*tan(1/2*d*x + 1/2*c)^2 - 1664*a*b^7*tan(1/2*d*x + 1/2*c)^2 - 336*a^2*b^6*tan(1/2*d*x + 1/2*c) - 33*b^8*tan(1/2*d*x + 1/2*c) - 1344*a^3*b^5 - 512*a*b^7)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
422,1,663,0,1.188046," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{105 \, {\left(8 \, a^{2} b^{6} + b^{8}\right)} {\left(d x + c\right)} + \frac{30 \, {\left(b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 16 \, a b^{7}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} + \frac{4 \, {\left(15 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 420 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 45 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 120 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 20 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 560 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2240 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 220 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1680 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 720 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 58 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 224 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3360 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4984 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 398 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 240 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 560 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4480 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1920 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 20 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 560 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2240 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 220 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 560 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2240 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1200 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 420 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 45 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, a^{7} b - 112 \, a^{5} b^{3} + 448 \, a^{3} b^{5} + 264 \, a b^{7}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{30 \, d}"," ",0,"-1/30*(105*(8*a^2*b^6 + b^8)*(d*x + c) + 30*(b^8*tan(1/2*d*x + 1/2*c)^3 - 16*a*b^7*tan(1/2*d*x + 1/2*c)^2 - b^8*tan(1/2*d*x + 1/2*c) - 16*a*b^7)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 + 4*(15*a^8*tan(1/2*d*x + 1/2*c)^9 + 420*a^2*b^6*tan(1/2*d*x + 1/2*c)^9 + 45*b^8*tan(1/2*d*x + 1/2*c)^9 + 120*a^7*b*tan(1/2*d*x + 1/2*c)^8 + 120*a*b^7*tan(1/2*d*x + 1/2*c)^8 - 20*a^8*tan(1/2*d*x + 1/2*c)^7 + 560*a^6*b^2*tan(1/2*d*x + 1/2*c)^7 - 2240*a^2*b^6*tan(1/2*d*x + 1/2*c)^7 - 220*b^8*tan(1/2*d*x + 1/2*c)^7 + 1680*a^5*b^3*tan(1/2*d*x + 1/2*c)^6 - 720*a*b^7*tan(1/2*d*x + 1/2*c)^6 + 58*a^8*tan(1/2*d*x + 1/2*c)^5 + 224*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 + 3360*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 + 4984*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 + 398*b^8*tan(1/2*d*x + 1/2*c)^5 + 240*a^7*b*tan(1/2*d*x + 1/2*c)^4 + 560*a^5*b^3*tan(1/2*d*x + 1/2*c)^4 + 4480*a^3*b^5*tan(1/2*d*x + 1/2*c)^4 + 1920*a*b^7*tan(1/2*d*x + 1/2*c)^4 - 20*a^8*tan(1/2*d*x + 1/2*c)^3 + 560*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 - 2240*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 - 220*b^8*tan(1/2*d*x + 1/2*c)^3 + 560*a^5*b^3*tan(1/2*d*x + 1/2*c)^2 - 2240*a^3*b^5*tan(1/2*d*x + 1/2*c)^2 - 1200*a*b^7*tan(1/2*d*x + 1/2*c)^2 + 15*a^8*tan(1/2*d*x + 1/2*c) + 420*a^2*b^6*tan(1/2*d*x + 1/2*c) + 45*b^8*tan(1/2*d*x + 1/2*c) + 24*a^7*b - 112*a^5*b^3 + 448*a^3*b^5 + 264*a*b^7)/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
423,1,726,0,0.697163," ","integrate(sec(d*x+c)^8*(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{105 \, {\left(d x + c\right)} b^{8} - \frac{2 \, {\left(105 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 105 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 840 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 210 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3920 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 770 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 11760 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 903 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3136 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 23520 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2471 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4200 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 11760 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 31360 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 636 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12768 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 20160 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 26880 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4572 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 23520 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 15680 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 13440 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 903 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3136 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 23520 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2471 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2520 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4704 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 9408 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8064 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 210 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3920 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 770 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2352 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3136 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2688 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 105 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, a^{7} b - 336 \, a^{5} b^{3} + 448 \, a^{3} b^{5} - 384 \, a b^{7}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{7}}}{105 \, d}"," ",0,"1/105*(105*(d*x + c)*b^8 - 2*(105*a^8*tan(1/2*d*x + 1/2*c)^13 - 105*b^8*tan(1/2*d*x + 1/2*c)^13 + 840*a^7*b*tan(1/2*d*x + 1/2*c)^12 - 210*a^8*tan(1/2*d*x + 1/2*c)^11 + 3920*a^6*b^2*tan(1/2*d*x + 1/2*c)^11 + 770*b^8*tan(1/2*d*x + 1/2*c)^11 + 11760*a^5*b^3*tan(1/2*d*x + 1/2*c)^10 + 903*a^8*tan(1/2*d*x + 1/2*c)^9 + 3136*a^6*b^2*tan(1/2*d*x + 1/2*c)^9 + 23520*a^4*b^4*tan(1/2*d*x + 1/2*c)^9 - 2471*b^8*tan(1/2*d*x + 1/2*c)^9 + 4200*a^7*b*tan(1/2*d*x + 1/2*c)^8 + 11760*a^5*b^3*tan(1/2*d*x + 1/2*c)^8 + 31360*a^3*b^5*tan(1/2*d*x + 1/2*c)^8 - 636*a^8*tan(1/2*d*x + 1/2*c)^7 + 12768*a^6*b^2*tan(1/2*d*x + 1/2*c)^7 + 20160*a^4*b^4*tan(1/2*d*x + 1/2*c)^7 + 26880*a^2*b^6*tan(1/2*d*x + 1/2*c)^7 + 4572*b^8*tan(1/2*d*x + 1/2*c)^7 + 23520*a^5*b^3*tan(1/2*d*x + 1/2*c)^6 + 15680*a^3*b^5*tan(1/2*d*x + 1/2*c)^6 + 13440*a*b^7*tan(1/2*d*x + 1/2*c)^6 + 903*a^8*tan(1/2*d*x + 1/2*c)^5 + 3136*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 + 23520*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 2471*b^8*tan(1/2*d*x + 1/2*c)^5 + 2520*a^7*b*tan(1/2*d*x + 1/2*c)^4 + 4704*a^5*b^3*tan(1/2*d*x + 1/2*c)^4 + 9408*a^3*b^5*tan(1/2*d*x + 1/2*c)^4 - 8064*a*b^7*tan(1/2*d*x + 1/2*c)^4 - 210*a^8*tan(1/2*d*x + 1/2*c)^3 + 3920*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 + 770*b^8*tan(1/2*d*x + 1/2*c)^3 + 2352*a^5*b^3*tan(1/2*d*x + 1/2*c)^2 - 3136*a^3*b^5*tan(1/2*d*x + 1/2*c)^2 + 2688*a*b^7*tan(1/2*d*x + 1/2*c)^2 + 105*a^8*tan(1/2*d*x + 1/2*c) - 105*b^8*tan(1/2*d*x + 1/2*c) + 120*a^7*b - 336*a^5*b^3 + 448*a^3*b^5 - 384*a*b^7)/(tan(1/2*d*x + 1/2*c)^2 - 1)^7)/d","A",0
424,1,892,0,1.921507," ","integrate(sec(d*x+c)^10*(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{2 \, {\left(315 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} + 2520 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{16} - 840 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 11760 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 35280 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} + 4788 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 14112 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 70560 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 23520 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 58800 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 94080 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 5112 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 79632 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 120960 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 80640 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 176400 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 141120 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 40320 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 10658 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 39872 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 244160 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 89600 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 8960 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 35280 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 105840 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 197568 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 24192 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 5112 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 79632 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120960 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 80640 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 105840 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 56448 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 10752 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 4788 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 14112 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 70560 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10080 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 15120 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 16128 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 4608 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 840 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 11760 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5040 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4032 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1152 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 315 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 280 \, a^{7} b - 560 \, a^{5} b^{3} + 448 \, a^{3} b^{5} - 128 \, a b^{7}\right)}}{315 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{9} d}"," ",0,"-2/315*(315*a^8*tan(1/2*d*x + 1/2*c)^17 + 2520*a^7*b*tan(1/2*d*x + 1/2*c)^16 - 840*a^8*tan(1/2*d*x + 1/2*c)^15 + 11760*a^6*b^2*tan(1/2*d*x + 1/2*c)^15 + 35280*a^5*b^3*tan(1/2*d*x + 1/2*c)^14 + 4788*a^8*tan(1/2*d*x + 1/2*c)^13 + 14112*a^6*b^2*tan(1/2*d*x + 1/2*c)^13 + 70560*a^4*b^4*tan(1/2*d*x + 1/2*c)^13 + 23520*a^7*b*tan(1/2*d*x + 1/2*c)^12 + 58800*a^5*b^3*tan(1/2*d*x + 1/2*c)^12 + 94080*a^3*b^5*tan(1/2*d*x + 1/2*c)^12 - 5112*a^8*tan(1/2*d*x + 1/2*c)^11 + 79632*a^6*b^2*tan(1/2*d*x + 1/2*c)^11 + 120960*a^4*b^4*tan(1/2*d*x + 1/2*c)^11 + 80640*a^2*b^6*tan(1/2*d*x + 1/2*c)^11 + 176400*a^5*b^3*tan(1/2*d*x + 1/2*c)^10 + 141120*a^3*b^5*tan(1/2*d*x + 1/2*c)^10 + 40320*a*b^7*tan(1/2*d*x + 1/2*c)^10 + 10658*a^8*tan(1/2*d*x + 1/2*c)^9 + 39872*a^6*b^2*tan(1/2*d*x + 1/2*c)^9 + 244160*a^4*b^4*tan(1/2*d*x + 1/2*c)^9 + 89600*a^2*b^6*tan(1/2*d*x + 1/2*c)^9 + 8960*b^8*tan(1/2*d*x + 1/2*c)^9 + 35280*a^7*b*tan(1/2*d*x + 1/2*c)^8 + 105840*a^5*b^3*tan(1/2*d*x + 1/2*c)^8 + 197568*a^3*b^5*tan(1/2*d*x + 1/2*c)^8 + 24192*a*b^7*tan(1/2*d*x + 1/2*c)^8 - 5112*a^8*tan(1/2*d*x + 1/2*c)^7 + 79632*a^6*b^2*tan(1/2*d*x + 1/2*c)^7 + 120960*a^4*b^4*tan(1/2*d*x + 1/2*c)^7 + 80640*a^2*b^6*tan(1/2*d*x + 1/2*c)^7 + 105840*a^5*b^3*tan(1/2*d*x + 1/2*c)^6 + 56448*a^3*b^5*tan(1/2*d*x + 1/2*c)^6 + 10752*a*b^7*tan(1/2*d*x + 1/2*c)^6 + 4788*a^8*tan(1/2*d*x + 1/2*c)^5 + 14112*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 + 70560*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 + 10080*a^7*b*tan(1/2*d*x + 1/2*c)^4 + 15120*a^5*b^3*tan(1/2*d*x + 1/2*c)^4 + 16128*a^3*b^5*tan(1/2*d*x + 1/2*c)^4 - 4608*a*b^7*tan(1/2*d*x + 1/2*c)^4 - 840*a^8*tan(1/2*d*x + 1/2*c)^3 + 11760*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 + 5040*a^5*b^3*tan(1/2*d*x + 1/2*c)^2 - 4032*a^3*b^5*tan(1/2*d*x + 1/2*c)^2 + 1152*a*b^7*tan(1/2*d*x + 1/2*c)^2 + 315*a^8*tan(1/2*d*x + 1/2*c) + 280*a^7*b - 560*a^5*b^3 + 448*a^3*b^5 - 128*a*b^7)/((tan(1/2*d*x + 1/2*c)^2 - 1)^9*d)","B",0
425,1,120,0,1.088679," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, b^{3} \sin\left(d x + c\right)^{4} - 4 \, a b^{2} \sin\left(d x + c\right)^{3} + 6 \, a^{2} b \sin\left(d x + c\right)^{2} - 12 \, b^{3} \sin\left(d x + c\right)^{2} - 12 \, a^{3} \sin\left(d x + c\right) + 24 \, a b^{2} \sin\left(d x + c\right)}{b^{4}} + \frac{12 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{5}}}{12 \, d}"," ",0,"1/12*((3*b^3*sin(d*x + c)^4 - 4*a*b^2*sin(d*x + c)^3 + 6*a^2*b*sin(d*x + c)^2 - 12*b^3*sin(d*x + c)^2 - 12*a^3*sin(d*x + c) + 24*a*b^2*sin(d*x + c))/b^4 + 12*(a^4 - 2*a^2*b^2 + b^4)*log(abs(b*sin(d*x + c) + a))/b^5)/d","A",0
426,1,56,0,0.796157," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{b \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right)}{b^{2}} + \frac{2 \, {\left(a^{2} - b^{2}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{3}}}{2 \, d}"," ",0,"-1/2*((b*sin(d*x + c)^2 - 2*a*sin(d*x + c))/b^2 + 2*(a^2 - b^2)*log(abs(b*sin(d*x + c) + a))/b^3)/d","A",0
427,1,19,0,0.374245," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b d}"," ",0,"log(abs(b*sin(d*x + c) + a))/(b*d)","A",0
428,1,71,0,0.408514," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, b^{2} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{2} b - b^{3}} - \frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a - b} + \frac{\log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a + b}}{2 \, d}"," ",0,"-1/2*(2*b^2*log(abs(b*sin(d*x + c) + a))/(a^2*b - b^3) - log(abs(sin(d*x + c) + 1))/(a - b) + log(abs(sin(d*x + c) - 1))/(a + b))/d","A",0
429,1,177,0,0.427944," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{4 \, b^{4} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{4} b - 2 \, a^{2} b^{3} + b^{5}} + \frac{{\left(a - 2 \, b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{{\left(a + 2 \, b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2} + 2 \, a b + b^{2}} + \frac{2 \, {\left(b^{3} \sin\left(d x + c\right)^{2} - a^{3} \sin\left(d x + c\right) + a b^{2} \sin\left(d x + c\right) + a^{2} b - 2 \, b^{3}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}}}{4 \, d}"," ",0,"1/4*(4*b^4*log(abs(b*sin(d*x + c) + a))/(a^4*b - 2*a^2*b^3 + b^5) + (a - 2*b)*log(abs(sin(d*x + c) + 1))/(a^2 - 2*a*b + b^2) - (a + 2*b)*log(abs(sin(d*x + c) - 1))/(a^2 + 2*a*b + b^2) + 2*(b^3*sin(d*x + c)^2 - a^3*sin(d*x + c) + a*b^2*sin(d*x + c) + a^2*b - 2*b^3)/((a^4 - 2*a^2*b^2 + b^4)*(sin(d*x + c)^2 - 1)))/d","A",0
430,1,332,0,0.471982," ","integrate(sec(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{16 \, b^{6} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}} - \frac{{\left(3 \, a^{2} - 9 \, a b + 8 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(3 \, a^{2} + 9 \, a b + 8 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(6 \, b^{5} \sin\left(d x + c\right)^{4} + 3 \, a^{5} \sin\left(d x + c\right)^{3} - 10 \, a^{3} b^{2} \sin\left(d x + c\right)^{3} + 7 \, a b^{4} \sin\left(d x + c\right)^{3} + 4 \, a^{2} b^{3} \sin\left(d x + c\right)^{2} - 16 \, b^{5} \sin\left(d x + c\right)^{2} - 5 \, a^{5} \sin\left(d x + c\right) + 14 \, a^{3} b^{2} \sin\left(d x + c\right) - 9 \, a b^{4} \sin\left(d x + c\right) + 2 \, a^{4} b - 8 \, a^{2} b^{3} + 12 \, b^{5}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(16*b^6*log(abs(b*sin(d*x + c) + a))/(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7) - (3*a^2 - 9*a*b + 8*b^2)*log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (3*a^2 + 9*a*b + 8*b^2)*log(abs(sin(d*x + c) - 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(6*b^5*sin(d*x + c)^4 + 3*a^5*sin(d*x + c)^3 - 10*a^3*b^2*sin(d*x + c)^3 + 7*a*b^4*sin(d*x + c)^3 + 4*a^2*b^3*sin(d*x + c)^2 - 16*b^5*sin(d*x + c)^2 - 5*a^5*sin(d*x + c) + 14*a^3*b^2*sin(d*x + c) - 9*a*b^4*sin(d*x + c) + 2*a^4*b - 8*a^2*b^3 + 12*b^5)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(sin(d*x + c)^2 - 1)^2))/d","A",0
431,1,496,0,0.490223," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{15 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} {\left(d x + c\right)}}{b^{6}} - \frac{240 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{6}} + \frac{2 \, {\left(60 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 135 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 360 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 360 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 120 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 150 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1200 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 720 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 720 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1600 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1120 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 150 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1040 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 560 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 60 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 135 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, a^{4} - 280 \, a^{2} b^{2} + 184 \, b^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5} b^{5}}}{120 \, d}"," ",0,"1/120*(15*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*(d*x + c)/b^6 - 240*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^6) + 2*(60*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 135*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*a^4*tan(1/2*d*x + 1/2*c)^8 - 360*a^2*b^2*tan(1/2*d*x + 1/2*c)^8 + 360*b^4*tan(1/2*d*x + 1/2*c)^8 + 120*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 150*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 480*a^4*tan(1/2*d*x + 1/2*c)^6 - 1200*a^2*b^2*tan(1/2*d*x + 1/2*c)^6 + 720*b^4*tan(1/2*d*x + 1/2*c)^6 + 720*a^4*tan(1/2*d*x + 1/2*c)^4 - 1600*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 1120*b^4*tan(1/2*d*x + 1/2*c)^4 - 120*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 150*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 480*a^4*tan(1/2*d*x + 1/2*c)^2 - 1040*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 560*b^4*tan(1/2*d*x + 1/2*c)^2 - 60*a^3*b*tan(1/2*d*x + 1/2*c) + 135*a*b^3*tan(1/2*d*x + 1/2*c) + 120*a^4 - 280*a^2*b^2 + 184*b^4)/((tan(1/2*d*x + 1/2*c)^2 + 1)^5*b^5))/d","B",0
432,1,226,0,2.808437," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)}}{b^{4}} - \frac{12 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{4}} + \frac{2 \, {\left(3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{2} - 8 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} b^{3}}}{6 \, d}"," ",0,"-1/6*(3*(2*a^3 - 3*a*b^2)*(d*x + c)/b^4 - 12*(a^4 - 2*a^2*b^2 + b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^4) + 2*(3*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*a^2*tan(1/2*d*x + 1/2*c)^4 - 12*b^2*tan(1/2*d*x + 1/2*c)^4 + 12*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*a*b*tan(1/2*d*x + 1/2*c) + 6*a^2 - 8*b^2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*b^3))/d","A",0
433,1,95,0,0.965605," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} a}{b^{2}} - \frac{2 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} \sqrt{a^{2} - b^{2}}}{b^{2}} + \frac{2}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} b}}{d}"," ",0,"((d*x + c)*a/b^2 - 2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*sqrt(a^2 - b^2)/b^2 + 2/((tan(1/2*d*x + 1/2*c)^2 + 1)*b))/d","A",0
434,1,107,0,1.168133," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b^{2}}{{\left(a^{2} - b^{2}\right)}^{\frac{3}{2}}} + \frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b}{{\left(a^{2} - b^{2}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}\right)}}{d}"," ",0,"-2*((pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*b^2/(a^2 - b^2)^(3/2) + (a*tan(1/2*d*x + 1/2*c) - b)/((a^2 - b^2)*(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
