1,1,115,0,1.705142," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^9,x, algorithm=""fricas"")","-\frac{280 \, a \cos\left(d x + c\right)^{9} + 315 \, a \cos\left(d x + c\right)^{8} - 1440 \, a \cos\left(d x + c\right)^{7} - 1680 \, a \cos\left(d x + c\right)^{6} + 3024 \, a \cos\left(d x + c\right)^{5} + 3780 \, a \cos\left(d x + c\right)^{4} - 3360 \, a \cos\left(d x + c\right)^{3} - 5040 \, a \cos\left(d x + c\right)^{2} + 2520 \, a \cos\left(d x + c\right) + 2520 \, a \log\left(-\cos\left(d x + c\right)\right)}{2520 \, d}"," ",0,"-1/2520*(280*a*cos(d*x + c)^9 + 315*a*cos(d*x + c)^8 - 1440*a*cos(d*x + c)^7 - 1680*a*cos(d*x + c)^6 + 3024*a*cos(d*x + c)^5 + 3780*a*cos(d*x + c)^4 - 3360*a*cos(d*x + c)^3 - 5040*a*cos(d*x + c)^2 + 2520*a*cos(d*x + c) + 2520*a*log(-cos(d*x + c)))/d","A",0
2,1,93,0,0.717475," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^7,x, algorithm=""fricas"")","\frac{60 \, a \cos\left(d x + c\right)^{7} + 70 \, a \cos\left(d x + c\right)^{6} - 252 \, a \cos\left(d x + c\right)^{5} - 315 \, a \cos\left(d x + c\right)^{4} + 420 \, a \cos\left(d x + c\right)^{3} + 630 \, a \cos\left(d x + c\right)^{2} - 420 \, a \cos\left(d x + c\right) - 420 \, a \log\left(-\cos\left(d x + c\right)\right)}{420 \, d}"," ",0,"1/420*(60*a*cos(d*x + c)^7 + 70*a*cos(d*x + c)^6 - 252*a*cos(d*x + c)^5 - 315*a*cos(d*x + c)^4 + 420*a*cos(d*x + c)^3 + 630*a*cos(d*x + c)^2 - 420*a*cos(d*x + c) - 420*a*log(-cos(d*x + c)))/d","A",0
3,1,71,0,0.510019," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^5,x, algorithm=""fricas"")","-\frac{12 \, a \cos\left(d x + c\right)^{5} + 15 \, a \cos\left(d x + c\right)^{4} - 40 \, a \cos\left(d x + c\right)^{3} - 60 \, a \cos\left(d x + c\right)^{2} + 60 \, a \cos\left(d x + c\right) + 60 \, a \log\left(-\cos\left(d x + c\right)\right)}{60 \, d}"," ",0,"-1/60*(12*a*cos(d*x + c)^5 + 15*a*cos(d*x + c)^4 - 40*a*cos(d*x + c)^3 - 60*a*cos(d*x + c)^2 + 60*a*cos(d*x + c) + 60*a*log(-cos(d*x + c)))/d","A",0
4,1,49,0,0.523190," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, a \cos\left(d x + c\right)^{3} + 3 \, a \cos\left(d x + c\right)^{2} - 6 \, a \cos\left(d x + c\right) - 6 \, a \log\left(-\cos\left(d x + c\right)\right)}{6 \, d}"," ",0,"1/6*(2*a*cos(d*x + c)^3 + 3*a*cos(d*x + c)^2 - 6*a*cos(d*x + c) - 6*a*log(-cos(d*x + c)))/d","A",0
5,1,25,0,0.511752," ","integrate((a+a*sec(d*x+c))*sin(d*x+c),x, algorithm=""fricas"")","-\frac{a \cos\left(d x + c\right) + a \log\left(-\cos\left(d x + c\right)\right)}{d}"," ",0,"-(a*cos(d*x + c) + a*log(-cos(d*x + c)))/d","A",0
6,1,31,0,0.480630," ","integrate(csc(d*x+c)*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{a \log\left(-\cos\left(d x + c\right)\right) - a \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{d}"," ",0,"-(a*log(-cos(d*x + c)) - a*log(-1/2*cos(d*x + c) + 1/2))/d","A",0
7,1,93,0,0.487089," ","integrate(csc(d*x+c)^3*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, {\left(a \cos\left(d x + c\right) - a\right)} \log\left(-\cos\left(d x + c\right)\right) - {\left(a \cos\left(d x + c\right) - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(a \cos\left(d x + c\right) - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, a}{4 \, {\left(d \cos\left(d x + c\right) - d\right)}}"," ",0,"-1/4*(4*(a*cos(d*x + c) - a)*log(-cos(d*x + c)) - (a*cos(d*x + c) - a)*log(1/2*cos(d*x + c) + 1/2) - 3*(a*cos(d*x + c) - a)*log(-1/2*cos(d*x + c) + 1/2) - 2*a)/(d*cos(d*x + c) - d)","A",0
8,1,193,0,0.742169," ","integrate(csc(d*x+c)^5*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - 16 \, {\left(a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) + a\right)} \log\left(-\cos\left(d x + c\right)\right) + 5 \, {\left(a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) + a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 11 \, {\left(a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) + a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 12 \, a}{16 \, {\left(d \cos\left(d x + c\right)^{3} - d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/16*(6*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - 16*(a*cos(d*x + c)^3 - a*cos(d*x + c)^2 - a*cos(d*x + c) + a)*log(-cos(d*x + c)) + 5*(a*cos(d*x + c)^3 - a*cos(d*x + c)^2 - a*cos(d*x + c) + a)*log(1/2*cos(d*x + c) + 1/2) + 11*(a*cos(d*x + c)^3 - a*cos(d*x + c)^2 - a*cos(d*x + c) + a)*log(-1/2*cos(d*x + c) + 1/2) - 12*a)/(d*cos(d*x + c)^3 - d*cos(d*x + c)^2 - d*cos(d*x + c) + d)","A",0
9,1,307,0,0.774879," ","integrate(csc(d*x+c)^7*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{30 \, a \cos\left(d x + c\right)^{4} + 18 \, a \cos\left(d x + c\right)^{3} - 98 \, a \cos\left(d x + c\right)^{2} - 22 \, a \cos\left(d x + c\right) - 96 \, {\left(a \cos\left(d x + c\right)^{5} - a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{3} + 2 \, a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right) - a\right)} \log\left(-\cos\left(d x + c\right)\right) + 33 \, {\left(a \cos\left(d x + c\right)^{5} - a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{3} + 2 \, a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right) - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 63 \, {\left(a \cos\left(d x + c\right)^{5} - a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{3} + 2 \, a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right) - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 88 \, a}{96 \, {\left(d \cos\left(d x + c\right)^{5} - d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{3} + 2 \, d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right) - d\right)}}"," ",0,"1/96*(30*a*cos(d*x + c)^4 + 18*a*cos(d*x + c)^3 - 98*a*cos(d*x + c)^2 - 22*a*cos(d*x + c) - 96*(a*cos(d*x + c)^5 - a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^3 + 2*a*cos(d*x + c)^2 + a*cos(d*x + c) - a)*log(-cos(d*x + c)) + 33*(a*cos(d*x + c)^5 - a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^3 + 2*a*cos(d*x + c)^2 + a*cos(d*x + c) - a)*log(1/2*cos(d*x + c) + 1/2) + 63*(a*cos(d*x + c)^5 - a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^3 + 2*a*cos(d*x + c)^2 + a*cos(d*x + c) - a)*log(-1/2*cos(d*x + c) + 1/2) + 88*a)/(d*cos(d*x + c)^5 - d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^3 + 2*d*cos(d*x + c)^2 + d*cos(d*x + c) - d)","B",0
10,1,123,0,1.666707," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^8,x, algorithm=""fricas"")","\frac{3675 \, a d x + 6720 \, a \log\left(\sin\left(d x + c\right) + 1\right) - 6720 \, a \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(1680 \, a \cos\left(d x + c\right)^{7} + 1920 \, a \cos\left(d x + c\right)^{6} - 7000 \, a \cos\left(d x + c\right)^{5} - 8448 \, a \cos\left(d x + c\right)^{4} + 11410 \, a \cos\left(d x + c\right)^{3} + 15616 \, a \cos\left(d x + c\right)^{2} - 9765 \, a \cos\left(d x + c\right) - 22528 \, a\right)} \sin\left(d x + c\right)}{13440 \, d}"," ",0,"1/13440*(3675*a*d*x + 6720*a*log(sin(d*x + c) + 1) - 6720*a*log(-sin(d*x + c) + 1) + (1680*a*cos(d*x + c)^7 + 1920*a*cos(d*x + c)^6 - 7000*a*cos(d*x + c)^5 - 8448*a*cos(d*x + c)^4 + 11410*a*cos(d*x + c)^3 + 15616*a*cos(d*x + c)^2 - 9765*a*cos(d*x + c) - 22528*a)*sin(d*x + c))/d","A",0
11,1,102,0,0.768283," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^6,x, algorithm=""fricas"")","\frac{75 \, a d x + 120 \, a \log\left(\sin\left(d x + c\right) + 1\right) - 120 \, a \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(40 \, a \cos\left(d x + c\right)^{5} + 48 \, a \cos\left(d x + c\right)^{4} - 130 \, a \cos\left(d x + c\right)^{3} - 176 \, a \cos\left(d x + c\right)^{2} + 165 \, a \cos\left(d x + c\right) + 368 \, a\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(75*a*d*x + 120*a*log(sin(d*x + c) + 1) - 120*a*log(-sin(d*x + c) + 1) - (40*a*cos(d*x + c)^5 + 48*a*cos(d*x + c)^4 - 130*a*cos(d*x + c)^3 - 176*a*cos(d*x + c)^2 + 165*a*cos(d*x + c) + 368*a)*sin(d*x + c))/d","A",0
12,1,79,0,0.701217," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^4,x, algorithm=""fricas"")","\frac{9 \, a d x + 12 \, a \log\left(\sin\left(d x + c\right) + 1\right) - 12 \, a \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, a \cos\left(d x + c\right)^{3} + 8 \, a \cos\left(d x + c\right)^{2} - 15 \, a \cos\left(d x + c\right) - 32 \, a\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(9*a*d*x + 12*a*log(sin(d*x + c) + 1) - 12*a*log(-sin(d*x + c) + 1) + (6*a*cos(d*x + c)^3 + 8*a*cos(d*x + c)^2 - 15*a*cos(d*x + c) - 32*a)*sin(d*x + c))/d","A",0
13,1,55,0,0.652308," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^2,x, algorithm=""fricas"")","\frac{a d x + a \log\left(\sin\left(d x + c\right) + 1\right) - a \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(a \cos\left(d x + c\right) + 2 \, a\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(a*d*x + a*log(sin(d*x + c) + 1) - a*log(-sin(d*x + c) + 1) - (a*cos(d*x + c) + 2*a)*sin(d*x + c))/d","A",0
14,1,63,0,0.657267," ","integrate(csc(d*x+c)^2*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{a \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - a \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 2 \, a}{2 \, d \sin\left(d x + c\right)}"," ",0,"1/2*(a*log(sin(d*x + c) + 1)*sin(d*x + c) - a*log(-sin(d*x + c) + 1)*sin(d*x + c) - 2*a*cos(d*x + c) - 2*a)/(d*sin(d*x + c))","A",0
15,1,108,0,0.723269," ","integrate(csc(d*x+c)^4*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, a \cos\left(d x + c\right)^{2} - 3 \, {\left(a \cos\left(d x + c\right) - a\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 3 \, {\left(a \cos\left(d x + c\right) - a\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 2 \, a \cos\left(d x + c\right) - 8 \, a}{6 \, {\left(d \cos\left(d x + c\right) - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/6*(4*a*cos(d*x + c)^2 - 3*(a*cos(d*x + c) - a)*log(sin(d*x + c) + 1)*sin(d*x + c) + 3*(a*cos(d*x + c) - a)*log(-sin(d*x + c) + 1)*sin(d*x + c) + 2*a*cos(d*x + c) - 8*a)/((d*cos(d*x + c) - d)*sin(d*x + c))","A",0
16,1,190,0,0.548992," ","integrate(csc(d*x+c)^6*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, a \cos\left(d x + c\right)^{4} + 14 \, a \cos\left(d x + c\right)^{3} - 54 \, a \cos\left(d x + c\right)^{2} - 15 \, {\left(a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) + a\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 15 \, {\left(a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) + a\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 16 \, a \cos\left(d x + c\right) + 46 \, a}{30 \, {\left(d \cos\left(d x + c\right)^{3} - d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/30*(16*a*cos(d*x + c)^4 + 14*a*cos(d*x + c)^3 - 54*a*cos(d*x + c)^2 - 15*(a*cos(d*x + c)^3 - a*cos(d*x + c)^2 - a*cos(d*x + c) + a)*log(sin(d*x + c) + 1)*sin(d*x + c) + 15*(a*cos(d*x + c)^3 - a*cos(d*x + c)^2 - a*cos(d*x + c) + a)*log(-sin(d*x + c) + 1)*sin(d*x + c) - 16*a*cos(d*x + c) + 46*a)/((d*cos(d*x + c)^3 - d*cos(d*x + c)^2 - d*cos(d*x + c) + d)*sin(d*x + c))","B",0
17,1,281,0,0.627775," ","integrate(csc(d*x+c)^8*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{96 \, a \cos\left(d x + c\right)^{6} + 114 \, a \cos\left(d x + c\right)^{5} - 450 \, a \cos\left(d x + c\right)^{4} - 250 \, a \cos\left(d x + c\right)^{3} + 670 \, a \cos\left(d x + c\right)^{2} - 105 \, {\left(a \cos\left(d x + c\right)^{5} - a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{3} + 2 \, a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right) - a\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 105 \, {\left(a \cos\left(d x + c\right)^{5} - a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{3} + 2 \, a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right) - a\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 142 \, a \cos\left(d x + c\right) - 352 \, a}{210 \, {\left(d \cos\left(d x + c\right)^{5} - d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{3} + 2 \, d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right) - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/210*(96*a*cos(d*x + c)^6 + 114*a*cos(d*x + c)^5 - 450*a*cos(d*x + c)^4 - 250*a*cos(d*x + c)^3 + 670*a*cos(d*x + c)^2 - 105*(a*cos(d*x + c)^5 - a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^3 + 2*a*cos(d*x + c)^2 + a*cos(d*x + c) - a)*log(sin(d*x + c) + 1)*sin(d*x + c) + 105*(a*cos(d*x + c)^5 - a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^3 + 2*a*cos(d*x + c)^2 + a*cos(d*x + c) - a)*log(-sin(d*x + c) + 1)*sin(d*x + c) + 142*a*cos(d*x + c) - 352*a)/((d*cos(d*x + c)^5 - d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^3 + 2*d*cos(d*x + c)^2 + d*cos(d*x + c) - d)*sin(d*x + c))","B",0
18,1,366,0,0.688417," ","integrate(csc(d*x+c)^10*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{256 \, a \cos\left(d x + c\right)^{8} + 374 \, a \cos\left(d x + c\right)^{7} - 1526 \, a \cos\left(d x + c\right)^{6} - 1204 \, a \cos\left(d x + c\right)^{5} + 3220 \, a \cos\left(d x + c\right)^{4} + 1316 \, a \cos\left(d x + c\right)^{3} - 2996 \, a \cos\left(d x + c\right)^{2} - 315 \, {\left(a \cos\left(d x + c\right)^{7} - a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{5} + 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{3} - 3 \, a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) + a\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 315 \, {\left(a \cos\left(d x + c\right)^{7} - a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{5} + 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{3} - 3 \, a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) + a\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 496 \, a \cos\left(d x + c\right) + 1126 \, a}{630 \, {\left(d \cos\left(d x + c\right)^{7} - d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{5} + 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{3} - 3 \, d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/630*(256*a*cos(d*x + c)^8 + 374*a*cos(d*x + c)^7 - 1526*a*cos(d*x + c)^6 - 1204*a*cos(d*x + c)^5 + 3220*a*cos(d*x + c)^4 + 1316*a*cos(d*x + c)^3 - 2996*a*cos(d*x + c)^2 - 315*(a*cos(d*x + c)^7 - a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^5 + 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^3 - 3*a*cos(d*x + c)^2 - a*cos(d*x + c) + a)*log(sin(d*x + c) + 1)*sin(d*x + c) + 315*(a*cos(d*x + c)^7 - a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^5 + 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^3 - 3*a*cos(d*x + c)^2 - a*cos(d*x + c) + a)*log(-sin(d*x + c) + 1)*sin(d*x + c) - 496*a*cos(d*x + c) + 1126*a)/((d*cos(d*x + c)^7 - d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^5 + 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^3 - 3*d*cos(d*x + c)^2 - d*cos(d*x + c) + d)*sin(d*x + c))","B",0
19,1,167,0,0.567880," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^9,x, algorithm=""fricas"")","-\frac{17920 \, a^{2} \cos\left(d x + c\right)^{10} + 40320 \, a^{2} \cos\left(d x + c\right)^{9} - 69120 \, a^{2} \cos\left(d x + c\right)^{8} - 215040 \, a^{2} \cos\left(d x + c\right)^{7} + 64512 \, a^{2} \cos\left(d x + c\right)^{6} + 483840 \, a^{2} \cos\left(d x + c\right)^{5} + 107520 \, a^{2} \cos\left(d x + c\right)^{4} - 645120 \, a^{2} \cos\left(d x + c\right)^{3} - 483840 \, a^{2} \cos\left(d x + c\right)^{2} + 322560 \, a^{2} \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right)\right) + 197295 \, a^{2} \cos\left(d x + c\right) - 161280 \, a^{2}}{161280 \, d \cos\left(d x + c\right)}"," ",0,"-1/161280*(17920*a^2*cos(d*x + c)^10 + 40320*a^2*cos(d*x + c)^9 - 69120*a^2*cos(d*x + c)^8 - 215040*a^2*cos(d*x + c)^7 + 64512*a^2*cos(d*x + c)^6 + 483840*a^2*cos(d*x + c)^5 + 107520*a^2*cos(d*x + c)^4 - 645120*a^2*cos(d*x + c)^3 - 483840*a^2*cos(d*x + c)^2 + 322560*a^2*cos(d*x + c)*log(-cos(d*x + c)) + 197295*a^2*cos(d*x + c) - 161280*a^2)/(d*cos(d*x + c))","A",0
20,1,128,0,0.690144," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^7,x, algorithm=""fricas"")","\frac{120 \, a^{2} \cos\left(d x + c\right)^{8} + 280 \, a^{2} \cos\left(d x + c\right)^{7} - 336 \, a^{2} \cos\left(d x + c\right)^{6} - 1260 \, a^{2} \cos\left(d x + c\right)^{5} + 2520 \, a^{2} \cos\left(d x + c\right)^{3} + 1680 \, a^{2} \cos\left(d x + c\right)^{2} - 1680 \, a^{2} \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right)\right) - 875 \, a^{2} \cos\left(d x + c\right) + 840 \, a^{2}}{840 \, d \cos\left(d x + c\right)}"," ",0,"1/840*(120*a^2*cos(d*x + c)^8 + 280*a^2*cos(d*x + c)^7 - 336*a^2*cos(d*x + c)^6 - 1260*a^2*cos(d*x + c)^5 + 2520*a^2*cos(d*x + c)^3 + 1680*a^2*cos(d*x + c)^2 - 1680*a^2*cos(d*x + c)*log(-cos(d*x + c)) - 875*a^2*cos(d*x + c) + 840*a^2)/(d*cos(d*x + c))","A",0
21,1,115,0,0.737011," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^5,x, algorithm=""fricas"")","-\frac{48 \, a^{2} \cos\left(d x + c\right)^{6} + 120 \, a^{2} \cos\left(d x + c\right)^{5} - 80 \, a^{2} \cos\left(d x + c\right)^{4} - 480 \, a^{2} \cos\left(d x + c\right)^{3} - 240 \, a^{2} \cos\left(d x + c\right)^{2} + 480 \, a^{2} \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right)\right) + 195 \, a^{2} \cos\left(d x + c\right) - 240 \, a^{2}}{240 \, d \cos\left(d x + c\right)}"," ",0,"-1/240*(48*a^2*cos(d*x + c)^6 + 120*a^2*cos(d*x + c)^5 - 80*a^2*cos(d*x + c)^4 - 480*a^2*cos(d*x + c)^3 - 240*a^2*cos(d*x + c)^2 + 480*a^2*cos(d*x + c)*log(-cos(d*x + c)) + 195*a^2*cos(d*x + c) - 240*a^2)/(d*cos(d*x + c))","A",0
22,1,76,0,0.847702," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, a^{2} \cos\left(d x + c\right)^{4} + 6 \, a^{2} \cos\left(d x + c\right)^{3} - 12 \, a^{2} \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right)\right) - 3 \, a^{2} \cos\left(d x + c\right) + 6 \, a^{2}}{6 \, d \cos\left(d x + c\right)}"," ",0,"1/6*(2*a^2*cos(d*x + c)^4 + 6*a^2*cos(d*x + c)^3 - 12*a^2*cos(d*x + c)*log(-cos(d*x + c)) - 3*a^2*cos(d*x + c) + 6*a^2)/(d*cos(d*x + c))","A",0
23,1,51,0,0.585599," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c),x, algorithm=""fricas"")","-\frac{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right)\right) - a^{2}}{d \cos\left(d x + c\right)}"," ",0,"-(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c)*log(-cos(d*x + c)) - a^2)/(d*cos(d*x + c))","A",0
24,1,61,0,0.691006," ","integrate(csc(d*x+c)*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right)\right) - 2 \, a^{2} \cos\left(d x + c\right) \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - a^{2}}{d \cos\left(d x + c\right)}"," ",0,"-(2*a^2*cos(d*x + c)*log(-cos(d*x + c)) - 2*a^2*cos(d*x + c)*log(-1/2*cos(d*x + c) + 1/2) - a^2)/(d*cos(d*x + c))","A",0
25,1,112,0,0.570611," ","integrate(csc(d*x+c)^3*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, a^{2} \cos\left(d x + c\right) - a^{2} - 2 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right)\right) + 2 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right)}"," ",0,"(2*a^2*cos(d*x + c) - a^2 - 2*(a^2*cos(d*x + c)^2 - a^2*cos(d*x + c))*log(-cos(d*x + c)) + 2*(a^2*cos(d*x + c)^2 - a^2*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^2 - d*cos(d*x + c))","A",0
26,1,209,0,0.593248," ","integrate(csc(d*x+c)^5*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{18 \, a^{2} \cos\left(d x + c\right)^{2} - 28 \, a^{2} \cos\left(d x + c\right) + 8 \, a^{2} - 16 \, {\left(a^{2} \cos\left(d x + c\right)^{3} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right)\right) - {\left(a^{2} \cos\left(d x + c\right)^{3} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 17 \, {\left(a^{2} \cos\left(d x + c\right)^{3} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{8 \, {\left(d \cos\left(d x + c\right)^{3} - 2 \, d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"1/8*(18*a^2*cos(d*x + c)^2 - 28*a^2*cos(d*x + c) + 8*a^2 - 16*(a^2*cos(d*x + c)^3 - 2*a^2*cos(d*x + c)^2 + a^2*cos(d*x + c))*log(-cos(d*x + c)) - (a^2*cos(d*x + c)^3 - 2*a^2*cos(d*x + c)^2 + a^2*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 17*(a^2*cos(d*x + c)^3 - 2*a^2*cos(d*x + c)^2 + a^2*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^3 - 2*d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
27,1,289,0,0.624938," ","integrate(csc(d*x+c)^7*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{30 \, a^{2} \cos\left(d x + c\right)^{4} - 48 \, a^{2} \cos\left(d x + c\right)^{3} - 14 \, a^{2} \cos\left(d x + c\right)^{2} + 46 \, a^{2} \cos\left(d x + c\right) - 12 \, a^{2} - 24 \, {\left(a^{2} \cos\left(d x + c\right)^{5} - 2 \, a^{2} \cos\left(d x + c\right)^{4} + 2 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right)\right) - 3 \, {\left(a^{2} \cos\left(d x + c\right)^{5} - 2 \, a^{2} \cos\left(d x + c\right)^{4} + 2 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 27 \, {\left(a^{2} \cos\left(d x + c\right)^{5} - 2 \, a^{2} \cos\left(d x + c\right)^{4} + 2 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{12 \, {\left(d \cos\left(d x + c\right)^{5} - 2 \, d \cos\left(d x + c\right)^{4} + 2 \, d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right)\right)}}"," ",0,"1/12*(30*a^2*cos(d*x + c)^4 - 48*a^2*cos(d*x + c)^3 - 14*a^2*cos(d*x + c)^2 + 46*a^2*cos(d*x + c) - 12*a^2 - 24*(a^2*cos(d*x + c)^5 - 2*a^2*cos(d*x + c)^4 + 2*a^2*cos(d*x + c)^2 - a^2*cos(d*x + c))*log(-cos(d*x + c)) - 3*(a^2*cos(d*x + c)^5 - 2*a^2*cos(d*x + c)^4 + 2*a^2*cos(d*x + c)^2 - a^2*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 27*(a^2*cos(d*x + c)^5 - 2*a^2*cos(d*x + c)^4 + 2*a^2*cos(d*x + c)^2 - a^2*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^5 - 2*d*cos(d*x + c)^4 + 2*d*cos(d*x + c)^2 - d*cos(d*x + c))","A",0