435,1,273,0,0.526880," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{3 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b^{4}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} - \frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2} b + 4 \, b^{3}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}\right)}}{3 \, d}"," ",0,"2/3*(3*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*b^4/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) - (3*a^3*tan(1/2*d*x + 1/2*c)^5 - 6*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 3*a^2*b*tan(1/2*d*x + 1/2*c)^4 + 6*b^3*tan(1/2*d*x + 1/2*c)^4 - 2*a^3*tan(1/2*d*x + 1/2*c)^3 + 8*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 6*b^3*tan(1/2*d*x + 1/2*c)^2 + 3*a^3*tan(1/2*d*x + 1/2*c) - 6*a*b^2*tan(1/2*d*x + 1/2*c) - a^2*b + 4*b^3)/((a^4 - 2*a^2*b^2 + b^4)*(tan(1/2*d*x + 1/2*c)^2 - 1)^3))/d","B",0
436,1,584,0,1.225926," ","integrate(sec(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{15 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b^{6}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{15 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 45 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 45 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 15 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 45 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 45 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 20 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 80 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 90 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 58 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 166 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 198 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 30 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 80 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 140 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 20 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 70 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 45 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{4} b + 11 \, a^{2} b^{3} - 23 \, b^{5}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}\right)}}{15 \, d}"," ",0,"-2/15*(15*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*b^6/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) + (15*a^5*tan(1/2*d*x + 1/2*c)^9 - 45*a^3*b^2*tan(1/2*d*x + 1/2*c)^9 + 45*a*b^4*tan(1/2*d*x + 1/2*c)^9 - 15*a^4*b*tan(1/2*d*x + 1/2*c)^8 + 45*a^2*b^3*tan(1/2*d*x + 1/2*c)^8 - 45*b^5*tan(1/2*d*x + 1/2*c)^8 - 20*a^5*tan(1/2*d*x + 1/2*c)^7 + 80*a^3*b^2*tan(1/2*d*x + 1/2*c)^7 - 120*a*b^4*tan(1/2*d*x + 1/2*c)^7 - 30*a^2*b^3*tan(1/2*d*x + 1/2*c)^6 + 90*b^5*tan(1/2*d*x + 1/2*c)^6 + 58*a^5*tan(1/2*d*x + 1/2*c)^5 - 166*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 198*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 30*a^4*b*tan(1/2*d*x + 1/2*c)^4 + 80*a^2*b^3*tan(1/2*d*x + 1/2*c)^4 - 140*b^5*tan(1/2*d*x + 1/2*c)^4 - 20*a^5*tan(1/2*d*x + 1/2*c)^3 + 80*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 120*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 10*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 + 70*b^5*tan(1/2*d*x + 1/2*c)^2 + 15*a^5*tan(1/2*d*x + 1/2*c) - 45*a^3*b^2*tan(1/2*d*x + 1/2*c) + 45*a*b^4*tan(1/2*d*x + 1/2*c) - 3*a^4*b + 11*a^2*b^3 - 23*b^5)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(tan(1/2*d*x + 1/2*c)^2 - 1)^5))/d","B",0
437,1,251,0,0.977229," ","integrate(cos(d*x+c)^7/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{7}} - \frac{10 \, {\left(6 \, a^{5} b \sin\left(d x + c\right) - 12 \, a^{3} b^{3} \sin\left(d x + c\right) + 6 \, a b^{5} \sin\left(d x + c\right) + 5 \, a^{6} - 9 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)} b^{7}} - \frac{2 \, b^{8} \sin\left(d x + c\right)^{5} - 5 \, a b^{7} \sin\left(d x + c\right)^{4} + 10 \, a^{2} b^{6} \sin\left(d x + c\right)^{3} - 10 \, b^{8} \sin\left(d x + c\right)^{3} - 20 \, a^{3} b^{5} \sin\left(d x + c\right)^{2} + 30 \, a b^{7} \sin\left(d x + c\right)^{2} + 50 \, a^{4} b^{4} \sin\left(d x + c\right) - 90 \, a^{2} b^{6} \sin\left(d x + c\right) + 30 \, b^{8} \sin\left(d x + c\right)}{b^{10}}}{10 \, d}"," ",0,"1/10*(60*(a^5 - 2*a^3*b^2 + a*b^4)*log(abs(b*sin(d*x + c) + a))/b^7 - 10*(6*a^5*b*sin(d*x + c) - 12*a^3*b^3*sin(d*x + c) + 6*a*b^5*sin(d*x + c) + 5*a^6 - 9*a^4*b^2 + 3*a^2*b^4 + b^6)/((b*sin(d*x + c) + a)*b^7) - (2*b^8*sin(d*x + c)^5 - 5*a*b^7*sin(d*x + c)^4 + 10*a^2*b^6*sin(d*x + c)^3 - 10*b^8*sin(d*x + c)^3 - 20*a^3*b^5*sin(d*x + c)^2 + 30*a*b^7*sin(d*x + c)^2 + 50*a^4*b^4*sin(d*x + c) - 90*a^2*b^6*sin(d*x + c) + 30*b^8*sin(d*x + c))/b^10)/d","A",0
438,1,150,0,0.840481," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(a^{3} - a b^{2}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{5}} - \frac{b^{4} \sin\left(d x + c\right)^{3} - 3 \, a b^{3} \sin\left(d x + c\right)^{2} + 9 \, a^{2} b^{2} \sin\left(d x + c\right) - 6 \, b^{4} \sin\left(d x + c\right)}{b^{6}} - \frac{3 \, {\left(4 \, a^{3} b \sin\left(d x + c\right) - 4 \, a b^{3} \sin\left(d x + c\right) + 3 \, a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)} b^{5}}}{3 \, d}"," ",0,"-1/3*(12*(a^3 - a*b^2)*log(abs(b*sin(d*x + c) + a))/b^5 - (b^4*sin(d*x + c)^3 - 3*a*b^3*sin(d*x + c)^2 + 9*a^2*b^2*sin(d*x + c) - 6*b^4*sin(d*x + c))/b^6 - 3*(4*a^3*b*sin(d*x + c) - 4*a*b^3*sin(d*x + c) + 3*a^4 - 2*a^2*b^2 - b^4)/((b*sin(d*x + c) + a)*b^5))/d","A",0
439,1,91,0,1.693360," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, a \log\left(\frac{{\left| b \sin\left(d x + c\right) + a \right|}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2} {\left| b \right|}}\right)}{b^{3}} + \frac{b \sin\left(d x + c\right) + a}{b^{3}} - \frac{a^{2}}{{\left(b \sin\left(d x + c\right) + a\right)} b^{3}} + \frac{1}{{\left(b \sin\left(d x + c\right) + a\right)} b}}{d}"," ",0,"-(2*a*log(abs(b*sin(d*x + c) + a)/((b*sin(d*x + c) + a)^2*abs(b)))/b^3 + (b*sin(d*x + c) + a)/b^3 - a^2/((b*sin(d*x + c) + a)*b^3) + 1/((b*sin(d*x + c) + a)*b))/d","A",0
440,1,20,0,0.361664," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{1}{{\left(b \sin\left(d x + c\right) + a\right)} b d}"," ",0,"-1/((b*sin(d*x + c) + a)*b*d)","A",0
441,1,147,0,1.284535," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, a b^{2} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{4} b - 2 \, a^{2} b^{3} + b^{5}} - \frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{\log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{2 \, {\left(2 \, a b^{2} \sin\left(d x + c\right) + 3 \, a^{2} b - b^{3}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \sin\left(d x + c\right) + a\right)}}}{2 \, d}"," ",0,"-1/2*(4*a*b^2*log(abs(b*sin(d*x + c) + a))/(a^4*b - 2*a^2*b^3 + b^5) - log(abs(sin(d*x + c) + 1))/(a^2 - 2*a*b + b^2) + log(abs(sin(d*x + c) - 1))/(a^2 + 2*a*b + b^2) - 2*(2*a*b^2*sin(d*x + c) + 3*a^2*b - b^3)/((a^4 - 2*a^2*b^2 + b^4)*(b*sin(d*x + c) + a)))/d","A",0
442,1,244,0,0.992455," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{16 \, a b^{4} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}} + \frac{{\left(a - 3 \, b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(a + 3 \, b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{2 \, {\left(a^{2} b \sin\left(d x + c\right)^{2} + 3 \, b^{3} \sin\left(d x + c\right)^{2} + a^{3} \sin\left(d x + c\right) - a b^{2} \sin\left(d x + c\right) - 2 \, a^{2} b - 2 \, b^{3}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \sin\left(d x + c\right)^{3} + a \sin\left(d x + c\right)^{2} - b \sin\left(d x + c\right) - a\right)}}}{4 \, d}"," ",0,"1/4*(16*a*b^4*log(abs(b*sin(d*x + c) + a))/(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7) + (a - 3*b)*log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (a + 3*b)*log(abs(sin(d*x + c) - 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 2*(a^2*b*sin(d*x + c)^2 + 3*b^3*sin(d*x + c)^2 + a^3*sin(d*x + c) - a*b^2*sin(d*x + c) - 2*a^2*b - 2*b^3)/((a^4 - 2*a^2*b^2 + b^4)*(b*sin(d*x + c)^3 + a*sin(d*x + c)^2 - b*sin(d*x + c) - a)))/d","A",0
443,1,460,0,0.436678," ","integrate(sec(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{96 \, a b^{6} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}} - \frac{3 \, {\left(a^{2} - 4 \, a b + 5 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} + \frac{3 \, {\left(a^{2} + 4 \, a b + 5 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{16 \, {\left(6 \, a b^{6} \sin\left(d x + c\right) + 7 \, a^{2} b^{5} - b^{7}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(b \sin\left(d x + c\right) + a\right)}} + \frac{2 \, {\left(36 \, a b^{5} \sin\left(d x + c\right)^{4} + 3 \, a^{6} \sin\left(d x + c\right)^{3} - 15 \, a^{4} b^{2} \sin\left(d x + c\right)^{3} + 5 \, a^{2} b^{4} \sin\left(d x + c\right)^{3} + 7 \, b^{6} \sin\left(d x + c\right)^{3} + 16 \, a^{3} b^{3} \sin\left(d x + c\right)^{2} - 88 \, a b^{5} \sin\left(d x + c\right)^{2} - 5 \, a^{6} \sin\left(d x + c\right) + 17 \, a^{4} b^{2} \sin\left(d x + c\right) - 3 \, a^{2} b^{4} \sin\left(d x + c\right) - 9 \, b^{6} \sin\left(d x + c\right) + 4 \, a^{5} b - 24 \, a^{3} b^{3} + 56 \, a b^{5}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(96*a*b^6*log(abs(b*sin(d*x + c) + a))/(a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9) - 3*(a^2 - 4*a*b + 5*b^2)*log(abs(sin(d*x + c) + 1))/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) + 3*(a^2 + 4*a*b + 5*b^2)*log(abs(sin(d*x + c) - 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - 16*(6*a*b^6*sin(d*x + c) + 7*a^2*b^5 - b^7)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(b*sin(d*x + c) + a)) + 2*(36*a*b^5*sin(d*x + c)^4 + 3*a^6*sin(d*x + c)^3 - 15*a^4*b^2*sin(d*x + c)^3 + 5*a^2*b^4*sin(d*x + c)^3 + 7*b^6*sin(d*x + c)^3 + 16*a^3*b^3*sin(d*x + c)^2 - 88*a*b^5*sin(d*x + c)^2 - 5*a^6*sin(d*x + c) + 17*a^4*b^2*sin(d*x + c) - 3*a^2*b^4*sin(d*x + c) - 9*b^6*sin(d*x + c) + 4*a^5*b - 24*a^3*b^3 + 56*a*b^5)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(sin(d*x + c)^2 - 1)^2))/d","A",0
444,1,469,0,2.498679," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(8 \, a^{4} - 12 \, a^{2} b^{2} + 3 \, b^{4}\right)} {\left(d x + c\right)}}{b^{6}} - \frac{240 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{6}} + \frac{48 \, {\left(a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a b^{5}} + \frac{2 \, {\left(36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 27 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 144 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 288 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 336 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 288 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 304 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, a^{3} - 112 \, a b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} b^{5}}}{24 \, d}"," ",0,"-1/24*(15*(8*a^4 - 12*a^2*b^2 + 3*b^4)*(d*x + c)/b^6 - 240*(a^5 - 2*a^3*b^2 + a*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^6) + 48*(a^4*b*tan(1/2*d*x + 1/2*c) - 2*a^2*b^3*tan(1/2*d*x + 1/2*c) + b^5*tan(1/2*d*x + 1/2*c) + a^5 - 2*a^3*b^2 + a*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a*b^5) + 2*(36*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 27*b^3*tan(1/2*d*x + 1/2*c)^7 + 96*a^3*tan(1/2*d*x + 1/2*c)^6 - 144*a*b^2*tan(1/2*d*x + 1/2*c)^6 + 36*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 3*b^3*tan(1/2*d*x + 1/2*c)^5 + 288*a^3*tan(1/2*d*x + 1/2*c)^4 - 336*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 36*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 3*b^3*tan(1/2*d*x + 1/2*c)^3 + 288*a^3*tan(1/2*d*x + 1/2*c)^2 - 304*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 36*a^2*b*tan(1/2*d*x + 1/2*c) + 27*b^3*tan(1/2*d*x + 1/2*c) + 96*a^3 - 112*a*b^2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*b^5))/d","B",0
445,1,235,0,1.396207," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, a^{2} - b^{2}\right)} {\left(d x + c\right)}}{b^{4}} - \frac{12 \, {\left(a^{3} - a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{4}} + \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} b^{3}} + \frac{4 \, {\left(a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3} - a b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a b^{3}}}{2 \, d}"," ",0,"1/2*(3*(2*a^2 - b^2)*(d*x + c)/b^4 - 12*(a^3 - a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^4) + 2*(b*tan(1/2*d*x + 1/2*c)^3 + 4*a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c) + 4*a)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*b^3) + 4*(a^2*b*tan(1/2*d*x + 1/2*c) - b^3*tan(1/2*d*x + 1/2*c) + a^3 - a*b^2)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a*b^3))/d","A",0
446,1,126,0,1.375934," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a}{\sqrt{a^{2} - b^{2}} b^{2}} - \frac{d x + c}{b^{2}} - \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a b}}{d}"," ",0,"(2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*a/(sqrt(a^2 - b^2)*b^2) - (d*x + c)/b^2 - 2*(b*tan(1/2*d*x + 1/2*c) + a)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a*b))/d","A",0
447,1,271,0,2.549857," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{3 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a b^{2}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{3} b - a b^{3}}{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}}\right)}}{d}"," ",0,"-2*(3*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*a*b^2/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (a^4*tan(1/2*d*x + 1/2*c)^3 + a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + b^4*tan(1/2*d*x + 1/2*c)^3 + 3*a*b^3*tan(1/2*d*x + 1/2*c)^2 + a^4*tan(1/2*d*x + 1/2*c) - 3*a^2*b^2*tan(1/2*d*x + 1/2*c) - b^4*tan(1/2*d*x + 1/2*c) - 2*a^3*b - a*b^3)/((a^5 - 2*a^3*b^2 + a*b^4)*(a*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^3 - 2*b*tan(1/2*d*x + 1/2*c) - a)))/d","B",0
448,1,427,0,0.667028," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{15 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a b^{4}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, {\left(b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a b^{5}\right)}}{{\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}} - \frac{3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 18 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{3} b + 14 \, a b^{3}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}\right)}}{3 \, d}"," ",0,"2/3*(15*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*a*b^4/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) + 3*(b^6*tan(1/2*d*x + 1/2*c) + a*b^5)/((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)) - (3*a^4*tan(1/2*d*x + 1/2*c)^5 - 9*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*a^3*b*tan(1/2*d*x + 1/2*c)^4 + 18*a*b^3*tan(1/2*d*x + 1/2*c)^4 - 2*a^4*tan(1/2*d*x + 1/2*c)^3 + 18*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 8*b^4*tan(1/2*d*x + 1/2*c)^3 - 24*a*b^3*tan(1/2*d*x + 1/2*c)^2 + 3*a^4*tan(1/2*d*x + 1/2*c) - 9*a^2*b^2*tan(1/2*d*x + 1/2*c) - 6*b^4*tan(1/2*d*x + 1/2*c) - 2*a^3*b + 14*a*b^3)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(tan(1/2*d*x + 1/2*c)^2 - 1)^3))/d","B",0
449,1,245,0,0.473183," ","integrate(cos(d*x+c)^7/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(5 \, a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{7}} - \frac{2 \, {\left(45 \, a^{4} b^{2} \sin\left(d x + c\right)^{2} - 54 \, a^{2} b^{4} \sin\left(d x + c\right)^{2} + 9 \, b^{6} \sin\left(d x + c\right)^{2} + 78 \, a^{5} b \sin\left(d x + c\right) - 84 \, a^{3} b^{3} \sin\left(d x + c\right) + 6 \, a b^{5} \sin\left(d x + c\right) + 34 \, a^{6} - 33 \, a^{4} b^{2} - b^{6}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2} b^{7}} + \frac{b^{9} \sin\left(d x + c\right)^{4} - 4 \, a b^{8} \sin\left(d x + c\right)^{3} + 12 \, a^{2} b^{7} \sin\left(d x + c\right)^{2} - 6 \, b^{9} \sin\left(d x + c\right)^{2} - 40 \, a^{3} b^{6} \sin\left(d x + c\right) + 36 \, a b^{8} \sin\left(d x + c\right)}{b^{12}}}{4 \, d}"," ",0,"-1/4*(12*(5*a^4 - 6*a^2*b^2 + b^4)*log(abs(b*sin(d*x + c) + a))/b^7 - 2*(45*a^4*b^2*sin(d*x + c)^2 - 54*a^2*b^4*sin(d*x + c)^2 + 9*b^6*sin(d*x + c)^2 + 78*a^5*b*sin(d*x + c) - 84*a^3*b^3*sin(d*x + c) + 6*a*b^5*sin(d*x + c) + 34*a^6 - 33*a^4*b^2 - b^6)/((b*sin(d*x + c) + a)^2*b^7) + (b^9*sin(d*x + c)^4 - 4*a*b^8*sin(d*x + c)^3 + 12*a^2*b^7*sin(d*x + c)^2 - 6*b^9*sin(d*x + c)^2 - 40*a^3*b^6*sin(d*x + c) + 36*a*b^8*sin(d*x + c))/b^12)/d","A",0
450,1,142,0,0.514300," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(3 \, a^{2} - b^{2}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{5}} + \frac{b^{3} \sin\left(d x + c\right)^{2} - 6 \, a b^{2} \sin\left(d x + c\right)}{b^{6}} - \frac{18 \, a^{2} b^{2} \sin\left(d x + c\right)^{2} - 6 \, b^{4} \sin\left(d x + c\right)^{2} + 28 \, a^{3} b \sin\left(d x + c\right) - 4 \, a b^{3} \sin\left(d x + c\right) + 11 \, a^{4} + b^{4}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2} b^{5}}}{2 \, d}"," ",0,"1/2*(4*(3*a^2 - b^2)*log(abs(b*sin(d*x + c) + a))/b^5 + (b^3*sin(d*x + c)^2 - 6*a*b^2*sin(d*x + c))/b^6 - (18*a^2*b^2*sin(d*x + c)^2 - 6*b^4*sin(d*x + c)^2 + 28*a^3*b*sin(d*x + c) - 4*a*b^3*sin(d*x + c) + 11*a^4 + b^4)/((b*sin(d*x + c) + a)^2*b^5))/d","A",0
451,1,62,0,1.017331," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{3}} + \frac{4 \, a \sin\left(d x + c\right) + \frac{3 \, a^{2} + b^{2}}{b}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2} b^{2}}}{2 \, d}"," ",0,"-1/2*(2*log(abs(b*sin(d*x + c) + a))/b^3 + (4*a*sin(d*x + c) + (3*a^2 + b^2)/b)/((b*sin(d*x + c) + a)^2*b^2))/d","A",0
452,1,20,0,0.407972," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{1}{2 \, {\left(b \sin\left(d x + c\right) + a\right)}^{2} b d}"," ",0,"-1/2/((b*sin(d*x + c) + a)^2*b*d)","A",0
453,1,242,0,0.691852," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}} - \frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{\log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{9 \, a^{2} b^{3} \sin\left(d x + c\right)^{2} + 3 \, b^{5} \sin\left(d x + c\right)^{2} + 22 \, a^{3} b^{2} \sin\left(d x + c\right) + 2 \, a b^{4} \sin\left(d x + c\right) + 14 \, a^{4} b - 3 \, a^{2} b^{3} + b^{5}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(2*(3*a^2*b^2 + b^4)*log(abs(b*sin(d*x + c) + a))/(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7) - log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + log(abs(sin(d*x + c) - 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - (9*a^2*b^3*sin(d*x + c)^2 + 3*b^5*sin(d*x + c)^2 + 22*a^3*b^2*sin(d*x + c) + 2*a*b^4*sin(d*x + c) + 14*a^4*b - 3*a^2*b^3 + b^5)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(b*sin(d*x + c) + a)^2))/d","A",0
454,1,413,0,1.375869," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{8 \, {\left(5 \, a^{2} b^{4} + b^{6}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}} + \frac{{\left(a - 4 \, b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} - \frac{{\left(a + 4 \, b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{2 \, {\left(10 \, a^{2} b^{3} \sin\left(d x + c\right)^{2} + 2 \, b^{5} \sin\left(d x + c\right)^{2} - a^{5} \sin\left(d x + c\right) - 2 \, a^{3} b^{2} \sin\left(d x + c\right) + 3 \, a b^{4} \sin\left(d x + c\right) + 3 \, a^{4} b - 12 \, a^{2} b^{3} - 3 \, b^{5}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}} - \frac{2 \, {\left(30 \, a^{2} b^{5} \sin\left(d x + c\right)^{2} + 6 \, b^{7} \sin\left(d x + c\right)^{2} + 68 \, a^{3} b^{4} \sin\left(d x + c\right) + 4 \, a b^{6} \sin\left(d x + c\right) + 39 \, a^{4} b^{3} - 4 \, a^{2} b^{5} + b^{7}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{2}}}{4 \, d}"," ",0,"1/4*(8*(5*a^2*b^4 + b^6)*log(abs(b*sin(d*x + c) + a))/(a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9) + (a - 4*b)*log(abs(sin(d*x + c) + 1))/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) - (a + 4*b)*log(abs(sin(d*x + c) - 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + 2*(10*a^2*b^3*sin(d*x + c)^2 + 2*b^5*sin(d*x + c)^2 - a^5*sin(d*x + c) - 2*a^3*b^2*sin(d*x + c) + 3*a*b^4*sin(d*x + c) + 3*a^4*b - 12*a^2*b^3 - 3*b^5)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(sin(d*x + c)^2 - 1)) - 2*(30*a^2*b^5*sin(d*x + c)^2 + 6*b^7*sin(d*x + c)^2 + 68*a^3*b^4*sin(d*x + c) + 4*a*b^6*sin(d*x + c) + 39*a^4*b^3 - 4*a^2*b^5 + b^7)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(b*sin(d*x + c) + a)^2))/d","A",0
455,1,575,0,0.725216," ","integrate(sec(d*x+c)^5/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{48 \, {\left(7 \, a^{2} b^{6} + b^{8}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{10} b - 5 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 10 \, a^{4} b^{7} + 5 \, a^{2} b^{9} - b^{11}} - \frac{3 \, {\left(a^{2} - 5 \, a b + 8 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}} + \frac{3 \, {\left(a^{2} + 5 \, a b + 8 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}} + \frac{2 \, {\left(3 \, a^{5} b^{2} \sin\left(d x + c\right)^{5} - 18 \, a^{3} b^{4} \sin\left(d x + c\right)^{5} - 81 \, a b^{6} \sin\left(d x + c\right)^{5} + 6 \, a^{6} b \sin\left(d x + c\right)^{4} - 36 \, a^{4} b^{3} \sin\left(d x + c\right)^{4} - 78 \, a^{2} b^{5} \sin\left(d x + c\right)^{4} + 12 \, b^{7} \sin\left(d x + c\right)^{4} + 3 \, a^{7} \sin\left(d x + c\right)^{3} - 23 \, a^{5} b^{2} \sin\left(d x + c\right)^{3} + 61 \, a^{3} b^{4} \sin\left(d x + c\right)^{3} + 151 \, a b^{6} \sin\left(d x + c\right)^{3} - 10 \, a^{6} b \sin\left(d x + c\right)^{2} + 74 \, a^{4} b^{3} \sin\left(d x + c\right)^{2} + 146 \, a^{2} b^{5} \sin\left(d x + c\right)^{2} - 18 \, b^{7} \sin\left(d x + c\right)^{2} - 5 \, a^{7} \sin\left(d x + c\right) + 26 \, a^{5} b^{2} \sin\left(d x + c\right) - 49 \, a^{3} b^{4} \sin\left(d x + c\right) - 68 \, a b^{6} \sin\left(d x + c\right) + 6 \, a^{6} b - 44 \, a^{4} b^{3} - 62 \, a^{2} b^{5} + 4 \, b^{7}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(b \sin\left(d x + c\right)^{3} + a \sin\left(d x + c\right)^{2} - b \sin\left(d x + c\right) - a\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(48*(7*a^2*b^6 + b^8)*log(abs(b*sin(d*x + c) + a))/(a^10*b - 5*a^8*b^3 + 10*a^6*b^5 - 10*a^4*b^7 + 5*a^2*b^9 - b^11) - 3*(a^2 - 5*a*b + 8*b^2)*log(abs(sin(d*x + c) + 1))/(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5) + 3*(a^2 + 5*a*b + 8*b^2)*log(abs(sin(d*x + c) - 1))/(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5) + 2*(3*a^5*b^2*sin(d*x + c)^5 - 18*a^3*b^4*sin(d*x + c)^5 - 81*a*b^6*sin(d*x + c)^5 + 6*a^6*b*sin(d*x + c)^4 - 36*a^4*b^3*sin(d*x + c)^4 - 78*a^2*b^5*sin(d*x + c)^4 + 12*b^7*sin(d*x + c)^4 + 3*a^7*sin(d*x + c)^3 - 23*a^5*b^2*sin(d*x + c)^3 + 61*a^3*b^4*sin(d*x + c)^3 + 151*a*b^6*sin(d*x + c)^3 - 10*a^6*b*sin(d*x + c)^2 + 74*a^4*b^3*sin(d*x + c)^2 + 146*a^2*b^5*sin(d*x + c)^2 - 18*b^7*sin(d*x + c)^2 - 5*a^7*sin(d*x + c) + 26*a^5*b^2*sin(d*x + c) - 49*a^3*b^4*sin(d*x + c) - 68*a*b^6*sin(d*x + c) + 6*a^6*b - 44*a^4*b^3 - 62*a^2*b^5 + 4*b^7)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(b*sin(d*x + c)^3 + a*sin(d*x + c)^2 - b*sin(d*x + c) - a)^2))/d","A",0
456,1,457,0,0.699020," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)}}{b^{6}} - \frac{30 \, {\left(4 \, a^{4} - 5 \, a^{2} b^{2} + b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{6}} + \frac{2 \, {\left(9 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 18 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 72 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, a^{2} - 14 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} b^{5}} + \frac{6 \, {\left(7 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 25 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 23 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, a^{6} - 7 \, a^{4} b^{2} - a^{2} b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} a^{2} b^{5}}}{6 \, d}"," ",0,"1/6*(15*(4*a^3 - 3*a*b^2)*(d*x + c)/b^6 - 30*(4*a^4 - 5*a^2*b^2 + b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^6) + 2*(9*a*b*tan(1/2*d*x + 1/2*c)^5 + 36*a^2*tan(1/2*d*x + 1/2*c)^4 - 18*b^2*tan(1/2*d*x + 1/2*c)^4 + 72*a^2*tan(1/2*d*x + 1/2*c)^2 - 24*b^2*tan(1/2*d*x + 1/2*c)^2 - 9*a*b*tan(1/2*d*x + 1/2*c) + 36*a^2 - 14*b^2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*b^5) + 6*(7*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 5*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 8*a^6*tan(1/2*d*x + 1/2*c)^2 + 9*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 - 15*a^2*b^4*tan(1/2*d*x + 1/2*c)^2 - 2*b^6*tan(1/2*d*x + 1/2*c)^2 + 25*a^5*b*tan(1/2*d*x + 1/2*c) - 23*a^3*b^3*tan(1/2*d*x + 1/2*c) - 2*a*b^5*tan(1/2*d*x + 1/2*c) + 8*a^6 - 7*a^4*b^2 - a^2*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*a^2*b^5))/d","B",0
457,1,272,0,0.421113," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)} a}{b^{4}} - \frac{3 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} {\left(2 \, a^{2} - b^{2}\right)}}{\sqrt{a^{2} - b^{2}} b^{4}} + \frac{2}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} b^{3}} + \frac{3 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 13 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a^{4} + a^{2} b^{2}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} a^{2} b^{3}}}{d}"," ",0,"-(3*(d*x + c)*a/b^4 - 3*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*(2*a^2 - b^2)/(sqrt(a^2 - b^2)*b^4) + 2/((tan(1/2*d*x + 1/2*c)^2 + 1)*b^3) + (3*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 2*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 4*a^4*tan(1/2*d*x + 1/2*c)^2 + 9*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 2*b^4*tan(1/2*d*x + 1/2*c)^2 + 13*a^3*b*tan(1/2*d*x + 1/2*c) + 2*a*b^3*tan(1/2*d*x + 1/2*c) + 4*a^4 + a^2*b^2)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*a^2*b^3))/d","B",0
458,1,207,0,0.546888," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)}{{\left(a^{2} - b^{2}\right)}^{\frac{3}{2}}} - \frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2} b}{{\left(a^{4} - a^{2} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2}}}{d}"," ",0,"((pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(a^2 - b^2)^(3/2) - (a^3*tan(1/2*d*x + 1/2*c)^3 - 2*a*b^2*tan(1/2*d*x + 1/2*c)^3 - a^2*b*tan(1/2*d*x + 1/2*c)^2 - 2*b^3*tan(1/2*d*x + 1/2*c)^2 - a^3*tan(1/2*d*x + 1/2*c) - 2*a*b^2*tan(1/2*d*x + 1/2*c) - a^2*b)/((a^4 - a^2*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2))/d","A",0
459,1,385,0,4.779557," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(4 \, a^{2} b^{2} + b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} b - b^{3}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}} + \frac{9 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 23 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, a^{4} b^{3} - a^{2} b^{5}}{{\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2}}}{d}"," ",0,"-(3*(4*a^2*b^2 + b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) + 2*(a^3*tan(1/2*d*x + 1/2*c) + 3*a*b^2*tan(1/2*d*x + 1/2*c) - 3*a^2*b - b^3)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(tan(1/2*d*x + 1/2*c)^2 - 1)) + (9*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 - 2*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 8*a^4*b^3*tan(1/2*d*x + 1/2*c)^2 + 15*a^2*b^5*tan(1/2*d*x + 1/2*c)^2 - 2*b^7*tan(1/2*d*x + 1/2*c)^2 + 23*a^3*b^4*tan(1/2*d*x + 1/2*c) - 2*a*b^6*tan(1/2*d*x + 1/2*c) + 8*a^4*b^3 - a^2*b^5)/((a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2))/d","B",0
460,1,622,0,9.088704," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(6 \, a^{2} b^{4} + b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, {\left(13 \, a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 23 \, a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, a^{4} b^{5} - a^{2} b^{7}\right)}}{{\left(a^{10} - 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} - 4 \, a^{4} b^{6} + a^{2} b^{8}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2}} - \frac{2 \, {\left(3 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 36 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 9 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 42 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 60 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{4} b + 32 \, a^{2} b^{3} + 7 \, b^{5}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(15*(6*a^2*b^4 + b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*sqrt(a^2 - b^2)) + 3*(13*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 - 2*a*b^8*tan(1/2*d*x + 1/2*c)^3 + 12*a^4*b^5*tan(1/2*d*x + 1/2*c)^2 + 23*a^2*b^7*tan(1/2*d*x + 1/2*c)^2 - 2*b^9*tan(1/2*d*x + 1/2*c)^2 + 35*a^3*b^6*tan(1/2*d*x + 1/2*c) - 2*a*b^8*tan(1/2*d*x + 1/2*c) + 12*a^4*b^5 - a^2*b^7)/((a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2) - 2*(3*a^5*tan(1/2*d*x + 1/2*c)^5 - 12*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 27*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 9*a^4*b*tan(1/2*d*x + 1/2*c)^4 + 36*a^2*b^3*tan(1/2*d*x + 1/2*c)^4 + 9*b^5*tan(1/2*d*x + 1/2*c)^4 - 2*a^5*tan(1/2*d*x + 1/2*c)^3 + 32*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 42*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 60*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 - 12*b^5*tan(1/2*d*x + 1/2*c)^2 + 3*a^5*tan(1/2*d*x + 1/2*c) - 12*a^3*b^2*tan(1/2*d*x + 1/2*c) - 27*a*b^4*tan(1/2*d*x + 1/2*c) - 3*a^4*b + 32*a^2*b^3 + 7*b^5)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(tan(1/2*d*x + 1/2*c)^2 - 1)^3))/d","B",0
461,1,215,0,3.884444," ","integrate(cos(d*x+c)^7/(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{35 \, b^{6} \sin\left(d x + c\right)^{6} + 105 \, a b^{5} \sin\left(d x + c\right)^{5} + 175 \, a^{2} b^{4} \sin\left(d x + c\right)^{4} - 35 \, b^{6} \sin\left(d x + c\right)^{4} + 175 \, a^{3} b^{3} \sin\left(d x + c\right)^{3} - 35 \, a b^{5} \sin\left(d x + c\right)^{3} + 105 \, a^{4} b^{2} \sin\left(d x + c\right)^{2} - 21 \, a^{2} b^{4} \sin\left(d x + c\right)^{2} + 21 \, b^{6} \sin\left(d x + c\right)^{2} + 35 \, a^{5} b \sin\left(d x + c\right) - 7 \, a^{3} b^{3} \sin\left(d x + c\right) + 7 \, a b^{5} \sin\left(d x + c\right) + 5 \, a^{6} - a^{4} b^{2} + a^{2} b^{4} - 5 \, b^{6}}{35 \, {\left(b \sin\left(d x + c\right) + a\right)}^{7} b^{7} d}"," ",0,"1/35*(35*b^6*sin(d*x + c)^6 + 105*a*b^5*sin(d*x + c)^5 + 175*a^2*b^4*sin(d*x + c)^4 - 35*b^6*sin(d*x + c)^4 + 175*a^3*b^3*sin(d*x + c)^3 - 35*a*b^5*sin(d*x + c)^3 + 105*a^4*b^2*sin(d*x + c)^2 - 21*a^2*b^4*sin(d*x + c)^2 + 21*b^6*sin(d*x + c)^2 + 35*a^5*b*sin(d*x + c) - 7*a^3*b^3*sin(d*x + c) + 7*a*b^5*sin(d*x + c) + 5*a^6 - a^4*b^2 + a^2*b^4 - 5*b^6)/((b*sin(d*x + c) + a)^7*b^7*d)","A",0
462,1,117,0,6.194026," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{35 \, b^{4} \sin\left(d x + c\right)^{4} + 35 \, a b^{3} \sin\left(d x + c\right)^{3} + 21 \, a^{2} b^{2} \sin\left(d x + c\right)^{2} - 42 \, b^{4} \sin\left(d x + c\right)^{2} + 7 \, a^{3} b \sin\left(d x + c\right) - 14 \, a b^{3} \sin\left(d x + c\right) + a^{4} - 2 \, a^{2} b^{2} + 15 \, b^{4}}{105 \, {\left(b \sin\left(d x + c\right) + a\right)}^{7} b^{5} d}"," ",0,"-1/105*(35*b^4*sin(d*x + c)^4 + 35*a*b^3*sin(d*x + c)^3 + 21*a^2*b^2*sin(d*x + c)^2 - 42*b^4*sin(d*x + c)^2 + 7*a^3*b*sin(d*x + c) - 14*a*b^3*sin(d*x + c) + a^4 - 2*a^2*b^2 + 15*b^4)/((b*sin(d*x + c) + a)^7*b^5*d)","A",0
463,1,52,0,4.463625," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{21 \, b^{2} \sin\left(d x + c\right)^{2} + 7 \, a b \sin\left(d x + c\right) + a^{2} - 15 \, b^{2}}{105 \, {\left(b \sin\left(d x + c\right) + a\right)}^{7} b^{3} d}"," ",0,"1/105*(21*b^2*sin(d*x + c)^2 + 7*a*b*sin(d*x + c) + a^2 - 15*b^2)/((b*sin(d*x + c) + a)^7*b^3*d)","A",0
464,1,20,0,2.567022," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{1}{7 \, {\left(b \sin\left(d x + c\right) + a\right)}^{7} b d}"," ",0,"-1/7/((b*sin(d*x + c) + a)^7*b*d)","A",0
465,1,1010,0,2.068052," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{\frac{1680 \, {\left(a^{7} b^{2} + 7 \, a^{5} b^{4} + 7 \, a^{3} b^{6} + a b^{8}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{16} b - 8 \, a^{14} b^{3} + 28 \, a^{12} b^{5} - 56 \, a^{10} b^{7} + 70 \, a^{8} b^{9} - 56 \, a^{6} b^{11} + 28 \, a^{4} b^{13} - 8 \, a^{2} b^{15} + b^{17}} - \frac{105 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{8} - 8 \, a^{7} b + 28 \, a^{6} b^{2} - 56 \, a^{5} b^{3} + 70 \, a^{4} b^{4} - 56 \, a^{3} b^{5} + 28 \, a^{2} b^{6} - 8 \, a b^{7} + b^{8}} + \frac{105 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{8} + 8 \, a^{7} b + 28 \, a^{6} b^{2} + 56 \, a^{5} b^{3} + 70 \, a^{4} b^{4} + 56 \, a^{3} b^{5} + 28 \, a^{2} b^{6} + 8 \, a b^{7} + b^{8}} - \frac{2 \, {\left(2178 \, a^{7} b^{8} \sin\left(d x + c\right)^{7} + 15246 \, a^{5} b^{10} \sin\left(d x + c\right)^{7} + 15246 \, a^{3} b^{12} \sin\left(d x + c\right)^{7} + 2178 \, a b^{14} \sin\left(d x + c\right)^{7} + 15981 \, a^{8} b^{7} \sin\left(d x + c\right)^{6} + 109662 \, a^{6} b^{9} \sin\left(d x + c\right)^{6} + 105252 \, a^{4} b^{11} \sin\left(d x + c\right)^{6} + 13146 \, a^{2} b^{13} \sin\left(d x + c\right)^{6} - 105 \, b^{15} \sin\left(d x + c\right)^{6} + 50463 \, a^{9} b^{6} \sin\left(d x + c\right)^{5} + 338226 \, a^{7} b^{8} \sin\left(d x + c\right)^{5} + 309876 \, a^{5} b^{10} \sin\left(d x + c\right)^{5} + 33558 \, a^{3} b^{12} \sin\left(d x + c\right)^{5} - 315 \, a b^{14} \sin\left(d x + c\right)^{5} + 89005 \, a^{10} b^{5} \sin\left(d x + c\right)^{4} + 579635 \, a^{8} b^{7} \sin\left(d x + c\right)^{4} + 503720 \, a^{6} b^{9} \sin\left(d x + c\right)^{4} + 47600 \, a^{4} b^{11} \sin\left(d x + c\right)^{4} - 245 \, a^{2} b^{13} \sin\left(d x + c\right)^{4} - 35 \, b^{15} \sin\left(d x + c\right)^{4} + 94885 \, a^{11} b^{4} \sin\left(d x + c\right)^{3} + 595595 \, a^{9} b^{6} \sin\left(d x + c\right)^{3} + 487760 \, a^{7} b^{8} \sin\left(d x + c\right)^{3} + 41720 \, a^{5} b^{10} \sin\left(d x + c\right)^{3} - 245 \, a^{3} b^{12} \sin\left(d x + c\right)^{3} - 35 \, a b^{14} \sin\left(d x + c\right)^{3} + 61341 \, a^{12} b^{3} \sin\left(d x + c\right)^{2} + 366177 \, a^{10} b^{5} \sin\left(d x + c\right)^{2} + 281631 \, a^{8} b^{7} \sin\left(d x + c\right)^{2} + 23268 \, a^{6} b^{9} \sin\left(d x + c\right)^{2} - 735 \, a^{4} b^{11} \sin\left(d x + c\right)^{2} + 147 \, a^{2} b^{13} \sin\left(d x + c\right)^{2} - 21 \, b^{15} \sin\left(d x + c\right)^{2} + 22407 \, a^{13} b^{2} \sin\left(d x + c\right) + 124019 \, a^{11} b^{4} \sin\left(d x + c\right) + 90797 \, a^{9} b^{6} \sin\left(d x + c\right) + 6916 \, a^{7} b^{8} \sin\left(d x + c\right) - 245 \, a^{5} b^{10} \sin\left(d x + c\right) + 49 \, a^{3} b^{12} \sin\left(d x + c\right) - 7 \, a b^{14} \sin\left(d x + c\right) + 3621 \, a^{14} b + 17507 \, a^{12} b^{3} + 13391 \, a^{10} b^{5} - 167 \, a^{8} b^{7} + 805 \, a^{6} b^{9} - 413 \, a^{4} b^{11} + 119 \, a^{2} b^{13} - 15 \, b^{15}\right)}}{{\left(a^{16} - 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} - 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} - 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{7}}}{210 \, d}"," ",0,"-1/210*(1680*(a^7*b^2 + 7*a^5*b^4 + 7*a^3*b^6 + a*b^8)*log(abs(b*sin(d*x + c) + a))/(a^16*b - 8*a^14*b^3 + 28*a^12*b^5 - 56*a^10*b^7 + 70*a^8*b^9 - 56*a^6*b^11 + 28*a^4*b^13 - 8*a^2*b^15 + b^17) - 105*log(abs(sin(d*x + c) + 1))/(a^8 - 8*a^7*b + 28*a^6*b^2 - 56*a^5*b^3 + 70*a^4*b^4 - 56*a^3*b^5 + 28*a^2*b^6 - 8*a*b^7 + b^8) + 105*log(abs(sin(d*x + c) - 1))/(a^8 + 8*a^7*b + 28*a^6*b^2 + 56*a^5*b^3 + 70*a^4*b^4 + 56*a^3*b^5 + 28*a^2*b^6 + 8*a*b^7 + b^8) - 2*(2178*a^7*b^8*sin(d*x + c)^7 + 15246*a^5*b^10*sin(d*x + c)^7 + 15246*a^3*b^12*sin(d*x + c)^7 + 2178*a*b^14*sin(d*x + c)^7 + 15981*a^8*b^7*sin(d*x + c)^6 + 109662*a^6*b^9*sin(d*x + c)^6 + 105252*a^4*b^11*sin(d*x + c)^6 + 13146*a^2*b^13*sin(d*x + c)^6 - 105*b^15*sin(d*x + c)^6 + 50463*a^9*b^6*sin(d*x + c)^5 + 338226*a^7*b^8*sin(d*x + c)^5 + 309876*a^5*b^10*sin(d*x + c)^5 + 33558*a^3*b^12*sin(d*x + c)^5 - 315*a*b^14*sin(d*x + c)^5 + 89005*a^10*b^5*sin(d*x + c)^4 + 579635*a^8*b^7*sin(d*x + c)^4 + 503720*a^6*b^9*sin(d*x + c)^4 + 47600*a^4*b^11*sin(d*x + c)^4 - 245*a^2*b^13*sin(d*x + c)^4 - 35*b^15*sin(d*x + c)^4 + 94885*a^11*b^4*sin(d*x + c)^3 + 595595*a^9*b^6*sin(d*x + c)^3 + 487760*a^7*b^8*sin(d*x + c)^3 + 41720*a^5*b^10*sin(d*x + c)^3 - 245*a^3*b^12*sin(d*x + c)^3 - 35*a*b^14*sin(d*x + c)^3 + 61341*a^12*b^3*sin(d*x + c)^2 + 366177*a^10*b^5*sin(d*x + c)^2 + 281631*a^8*b^7*sin(d*x + c)^2 + 23268*a^6*b^9*sin(d*x + c)^2 - 735*a^4*b^11*sin(d*x + c)^2 + 147*a^2*b^13*sin(d*x + c)^2 - 21*b^15*sin(d*x + c)^2 + 22407*a^13*b^2*sin(d*x + c) + 124019*a^11*b^4*sin(d*x + c) + 90797*a^9*b^6*sin(d*x + c) + 6916*a^7*b^8*sin(d*x + c) - 245*a^5*b^10*sin(d*x + c) + 49*a^3*b^12*sin(d*x + c) - 7*a*b^14*sin(d*x + c) + 3621*a^14*b + 17507*a^12*b^3 + 13391*a^10*b^5 - 167*a^8*b^7 + 805*a^6*b^9 - 413*a^4*b^11 + 119*a^2*b^13 - 15*b^15)/((a^16 - 8*a^14*b^2 + 28*a^12*b^4 - 56*a^10*b^6 + 70*a^8*b^8 - 56*a^6*b^10 + 28*a^4*b^12 - 8*a^2*b^14 + b^16)*(b*sin(d*x + c) + a)^7))/d","B",0
466,1,1327,0,4.381298," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{\frac{3360 \, {\left(15 \, a^{7} b^{4} + 63 \, a^{5} b^{6} + 45 \, a^{3} b^{8} + 5 \, a b^{10}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{18} b - 9 \, a^{16} b^{3} + 36 \, a^{14} b^{5} - 84 \, a^{12} b^{7} + 126 \, a^{10} b^{9} - 126 \, a^{8} b^{11} + 84 \, a^{6} b^{13} - 36 \, a^{4} b^{15} + 9 \, a^{2} b^{17} - b^{19}} + \frac{105 \, {\left(a - 9 \, b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{9} - 9 \, a^{8} b + 36 \, a^{7} b^{2} - 84 \, a^{6} b^{3} + 126 \, a^{5} b^{4} - 126 \, a^{4} b^{5} + 84 \, a^{3} b^{6} - 36 \, a^{2} b^{7} + 9 \, a b^{8} - b^{9}} - \frac{105 \, {\left(a + 9 \, b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{9} + 9 \, a^{8} b + 36 \, a^{7} b^{2} + 84 \, a^{6} b^{3} + 126 \, a^{5} b^{4} + 126 \, a^{4} b^{5} + 84 \, a^{3} b^{6} + 36 \, a^{2} b^{7} + 9 \, a b^{8} + b^{9}} + \frac{210 \, {\left(120 \, a^{7} b^{3} \sin\left(d x + c\right)^{2} + 504 \, a^{5} b^{5} \sin\left(d x + c\right)^{2} + 360 \, a^{3} b^{7} \sin\left(d x + c\right)^{2} + 40 \, a b^{9} \sin\left(d x + c\right)^{2} - a^{10} \sin\left(d x + c\right) - 27 \, a^{8} b^{2} \sin\left(d x + c\right) - 42 \, a^{6} b^{4} \sin\left(d x + c\right) + 42 \, a^{4} b^{6} \sin\left(d x + c\right) + 27 \, a^{2} b^{8} \sin\left(d x + c\right) + b^{10} \sin\left(d x + c\right) + 8 \, a^{9} b - 72 \, a^{7} b^{3} - 504 \, a^{5} b^{5} - 408 \, a^{3} b^{7} - 48 \, a b^{9}\right)}}{{\left(a^{18} - 9 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 84 \, a^{12} b^{6} + 126 \, a^{10} b^{8} - 126 \, a^{8} b^{10} + 84 \, a^{6} b^{12} - 36 \, a^{4} b^{14} + 9 \, a^{2} b^{16} - b^{18}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}} - \frac{4 \, {\left(32670 \, a^{7} b^{10} \sin\left(d x + c\right)^{7} + 137214 \, a^{5} b^{12} \sin\left(d x + c\right)^{7} + 98010 \, a^{3} b^{14} \sin\left(d x + c\right)^{7} + 10890 \, a b^{16} \sin\left(d x + c\right)^{7} + 237510 \, a^{8} b^{9} \sin\left(d x + c\right)^{6} + 978138 \, a^{6} b^{11} \sin\left(d x + c\right)^{6} + 670950 \, a^{4} b^{13} \sin\left(d x + c\right)^{6} + 65310 \, a^{2} b^{15} \sin\left(d x + c\right)^{6} - 420 \, b^{17} \sin\left(d x + c\right)^{6} + 741930 \, a^{9} b^{8} \sin\left(d x + c\right)^{5} + 2987334 \, a^{7} b^{10} \sin\left(d x + c\right)^{5} + 1959930 \, a^{5} b^{12} \sin\left(d x + c\right)^{5} + 166530 \, a^{3} b^{14} \sin\left(d x + c\right)^{5} - 1260 \, a b^{16} \sin\left(d x + c\right)^{5} + 1291675 \, a^{10} b^{7} \sin\left(d x + c\right)^{4} + 5064885 \, a^{8} b^{9} \sin\left(d x + c\right)^{4} + 3165120 \, a^{6} b^{11} \sin\left(d x + c\right)^{4} + 237020 \, a^{4} b^{13} \sin\left(d x + c\right)^{4} - 1155 \, a^{2} b^{15} \sin\left(d x + c\right)^{4} - 105 \, b^{17} \sin\left(d x + c\right)^{4} + 1354675 \, a^{11} b^{6} \sin\left(d x + c\right)^{3} + 5144685 \, a^{9} b^{8} \sin\left(d x + c\right)^{3} + 3051720 \, a^{7} b^{10} \sin\left(d x + c\right)^{3} + 207620 \, a^{5} b^{12} \sin\left(d x + c\right)^{3} - 1155 \, a^{3} b^{14} \sin\left(d x + c\right)^{3} - 105 \, a b^{16} \sin\left(d x + c\right)^{3} + 856905 \, a^{12} b^{5} \sin\left(d x + c\right)^{2} + 3126501 \, a^{10} b^{7} \sin\left(d x + c\right)^{2} + 1759590 \, a^{8} b^{9} \sin\left(d x + c\right)^{2} + 113400 \, a^{6} b^{11} \sin\left(d x + c\right)^{2} - 2205 \, a^{4} b^{13} \sin\left(d x + c\right)^{2} + 315 \, a^{2} b^{15} \sin\left(d x + c\right)^{2} - 42 \, b^{17} \sin\left(d x + c\right)^{2} + 303275 \, a^{13} b^{4} \sin\left(d x + c\right) + 1049727 \, a^{11} b^{6} \sin\left(d x + c\right) + 565530 \, a^{9} b^{8} \sin\left(d x + c\right) + 33600 \, a^{7} b^{10} \sin\left(d x + c\right) - 735 \, a^{5} b^{12} \sin\left(d x + c\right) + 105 \, a^{3} b^{14} \sin\left(d x + c\right) - 14 \, a b^{16} \sin\left(d x + c\right) + 46475 \, a^{14} b^{3} + 149331 \, a^{12} b^{5} + 79845 \, a^{10} b^{7} + 2385 \, a^{8} b^{9} + 1155 \, a^{6} b^{11} - 525 \, a^{4} b^{13} + 133 \, a^{2} b^{15} - 15 \, b^{17}\right)}}{{\left(a^{18} - 9 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 84 \, a^{12} b^{6} + 126 \, a^{10} b^{8} - 126 \, a^{8} b^{10} + 84 \, a^{6} b^{12} - 36 \, a^{4} b^{14} + 9 \, a^{2} b^{16} - b^{18}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{7}}}{420 \, d}"," ",0,"1/420*(3360*(15*a^7*b^4 + 63*a^5*b^6 + 45*a^3*b^8 + 5*a*b^10)*log(abs(b*sin(d*x + c) + a))/(a^18*b - 9*a^16*b^3 + 36*a^14*b^5 - 84*a^12*b^7 + 126*a^10*b^9 - 126*a^8*b^11 + 84*a^6*b^13 - 36*a^4*b^15 + 9*a^2*b^17 - b^19) + 105*(a - 9*b)*log(abs(sin(d*x + c) + 1))/(a^9 - 9*a^8*b + 36*a^7*b^2 - 84*a^6*b^3 + 126*a^5*b^4 - 126*a^4*b^5 + 84*a^3*b^6 - 36*a^2*b^7 + 9*a*b^8 - b^9) - 105*(a + 9*b)*log(abs(sin(d*x + c) - 1))/(a^9 + 9*a^8*b + 36*a^7*b^2 + 84*a^6*b^3 + 126*a^5*b^4 + 126*a^4*b^5 + 84*a^3*b^6 + 36*a^2*b^7 + 9*a*b^8 + b^9) + 210*(120*a^7*b^3*sin(d*x + c)^2 + 504*a^5*b^5*sin(d*x + c)^2 + 360*a^3*b^7*sin(d*x + c)^2 + 40*a*b^9*sin(d*x + c)^2 - a^10*sin(d*x + c) - 27*a^8*b^2*sin(d*x + c) - 42*a^6*b^4*sin(d*x + c) + 42*a^4*b^6*sin(d*x + c) + 27*a^2*b^8*sin(d*x + c) + b^10*sin(d*x + c) + 8*a^9*b - 72*a^7*b^3 - 504*a^5*b^5 - 408*a^3*b^7 - 48*a*b^9)/((a^18 - 9*a^16*b^2 + 36*a^14*b^4 - 84*a^12*b^6 + 126*a^10*b^8 - 126*a^8*b^10 + 84*a^6*b^12 - 36*a^4*b^14 + 9*a^2*b^16 - b^18)*(sin(d*x + c)^2 - 1)) - 4*(32670*a^7*b^10*sin(d*x + c)^7 + 137214*a^5*b^12*sin(d*x + c)^7 + 98010*a^3*b^14*sin(d*x + c)^7 + 10890*a*b^16*sin(d*x + c)^7 + 237510*a^8*b^9*sin(d*x + c)^6 + 978138*a^6*b^11*sin(d*x + c)^6 + 670950*a^4*b^13*sin(d*x + c)^6 + 65310*a^2*b^15*sin(d*x + c)^6 - 420*b^17*sin(d*x + c)^6 + 741930*a^9*b^8*sin(d*x + c)^5 + 2987334*a^7*b^10*sin(d*x + c)^5 + 1959930*a^5*b^12*sin(d*x + c)^5 + 166530*a^3*b^14*sin(d*x + c)^5 - 1260*a*b^16*sin(d*x + c)^5 + 1291675*a^10*b^7*sin(d*x + c)^4 + 5064885*a^8*b^9*sin(d*x + c)^4 + 3165120*a^6*b^11*sin(d*x + c)^4 + 237020*a^4*b^13*sin(d*x + c)^4 - 1155*a^2*b^15*sin(d*x + c)^4 - 105*b^17*sin(d*x + c)^4 + 1354675*a^11*b^6*sin(d*x + c)^3 + 5144685*a^9*b^8*sin(d*x + c)^3 + 3051720*a^7*b^10*sin(d*x + c)^3 + 207620*a^5*b^12*sin(d*x + c)^3 - 1155*a^3*b^14*sin(d*x + c)^3 - 105*a*b^16*sin(d*x + c)^3 + 856905*a^12*b^5*sin(d*x + c)^2 + 3126501*a^10*b^7*sin(d*x + c)^2 + 1759590*a^8*b^9*sin(d*x + c)^2 + 113400*a^6*b^11*sin(d*x + c)^2 - 2205*a^4*b^13*sin(d*x + c)^2 + 315*a^2*b^15*sin(d*x + c)^2 - 42*b^17*sin(d*x + c)^2 + 303275*a^13*b^4*sin(d*x + c) + 1049727*a^11*b^6*sin(d*x + c) + 565530*a^9*b^8*sin(d*x + c) + 33600*a^7*b^10*sin(d*x + c) - 735*a^5*b^12*sin(d*x + c) + 105*a^3*b^14*sin(d*x + c) - 14*a*b^16*sin(d*x + c) + 46475*a^14*b^3 + 149331*a^12*b^5 + 79845*a^10*b^7 + 2385*a^8*b^9 + 1155*a^6*b^11 - 525*a^4*b^13 + 133*a^2*b^15 - 15*b^17)/((a^18 - 9*a^16*b^2 + 36*a^14*b^4 - 84*a^12*b^6 + 126*a^10*b^8 - 126*a^8*b^10 + 84*a^6*b^12 - 36*a^4*b^14 + 9*a^2*b^16 - b^18)*(b*sin(d*x + c) + a)^7))/d","B",0