28,1,461,0,0.641922," ","integrate(csc(d*x+c)^9*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{1050 \, a^{2} \cos\left(d x + c\right)^{6} - 1716 \, a^{2} \cos\left(d x + c\right)^{5} - 1468 \, a^{2} \cos\left(d x + c\right)^{4} + 3308 \, a^{2} \cos\left(d x + c\right)^{3} - 38 \, a^{2} \cos\left(d x + c\right)^{2} - 1568 \, a^{2} \cos\left(d x + c\right) + 384 \, a^{2} - 768 \, {\left(a^{2} \cos\left(d x + c\right)^{7} - 2 \, a^{2} \cos\left(d x + c\right)^{6} - a^{2} \cos\left(d x + c\right)^{5} + 4 \, a^{2} \cos\left(d x + c\right)^{4} - a^{2} \cos\left(d x + c\right)^{3} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right)\right) - 141 \, {\left(a^{2} \cos\left(d x + c\right)^{7} - 2 \, a^{2} \cos\left(d x + c\right)^{6} - a^{2} \cos\left(d x + c\right)^{5} + 4 \, a^{2} \cos\left(d x + c\right)^{4} - a^{2} \cos\left(d x + c\right)^{3} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 909 \, {\left(a^{2} \cos\left(d x + c\right)^{7} - 2 \, a^{2} \cos\left(d x + c\right)^{6} - a^{2} \cos\left(d x + c\right)^{5} + 4 \, a^{2} \cos\left(d x + c\right)^{4} - a^{2} \cos\left(d x + c\right)^{3} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{384 \, {\left(d \cos\left(d x + c\right)^{7} - 2 \, d \cos\left(d x + c\right)^{6} - d \cos\left(d x + c\right)^{5} + 4 \, d \cos\left(d x + c\right)^{4} - d \cos\left(d x + c\right)^{3} - 2 \, d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"1/384*(1050*a^2*cos(d*x + c)^6 - 1716*a^2*cos(d*x + c)^5 - 1468*a^2*cos(d*x + c)^4 + 3308*a^2*cos(d*x + c)^3 - 38*a^2*cos(d*x + c)^2 - 1568*a^2*cos(d*x + c) + 384*a^2 - 768*(a^2*cos(d*x + c)^7 - 2*a^2*cos(d*x + c)^6 - a^2*cos(d*x + c)^5 + 4*a^2*cos(d*x + c)^4 - a^2*cos(d*x + c)^3 - 2*a^2*cos(d*x + c)^2 + a^2*cos(d*x + c))*log(-cos(d*x + c)) - 141*(a^2*cos(d*x + c)^7 - 2*a^2*cos(d*x + c)^6 - a^2*cos(d*x + c)^5 + 4*a^2*cos(d*x + c)^4 - a^2*cos(d*x + c)^3 - 2*a^2*cos(d*x + c)^2 + a^2*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 909*(a^2*cos(d*x + c)^7 - 2*a^2*cos(d*x + c)^6 - a^2*cos(d*x + c)^5 + 4*a^2*cos(d*x + c)^4 - a^2*cos(d*x + c)^3 - 2*a^2*cos(d*x + c)^2 + a^2*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^7 - 2*d*cos(d*x + c)^6 - d*cos(d*x + c)^5 + 4*d*cos(d*x + c)^4 - d*cos(d*x + c)^3 - 2*d*cos(d*x + c)^2 + d*cos(d*x + c))","B",0
29,1,185,0,0.710874," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^8,x, algorithm=""fricas"")","-\frac{25725 \, a^{2} d x \cos\left(d x + c\right) - 13440 \, a^{2} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + 13440 \, a^{2} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(1680 \, a^{2} \cos\left(d x + c\right)^{8} + 3840 \, a^{2} \cos\left(d x + c\right)^{7} - 4760 \, a^{2} \cos\left(d x + c\right)^{6} - 16896 \, a^{2} \cos\left(d x + c\right)^{5} + 770 \, a^{2} \cos\left(d x + c\right)^{4} + 31232 \, a^{2} \cos\left(d x + c\right)^{3} + 14595 \, a^{2} \cos\left(d x + c\right)^{2} - 45056 \, a^{2} \cos\left(d x + c\right) + 13440 \, a^{2}\right)} \sin\left(d x + c\right)}{13440 \, d \cos\left(d x + c\right)}"," ",0,"-1/13440*(25725*a^2*d*x*cos(d*x + c) - 13440*a^2*cos(d*x + c)*log(sin(d*x + c) + 1) + 13440*a^2*cos(d*x + c)*log(-sin(d*x + c) + 1) - (1680*a^2*cos(d*x + c)^8 + 3840*a^2*cos(d*x + c)^7 - 4760*a^2*cos(d*x + c)^6 - 16896*a^2*cos(d*x + c)^5 + 770*a^2*cos(d*x + c)^4 + 31232*a^2*cos(d*x + c)^3 + 14595*a^2*cos(d*x + c)^2 - 45056*a^2*cos(d*x + c) + 13440*a^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
30,1,158,0,0.678292," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^6,x, algorithm=""fricas"")","-\frac{375 \, a^{2} d x \cos\left(d x + c\right) - 240 \, a^{2} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + 240 \, a^{2} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(40 \, a^{2} \cos\left(d x + c\right)^{6} + 96 \, a^{2} \cos\left(d x + c\right)^{5} - 70 \, a^{2} \cos\left(d x + c\right)^{4} - 352 \, a^{2} \cos\left(d x + c\right)^{3} - 105 \, a^{2} \cos\left(d x + c\right)^{2} + 736 \, a^{2} \cos\left(d x + c\right) - 240 \, a^{2}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)}"," ",0,"-1/240*(375*a^2*d*x*cos(d*x + c) - 240*a^2*cos(d*x + c)*log(sin(d*x + c) + 1) + 240*a^2*cos(d*x + c)*log(-sin(d*x + c) + 1) + (40*a^2*cos(d*x + c)^6 + 96*a^2*cos(d*x + c)^5 - 70*a^2*cos(d*x + c)^4 - 352*a^2*cos(d*x + c)^3 - 105*a^2*cos(d*x + c)^2 + 736*a^2*cos(d*x + c) - 240*a^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
31,1,133,0,0.945879," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^4,x, algorithm=""fricas"")","-\frac{27 \, a^{2} d x \cos\left(d x + c\right) - 24 \, a^{2} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + 24 \, a^{2} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(6 \, a^{2} \cos\left(d x + c\right)^{4} + 16 \, a^{2} \cos\left(d x + c\right)^{3} - 3 \, a^{2} \cos\left(d x + c\right)^{2} - 64 \, a^{2} \cos\left(d x + c\right) + 24 \, a^{2}\right)} \sin\left(d x + c\right)}{24 \, d \cos\left(d x + c\right)}"," ",0,"-1/24*(27*a^2*d*x*cos(d*x + c) - 24*a^2*cos(d*x + c)*log(sin(d*x + c) + 1) + 24*a^2*cos(d*x + c)*log(-sin(d*x + c) + 1) - (6*a^2*cos(d*x + c)^4 + 16*a^2*cos(d*x + c)^3 - 3*a^2*cos(d*x + c)^2 - 64*a^2*cos(d*x + c) + 24*a^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
32,1,104,0,1.608239," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^2,x, algorithm=""fricas"")","-\frac{a^{2} d x \cos\left(d x + c\right) - 2 \, a^{2} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, a^{2} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(a^{2} \cos\left(d x + c\right)^{2} + 4 \, a^{2} \cos\left(d x + c\right) - 2 \, a^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"-1/2*(a^2*d*x*cos(d*x + c) - 2*a^2*cos(d*x + c)*log(sin(d*x + c) + 1) + 2*a^2*cos(d*x + c)*log(-sin(d*x + c) + 1) + (a^2*cos(d*x + c)^2 + 4*a^2*cos(d*x + c) - 2*a^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
33,1,101,0,0.642644," ","integrate(csc(d*x+c)^2*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{a^{2} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - a^{2} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 3 \, a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}{d \cos\left(d x + c\right) \sin\left(d x + c\right)}"," ",0,"(a^2*cos(d*x + c)*log(sin(d*x + c) + 1)*sin(d*x + c) - a^2*cos(d*x + c)*log(-sin(d*x + c) + 1)*sin(d*x + c) - 3*a^2*cos(d*x + c)^2 - 2*a^2*cos(d*x + c) + a^2)/(d*cos(d*x + c)*sin(d*x + c))","A",0
34,1,159,0,0.690350," ","integrate(csc(d*x+c)^4*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{10 \, a^{2} \cos\left(d x + c\right)^{3} - 4 \, a^{2} \cos\left(d x + c\right)^{2} - 11 \, a^{2} \cos\left(d x + c\right) - 3 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 3 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 3 \, a^{2}}{3 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}"," ",0,"-1/3*(10*a^2*cos(d*x + c)^3 - 4*a^2*cos(d*x + c)^2 - 11*a^2*cos(d*x + c) - 3*(a^2*cos(d*x + c)^2 - a^2*cos(d*x + c))*log(sin(d*x + c) + 1)*sin(d*x + c) + 3*(a^2*cos(d*x + c)^2 - a^2*cos(d*x + c))*log(-sin(d*x + c) + 1)*sin(d*x + c) + 3*a^2)/((d*cos(d*x + c)^2 - d*cos(d*x + c))*sin(d*x + c))","A",0
35,1,206,0,0.571493," ","integrate(csc(d*x+c)^6*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{56 \, a^{2} \cos\left(d x + c\right)^{4} - 82 \, a^{2} \cos\left(d x + c\right)^{3} - 32 \, a^{2} \cos\left(d x + c\right)^{2} + 76 \, a^{2} \cos\left(d x + c\right) - 15 \, {\left(a^{2} \cos\left(d x + c\right)^{3} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 15 \, {\left(a^{2} \cos\left(d x + c\right)^{3} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 15 \, a^{2}}{15 \, {\left(d \cos\left(d x + c\right)^{3} - 2 \, d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}"," ",0,"-1/15*(56*a^2*cos(d*x + c)^4 - 82*a^2*cos(d*x + c)^3 - 32*a^2*cos(d*x + c)^2 + 76*a^2*cos(d*x + c) - 15*(a^2*cos(d*x + c)^3 - 2*a^2*cos(d*x + c)^2 + a^2*cos(d*x + c))*log(sin(d*x + c) + 1)*sin(d*x + c) + 15*(a^2*cos(d*x + c)^3 - 2*a^2*cos(d*x + c)^2 + a^2*cos(d*x + c))*log(-sin(d*x + c) + 1)*sin(d*x + c) - 15*a^2)/((d*cos(d*x + c)^3 - 2*d*cos(d*x + c)^2 + d*cos(d*x + c))*sin(d*x + c))","A",0
36,1,272,0,0.743963," ","integrate(csc(d*x+c)^8*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{432 \, a^{2} \cos\left(d x + c\right)^{6} - 654 \, a^{2} \cos\left(d x + c\right)^{5} - 636 \, a^{2} \cos\left(d x + c\right)^{4} + 1226 \, a^{2} \cos\left(d x + c\right)^{3} + 74 \, a^{2} \cos\left(d x + c\right)^{2} - 562 \, a^{2} \cos\left(d x + c\right) - 105 \, {\left(a^{2} \cos\left(d x + c\right)^{5} - 2 \, a^{2} \cos\left(d x + c\right)^{4} + 2 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 105 \, {\left(a^{2} \cos\left(d x + c\right)^{5} - 2 \, a^{2} \cos\left(d x + c\right)^{4} + 2 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 105 \, a^{2}}{105 \, {\left(d \cos\left(d x + c\right)^{5} - 2 \, d \cos\left(d x + c\right)^{4} + 2 \, d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}"," ",0,"-1/105*(432*a^2*cos(d*x + c)^6 - 654*a^2*cos(d*x + c)^5 - 636*a^2*cos(d*x + c)^4 + 1226*a^2*cos(d*x + c)^3 + 74*a^2*cos(d*x + c)^2 - 562*a^2*cos(d*x + c) - 105*(a^2*cos(d*x + c)^5 - 2*a^2*cos(d*x + c)^4 + 2*a^2*cos(d*x + c)^2 - a^2*cos(d*x + c))*log(sin(d*x + c) + 1)*sin(d*x + c) + 105*(a^2*cos(d*x + c)^5 - 2*a^2*cos(d*x + c)^4 + 2*a^2*cos(d*x + c)^2 - a^2*cos(d*x + c))*log(-sin(d*x + c) + 1)*sin(d*x + c) + 105*a^2)/((d*cos(d*x + c)^5 - 2*d*cos(d*x + c)^4 + 2*d*cos(d*x + c)^2 - d*cos(d*x + c))*sin(d*x + c))","A",0
37,1,406,0,3.264855," ","integrate(csc(d*x+c)^10*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{1408 \, a^{2} \cos\left(d x + c\right)^{8} - 2186 \, a^{2} \cos\left(d x + c\right)^{7} - 3372 \, a^{2} \cos\left(d x + c\right)^{6} + 6200 \, a^{2} \cos\left(d x + c\right)^{5} + 2060 \, a^{2} \cos\left(d x + c\right)^{4} - 5784 \, a^{2} \cos\left(d x + c\right)^{3} + 268 \, a^{2} \cos\left(d x + c\right)^{2} + 1756 \, a^{2} \cos\left(d x + c\right) - 315 \, {\left(a^{2} \cos\left(d x + c\right)^{7} - 2 \, a^{2} \cos\left(d x + c\right)^{6} - a^{2} \cos\left(d x + c\right)^{5} + 4 \, a^{2} \cos\left(d x + c\right)^{4} - a^{2} \cos\left(d x + c\right)^{3} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 315 \, {\left(a^{2} \cos\left(d x + c\right)^{7} - 2 \, a^{2} \cos\left(d x + c\right)^{6} - a^{2} \cos\left(d x + c\right)^{5} + 4 \, a^{2} \cos\left(d x + c\right)^{4} - a^{2} \cos\left(d x + c\right)^{3} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 315 \, a^{2}}{315 \, {\left(d \cos\left(d x + c\right)^{7} - 2 \, d \cos\left(d x + c\right)^{6} - d \cos\left(d x + c\right)^{5} + 4 \, d \cos\left(d x + c\right)^{4} - d \cos\left(d x + c\right)^{3} - 2 \, d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}"," ",0,"-1/315*(1408*a^2*cos(d*x + c)^8 - 2186*a^2*cos(d*x + c)^7 - 3372*a^2*cos(d*x + c)^6 + 6200*a^2*cos(d*x + c)^5 + 2060*a^2*cos(d*x + c)^4 - 5784*a^2*cos(d*x + c)^3 + 268*a^2*cos(d*x + c)^2 + 1756*a^2*cos(d*x + c) - 315*(a^2*cos(d*x + c)^7 - 2*a^2*cos(d*x + c)^6 - a^2*cos(d*x + c)^5 + 4*a^2*cos(d*x + c)^4 - a^2*cos(d*x + c)^3 - 2*a^2*cos(d*x + c)^2 + a^2*cos(d*x + c))*log(sin(d*x + c) + 1)*sin(d*x + c) + 315*(a^2*cos(d*x + c)^7 - 2*a^2*cos(d*x + c)^6 - a^2*cos(d*x + c)^5 + 4*a^2*cos(d*x + c)^4 - a^2*cos(d*x + c)^3 - 2*a^2*cos(d*x + c)^2 + a^2*cos(d*x + c))*log(-sin(d*x + c) + 1)*sin(d*x + c) - 315*a^2)/((d*cos(d*x + c)^7 - 2*d*cos(d*x + c)^6 - d*cos(d*x + c)^5 + 4*d*cos(d*x + c)^4 - d*cos(d*x + c)^3 - 2*d*cos(d*x + c)^2 + d*cos(d*x + c))*sin(d*x + c))","B",0
38,1,182,0,0.702231," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^9,x, algorithm=""fricas"")","-\frac{35840 \, a^{3} \cos\left(d x + c\right)^{11} + 120960 \, a^{3} \cos\left(d x + c\right)^{10} - 46080 \, a^{3} \cos\left(d x + c\right)^{9} - 591360 \, a^{3} \cos\left(d x + c\right)^{8} - 387072 \, a^{3} \cos\left(d x + c\right)^{7} + 1128960 \, a^{3} \cos\left(d x + c\right)^{6} + 1505280 \, a^{3} \cos\left(d x + c\right)^{5} - 967680 \, a^{3} \cos\left(d x + c\right)^{4} - 3548160 \, a^{3} \cos\left(d x + c\right)^{3} - 322560 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(-\cos\left(d x + c\right)\right) + 212205 \, a^{3} \cos\left(d x + c\right)^{2} - 967680 \, a^{3} \cos\left(d x + c\right) - 161280 \, a^{3}}{322560 \, d \cos\left(d x + c\right)^{2}}"," ",0,"-1/322560*(35840*a^3*cos(d*x + c)^11 + 120960*a^3*cos(d*x + c)^10 - 46080*a^3*cos(d*x + c)^9 - 591360*a^3*cos(d*x + c)^8 - 387072*a^3*cos(d*x + c)^7 + 1128960*a^3*cos(d*x + c)^6 + 1505280*a^3*cos(d*x + c)^5 - 967680*a^3*cos(d*x + c)^4 - 3548160*a^3*cos(d*x + c)^3 - 322560*a^3*cos(d*x + c)^2*log(-cos(d*x + c)) + 212205*a^3*cos(d*x + c)^2 - 967680*a^3*cos(d*x + c) - 161280*a^3)/(d*cos(d*x + c)^2)","A",0
39,1,121,0,0.774659," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^7,x, algorithm=""fricas"")","\frac{32 \, a^{3} \cos\left(d x + c\right)^{9} + 112 \, a^{3} \cos\left(d x + c\right)^{8} - 448 \, a^{3} \cos\left(d x + c\right)^{6} - 448 \, a^{3} \cos\left(d x + c\right)^{5} + 672 \, a^{3} \cos\left(d x + c\right)^{4} + 1792 \, a^{3} \cos\left(d x + c\right)^{3} - 203 \, a^{3} \cos\left(d x + c\right)^{2} + 672 \, a^{3} \cos\left(d x + c\right) + 112 \, a^{3}}{224 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/224*(32*a^3*cos(d*x + c)^9 + 112*a^3*cos(d*x + c)^8 - 448*a^3*cos(d*x + c)^6 - 448*a^3*cos(d*x + c)^5 + 672*a^3*cos(d*x + c)^4 + 1792*a^3*cos(d*x + c)^3 - 203*a^3*cos(d*x + c)^2 + 672*a^3*cos(d*x + c) + 112*a^3)/(d*cos(d*x + c)^2)","A",0
40,1,130,0,0.686851," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^5,x, algorithm=""fricas"")","-\frac{96 \, a^{3} \cos\left(d x + c\right)^{7} + 360 \, a^{3} \cos\left(d x + c\right)^{6} + 160 \, a^{3} \cos\left(d x + c\right)^{5} - 1200 \, a^{3} \cos\left(d x + c\right)^{4} - 2400 \, a^{3} \cos\left(d x + c\right)^{3} + 480 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(-\cos\left(d x + c\right)\right) + 465 \, a^{3} \cos\left(d x + c\right)^{2} - 1440 \, a^{3} \cos\left(d x + c\right) - 240 \, a^{3}}{480 \, d \cos\left(d x + c\right)^{2}}"," ",0,"-1/480*(96*a^3*cos(d*x + c)^7 + 360*a^3*cos(d*x + c)^6 + 160*a^3*cos(d*x + c)^5 - 1200*a^3*cos(d*x + c)^4 - 2400*a^3*cos(d*x + c)^3 + 480*a^3*cos(d*x + c)^2*log(-cos(d*x + c)) + 465*a^3*cos(d*x + c)^2 - 1440*a^3*cos(d*x + c) - 240*a^3)/(d*cos(d*x + c)^2)","A",0
41,1,104,0,0.699151," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^3,x, algorithm=""fricas"")","\frac{4 \, a^{3} \cos\left(d x + c\right)^{5} + 18 \, a^{3} \cos\left(d x + c\right)^{4} + 24 \, a^{3} \cos\left(d x + c\right)^{3} - 24 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(-\cos\left(d x + c\right)\right) - 9 \, a^{3} \cos\left(d x + c\right)^{2} + 36 \, a^{3} \cos\left(d x + c\right) + 6 \, a^{3}}{12 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/12*(4*a^3*cos(d*x + c)^5 + 18*a^3*cos(d*x + c)^4 + 24*a^3*cos(d*x + c)^3 - 24*a^3*cos(d*x + c)^2*log(-cos(d*x + c)) - 9*a^3*cos(d*x + c)^2 + 36*a^3*cos(d*x + c) + 6*a^3)/(d*cos(d*x + c)^2)","A",0
42,1,65,0,0.860973," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c),x, algorithm=""fricas"")","-\frac{2 \, a^{3} \cos\left(d x + c\right)^{3} + 6 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(-\cos\left(d x + c\right)\right) - 6 \, a^{3} \cos\left(d x + c\right) - a^{3}}{2 \, d \cos\left(d x + c\right)^{2}}"," ",0,"-1/2*(2*a^3*cos(d*x + c)^3 + 6*a^3*cos(d*x + c)^2*log(-cos(d*x + c)) - 6*a^3*cos(d*x + c) - a^3)/(d*cos(d*x + c)^2)","A",0
43,1,76,0,0.735595," ","integrate(csc(d*x+c)*(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{8 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(-\cos\left(d x + c\right)\right) - 8 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 6 \, a^{3} \cos\left(d x + c\right) - a^{3}}{2 \, d \cos\left(d x + c\right)^{2}}"," ",0,"-1/2*(8*a^3*cos(d*x + c)^2*log(-cos(d*x + c)) - 8*a^3*cos(d*x + c)^2*log(-1/2*cos(d*x + c) + 1/2) - 6*a^3*cos(d*x + c) - a^3)/(d*cos(d*x + c)^2)","A",0
44,1,132,0,0.741673," ","integrate(csc(d*x+c)^3*(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{10 \, a^{3} \cos\left(d x + c\right)^{2} - 5 \, a^{3} \cos\left(d x + c\right) - a^{3} - 10 \, {\left(a^{3} \cos\left(d x + c\right)^{3} - a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(-\cos\left(d x + c\right)\right) + 10 \, {\left(a^{3} \cos\left(d x + c\right)^{3} - a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left(d \cos\left(d x + c\right)^{3} - d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/2*(10*a^3*cos(d*x + c)^2 - 5*a^3*cos(d*x + c) - a^3 - 10*(a^3*cos(d*x + c)^3 - a^3*cos(d*x + c)^2)*log(-cos(d*x + c)) + 10*(a^3*cos(d*x + c)^3 - a^3*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^3 - d*cos(d*x + c)^2)","A",0
45,1,177,0,0.786319," ","integrate(csc(d*x+c)^5*(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{12 \, a^{3} \cos\left(d x + c\right)^{3} - 18 \, a^{3} \cos\left(d x + c\right)^{2} + 4 \, a^{3} \cos\left(d x + c\right) + a^{3} - 12 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(-\cos\left(d x + c\right)\right) + 12 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/2*(12*a^3*cos(d*x + c)^3 - 18*a^3*cos(d*x + c)^2 + 4*a^3*cos(d*x + c) + a^3 - 12*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^3 + a^3*cos(d*x + c)^2)*log(-cos(d*x + c)) + 12*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^3 + a^3*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
46,1,297,0,0.670953," ","integrate(csc(d*x+c)^7*(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{330 \, a^{3} \cos\left(d x + c\right)^{4} - 822 \, a^{3} \cos\left(d x + c\right)^{3} + 596 \, a^{3} \cos\left(d x + c\right)^{2} - 72 \, a^{3} \cos\left(d x + c\right) - 24 \, a^{3} - 336 \, {\left(a^{3} \cos\left(d x + c\right)^{5} - 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{3} - a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(-\cos\left(d x + c\right)\right) + 3 \, {\left(a^{3} \cos\left(d x + c\right)^{5} - 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{3} - a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 333 \, {\left(a^{3} \cos\left(d x + c\right)^{5} - 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{3} - a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{48 \, {\left(d \cos\left(d x + c\right)^{5} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{3} - d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/48*(330*a^3*cos(d*x + c)^4 - 822*a^3*cos(d*x + c)^3 + 596*a^3*cos(d*x + c)^2 - 72*a^3*cos(d*x + c) - 24*a^3 - 336*(a^3*cos(d*x + c)^5 - 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^3 - a^3*cos(d*x + c)^2)*log(-cos(d*x + c)) + 3*(a^3*cos(d*x + c)^5 - 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^3 - a^3*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) + 333*(a^3*cos(d*x + c)^5 - 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^3 - a^3*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^5 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^3 - d*cos(d*x + c)^2)","B",0
47,1,419,0,1.584068," ","integrate(csc(d*x+c)^9*(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{1470 \, a^{3} \cos\left(d x + c\right)^{6} - 3642 \, a^{3} \cos\left(d x + c\right)^{5} + 1126 \, a^{3} \cos\left(d x + c\right)^{4} + 3390 \, a^{3} \cos\left(d x + c\right)^{3} - 2752 \, a^{3} \cos\left(d x + c\right)^{2} + 288 \, a^{3} \cos\left(d x + c\right) + 96 \, a^{3} - 1536 \, {\left(a^{3} \cos\left(d x + c\right)^{7} - 3 \, a^{3} \cos\left(d x + c\right)^{6} + 2 \, a^{3} \cos\left(d x + c\right)^{5} + 2 \, a^{3} \cos\left(d x + c\right)^{4} - 3 \, a^{3} \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(-\cos\left(d x + c\right)\right) + 33 \, {\left(a^{3} \cos\left(d x + c\right)^{7} - 3 \, a^{3} \cos\left(d x + c\right)^{6} + 2 \, a^{3} \cos\left(d x + c\right)^{5} + 2 \, a^{3} \cos\left(d x + c\right)^{4} - 3 \, a^{3} \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 1503 \, {\left(a^{3} \cos\left(d x + c\right)^{7} - 3 \, a^{3} \cos\left(d x + c\right)^{6} + 2 \, a^{3} \cos\left(d x + c\right)^{5} + 2 \, a^{3} \cos\left(d x + c\right)^{4} - 3 \, a^{3} \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{192 \, {\left(d \cos\left(d x + c\right)^{7} - 3 \, d \cos\left(d x + c\right)^{6} + 2 \, d \cos\left(d x + c\right)^{5} + 2 \, d \cos\left(d x + c\right)^{4} - 3 \, d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/192*(1470*a^3*cos(d*x + c)^6 - 3642*a^3*cos(d*x + c)^5 + 1126*a^3*cos(d*x + c)^4 + 3390*a^3*cos(d*x + c)^3 - 2752*a^3*cos(d*x + c)^2 + 288*a^3*cos(d*x + c) + 96*a^3 - 1536*(a^3*cos(d*x + c)^7 - 3*a^3*cos(d*x + c)^6 + 2*a^3*cos(d*x + c)^5 + 2*a^3*cos(d*x + c)^4 - 3*a^3*cos(d*x + c)^3 + a^3*cos(d*x + c)^2)*log(-cos(d*x + c)) + 33*(a^3*cos(d*x + c)^7 - 3*a^3*cos(d*x + c)^6 + 2*a^3*cos(d*x + c)^5 + 2*a^3*cos(d*x + c)^4 - 3*a^3*cos(d*x + c)^3 + a^3*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) + 1503*(a^3*cos(d*x + c)^7 - 3*a^3*cos(d*x + c)^6 + 2*a^3*cos(d*x + c)^5 + 2*a^3*cos(d*x + c)^4 - 3*a^3*cos(d*x + c)^3 + a^3*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^7 - 3*d*cos(d*x + c)^6 + 2*d*cos(d*x + c)^5 + 2*d*cos(d*x + c)^4 - 3*d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","B",0