467,1,2326,0,9.879257," ","integrate(cos(d*x+c)^8/(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{\frac{105 \, {\left(16 \, a^{7} - 56 \, a^{5} b^{2} + 70 \, a^{3} b^{4} - 35 \, a b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} b^{8} - 3 \, a^{4} b^{10} + 3 \, a^{2} b^{12} - b^{14}\right)} \sqrt{a^{2} - b^{2}}} - \frac{840 \, a^{18} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 2310 \, a^{16} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1995 \, a^{14} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1680 \, a^{12} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 5040 \, a^{10} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 5040 \, a^{8} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1680 \, a^{6} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1680 \, a^{19} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 5880 \, a^{17} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 24990 \, a^{15} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 24255 \, a^{13} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 10080 \, a^{11} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 30240 \, a^{9} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 30240 \, a^{7} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 10080 \, a^{5} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 26880 \, a^{18} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 19320 \, a^{16} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 87640 \, a^{14} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 118790 \, a^{12} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 26880 \, a^{10} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 94080 \, a^{8} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 98560 \, a^{6} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 33600 \, a^{4} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 10080 \, a^{19} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 144480 \, a^{17} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 299880 \, a^{15} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 15680 \, a^{13} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 276430 \, a^{11} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 36960 \, a^{9} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 97440 \, a^{7} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 166880 \, a^{5} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 67200 \, a^{3} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 121800 \, a^{18} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 238770 \, a^{16} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1067605 \, a^{14} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 656390 \, a^{12} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 345156 \, a^{10} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 214032 \, a^{8} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 87472 \, a^{6} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 126336 \, a^{4} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 80640 \, a^{2} b^{17} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 25200 \, a^{19} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 514360 \, a^{17} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 490350 \, a^{15} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1389885 \, a^{13} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 1764630 \, a^{11} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 201544 \, a^{9} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 305088 \, a^{7} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 336448 \, a^{5} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 27776 \, a^{3} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 53760 \, a b^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 235200 \, a^{18} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 744800 \, a^{16} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2263800 \, a^{14} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 382620 \, a^{12} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1776432 \, a^{10} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 204848 \, a^{8} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 47616 \, a^{6} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 258560 \, a^{4} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 111616 \, a^{2} b^{17} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15360 \, b^{19} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33600 \, a^{19} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 730240 \, a^{17} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 534240 \, a^{15} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 2260440 \, a^{13} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 2443980 \, a^{11} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 593824 \, a^{9} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 148848 \, a^{7} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 336448 \, a^{5} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 27776 \, a^{3} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 53760 \, a b^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 231000 \, a^{18} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 643230 \, a^{16} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2226175 \, a^{14} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 749980 \, a^{12} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1482936 \, a^{10} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72128 \, a^{8} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 87472 \, a^{6} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 126336 \, a^{4} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 80640 \, a^{2} b^{17} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25200 \, a^{19} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 461160 \, a^{17} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 667674 \, a^{15} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 857003 \, a^{13} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1686188 \, a^{11} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 290976 \, a^{9} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 118160 \, a^{7} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 166880 \, a^{5} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 67200 \, a^{3} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 114240 \, a^{18} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 89880 \, a^{16} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 881776 \, a^{14} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 996478 \, a^{12} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 212688 \, a^{10} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 108976 \, a^{8} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 98560 \, a^{6} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33600 \, a^{4} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10080 \, a^{19} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 101920 \, a^{17} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 344568 \, a^{15} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 331128 \, a^{13} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 79226 \, a^{11} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 44800 \, a^{9} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 33264 \, a^{7} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10080 \, a^{5} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 22680 \, a^{18} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 64330 \, a^{16} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 58569 \, a^{14} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 14322 \, a^{12} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8372 \, a^{10} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5824 \, a^{8} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1680 \, a^{6} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1680 \, a^{19} - 4760 \, a^{17} b^{2} + 4326 \, a^{15} b^{4} - 1143 \, a^{13} b^{6} + 958 \, a^{11} b^{8} - 776 \, a^{9} b^{10} + 240 \, a^{7} b^{12}}{{\left(a^{13} b^{7} - 3 \, a^{11} b^{9} + 3 \, a^{9} b^{11} - a^{7} b^{13}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{7}} - \frac{840 \, {\left(d x + c\right)}}{b^{8}}}{840 \, d}"," ",0,"-1/840*(105*(16*a^7 - 56*a^5*b^2 + 70*a^3*b^4 - 35*a*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^6*b^8 - 3*a^4*b^10 + 3*a^2*b^12 - b^14)*sqrt(a^2 - b^2)) - (840*a^18*b*tan(1/2*d*x + 1/2*c)^13 - 2310*a^16*b^3*tan(1/2*d*x + 1/2*c)^13 + 1995*a^14*b^5*tan(1/2*d*x + 1/2*c)^13 - 1680*a^12*b^7*tan(1/2*d*x + 1/2*c)^13 + 5040*a^10*b^9*tan(1/2*d*x + 1/2*c)^13 - 5040*a^8*b^11*tan(1/2*d*x + 1/2*c)^13 + 1680*a^6*b^13*tan(1/2*d*x + 1/2*c)^13 + 1680*a^19*tan(1/2*d*x + 1/2*c)^12 + 5880*a^17*b^2*tan(1/2*d*x + 1/2*c)^12 - 24990*a^15*b^4*tan(1/2*d*x + 1/2*c)^12 + 24255*a^13*b^6*tan(1/2*d*x + 1/2*c)^12 - 10080*a^11*b^8*tan(1/2*d*x + 1/2*c)^12 + 30240*a^9*b^10*tan(1/2*d*x + 1/2*c)^12 - 30240*a^7*b^12*tan(1/2*d*x + 1/2*c)^12 + 10080*a^5*b^14*tan(1/2*d*x + 1/2*c)^12 + 26880*a^18*b*tan(1/2*d*x + 1/2*c)^11 - 19320*a^16*b^3*tan(1/2*d*x + 1/2*c)^11 - 87640*a^14*b^5*tan(1/2*d*x + 1/2*c)^11 + 118790*a^12*b^7*tan(1/2*d*x + 1/2*c)^11 - 26880*a^10*b^9*tan(1/2*d*x + 1/2*c)^11 + 94080*a^8*b^11*tan(1/2*d*x + 1/2*c)^11 - 98560*a^6*b^13*tan(1/2*d*x + 1/2*c)^11 + 33600*a^4*b^15*tan(1/2*d*x + 1/2*c)^11 + 10080*a^19*tan(1/2*d*x + 1/2*c)^10 + 144480*a^17*b^2*tan(1/2*d*x + 1/2*c)^10 - 299880*a^15*b^4*tan(1/2*d*x + 1/2*c)^10 - 15680*a^13*b^6*tan(1/2*d*x + 1/2*c)^10 + 276430*a^11*b^8*tan(1/2*d*x + 1/2*c)^10 + 36960*a^9*b^10*tan(1/2*d*x + 1/2*c)^10 + 97440*a^7*b^12*tan(1/2*d*x + 1/2*c)^10 - 166880*a^5*b^14*tan(1/2*d*x + 1/2*c)^10 + 67200*a^3*b^16*tan(1/2*d*x + 1/2*c)^10 + 121800*a^18*b*tan(1/2*d*x + 1/2*c)^9 + 238770*a^16*b^3*tan(1/2*d*x + 1/2*c)^9 - 1067605*a^14*b^5*tan(1/2*d*x + 1/2*c)^9 + 656390*a^12*b^7*tan(1/2*d*x + 1/2*c)^9 + 345156*a^10*b^9*tan(1/2*d*x + 1/2*c)^9 + 214032*a^8*b^11*tan(1/2*d*x + 1/2*c)^9 - 87472*a^6*b^13*tan(1/2*d*x + 1/2*c)^9 - 126336*a^4*b^15*tan(1/2*d*x + 1/2*c)^9 + 80640*a^2*b^17*tan(1/2*d*x + 1/2*c)^9 + 25200*a^19*tan(1/2*d*x + 1/2*c)^8 + 514360*a^17*b^2*tan(1/2*d*x + 1/2*c)^8 - 490350*a^15*b^4*tan(1/2*d*x + 1/2*c)^8 - 1389885*a^13*b^6*tan(1/2*d*x + 1/2*c)^8 + 1764630*a^11*b^8*tan(1/2*d*x + 1/2*c)^8 + 201544*a^9*b^10*tan(1/2*d*x + 1/2*c)^8 + 305088*a^7*b^12*tan(1/2*d*x + 1/2*c)^8 - 336448*a^5*b^14*tan(1/2*d*x + 1/2*c)^8 + 27776*a^3*b^16*tan(1/2*d*x + 1/2*c)^8 + 53760*a*b^18*tan(1/2*d*x + 1/2*c)^8 + 235200*a^18*b*tan(1/2*d*x + 1/2*c)^7 + 744800*a^16*b^3*tan(1/2*d*x + 1/2*c)^7 - 2263800*a^14*b^5*tan(1/2*d*x + 1/2*c)^7 + 382620*a^12*b^7*tan(1/2*d*x + 1/2*c)^7 + 1776432*a^10*b^9*tan(1/2*d*x + 1/2*c)^7 + 204848*a^8*b^11*tan(1/2*d*x + 1/2*c)^7 - 47616*a^6*b^13*tan(1/2*d*x + 1/2*c)^7 - 258560*a^4*b^15*tan(1/2*d*x + 1/2*c)^7 + 111616*a^2*b^17*tan(1/2*d*x + 1/2*c)^7 + 15360*b^19*tan(1/2*d*x + 1/2*c)^7 + 33600*a^19*tan(1/2*d*x + 1/2*c)^6 + 730240*a^17*b^2*tan(1/2*d*x + 1/2*c)^6 - 534240*a^15*b^4*tan(1/2*d*x + 1/2*c)^6 - 2260440*a^13*b^6*tan(1/2*d*x + 1/2*c)^6 + 2443980*a^11*b^8*tan(1/2*d*x + 1/2*c)^6 + 593824*a^9*b^10*tan(1/2*d*x + 1/2*c)^6 + 148848*a^7*b^12*tan(1/2*d*x + 1/2*c)^6 - 336448*a^5*b^14*tan(1/2*d*x + 1/2*c)^6 + 27776*a^3*b^16*tan(1/2*d*x + 1/2*c)^6 + 53760*a*b^18*tan(1/2*d*x + 1/2*c)^6 + 231000*a^18*b*tan(1/2*d*x + 1/2*c)^5 + 643230*a^16*b^3*tan(1/2*d*x + 1/2*c)^5 - 2226175*a^14*b^5*tan(1/2*d*x + 1/2*c)^5 + 749980*a^12*b^7*tan(1/2*d*x + 1/2*c)^5 + 1482936*a^10*b^9*tan(1/2*d*x + 1/2*c)^5 - 72128*a^8*b^11*tan(1/2*d*x + 1/2*c)^5 - 87472*a^6*b^13*tan(1/2*d*x + 1/2*c)^5 - 126336*a^4*b^15*tan(1/2*d*x + 1/2*c)^5 + 80640*a^2*b^17*tan(1/2*d*x + 1/2*c)^5 + 25200*a^19*tan(1/2*d*x + 1/2*c)^4 + 461160*a^17*b^2*tan(1/2*d*x + 1/2*c)^4 - 667674*a^15*b^4*tan(1/2*d*x + 1/2*c)^4 - 857003*a^13*b^6*tan(1/2*d*x + 1/2*c)^4 + 1686188*a^11*b^8*tan(1/2*d*x + 1/2*c)^4 - 290976*a^9*b^10*tan(1/2*d*x + 1/2*c)^4 + 118160*a^7*b^12*tan(1/2*d*x + 1/2*c)^4 - 166880*a^5*b^14*tan(1/2*d*x + 1/2*c)^4 + 67200*a^3*b^16*tan(1/2*d*x + 1/2*c)^4 + 114240*a^18*b*tan(1/2*d*x + 1/2*c)^3 + 89880*a^16*b^3*tan(1/2*d*x + 1/2*c)^3 - 881776*a^14*b^5*tan(1/2*d*x + 1/2*c)^3 + 996478*a^12*b^7*tan(1/2*d*x + 1/2*c)^3 - 212688*a^10*b^9*tan(1/2*d*x + 1/2*c)^3 + 108976*a^8*b^11*tan(1/2*d*x + 1/2*c)^3 - 98560*a^6*b^13*tan(1/2*d*x + 1/2*c)^3 + 33600*a^4*b^15*tan(1/2*d*x + 1/2*c)^3 + 10080*a^19*tan(1/2*d*x + 1/2*c)^2 + 101920*a^17*b^2*tan(1/2*d*x + 1/2*c)^2 - 344568*a^15*b^4*tan(1/2*d*x + 1/2*c)^2 + 331128*a^13*b^6*tan(1/2*d*x + 1/2*c)^2 - 79226*a^11*b^8*tan(1/2*d*x + 1/2*c)^2 + 44800*a^9*b^10*tan(1/2*d*x + 1/2*c)^2 - 33264*a^7*b^12*tan(1/2*d*x + 1/2*c)^2 + 10080*a^5*b^14*tan(1/2*d*x + 1/2*c)^2 + 22680*a^18*b*tan(1/2*d*x + 1/2*c) - 64330*a^16*b^3*tan(1/2*d*x + 1/2*c) + 58569*a^14*b^5*tan(1/2*d*x + 1/2*c) - 14322*a^12*b^7*tan(1/2*d*x + 1/2*c) + 8372*a^10*b^9*tan(1/2*d*x + 1/2*c) - 5824*a^8*b^11*tan(1/2*d*x + 1/2*c) + 1680*a^6*b^13*tan(1/2*d*x + 1/2*c) + 1680*a^19 - 4760*a^17*b^2 + 4326*a^15*b^4 - 1143*a^13*b^6 + 958*a^11*b^8 - 776*a^9*b^10 + 240*a^7*b^12)/((a^13*b^7 - 3*a^11*b^9 + 3*a^9*b^11 - a^7*b^13)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^7) - 840*(d*x + c)/b^8)/d","B",0
468,1,1650,0,9.949312," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{\frac{105 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} \sqrt{a^{2} - b^{2}}} - \frac{231 \, a^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1344 \, a^{12} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2016 \, a^{10} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1344 \, a^{8} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 336 \, a^{6} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 651 \, a^{13} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 8064 \, a^{11} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 12096 \, a^{9} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 8064 \, a^{7} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 2016 \, a^{5} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 196 \, a^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 4354 \, a^{12} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 21504 \, a^{10} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 36736 \, a^{8} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 25984 \, a^{6} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 6720 \, a^{4} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 140 \, a^{13} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 40250 \, a^{11} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 6720 \, a^{9} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 49280 \, a^{7} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 45920 \, a^{5} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 13440 \, a^{3} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 595 \, a^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 20650 \, a^{12} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 103740 \, a^{10} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 70336 \, a^{8} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2576 \, a^{6} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 40320 \, a^{4} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 16128 \, a^{2} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3045 \, a^{13} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 100450 \, a^{11} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 92120 \, a^{9} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 129024 \, a^{7} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 74816 \, a^{5} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 4480 \, a^{3} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 10752 \, a b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 39060 \, a^{12} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 188720 \, a^{10} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 58352 \, a^{8} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 39936 \, a^{6} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 73216 \, a^{4} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 19456 \, a^{2} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3072 \, b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6720 \, a^{13} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 122500 \, a^{11} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 109760 \, a^{9} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 127344 \, a^{7} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 74816 \, a^{5} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 4480 \, a^{3} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 10752 \, a b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 595 \, a^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 37940 \, a^{12} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 140280 \, a^{10} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 65296 \, a^{8} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2576 \, a^{6} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40320 \, a^{4} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16128 \, a^{2} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5999 \, a^{13} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 70084 \, a^{11} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 16800 \, a^{9} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 50288 \, a^{7} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 45920 \, a^{5} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 13440 \, a^{3} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 196 \, a^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 19082 \, a^{12} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 29232 \, a^{10} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 37744 \, a^{8} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25984 \, a^{6} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6720 \, a^{4} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2604 \, a^{13} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 13090 \, a^{11} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 13888 \, a^{9} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8400 \, a^{7} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2016 \, a^{5} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 231 \, a^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2562 \, a^{12} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2548 \, a^{10} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1456 \, a^{8} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 336 \, a^{6} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 279 \, a^{13} b + 326 \, a^{11} b^{3} - 200 \, a^{9} b^{5} + 48 \, a^{7} b^{7}}{{\left(a^{15} - 4 \, a^{13} b^{2} + 6 \, a^{11} b^{4} - 4 \, a^{9} b^{6} + a^{7} b^{8}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{7}}}{168 \, d}"," ",0,"1/168*(105*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*a/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*sqrt(a^2 - b^2)) - (231*a^14*tan(1/2*d*x + 1/2*c)^13 - 1344*a^12*b^2*tan(1/2*d*x + 1/2*c)^13 + 2016*a^10*b^4*tan(1/2*d*x + 1/2*c)^13 - 1344*a^8*b^6*tan(1/2*d*x + 1/2*c)^13 + 336*a^6*b^8*tan(1/2*d*x + 1/2*c)^13 + 651*a^13*b*tan(1/2*d*x + 1/2*c)^12 - 8064*a^11*b^3*tan(1/2*d*x + 1/2*c)^12 + 12096*a^9*b^5*tan(1/2*d*x + 1/2*c)^12 - 8064*a^7*b^7*tan(1/2*d*x + 1/2*c)^12 + 2016*a^5*b^9*tan(1/2*d*x + 1/2*c)^12 + 196*a^14*tan(1/2*d*x + 1/2*c)^11 - 4354*a^12*b^2*tan(1/2*d*x + 1/2*c)^11 - 21504*a^10*b^4*tan(1/2*d*x + 1/2*c)^11 + 36736*a^8*b^6*tan(1/2*d*x + 1/2*c)^11 - 25984*a^6*b^8*tan(1/2*d*x + 1/2*c)^11 + 6720*a^4*b^10*tan(1/2*d*x + 1/2*c)^11 + 140*a^13*b*tan(1/2*d*x + 1/2*c)^10 - 40250*a^11*b^3*tan(1/2*d*x + 1/2*c)^10 - 6720*a^9*b^5*tan(1/2*d*x + 1/2*c)^10 + 49280*a^7*b^7*tan(1/2*d*x + 1/2*c)^10 - 45920*a^5*b^9*tan(1/2*d*x + 1/2*c)^10 + 13440*a^3*b^11*tan(1/2*d*x + 1/2*c)^10 + 595*a^14*tan(1/2*d*x + 1/2*c)^9 - 20650*a^12*b^2*tan(1/2*d*x + 1/2*c)^9 - 103740*a^10*b^4*tan(1/2*d*x + 1/2*c)^9 + 70336*a^8*b^6*tan(1/2*d*x + 1/2*c)^9 + 2576*a^6*b^8*tan(1/2*d*x + 1/2*c)^9 - 40320*a^4*b^10*tan(1/2*d*x + 1/2*c)^9 + 16128*a^2*b^12*tan(1/2*d*x + 1/2*c)^9 - 3045*a^13*b*tan(1/2*d*x + 1/2*c)^8 - 100450*a^11*b^3*tan(1/2*d*x + 1/2*c)^8 - 92120*a^9*b^5*tan(1/2*d*x + 1/2*c)^8 + 129024*a^7*b^7*tan(1/2*d*x + 1/2*c)^8 - 74816*a^5*b^9*tan(1/2*d*x + 1/2*c)^8 - 4480*a^3*b^11*tan(1/2*d*x + 1/2*c)^8 + 10752*a*b^13*tan(1/2*d*x + 1/2*c)^8 - 39060*a^12*b^2*tan(1/2*d*x + 1/2*c)^7 - 188720*a^10*b^4*tan(1/2*d*x + 1/2*c)^7 + 58352*a^8*b^6*tan(1/2*d*x + 1/2*c)^7 + 39936*a^6*b^8*tan(1/2*d*x + 1/2*c)^7 - 73216*a^4*b^10*tan(1/2*d*x + 1/2*c)^7 + 19456*a^2*b^12*tan(1/2*d*x + 1/2*c)^7 + 3072*b^14*tan(1/2*d*x + 1/2*c)^7 - 6720*a^13*b*tan(1/2*d*x + 1/2*c)^6 - 122500*a^11*b^3*tan(1/2*d*x + 1/2*c)^6 - 109760*a^9*b^5*tan(1/2*d*x + 1/2*c)^6 + 127344*a^7*b^7*tan(1/2*d*x + 1/2*c)^6 - 74816*a^5*b^9*tan(1/2*d*x + 1/2*c)^6 - 4480*a^3*b^11*tan(1/2*d*x + 1/2*c)^6 + 10752*a*b^13*tan(1/2*d*x + 1/2*c)^6 - 595*a^14*tan(1/2*d*x + 1/2*c)^5 - 37940*a^12*b^2*tan(1/2*d*x + 1/2*c)^5 - 140280*a^10*b^4*tan(1/2*d*x + 1/2*c)^5 + 65296*a^8*b^6*tan(1/2*d*x + 1/2*c)^5 + 2576*a^6*b^8*tan(1/2*d*x + 1/2*c)^5 - 40320*a^4*b^10*tan(1/2*d*x + 1/2*c)^5 + 16128*a^2*b^12*tan(1/2*d*x + 1/2*c)^5 - 5999*a^13*b*tan(1/2*d*x + 1/2*c)^4 - 70084*a^11*b^3*tan(1/2*d*x + 1/2*c)^4 - 16800*a^9*b^5*tan(1/2*d*x + 1/2*c)^4 + 50288*a^7*b^7*tan(1/2*d*x + 1/2*c)^4 - 45920*a^5*b^9*tan(1/2*d*x + 1/2*c)^4 + 13440*a^3*b^11*tan(1/2*d*x + 1/2*c)^4 - 196*a^14*tan(1/2*d*x + 1/2*c)^3 - 19082*a^12*b^2*tan(1/2*d*x + 1/2*c)^3 - 29232*a^10*b^4*tan(1/2*d*x + 1/2*c)^3 + 37744*a^8*b^6*tan(1/2*d*x + 1/2*c)^3 - 25984*a^6*b^8*tan(1/2*d*x + 1/2*c)^3 + 6720*a^4*b^10*tan(1/2*d*x + 1/2*c)^3 - 2604*a^13*b*tan(1/2*d*x + 1/2*c)^2 - 13090*a^11*b^3*tan(1/2*d*x + 1/2*c)^2 + 13888*a^9*b^5*tan(1/2*d*x + 1/2*c)^2 - 8400*a^7*b^7*tan(1/2*d*x + 1/2*c)^2 + 2016*a^5*b^9*tan(1/2*d*x + 1/2*c)^2 - 231*a^14*tan(1/2*d*x + 1/2*c) - 2562*a^12*b^2*tan(1/2*d*x + 1/2*c) + 2548*a^10*b^4*tan(1/2*d*x + 1/2*c) - 1456*a^8*b^6*tan(1/2*d*x + 1/2*c) + 336*a^6*b^8*tan(1/2*d*x + 1/2*c) - 279*a^13*b + 326*a^11*b^3 - 200*a^9*b^5 + 48*a^7*b^7)/((a^15 - 4*a^13*b^2 + 6*a^11*b^4 - 4*a^9*b^6 + a^7*b^8)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^7))/d","B",0
469,1,1932,0,5.093212," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{\frac{105 \, {\left(2 \, a^{3} + a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{10} - 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} - 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}\right)} \sqrt{a^{2} - b^{2}}} - \frac{350 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 2905 \, a^{14} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 5600 \, a^{12} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 5600 \, a^{10} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2800 \, a^{8} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 560 \, a^{6} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 630 \, a^{15} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 18165 \, a^{13} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 33600 \, a^{11} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 33600 \, a^{9} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 16800 \, a^{7} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 3360 \, a^{5} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 840 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 15680 \, a^{14} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 41090 \, a^{12} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 89600 \, a^{10} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 100800 \, a^{8} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 53760 \, a^{6} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 11200 \, a^{4} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 840 \, a^{15} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 102760 \, a^{13} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 11270 \, a^{11} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 78400 \, a^{9} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 151200 \, a^{7} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 97440 \, a^{5} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 22400 \, a^{3} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 630 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 51905 \, a^{14} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 249410 \, a^{12} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 202244 \, a^{10} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 129360 \, a^{8} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 62832 \, a^{6} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 92288 \, a^{4} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 26880 \, a^{2} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 8330 \, a^{15} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 248745 \, a^{13} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 190610 \, a^{11} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 253736 \, a^{9} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 338240 \, a^{7} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 120512 \, a^{5} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 24192 \, a^{3} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 17920 \, a b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 96040 \, a^{14} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 452340 \, a^{12} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 164528 \, a^{10} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 99344 \, a^{8} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 177664 \, a^{6} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 153088 \, a^{4} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 27648 \, a^{2} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5120 \, b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15680 \, a^{15} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 296520 \, a^{13} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 247940 \, a^{11} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 232736 \, a^{9} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 339920 \, a^{7} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 120512 \, a^{5} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 24192 \, a^{3} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 17920 \, a b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 630 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 92155 \, a^{14} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 333060 \, a^{12} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 151144 \, a^{10} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 133280 \, a^{8} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 62832 \, a^{6} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 92288 \, a^{4} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 26880 \, a^{2} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 13566 \, a^{15} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 166775 \, a^{13} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 41412 \, a^{11} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 72128 \, a^{9} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 150640 \, a^{7} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 97440 \, a^{5} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 22400 \, a^{3} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 840 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 41944 \, a^{14} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 76650 \, a^{12} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 87472 \, a^{10} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 100688 \, a^{8} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 53760 \, a^{6} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 11200 \, a^{4} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5432 \, a^{15} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 33264 \, a^{13} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 34846 \, a^{11} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 34272 \, a^{9} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 16912 \, a^{7} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3360 \, a^{5} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 350 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6699 \, a^{14} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6790 \, a^{12} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6188 \, a^{10} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2912 \, a^{8} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 560 \, a^{6} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 686 \, a^{15} b + 885 \, a^{13} b^{3} - 842 \, a^{11} b^{5} + 408 \, a^{9} b^{7} - 80 \, a^{7} b^{9}}{{\left(a^{17} - 5 \, a^{15} b^{2} + 10 \, a^{13} b^{4} - 10 \, a^{11} b^{6} + 5 \, a^{9} b^{8} - a^{7} b^{10}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{7}}}{280 \, d}"," ",0,"1/280*(105*(2*a^3 + a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^10 - 5*a^8*b^2 + 10*a^6*b^4 - 10*a^4*b^6 + 5*a^2*b^8 - b^10)*sqrt(a^2 - b^2)) - (350*a^16*tan(1/2*d*x + 1/2*c)^13 - 2905*a^14*b^2*tan(1/2*d*x + 1/2*c)^13 + 5600*a^12*b^4*tan(1/2*d*x + 1/2*c)^13 - 5600*a^10*b^6*tan(1/2*d*x + 1/2*c)^13 + 2800*a^8*b^8*tan(1/2*d*x + 1/2*c)^13 - 560*a^6*b^10*tan(1/2*d*x + 1/2*c)^13 + 630*a^15*b*tan(1/2*d*x + 1/2*c)^12 - 18165*a^13*b^3*tan(1/2*d*x + 1/2*c)^12 + 33600*a^11*b^5*tan(1/2*d*x + 1/2*c)^12 - 33600*a^9*b^7*tan(1/2*d*x + 1/2*c)^12 + 16800*a^7*b^9*tan(1/2*d*x + 1/2*c)^12 - 3360*a^5*b^11*tan(1/2*d*x + 1/2*c)^12 + 840*a^16*tan(1/2*d*x + 1/2*c)^11 - 15680*a^14*b^2*tan(1/2*d*x + 1/2*c)^11 - 41090*a^12*b^4*tan(1/2*d*x + 1/2*c)^11 + 89600*a^10*b^6*tan(1/2*d*x + 1/2*c)^11 - 100800*a^8*b^8*tan(1/2*d*x + 1/2*c)^11 + 53760*a^6*b^10*tan(1/2*d*x + 1/2*c)^11 - 11200*a^4*b^12*tan(1/2*d*x + 1/2*c)^11 - 840*a^15*b*tan(1/2*d*x + 1/2*c)^10 - 102760*a^13*b^3*tan(1/2*d*x + 1/2*c)^10 + 11270*a^11*b^5*tan(1/2*d*x + 1/2*c)^10 + 78400*a^9*b^7*tan(1/2*d*x + 1/2*c)^10 - 151200*a^7*b^9*tan(1/2*d*x + 1/2*c)^10 + 97440*a^5*b^11*tan(1/2*d*x + 1/2*c)^10 - 22400*a^3*b^13*tan(1/2*d*x + 1/2*c)^10 + 630*a^16*tan(1/2*d*x + 1/2*c)^9 - 51905*a^14*b^2*tan(1/2*d*x + 1/2*c)^9 - 249410*a^12*b^4*tan(1/2*d*x + 1/2*c)^9 + 202244*a^10*b^6*tan(1/2*d*x + 1/2*c)^9 - 129360*a^8*b^8*tan(1/2*d*x + 1/2*c)^9 - 62832*a^6*b^10*tan(1/2*d*x + 1/2*c)^9 + 92288*a^4*b^12*tan(1/2*d*x + 1/2*c)^9 - 26880*a^2*b^14*tan(1/2*d*x + 1/2*c)^9 - 8330*a^15*b*tan(1/2*d*x + 1/2*c)^8 - 248745*a^13*b^3*tan(1/2*d*x + 1/2*c)^8 - 190610*a^11*b^5*tan(1/2*d*x + 1/2*c)^8 + 253736*a^9*b^7*tan(1/2*d*x + 1/2*c)^8 - 338240*a^7*b^9*tan(1/2*d*x + 1/2*c)^8 + 120512*a^5*b^11*tan(1/2*d*x + 1/2*c)^8 + 24192*a^3*b^13*tan(1/2*d*x + 1/2*c)^8 - 17920*a*b^15*tan(1/2*d*x + 1/2*c)^8 - 96040*a^14*b^2*tan(1/2*d*x + 1/2*c)^7 - 452340*a^12*b^4*tan(1/2*d*x + 1/2*c)^7 + 164528*a^10*b^6*tan(1/2*d*x + 1/2*c)^7 - 99344*a^8*b^8*tan(1/2*d*x + 1/2*c)^7 - 177664*a^6*b^10*tan(1/2*d*x + 1/2*c)^7 + 153088*a^4*b^12*tan(1/2*d*x + 1/2*c)^7 - 27648*a^2*b^14*tan(1/2*d*x + 1/2*c)^7 - 5120*b^16*tan(1/2*d*x + 1/2*c)^7 - 15680*a^15*b*tan(1/2*d*x + 1/2*c)^6 - 296520*a^13*b^3*tan(1/2*d*x + 1/2*c)^6 - 247940*a^11*b^5*tan(1/2*d*x + 1/2*c)^6 + 232736*a^9*b^7*tan(1/2*d*x + 1/2*c)^6 - 339920*a^7*b^9*tan(1/2*d*x + 1/2*c)^6 + 120512*a^5*b^11*tan(1/2*d*x + 1/2*c)^6 + 24192*a^3*b^13*tan(1/2*d*x + 1/2*c)^6 - 17920*a*b^15*tan(1/2*d*x + 1/2*c)^6 - 630*a^16*tan(1/2*d*x + 1/2*c)^5 - 92155*a^14*b^2*tan(1/2*d*x + 1/2*c)^5 - 333060*a^12*b^4*tan(1/2*d*x + 1/2*c)^5 + 151144*a^10*b^6*tan(1/2*d*x + 1/2*c)^5 - 133280*a^8*b^8*tan(1/2*d*x + 1/2*c)^5 - 62832*a^6*b^10*tan(1/2*d*x + 1/2*c)^5 + 92288*a^4*b^12*tan(1/2*d*x + 1/2*c)^5 - 26880*a^2*b^14*tan(1/2*d*x + 1/2*c)^5 - 13566*a^15*b*tan(1/2*d*x + 1/2*c)^4 - 166775*a^13*b^3*tan(1/2*d*x + 1/2*c)^4 - 41412*a^11*b^5*tan(1/2*d*x + 1/2*c)^4 + 72128*a^9*b^7*tan(1/2*d*x + 1/2*c)^4 - 150640*a^7*b^9*tan(1/2*d*x + 1/2*c)^4 + 97440*a^5*b^11*tan(1/2*d*x + 1/2*c)^4 - 22400*a^3*b^13*tan(1/2*d*x + 1/2*c)^4 - 840*a^16*tan(1/2*d*x + 1/2*c)^3 - 41944*a^14*b^2*tan(1/2*d*x + 1/2*c)^3 - 76650*a^12*b^4*tan(1/2*d*x + 1/2*c)^3 + 87472*a^10*b^6*tan(1/2*d*x + 1/2*c)^3 - 100688*a^8*b^8*tan(1/2*d*x + 1/2*c)^3 + 53760*a^6*b^10*tan(1/2*d*x + 1/2*c)^3 - 11200*a^4*b^12*tan(1/2*d*x + 1/2*c)^3 - 5432*a^15*b*tan(1/2*d*x + 1/2*c)^2 - 33264*a^13*b^3*tan(1/2*d*x + 1/2*c)^2 + 34846*a^11*b^5*tan(1/2*d*x + 1/2*c)^2 - 34272*a^9*b^7*tan(1/2*d*x + 1/2*c)^2 + 16912*a^7*b^9*tan(1/2*d*x + 1/2*c)^2 - 3360*a^5*b^11*tan(1/2*d*x + 1/2*c)^2 - 350*a^16*tan(1/2*d*x + 1/2*c) - 6699*a^14*b^2*tan(1/2*d*x + 1/2*c) + 6790*a^12*b^4*tan(1/2*d*x + 1/2*c) - 6188*a^10*b^6*tan(1/2*d*x + 1/2*c) + 2912*a^8*b^8*tan(1/2*d*x + 1/2*c) - 560*a^6*b^10*tan(1/2*d*x + 1/2*c) - 686*a^15*b + 885*a^13*b^3 - 842*a^11*b^5 + 408*a^9*b^7 - 80*a^7*b^9)/((a^17 - 5*a^15*b^2 + 10*a^13*b^4 - 10*a^11*b^6 + 5*a^9*b^8 - a^7*b^10)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^7))/d","B",0
470,1,2207,0,3.818733," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{\frac{105 \, {\left(8 \, a^{5} + 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{12} - 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} - 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 6 \, a^{2} b^{10} + b^{12}\right)} \sqrt{a^{2} - b^{2}}} - \frac{840 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 12180 \, a^{16} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 24675 \, a^{14} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 33600 \, a^{12} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 25200 \, a^{10} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 10080 \, a^{8} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1680 \, a^{6} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 840 \, a^{17} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 87780 \, a^{15} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 144375 \, a^{13} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 201600 \, a^{11} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 151200 \, a^{9} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 60480 \, a^{7} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 10080 \, a^{5} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 3360 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 94080 \, a^{16} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 220500 \, a^{14} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 287350 \, a^{12} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 537600 \, a^{10} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 450240 \, a^{8} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 192640 \, a^{6} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 33600 \, a^{4} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 13440 \, a^{17} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 554400 \, a^{15} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 165900 \, a^{13} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 66850 \, a^{11} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 621600 \, a^{9} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 719040 \, a^{7} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 355040 \, a^{5} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 67200 \, a^{3} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 4200 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 304500 \, a^{16} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1418025 \, a^{14} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 147070 \, a^{12} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1316700 \, a^{10} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 242592 \, a^{8} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 439376 \, a^{6} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 352128 \, a^{4} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 80640 \, a^{2} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 49000 \, a^{17} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1357300 \, a^{15} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1726305 \, a^{13} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 346570 \, a^{11} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1972600 \, a^{9} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 1360128 \, a^{7} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 298816 \, a^{5} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 122752 \, a^{3} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 53760 \, a b^{17} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 509600 \, a^{16} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2685200 \, a^{14} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 900900 \, a^{12} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2070320 \, a^{10} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 278096 \, a^{8} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 952320 \, a^{6} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 538112 \, a^{4} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 68608 \, a^{2} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15360 \, b^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 78400 \, a^{17} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1607200 \, a^{15} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 2326800 \, a^{13} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 823060 \, a^{11} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 2094400 \, a^{9} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1351728 \, a^{7} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 298816 \, a^{5} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 122752 \, a^{3} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 53760 \, a b^{17} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 4200 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 459900 \, a^{16} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2100175 \, a^{14} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 647780 \, a^{12} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1643880 \, a^{10} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 228592 \, a^{8} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 439376 \, a^{6} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 352128 \, a^{4} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 80640 \, a^{2} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 63000 \, a^{17} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 918540 \, a^{15} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 858683 \, a^{13} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 434644 \, a^{11} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 634368 \, a^{9} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 719600 \, a^{7} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 355040 \, a^{5} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 