48,1,204,0,0.735660," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^8,x, algorithm=""fricas"")","-\frac{84525 \, a^{3} d x \cos\left(d x + c\right)^{2} + 3360 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3360 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(1680 \, a^{3} \cos\left(d x + c\right)^{9} + 5760 \, a^{3} \cos\left(d x + c\right)^{8} - 280 \, a^{3} \cos\left(d x + c\right)^{7} - 22656 \, a^{3} \cos\left(d x + c\right)^{6} - 20510 \, a^{3} \cos\left(d x + c\right)^{5} + 32512 \, a^{3} \cos\left(d x + c\right)^{4} + 63315 \, a^{3} \cos\left(d x + c\right)^{3} - 15616 \, a^{3} \cos\left(d x + c\right)^{2} + 40320 \, a^{3} \cos\left(d x + c\right) + 6720 \, a^{3}\right)} \sin\left(d x + c\right)}{13440 \, d \cos\left(d x + c\right)^{2}}"," ",0,"-1/13440*(84525*a^3*d*x*cos(d*x + c)^2 + 3360*a^3*cos(d*x + c)^2*log(sin(d*x + c) + 1) - 3360*a^3*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - (1680*a^3*cos(d*x + c)^9 + 5760*a^3*cos(d*x + c)^8 - 280*a^3*cos(d*x + c)^7 - 22656*a^3*cos(d*x + c)^6 - 20510*a^3*cos(d*x + c)^5 + 32512*a^3*cos(d*x + c)^4 + 63315*a^3*cos(d*x + c)^3 - 15616*a^3*cos(d*x + c)^2 + 40320*a^3*cos(d*x + c) + 6720*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
49,1,177,0,0.738618," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^6,x, algorithm=""fricas"")","-\frac{1275 \, a^{3} d x \cos\left(d x + c\right)^{2} - 60 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + 60 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(40 \, a^{3} \cos\left(d x + c\right)^{7} + 144 \, a^{3} \cos\left(d x + c\right)^{6} + 50 \, a^{3} \cos\left(d x + c\right)^{5} - 448 \, a^{3} \cos\left(d x + c\right)^{4} - 645 \, a^{3} \cos\left(d x + c\right)^{3} + 544 \, a^{3} \cos\left(d x + c\right)^{2} - 720 \, a^{3} \cos\left(d x + c\right) - 120 \, a^{3}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{2}}"," ",0,"-1/240*(1275*a^3*d*x*cos(d*x + c)^2 - 60*a^3*cos(d*x + c)^2*log(sin(d*x + c) + 1) + 60*a^3*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + (40*a^3*cos(d*x + c)^7 + 144*a^3*cos(d*x + c)^6 + 50*a^3*cos(d*x + c)^5 - 448*a^3*cos(d*x + c)^4 - 645*a^3*cos(d*x + c)^3 + 544*a^3*cos(d*x + c)^2 - 720*a^3*cos(d*x + c) - 120*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
50,1,152,0,0.735518," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^4,x, algorithm=""fricas"")","-\frac{33 \, a^{3} d x \cos\left(d x + c\right)^{2} - 6 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + 6 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(2 \, a^{3} \cos\left(d x + c\right)^{5} + 8 \, a^{3} \cos\left(d x + c\right)^{4} + 7 \, a^{3} \cos\left(d x + c\right)^{3} - 24 \, a^{3} \cos\left(d x + c\right)^{2} + 24 \, a^{3} \cos\left(d x + c\right) + 4 \, a^{3}\right)} \sin\left(d x + c\right)}{8 \, d \cos\left(d x + c\right)^{2}}"," ",0,"-1/8*(33*a^3*d*x*cos(d*x + c)^2 - 6*a^3*cos(d*x + c)^2*log(sin(d*x + c) + 1) + 6*a^3*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - (2*a^3*cos(d*x + c)^5 + 8*a^3*cos(d*x + c)^4 + 7*a^3*cos(d*x + c)^3 - 24*a^3*cos(d*x + c)^2 + 24*a^3*cos(d*x + c) + 4*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
51,1,125,0,0.595630," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^2,x, algorithm=""fricas"")","-\frac{10 \, a^{3} d x \cos\left(d x + c\right)^{2} - 5 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + 5 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{3} \cos\left(d x + c\right)^{3} + 6 \, a^{3} \cos\left(d x + c\right)^{2} - 6 \, a^{3} \cos\left(d x + c\right) - a^{3}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"-1/4*(10*a^3*d*x*cos(d*x + c)^2 - 5*a^3*cos(d*x + c)^2*log(sin(d*x + c) + 1) + 5*a^3*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(a^3*cos(d*x + c)^3 + 6*a^3*cos(d*x + c)^2 - 6*a^3*cos(d*x + c) - a^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
52,1,122,0,0.499848," ","integrate(csc(d*x+c)^2*(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{9 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 9 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 28 \, a^{3} \cos\left(d x + c\right)^{3} - 18 \, a^{3} \cos\left(d x + c\right)^{2} + 12 \, a^{3} \cos\left(d x + c\right) + 2 \, a^{3}}{4 \, d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)}"," ",0,"1/4*(9*a^3*cos(d*x + c)^2*log(sin(d*x + c) + 1)*sin(d*x + c) - 9*a^3*cos(d*x + c)^2*log(-sin(d*x + c) + 1)*sin(d*x + c) - 28*a^3*cos(d*x + c)^3 - 18*a^3*cos(d*x + c)^2 + 12*a^3*cos(d*x + c) + 2*a^3)/(d*cos(d*x + c)^2*sin(d*x + c))","A",0
53,1,178,0,0.600426," ","integrate(csc(d*x+c)^4*(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{104 \, a^{3} \cos\left(d x + c\right)^{4} - 38 \, a^{3} \cos\left(d x + c\right)^{3} - 118 \, a^{3} \cos\left(d x + c\right)^{2} + 30 \, a^{3} \cos\left(d x + c\right) + 6 \, a^{3} - 33 \, {\left(a^{3} \cos\left(d x + c\right)^{3} - a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 33 \, {\left(a^{3} \cos\left(d x + c\right)^{3} - a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{3} - d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}"," ",0,"-1/12*(104*a^3*cos(d*x + c)^4 - 38*a^3*cos(d*x + c)^3 - 118*a^3*cos(d*x + c)^2 + 30*a^3*cos(d*x + c) + 6*a^3 - 33*(a^3*cos(d*x + c)^3 - a^3*cos(d*x + c)^2)*log(sin(d*x + c) + 1)*sin(d*x + c) + 33*(a^3*cos(d*x + c)^3 - a^3*cos(d*x + c)^2)*log(-sin(d*x + c) + 1)*sin(d*x + c))/((d*cos(d*x + c)^3 - d*cos(d*x + c)^2)*sin(d*x + c))","A",0
54,1,225,0,0.744264," ","integrate(csc(d*x+c)^6*(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{608 \, a^{3} \cos\left(d x + c\right)^{5} - 826 \, a^{3} \cos\left(d x + c\right)^{4} - 476 \, a^{3} \cos\left(d x + c\right)^{3} + 868 \, a^{3} \cos\left(d x + c\right)^{2} - 120 \, a^{3} \cos\left(d x + c\right) - 30 \, a^{3} - 195 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 195 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right)}{60 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}"," ",0,"-1/60*(608*a^3*cos(d*x + c)^5 - 826*a^3*cos(d*x + c)^4 - 476*a^3*cos(d*x + c)^3 + 868*a^3*cos(d*x + c)^2 - 120*a^3*cos(d*x + c) - 30*a^3 - 195*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^3 + a^3*cos(d*x + c)^2)*log(sin(d*x + c) + 1)*sin(d*x + c) + 195*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^3 + a^3*cos(d*x + c)^2)*log(-sin(d*x + c) + 1)*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^3 + d*cos(d*x + c)^2)*sin(d*x + c))","A",0
55,1,278,0,0.620820," ","integrate(csc(d*x+c)^8*(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{320 \, a^{3} \cos\left(d x + c\right)^{6} - 750 \, a^{3} \cos\left(d x + c\right)^{5} + 170 \, a^{3} \cos\left(d x + c\right)^{4} + 720 \, a^{3} \cos\left(d x + c\right)^{3} - 520 \, a^{3} \cos\left(d x + c\right)^{2} + 42 \, a^{3} \cos\left(d x + c\right) + 14 \, a^{3} - 105 \, {\left(a^{3} \cos\left(d x + c\right)^{5} - 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{3} - a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 105 \, {\left(a^{3} \cos\left(d x + c\right)^{5} - 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{3} - a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right)}{28 \, {\left(d \cos\left(d x + c\right)^{5} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{3} - d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}"," ",0,"-1/28*(320*a^3*cos(d*x + c)^6 - 750*a^3*cos(d*x + c)^5 + 170*a^3*cos(d*x + c)^4 + 720*a^3*cos(d*x + c)^3 - 520*a^3*cos(d*x + c)^2 + 42*a^3*cos(d*x + c) + 14*a^3 - 105*(a^3*cos(d*x + c)^5 - 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^3 - a^3*cos(d*x + c)^2)*log(sin(d*x + c) + 1)*sin(d*x + c) + 105*(a^3*cos(d*x + c)^5 - 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^3 - a^3*cos(d*x + c)^2)*log(-sin(d*x + c) + 1)*sin(d*x + c))/((d*cos(d*x + c)^5 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^3 - d*cos(d*x + c)^2)*sin(d*x + c))","A",0
56,1,375,0,0.890970," ","integrate(csc(d*x+c)^10*(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15872 \, a^{3} \cos\left(d x + c\right)^{8} - 36906 \, a^{3} \cos\left(d x + c\right)^{7} - 8322 \, a^{3} \cos\left(d x + c\right)^{6} + 73402 \, a^{3} \cos\left(d x + c\right)^{5} - 33342 \, a^{3} \cos\left(d x + c\right)^{4} - 34746 \, a^{3} \cos\left(d x + c\right)^{3} + 26702 \, a^{3} \cos\left(d x + c\right)^{2} - 1890 \, a^{3} \cos\left(d x + c\right) - 630 \, a^{3} - 5355 \, {\left(a^{3} \cos\left(d x + c\right)^{7} - 3 \, a^{3} \cos\left(d x + c\right)^{6} + 2 \, a^{3} \cos\left(d x + c\right)^{5} + 2 \, a^{3} \cos\left(d x + c\right)^{4} - 3 \, a^{3} \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 5355 \, {\left(a^{3} \cos\left(d x + c\right)^{7} - 3 \, a^{3} \cos\left(d x + c\right)^{6} + 2 \, a^{3} \cos\left(d x + c\right)^{5} + 2 \, a^{3} \cos\left(d x + c\right)^{4} - 3 \, a^{3} \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right)}{1260 \, {\left(d \cos\left(d x + c\right)^{7} - 3 \, d \cos\left(d x + c\right)^{6} + 2 \, d \cos\left(d x + c\right)^{5} + 2 \, d \cos\left(d x + c\right)^{4} - 3 \, d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}"," ",0,"-1/1260*(15872*a^3*cos(d*x + c)^8 - 36906*a^3*cos(d*x + c)^7 - 8322*a^3*cos(d*x + c)^6 + 73402*a^3*cos(d*x + c)^5 - 33342*a^3*cos(d*x + c)^4 - 34746*a^3*cos(d*x + c)^3 + 26702*a^3*cos(d*x + c)^2 - 1890*a^3*cos(d*x + c) - 630*a^3 - 5355*(a^3*cos(d*x + c)^7 - 3*a^3*cos(d*x + c)^6 + 2*a^3*cos(d*x + c)^5 + 2*a^3*cos(d*x + c)^4 - 3*a^3*cos(d*x + c)^3 + a^3*cos(d*x + c)^2)*log(sin(d*x + c) + 1)*sin(d*x + c) + 5355*(a^3*cos(d*x + c)^7 - 3*a^3*cos(d*x + c)^6 + 2*a^3*cos(d*x + c)^5 + 2*a^3*cos(d*x + c)^4 - 3*a^3*cos(d*x + c)^3 + a^3*cos(d*x + c)^2)*log(-sin(d*x + c) + 1)*sin(d*x + c))/((d*cos(d*x + c)^7 - 3*d*cos(d*x + c)^6 + 2*d*cos(d*x + c)^5 + 2*d*cos(d*x + c)^4 - 3*d*cos(d*x + c)^3 + d*cos(d*x + c)^2)*sin(d*x + c))","A",0
57,1,89,0,0.821149," ","integrate(sin(d*x+c)^9/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{280 \, \cos\left(d x + c\right)^{9} - 315 \, \cos\left(d x + c\right)^{8} - 1080 \, \cos\left(d x + c\right)^{7} + 1260 \, \cos\left(d x + c\right)^{6} + 1512 \, \cos\left(d x + c\right)^{5} - 1890 \, \cos\left(d x + c\right)^{4} - 840 \, \cos\left(d x + c\right)^{3} + 1260 \, \cos\left(d x + c\right)^{2}}{2520 \, a d}"," ",0,"-1/2520*(280*cos(d*x + c)^9 - 315*cos(d*x + c)^8 - 1080*cos(d*x + c)^7 + 1260*cos(d*x + c)^6 + 1512*cos(d*x + c)^5 - 1890*cos(d*x + c)^4 - 840*cos(d*x + c)^3 + 1260*cos(d*x + c)^2)/(a*d)","A",0
58,1,69,0,0.482145," ","integrate(sin(d*x+c)^7/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{30 \, \cos\left(d x + c\right)^{7} - 35 \, \cos\left(d x + c\right)^{6} - 84 \, \cos\left(d x + c\right)^{5} + 105 \, \cos\left(d x + c\right)^{4} + 70 \, \cos\left(d x + c\right)^{3} - 105 \, \cos\left(d x + c\right)^{2}}{210 \, a d}"," ",0,"1/210*(30*cos(d*x + c)^7 - 35*cos(d*x + c)^6 - 84*cos(d*x + c)^5 + 105*cos(d*x + c)^4 + 70*cos(d*x + c)^3 - 105*cos(d*x + c)^2)/(a*d)","A",0
59,1,49,0,0.529529," ","integrate(sin(d*x+c)^5/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{12 \, \cos\left(d x + c\right)^{5} - 15 \, \cos\left(d x + c\right)^{4} - 20 \, \cos\left(d x + c\right)^{3} + 30 \, \cos\left(d x + c\right)^{2}}{60 \, a d}"," ",0,"-1/60*(12*cos(d*x + c)^5 - 15*cos(d*x + c)^4 - 20*cos(d*x + c)^3 + 30*cos(d*x + c)^2)/(a*d)","A",0
60,1,29,0,0.674407," ","integrate(sin(d*x+c)^3/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)^{2}}{6 \, a d}"," ",0,"1/6*(2*cos(d*x + c)^3 - 3*cos(d*x + c)^2)/(a*d)","A",0
61,1,28,0,0.833264," ","integrate(sin(d*x+c)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right) - \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{a d}"," ",0,"-(cos(d*x + c) - log(1/2*cos(d*x + c) + 1/2))/(a*d)","A",0
62,1,60,0,0.872549," ","integrate(csc(d*x+c)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(\cos\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(\cos\left(d x + c\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2}{4 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"-1/4*((cos(d*x + c) + 1)*log(1/2*cos(d*x + c) + 1/2) - (cos(d*x + c) + 1)*log(-1/2*cos(d*x + c) + 1/2) + 2)/(a*d*cos(d*x + c) + a*d)","A",0
63,1,138,0,0.731415," ","integrate(csc(d*x+c)^3/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, \cos\left(d x + c\right) + 4}{16 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2} - a d \cos\left(d x + c\right) - a d\right)}}"," ",0,"1/16*(2*cos(d*x + c)^2 - (cos(d*x + c)^3 + cos(d*x + c)^2 - cos(d*x + c) - 1)*log(1/2*cos(d*x + c) + 1/2) + (cos(d*x + c)^3 + cos(d*x + c)^2 - cos(d*x + c) - 1)*log(-1/2*cos(d*x + c) + 1/2) + 2*cos(d*x + c) + 4)/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2 - a*d*cos(d*x + c) - a*d)","A",0
64,1,217,0,0.913641," ","integrate(csc(d*x+c)^5/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, \cos\left(d x + c\right)^{4} + 6 \, \cos\left(d x + c\right)^{3} - 10 \, \cos\left(d x + c\right)^{2} - 3 \, {\left(\cos\left(d x + c\right)^{5} + \cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(\cos\left(d x + c\right)^{5} + \cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 10 \, \cos\left(d x + c\right) - 16}{96 \, {\left(a d \cos\left(d x + c\right)^{5} + a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{3} - 2 \, a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/96*(6*cos(d*x + c)^4 + 6*cos(d*x + c)^3 - 10*cos(d*x + c)^2 - 3*(cos(d*x + c)^5 + cos(d*x + c)^4 - 2*cos(d*x + c)^3 - 2*cos(d*x + c)^2 + cos(d*x + c) + 1)*log(1/2*cos(d*x + c) + 1/2) + 3*(cos(d*x + c)^5 + cos(d*x + c)^4 - 2*cos(d*x + c)^3 - 2*cos(d*x + c)^2 + cos(d*x + c) + 1)*log(-1/2*cos(d*x + c) + 1/2) - 10*cos(d*x + c) - 16)/(a*d*cos(d*x + c)^5 + a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^3 - 2*a*d*cos(d*x + c)^2 + a*d*cos(d*x + c) + a*d)","B",0
65,1,91,0,0.855471," ","integrate(sin(d*x+c)^8/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{105 \, d x - {\left(336 \, \cos\left(d x + c\right)^{7} - 384 \, \cos\left(d x + c\right)^{6} - 952 \, \cos\left(d x + c\right)^{5} + 1152 \, \cos\left(d x + c\right)^{4} + 826 \, \cos\left(d x + c\right)^{3} - 1152 \, \cos\left(d x + c\right)^{2} - 105 \, \cos\left(d x + c\right) + 384\right)} \sin\left(d x + c\right)}{2688 \, a d}"," ",0,"-1/2688*(105*d*x - (336*cos(d*x + c)^7 - 384*cos(d*x + c)^6 - 952*cos(d*x + c)^5 + 1152*cos(d*x + c)^4 + 826*cos(d*x + c)^3 - 1152*cos(d*x + c)^2 - 105*cos(d*x + c) + 384)*sin(d*x + c))/(a*d)","A",0
66,1,70,0,0.890729," ","integrate(sin(d*x+c)^6/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{15 \, d x + {\left(40 \, \cos\left(d x + c\right)^{5} - 48 \, \cos\left(d x + c\right)^{4} - 70 \, \cos\left(d x + c\right)^{3} + 96 \, \cos\left(d x + c\right)^{2} + 15 \, \cos\left(d x + c\right) - 48\right)} \sin\left(d x + c\right)}{240 \, a d}"," ",0,"-1/240*(15*d*x + (40*cos(d*x + c)^5 - 48*cos(d*x + c)^4 - 70*cos(d*x + c)^3 + 96*cos(d*x + c)^2 + 15*cos(d*x + c) - 48)*sin(d*x + c))/(a*d)","A",0
67,1,51,0,1.011963," ","integrate(sin(d*x+c)^4/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, d x - {\left(6 \, \cos\left(d x + c\right)^{3} - 8 \, \cos\left(d x + c\right)^{2} - 3 \, \cos\left(d x + c\right) + 8\right)} \sin\left(d x + c\right)}{24 \, a d}"," ",0,"-1/24*(3*d*x - (6*cos(d*x + c)^3 - 8*cos(d*x + c)^2 - 3*cos(d*x + c) + 8)*sin(d*x + c))/(a*d)","A",0
68,1,27,0,1.685191," ","integrate(sin(d*x+c)^2/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{d x + {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right)}{2 \, a d}"," ",0,"-1/2*(d*x + (cos(d*x + c) - 2)*sin(d*x + c))/(a*d)","A",0
69,1,41,0,0.710223," ","integrate(csc(d*x+c)^2/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right) + 1}{3 \, {\left(a d \cos\left(d x + c\right) + a d\right)} \sin\left(d x + c\right)}"," ",0,"-1/3*(cos(d*x + c)^2 + cos(d*x + c) + 1)/((a*d*cos(d*x + c) + a*d)*sin(d*x + c))","A",0
70,1,89,0,0.668350," ","integrate(csc(d*x+c)^4/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, \cos\left(d x + c\right)^{4} + 2 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)^{2} - 3 \, \cos\left(d x + c\right) - 3}{15 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2} - a d \cos\left(d x + c\right) - a d\right)} \sin\left(d x + c\right)}"," ",0,"-1/15*(2*cos(d*x + c)^4 + 2*cos(d*x + c)^3 - 3*cos(d*x + c)^2 - 3*cos(d*x + c) - 3)/((a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2 - a*d*cos(d*x + c) - a*d)*sin(d*x + c))","A",0
71,1,131,0,0.881301," ","integrate(csc(d*x+c)^6/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, \cos\left(d x + c\right)^{6} + 8 \, \cos\left(d x + c\right)^{5} - 20 \, \cos\left(d x + c\right)^{4} - 20 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)^{2} + 15 \, \cos\left(d x + c\right) + 15}{105 \, {\left(a d \cos\left(d x + c\right)^{5} + a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{3} - 2 \, a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right) + a d\right)} \sin\left(d x + c\right)}"," ",0,"-1/105*(8*cos(d*x + c)^6 + 8*cos(d*x + c)^5 - 20*cos(d*x + c)^4 - 20*cos(d*x + c)^3 + 15*cos(d*x + c)^2 + 15*cos(d*x + c) + 15)/((a*d*cos(d*x + c)^5 + a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^3 - 2*a*d*cos(d*x + c)^2 + a*d*cos(d*x + c) + a*d)*sin(d*x + c))","B",0
72,1,177,0,0.762965," ","integrate(csc(d*x+c)^8/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, \cos\left(d x + c\right)^{8} + 16 \, \cos\left(d x + c\right)^{7} - 56 \, \cos\left(d x + c\right)^{6} - 56 \, \cos\left(d x + c\right)^{5} + 70 \, \cos\left(d x + c\right)^{4} + 70 \, \cos\left(d x + c\right)^{3} - 35 \, \cos\left(d x + c\right)^{2} - 35 \, \cos\left(d x + c\right) - 35}{315 \, {\left(a d \cos\left(d x + c\right)^{7} + a d \cos\left(d x + c\right)^{6} - 3 \, a d \cos\left(d x + c\right)^{5} - 3 \, a d \cos\left(d x + c\right)^{4} + 3 \, a d \cos\left(d x + c\right)^{3} + 3 \, a d \cos\left(d x + c\right)^{2} - a d \cos\left(d x + c\right) - a d\right)} \sin\left(d x + c\right)}"," ",0,"-1/315*(16*cos(d*x + c)^8 + 16*cos(d*x + c)^7 - 56*cos(d*x + c)^6 - 56*cos(d*x + c)^5 + 70*cos(d*x + c)^4 + 70*cos(d*x + c)^3 - 35*cos(d*x + c)^2 - 35*cos(d*x + c) - 35)/((a*d*cos(d*x + c)^7 + a*d*cos(d*x + c)^6 - 3*a*d*cos(d*x + c)^5 - 3*a*d*cos(d*x + c)^4 + 3*a*d*cos(d*x + c)^3 + 3*a*d*cos(d*x + c)^2 - a*d*cos(d*x + c) - a*d)*sin(d*x + c))","B",0
73,1,219,0,0.603816," ","integrate(csc(d*x+c)^10/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{128 \, \cos\left(d x + c\right)^{10} + 128 \, \cos\left(d x + c\right)^{9} - 576 \, \cos\left(d x + c\right)^{8} - 576 \, \cos\left(d x + c\right)^{7} + 1008 \, \cos\left(d x + c\right)^{6} + 1008 \, \cos\left(d x + c\right)^{5} - 840 \, \cos\left(d x + c\right)^{4} - 840 \, \cos\left(d x + c\right)^{3} + 315 \, \cos\left(d x + c\right)^{2} + 315 \, \cos\left(d x + c\right) + 315}{3465 \, {\left(a d \cos\left(d x + c\right)^{9} + a d \cos\left(d x + c\right)^{8} - 4 \, a d \cos\left(d x + c\right)^{7} - 4 \, a d \cos\left(d x + c\right)^{6} + 6 \, a d \cos\left(d x + c\right)^{5} + 6 \, a d \cos\left(d x + c\right)^{4} - 4 \, a d \cos\left(d x + c\right)^{3} - 4 \, a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right) + a d\right)} \sin\left(d x + c\right)}"," ",0,"-1/3465*(128*cos(d*x + c)^10 + 128*cos(d*x + c)^9 - 576*cos(d*x + c)^8 - 576*cos(d*x + c)^7 + 1008*cos(d*x + c)^6 + 1008*cos(d*x + c)^5 - 840*cos(d*x + c)^4 - 840*cos(d*x + c)^3 + 315*cos(d*x + c)^2 + 315*cos(d*x + c) + 315)/((a*d*cos(d*x + c)^9 + a*d*cos(d*x + c)^8 - 4*a*d*cos(d*x + c)^7 - 4*a*d*cos(d*x + c)^6 + 6*a*d*cos(d*x + c)^5 + 6*a*d*cos(d*x + c)^4 - 4*a*d*cos(d*x + c)^3 - 4*a*d*cos(d*x + c)^2 + a*d*cos(d*x + c) + a*d)*sin(d*x + c))","B",0
74,1,89,0,1.511779," ","integrate(sin(d*x+c)^11/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{180 \, \cos\left(d x + c\right)^{11} - 396 \, \cos\left(d x + c\right)^{10} - 440 \, \cos\left(d x + c\right)^{9} + 1485 \, \cos\left(d x + c\right)^{8} - 1980 \, \cos\left(d x + c\right)^{6} + 792 \, \cos\left(d x + c\right)^{5} + 990 \, \cos\left(d x + c\right)^{4} - 660 \, \cos\left(d x + c\right)^{3}}{1980 \, a^{2} d}"," ",0,"1/1980*(180*cos(d*x + c)^11 - 396*cos(d*x + c)^10 - 440*cos(d*x + c)^9 + 1485*cos(d*x + c)^8 - 1980*cos(d*x + c)^6 + 792*cos(d*x + c)^5 + 990*cos(d*x + c)^4 - 660*cos(d*x + c)^3)/(a^2*d)","A",0
75,1,79,0,0.599391," ","integrate(sin(d*x+c)^9/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{140 \, \cos\left(d x + c\right)^{9} - 315 \, \cos\left(d x + c\right)^{8} - 180 \, \cos\left(d x + c\right)^{7} + 840 \, \cos\left(d x + c\right)^{6} - 252 \, \cos\left(d x + c\right)^{5} - 630 \, \cos\left(d x + c\right)^{4} + 420 \, \cos\left(d x + c\right)^{3}}{1260 \, a^{2} d}"," ",0,"-1/1260*(140*cos(d*x + c)^9 - 315*cos(d*x + c)^8 - 180*cos(d*x + c)^7 + 840*cos(d*x + c)^6 - 252*cos(d*x + c)^5 - 630*cos(d*x + c)^4 + 420*cos(d*x + c)^3)/(a^2*d)","A",0
76,1,49,0,0.748970," ","integrate(sin(d*x+c)^7/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{6 \, \cos\left(d x + c\right)^{7} - 14 \, \cos\left(d x + c\right)^{6} + 21 \, \cos\left(d x + c\right)^{4} - 14 \, \cos\left(d x + c\right)^{3}}{42 \, a^{2} d}"," ",0,"1/42*(6*cos(d*x + c)^7 - 14*cos(d*x + c)^6 + 21*cos(d*x + c)^4 - 14*cos(d*x + c)^3)/(a^2*d)","A",0
77,1,39,0,1.458420," ","integrate(sin(d*x+c)^5/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, \cos\left(d x + c\right)^{5} - 15 \, \cos\left(d x + c\right)^{4} + 10 \, \cos\left(d x + c\right)^{3}}{30 \, a^{2} d}"," ",0,"-1/30*(6*cos(d*x + c)^5 - 15*cos(d*x + c)^4 + 10*cos(d*x + c)^3)/(a^2*d)","A",0
78,1,48,0,0.453887," ","integrate(sin(d*x+c)^3/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)^{2} + 6 \, \cos\left(d x + c\right) - 6 \, \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{3 \, a^{2} d}"," ",0,"1/3*(cos(d*x + c)^3 - 3*cos(d*x + c)^2 + 6*cos(d*x + c) - 6*log(1/2*cos(d*x + c) + 1/2))/(a^2*d)","A",0
79,1,58,0,0.674191," ","integrate(sin(d*x+c)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right)^{2} - 2 \, {\left(\cos\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + \cos\left(d x + c\right) - 1}{a^{2} d \cos\left(d x + c\right) + a^{2} d}"," ",0,"-(cos(d*x + c)^2 - 2*(cos(d*x + c) + 1)*log(1/2*cos(d*x + c) + 1/2) + cos(d*x + c) - 1)/(a^2*d*cos(d*x + c) + a^2*d)","A",0
80,1,106,0,1.464494," ","integrate(csc(d*x+c)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 6 \, \cos\left(d x + c\right) + 4}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/8*((cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*log(1/2*cos(d*x + c) + 1/2) - (cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*log(-1/2*cos(d*x + c) + 1/2) + 6*cos(d*x + c) + 4)/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
81,1,60,0,0.657075," ","integrate(csc(d*x+c)^3/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, \cos\left(d x + c\right) + 1}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} + 2 \, a^{2} d \cos\left(d x + c\right)^{3} - 2 \, a^{2} d \cos\left(d x + c\right) - a^{2} d\right)}}"," ",0,"1/6*(2*cos(d*x + c) + 1)/(a^2*d*cos(d*x + c)^4 + 2*a^2*d*cos(d*x + c)^3 - 2*a^2*d*cos(d*x + c) - a^2*d)","A",0
82,1,283,0,0.641030," ","integrate(csc(d*x+c)^5/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, \cos\left(d x + c\right)^{5} + 12 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{3} - 20 \, \cos\left(d x + c\right)^{2} - 3 \, {\left(\cos\left(d x + c\right)^{6} + 2 \, \cos\left(d x + c\right)^{5} - \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(\cos\left(d x + c\right)^{6} + 2 \, \cos\left(d x + c\right)^{5} - \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 70 \, \cos\left(d x + c\right) + 32}{384 \, {\left(a^{2} d \cos\left(d x + c\right)^{6} + 2 \, a^{2} d \cos\left(d x + c\right)^{5} - a^{2} d \cos\left(d x + c\right)^{4} - 4 \, a^{2} d \cos\left(d x + c\right)^{3} - a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/384*(6*cos(d*x + c)^5 + 12*cos(d*x + c)^4 - 4*cos(d*x + c)^3 - 20*cos(d*x + c)^2 - 3*(cos(d*x + c)^6 + 2*cos(d*x + c)^5 - cos(d*x + c)^4 - 4*cos(d*x + c)^3 - cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*log(1/2*cos(d*x + c) + 1/2) + 3*(cos(d*x + c)^6 + 2*cos(d*x + c)^5 - cos(d*x + c)^4 - 4*cos(d*x + c)^3 - cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*log(-1/2*cos(d*x + c) + 1/2) + 70*cos(d*x + c) + 32)/(a^2*d*cos(d*x + c)^6 + 2*a^2*d*cos(d*x + c)^5 - a^2*d*cos(d*x + c)^4 - 4*a^2*d*cos(d*x + c)^3 - a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","B",0
83,1,90,0,0.698111," ","integrate(sin(d*x+c)^8/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{1155 \, d x + {\left(1680 \, \cos\left(d x + c\right)^{7} - 3840 \, \cos\left(d x + c\right)^{6} - 280 \, \cos\left(d x + c\right)^{5} + 6144 \, \cos\left(d x + c\right)^{4} - 3710 \, \cos\left(d x + c\right)^{3} - 768 \, \cos\left(d x + c\right)^{2} + 1155 \, \cos\left(d x + c\right) - 1536\right)} \sin\left(d x + c\right)}{13440 \, a^{2} d}"," ",0,"1/13440*(1155*d*x + (1680*cos(d*x + c)^7 - 3840*cos(d*x + c)^6 - 280*cos(d*x + c)^5 + 6144*cos(d*x + c)^4 - 3710*cos(d*x + c)^3 - 768*cos(d*x + c)^2 + 1155*cos(d*x + c) - 1536)*sin(d*x + c))/(a^2*d)","A",0
84,1,71,0,1.433682," ","integrate(sin(d*x+c)^6/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{45 \, d x - {\left(40 \, \cos\left(d x + c\right)^{5} - 96 \, \cos\left(d x + c\right)^{4} + 50 \, \cos\left(d x + c\right)^{3} + 32 \, \cos\left(d x + c\right)^{2} - 45 \, \cos\left(d x + c\right) + 64\right)} \sin\left(d x + c\right)}{240 \, a^{2} d}"," ",0,"1/240*(45*d*x - (40*cos(d*x + c)^5 - 96*cos(d*x + c)^4 + 50*cos(d*x + c)^3 + 32*cos(d*x + c)^2 - 45*cos(d*x + c) + 64)*sin(d*x + c))/(a^2*d)","A",0
85,1,50,0,0.994499," ","integrate(sin(d*x+c)^4/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{21 \, d x + {\left(6 \, \cos\left(d x + c\right)^{3} - 16 \, \cos\left(d x + c\right)^{2} + 21 \, \cos\left(d x + c\right) - 32\right)} \sin\left(d x + c\right)}{24 \, a^{2} d}"," ",0,"1/24*(21*d*x + (6*cos(d*x + c)^3 - 16*cos(d*x + c)^2 + 21*cos(d*x + c) - 32)*sin(d*x + c))/(a^2*d)","A",0
86,1,61,0,0.879849," ","integrate(sin(d*x+c)^2/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{5 \, d x \cos\left(d x + c\right) + 5 \, d x + {\left(\cos\left(d x + c\right)^{2} - 3 \, \cos\left(d x + c\right) - 8\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/2*(5*d*x*cos(d*x + c) + 5*d*x + (cos(d*x + c)^2 - 3*cos(d*x + c) - 8)*sin(d*x + c))/(a^2*d*cos(d*x + c) + a^2*d)","A",0
87,1,71,0,0.591420," ","integrate(csc(d*x+c)^2/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right)^{3} + 2 \, \cos\left(d x + c\right)^{2} + 8 \, \cos\left(d x + c\right) + 4}{15 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)} \sin\left(d x + c\right)}"," ",0,"-1/15*(cos(d*x + c)^3 + 2*cos(d*x + c)^2 + 8*cos(d*x + c) + 4)/((a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)*sin(d*x + c))","A",0
88,1,108,0,0.794312," ","integrate(csc(d*x+c)^4/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, \cos\left(d x + c\right)^{5} + 4 \, \cos\left(d x + c\right)^{4} - \cos\left(d x + c\right)^{3} - 6 \, \cos\left(d x + c\right)^{2} + 24 \, \cos\left(d x + c\right) + 12}{105 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} + 2 \, a^{2} d \cos\left(d x + c\right)^{3} - 2 \, a^{2} d \cos\left(d x + c\right) - a^{2} d\right)} \sin\left(d x + c\right)}"," ",0,"1/105*(2*cos(d*x + c)^5 + 4*cos(d*x + c)^4 - cos(d*x + c)^3 - 6*cos(d*x + c)^2 + 24*cos(d*x + c) + 12)/((a^2*d*cos(d*x + c)^4 + 2*a^2*d*cos(d*x + c)^3 - 2*a^2*d*cos(d*x + c) - a^2*d)*sin(d*x + c))","A",0
89,1,169,0,1.301924," ","integrate(csc(d*x+c)^6/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{8 \, \cos\left(d x + c\right)^{7} + 16 \, \cos\left(d x + c\right)^{6} - 12 \, \cos\left(d x + c\right)^{5} - 40 \, \cos\left(d x + c\right)^{4} - 5 \, \cos\left(d x + c\right)^{3} + 30 \, \cos\left(d x + c\right)^{2} - 40 \, \cos\left(d x + c\right) - 20}{315 \, {\left(a^{2} d \cos\left(d x + c\right)^{6} + 2 \, a^{2} d \cos\left(d x + c\right)^{5} - a^{2} d \cos\left(d x + c\right)^{4} - 4 \, a^{2} d \cos\left(d x + c\right)^{3} - a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)} \sin\left(d x + c\right)}"," ",0,"1/315*(8*cos(d*x + c)^7 + 16*cos(d*x + c)^6 - 12*cos(d*x + c)^5 - 40*cos(d*x + c)^4 - 5*cos(d*x + c)^3 + 30*cos(d*x + c)^2 - 40*cos(d*x + c) - 20)/((a^2*d*cos(d*x + c)^6 + 2*a^2*d*cos(d*x + c)^5 - a^2*d*cos(d*x + c)^4 - 4*a^2*d*cos(d*x + c)^3 - a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)*sin(d*x + c))","A",0
90,1,204,0,1.540646," ","integrate(csc(d*x+c)^8/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{16 \, \cos\left(d x + c\right)^{9} + 32 \, \cos\left(d x + c\right)^{8} - 40 \, \cos\left(d x + c\right)^{7} - 112 \, \cos\left(d x + c\right)^{6} + 14 \, \cos\left(d x + c\right)^{5} + 140 \, \cos\left(d x + c\right)^{4} + 35 \, \cos\left(d x + c\right)^{3} - 70 \, \cos\left(d x + c\right)^{2} + 56 \, \cos\left(d x + c\right) + 28}{693 \, {\left(a^{2} d \cos\left(d x + c\right)^{8} + 2 \, a^{2} d \cos\left(d x + c\right)^{7} - 2 \, a^{2} d \cos\left(d x + c\right)^{6} - 6 \, a^{2} d \cos\left(d x + c\right)^{5} + 6 \, a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} - 2 \, a^{2} d \cos\left(d x + c\right) - a^{2} d\right)} \sin\left(d x + c\right)}"," ",0,"1/693*(16*cos(d*x + c)^9 + 32*cos(d*x + c)^8 - 40*cos(d*x + c)^7 - 112*cos(d*x + c)^6 + 14*cos(d*x + c)^5 + 140*cos(d*x + c)^4 + 35*cos(d*x + c)^3 - 70*cos(d*x + c)^2 + 56*cos(d*x + c) + 28)/((a^2*d*cos(d*x + c)^8 + 2*a^2*d*cos(d*x + c)^7 - 2*a^2*d*cos(d*x + c)^6 - 6*a^2*d*cos(d*x + c)^5 + 6*a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 - 2*a^2*d*cos(d*x + c) - a^2*d)*sin(d*x + c))","A",0
91,1,89,0,0.740675," ","integrate(sin(d*x+c)^11/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{2520 \, \cos\left(d x + c\right)^{11} - 8316 \, \cos\left(d x + c\right)^{10} + 3080 \, \cos\left(d x + c\right)^{9} + 17325 \, \cos\left(d x + c\right)^{8} - 19800 \, \cos\left(d x + c\right)^{7} - 4620 \, \cos\left(d x + c\right)^{6} + 16632 \, \cos\left(d x + c\right)^{5} - 6930 \, \cos\left(d x + c\right)^{4}}{27720 \, a^{3} d}"," ",0,"1/27720*(2520*cos(d*x + c)^11 - 8316*cos(d*x + c)^10 + 3080*cos(d*x + c)^9 + 17325*cos(d*x + c)^8 - 19800*cos(d*x + c)^7 - 4620*cos(d*x + c)^6 + 16632*cos(d*x + c)^5 - 6930*cos(d*x + c)^4)/(a^3*d)","A",0
92,1,69,0,1.295317," ","integrate(sin(d*x+c)^9/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{280 \, \cos\left(d x + c\right)^{9} - 945 \, \cos\left(d x + c\right)^{8} + 720 \, \cos\left(d x + c\right)^{7} + 840 \, \cos\left(d x + c\right)^{6} - 1512 \, \cos\left(d x + c\right)^{5} + 630 \, \cos\left(d x + c\right)^{4}}{2520 \, a^{3} d}"," ",0,"-1/2520*(280*cos(d*x + c)^9 - 945*cos(d*x + c)^8 + 720*cos(d*x + c)^7 + 840*cos(d*x + c)^6 - 1512*cos(d*x + c)^5 + 630*cos(d*x + c)^4)/(a^3*d)","A",0
93,1,49,0,0.670420," ","integrate(sin(d*x+c)^7/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{20 \, \cos\left(d x + c\right)^{7} - 70 \, \cos\left(d x + c\right)^{6} + 84 \, \cos\left(d x + c\right)^{5} - 35 \, \cos\left(d x + c\right)^{4}}{140 \, a^{3} d}"," ",0,"1/140*(20*cos(d*x + c)^7 - 70*cos(d*x + c)^6 + 84*cos(d*x + c)^5 - 35*cos(d*x + c)^4)/(a^3*d)","A",0
94,1,70,0,0.818898," ","integrate(sin(d*x+c)^5/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{12 \, \cos\left(d x + c\right)^{5} - 45 \, \cos\left(d x + c\right)^{4} + 80 \, \cos\left(d x + c\right)^{3} - 120 \, \cos\left(d x + c\right)^{2} + 240 \, \cos\left(d x + c\right) - 240 \, \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{60 \, a^{3} d}"," ",0,"-1/60*(12*cos(d*x + c)^5 - 45*cos(d*x + c)^4 + 80*cos(d*x + c)^3 - 120*cos(d*x + c)^2 + 240*cos(d*x + c) - 240*log(1/2*cos(d*x + c) + 1/2))/(a^3*d)","A",0
95,1,82,0,0.796076," ","integrate(sin(d*x+c)^3/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, \cos\left(d x + c\right)^{4} - 14 \, \cos\left(d x + c\right)^{3} + 42 \, \cos\left(d x + c\right)^{2} - 84 \, {\left(\cos\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 69 \, \cos\left(d x + c\right) - 15}{12 \, {\left(a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/12*(4*cos(d*x + c)^4 - 14*cos(d*x + c)^3 + 42*cos(d*x + c)^2 - 84*(cos(d*x + c) + 1)*log(1/2*cos(d*x + c) + 1/2) + 69*cos(d*x + c) - 15)/(a^3*d*cos(d*x + c) + a^3*d)","A",0
96,1,96,0,0.563385," ","integrate(sin(d*x+c)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, \cos\left(d x + c\right)^{3} + 4 \, \cos\left(d x + c\right)^{2} - 6 \, {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 4 \, \cos\left(d x + c\right) - 5}{2 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} + 2 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/2*(2*cos(d*x + c)^3 + 4*cos(d*x + c)^2 - 6*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*log(1/2*cos(d*x + c) + 1/2) - 4*cos(d*x + c) - 5)/(a^3*d*cos(d*x + c)^2 + 2*a^3*d*cos(d*x + c) + a^3*d)","A",0
97,1,151,0,0.669888," ","integrate(csc(d*x+c)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{42 \, \cos\left(d x + c\right)^{2} + 3 \, {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 54 \, \cos\left(d x + c\right) + 20}{48 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/48*(42*cos(d*x + c)^2 + 3*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*log(1/2*cos(d*x + c) + 1/2) - 3*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*log(-1/2*cos(d*x + c) + 1/2) + 54*cos(d*x + c) + 20)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","B",0
98,1,240,0,0.762869," ","integrate(csc(d*x+c)^3/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{6 \, \cos\left(d x + c\right)^{4} + 18 \, \cos\left(d x + c\right)^{3} - 50 \, \cos\left(d x + c\right)^{2} - 3 \, {\left(\cos\left(d x + c\right)^{5} + 3 \, \cos\left(d x + c\right)^{4} + 2 \, \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2} - 3 \, \cos\left(d x + c\right) - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(\cos\left(d x + c\right)^{5} + 3 \, \cos\left(d x + c\right)^{4} + 2 \, \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2} - 3 \, \cos\left(d x + c\right) - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 54 \, \cos\left(d x + c\right) - 16}{192 \, {\left(a^{3} d \cos\left(d x + c\right)^{5} + 3 \, a^{3} d \cos\left(d x + c\right)^{4} + 2 \, a^{3} d \cos\left(d x + c\right)^{3} - 2 \, a^{3} d \cos\left(d x + c\right)^{2} - 3 \, a^{3} d \cos\left(d x + c\right) - a^{3} d\right)}}"," ",0,"-1/192*(6*cos(d*x + c)^4 + 18*cos(d*x + c)^3 - 50*cos(d*x + c)^2 - 3*(cos(d*x + c)^5 + 3*cos(d*x + c)^4 + 2*cos(d*x + c)^3 - 2*cos(d*x + c)^2 - 3*cos(d*x + c) - 1)*log(1/2*cos(d*x + c) + 1/2) + 3*(cos(d*x + c)^5 + 3*cos(d*x + c)^4 + 2*cos(d*x + c)^3 - 2*cos(d*x + c)^2 - 3*cos(d*x + c) - 1)*log(-1/2*cos(d*x + c) + 1/2) - 54*cos(d*x + c) - 16)/(a^3*d*cos(d*x + c)^5 + 3*a^3*d*cos(d*x + c)^4 + 2*a^3*d*cos(d*x + c)^3 - 2*a^3*d*cos(d*x + c)^2 - 3*a^3*d*cos(d*x + c) - a^3*d)","B",0
99,1,317,0,0.854820," ","integrate(csc(d*x+c)^5/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{30 \, \cos\left(d x + c\right)^{6} + 90 \, \cos\left(d x + c\right)^{5} + 40 \, \cos\left(d x + c\right)^{4} - 120 \, \cos\left(d x + c\right)^{3} + 122 \, \cos\left(d x + c\right)^{2} - 15 \, {\left(\cos\left(d x + c\right)^{7} + 3 \, \cos\left(d x + c\right)^{6} + \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{4} - 5 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left(\cos\left(d x + c\right)^{7} + 3 \, \cos\left(d x + c\right)^{6} + \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{4} - 5 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 126 \, \cos\left(d x + c\right) + 32}{1280 \, {\left(a^{3} d \cos\left(d x + c\right)^{7} + 3 \, a^{3} d \cos\left(d x + c\right)^{6} + a^{3} d \cos\left(d x + c\right)^{5} - 5 \, a^{3} d \cos\left(d x + c\right)^{4} - 5 \, a^{3} d \cos\left(d x + c\right)^{3} + a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/1280*(30*cos(d*x + c)^6 + 90*cos(d*x + c)^5 + 40*cos(d*x + c)^4 - 120*cos(d*x + c)^3 + 122*cos(d*x + c)^2 - 15*(cos(d*x + c)^7 + 3*cos(d*x + c)^6 + cos(d*x + c)^5 - 5*cos(d*x + c)^4 - 5*cos(d*x + c)^3 + cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*log(1/2*cos(d*x + c) + 1/2) + 15*(cos(d*x + c)^7 + 3*cos(d*x + c)^6 + cos(d*x + c)^5 - 5*cos(d*x + c)^4 - 5*cos(d*x + c)^3 + cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*log(-1/2*cos(d*x + c) + 1/2) + 126*cos(d*x + c) + 32)/(a^3*d*cos(d*x + c)^7 + 3*a^3*d*cos(d*x + c)^6 + a^3*d*cos(d*x + c)^5 - 5*a^3*d*cos(d*x + c)^4 - 5*a^3*d*cos(d*x + c)^3 + a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","B",0
100,1,91,0,0.684704," ","integrate(sin(d*x+c)^8/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3045 \, d x - {\left(1680 \, \cos\left(d x + c\right)^{7} - 5760 \, \cos\left(d x + c\right)^{6} + 6440 \, \cos\left(d x + c\right)^{5} - 1536 \, \cos\left(d x + c\right)^{4} - 2030 \, \cos\left(d x + c\right)^{3} + 2432 \, \cos\left(d x + c\right)^{2} - 3045 \, \cos\left(d x + c\right) + 4864\right)} \sin\left(d x + c\right)}{13440 \, a^{3} d}"," ",0,"-1/13440*(3045*d*x - (1680*cos(d*x + c)^7 - 5760*cos(d*x + c)^6 + 6440*cos(d*x + c)^5 - 1536*cos(d*x + c)^4 - 2030*cos(d*x + c)^3 + 2432*cos(d*x + c)^2 - 3045*cos(d*x + c) + 4864)*sin(d*x + c))/(a^3*d)","A",0
101,1,70,0,0.721456," ","integrate(sin(d*x+c)^6/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{345 \, d x + {\left(40 \, \cos\left(d x + c\right)^{5} - 144 \, \cos\left(d x + c\right)^{4} + 230 \, \cos\left(d x + c\right)^{3} - 272 \, \cos\left(d x + c\right)^{2} + 345 \, \cos\left(d x + c\right) - 544\right)} \sin\left(d x + c\right)}{240 \, a^{3} d}"," ",0,"-1/240*(345*d*x + (40*cos(d*x + c)^5 - 144*cos(d*x + c)^4 + 230*cos(d*x + c)^3 - 272*cos(d*x + c)^2 + 345*cos(d*x + c) - 544)*sin(d*x + c))/(a^3*d)","A",0
102,1,83,0,0.636505," ","integrate(sin(d*x+c)^4/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{51 \, d x \cos\left(d x + c\right) + 51 \, d x + {\left(2 \, \cos\left(d x + c\right)^{4} - 6 \, \cos\left(d x + c\right)^{3} + 11 \, \cos\left(d x + c\right)^{2} - 29 \, \cos\left(d x + c\right) - 80\right)} \sin\left(d x + c\right)}{8 \, {\left(a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/8*(51*d*x*cos(d*x + c) + 51*d*x + (2*cos(d*x + c)^4 - 6*cos(d*x + c)^3 + 11*cos(d*x + c)^2 - 29*cos(d*x + c) - 80)*sin(d*x + c))/(a^3*d*cos(d*x + c) + a^3*d)","A",0
103,1,99,0,0.714979," ","integrate(sin(d*x+c)^2/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{33 \, d x \cos\left(d x + c\right)^{2} + 66 \, d x \cos\left(d x + c\right) + 33 \, d x + {\left(3 \, \cos\left(d x + c\right)^{3} - 12 \, \cos\left(d x + c\right)^{2} - 71 \, \cos\left(d x + c\right) - 52\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} + 2 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/6*(33*d*x*cos(d*x + c)^2 + 66*d*x*cos(d*x + c) + 33*d*x + (3*cos(d*x + c)^3 - 12*cos(d*x + c)^2 - 71*cos(d*x + c) - 52)*sin(d*x + c))/(a^3*d*cos(d*x + c)^2 + 2*a^3*d*cos(d*x + c) + a^3*d)","A",0
104,1,95,0,0.548603," ","integrate(csc(d*x+c)^2/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{\cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{3} - 15 \, \cos\left(d x + c\right)^{2} - 18 \, \cos\left(d x + c\right) - 6}{35 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)} \sin\left(d x + c\right)}"," ",0,"1/35*(cos(d*x + c)^4 + 3*cos(d*x + c)^3 - 15*cos(d*x + c)^2 - 18*cos(d*x + c) - 6)/((a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)*sin(d*x + c))","A",0
105,1,146,0,0.699411," ","integrate(csc(d*x+c)^4/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, \cos\left(d x + c\right)^{6} + 6 \, \cos\left(d x + c\right)^{5} + 3 \, \cos\left(d x + c\right)^{4} - 7 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 6 \, \cos\left(d x + c\right) + 2}{45 \, {\left(a^{3} d \cos\left(d x + c\right)^{5} + 3 \, a^{3} d \cos\left(d x + c\right)^{4} + 2 \, a^{3} d \cos\left(d x + c\right)^{3} - 2 \, a^{3} d \cos\left(d x + c\right)^{2} - 3 \, a^{3} d \cos\left(d x + c\right) - a^{3} d\right)} \sin\left(d x + c\right)}"," ",0,"1/45*(2*cos(d*x + c)^6 + 6*cos(d*x + c)^5 + 3*cos(d*x + c)^4 - 7*cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 6*cos(d*x + c) + 2)/((a^3*d*cos(d*x + c)^5 + 3*a^3*d*cos(d*x + c)^4 + 2*a^3*d*cos(d*x + c)^3 - 2*a^3*d*cos(d*x + c)^2 - 3*a^3*d*cos(d*x + c) - a^3*d)*sin(d*x + c))","A",0
106,1,191,0,0.677340," ","integrate(csc(d*x+c)^6/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{104 \, \cos\left(d x + c\right)^{8} + 312 \, \cos\left(d x + c\right)^{7} + 52 \, \cos\left(d x + c\right)^{6} - 676 \, \cos\left(d x + c\right)^{5} - 585 \, \cos\left(d x + c\right)^{4} + 325 \, \cos\left(d x + c\right)^{3} - 25 \, \cos\left(d x + c\right)^{2} - 150 \, \cos\left(d x + c\right) - 50}{3465 \, {\left(a^{3} d \cos\left(d x + c\right)^{7} + 3 \, a^{3} d \cos\left(d x + c\right)^{6} + a^{3} d \cos\left(d x + c\right)^{5} - 5 \, a^{3} d \cos\left(d x + c\right)^{4} - 5 \, a^{3} d \cos\left(d x + c\right)^{3} + a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)} \sin\left(d x + c\right)}"," ",0,"1/3465*(104*cos(d*x + c)^8 + 312*cos(d*x + c)^7 + 52*cos(d*x + c)^6 - 676*cos(d*x + c)^5 - 585*cos(d*x + c)^4 + 325*cos(d*x + c)^3 - 25*cos(d*x + c)^2 - 150*cos(d*x + c) - 50)/((a^3*d*cos(d*x + c)^7 + 3*a^3*d*cos(d*x + c)^6 + a^3*d*cos(d*x + c)^5 - 5*a^3*d*cos(d*x + c)^4 - 5*a^3*d*cos(d*x + c)^3 + a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)*sin(d*x + c))","A",0
107,1,214,0,0.644929," ","integrate(csc(d*x+c)^8/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{304 \, \cos\left(d x + c\right)^{10} + 912 \, \cos\left(d x + c\right)^{9} - 152 \, \cos\left(d x + c\right)^{8} - 2888 \, \cos\left(d x + c\right)^{7} - 1862 \, \cos\left(d x + c\right)^{6} + 2926 \, \cos\left(d x + c\right)^{5} + 3325 \, \cos\left(d x + c\right)^{4} - 665 \, \cos\left(d x + c\right)^{3} - 35 \, \cos\left(d x + c\right)^{2} + 210 \, \cos\left(d x + c\right) + 70}{15015 \, {\left(a^{3} d \cos\left(d x + c\right)^{9} + 3 \, a^{3} d \cos\left(d x + c\right)^{8} - 8 \, a^{3} d \cos\left(d x + c\right)^{6} - 6 \, a^{3} d \cos\left(d x + c\right)^{5} + 6 \, a^{3} d \cos\left(d x + c\right)^{4} + 8 \, a^{3} d \cos\left(d x + c\right)^{3} - 3 \, a^{3} d \cos\left(d x + c\right) - a^{3} d\right)} \sin\left(d x + c\right)}"," ",0,"1/15015*(304*cos(d*x + c)^10 + 912*cos(d*x + c)^9 - 152*cos(d*x + c)^8 - 2888*cos(d*x + c)^7 - 1862*cos(d*x + c)^6 + 2926*cos(d*x + c)^5 + 3325*cos(d*x + c)^4 - 665*cos(d*x + c)^3 - 35*cos(d*x + c)^2 + 210*cos(d*x + c) + 70)/((a^3*d*cos(d*x + c)^9 + 3*a^3*d*cos(d*x + c)^8 - 8*a^3*d*cos(d*x + c)^6 - 6*a^3*d*cos(d*x + c)^5 + 6*a^3*d*cos(d*x + c)^4 + 8*a^3*d*cos(d*x + c)^3 - 3*a^3*d*cos(d*x + c) - a^3*d)*sin(d*x + c))","A",0
108,0,0,0,0.970006," ","integrate((a+a*sec(d*x+c))*(e*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a e^{2} \cos\left(d x + c\right)^{2} - a e^{2} + {\left(a e^{2} \cos\left(d x + c\right)^{2} - a e^{2}\right)} \sec\left(d x + c\right)\right)} \sqrt{e \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-(a*e^2*cos(d*x + c)^2 - a*e^2 + (a*e^2*cos(d*x + c)^2 - a*e^2)*sec(d*x + c))*sqrt(e*sin(d*x + c)), x)","F",0
109,0,0,0,1.888028," ","integrate((a+a*sec(d*x+c))*(e*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e \sec\left(d x + c\right) + a e\right)} \sqrt{e \sin\left(d x + c\right)} \sin\left(d x + c\right), x\right)"," ",0,"integral((a*e*sec(d*x + c) + a*e)*sqrt(e*sin(d*x + c))*sin(d*x + c), x)","F",0