67200 \, a^{3} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3360 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 211680 \, a^{16} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 575260 \, a^{14} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 43918 \, a^{12} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 534576 \, a^{10} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 449008 \, a^{8} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 192640 \, a^{6} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33600 \, a^{4} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24640 \, a^{17} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 199360 \, a^{15} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 44604 \, a^{13} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 186410 \, a^{11} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 144928 \, a^{9} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 59472 \, a^{7} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10080 \, a^{5} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 840 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 38780 \, a^{16} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12565 \, a^{14} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 35322 \, a^{12} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 25844 \, a^{10} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 10192 \, a^{8} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1680 \, a^{6} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3640 \, a^{17} b + 2660 \, a^{15} b^{3} - 4923 \, a^{13} b^{5} + 3646 \, a^{11} b^{7} - 1448 \, a^{9} b^{9} + 240 \, a^{7} b^{11}}{{\left(a^{19} - 6 \, a^{17} b^{2} + 15 \, a^{15} b^{4} - 20 \, a^{13} b^{6} + 15 \, a^{11} b^{8} - 6 \, a^{9} b^{10} + a^{7} b^{12}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{7}}}{840 \, d}"," ",0,"1/840*(105*(8*a^5 + 20*a^3*b^2 + 5*a*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^12 - 6*a^10*b^2 + 15*a^8*b^4 - 20*a^6*b^6 + 15*a^4*b^8 - 6*a^2*b^10 + b^12)*sqrt(a^2 - b^2)) - (840*a^18*tan(1/2*d*x + 1/2*c)^13 - 12180*a^16*b^2*tan(1/2*d*x + 1/2*c)^13 + 24675*a^14*b^4*tan(1/2*d*x + 1/2*c)^13 - 33600*a^12*b^6*tan(1/2*d*x + 1/2*c)^13 + 25200*a^10*b^8*tan(1/2*d*x + 1/2*c)^13 - 10080*a^8*b^10*tan(1/2*d*x + 1/2*c)^13 + 1680*a^6*b^12*tan(1/2*d*x + 1/2*c)^13 - 840*a^17*b*tan(1/2*d*x + 1/2*c)^12 - 87780*a^15*b^3*tan(1/2*d*x + 1/2*c)^12 + 144375*a^13*b^5*tan(1/2*d*x + 1/2*c)^12 - 201600*a^11*b^7*tan(1/2*d*x + 1/2*c)^12 + 151200*a^9*b^9*tan(1/2*d*x + 1/2*c)^12 - 60480*a^7*b^11*tan(1/2*d*x + 1/2*c)^12 + 10080*a^5*b^13*tan(1/2*d*x + 1/2*c)^12 + 3360*a^18*tan(1/2*d*x + 1/2*c)^11 - 94080*a^16*b^2*tan(1/2*d*x + 1/2*c)^11 - 220500*a^14*b^4*tan(1/2*d*x + 1/2*c)^11 + 287350*a^12*b^6*tan(1/2*d*x + 1/2*c)^11 - 537600*a^10*b^8*tan(1/2*d*x + 1/2*c)^11 + 450240*a^8*b^10*tan(1/2*d*x + 1/2*c)^11 - 192640*a^6*b^12*tan(1/2*d*x + 1/2*c)^11 + 33600*a^4*b^14*tan(1/2*d*x + 1/2*c)^11 - 13440*a^17*b*tan(1/2*d*x + 1/2*c)^10 - 554400*a^15*b^3*tan(1/2*d*x + 1/2*c)^10 - 165900*a^13*b^5*tan(1/2*d*x + 1/2*c)^10 - 66850*a^11*b^7*tan(1/2*d*x + 1/2*c)^10 - 621600*a^9*b^9*tan(1/2*d*x + 1/2*c)^10 + 719040*a^7*b^11*tan(1/2*d*x + 1/2*c)^10 - 355040*a^5*b^13*tan(1/2*d*x + 1/2*c)^10 + 67200*a^3*b^15*tan(1/2*d*x + 1/2*c)^10 + 4200*a^18*tan(1/2*d*x + 1/2*c)^9 - 304500*a^16*b^2*tan(1/2*d*x + 1/2*c)^9 - 1418025*a^14*b^4*tan(1/2*d*x + 1/2*c)^9 + 147070*a^12*b^6*tan(1/2*d*x + 1/2*c)^9 - 1316700*a^10*b^8*tan(1/2*d*x + 1/2*c)^9 + 242592*a^8*b^10*tan(1/2*d*x + 1/2*c)^9 + 439376*a^6*b^12*tan(1/2*d*x + 1/2*c)^9 - 352128*a^4*b^14*tan(1/2*d*x + 1/2*c)^9 + 80640*a^2*b^16*tan(1/2*d*x + 1/2*c)^9 - 49000*a^17*b*tan(1/2*d*x + 1/2*c)^8 - 1357300*a^15*b^3*tan(1/2*d*x + 1/2*c)^8 - 1726305*a^13*b^5*tan(1/2*d*x + 1/2*c)^8 - 346570*a^11*b^7*tan(1/2*d*x + 1/2*c)^8 - 1972600*a^9*b^9*tan(1/2*d*x + 1/2*c)^8 + 1360128*a^7*b^11*tan(1/2*d*x + 1/2*c)^8 - 298816*a^5*b^13*tan(1/2*d*x + 1/2*c)^8 - 122752*a^3*b^15*tan(1/2*d*x + 1/2*c)^8 + 53760*a*b^17*tan(1/2*d*x + 1/2*c)^8 - 509600*a^16*b^2*tan(1/2*d*x + 1/2*c)^7 - 2685200*a^14*b^4*tan(1/2*d*x + 1/2*c)^7 - 900900*a^12*b^6*tan(1/2*d*x + 1/2*c)^7 - 2070320*a^10*b^8*tan(1/2*d*x + 1/2*c)^7 - 278096*a^8*b^10*tan(1/2*d*x + 1/2*c)^7 + 952320*a^6*b^12*tan(1/2*d*x + 1/2*c)^7 - 538112*a^4*b^14*tan(1/2*d*x + 1/2*c)^7 + 68608*a^2*b^16*tan(1/2*d*x + 1/2*c)^7 + 15360*b^18*tan(1/2*d*x + 1/2*c)^7 - 78400*a^17*b*tan(1/2*d*x + 1/2*c)^6 - 1607200*a^15*b^3*tan(1/2*d*x + 1/2*c)^6 - 2326800*a^13*b^5*tan(1/2*d*x + 1/2*c)^6 - 823060*a^11*b^7*tan(1/2*d*x + 1/2*c)^6 - 2094400*a^9*b^9*tan(1/2*d*x + 1/2*c)^6 + 1351728*a^7*b^11*tan(1/2*d*x + 1/2*c)^6 - 298816*a^5*b^13*tan(1/2*d*x + 1/2*c)^6 - 122752*a^3*b^15*tan(1/2*d*x + 1/2*c)^6 + 53760*a*b^17*tan(1/2*d*x + 1/2*c)^6 - 4200*a^18*tan(1/2*d*x + 1/2*c)^5 - 459900*a^16*b^2*tan(1/2*d*x + 1/2*c)^5 - 2100175*a^14*b^4*tan(1/2*d*x + 1/2*c)^5 - 647780*a^12*b^6*tan(1/2*d*x + 1/2*c)^5 - 1643880*a^10*b^8*tan(1/2*d*x + 1/2*c)^5 + 228592*a^8*b^10*tan(1/2*d*x + 1/2*c)^5 + 439376*a^6*b^12*tan(1/2*d*x + 1/2*c)^5 - 352128*a^4*b^14*tan(1/2*d*x + 1/2*c)^5 + 80640*a^2*b^16*tan(1/2*d*x + 1/2*c)^5 - 63000*a^17*b*tan(1/2*d*x + 1/2*c)^4 - 918540*a^15*b^3*tan(1/2*d*x + 1/2*c)^4 - 858683*a^13*b^5*tan(1/2*d*x + 1/2*c)^4 - 434644*a^11*b^7*tan(1/2*d*x + 1/2*c)^4 - 634368*a^9*b^9*tan(1/2*d*x + 1/2*c)^4 + 719600*a^7*b^11*tan(1/2*d*x + 1/2*c)^4 - 355040*a^5*b^13*tan(1/2*d*x + 1/2*c)^4 + 67200*a^3*b^15*tan(1/2*d*x + 1/2*c)^4 - 3360*a^18*tan(1/2*d*x + 1/2*c)^3 - 211680*a^16*b^2*tan(1/2*d*x + 1/2*c)^3 - 575260*a^14*b^4*tan(1/2*d*x + 1/2*c)^3 + 43918*a^12*b^6*tan(1/2*d*x + 1/2*c)^3 - 534576*a^10*b^8*tan(1/2*d*x + 1/2*c)^3 + 449008*a^8*b^10*tan(1/2*d*x + 1/2*c)^3 - 192640*a^6*b^12*tan(1/2*d*x + 1/2*c)^3 + 33600*a^4*b^14*tan(1/2*d*x + 1/2*c)^3 - 24640*a^17*b*tan(1/2*d*x + 1/2*c)^2 - 199360*a^15*b^3*tan(1/2*d*x + 1/2*c)^2 + 44604*a^13*b^5*tan(1/2*d*x + 1/2*c)^2 - 186410*a^11*b^7*tan(1/2*d*x + 1/2*c)^2 + 144928*a^9*b^9*tan(1/2*d*x + 1/2*c)^2 - 59472*a^7*b^11*tan(1/2*d*x + 1/2*c)^2 + 10080*a^5*b^13*tan(1/2*d*x + 1/2*c)^2 - 840*a^18*tan(1/2*d*x + 1/2*c) - 38780*a^16*b^2*tan(1/2*d*x + 1/2*c) + 12565*a^14*b^4*tan(1/2*d*x + 1/2*c) - 35322*a^12*b^6*tan(1/2*d*x + 1/2*c) + 25844*a^10*b^8*tan(1/2*d*x + 1/2*c) - 10192*a^8*b^10*tan(1/2*d*x + 1/2*c) + 1680*a^6*b^12*tan(1/2*d*x + 1/2*c) - 3640*a^17*b + 2660*a^15*b^3 - 4923*a^13*b^5 + 3646*a^11*b^7 - 1448*a^9*b^9 + 240*a^7*b^11)/((a^19 - 6*a^17*b^2 + 15*a^15*b^4 - 20*a^13*b^6 + 15*a^11*b^8 - 6*a^9*b^10 + a^7*b^12)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^7))/d","B",0
471,1,2610,0,7.972742," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","-\frac{\frac{315 \, {\left(64 \, a^{7} b^{2} + 336 \, a^{5} b^{4} + 280 \, a^{3} b^{6} + 35 \, a b^{8}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{16} - 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} - 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} - 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sqrt{a^{2} - b^{2}}} + \frac{560 \, {\left(a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 28 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 70 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 28 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a^{7} b - 56 \, a^{5} b^{3} - 56 \, a^{3} b^{5} - 8 \, a b^{7}\right)}}{{\left(a^{16} - 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} - 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} - 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}} + \frac{82320 \, a^{18} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 41160 \, a^{16} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 49665 \, a^{14} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 31360 \, a^{12} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 15680 \, a^{10} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 4480 \, a^{8} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 560 \, a^{6} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 47040 \, a^{19} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 952560 \, a^{17} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 743400 \, a^{15} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 370685 \, a^{13} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 188160 \, a^{11} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 94080 \, a^{9} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 26880 \, a^{7} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 3360 \, a^{5} b^{17} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 987840 \, a^{18} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 5221440 \, a^{16} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 4792620 \, a^{14} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1272530 \, a^{12} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 501760 \, a^{10} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 277760 \, a^{8} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 85120 \, a^{6} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 11200 \, a^{4} b^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 282240 \, a^{19} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 7056000 \, a^{17} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 18695040 \, a^{15} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 15575140 \, a^{13} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 2689610 \, a^{11} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 721280 \, a^{9} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 474880 \, a^{7} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 160160 \, a^{5} b^{17} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 22400 \, a^{3} b^{19} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 3704400 \, a^{18} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 26948040 \, a^{16} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 46663365 \, a^{14} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 29114330 \, a^{12} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3411772 \, a^{10} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 305536 \, a^{8} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 388976 \, a^{6} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 167552 \, a^{4} b^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 26880 \, a^{2} b^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 705600 \, a^{19} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 18780720 \, a^{17} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 65305800 \, a^{15} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 77673085 \, a^{13} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 32483570 \, a^{11} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 2139928 \, a^{9} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 587776 \, a^{7} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 7616 \, a^{5} b^{17} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 74368 \, a^{3} b^{19} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 17920 \, a b^{21} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 6585600 \, a^{18} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 51038400 \, a^{16} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 104499360 \, a^{14} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 80185140 \, a^{12} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 20029744 \, a^{10} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 661136 \, a^{8} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 683008 \, a^{6} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 217600 \, a^{4} b^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 13312 \, a^{2} b^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5120 \, b^{22} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 940800 \, a^{19} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 23614080 \, a^{17} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 83805120 \, a^{15} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 103990880 \, a^{13} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 45853220 \, a^{11} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 4650688 \, a^{9} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 692496 \, a^{7} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 7616 \, a^{5} b^{17} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 74368 \, a^{3} b^{19} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 17920 \, a b^{21} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 6174000 \, a^{18} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 43023960 \, a^{16} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 82755435 \, a^{14} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 55248340 \, a^{12} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10337432 \, a^{10} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 175056 \, a^{8} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 388976 \, a^{6} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 167552 \, a^{4} b^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 26880 \, a^{2} b^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 705600 \, a^{19} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 14429520 \, a^{17} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 42782712 \, a^{15} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 41655719 \, a^{13} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 10567396 \, a^{11} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 704032 \, a^{9} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 485520 \, a^{7} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 160160 \, a^{5} b^{17} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 22400 \, a^{3} b^{19} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2963520 \, a^{18} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 14864640 \, a^{16} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20500788 \, a^{14} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5857306 \, a^{12} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 479696 \, a^{10} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 281232 \, a^{8} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 85120 \, a^{6} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 11200 \, a^{4} b^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 282240 \, a^{19} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3575040 \, a^{17} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6358464 \, a^{15} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1843996 \, a^{13} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 146062 \, a^{11} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 85120 \, a^{9} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 25648 \, a^{7} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3360 \, a^{5} b^{17} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 576240 \, a^{18} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1111320 \, a^{16} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 324303 \, a^{14} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 26894 \, a^{12} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 14924 \, a^{10} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4368 \, a^{8} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 560 \, a^{6} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 47040 \, a^{19} b^{3} + 82320 \, a^{17} b^{5} + 26712 \, a^{15} b^{7} - 4161 \, a^{13} b^{9} + 2186 \, a^{11} b^{11} - 632 \, a^{9} b^{13} + 80 \, a^{7} b^{15}}{{\left(a^{23} - 8 \, a^{21} b^{2} + 28 \, a^{19} b^{4} - 56 \, a^{17} b^{6} + 70 \, a^{15} b^{8} - 56 \, a^{13} b^{10} + 28 \, a^{11} b^{12} - 8 \, a^{9} b^{14} + a^{7} b^{16}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{7}}}{280 \, d}"," ",0,"-1/280*(315*(64*a^7*b^2 + 336*a^5*b^4 + 280*a^3*b^6 + 35*a*b^8)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^16 - 8*a^14*b^2 + 28*a^12*b^4 - 56*a^10*b^6 + 70*a^8*b^8 - 56*a^6*b^10 + 28*a^4*b^12 - 8*a^2*b^14 + b^16)*sqrt(a^2 - b^2)) + 560*(a^8*tan(1/2*d*x + 1/2*c) + 28*a^6*b^2*tan(1/2*d*x + 1/2*c) + 70*a^4*b^4*tan(1/2*d*x + 1/2*c) + 28*a^2*b^6*tan(1/2*d*x + 1/2*c) + b^8*tan(1/2*d*x + 1/2*c) - 8*a^7*b - 56*a^5*b^3 - 56*a^3*b^5 - 8*a*b^7)/((a^16 - 8*a^14*b^2 + 28*a^12*b^4 - 56*a^10*b^6 + 70*a^8*b^8 - 56*a^6*b^10 + 28*a^4*b^12 - 8*a^2*b^14 + b^16)*(tan(1/2*d*x + 1/2*c)^2 - 1)) + (82320*a^18*b^4*tan(1/2*d*x + 1/2*c)^13 + 41160*a^16*b^6*tan(1/2*d*x + 1/2*c)^13 + 49665*a^14*b^8*tan(1/2*d*x + 1/2*c)^13 - 31360*a^12*b^10*tan(1/2*d*x + 1/2*c)^13 + 15680*a^10*b^12*tan(1/2*d*x + 1/2*c)^13 - 4480*a^8*b^14*tan(1/2*d*x + 1/2*c)^13 + 560*a^6*b^16*tan(1/2*d*x + 1/2*c)^13 + 47040*a^19*b^3*tan(1/2*d*x + 1/2*c)^12 + 952560*a^17*b^5*tan(1/2*d*x + 1/2*c)^12 + 743400*a^15*b^7*tan(1/2*d*x + 1/2*c)^12 + 370685*a^13*b^9*tan(1/2*d*x + 1/2*c)^12 - 188160*a^11*b^11*tan(1/2*d*x + 1/2*c)^12 + 94080*a^9*b^13*tan(1/2*d*x + 1/2*c)^12 - 26880*a^7*b^15*tan(1/2*d*x + 1/2*c)^12 + 3360*a^5*b^17*tan(1/2*d*x + 1/2*c)^12 + 987840*a^18*b^4*tan(1/2*d*x + 1/2*c)^11 + 5221440*a^16*b^6*tan(1/2*d*x + 1/2*c)^11 + 4792620*a^14*b^8*tan(1/2*d*x + 1/2*c)^11 + 1272530*a^12*b^10*tan(1/2*d*x + 1/2*c)^11 - 501760*a^10*b^12*tan(1/2*d*x + 1/2*c)^11 + 277760*a^8*b^14*tan(1/2*d*x + 1/2*c)^11 - 85120*a^6*b^16*tan(1/2*d*x + 1/2*c)^11 + 11200*a^4*b^18*tan(1/2*d*x + 1/2*c)^11 + 282240*a^19*b^3*tan(1/2*d*x + 1/2*c)^10 + 7056000*a^17*b^5*tan(1/2*d*x + 1/2*c)^10 + 18695040*a^15*b^7*tan(1/2*d*x + 1/2*c)^10 + 15575140*a^13*b^9*tan(1/2*d*x + 1/2*c)^10 + 2689610*a^11*b^11*tan(1/2*d*x + 1/2*c)^10 - 721280*a^9*b^13*tan(1/2*d*x + 1/2*c)^10 + 474880*a^7*b^15*tan(1/2*d*x + 1/2*c)^10 - 160160*a^5*b^17*tan(1/2*d*x + 1/2*c)^10 + 22400*a^3*b^19*tan(1/2*d*x + 1/2*c)^10 + 3704400*a^18*b^4*tan(1/2*d*x + 1/2*c)^9 + 26948040*a^16*b^6*tan(1/2*d*x + 1/2*c)^9 + 46663365*a^14*b^8*tan(1/2*d*x + 1/2*c)^9 + 29114330*a^12*b^10*tan(1/2*d*x + 1/2*c)^9 + 3411772*a^10*b^12*tan(1/2*d*x + 1/2*c)^9 - 305536*a^8*b^14*tan(1/2*d*x + 1/2*c)^9 + 388976*a^6*b^16*tan(1/2*d*x + 1/2*c)^9 - 167552*a^4*b^18*tan(1/2*d*x + 1/2*c)^9 + 26880*a^2*b^20*tan(1/2*d*x + 1/2*c)^9 + 705600*a^19*b^3*tan(1/2*d*x + 1/2*c)^8 + 18780720*a^17*b^5*tan(1/2*d*x + 1/2*c)^8 + 65305800*a^15*b^7*tan(1/2*d*x + 1/2*c)^8 + 77673085*a^13*b^9*tan(1/2*d*x + 1/2*c)^8 + 32483570*a^11*b^11*tan(1/2*d*x + 1/2*c)^8 + 2139928*a^9*b^13*tan(1/2*d*x + 1/2*c)^8 + 587776*a^7*b^15*tan(1/2*d*x + 1/2*c)^8 - 7616*a^5*b^17*tan(1/2*d*x + 1/2*c)^8 - 74368*a^3*b^19*tan(1/2*d*x + 1/2*c)^8 + 17920*a*b^21*tan(1/2*d*x + 1/2*c)^8 + 6585600*a^18*b^4*tan(1/2*d*x + 1/2*c)^7 + 51038400*a^16*b^6*tan(1/2*d*x + 1/2*c)^7 + 104499360*a^14*b^8*tan(1/2*d*x + 1/2*c)^7 + 80185140*a^12*b^10*tan(1/2*d*x + 1/2*c)^7 + 20029744*a^10*b^12*tan(1/2*d*x + 1/2*c)^7 + 661136*a^8*b^14*tan(1/2*d*x + 1/2*c)^7 + 683008*a^6*b^16*tan(1/2*d*x + 1/2*c)^7 - 217600*a^4*b^18*tan(1/2*d*x + 1/2*c)^7 + 13312*a^2*b^20*tan(1/2*d*x + 1/2*c)^7 + 5120*b^22*tan(1/2*d*x + 1/2*c)^7 + 940800*a^19*b^3*tan(1/2*d*x + 1/2*c)^6 + 23614080*a^17*b^5*tan(1/2*d*x + 1/2*c)^6 + 83805120*a^15*b^7*tan(1/2*d*x + 1/2*c)^6 + 103990880*a^13*b^9*tan(1/2*d*x + 1/2*c)^6 + 45853220*a^11*b^11*tan(1/2*d*x + 1/2*c)^6 + 4650688*a^9*b^13*tan(1/2*d*x + 1/2*c)^6 + 692496*a^7*b^15*tan(1/2*d*x + 1/2*c)^6 - 7616*a^5*b^17*tan(1/2*d*x + 1/2*c)^6 - 74368*a^3*b^19*tan(1/2*d*x + 1/2*c)^6 + 17920*a*b^21*tan(1/2*d*x + 1/2*c)^6 + 6174000*a^18*b^4*tan(1/2*d*x + 1/2*c)^5 + 43023960*a^16*b^6*tan(1/2*d*x + 1/2*c)^5 + 82755435*a^14*b^8*tan(1/2*d*x + 1/2*c)^5 + 55248340*a^12*b^10*tan(1/2*d*x + 1/2*c)^5 + 10337432*a^10*b^12*tan(1/2*d*x + 1/2*c)^5 - 175056*a^8*b^14*tan(1/2*d*x + 1/2*c)^5 + 388976*a^6*b^16*tan(1/2*d*x + 1/2*c)^5 - 167552*a^4*b^18*tan(1/2*d*x + 1/2*c)^5 + 26880*a^2*b^20*tan(1/2*d*x + 1/2*c)^5 + 705600*a^19*b^3*tan(1/2*d*x + 1/2*c)^4 + 14429520*a^17*b^5*tan(1/2*d*x + 1/2*c)^4 + 42782712*a^15*b^7*tan(1/2*d*x + 1/2*c)^4 + 41655719*a^13*b^9*tan(1/2*d*x + 1/2*c)^4 + 10567396*a^11*b^11*tan(1/2*d*x + 1/2*c)^4 - 704032*a^9*b^13*tan(1/2*d*x + 1/2*c)^4 + 485520*a^7*b^15*tan(1/2*d*x + 1/2*c)^4 - 160160*a^5*b^17*tan(1/2*d*x + 1/2*c)^4 + 22400*a^3*b^19*tan(1/2*d*x + 1/2*c)^4 + 2963520*a^18*b^4*tan(1/2*d*x + 1/2*c)^3 + 14864640*a^16*b^6*tan(1/2*d*x + 1/2*c)^3 + 20500788*a^14*b^8*tan(1/2*d*x + 1/2*c)^3 + 5857306*a^12*b^10*tan(1/2*d*x + 1/2*c)^3 - 479696*a^10*b^12*tan(1/2*d*x + 1/2*c)^3 + 281232*a^8*b^14*tan(1/2*d*x + 1/2*c)^3 - 85120*a^6*b^16*tan(1/2*d*x + 1/2*c)^3 + 11200*a^4*b^18*tan(1/2*d*x + 1/2*c)^3 + 282240*a^19*b^3*tan(1/2*d*x + 1/2*c)^2 + 3575040*a^17*b^5*tan(1/2*d*x + 1/2*c)^2 + 6358464*a^15*b^7*tan(1/2*d*x + 1/2*c)^2 + 1843996*a^13*b^9*tan(1/2*d*x + 1/2*c)^2 - 146062*a^11*b^11*tan(1/2*d*x + 1/2*c)^2 + 85120*a^9*b^13*tan(1/2*d*x + 1/2*c)^2 - 25648*a^7*b^15*tan(1/2*d*x + 1/2*c)^2 + 3360*a^5*b^17*tan(1/2*d*x + 1/2*c)^2 + 576240*a^18*b^4*tan(1/2*d*x + 1/2*c) + 1111320*a^16*b^6*tan(1/2*d*x + 1/2*c) + 324303*a^14*b^8*tan(1/2*d*x + 1/2*c) - 26894*a^12*b^10*tan(1/2*d*x + 1/2*c) + 14924*a^10*b^12*tan(1/2*d*x + 1/2*c) - 4368*a^8*b^14*tan(1/2*d*x + 1/2*c) + 560*a^6*b^16*tan(1/2*d*x + 1/2*c) + 47040*a^19*b^3 + 82320*a^17*b^5 + 26712*a^15*b^7 - 4161*a^13*b^9 + 2186*a^11*b^11 - 632*a^9*b^13 + 80*a^7*b^15)/((a^23 - 8*a^21*b^2 + 28*a^19*b^4 - 56*a^17*b^6 + 70*a^15*b^8 - 56*a^13*b^10 + 28*a^11*b^12 - 8*a^9*b^14 + a^7*b^16)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^7))/d","B",0