110,0,0,0,1.059213," ","integrate((a+a*sec(d*x+c))*(e*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)} \sqrt{e \sin\left(d x + c\right)}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)*sqrt(e*sin(d*x + c)), x)","F",0
111,0,0,0,0.735088," ","integrate((a+a*sec(d*x+c))/(e*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{e \sin\left(d x + c\right)}}{e \sin\left(d x + c\right)}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)*sqrt(e*sin(d*x + c))/(e*sin(d*x + c)), x)","F",0
112,0,0,0,1.128000," ","integrate((a+a*sec(d*x+c))/(e*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{e \sin\left(d x + c\right)}}{e^{2} \cos\left(d x + c\right)^{2} - e^{2}}, x\right)"," ",0,"integral(-(a*sec(d*x + c) + a)*sqrt(e*sin(d*x + c))/(e^2*cos(d*x + c)^2 - e^2), x)","F",0
113,0,0,0,0.802222," ","integrate((a+a*sec(d*x+c))/(e*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{e \sin\left(d x + c\right)}}{{\left(e^{3} \cos\left(d x + c\right)^{2} - e^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-(a*sec(d*x + c) + a)*sqrt(e*sin(d*x + c))/((e^3*cos(d*x + c)^2 - e^3)*sin(d*x + c)), x)","F",0
114,0,0,0,1.907589," ","integrate((a+a*sec(d*x+c))^2*(e*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} e^{2} \cos\left(d x + c\right)^{2} - a^{2} e^{2} + {\left(a^{2} e^{2} \cos\left(d x + c\right)^{2} - a^{2} e^{2}\right)} \sec\left(d x + c\right)^{2} + 2 \, {\left(a^{2} e^{2} \cos\left(d x + c\right)^{2} - a^{2} e^{2}\right)} \sec\left(d x + c\right)\right)} \sqrt{e \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-(a^2*e^2*cos(d*x + c)^2 - a^2*e^2 + (a^2*e^2*cos(d*x + c)^2 - a^2*e^2)*sec(d*x + c)^2 + 2*(a^2*e^2*cos(d*x + c)^2 - a^2*e^2)*sec(d*x + c))*sqrt(e*sin(d*x + c)), x)","F",0
115,0,0,0,0.982904," ","integrate((a+a*sec(d*x+c))^2*(e*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} e \sec\left(d x + c\right)^{2} + 2 \, a^{2} e \sec\left(d x + c\right) + a^{2} e\right)} \sqrt{e \sin\left(d x + c\right)} \sin\left(d x + c\right), x\right)"," ",0,"integral((a^2*e*sec(d*x + c)^2 + 2*a^2*e*sec(d*x + c) + a^2*e)*sqrt(e*sin(d*x + c))*sin(d*x + c), x)","F",0
116,0,0,0,1.940533," ","integrate((a+a*sec(d*x+c))^2*(e*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}\right)} \sqrt{e \sin\left(d x + c\right)}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)*sqrt(e*sin(d*x + c)), x)","F",0
117,0,0,0,0.742768," ","integrate((a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}\right)} \sqrt{e \sin\left(d x + c\right)}}{e \sin\left(d x + c\right)}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)*sqrt(e*sin(d*x + c))/(e*sin(d*x + c)), x)","F",0
118,0,0,0,0.739822," ","integrate((a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}\right)} \sqrt{e \sin\left(d x + c\right)}}{e^{2} \cos\left(d x + c\right)^{2} - e^{2}}, x\right)"," ",0,"integral(-(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)*sqrt(e*sin(d*x + c))/(e^2*cos(d*x + c)^2 - e^2), x)","F",0
119,0,0,0,0.847192," ","integrate((a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}\right)} \sqrt{e \sin\left(d x + c\right)}}{{\left(e^{3} \cos\left(d x + c\right)^{2} - e^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)*sqrt(e*sin(d*x + c))/((e^3*cos(d*x + c)^2 - e^3)*sin(d*x + c)), x)","F",0
120,0,0,0,1.125038," ","integrate((e*sin(d*x+c))^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(e^{3} \cos\left(d x + c\right)^{2} - e^{3}\right)} \sqrt{e \sin\left(d x + c\right)} \sin\left(d x + c\right)}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(-(e^3*cos(d*x + c)^2 - e^3)*sqrt(e*sin(d*x + c))*sin(d*x + c)/(a*sec(d*x + c) + a), x)","F",0
121,0,0,0,0.776018," ","integrate((e*sin(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(e^{2} \cos\left(d x + c\right)^{2} - e^{2}\right)} \sqrt{e \sin\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(-(e^2*cos(d*x + c)^2 - e^2)*sqrt(e*sin(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
122,0,0,0,0.668240," ","integrate((e*sin(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \sin\left(d x + c\right)} e \sin\left(d x + c\right)}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(e*sin(d*x + c))*e*sin(d*x + c)/(a*sec(d*x + c) + a), x)","F",0
123,0,0,0,0.705681," ","integrate((e*sin(d*x+c))^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \sin\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(e*sin(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
124,0,0,0,0.645205," ","integrate(1/(a+a*sec(d*x+c))/(e*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \sin\left(d x + c\right)}}{{\left(a e \sec\left(d x + c\right) + a e\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*sin(d*x + c))/((a*e*sec(d*x + c) + a*e)*sin(d*x + c)), x)","F",0
125,0,0,0,0.541267," ","integrate(1/(a+a*sec(d*x+c))/(e*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \sin\left(d x + c\right)}}{a e^{2} \cos\left(d x + c\right)^{2} - a e^{2} + {\left(a e^{2} \cos\left(d x + c\right)^{2} - a e^{2}\right)} \sec\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(e*sin(d*x + c))/(a*e^2*cos(d*x + c)^2 - a*e^2 + (a*e^2*cos(d*x + c)^2 - a*e^2)*sec(d*x + c)), x)","F",0
126,0,0,0,1.465172," ","integrate(1/(a+a*sec(d*x+c))/(e*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \sin\left(d x + c\right)}}{{\left(a e^{3} \cos\left(d x + c\right)^{2} - a e^{3} + {\left(a e^{3} \cos\left(d x + c\right)^{2} - a e^{3}\right)} \sec\left(d x + c\right)\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(e*sin(d*x + c))/((a*e^3*cos(d*x + c)^2 - a*e^3 + (a*e^3*cos(d*x + c)^2 - a*e^3)*sec(d*x + c))*sin(d*x + c)), x)","F",0
127,0,0,0,0.621340," ","integrate((e*sin(d*x+c))^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(e^{3} \cos\left(d x + c\right)^{2} - e^{3}\right)} \sqrt{e \sin\left(d x + c\right)} \sin\left(d x + c\right)}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(-(e^3*cos(d*x + c)^2 - e^3)*sqrt(e*sin(d*x + c))*sin(d*x + c)/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
128,0,0,0,0.456051," ","integrate((e*sin(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(e^{2} \cos\left(d x + c\right)^{2} - e^{2}\right)} \sqrt{e \sin\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(-(e^2*cos(d*x + c)^2 - e^2)*sqrt(e*sin(d*x + c))/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
129,0,0,0,0.513361," ","integrate((e*sin(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \sin\left(d x + c\right)} e \sin\left(d x + c\right)}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(e*sin(d*x + c))*e*sin(d*x + c)/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
130,0,0,0,0.520013," ","integrate((e*sin(d*x+c))^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \sin\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(e*sin(d*x + c))/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
131,0,0,0,0.782690," ","integrate(1/(a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \sin\left(d x + c\right)}}{{\left(a^{2} e \sec\left(d x + c\right)^{2} + 2 \, a^{2} e \sec\left(d x + c\right) + a^{2} e\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*sin(d*x + c))/((a^2*e*sec(d*x + c)^2 + 2*a^2*e*sec(d*x + c) + a^2*e)*sin(d*x + c)), x)","F",0
132,0,0,0,0.572074," ","integrate(1/(a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \sin\left(d x + c\right)}}{a^{2} e^{2} \cos\left(d x + c\right)^{2} - a^{2} e^{2} + {\left(a^{2} e^{2} \cos\left(d x + c\right)^{2} - a^{2} e^{2}\right)} \sec\left(d x + c\right)^{2} + 2 \, {\left(a^{2} e^{2} \cos\left(d x + c\right)^{2} - a^{2} e^{2}\right)} \sec\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(e*sin(d*x + c))/(a^2*e^2*cos(d*x + c)^2 - a^2*e^2 + (a^2*e^2*cos(d*x + c)^2 - a^2*e^2)*sec(d*x + c)^2 + 2*(a^2*e^2*cos(d*x + c)^2 - a^2*e^2)*sec(d*x + c)), x)","F",0
133,0,0,0,0.588162," ","integrate(1/(a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \sin\left(d x + c\right)}}{{\left(a^{2} e^{3} \cos\left(d x + c\right)^{2} - a^{2} e^{3} + {\left(a^{2} e^{3} \cos\left(d x + c\right)^{2} - a^{2} e^{3}\right)} \sec\left(d x + c\right)^{2} + 2 \, {\left(a^{2} e^{3} \cos\left(d x + c\right)^{2} - a^{2} e^{3}\right)} \sec\left(d x + c\right)\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(e*sin(d*x + c))/((a^2*e^3*cos(d*x + c)^2 - a^2*e^3 + (a^2*e^3*cos(d*x + c)^2 - a^2*e^3)*sec(d*x + c)^2 + 2*(a^2*e^3*cos(d*x + c)^2 - a^2*e^3)*sec(d*x + c))*sin(d*x + c)), x)","F",0
134,0,0,0,0.650700," ","integrate((a+a*sec(d*x+c))^3*(e*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}\right)} \left(e \sin\left(d x + c\right)\right)^{m}, x\right)"," ",0,"integral((a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3)*(e*sin(d*x + c))^m, x)","F",0
135,0,0,0,0.640316," ","integrate((a+a*sec(d*x+c))^2*(e*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}\right)} \left(e \sin\left(d x + c\right)\right)^{m}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)*(e*sin(d*x + c))^m, x)","F",0
136,0,0,0,0.623526," ","integrate((a+a*sec(d*x+c))*(e*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{m}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)*(e*sin(d*x + c))^m, x)","F",0
137,0,0,0,0.858966," ","integrate((e*sin(d*x+c))^m/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \sin\left(d x + c\right)\right)^{m}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((e*sin(d*x + c))^m/(a*sec(d*x + c) + a), x)","F",0
138,0,0,0,0.945811," ","integrate((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \sin\left(d x + c\right)\right)^{m}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((e*sin(d*x + c))^m/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
139,0,0,0,0.876329," ","integrate((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \sin\left(d x + c\right)\right)^{m}}{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((e*sin(d*x + c))^m/(a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3), x)","F",0
140,0,0,0,1.499333," ","integrate((a+a*sec(d*x+c))^(3/2)*(e*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \left(e \sin\left(d x + c\right)\right)^{m}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)^(3/2)*(e*sin(d*x + c))^m, x)","F",0
141,0,0,0,0.556746," ","integrate((a+a*sec(d*x+c))^(1/2)*(e*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \sec\left(d x + c\right) + a} \left(e \sin\left(d x + c\right)\right)^{m}, x\right)"," ",0,"integral(sqrt(a*sec(d*x + c) + a)*(e*sin(d*x + c))^m, x)","F",0
142,0,0,0,0.676424," ","integrate((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \sin\left(d x + c\right)\right)^{m}}{\sqrt{a \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((e*sin(d*x + c))^m/sqrt(a*sec(d*x + c) + a), x)","F",0
143,0,0,0,1.432470," ","integrate((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sec\left(d x + c\right) + a} \left(e \sin\left(d x + c\right)\right)^{m}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(a*sec(d*x + c) + a)*(e*sin(d*x + c))^m/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
144,0,0,0,0.559296," ","integrate((a+a*sec(d*x+c))^n*(e*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)}^{n} \left(e \sin\left(d x + c\right)\right)^{m}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)^n*(e*sin(d*x + c))^m, x)","F",0
145,0,0,0,0.625259," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^7,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right), x\right)"," ",0,"integral(-(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*(a*sec(d*x + c) + a)^n*sin(d*x + c), x)","F",0
146,0,0,0,0.868327," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^5,x, algorithm=""fricas"")","{\rm integral}\left({\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right), x\right)"," ",0,"integral((cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*(a*sec(d*x + c) + a)^n*sin(d*x + c), x)","F",0
147,0,0,0,0.603459," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(d x + c\right)^{2} - 1\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right), x\right)"," ",0,"integral(-(cos(d*x + c)^2 - 1)*(a*sec(d*x + c) + a)^n*sin(d*x + c), x)","F",0
148,0,0,0,1.255075," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right), x\right)"," ",0,"integral((a*sec(d*x + c) + a)^n*sin(d*x + c), x)","F",0
149,0,0,0,0.772987," ","integrate(csc(d*x+c)*(a+a*sec(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right), x\right)"," ",0,"integral((a*sec(d*x + c) + a)^n*csc(d*x + c), x)","F",0
150,0,0,0,1.886778," ","integrate(csc(d*x+c)^3*(a+a*sec(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{3}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)^n*csc(d*x + c)^3, x)","F",0
151,0,0,0,0.500521," ","integrate(csc(d*x+c)^5*(a+a*sec(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{5}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)^n*csc(d*x + c)^5, x)","F",0
152,0,0,0,2.276975," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral((cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*(a*sec(d*x + c) + a)^n, x)","F",0
153,0,0,0,1.264665," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(d x + c\right)^{2} - 1\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral(-(cos(d*x + c)^2 - 1)*(a*sec(d*x + c) + a)^n, x)","F",0
154,0,0,0,0.622102," ","integrate(csc(d*x+c)^2*(a+a*sec(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{2}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)^n*csc(d*x + c)^2, x)","F",0
155,0,0,0,0.687999," ","integrate(csc(d*x+c)^4*(a+a*sec(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{4}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)^n*csc(d*x + c)^4, x)","F",0
156,0,0,0,0.650754," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)^n*sin(d*x + c)^(3/2), x)","F",0
157,0,0,0,0.494101," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)}^{n} \sqrt{\sin\left(d x + c\right)}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)^n*sqrt(sin(d*x + c)), x)","F",0
158,0,0,0,0.519315," ","integrate((a+a*sec(d*x+c))^n/sin(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a \sec\left(d x + c\right) + a\right)}^{n}}{\sqrt{\sin\left(d x + c\right)}}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)^n/sqrt(sin(d*x + c)), x)","F",0
159,0,0,0,0.636642," ","integrate((a+a*sec(d*x+c))^n/sin(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a \sec\left(d x + c\right) + a\right)}^{n} \sqrt{\sin\left(d x + c\right)}}{\cos\left(d x + c\right)^{2} - 1}, x\right)"," ",0,"integral(-(a*sec(d*x + c) + a)^n*sqrt(sin(d*x + c))/(cos(d*x + c)^2 - 1), x)","F",0
160,1,93,0,0.727826," ","integrate((a+b*sec(d*x+c))*sin(d*x+c)^7,x, algorithm=""fricas"")","\frac{60 \, a \cos\left(d x + c\right)^{7} + 70 \, b \cos\left(d x + c\right)^{6} - 252 \, a \cos\left(d x + c\right)^{5} - 315 \, b \cos\left(d x + c\right)^{4} + 420 \, a \cos\left(d x + c\right)^{3} + 630 \, b \cos\left(d x + c\right)^{2} - 420 \, a \cos\left(d x + c\right) - 420 \, b \log\left(-\cos\left(d x + c\right)\right)}{420 \, d}"," ",0,"1/420*(60*a*cos(d*x + c)^7 + 70*b*cos(d*x + c)^6 - 252*a*cos(d*x + c)^5 - 315*b*cos(d*x + c)^4 + 420*a*cos(d*x + c)^3 + 630*b*cos(d*x + c)^2 - 420*a*cos(d*x + c) - 420*b*log(-cos(d*x + c)))/d","A",0
161,1,71,0,0.780037," ","integrate((a+b*sec(d*x+c))*sin(d*x+c)^5,x, algorithm=""fricas"")","-\frac{12 \, a \cos\left(d x + c\right)^{5} + 15 \, b \cos\left(d x + c\right)^{4} - 40 \, a \cos\left(d x + c\right)^{3} - 60 \, b \cos\left(d x + c\right)^{2} + 60 \, a \cos\left(d x + c\right) + 60 \, b \log\left(-\cos\left(d x + c\right)\right)}{60 \, d}"," ",0,"-1/60*(12*a*cos(d*x + c)^5 + 15*b*cos(d*x + c)^4 - 40*a*cos(d*x + c)^3 - 60*b*cos(d*x + c)^2 + 60*a*cos(d*x + c) + 60*b*log(-cos(d*x + c)))/d","A",0
162,1,49,0,0.623338," ","integrate((a+b*sec(d*x+c))*sin(d*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, a \cos\left(d x + c\right)^{3} + 3 \, b \cos\left(d x + c\right)^{2} - 6 \, a \cos\left(d x + c\right) - 6 \, b \log\left(-\cos\left(d x + c\right)\right)}{6 \, d}"," ",0,"1/6*(2*a*cos(d*x + c)^3 + 3*b*cos(d*x + c)^2 - 6*a*cos(d*x + c) - 6*b*log(-cos(d*x + c)))/d","A",0
163,1,25,0,0.698846," ","integrate((a+b*sec(d*x+c))*sin(d*x+c),x, algorithm=""fricas"")","-\frac{a \cos\left(d x + c\right) + b \log\left(-\cos\left(d x + c\right)\right)}{d}"," ",0,"-(a*cos(d*x + c) + b*log(-cos(d*x + c)))/d","A",0
164,1,51,0,0.483067," ","integrate(csc(d*x+c)*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b \log\left(-\cos\left(d x + c\right)\right) + {\left(a - b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a + b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, d}"," ",0,"-1/2*(2*b*log(-cos(d*x + c)) + (a - b)*log(1/2*cos(d*x + c) + 1/2) - (a + b)*log(-1/2*cos(d*x + c) + 1/2))/d","A",0
165,1,123,0,0.494458," ","integrate(csc(d*x+c)^3*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a \cos\left(d x + c\right) - 4 \, {\left(b \cos\left(d x + c\right)^{2} - b\right)} \log\left(-\cos\left(d x + c\right)\right) - {\left({\left(a - 2 \, b\right)} \cos\left(d x + c\right)^{2} - a + 2 \, b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left({\left(a + 2 \, b\right)} \cos\left(d x + c\right)^{2} - a - 2 \, b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, b}{4 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/4*(2*a*cos(d*x + c) - 4*(b*cos(d*x + c)^2 - b)*log(-cos(d*x + c)) - ((a - 2*b)*cos(d*x + c)^2 - a + 2*b)*log(1/2*cos(d*x + c) + 1/2) + ((a + 2*b)*cos(d*x + c)^2 - a - 2*b)*log(-1/2*cos(d*x + c) + 1/2) + 2*b)/(d*cos(d*x + c)^2 - d)","B",0
166,1,201,0,0.509093," ","integrate(csc(d*x+c)^5*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, a \cos\left(d x + c\right)^{3} + 8 \, b \cos\left(d x + c\right)^{2} - 10 \, a \cos\left(d x + c\right) - 16 \, {\left(b \cos\left(d x + c\right)^{4} - 2 \, b \cos\left(d x + c\right)^{2} + b\right)} \log\left(-\cos\left(d x + c\right)\right) - {\left({\left(3 \, a - 8 \, b\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a - 8 \, b\right)} \cos\left(d x + c\right)^{2} + 3 \, a - 8 \, b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left({\left(3 \, a + 8 \, b\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a + 8 \, b\right)} \cos\left(d x + c\right)^{2} + 3 \, a + 8 \, b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 12 \, b}{16 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/16*(6*a*cos(d*x + c)^3 + 8*b*cos(d*x + c)^2 - 10*a*cos(d*x + c) - 16*(b*cos(d*x + c)^4 - 2*b*cos(d*x + c)^2 + b)*log(-cos(d*x + c)) - ((3*a - 8*b)*cos(d*x + c)^4 - 2*(3*a - 8*b)*cos(d*x + c)^2 + 3*a - 8*b)*log(1/2*cos(d*x + c) + 1/2) + ((3*a + 8*b)*cos(d*x + c)^4 - 2*(3*a + 8*b)*cos(d*x + c)^2 + 3*a + 8*b)*log(-1/2*cos(d*x + c) + 1/2) - 12*b)/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","B",0
167,1,284,0,0.462157," ","integrate(csc(d*x+c)^7*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\frac{30 \, a \cos\left(d x + c\right)^{5} + 48 \, b \cos\left(d x + c\right)^{4} - 80 \, a \cos\left(d x + c\right)^{3} - 120 \, b \cos\left(d x + c\right)^{2} + 66 \, a \cos\left(d x + c\right) - 96 \, {\left(b \cos\left(d x + c\right)^{6} - 3 \, b \cos\left(d x + c\right)^{4} + 3 \, b \cos\left(d x + c\right)^{2} - b\right)} \log\left(-\cos\left(d x + c\right)\right) - 3 \, {\left({\left(5 \, a - 16 \, b\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(5 \, a - 16 \, b\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(5 \, a - 16 \, b\right)} \cos\left(d x + c\right)^{2} - 5 \, a + 16 \, b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left({\left(5 \, a + 16 \, b\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(5 \, a + 16 \, b\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(5 \, a + 16 \, b\right)} \cos\left(d x + c\right)^{2} - 5 \, a - 16 \, b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 88 \, b}{96 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/96*(30*a*cos(d*x + c)^5 + 48*b*cos(d*x + c)^4 - 80*a*cos(d*x + c)^3 - 120*b*cos(d*x + c)^2 + 66*a*cos(d*x + c) - 96*(b*cos(d*x + c)^6 - 3*b*cos(d*x + c)^4 + 3*b*cos(d*x + c)^2 - b)*log(-cos(d*x + c)) - 3*((5*a - 16*b)*cos(d*x + c)^6 - 3*(5*a - 16*b)*cos(d*x + c)^4 + 3*(5*a - 16*b)*cos(d*x + c)^2 - 5*a + 16*b)*log(1/2*cos(d*x + c) + 1/2) + 3*((5*a + 16*b)*cos(d*x + c)^6 - 3*(5*a + 16*b)*cos(d*x + c)^4 + 3*(5*a + 16*b)*cos(d*x + c)^2 - 5*a - 16*b)*log(-1/2*cos(d*x + c) + 1/2) + 88*b)/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","B",0
168,1,102,0,0.492689," ","integrate((a+b*sec(d*x+c))*sin(d*x+c)^6,x, algorithm=""fricas"")","\frac{75 \, a d x + 120 \, b \log\left(\sin\left(d x + c\right) + 1\right) - 120 \, b \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(40 \, a \cos\left(d x + c\right)^{5} + 48 \, b \cos\left(d x + c\right)^{4} - 130 \, a \cos\left(d x + c\right)^{3} - 176 \, b \cos\left(d x + c\right)^{2} + 165 \, a \cos\left(d x + c\right) + 368 \, b\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(75*a*d*x + 120*b*log(sin(d*x + c) + 1) - 120*b*log(-sin(d*x + c) + 1) - (40*a*cos(d*x + c)^5 + 48*b*cos(d*x + c)^4 - 130*a*cos(d*x + c)^3 - 176*b*cos(d*x + c)^2 + 165*a*cos(d*x + c) + 368*b)*sin(d*x + c))/d","A",0
169,1,79,0,0.475986," ","integrate((a+b*sec(d*x+c))*sin(d*x+c)^4,x, algorithm=""fricas"")","\frac{9 \, a d x + 12 \, b \log\left(\sin\left(d x + c\right) + 1\right) - 12 \, b \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, a \cos\left(d x + c\right)^{3} + 8 \, b \cos\left(d x + c\right)^{2} - 15 \, a \cos\left(d x + c\right) - 32 \, b\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(9*a*d*x + 12*b*log(sin(d*x + c) + 1) - 12*b*log(-sin(d*x + c) + 1) + (6*a*cos(d*x + c)^3 + 8*b*cos(d*x + c)^2 - 15*a*cos(d*x + c) - 32*b)*sin(d*x + c))/d","A",0
170,1,55,0,0.503219," ","integrate((a+b*sec(d*x+c))*sin(d*x+c)^2,x, algorithm=""fricas"")","\frac{a d x + b \log\left(\sin\left(d x + c\right) + 1\right) - b \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(a \cos\left(d x + c\right) + 2 \, b\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(a*d*x + b*log(sin(d*x + c) + 1) - b*log(-sin(d*x + c) + 1) - (a*cos(d*x + c) + 2*b)*sin(d*x + c))/d","A",0
171,1,63,0,0.602508," ","integrate(csc(d*x+c)^2*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\frac{b \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - b \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 2 \, b}{2 \, d \sin\left(d x + c\right)}"," ",0,"1/2*(b*log(sin(d*x + c) + 1)*sin(d*x + c) - b*log(-sin(d*x + c) + 1)*sin(d*x + c) - 2*a*cos(d*x + c) - 2*b)/(d*sin(d*x + c))","A",0
172,1,125,0,0.696166," ","integrate(csc(d*x+c)^4*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, a \cos\left(d x + c\right)^{3} + 6 \, b \cos\left(d x + c\right)^{2} - 3 \, {\left(b \cos\left(d x + c\right)^{2} - b\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 3 \, {\left(b \cos\left(d x + c\right)^{2} - b\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 6 \, a \cos\left(d x + c\right) - 8 \, b}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/6*(4*a*cos(d*x + c)^3 + 6*b*cos(d*x + c)^2 - 3*(b*cos(d*x + c)^2 - b)*log(sin(d*x + c) + 1)*sin(d*x + c) + 3*(b*cos(d*x + c)^2 - b)*log(-sin(d*x + c) + 1)*sin(d*x + c) - 6*a*cos(d*x + c) - 8*b)/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
173,1,174,0,0.695313," ","integrate(csc(d*x+c)^6*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, a \cos\left(d x + c\right)^{5} + 30 \, b \cos\left(d x + c\right)^{4} - 40 \, a \cos\left(d x + c\right)^{3} - 70 \, b \cos\left(d x + c\right)^{2} - 15 \, {\left(b \cos\left(d x + c\right)^{4} - 2 \, b \cos\left(d x + c\right)^{2} + b\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 15 \, {\left(b \cos\left(d x + c\right)^{4} - 2 \, b \cos\left(d x + c\right)^{2} + b\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 30 \, a \cos\left(d x + c\right) + 46 \, b}{30 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/30*(16*a*cos(d*x + c)^5 + 30*b*cos(d*x + c)^4 - 40*a*cos(d*x + c)^3 - 70*b*cos(d*x + c)^2 - 15*(b*cos(d*x + c)^4 - 2*b*cos(d*x + c)^2 + b)*log(sin(d*x + c) + 1)*sin(d*x + c) + 15*(b*cos(d*x + c)^4 - 2*b*cos(d*x + c)^2 + b)*log(-sin(d*x + c) + 1)*sin(d*x + c) + 30*a*cos(d*x + c) + 46*b)/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
174,1,125,0,0.726496," ","integrate((a+b*sec(d*x+c))^2*sin(d*x+c)^5,x, algorithm=""fricas"")","-\frac{48 \, a^{2} \cos\left(d x + c\right)^{6} + 120 \, a b \cos\left(d x + c\right)^{5} - 480 \, a b \cos\left(d x + c\right)^{3} - 80 \, {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} + 480 \, a b \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right)\right) + 195 \, a b \cos\left(d x + c\right) + 240 \, {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 240 \, b^{2}}{240 \, d \cos\left(d x + c\right)}"," ",0,"-1/240*(48*a^2*cos(d*x + c)^6 + 120*a*b*cos(d*x + c)^5 - 480*a*b*cos(d*x + c)^3 - 80*(2*a^2 - b^2)*cos(d*x + c)^4 + 480*a*b*cos(d*x + c)*log(-cos(d*x + c)) + 195*a*b*cos(d*x + c) + 240*(a^2 - 2*b^2)*cos(d*x + c)^2 - 240*b^2)/(d*cos(d*x + c))","A",0
175,1,92,0,0.588712," ","integrate((a+b*sec(d*x+c))^2*sin(d*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, a^{2} \cos\left(d x + c\right)^{4} + 6 \, a b \cos\left(d x + c\right)^{3} - 12 \, a b \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right)\right) - 3 \, a b \cos\left(d x + c\right) - 6 \, {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 6 \, b^{2}}{6 \, d \cos\left(d x + c\right)}"," ",0,"1/6*(2*a^2*cos(d*x + c)^4 + 6*a*b*cos(d*x + c)^3 - 12*a*b*cos(d*x + c)*log(-cos(d*x + c)) - 3*a*b*cos(d*x + c) - 6*(a^2 - b^2)*cos(d*x + c)^2 + 6*b^2)/(d*cos(d*x + c))","A",0
176,1,50,0,0.625903," ","integrate((a+b*sec(d*x+c))^2*sin(d*x+c),x, algorithm=""fricas"")","-\frac{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right)\right) - b^{2}}{d \cos\left(d x + c\right)}"," ",0,"-(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c)*log(-cos(d*x + c)) - b^2)/(d*cos(d*x + c))","A",0
177,1,97,0,0.531575," ","integrate(csc(d*x+c)*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, a b \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right)\right) + {\left(a^{2} - 2 \, a b + b^{2}\right)} \cos\left(d x + c\right) \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a^{2} + 2 \, a b + b^{2}\right)} \cos\left(d x + c\right) \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, b^{2}}{2 \, d \cos\left(d x + c\right)}"," ",0,"-1/2*(4*a*b*cos(d*x + c)*log(-cos(d*x + c)) + (a^2 - 2*a*b + b^2)*cos(d*x + c)*log(1/2*cos(d*x + c) + 1/2) - (a^2 + 2*a*b + b^2)*cos(d*x + c)*log(-1/2*cos(d*x + c) + 1/2) - 2*b^2)/(d*cos(d*x + c))","A",0
178,1,205,0,0.535740," ","integrate(csc(d*x+c)^3*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, a b \cos\left(d x + c\right) + 2 \, {\left(a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 4 \, b^{2} - 8 \, {\left(a b \cos\left(d x + c\right)^{3} - a b \cos\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right)\right) - {\left({\left(a^{2} - 4 \, a b + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{2} - 4 \, a b + 3 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left({\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(d \cos\left(d x + c\right)^{3} - d \cos\left(d x + c\right)\right)}}"," ",0,"1/4*(4*a*b*cos(d*x + c) + 2*(a^2 + 3*b^2)*cos(d*x + c)^2 - 4*b^2 - 8*(a*b*cos(d*x + c)^3 - a*b*cos(d*x + c))*log(-cos(d*x + c)) - ((a^2 - 4*a*b + 3*b^2)*cos(d*x + c)^3 - (a^2 - 4*a*b + 3*b^2)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + ((a^2 + 4*a*b + 3*b^2)*cos(d*x + c)^3 - (a^2 + 4*a*b + 3*b^2)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^3 - d*cos(d*x + c))","A",0
179,1,176,0,0.489083," ","integrate((a+b*sec(d*x+c))^2*sin(d*x+c)^6,x, algorithm=""fricas"")","\frac{75 \, {\left(a^{2} - 6 \, b^{2}\right)} d x \cos\left(d x + c\right) + 240 \, a b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 240 \, a b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(40 \, a^{2} \cos\left(d x + c\right)^{6} + 96 \, a b \cos\left(d x + c\right)^{5} - 352 \, a b \cos\left(d x + c\right)^{3} - 10 \, {\left(13 \, a^{2} - 6 \, b^{2}\right)} \cos\left(d x + c\right)^{4} + 736 \, a b \cos\left(d x + c\right) + 15 \, {\left(11 \, a^{2} - 18 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 240 \, b^{2}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)}"," ",0,"1/240*(75*(a^2 - 6*b^2)*d*x*cos(d*x + c) + 240*a*b*cos(d*x + c)*log(sin(d*x + c) + 1) - 240*a*b*cos(d*x + c)*log(-sin(d*x + c) + 1) - (40*a^2*cos(d*x + c)^6 + 96*a*b*cos(d*x + c)^5 - 352*a*b*cos(d*x + c)^3 - 10*(13*a^2 - 6*b^2)*cos(d*x + c)^4 + 736*a*b*cos(d*x + c) + 15*(11*a^2 - 18*b^2)*cos(d*x + c)^2 - 240*b^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
180,1,142,0,0.621526," ","integrate((a+b*sec(d*x+c))^2*sin(d*x+c)^4,x, algorithm=""fricas"")","\frac{9 \, {\left(a^{2} - 4 \, b^{2}\right)} d x \cos\left(d x + c\right) + 24 \, a b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 24 \, a b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, a^{2} \cos\left(d x + c\right)^{4} + 16 \, a b \cos\left(d x + c\right)^{3} - 64 \, a b \cos\left(d x + c\right) - 3 \, {\left(5 \, a^{2} - 4 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 24 \, b^{2}\right)} \sin\left(d x + c\right)}{24 \, d \cos\left(d x + c\right)}"," ",0,"1/24*(9*(a^2 - 4*b^2)*d*x*cos(d*x + c) + 24*a*b*cos(d*x + c)*log(sin(d*x + c) + 1) - 24*a*b*cos(d*x + c)*log(-sin(d*x + c) + 1) + (6*a^2*cos(d*x + c)^4 + 16*a*b*cos(d*x + c)^3 - 64*a*b*cos(d*x + c) - 3*(5*a^2 - 4*b^2)*cos(d*x + c)^2 + 24*b^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
181,1,108,0,0.496238," ","integrate((a+b*sec(d*x+c))^2*sin(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} - 2 \, b^{2}\right)} d x \cos\left(d x + c\right) + 2 \, a b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, a b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(a^{2} \cos\left(d x + c\right)^{2} + 4 \, a b \cos\left(d x + c\right) - 2 \, b^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*((a^2 - 2*b^2)*d*x*cos(d*x + c) + 2*a*b*cos(d*x + c)*log(sin(d*x + c) + 1) - 2*a*b*cos(d*x + c)*log(-sin(d*x + c) + 1) - (a^2*cos(d*x + c)^2 + 4*a*b*cos(d*x + c) - 2*b^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
182,1,104,0,0.479502," ","integrate(csc(d*x+c)^2*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{a b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - a b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 2 \, a b \cos\left(d x + c\right) - {\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}{d \cos\left(d x + c\right) \sin\left(d x + c\right)}"," ",0,"(a*b*cos(d*x + c)*log(sin(d*x + c) + 1)*sin(d*x + c) - a*b*cos(d*x + c)*log(-sin(d*x + c) + 1)*sin(d*x + c) - 2*a*b*cos(d*x + c) - (a^2 + 2*b^2)*cos(d*x + c)^2 + b^2)/(d*cos(d*x + c)*sin(d*x + c))","A",0
183,1,178,0,0.547377," ","integrate(csc(d*x+c)^4*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, a b \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{4} - 8 \, a b \cos\left(d x + c\right) - 3 \, {\left(a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a b \cos\left(d x + c\right)^{3} - a b \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 3 \, {\left(a b \cos\left(d x + c\right)^{3} - a b \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 3 \, b^{2}}{3 \, {\left(d \cos\left(d x + c\right)^{3} - d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}"," ",0,"-1/3*(6*a*b*cos(d*x + c)^3 + 2*(a^2 + 4*b^2)*cos(d*x + c)^4 - 8*a*b*cos(d*x + c) - 3*(a^2 + 4*b^2)*cos(d*x + c)^2 - 3*(a*b*cos(d*x + c)^3 - a*b*cos(d*x + c))*log(sin(d*x + c) + 1)*sin(d*x + c) + 3*(a*b*cos(d*x + c)^3 - a*b*cos(d*x + c))*log(-sin(d*x + c) + 1)*sin(d*x + c) + 3*b^2)/((d*cos(d*x + c)^3 - d*cos(d*x + c))*sin(d*x + c))","A",0
184,1,241,0,0.527579," ","integrate(csc(d*x+c)^6*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{30 \, a b \cos\left(d x + c\right)^{5} + 8 \, {\left(a^{2} + 6 \, b^{2}\right)} \cos\left(d x + c\right)^{6} - 70 \, a b \cos\left(d x + c\right)^{3} - 20 \, {\left(a^{2} + 6 \, b^{2}\right)} \cos\left(d x + c\right)^{4} + 46 \, a b \cos\left(d x + c\right) + 15 \, {\left(a^{2} + 6 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 15 \, {\left(a b \cos\left(d x + c\right)^{5} - 2 \, a b \cos\left(d x + c\right)^{3} + a b \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 15 \, {\left(a b \cos\left(d x + c\right)^{5} - 2 \, a b \cos\left(d x + c\right)^{3} + a b \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 15 \, b^{2}}{15 \, {\left(d \cos\left(d x + c\right)^{5} - 2 \, d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}"," ",0,"-1/15*(30*a*b*cos(d*x + c)^5 + 8*(a^2 + 6*b^2)*cos(d*x + c)^6 - 70*a*b*cos(d*x + c)^3 - 20*(a^2 + 6*b^2)*cos(d*x + c)^4 + 46*a*b*cos(d*x + c) + 15*(a^2 + 6*b^2)*cos(d*x + c)^2 - 15*(a*b*cos(d*x + c)^5 - 2*a*b*cos(d*x + c)^3 + a*b*cos(d*x + c))*log(sin(d*x + c) + 1)*sin(d*x + c) + 15*(a*b*cos(d*x + c)^5 - 2*a*b*cos(d*x + c)^3 + a*b*cos(d*x + c))*log(-sin(d*x + c) + 1)*sin(d*x + c) - 15*b^2)/((d*cos(d*x + c)^5 - 2*d*cos(d*x + c)^3 + d*cos(d*x + c))*sin(d*x + c))","A",0
185,1,175,0,0.530546," ","integrate((a+b*sec(d*x+c))^3*sin(d*x+c)^5,x, algorithm=""fricas"")","-\frac{96 \, a^{3} \cos\left(d x + c\right)^{7} + 360 \, a^{2} b \cos\left(d x + c\right)^{6} - 160 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} - 240 \, {\left(6 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{4} - 1440 \, a b^{2} \cos\left(d x + c\right) + 480 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 480 \, {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\cos\left(d x + c\right)\right) - 240 \, b^{3} + 15 \, {\left(39 \, a^{2} b - 8 \, b^{3}\right)} \cos\left(d x + c\right)^{2}}{480 \, d \cos\left(d x + c\right)^{2}}"," ",0,"-1/480*(96*a^3*cos(d*x + c)^7 + 360*a^2*b*cos(d*x + c)^6 - 160*(2*a^3 - 3*a*b^2)*cos(d*x + c)^5 - 240*(6*a^2*b - b^3)*cos(d*x + c)^4 - 1440*a*b^2*cos(d*x + c) + 480*(a^3 - 6*a*b^2)*cos(d*x + c)^3 + 480*(3*a^2*b - 2*b^3)*cos(d*x + c)^2*log(-cos(d*x + c)) - 240*b^3 + 15*(39*a^2*b - 8*b^3)*cos(d*x + c)^2)/(d*cos(d*x + c)^2)","A",0
186,1,123,0,0.505854," ","integrate((a+b*sec(d*x+c))^3*sin(d*x+c)^3,x, algorithm=""fricas"")","\frac{4 \, a^{3} \cos\left(d x + c\right)^{5} + 18 \, a^{2} b \cos\left(d x + c\right)^{4} - 9 \, a^{2} b \cos\left(d x + c\right)^{2} + 36 \, a b^{2} \cos\left(d x + c\right) - 12 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - 12 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\cos\left(d x + c\right)\right) + 6 \, b^{3}}{12 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/12*(4*a^3*cos(d*x + c)^5 + 18*a^2*b*cos(d*x + c)^4 - 9*a^2*b*cos(d*x + c)^2 + 36*a*b^2*cos(d*x + c) - 12*(a^3 - 3*a*b^2)*cos(d*x + c)^3 - 12*(3*a^2*b - b^3)*cos(d*x + c)^2*log(-cos(d*x + c)) + 6*b^3)/(d*cos(d*x + c)^2)","A",0
187,1,67,0,0.538961," ","integrate((a+b*sec(d*x+c))^3*sin(d*x+c),x, algorithm=""fricas"")","-\frac{2 \, a^{3} \cos\left(d x + c\right)^{3} + 6 \, a^{2} b \cos\left(d x + c\right)^{2} \log\left(-\cos\left(d x + c\right)\right) - 6 \, a b^{2} \cos\left(d x + c\right) - b^{3}}{2 \, d \cos\left(d x + c\right)^{2}}"," ",0,"-1/2*(2*a^3*cos(d*x + c)^3 + 6*a^2*b*cos(d*x + c)^2*log(-cos(d*x + c)) - 6*a*b^2*cos(d*x + c) - b^3)/(d*cos(d*x + c)^2)","A",0
188,1,139,0,0.506687," ","integrate(csc(d*x+c)*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{6 \, a b^{2} \cos\left(d x + c\right) - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\cos\left(d x + c\right)\right) - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + b^{3}}{2 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/2*(6*a*b^2*cos(d*x + c) - 2*(3*a^2*b + b^3)*cos(d*x + c)^2*log(-cos(d*x + c)) - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cos(d*x + c)^2*log(1/2*cos(d*x + c) + 1/2) + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cos(d*x + c)^2*log(-1/2*cos(d*x + c) + 1/2) + b^3)/(d*cos(d*x + c)^2)","A",0
189,1,290,0,0.510385," ","integrate(csc(d*x+c)^3*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{12 \, a b^{2} \cos\left(d x + c\right) - 2 \, {\left(a^{3} + 9 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 2 \, b^{3} - 2 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{4} - {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\cos\left(d x + c\right)\right) + {\left({\left(a^{3} - 6 \, a^{2} b + 9 \, a b^{2} - 4 \, b^{3}\right)} \cos\left(d x + c\right)^{4} - {\left(a^{3} - 6 \, a^{2} b + 9 \, a b^{2} - 4 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left({\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cos\left(d x + c\right)^{4} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(d \cos\left(d x + c\right)^{4} - d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/4*(12*a*b^2*cos(d*x + c) - 2*(a^3 + 9*a*b^2)*cos(d*x + c)^3 + 2*b^3 - 2*(3*a^2*b + 2*b^3)*cos(d*x + c)^2 + 4*((3*a^2*b + 2*b^3)*cos(d*x + c)^4 - (3*a^2*b + 2*b^3)*cos(d*x + c)^2)*log(-cos(d*x + c)) + ((a^3 - 6*a^2*b + 9*a*b^2 - 4*b^3)*cos(d*x + c)^4 - (a^3 - 6*a^2*b + 9*a*b^2 - 4*b^3)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) - ((a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cos(d*x + c)^4 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^4 - d*cos(d*x + c)^2)","A",0
190,1,241,0,0.534514," ","integrate((a+b*sec(d*x+c))^3*sin(d*x+c)^6,x, algorithm=""fricas"")","\frac{75 \, {\left(a^{3} - 18 \, a b^{2}\right)} d x \cos\left(d x + c\right)^{2} + 60 \, {\left(6 \, a^{2} b - 5 \, b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 60 \, {\left(6 \, a^{2} b - 5 \, b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(40 \, a^{3} \cos\left(d x + c\right)^{7} + 144 \, a^{2} b \cos\left(d x + c\right)^{6} - 10 \, {\left(13 \, a^{3} - 18 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} - 16 \, {\left(33 \, a^{2} b - 5 \, b^{3}\right)} \cos\left(d x + c\right)^{4} - 720 \, a b^{2} \cos\left(d x + c\right) + 15 \, {\left(11 \, a^{3} - 54 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - 120 \, b^{3} + 16 \, {\left(69 \, a^{2} b - 35 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/240*(75*(a^3 - 18*a*b^2)*d*x*cos(d*x + c)^2 + 60*(6*a^2*b - 5*b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - 60*(6*a^2*b - 5*b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - (40*a^3*cos(d*x + c)^7 + 144*a^2*b*cos(d*x + c)^6 - 10*(13*a^3 - 18*a*b^2)*cos(d*x + c)^5 - 16*(33*a^2*b - 5*b^3)*cos(d*x + c)^4 - 720*a*b^2*cos(d*x + c) + 15*(11*a^3 - 54*a*b^2)*cos(d*x + c)^3 - 120*b^3 + 16*(69*a^2*b - 35*b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
191,1,196,0,0.565115," ","integrate((a+b*sec(d*x+c))^3*sin(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{3} - 12 \, a b^{2}\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(2 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 6 \, {\left(2 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, a^{3} \cos\left(d x + c\right)^{5} + 8 \, a^{2} b \cos\left(d x + c\right)^{4} + 24 \, a b^{2} \cos\left(d x + c\right) - {\left(5 \, a^{3} - 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 4 \, b^{3} - 8 \, {\left(4 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{8 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/8*(3*(a^3 - 12*a*b^2)*d*x*cos(d*x + c)^2 + 6*(2*a^2*b - b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - 6*(2*a^2*b - b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + (2*a^3*cos(d*x + c)^5 + 8*a^2*b*cos(d*x + c)^4 + 24*a*b^2*cos(d*x + c) - (5*a^3 - 12*a*b^2)*cos(d*x + c)^3 + 4*b^3 - 8*(4*a^2*b - b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
192,1,151,0,0.506293," ","integrate((a+b*sec(d*x+c))^3*sin(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} - 6 \, a b^{2}\right)} d x \cos\left(d x + c\right)^{2} + {\left(6 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(6 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{3} \cos\left(d x + c\right)^{3} + 6 \, a^{2} b \cos\left(d x + c\right)^{2} - 6 \, a b^{2} \cos\left(d x + c\right) - b^{3}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(2*(a^3 - 6*a*b^2)*d*x*cos(d*x + c)^2 + (6*a^2*b - b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (6*a^2*b - b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*(a^3*cos(d*x + c)^3 + 6*a^2*b*cos(d*x + c)^2 - 6*a*b^2*cos(d*x + c) - b^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
193,1,151,0,0.692858," ","integrate(csc(d*x+c)^2*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 3 \, {\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 12 \, a b^{2} \cos\left(d x + c\right) - 4 \, {\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 2 \, b^{3} - 6 \, {\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}}{4 \, d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)}"," ",0,"1/4*(3*(2*a^2*b + b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1)*sin(d*x + c) - 3*(2*a^2*b + b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1)*sin(d*x + c) + 12*a*b^2*cos(d*x + c) - 4*(a^3 + 6*a*b^2)*cos(d*x + c)^3 + 2*b^3 - 6*(2*a^2*b + b^3)*cos(d*x + c)^2)/(d*cos(d*x + c)^2*sin(d*x + c))","A",0
194,1,260,0,1.211904," ","integrate(csc(d*x+c)^4*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{8 \, {\left(a^{3} + 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} + 6 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cos\left(d x + c\right)^{4} + 36 \, a b^{2} \cos\left(d x + c\right) - 12 \, {\left(a^{3} + 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 6 \, b^{3} - 8 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left({\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cos\left(d x + c\right)^{4} - {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 3 \, {\left({\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cos\left(d x + c\right)^{4} - {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{4} - d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}"," ",0,"-1/12*(8*(a^3 + 12*a*b^2)*cos(d*x + c)^5 + 6*(6*a^2*b + 5*b^3)*cos(d*x + c)^4 + 36*a*b^2*cos(d*x + c) - 12*(a^3 + 12*a*b^2)*cos(d*x + c)^3 + 6*b^3 - 8*(6*a^2*b + 5*b^3)*cos(d*x + c)^2 - 3*((6*a^2*b + 5*b^3)*cos(d*x + c)^4 - (6*a^2*b + 5*b^3)*cos(d*x + c)^2)*log(sin(d*x + c) + 1)*sin(d*x + c) + 3*((6*a^2*b + 5*b^3)*cos(d*x + c)^4 - (6*a^2*b + 5*b^3)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1)*sin(d*x + c))/((d*cos(d*x + c)^4 - d*cos(d*x + c)^2)*sin(d*x + c))","A",0