472,1,3047,0,20.509490," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","\frac{\frac{3465 \, {\left(32 \, a^{7} b^{4} + 112 \, a^{5} b^{6} + 70 \, a^{3} b^{8} + 7 \, a b^{10}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{18} - 9 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 84 \, a^{12} b^{6} + 126 \, a^{10} b^{8} - 126 \, a^{8} b^{10} + 84 \, a^{6} b^{12} - 36 \, a^{4} b^{14} + 9 \, a^{2} b^{16} - b^{18}\right)} \sqrt{a^{2} - b^{2}}} - \frac{112 \, {\left(3 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 882 \, a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1638 \, a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 513 \, a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, a^{9} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 216 \, a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1512 \, a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1224 \, a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 144 \, a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 162 \, a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1932 \, a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3108 \, a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 918 \, a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 26 \, b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 720 \, a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3024 \, a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2160 \, a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 240 \, a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 882 \, a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1638 \, a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 513 \, a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a^{9} b + 312 \, a^{7} b^{3} + 1512 \, a^{5} b^{5} + 1128 \, a^{3} b^{7} + 128 \, a b^{9}\right)}}{{\left(a^{18} - 9 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 84 \, a^{12} b^{6} + 126 \, a^{10} b^{8} - 126 \, a^{8} b^{10} + 84 \, a^{6} b^{12} - 36 \, a^{4} b^{14} + 9 \, a^{2} b^{16} - b^{18}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}} + \frac{232848 \, a^{18} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 142758 \, a^{16} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 64911 \, a^{14} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 28224 \, a^{12} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 12096 \, a^{10} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 3024 \, a^{8} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 336 \, a^{6} b^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 155232 \, a^{19} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 2783088 \, a^{17} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 2110878 \, a^{15} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 545811 \, a^{13} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 169344 \, a^{11} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 72576 \, a^{9} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 18144 \, a^{7} b^{17} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 2016 \, a^{5} b^{19} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 3104640 \, a^{18} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 15506568 \, a^{16} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 12397616 \, a^{14} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 2172366 \, a^{12} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 451584 \, a^{10} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 213696 \, a^{8} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 57344 \, a^{6} b^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 6720 \, a^{4} b^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 931392 \, a^{19} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 22042944 \, a^{17} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 54377400 \, a^{15} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 38316040 \, a^{13} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 5346390 \, a^{11} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 685440 \, a^{9} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 372960 \, a^{7} b^{17} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 108640 \, a^{5} b^{19} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 13440 \, a^{3} b^{21} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 12030480 \, a^{18} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 83208510 \, a^{16} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 129442775 \, a^{14} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 68997390 \, a^{12} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 8026116 \, a^{10} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 418320 \, a^{8} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 328720 \, a^{6} b^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 115584 \, a^{4} b^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 16128 \, a^{2} b^{22} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2328480 \, a^{19} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 60558960 \, a^{17} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 194655230 \, a^{15} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 204067311 \, a^{13} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 74359166 \, a^{11} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 6423144 \, a^{9} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 342720 \, a^{7} b^{17} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 38080 \, a^{5} b^{19} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 54656 \, a^{3} b^{21} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 10752 \, a b^{23} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 21732480 \, a^{18} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 160923840 \, a^{16} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 294582904 \, a^{14} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 198535596 \, a^{12} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 45251248 \, a^{10} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2197104 \, a^{8} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 545280 \, a^{6} b^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 137728 \, a^{4} b^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5120 \, a^{2} b^{22} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3072 \, b^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3104640 \, a^{19} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 77468160 \, a^{17} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 251081600 \, a^{15} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 274259160 \, a^{13} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 105524636 \, a^{11} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 11690784 \, a^{9} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 515760 \, a^{7} b^{17} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 38080 \, a^{5} b^{19} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 54656 \, a^{3} b^{21} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 10752 \, a b^{23} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 20568240 \, a^{18} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 136444770 \, a^{16} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 229744669 \, a^{14} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 133540988 \, a^{12} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 22390536 \, a^{10} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 189280 \, a^{8} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 328720 \, a^{6} b^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 115584 \, a^{4} b^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16128 \, a^{2} b^{22} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2328480 \, a^{19} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 47733840 \, a^{17} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 125203386 \, a^{15} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 105004865 \, a^{13} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 21568540 \, a^{11} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 612864 \, a^{9} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 385168 \, a^{7} b^{17} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 108640 \, a^{5} b^{19} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 13440 \, a^{3} b^{21} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 9934848 \, a^{18} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 46275768 \, a^{16} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 52916248 \, a^{14} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 11715494 \, a^{12} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 403536 \, a^{10} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 218288 \, a^{8} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 57344 \, a^{6} b^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6720 \, a^{4} b^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 931392 \, a^{19} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 11782848 \, a^{17} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 16561160 \, a^{15} b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3685248 \, a^{13} b^{11} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 117586 \, a^{11} b^{13} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 64736 \, a^{9} b^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 17136 \, a^{7} b^{17} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2016 \, a^{5} b^{19} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1940400 \, a^{18} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2910138 \, a^{16} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 644413 \, a^{14} b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 21546 \, a^{12} b^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11284 \, a^{10} b^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2912 \, a^{8} b^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 336 \, a^{6} b^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 155232 \, a^{19} b^{5} + 218064 \, a^{17} b^{7} + 50666 \, a^{15} b^{9} - 3555 \, a^{13} b^{11} + 1670 \, a^{11} b^{13} - 424 \, a^{9} b^{15} + 48 \, a^{7} b^{17}}{{\left(a^{25} - 9 \, a^{23} b^{2} + 36 \, a^{21} b^{4} - 84 \, a^{19} b^{6} + 126 \, a^{17} b^{8} - 126 \, a^{15} b^{10} + 84 \, a^{13} b^{12} - 36 \, a^{11} b^{14} + 9 \, a^{9} b^{16} - a^{7} b^{18}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{7}}}{168 \, d}"," ",0,"1/168*(3465*(32*a^7*b^4 + 112*a^5*b^6 + 70*a^3*b^8 + 7*a*b^10)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^18 - 9*a^16*b^2 + 36*a^14*b^4 - 84*a^12*b^6 + 126*a^10*b^8 - 126*a^8*b^10 + 84*a^6*b^12 - 36*a^4*b^14 + 9*a^2*b^16 - b^18)*sqrt(a^2 - b^2)) - 112*(3*a^10*tan(1/2*d*x + 1/2*c)^5 - 27*a^8*b^2*tan(1/2*d*x + 1/2*c)^5 - 882*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 - 1638*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 - 513*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 - 15*b^10*tan(1/2*d*x + 1/2*c)^5 - 24*a^9*b*tan(1/2*d*x + 1/2*c)^4 + 216*a^7*b^3*tan(1/2*d*x + 1/2*c)^4 + 1512*a^5*b^5*tan(1/2*d*x + 1/2*c)^4 + 1224*a^3*b^7*tan(1/2*d*x + 1/2*c)^4 + 144*a*b^9*tan(1/2*d*x + 1/2*c)^4 - 2*a^10*tan(1/2*d*x + 1/2*c)^3 + 162*a^8*b^2*tan(1/2*d*x + 1/2*c)^3 + 1932*a^6*b^4*tan(1/2*d*x + 1/2*c)^3 + 3108*a^4*b^6*tan(1/2*d*x + 1/2*c)^3 + 918*a^2*b^8*tan(1/2*d*x + 1/2*c)^3 + 26*b^10*tan(1/2*d*x + 1/2*c)^3 - 720*a^7*b^3*tan(1/2*d*x + 1/2*c)^2 - 3024*a^5*b^5*tan(1/2*d*x + 1/2*c)^2 - 2160*a^3*b^7*tan(1/2*d*x + 1/2*c)^2 - 240*a*b^9*tan(1/2*d*x + 1/2*c)^2 + 3*a^10*tan(1/2*d*x + 1/2*c) - 27*a^8*b^2*tan(1/2*d*x + 1/2*c) - 882*a^6*b^4*tan(1/2*d*x + 1/2*c) - 1638*a^4*b^6*tan(1/2*d*x + 1/2*c) - 513*a^2*b^8*tan(1/2*d*x + 1/2*c) - 15*b^10*tan(1/2*d*x + 1/2*c) - 8*a^9*b + 312*a^7*b^3 + 1512*a^5*b^5 + 1128*a^3*b^7 + 128*a*b^9)/((a^18 - 9*a^16*b^2 + 36*a^14*b^4 - 84*a^12*b^6 + 126*a^10*b^8 - 126*a^8*b^10 + 84*a^6*b^12 - 36*a^4*b^14 + 9*a^2*b^16 - b^18)*(tan(1/2*d*x + 1/2*c)^2 - 1)^3) + (232848*a^18*b^6*tan(1/2*d*x + 1/2*c)^13 + 142758*a^16*b^8*tan(1/2*d*x + 1/2*c)^13 + 64911*a^14*b^10*tan(1/2*d*x + 1/2*c)^13 - 28224*a^12*b^12*tan(1/2*d*x + 1/2*c)^13 + 12096*a^10*b^14*tan(1/2*d*x + 1/2*c)^13 - 3024*a^8*b^16*tan(1/2*d*x + 1/2*c)^13 + 336*a^6*b^18*tan(1/2*d*x + 1/2*c)^13 + 155232*a^19*b^5*tan(1/2*d*x + 1/2*c)^12 + 2783088*a^17*b^7*tan(1/2*d*x + 1/2*c)^12 + 2110878*a^15*b^9*tan(1/2*d*x + 1/2*c)^12 + 545811*a^13*b^11*tan(1/2*d*x + 1/2*c)^12 - 169344*a^11*b^13*tan(1/2*d*x + 1/2*c)^12 + 72576*a^9*b^15*tan(1/2*d*x + 1/2*c)^12 - 18144*a^7*b^17*tan(1/2*d*x + 1/2*c)^12 + 2016*a^5*b^19*tan(1/2*d*x + 1/2*c)^12 + 3104640*a^18*b^6*tan(1/2*d*x + 1/2*c)^11 + 15506568*a^16*b^8*tan(1/2*d*x + 1/2*c)^11 + 12397616*a^14*b^10*tan(1/2*d*x + 1/2*c)^11 + 2172366*a^12*b^12*tan(1/2*d*x + 1/2*c)^11 - 451584*a^10*b^14*tan(1/2*d*x + 1/2*c)^11 + 213696*a^8*b^16*tan(1/2*d*x + 1/2*c)^11 - 57344*a^6*b^18*tan(1/2*d*x + 1/2*c)^11 + 6720*a^4*b^20*tan(1/2*d*x + 1/2*c)^11 + 931392*a^19*b^5*tan(1/2*d*x + 1/2*c)^10 + 22042944*a^17*b^7*tan(1/2*d*x + 1/2*c)^10 + 54377400*a^15*b^9*tan(1/2*d*x + 1/2*c)^10 + 38316040*a^13*b^11*tan(1/2*d*x + 1/2*c)^10 + 5346390*a^11*b^13*tan(1/2*d*x + 1/2*c)^10 - 685440*a^9*b^15*tan(1/2*d*x + 1/2*c)^10 + 372960*a^7*b^17*tan(1/2*d*x + 1/2*c)^10 - 108640*a^5*b^19*tan(1/2*d*x + 1/2*c)^10 + 13440*a^3*b^21*tan(1/2*d*x + 1/2*c)^10 + 12030480*a^18*b^6*tan(1/2*d*x + 1/2*c)^9 + 83208510*a^16*b^8*tan(1/2*d*x + 1/2*c)^9 + 129442775*a^14*b^10*tan(1/2*d*x + 1/2*c)^9 + 68997390*a^12*b^12*tan(1/2*d*x + 1/2*c)^9 + 8026116*a^10*b^14*tan(1/2*d*x + 1/2*c)^9 - 418320*a^8*b^16*tan(1/2*d*x + 1/2*c)^9 + 328720*a^6*b^18*tan(1/2*d*x + 1/2*c)^9 - 115584*a^4*b^20*tan(1/2*d*x + 1/2*c)^9 + 16128*a^2*b^22*tan(1/2*d*x + 1/2*c)^9 + 2328480*a^19*b^5*tan(1/2*d*x + 1/2*c)^8 + 60558960*a^17*b^7*tan(1/2*d*x + 1/2*c)^8 + 194655230*a^15*b^9*tan(1/2*d*x + 1/2*c)^8 + 204067311*a^13*b^11*tan(1/2*d*x + 1/2*c)^8 + 74359166*a^11*b^13*tan(1/2*d*x + 1/2*c)^8 + 6423144*a^9*b^15*tan(1/2*d*x + 1/2*c)^8 + 342720*a^7*b^17*tan(1/2*d*x + 1/2*c)^8 + 38080*a^5*b^19*tan(1/2*d*x + 1/2*c)^8 - 54656*a^3*b^21*tan(1/2*d*x + 1/2*c)^8 + 10752*a*b^23*tan(1/2*d*x + 1/2*c)^8 + 21732480*a^18*b^6*tan(1/2*d*x + 1/2*c)^7 + 160923840*a^16*b^8*tan(1/2*d*x + 1/2*c)^7 + 294582904*a^14*b^10*tan(1/2*d*x + 1/2*c)^7 + 198535596*a^12*b^12*tan(1/2*d*x + 1/2*c)^7 + 45251248*a^10*b^14*tan(1/2*d*x + 1/2*c)^7 + 2197104*a^8*b^16*tan(1/2*d*x + 1/2*c)^7 + 545280*a^6*b^18*tan(1/2*d*x + 1/2*c)^7 - 137728*a^4*b^20*tan(1/2*d*x + 1/2*c)^7 + 5120*a^2*b^22*tan(1/2*d*x + 1/2*c)^7 + 3072*b^24*tan(1/2*d*x + 1/2*c)^7 + 3104640*a^19*b^5*tan(1/2*d*x + 1/2*c)^6 + 77468160*a^17*b^7*tan(1/2*d*x + 1/2*c)^6 + 251081600*a^15*b^9*tan(1/2*d*x + 1/2*c)^6 + 274259160*a^13*b^11*tan(1/2*d*x + 1/2*c)^6 + 105524636*a^11*b^13*tan(1/2*d*x + 1/2*c)^6 + 11690784*a^9*b^15*tan(1/2*d*x + 1/2*c)^6 + 515760*a^7*b^17*tan(1/2*d*x + 1/2*c)^6 + 38080*a^5*b^19*tan(1/2*d*x + 1/2*c)^6 - 54656*a^3*b^21*tan(1/2*d*x + 1/2*c)^6 + 10752*a*b^23*tan(1/2*d*x + 1/2*c)^6 + 20568240*a^18*b^6*tan(1/2*d*x + 1/2*c)^5 + 136444770*a^16*b^8*tan(1/2*d*x + 1/2*c)^5 + 229744669*a^14*b^10*tan(1/2*d*x + 1/2*c)^5 + 133540988*a^12*b^12*tan(1/2*d*x + 1/2*c)^5 + 22390536*a^10*b^14*tan(1/2*d*x + 1/2*c)^5 - 189280*a^8*b^16*tan(1/2*d*x + 1/2*c)^5 + 328720*a^6*b^18*tan(1/2*d*x + 1/2*c)^5 - 115584*a^4*b^20*tan(1/2*d*x + 1/2*c)^5 + 16128*a^2*b^22*tan(1/2*d*x + 1/2*c)^5 + 2328480*a^19*b^5*tan(1/2*d*x + 1/2*c)^4 + 47733840*a^17*b^7*tan(1/2*d*x + 1/2*c)^4 + 125203386*a^15*b^9*tan(1/2*d*x + 1/2*c)^4 + 105004865*a^13*b^11*tan(1/2*d*x + 1/2*c)^4 + 21568540*a^11*b^13*tan(1/2*d*x + 1/2*c)^4 - 612864*a^9*b^15*tan(1/2*d*x + 1/2*c)^4 + 385168*a^7*b^17*tan(1/2*d*x + 1/2*c)^4 - 108640*a^5*b^19*tan(1/2*d*x + 1/2*c)^4 + 13440*a^3*b^21*tan(1/2*d*x + 1/2*c)^4 + 9934848*a^18*b^6*tan(1/2*d*x + 1/2*c)^3 + 46275768*a^16*b^8*tan(1/2*d*x + 1/2*c)^3 + 52916248*a^14*b^10*tan(1/2*d*x + 1/2*c)^3 + 11715494*a^12*b^12*tan(1/2*d*x + 1/2*c)^3 - 403536*a^10*b^14*tan(1/2*d*x + 1/2*c)^3 + 218288*a^8*b^16*tan(1/2*d*x + 1/2*c)^3 - 57344*a^6*b^18*tan(1/2*d*x + 1/2*c)^3 + 6720*a^4*b^20*tan(1/2*d*x + 1/2*c)^3 + 931392*a^19*b^5*tan(1/2*d*x + 1/2*c)^2 + 11782848*a^17*b^7*tan(1/2*d*x + 1/2*c)^2 + 16561160*a^15*b^9*tan(1/2*d*x + 1/2*c)^2 + 3685248*a^13*b^11*tan(1/2*d*x + 1/2*c)^2 - 117586*a^11*b^13*tan(1/2*d*x + 1/2*c)^2 + 64736*a^9*b^15*tan(1/2*d*x + 1/2*c)^2 - 17136*a^7*b^17*tan(1/2*d*x + 1/2*c)^2 + 2016*a^5*b^19*tan(1/2*d*x + 1/2*c)^2 + 1940400*a^18*b^6*tan(1/2*d*x + 1/2*c) + 2910138*a^16*b^8*tan(1/2*d*x + 1/2*c) + 644413*a^14*b^10*tan(1/2*d*x + 1/2*c) - 21546*a^12*b^12*tan(1/2*d*x + 1/2*c) + 11284*a^10*b^14*tan(1/2*d*x + 1/2*c) - 2912*a^8*b^16*tan(1/2*d*x + 1/2*c) + 336*a^6*b^18*tan(1/2*d*x + 1/2*c) + 155232*a^19*b^5 + 218064*a^17*b^7 + 50666*a^15*b^9 - 3555*a^13*b^11 + 1670*a^11*b^13 - 424*a^9*b^15 + 48*a^7*b^17)/((a^25 - 9*a^23*b^2 + 36*a^21*b^4 - 84*a^19*b^6 + 126*a^17*b^8 - 126*a^15*b^10 + 84*a^13*b^12 - 36*a^11*b^14 + 9*a^9*b^16 - a^7*b^18)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^7))/d","B",0
473,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^5, x)","F",0
474,1,78,0,2.172271," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{15 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}}}{b^{3}} - \frac{42 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a}{b^{3}} + \frac{35 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{2}}{b^{3}} - \frac{35 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{b}\right)}}{105 \, d}"," ",0,"-2/105*(15*(b*sin(d*x + c) + a)^(7/2)/b^3 - 42*(b*sin(d*x + c) + a)^(5/2)*a/b^3 + 35*(b*sin(d*x + c) + a)^(3/2)*a^2/b^3 - 35*(b*sin(d*x + c) + a)^(3/2)/b)/d","A",0
475,1,20,0,1.447228," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{3 \, b d}"," ",0,"2/3*(b*sin(d*x + c) + a)^(3/2)/(b*d)","A",0
476,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*sec(d*x + c), x)","F",0
477,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
478,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*sec(d*x + c)^5, x)","F",0
479,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^4, x)","F",0
480,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
481,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
482,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*sec(d*x + c)^4, x)","F",0
483,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^5, x)","F",0
484,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^3, x)","F",0
485,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
486,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,-1,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
489,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4, x)","F",0
490,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
491,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
492,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
493,-1,0,0,0.000000," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
494,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*cos(d*x + c)^5, x)","F",0
495,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*cos(d*x + c)^3, x)","F",0
496,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*cos(d*x + c), x)","F",0
497,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
498,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
499,-1,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
500,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*cos(d*x + c)^4, x)","F",0
501,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
502,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
503,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,-1,0,0,0.000000," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
505,-1,0,0,0.000000," ","integrate(sec(d*x+c)^8*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
506,0,0,0,0.000000," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{5}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^5/sqrt(b*sin(d*x + c) + a), x)","F",0