195,1,354,0,0.619233," ","integrate(csc(d*x+c)^6*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{32 \, {\left(a^{3} + 18 \, a b^{2}\right)} \cos\left(d x + c\right)^{7} + 30 \, {\left(6 \, a^{2} b + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{6} - 80 \, {\left(a^{3} + 18 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} - 70 \, {\left(6 \, a^{2} b + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{4} - 180 \, a b^{2} \cos\left(d x + c\right) + 60 \, {\left(a^{3} + 18 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - 30 \, b^{3} + 46 \, {\left(6 \, a^{2} b + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - 15 \, {\left({\left(6 \, a^{2} b + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{6} - 2 \, {\left(6 \, a^{2} b + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{4} + {\left(6 \, a^{2} b + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 15 \, {\left({\left(6 \, a^{2} b + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{6} - 2 \, {\left(6 \, a^{2} b + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{4} + {\left(6 \, a^{2} b + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right)}{60 \, {\left(d \cos\left(d x + c\right)^{6} - 2 \, d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}"," ",0,"-1/60*(32*(a^3 + 18*a*b^2)*cos(d*x + c)^7 + 30*(6*a^2*b + 7*b^3)*cos(d*x + c)^6 - 80*(a^3 + 18*a*b^2)*cos(d*x + c)^5 - 70*(6*a^2*b + 7*b^3)*cos(d*x + c)^4 - 180*a*b^2*cos(d*x + c) + 60*(a^3 + 18*a*b^2)*cos(d*x + c)^3 - 30*b^3 + 46*(6*a^2*b + 7*b^3)*cos(d*x + c)^2 - 15*((6*a^2*b + 7*b^3)*cos(d*x + c)^6 - 2*(6*a^2*b + 7*b^3)*cos(d*x + c)^4 + (6*a^2*b + 7*b^3)*cos(d*x + c)^2)*log(sin(d*x + c) + 1)*sin(d*x + c) + 15*((6*a^2*b + 7*b^3)*cos(d*x + c)^6 - 2*(6*a^2*b + 7*b^3)*cos(d*x + c)^4 + (6*a^2*b + 7*b^3)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1)*sin(d*x + c))/((d*cos(d*x + c)^6 - 2*d*cos(d*x + c)^4 + d*cos(d*x + c)^2)*sin(d*x + c))","A",0
196,1,222,0,0.611662," ","integrate(sin(d*x+c)^7/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\frac{60 \, a^{7} \cos\left(d x + c\right)^{7} - 70 \, a^{6} b \cos\left(d x + c\right)^{6} - 84 \, {\left(3 \, a^{7} - a^{5} b^{2}\right)} \cos\left(d x + c\right)^{5} + 105 \, {\left(3 \, a^{6} b - a^{4} b^{3}\right)} \cos\left(d x + c\right)^{4} + 140 \, {\left(3 \, a^{7} - 3 \, a^{5} b^{2} + a^{3} b^{4}\right)} \cos\left(d x + c\right)^{3} - 210 \, {\left(3 \, a^{6} b - 3 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} - 420 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right) + 420 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{420 \, a^{8} d}"," ",0,"1/420*(60*a^7*cos(d*x + c)^7 - 70*a^6*b*cos(d*x + c)^6 - 84*(3*a^7 - a^5*b^2)*cos(d*x + c)^5 + 105*(3*a^6*b - a^4*b^3)*cos(d*x + c)^4 + 140*(3*a^7 - 3*a^5*b^2 + a^3*b^4)*cos(d*x + c)^3 - 210*(3*a^6*b - 3*a^4*b^3 + a^2*b^5)*cos(d*x + c)^2 - 420*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cos(d*x + c) + 420*(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*log(a*cos(d*x + c) + b))/(a^8*d)","A",0
197,1,140,0,0.609609," ","integrate(sin(d*x+c)^5/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{12 \, a^{5} \cos\left(d x + c\right)^{5} - 15 \, a^{4} b \cos\left(d x + c\right)^{4} - 20 \, {\left(2 \, a^{5} - a^{3} b^{2}\right)} \cos\left(d x + c\right)^{3} + 30 \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} + 60 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) - 60 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{60 \, a^{6} d}"," ",0,"-1/60*(12*a^5*cos(d*x + c)^5 - 15*a^4*b*cos(d*x + c)^4 - 20*(2*a^5 - a^3*b^2)*cos(d*x + c)^3 + 30*(2*a^4*b - a^2*b^3)*cos(d*x + c)^2 + 60*(a^5 - 2*a^3*b^2 + a*b^4)*cos(d*x + c) - 60*(a^4*b - 2*a^2*b^3 + b^5)*log(a*cos(d*x + c) + b))/(a^6*d)","A",0
198,1,78,0,0.557605," ","integrate(sin(d*x+c)^3/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a^{3} \cos\left(d x + c\right)^{3} - 3 \, a^{2} b \cos\left(d x + c\right)^{2} - 6 \, {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right) + 6 \, {\left(a^{2} b - b^{3}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{6 \, a^{4} d}"," ",0,"1/6*(2*a^3*cos(d*x + c)^3 - 3*a^2*b*cos(d*x + c)^2 - 6*(a^3 - a*b^2)*cos(d*x + c) + 6*(a^2*b - b^3)*log(a*cos(d*x + c) + b))/(a^4*d)","A",0
199,1,31,0,0.513595," ","integrate(sin(d*x+c)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{a \cos\left(d x + c\right) - b \log\left(a \cos\left(d x + c\right) + b\right)}{a^{2} d}"," ",0,"-(a*cos(d*x + c) - b*log(a*cos(d*x + c) + b))/(a^2*d)","A",0
200,1,64,0,0.522132," ","integrate(csc(d*x+c)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, b \log\left(a \cos\left(d x + c\right) + b\right) - {\left(a + b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a - b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left(a^{2} - b^{2}\right)} d}"," ",0,"1/2*(2*b*log(a*cos(d*x + c) + b) - (a + b)*log(1/2*cos(d*x + c) + 1/2) + (a - b)*log(-1/2*cos(d*x + c) + 1/2))/((a^2 - b^2)*d)","A",0
201,1,216,0,0.552598," ","integrate(csc(d*x+c)^3/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a^{2} b - 2 \, b^{3} - 2 \, {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right) - 4 \, {\left(a^{2} b \cos\left(d x + c\right)^{2} - a^{2} b\right)} \log\left(a \cos\left(d x + c\right) + b\right) - {\left(a^{3} + 2 \, a^{2} b + a b^{2} - {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{3} - 2 \, a^{2} b + a b^{2} - {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d\right)}}"," ",0,"-1/4*(2*a^2*b - 2*b^3 - 2*(a^3 - a*b^2)*cos(d*x + c) - 4*(a^2*b*cos(d*x + c)^2 - a^2*b)*log(a*cos(d*x + c) + b) - (a^3 + 2*a^2*b + a*b^2 - (a^3 + 2*a^2*b + a*b^2)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) + (a^3 - 2*a^2*b + a*b^2 - (a^3 - 2*a^2*b + a*b^2)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2))/((a^4 - 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2 - (a^4 - 2*a^2*b^2 + b^4)*d)","A",0
202,1,469,0,0.597696," ","integrate(csc(d*x+c)^5/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\frac{12 \, a^{4} b - 16 \, a^{2} b^{3} + 4 \, b^{5} + 2 \, {\left(3 \, a^{5} - 2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{3} - 8 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(5 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + 16 \, {\left(a^{4} b \cos\left(d x + c\right)^{4} - 2 \, a^{4} b \cos\left(d x + c\right)^{2} + a^{4} b\right)} \log\left(a \cos\left(d x + c\right) + b\right) - {\left(3 \, a^{5} + 8 \, a^{4} b + 6 \, a^{3} b^{2} - a b^{4} + {\left(3 \, a^{5} + 8 \, a^{4} b + 6 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 6 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(3 \, a^{5} - 8 \, a^{4} b + 6 \, a^{3} b^{2} - a b^{4} + {\left(3 \, a^{5} - 8 \, a^{4} b + 6 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} - 8 \, a^{4} b + 6 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{16 \, {\left({\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d\right)}}"," ",0,"1/16*(12*a^4*b - 16*a^2*b^3 + 4*b^5 + 2*(3*a^5 - 2*a^3*b^2 - a*b^4)*cos(d*x + c)^3 - 8*(a^4*b - a^2*b^3)*cos(d*x + c)^2 - 2*(5*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + 16*(a^4*b*cos(d*x + c)^4 - 2*a^4*b*cos(d*x + c)^2 + a^4*b)*log(a*cos(d*x + c) + b) - (3*a^5 + 8*a^4*b + 6*a^3*b^2 - a*b^4 + (3*a^5 + 8*a^4*b + 6*a^3*b^2 - a*b^4)*cos(d*x + c)^4 - 2*(3*a^5 + 8*a^4*b + 6*a^3*b^2 - a*b^4)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) + (3*a^5 - 8*a^4*b + 6*a^3*b^2 - a*b^4 + (3*a^5 - 8*a^4*b + 6*a^3*b^2 - a*b^4)*cos(d*x + c)^4 - 2*(3*a^5 - 8*a^4*b + 6*a^3*b^2 - a*b^4)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^4 - 2*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^2 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d)","B",0
203,1,553,0,0.597286," ","integrate(sin(d*x+c)^6/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(5 \, a^{6} - 30 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 16 \, b^{6}\right)} d x + 120 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - {\left(40 \, a^{6} \cos\left(d x + c\right)^{5} - 48 \, a^{5} b \cos\left(d x + c\right)^{4} - 368 \, a^{5} b + 560 \, a^{3} b^{3} - 240 \, a b^{5} - 10 \, {\left(13 \, a^{6} - 6 \, a^{4} b^{2}\right)} \cos\left(d x + c\right)^{3} + 16 \, {\left(11 \, a^{5} b - 5 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(11 \, a^{6} - 18 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, a^{7} d}, \frac{15 \, {\left(5 \, a^{6} - 30 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 16 \, b^{6}\right)} d x - 240 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(40 \, a^{6} \cos\left(d x + c\right)^{5} - 48 \, a^{5} b \cos\left(d x + c\right)^{4} - 368 \, a^{5} b + 560 \, a^{3} b^{3} - 240 \, a b^{5} - 10 \, {\left(13 \, a^{6} - 6 \, a^{4} b^{2}\right)} \cos\left(d x + c\right)^{3} + 16 \, {\left(11 \, a^{5} b - 5 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(11 \, a^{6} - 18 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, a^{7} d}\right]"," ",0,"[1/240*(15*(5*a^6 - 30*a^4*b^2 + 40*a^2*b^4 - 16*b^6)*d*x + 120*(a^4*b - 2*a^2*b^3 + b^5)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - (40*a^6*cos(d*x + c)^5 - 48*a^5*b*cos(d*x + c)^4 - 368*a^5*b + 560*a^3*b^3 - 240*a*b^5 - 10*(13*a^6 - 6*a^4*b^2)*cos(d*x + c)^3 + 16*(11*a^5*b - 5*a^3*b^3)*cos(d*x + c)^2 + 15*(11*a^6 - 18*a^4*b^2 + 8*a^2*b^4)*cos(d*x + c))*sin(d*x + c))/(a^7*d), 1/240*(15*(5*a^6 - 30*a^4*b^2 + 40*a^2*b^4 - 16*b^6)*d*x - 240*(a^4*b - 2*a^2*b^3 + b^5)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (40*a^6*cos(d*x + c)^5 - 48*a^5*b*cos(d*x + c)^4 - 368*a^5*b + 560*a^3*b^3 - 240*a*b^5 - 10*(13*a^6 - 6*a^4*b^2)*cos(d*x + c)^3 + 16*(11*a^5*b - 5*a^3*b^3)*cos(d*x + c)^2 + 15*(11*a^6 - 18*a^4*b^2 + 8*a^2*b^4)*cos(d*x + c))*sin(d*x + c))/(a^7*d)]","A",0
204,1,393,0,0.656705," ","integrate(sin(d*x+c)^4/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} d x - 12 \, {\left(a^{2} b - b^{3}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + {\left(6 \, a^{4} \cos\left(d x + c\right)^{3} - 8 \, a^{3} b \cos\left(d x + c\right)^{2} + 32 \, a^{3} b - 24 \, a b^{3} - 3 \, {\left(5 \, a^{4} - 4 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, a^{5} d}, \frac{3 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} d x - 24 \, {\left(a^{2} b - b^{3}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(6 \, a^{4} \cos\left(d x + c\right)^{3} - 8 \, a^{3} b \cos\left(d x + c\right)^{2} + 32 \, a^{3} b - 24 \, a b^{3} - 3 \, {\left(5 \, a^{4} - 4 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, a^{5} d}\right]"," ",0,"[1/24*(3*(3*a^4 - 12*a^2*b^2 + 8*b^4)*d*x - 12*(a^2*b - b^3)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + (6*a^4*cos(d*x + c)^3 - 8*a^3*b*cos(d*x + c)^2 + 32*a^3*b - 24*a*b^3 - 3*(5*a^4 - 4*a^2*b^2)*cos(d*x + c))*sin(d*x + c))/(a^5*d), 1/24*(3*(3*a^4 - 12*a^2*b^2 + 8*b^4)*d*x - 24*(a^2*b - b^3)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (6*a^4*cos(d*x + c)^3 - 8*a^3*b*cos(d*x + c)^2 + 32*a^3*b - 24*a*b^3 - 3*(5*a^4 - 4*a^2*b^2)*cos(d*x + c))*sin(d*x + c))/(a^5*d)]","A",0
205,1,258,0,0.491432," ","integrate(sin(d*x+c)^2/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} - 2 \, b^{2}\right)} d x + \sqrt{a^{2} - b^{2}} b \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - {\left(a^{2} \cos\left(d x + c\right) - 2 \, a b\right)} \sin\left(d x + c\right)}{2 \, a^{3} d}, \frac{{\left(a^{2} - 2 \, b^{2}\right)} d x - 2 \, \sqrt{-a^{2} + b^{2}} b \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(a^{2} \cos\left(d x + c\right) - 2 \, a b\right)} \sin\left(d x + c\right)}{2 \, a^{3} d}\right]"," ",0,"[1/2*((a^2 - 2*b^2)*d*x + sqrt(a^2 - b^2)*b*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - (a^2*cos(d*x + c) - 2*a*b)*sin(d*x + c))/(a^3*d), 1/2*((a^2 - 2*b^2)*d*x - 2*sqrt(-a^2 + b^2)*b*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (a^2*cos(d*x + c) - 2*a*b)*sin(d*x + c))/(a^3*d)]","A",0
206,1,300,0,0.558520," ","integrate(csc(d*x+c)^2/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{a^{2} - b^{2}} a b \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) \sin\left(d x + c\right) - 2 \, a^{2} b + 2 \, b^{3} + 2 \, {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)}{2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \sin\left(d x + c\right)}, -\frac{\sqrt{-a^{2} + b^{2}} a b \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - a^{2} b + b^{3} + {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \sin\left(d x + c\right)}\right]"," ",0,"[-1/2*(sqrt(a^2 - b^2)*a*b*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2))*sin(d*x + c) - 2*a^2*b + 2*b^3 + 2*(a^3 - a*b^2)*cos(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d*sin(d*x + c)), -(sqrt(-a^2 + b^2)*a*b*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*sin(d*x + c) - a^2*b + b^3 + (a^3 - a*b^2)*cos(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d*sin(d*x + c))]","A",0
207,1,558,0,0.852829," ","integrate(csc(d*x+c)^4/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{8 \, a^{4} b - 10 \, a^{2} b^{3} + 2 \, b^{5} + 2 \, {\left(2 \, a^{5} - a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b \cos\left(d x + c\right)^{2} - a^{3} b\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) \sin\left(d x + c\right) - 6 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} - 6 \, {\left(a^{5} - a^{3} b^{2}\right)} \cos\left(d x + c\right)}{6 \, {\left({\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d\right)} \sin\left(d x + c\right)}, -\frac{4 \, a^{4} b - 5 \, a^{2} b^{3} + b^{5} + {\left(2 \, a^{5} - a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{3} b \cos\left(d x + c\right)^{2} - a^{3} b\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{5} - a^{3} b^{2}\right)} \cos\left(d x + c\right)}{3 \, {\left({\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/6*(8*a^4*b - 10*a^2*b^3 + 2*b^5 + 2*(2*a^5 - a^3*b^2 - a*b^4)*cos(d*x + c)^3 - 3*(a^3*b*cos(d*x + c)^2 - a^3*b)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2))*sin(d*x + c) - 6*(a^4*b - a^2*b^3)*cos(d*x + c)^2 - 6*(a^5 - a^3*b^2)*cos(d*x + c))/(((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^2 - (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d)*sin(d*x + c)), -1/3*(4*a^4*b - 5*a^2*b^3 + b^5 + (2*a^5 - a^3*b^2 - a*b^4)*cos(d*x + c)^3 + 3*(a^3*b*cos(d*x + c)^2 - a^3*b)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*sin(d*x + c) - 3*(a^4*b - a^2*b^3)*cos(d*x + c)^2 - 3*(a^5 - a^3*b^2)*cos(d*x + c))/(((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^2 - (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d)*sin(d*x + c))]","A",0
208,1,861,0,0.890907," ","integrate(csc(d*x+c)^6/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{46 \, a^{6} b - 68 \, a^{4} b^{3} + 28 \, a^{2} b^{5} - 6 \, b^{7} - 2 \, {\left(8 \, a^{7} + a^{5} b^{2} - 11 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} + 30 \, {\left(a^{6} b - a^{4} b^{3}\right)} \cos\left(d x + c\right)^{4} + 10 \, {\left(4 \, a^{7} - a^{5} b^{2} - 4 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(a^{5} b \cos\left(d x + c\right)^{4} - 2 \, a^{5} b \cos\left(d x + c\right)^{2} + a^{5} b\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) \sin\left(d x + c\right) - 10 \, {\left(7 \, a^{6} b - 8 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} - 30 \, {\left(a^{7} - a^{5} b^{2}\right)} \cos\left(d x + c\right)}{30 \, {\left({\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d\right)} \sin\left(d x + c\right)}, \frac{23 \, a^{6} b - 34 \, a^{4} b^{3} + 14 \, a^{2} b^{5} - 3 \, b^{7} - {\left(8 \, a^{7} + a^{5} b^{2} - 11 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} + 15 \, {\left(a^{6} b - a^{4} b^{3}\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(4 \, a^{7} - a^{5} b^{2} - 4 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(a^{5} b \cos\left(d x + c\right)^{4} - 2 \, a^{5} b \cos\left(d x + c\right)^{2} + a^{5} b\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 5 \, {\left(7 \, a^{6} b - 8 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} - 15 \, {\left(a^{7} - a^{5} b^{2}\right)} \cos\left(d x + c\right)}{15 \, {\left({\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[1/30*(46*a^6*b - 68*a^4*b^3 + 28*a^2*b^5 - 6*b^7 - 2*(8*a^7 + a^5*b^2 - 11*a^3*b^4 + 2*a*b^6)*cos(d*x + c)^5 + 30*(a^6*b - a^4*b^3)*cos(d*x + c)^4 + 10*(4*a^7 - a^5*b^2 - 4*a^3*b^4 + a*b^6)*cos(d*x + c)^3 - 15*(a^5*b*cos(d*x + c)^4 - 2*a^5*b*cos(d*x + c)^2 + a^5*b)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2))*sin(d*x + c) - 10*(7*a^6*b - 8*a^4*b^3 + a^2*b^5)*cos(d*x + c)^2 - 30*(a^7 - a^5*b^2)*cos(d*x + c))/(((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*d*cos(d*x + c)^4 - 2*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*d*cos(d*x + c)^2 + (a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*d)*sin(d*x + c)), 1/15*(23*a^6*b - 34*a^4*b^3 + 14*a^2*b^5 - 3*b^7 - (8*a^7 + a^5*b^2 - 11*a^3*b^4 + 2*a*b^6)*cos(d*x + c)^5 + 15*(a^6*b - a^4*b^3)*cos(d*x + c)^4 + 5*(4*a^7 - a^5*b^2 - 4*a^3*b^4 + a*b^6)*cos(d*x + c)^3 - 15*(a^5*b*cos(d*x + c)^4 - 2*a^5*b*cos(d*x + c)^2 + a^5*b)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*sin(d*x + c) - 5*(7*a^6*b - 8*a^4*b^3 + a^2*b^5)*cos(d*x + c)^2 - 15*(a^7 - a^5*b^2)*cos(d*x + c))/(((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*d*cos(d*x + c)^4 - 2*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*d*cos(d*x + c)^2 + (a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*d)*sin(d*x + c))]","B",0
209,1,344,0,0.821622," ","integrate(sin(d*x+c)^7/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{120 \, a^{8} \cos\left(d x + c\right)^{8} - 160 \, a^{7} b \cos\left(d x + c\right)^{7} + 1715 \, a^{6} b^{2} - 4725 \, a^{4} b^{4} + 3780 \, a^{2} b^{6} - 840 \, b^{8} - 56 \, {\left(9 \, a^{8} - 4 \, a^{6} b^{2}\right)} \cos\left(d x + c\right)^{6} + 84 \, {\left(9 \, a^{7} b - 4 \, a^{5} b^{3}\right)} \cos\left(d x + c\right)^{5} + 140 \, {\left(6 \, a^{8} - 9 \, a^{6} b^{2} + 4 \, a^{4} b^{4}\right)} \cos\left(d x + c\right)^{4} - 280 \, {\left(6 \, a^{7} b - 9 \, a^{5} b^{3} + 4 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{3} - 840 \, {\left(a^{8} - 6 \, a^{6} b^{2} + 9 \, a^{4} b^{4} - 4 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 35 \, {\left(a^{7} b + 153 \, a^{5} b^{3} - 324 \, a^{3} b^{5} + 168 \, a b^{7}\right)} \cos\left(d x + c\right) + 1680 \, {\left(a^{6} b^{2} - 6 \, a^{4} b^{4} + 9 \, a^{2} b^{6} - 4 \, b^{8} + {\left(a^{7} b - 6 \, a^{5} b^{3} + 9 \, a^{3} b^{5} - 4 \, a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{840 \, {\left(a^{10} d \cos\left(d x + c\right) + a^{9} b d\right)}}"," ",0,"1/840*(120*a^8*cos(d*x + c)^8 - 160*a^7*b*cos(d*x + c)^7 + 1715*a^6*b^2 - 4725*a^4*b^4 + 3780*a^2*b^6 - 840*b^8 - 56*(9*a^8 - 4*a^6*b^2)*cos(d*x + c)^6 + 84*(9*a^7*b - 4*a^5*b^3)*cos(d*x + c)^5 + 140*(6*a^8 - 9*a^6*b^2 + 4*a^4*b^4)*cos(d*x + c)^4 - 280*(6*a^7*b - 9*a^5*b^3 + 4*a^3*b^5)*cos(d*x + c)^3 - 840*(a^8 - 6*a^6*b^2 + 9*a^4*b^4 - 4*a^2*b^6)*cos(d*x + c)^2 + 35*(a^7*b + 153*a^5*b^3 - 324*a^3*b^5 + 168*a*b^7)*cos(d*x + c) + 1680*(a^6*b^2 - 6*a^4*b^4 + 9*a^2*b^6 - 4*b^8 + (a^7*b - 6*a^5*b^3 + 9*a^3*b^5 - 4*a*b^7)*cos(d*x + c))*log(a*cos(d*x + c) + b))/(a^10*d*cos(d*x + c) + a^9*b*d)","A",0
210,1,240,0,0.581610," ","integrate(sin(d*x+c)^5/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{48 \, a^{6} \cos\left(d x + c\right)^{6} - 72 \, a^{5} b \cos\left(d x + c\right)^{5} - 435 \, a^{4} b^{2} + 720 \, a^{2} b^{4} - 240 \, b^{6} - 40 \, {\left(4 \, a^{6} - 3 \, a^{4} b^{2}\right)} \cos\left(d x + c\right)^{4} + 80 \, {\left(4 \, a^{5} b - 3 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + 240 \, {\left(a^{6} - 4 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(3 \, a^{5} b - 80 \, a^{3} b^{3} + 80 \, a b^{5}\right)} \cos\left(d x + c\right) - 480 \, {\left(a^{4} b^{2} - 4 \, a^{2} b^{4} + 3 \, b^{6} + {\left(a^{5} b - 4 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{240 \, {\left(a^{8} d \cos\left(d x + c\right) + a^{7} b d\right)}}"," ",0,"-1/240*(48*a^6*cos(d*x + c)^6 - 72*a^5*b*cos(d*x + c)^5 - 435*a^4*b^2 + 720*a^2*b^4 - 240*b^6 - 40*(4*a^6 - 3*a^4*b^2)*cos(d*x + c)^4 + 80*(4*a^5*b - 3*a^3*b^3)*cos(d*x + c)^3 + 240*(a^6 - 4*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c)^2 + 15*(3*a^5*b - 80*a^3*b^3 + 80*a*b^5)*cos(d*x + c) - 480*(a^4*b^2 - 4*a^2*b^4 + 3*b^6 + (a^5*b - 4*a^3*b^3 + 3*a*b^5)*cos(d*x + c))*log(a*cos(d*x + c) + b))/(a^8*d*cos(d*x + c) + a^7*b*d)","A",0
211,1,150,0,0.553672," ","integrate(sin(d*x+c)^3/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, a^{4} \cos\left(d x + c\right)^{4} - 4 \, a^{3} b \cos\left(d x + c\right)^{3} + 9 \, a^{2} b^{2} - 6 \, b^{4} - 6 \, {\left(a^{4} - 2 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{3} b - 6 \, a b^{3}\right)} \cos\left(d x + c\right) + 12 \, {\left(a^{2} b^{2} - 2 \, b^{4} + {\left(a^{3} b - 2 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{6 \, {\left(a^{6} d \cos\left(d x + c\right) + a^{5} b d\right)}}"," ",0,"1/6*(2*a^4*cos(d*x + c)^4 - 4*a^3*b*cos(d*x + c)^3 + 9*a^2*b^2 - 6*b^4 - 6*(a^4 - 2*a^2*b^2)*cos(d*x + c)^2 - 3*(a^3*b - 6*a*b^3)*cos(d*x + c) + 12*(a^2*b^2 - 2*b^4 + (a^3*b - 2*a*b^3)*cos(d*x + c))*log(a*cos(d*x + c) + b))/(a^6*d*cos(d*x + c) + a^5*b*d)","A",0
212,1,75,0,0.609588," ","integrate(sin(d*x+c)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a^{2} \cos\left(d x + c\right)^{2} + a b \cos\left(d x + c\right) - b^{2} - 2 \, {\left(a b \cos\left(d x + c\right) + b^{2}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{4} d \cos\left(d x + c\right) + a^{3} b d}"," ",0,"-(a^2*cos(d*x + c)^2 + a*b*cos(d*x + c) - b^2 - 2*(a*b*cos(d*x + c) + b^2)*log(a*cos(d*x + c) + b))/(a^4*d*cos(d*x + c) + a^3*b*d)","A",0
213,1,210,0,0.638578," ","integrate(csc(d*x+c)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, a^{2} b^{2} - 2 \, b^{4} + 4 \, {\left(a^{3} b \cos\left(d x + c\right) + a^{2} b^{2}\right)} \log\left(a \cos\left(d x + c\right) + b\right) - {\left(a^{3} b + 2 \, a^{2} b^{2} + a b^{3} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3} + {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left({\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d\right)}}"," ",0,"1/2*(2*a^2*b^2 - 2*b^4 + 4*(a^3*b*cos(d*x + c) + a^2*b^2)*log(a*cos(d*x + c) + b) - (a^3*b + 2*a^2*b^2 + a*b^3 + (a^4 + 2*a^3*b + a^2*b^2)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (a^3*b - 2*a^2*b^2 + a*b^3 + (a^4 - 2*a^3*b + a^2*b^2)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^6 - 2*a^4*b^2 + a^2*b^4)*d*cos(d*x + c) + (a^5*b - 2*a^3*b^3 + a*b^5)*d)","A",0