507,1,75,0,1.883801," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(15 \, \sqrt{b \sin\left(d x + c\right) + a} - \frac{3 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 10 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{b \sin\left(d x + c\right) + a} a^{2}}{b^{2}}\right)}}{15 \, b d}"," ",0,"2/15*(15*sqrt(b*sin(d*x + c) + a) - (3*(b*sin(d*x + c) + a)^(5/2) - 10*(b*sin(d*x + c) + a)^(3/2)*a + 15*sqrt(b*sin(d*x + c) + a)*a^2)/b^2)/(b*d)","A",0
508,1,20,0,1.790460," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{b \sin\left(d x + c\right) + a}}{b d}"," ",0,"2*sqrt(b*sin(d*x + c) + a)/(b*d)","A",0
509,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)/sqrt(b*sin(d*x + c) + a), x)","F",0
510,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{3}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/sqrt(b*sin(d*x + c) + a), x)","F",0
511,0,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{5}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^5/sqrt(b*sin(d*x + c) + a), x)","F",0
512,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{4}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4/sqrt(b*sin(d*x + c) + a), x)","F",0
513,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{2}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/sqrt(b*sin(d*x + c) + a), x)","F",0
514,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{2}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/sqrt(b*sin(d*x + c) + a), x)","F",0
515,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{4}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/sqrt(b*sin(d*x + c) + a), x)","F",0
516,0,0,0,0.000000," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{5}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^5/(b*sin(d*x + c) + a)^(3/2), x)","F",0
517,1,72,0,0.562968," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{3 \, {\left(a^{2} - b^{2}\right)}}{\sqrt{b \sin\left(d x + c\right) + a} b^{3}} - \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} b^{6} - 6 \, \sqrt{b \sin\left(d x + c\right) + a} a b^{6}}{b^{9}}\right)}}{3 \, d}"," ",0,"2/3*(3*(a^2 - b^2)/(sqrt(b*sin(d*x + c) + a)*b^3) - ((b*sin(d*x + c) + a)^(3/2)*b^6 - 6*sqrt(b*sin(d*x + c) + a)*a*b^6)/b^9)/d","A",0
518,1,20,0,1.901266," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{2}{\sqrt{b \sin\left(d x + c\right) + a} b d}"," ",0,"-2/(sqrt(b*sin(d*x + c) + a)*b*d)","A",0
519,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sin(d*x + c) + a)^(3/2), x)","F",0
520,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{3}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(b*sin(d*x + c) + a)^(3/2), x)","F",0
521,0,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{5}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^5/(b*sin(d*x + c) + a)^(3/2), x)","F",0
522,0,0,0,0.000000," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{6}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^6/(b*sin(d*x + c) + a)^(3/2), x)","F",0
523,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{4}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4/(b*sin(d*x + c) + a)^(3/2), x)","F",0
524,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{2}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*sin(d*x + c) + a)^(3/2), x)","F",0
525,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*sin(d*x + c) + a)^(3/2), x)","F",0
526,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{4}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/(b*sin(d*x + c) + a)^(3/2), x)","F",0
527,0,0,0,0.000000," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{5}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^5/(b*sin(d*x + c) + a)^(5/2), x)","F",0
528,1,61,0,0.856240," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{3 \, \sqrt{b \sin\left(d x + c\right) + a}}{b^{3}} + \frac{6 \, {\left(b \sin\left(d x + c\right) + a\right)} a - a^{2} + b^{2}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} b^{3}}\right)}}{3 \, d}"," ",0,"-2/3*(3*sqrt(b*sin(d*x + c) + a)/b^3 + (6*(b*sin(d*x + c) + a)*a - a^2 + b^2)/((b*sin(d*x + c) + a)^(3/2)*b^3))/d","A",0
529,1,20,0,0.886816," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{2}{3 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} b d}"," ",0,"-2/3/((b*sin(d*x + c) + a)^(3/2)*b*d)","A",0
530,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sin(d*x + c) + a)^(5/2), x)","F",0
531,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{3}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(b*sin(d*x + c) + a)^(5/2), x)","F",0
532,0,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{5}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^5/(b*sin(d*x + c) + a)^(5/2), x)","F",0
533,0,0,0,0.000000," ","integrate(cos(d*x+c)^8/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{8}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^8/(b*sin(d*x + c) + a)^(5/2), x)","F",0
534,0,0,0,0.000000," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{6}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^6/(b*sin(d*x + c) + a)^(5/2), x)","F",0
535,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{4}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4/(b*sin(d*x + c) + a)^(5/2), x)","F",0
536,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{2}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*sin(d*x + c) + a)^(5/2), x)","F",0
537,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*sin(d*x + c) + a)^(5/2), x)","F",0
538,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{4}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/(b*sin(d*x + c) + a)^(5/2), x)","F",0
539,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(b \sin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)*(b*sin(d*x + c) + a), x)","F",0
540,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(b \sin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(b*sin(d*x + c) + a), x)","F",0
541,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(b \sin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(b*sin(d*x + c) + a), x)","F",0
542,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))*(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a), x)","F",0
543,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{b \sin\left(d x + c\right) + a}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)/sqrt(e*cos(d*x + c)), x)","F",0
544,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))/(e*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{b \sin\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)/(e*cos(d*x + c))^(3/2), x)","F",0
545,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))/(e*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{b \sin\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)/(e*cos(d*x + c))^(5/2), x)","F",0
546,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))/(e*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{b \sin\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)/(e*cos(d*x + c))^(7/2), x)","F",0
547,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)*(b*sin(d*x + c) + a)^2, x)","F",0
548,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(b*sin(d*x + c) + a)^2, x)","F",0
549,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(b*sin(d*x + c) + a)^2, x)","F",0
550,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^2*(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^2, x)","F",0
551,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^2/sqrt(e*cos(d*x + c)), x)","F",0
552,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^2/(e*cos(d*x + c))^(3/2), x)","F",0
553,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^2/(e*cos(d*x + c))^(5/2), x)","F",0
554,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^2/(e*cos(d*x + c))^(7/2), x)","F",0
555,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)*(b*sin(d*x + c) + a)^3, x)","F",0
556,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(b*sin(d*x + c) + a)^3, x)","F",0
557,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(b*sin(d*x + c) + a)^3, x)","F",0
558,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^3*(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^3, x)","F",0
559,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^3/sqrt(e*cos(d*x + c)), x)","F",0
560,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(3/2), x)","F",0
561,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(5/2), x)","F",0
562,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(7/2), x)","F",0
563,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(9/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(9/2), x)","F",0
564,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^4,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{4}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)*(b*sin(d*x + c) + a)^4, x)","F",0
565,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^4,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{4}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(b*sin(d*x + c) + a)^4, x)","F",0
566,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^4,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{4}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(b*sin(d*x + c) + a)^4, x)","F",0
567,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^4*(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{4}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^4, x)","F",0
568,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{4}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^4/sqrt(e*cos(d*x + c)), x)","F",0
569,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(3/2), x)","F",0
570,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(5/2), x)","F",0
571,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(7/2), x)","F",0
572,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(9/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(9/2), x)","F",0
573,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(11/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(11/2), x)","F",0
574,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
575,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
576,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)/(b*sin(d*x + c) + a), x)","F",0
577,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)/(b*sin(d*x + c) + a), x)","F",0
578,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)/(b*sin(d*x + c) + a), x)","F",0
579,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(b*sin(d*x + c) + a), x)","F",0
580,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)), x)","F",0
581,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(b \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(3/2)*(b*sin(d*x + c) + a)), x)","F",0
582,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(b \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(5/2)*(b*sin(d*x + c) + a)), x)","F",0
583,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(b \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(7/2)*(b*sin(d*x + c) + a)), x)","F",0
584,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
588,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
589,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(b*sin(d*x + c) + a)^2, x)","F",0
590,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^2), x)","F",0
591,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(3/2)*(b*sin(d*x + c) + a)^2), x)","F",0
592,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(5/2)*(b*sin(d*x + c) + a)^2), x)","F",0
593,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(7/2)*(b*sin(d*x + c) + a)^2), x)","F",0
594,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(13/2)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
595,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
596,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
597,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
598,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
599,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(b*sin(d*x + c) + a)^3, x)","F",0
601,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^3), x)","F",0
602,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(3/2)*(b*sin(d*x + c) + a)^3), x)","F",0
603,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(5/2)*(b*sin(d*x + c) + a)^3), x)","F",0
604,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(7/2)*(b*sin(d*x + c) + a)^3), x)","F",0
605,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(15/2)/(a+b*sin(d*x+c))^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(13/2)/(a+b*sin(d*x+c))^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
607,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c))^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
608,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c))^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
609,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
610,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
611,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
612,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+b*sin(d*x+c))^4,x, algorithm=""giac"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{{\left(b \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(b*sin(d*x + c) + a)^4, x)","F",0
613,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^4), x)","F",0
614,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^4,x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(3/2)*(b*sin(d*x + c) + a)^4), x)","F",0
615,0,0,0,0.000000," ","integrate(1/(c*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c \cos\left(f x + e\right)} \sqrt{b \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(1/(sqrt(c*cos(f*x + e))*sqrt(b*sin(f*x + e) + a)), x)","F",0
616,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{3} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^3*(e*cos(d*x + c))^p, x)","F",0
617,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{2} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^2*(e*cos(d*x + c))^p, x)","F",0
618,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)*(e*cos(d*x + c))^p, x)","F",0
619,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(b*sin(d*x + c) + a), x)","F",0
620,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(b*sin(d*x + c) + a)^2, x)","F",0
621,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(b*sin(d*x + c) + a)^3, x)","F",0
622,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^8,x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(b \sin\left(d x + c\right) + a\right)}^{8}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(b*sin(d*x + c) + a)^8, x)","F",0
623,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*(e*cos(d*x + c))^p, x)","F",0
624,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*(e*cos(d*x + c))^p, x)","F",0
625,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(d x + c\right) + a} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*(e*cos(d*x + c))^p, x)","F",0
626,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/sqrt(b*sin(d*x + c) + a), x)","F",0
627,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(b*sin(d*x + c) + a)^(3/2), x)","F",0
628,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(b*sin(d*x + c) + a)^(5/2), x)","F",0
629,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{p} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p*(b*sin(d*x + c) + a)^m, x)","F",0
630,-1,0,0,0.000000," ","integrate(cos(d*x+c)^7*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
631,-1,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
632,1,340,0,0.355305," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","-\frac{{\left(b \sin\left(d x + c\right) + a\right)}^{m} b^{3} m^{2} \sin\left(d x + c\right)^{3} + {\left(b \sin\left(d x + c\right) + a\right)}^{m} a b^{2} m^{2} \sin\left(d x + c\right)^{2} + 3 \, {\left(b \sin\left(d x + c\right) + a\right)}^{m} b^{3} m \sin\left(d x + c\right)^{3} - {\left(b \sin\left(d x + c\right) + a\right)}^{m} b^{3} m^{2} \sin\left(d x + c\right) + {\left(b \sin\left(d x + c\right) + a\right)}^{m} a b^{2} m \sin\left(d x + c\right)^{2} + 2 \, {\left(b \sin\left(d x + c\right) + a\right)}^{m} b^{3} \sin\left(d x + c\right)^{3} - {\left(b \sin\left(d x + c\right) + a\right)}^{m} a b^{2} m^{2} - 2 \, {\left(b \sin\left(d x + c\right) + a\right)}^{m} a^{2} b m \sin\left(d x + c\right) - 5 \, {\left(b \sin\left(d x + c\right) + a\right)}^{m} b^{3} m \sin\left(d x + c\right) - 5 \, {\left(b \sin\left(d x + c\right) + a\right)}^{m} a b^{2} m - 6 \, {\left(b \sin\left(d x + c\right) + a\right)}^{m} b^{3} \sin\left(d x + c\right) + 2 \, {\left(b \sin\left(d x + c\right) + a\right)}^{m} a^{3} - 6 \, {\left(b \sin\left(d x + c\right) + a\right)}^{m} a b^{2}}{{\left(b^{3} m^{3} + 6 \, b^{3} m^{2} + 11 \, b^{3} m + 6 \, b^{3}\right)} d}"," ",0,"-((b*sin(d*x + c) + a)^m*b^3*m^2*sin(d*x + c)^3 + (b*sin(d*x + c) + a)^m*a*b^2*m^2*sin(d*x + c)^2 + 3*(b*sin(d*x + c) + a)^m*b^3*m*sin(d*x + c)^3 - (b*sin(d*x + c) + a)^m*b^3*m^2*sin(d*x + c) + (b*sin(d*x + c) + a)^m*a*b^2*m*sin(d*x + c)^2 + 2*(b*sin(d*x + c) + a)^m*b^3*sin(d*x + c)^3 - (b*sin(d*x + c) + a)^m*a*b^2*m^2 - 2*(b*sin(d*x + c) + a)^m*a^2*b*m*sin(d*x + c) - 5*(b*sin(d*x + c) + a)^m*b^3*m*sin(d*x + c) - 5*(b*sin(d*x + c) + a)^m*a*b^2*m - 6*(b*sin(d*x + c) + a)^m*b^3*sin(d*x + c) + 2*(b*sin(d*x + c) + a)^m*a^3 - 6*(b*sin(d*x + c) + a)^m*a*b^2)/((b^3*m^3 + 6*b^3*m^2 + 11*b^3*m + 6*b^3)*d)","B",0
633,1,26,0,1.273388," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\frac{{\left(b \sin\left(d x + c\right) + a\right)}^{m + 1}}{b d {\left(m + 1\right)}}"," ",0,"(b*sin(d*x + c) + a)^(m + 1)/(b*d*(m + 1))","A",0
634,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m*sec(d*x + c), x)","F",0
635,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m*sec(d*x + c)^3, x)","F",0
636,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m*sec(d*x + c)^5, x)","F",0
637,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m*cos(d*x + c)^4, x)","F",0
638,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m*cos(d*x + c)^2, x)","F",0
639,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m*sec(d*x + c)^2, x)","F",0
640,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m*sec(d*x + c)^4, x)","F",0
641,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(b*sin(d*x + c) + a)^m, x)","F",0
642,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(b*sin(d*x + c) + a)^m, x)","F",0
643,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^m, x)","F",0
644,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^m/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{m}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m/sqrt(e*cos(d*x + c)), x)","F",0
645,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^m/(e*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{m}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m/(e*cos(d*x + c))^(3/2), x)","F",0
646,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^m/(e*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{m}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m/(e*cos(d*x + c))^(5/2), x)","F",0
647,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-4-m)*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-m - 4} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m - 4)*(b*sin(d*x + c) + a)^m, x)","F",0
648,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-3-m)*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-m - 3} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m - 3)*(b*sin(d*x + c) + a)^m, x)","F",0
649,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-2-m)*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-m - 2} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m - 2)*(b*sin(d*x + c) + a)^m, x)","F",0
650,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-1-m)*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-m - 1} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m - 1)*(b*sin(d*x + c) + a)^m, x)","F",0
651,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^m/((e*cos(d*x+c))^m),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{m}}{\left(e \cos\left(d x + c\right)\right)^{m}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m/(e*cos(d*x + c))^m, x)","F",0
652,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1-m)*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-m + 1} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m + 1)*(b*sin(d*x + c) + a)^m, x)","F",0
653,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(2-m)*(a+b*sin(d*x+c))^m,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{-m + 2} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m + 2)*(b*sin(d*x + c) + a)^m, x)","F",0