214,1,630,0,0.762643," ","integrate(csc(d*x+c)^3/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{8 \, a^{3} b^{2} - 8 \, a b^{4} - 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right) + 8 \, {\left(a^{3} b^{2} + a b^{4} - {\left(a^{4} b + a^{2} b^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} b + a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right) - {\left(a^{4} b + 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 4 \, a b^{4} + b^{5} - {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{4} b + 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 4 \, a b^{4} + b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5} - {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left({\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right) - {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d\right)}}"," ",0,"-1/4*(8*a^3*b^2 - 8*a*b^4 - 2*(a^5 + 2*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^2 + 2*(a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c) + 8*(a^3*b^2 + a*b^4 - (a^4*b + a^2*b^3)*cos(d*x + c)^3 - (a^3*b^2 + a*b^4)*cos(d*x + c)^2 + (a^4*b + a^2*b^3)*cos(d*x + c))*log(a*cos(d*x + c) + b) - (a^4*b + 4*a^3*b^2 + 6*a^2*b^3 + 4*a*b^4 + b^5 - (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cos(d*x + c)^3 - (a^4*b + 4*a^3*b^2 + 6*a^2*b^3 + 4*a*b^4 + b^5)*cos(d*x + c)^2 + (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5 - (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*cos(d*x + c)^3 - (a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*cos(d*x + c)^2 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c)^3 + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d*cos(d*x + c)^2 - (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c) - (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d)","B",0
215,1,1205,0,0.874093," ","integrate(csc(d*x+c)^5/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{40 \, a^{5} b^{2} - 32 \, a^{3} b^{4} - 8 \, a b^{6} + 2 \, {\left(3 \, a^{7} + 17 \, a^{5} b^{2} - 19 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(5 \, a^{6} b - 9 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(5 \, a^{7} + 31 \, a^{5} b^{2} - 29 \, a^{3} b^{4} - 7 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, a^{6} b - 15 \, a^{4} b^{3} + 9 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right) + 32 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + {\left(a^{6} b + 2 \, a^{4} b^{3}\right)} \cos\left(d x + c\right)^{5} + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{6} b + 2 \, a^{4} b^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right) - {\left(3 \, a^{6} b + 16 \, a^{5} b^{2} + 33 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 13 \, a^{2} b^{5} - b^{7} + {\left(3 \, a^{7} + 16 \, a^{6} b + 33 \, a^{5} b^{2} + 32 \, a^{4} b^{3} + 13 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{5} + {\left(3 \, a^{6} b + 16 \, a^{5} b^{2} + 33 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 13 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{7} + 16 \, a^{6} b + 33 \, a^{5} b^{2} + 32 \, a^{4} b^{3} + 13 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(3 \, a^{6} b + 16 \, a^{5} b^{2} + 33 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 13 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 16 \, a^{6} b + 33 \, a^{5} b^{2} + 32 \, a^{4} b^{3} + 13 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(3 \, a^{6} b - 16 \, a^{5} b^{2} + 33 \, a^{4} b^{3} - 32 \, a^{3} b^{4} + 13 \, a^{2} b^{5} - b^{7} + {\left(3 \, a^{7} - 16 \, a^{6} b + 33 \, a^{5} b^{2} - 32 \, a^{4} b^{3} + 13 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{5} + {\left(3 \, a^{6} b - 16 \, a^{5} b^{2} + 33 \, a^{4} b^{3} - 32 \, a^{3} b^{4} + 13 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{7} - 16 \, a^{6} b + 33 \, a^{5} b^{2} - 32 \, a^{4} b^{3} + 13 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(3 \, a^{6} b - 16 \, a^{5} b^{2} + 33 \, a^{4} b^{3} - 32 \, a^{3} b^{4} + 13 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{7} - 16 \, a^{6} b + 33 \, a^{5} b^{2} - 32 \, a^{4} b^{3} + 13 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{16 \, {\left({\left(a^{9} - 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{5} + {\left(a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{9} - 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{9} - 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} d\right)}}"," ",0,"1/16*(40*a^5*b^2 - 32*a^3*b^4 - 8*a*b^6 + 2*(3*a^7 + 17*a^5*b^2 - 19*a^3*b^4 - a*b^6)*cos(d*x + c)^4 - 2*(5*a^6*b - 9*a^4*b^3 + 3*a^2*b^5 + b^7)*cos(d*x + c)^3 - 2*(5*a^7 + 31*a^5*b^2 - 29*a^3*b^4 - 7*a*b^6)*cos(d*x + c)^2 + 2*(7*a^6*b - 15*a^4*b^3 + 9*a^2*b^5 - b^7)*cos(d*x + c) + 32*(a^5*b^2 + 2*a^3*b^4 + (a^6*b + 2*a^4*b^3)*cos(d*x + c)^5 + (a^5*b^2 + 2*a^3*b^4)*cos(d*x + c)^4 - 2*(a^6*b + 2*a^4*b^3)*cos(d*x + c)^3 - 2*(a^5*b^2 + 2*a^3*b^4)*cos(d*x + c)^2 + (a^6*b + 2*a^4*b^3)*cos(d*x + c))*log(a*cos(d*x + c) + b) - (3*a^6*b + 16*a^5*b^2 + 33*a^4*b^3 + 32*a^3*b^4 + 13*a^2*b^5 - b^7 + (3*a^7 + 16*a^6*b + 33*a^5*b^2 + 32*a^4*b^3 + 13*a^3*b^4 - a*b^6)*cos(d*x + c)^5 + (3*a^6*b + 16*a^5*b^2 + 33*a^4*b^3 + 32*a^3*b^4 + 13*a^2*b^5 - b^7)*cos(d*x + c)^4 - 2*(3*a^7 + 16*a^6*b + 33*a^5*b^2 + 32*a^4*b^3 + 13*a^3*b^4 - a*b^6)*cos(d*x + c)^3 - 2*(3*a^6*b + 16*a^5*b^2 + 33*a^4*b^3 + 32*a^3*b^4 + 13*a^2*b^5 - b^7)*cos(d*x + c)^2 + (3*a^7 + 16*a^6*b + 33*a^5*b^2 + 32*a^4*b^3 + 13*a^3*b^4 - a*b^6)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (3*a^6*b - 16*a^5*b^2 + 33*a^4*b^3 - 32*a^3*b^4 + 13*a^2*b^5 - b^7 + (3*a^7 - 16*a^6*b + 33*a^5*b^2 - 32*a^4*b^3 + 13*a^3*b^4 - a*b^6)*cos(d*x + c)^5 + (3*a^6*b - 16*a^5*b^2 + 33*a^4*b^3 - 32*a^3*b^4 + 13*a^2*b^5 - b^7)*cos(d*x + c)^4 - 2*(3*a^7 - 16*a^6*b + 33*a^5*b^2 - 32*a^4*b^3 + 13*a^3*b^4 - a*b^6)*cos(d*x + c)^3 - 2*(3*a^6*b - 16*a^5*b^2 + 33*a^4*b^3 - 32*a^3*b^4 + 13*a^2*b^5 - b^7)*cos(d*x + c)^2 + (3*a^7 - 16*a^6*b + 33*a^5*b^2 - 32*a^4*b^3 + 13*a^3*b^4 - a*b^6)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^9 - 4*a^7*b^2 + 6*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c)^5 + (a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9)*d*cos(d*x + c)^4 - 2*(a^9 - 4*a^7*b^2 + 6*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c)^3 - 2*(a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9)*d*cos(d*x + c)^2 + (a^9 - 4*a^7*b^2 + 6*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c) + (a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9)*d)","B",0
216,1,793,0,0.648059," ","integrate(sin(d*x+c)^6/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6}\right)} d x \cos\left(d x + c\right) + 15 \, {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7}\right)} d x + 120 \, {\left(2 \, a^{4} b^{2} - 9 \, a^{2} b^{4} + 7 \, b^{6} + {\left(2 \, a^{5} b - 9 \, a^{3} b^{3} + 7 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - {\left(40 \, a^{7} \cos\left(d x + c\right)^{6} - 56 \, a^{6} b \cos\left(d x + c\right)^{5} - 976 \, a^{5} b^{2} + 2720 \, a^{3} b^{4} - 1680 \, a b^{6} - 2 \, {\left(65 \, a^{7} - 42 \, a^{5} b^{2}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(111 \, a^{6} b - 70 \, a^{4} b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(165 \, a^{7} - 458 \, a^{5} b^{2} + 280 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)^{2} - {\left(571 \, a^{6} b - 1430 \, a^{4} b^{3} + 840 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(a^{9} d \cos\left(d x + c\right) + a^{8} b d\right)}}, \frac{15 \, {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6}\right)} d x \cos\left(d x + c\right) + 15 \, {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7}\right)} d x - 240 \, {\left(2 \, a^{4} b^{2} - 9 \, a^{2} b^{4} + 7 \, b^{6} + {\left(2 \, a^{5} b - 9 \, a^{3} b^{3} + 7 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(40 \, a^{7} \cos\left(d x + c\right)^{6} - 56 \, a^{6} b \cos\left(d x + c\right)^{5} - 976 \, a^{5} b^{2} + 2720 \, a^{3} b^{4} - 1680 \, a b^{6} - 2 \, {\left(65 \, a^{7} - 42 \, a^{5} b^{2}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(111 \, a^{6} b - 70 \, a^{4} b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(165 \, a^{7} - 458 \, a^{5} b^{2} + 280 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)^{2} - {\left(571 \, a^{6} b - 1430 \, a^{4} b^{3} + 840 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(a^{9} d \cos\left(d x + c\right) + a^{8} b d\right)}}\right]"," ",0,"[1/240*(15*(5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6)*d*x*cos(d*x + c) + 15*(5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7)*d*x + 120*(2*a^4*b^2 - 9*a^2*b^4 + 7*b^6 + (2*a^5*b - 9*a^3*b^3 + 7*a*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - (40*a^7*cos(d*x + c)^6 - 56*a^6*b*cos(d*x + c)^5 - 976*a^5*b^2 + 2720*a^3*b^4 - 1680*a*b^6 - 2*(65*a^7 - 42*a^5*b^2)*cos(d*x + c)^4 + 2*(111*a^6*b - 70*a^4*b^3)*cos(d*x + c)^3 + (165*a^7 - 458*a^5*b^2 + 280*a^3*b^4)*cos(d*x + c)^2 - (571*a^6*b - 1430*a^4*b^3 + 840*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/(a^9*d*cos(d*x + c) + a^8*b*d), 1/240*(15*(5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6)*d*x*cos(d*x + c) + 15*(5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7)*d*x - 240*(2*a^4*b^2 - 9*a^2*b^4 + 7*b^6 + (2*a^5*b - 9*a^3*b^3 + 7*a*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (40*a^7*cos(d*x + c)^6 - 56*a^6*b*cos(d*x + c)^5 - 976*a^5*b^2 + 2720*a^3*b^4 - 1680*a*b^6 - 2*(65*a^7 - 42*a^5*b^2)*cos(d*x + c)^4 + 2*(111*a^6*b - 70*a^4*b^3)*cos(d*x + c)^3 + (165*a^7 - 458*a^5*b^2 + 280*a^3*b^4)*cos(d*x + c)^2 - (571*a^6*b - 1430*a^4*b^3 + 840*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/(a^9*d*cos(d*x + c) + a^8*b*d)]","A",0
217,1,581,0,0.566075," ","integrate(sin(d*x+c)^4/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, a^{5} - 36 \, a^{3} b^{2} + 40 \, a b^{4}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(3 \, a^{4} b - 36 \, a^{2} b^{3} + 40 \, b^{5}\right)} d x - 12 \, {\left(2 \, a^{2} b^{2} - 5 \, b^{4} + {\left(2 \, a^{3} b - 5 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + {\left(6 \, a^{5} \cos\left(d x + c\right)^{4} - 10 \, a^{4} b \cos\left(d x + c\right)^{3} + 88 \, a^{3} b^{2} - 120 \, a b^{4} - 5 \, {\left(3 \, a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(49 \, a^{4} b - 60 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(a^{7} d \cos\left(d x + c\right) + a^{6} b d\right)}}, \frac{3 \, {\left(3 \, a^{5} - 36 \, a^{3} b^{2} + 40 \, a b^{4}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(3 \, a^{4} b - 36 \, a^{2} b^{3} + 40 \, b^{5}\right)} d x - 24 \, {\left(2 \, a^{2} b^{2} - 5 \, b^{4} + {\left(2 \, a^{3} b - 5 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(6 \, a^{5} \cos\left(d x + c\right)^{4} - 10 \, a^{4} b \cos\left(d x + c\right)^{3} + 88 \, a^{3} b^{2} - 120 \, a b^{4} - 5 \, {\left(3 \, a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(49 \, a^{4} b - 60 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(a^{7} d \cos\left(d x + c\right) + a^{6} b d\right)}}\right]"," ",0,"[1/24*(3*(3*a^5 - 36*a^3*b^2 + 40*a*b^4)*d*x*cos(d*x + c) + 3*(3*a^4*b - 36*a^2*b^3 + 40*b^5)*d*x - 12*(2*a^2*b^2 - 5*b^4 + (2*a^3*b - 5*a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + (6*a^5*cos(d*x + c)^4 - 10*a^4*b*cos(d*x + c)^3 + 88*a^3*b^2 - 120*a*b^4 - 5*(3*a^5 - 4*a^3*b^2)*cos(d*x + c)^2 + (49*a^4*b - 60*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/(a^7*d*cos(d*x + c) + a^6*b*d), 1/24*(3*(3*a^5 - 36*a^3*b^2 + 40*a*b^4)*d*x*cos(d*x + c) + 3*(3*a^4*b - 36*a^2*b^3 + 40*b^5)*d*x - 24*(2*a^2*b^2 - 5*b^4 + (2*a^3*b - 5*a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (6*a^5*cos(d*x + c)^4 - 10*a^4*b*cos(d*x + c)^3 + 88*a^3*b^2 - 120*a*b^4 - 5*(3*a^5 - 4*a^3*b^2)*cos(d*x + c)^2 + (49*a^4*b - 60*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/(a^7*d*cos(d*x + c) + a^6*b*d)]","A",0
218,1,551,0,0.552534," ","integrate(sin(d*x+c)^2/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4}\right)} d x \cos\left(d x + c\right) + {\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5}\right)} d x - {\left(2 \, a^{2} b^{2} - 3 \, b^{4} + {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + {\left(6 \, a^{3} b^{2} - 6 \, a b^{4} - {\left(a^{5} - a^{3} b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{7} - a^{5} b^{2}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3}\right)} d\right)}}, \frac{{\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4}\right)} d x \cos\left(d x + c\right) + {\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5}\right)} d x - 2 \, {\left(2 \, a^{2} b^{2} - 3 \, b^{4} + {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(6 \, a^{3} b^{2} - 6 \, a b^{4} - {\left(a^{5} - a^{3} b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{7} - a^{5} b^{2}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3}\right)} d\right)}}\right]"," ",0,"[1/2*((a^5 - 7*a^3*b^2 + 6*a*b^4)*d*x*cos(d*x + c) + (a^4*b - 7*a^2*b^3 + 6*b^5)*d*x - (2*a^2*b^2 - 3*b^4 + (2*a^3*b - 3*a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + (6*a^3*b^2 - 6*a*b^4 - (a^5 - a^3*b^2)*cos(d*x + c)^2 + 3*(a^4*b - a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^7 - a^5*b^2)*d*cos(d*x + c) + (a^6*b - a^4*b^3)*d), 1/2*((a^5 - 7*a^3*b^2 + 6*a*b^4)*d*x*cos(d*x + c) + (a^4*b - 7*a^2*b^3 + 6*b^5)*d*x - 2*(2*a^2*b^2 - 3*b^4 + (2*a^3*b - 3*a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (6*a^3*b^2 - 6*a*b^4 - (a^5 - a^3*b^2)*cos(d*x + c)^2 + 3*(a^4*b - a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^7 - a^5*b^2)*d*cos(d*x + c) + (a^6*b - a^4*b^3)*d)]","A",0
219,1,526,0,0.601876," ","integrate(csc(d*x+c)^2/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{6 \, a^{3} b^{2} - 6 \, a b^{4} + {\left(2 \, a^{2} b^{2} + b^{4} + {\left(2 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) \sin\left(d x + c\right) - 2 \, {\left(a^{5} + a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)}{2 \, {\left({\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d\right)} \sin\left(d x + c\right)}, \frac{3 \, a^{3} b^{2} - 3 \, a b^{4} - {\left(2 \, a^{2} b^{2} + b^{4} + {\left(2 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - {\left(a^{5} + a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)}{{\left({\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[1/2*(6*a^3*b^2 - 6*a*b^4 + (2*a^2*b^2 + b^4 + (2*a^3*b + a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2))*sin(d*x + c) - 2*(a^5 + a^3*b^2 - 2*a*b^4)*cos(d*x + c)^2 + 2*(a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c))/(((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c) + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d)*sin(d*x + c)), (3*a^3*b^2 - 3*a*b^4 - (2*a^2*b^2 + b^4 + (2*a^3*b + a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*sin(d*x + c) - (a^5 + a^3*b^2 - 2*a*b^4)*cos(d*x + c)^2 + (a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c))/(((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c) + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d)*sin(d*x + c))]","A",0
220,1,1040,0,0.704802," ","integrate(csc(d*x+c)^4/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{22 \, a^{5} b^{2} - 14 \, a^{3} b^{4} - 8 \, a b^{6} + 2 \, {\left(2 \, a^{7} + 10 \, a^{5} b^{2} - 11 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(4 \, a^{6} b - 7 \, a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - {\left(2 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(2 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) \sin\left(d x + c\right) - 6 \, {\left(a^{7} + 6 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 2 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 10 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right)}{6 \, {\left({\left(a^{9} - 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{9} - 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right) - {\left(a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} d\right)} \sin\left(d x + c\right)}, -\frac{11 \, a^{5} b^{2} - 7 \, a^{3} b^{4} - 4 \, a b^{6} + {\left(2 \, a^{7} + 10 \, a^{5} b^{2} - 11 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{4} - {\left(4 \, a^{6} b - 7 \, a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - {\left(2 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(2 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 3 \, {\left(a^{7} + 6 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 2 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right)}{3 \, {\left({\left(a^{9} - 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{9} - 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right) - {\left(a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/6*(22*a^5*b^2 - 14*a^3*b^4 - 8*a*b^6 + 2*(2*a^7 + 10*a^5*b^2 - 11*a^3*b^4 - a*b^6)*cos(d*x + c)^4 - 2*(4*a^6*b - 7*a^4*b^3 + 2*a^2*b^5 + b^7)*cos(d*x + c)^3 - 3*(2*a^4*b^2 + 3*a^2*b^4 - (2*a^5*b + 3*a^3*b^3)*cos(d*x + c)^3 - (2*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c)^2 + (2*a^5*b + 3*a^3*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2))*sin(d*x + c) - 6*(a^7 + 6*a^5*b^2 - 5*a^3*b^4 - 2*a*b^6)*cos(d*x + c)^2 + 10*(a^6*b - 2*a^4*b^3 + a^2*b^5)*cos(d*x + c))/(((a^9 - 4*a^7*b^2 + 6*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c)^3 + (a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9)*d*cos(d*x + c)^2 - (a^9 - 4*a^7*b^2 + 6*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c) - (a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9)*d)*sin(d*x + c)), -1/3*(11*a^5*b^2 - 7*a^3*b^4 - 4*a*b^6 + (2*a^7 + 10*a^5*b^2 - 11*a^3*b^4 - a*b^6)*cos(d*x + c)^4 - (4*a^6*b - 7*a^4*b^3 + 2*a^2*b^5 + b^7)*cos(d*x + c)^3 - 3*(2*a^4*b^2 + 3*a^2*b^4 - (2*a^5*b + 3*a^3*b^3)*cos(d*x + c)^3 - (2*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c)^2 + (2*a^5*b + 3*a^3*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*sin(d*x + c) - 3*(a^7 + 6*a^5*b^2 - 5*a^3*b^4 - 2*a*b^6)*cos(d*x + c)^2 + 5*(a^6*b - 2*a^4*b^3 + a^2*b^5)*cos(d*x + c))/(((a^9 - 4*a^7*b^2 + 6*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c)^3 + (a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9)*d*cos(d*x + c)^2 - (a^9 - 4*a^7*b^2 + 6*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c) - (a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9)*d)*sin(d*x + c))]","A",0
221,1,447,0,0.806548," ","integrate(sin(d*x+c)^7/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{80 \, a^{9} \cos\left(d x + c\right)^{9} - 120 \, a^{8} b \cos\left(d x + c\right)^{8} + 2275 \, a^{6} b^{3} - 11235 \, a^{4} b^{5} + 13860 \, a^{2} b^{7} - 4760 \, b^{9} - 48 \, {\left(7 \, a^{9} - 4 \, a^{7} b^{2}\right)} \cos\left(d x + c\right)^{7} + 84 \, {\left(7 \, a^{8} b - 4 \, a^{6} b^{3}\right)} \cos\left(d x + c\right)^{6} + 56 \, {\left(10 \, a^{9} - 21 \, a^{7} b^{2} + 12 \, a^{5} b^{4}\right)} \cos\left(d x + c\right)^{5} - 140 \, {\left(10 \, a^{8} b - 21 \, a^{6} b^{3} + 12 \, a^{4} b^{5}\right)} \cos\left(d x + c\right)^{4} - 560 \, {\left(a^{9} - 10 \, a^{7} b^{2} + 21 \, a^{5} b^{4} - 12 \, a^{3} b^{6}\right)} \cos\left(d x + c\right)^{3} - 35 \, {\left(7 \, a^{8} b - 399 \, a^{6} b^{3} + 1116 \, a^{4} b^{5} - 728 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + 70 \, {\left(41 \, a^{7} b^{2} - 81 \, a^{5} b^{4} - 108 \, a^{3} b^{6} + 152 \, a b^{8}\right)} \cos\left(d x + c\right) + 1680 \, {\left(a^{6} b^{3} - 10 \, a^{4} b^{5} + 21 \, a^{2} b^{7} - 12 \, b^{9} + {\left(a^{8} b - 10 \, a^{6} b^{3} + 21 \, a^{4} b^{5} - 12 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{2} - 10 \, a^{5} b^{4} + 21 \, a^{3} b^{6} - 12 \, a b^{8}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{560 \, {\left(a^{12} d \cos\left(d x + c\right)^{2} + 2 \, a^{11} b d \cos\left(d x + c\right) + a^{10} b^{2} d\right)}}"," ",0,"1/560*(80*a^9*cos(d*x + c)^9 - 120*a^8*b*cos(d*x + c)^8 + 2275*a^6*b^3 - 11235*a^4*b^5 + 13860*a^2*b^7 - 4760*b^9 - 48*(7*a^9 - 4*a^7*b^2)*cos(d*x + c)^7 + 84*(7*a^8*b - 4*a^6*b^3)*cos(d*x + c)^6 + 56*(10*a^9 - 21*a^7*b^2 + 12*a^5*b^4)*cos(d*x + c)^5 - 140*(10*a^8*b - 21*a^6*b^3 + 12*a^4*b^5)*cos(d*x + c)^4 - 560*(a^9 - 10*a^7*b^2 + 21*a^5*b^4 - 12*a^3*b^6)*cos(d*x + c)^3 - 35*(7*a^8*b - 399*a^6*b^3 + 1116*a^4*b^5 - 728*a^2*b^7)*cos(d*x + c)^2 + 70*(41*a^7*b^2 - 81*a^5*b^4 - 108*a^3*b^6 + 152*a*b^8)*cos(d*x + c) + 1680*(a^6*b^3 - 10*a^4*b^5 + 21*a^2*b^7 - 12*b^9 + (a^8*b - 10*a^6*b^3 + 21*a^4*b^5 - 12*a^2*b^7)*cos(d*x + c)^2 + 2*(a^7*b^2 - 10*a^5*b^4 + 21*a^3*b^6 - 12*a*b^8)*cos(d*x + c))*log(a*cos(d*x + c) + b))/(a^12*d*cos(d*x + c)^2 + 2*a^11*b*d*cos(d*x + c) + a^10*b^2*d)","A",0
222,1,331,0,0.708236," ","integrate(sin(d*x+c)^5/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{96 \, a^{7} \cos\left(d x + c\right)^{7} - 168 \, a^{6} b \cos\left(d x + c\right)^{6} - 1785 \, a^{4} b^{3} + 5520 \, a^{2} b^{5} - 3120 \, b^{7} - 16 \, {\left(20 \, a^{7} - 21 \, a^{5} b^{2}\right)} \cos\left(d x + c\right)^{5} + 40 \, {\left(20 \, a^{6} b - 21 \, a^{4} b^{3}\right)} \cos\left(d x + c\right)^{4} + 160 \, {\left(3 \, a^{7} - 20 \, a^{5} b^{2} + 21 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(25 \, a^{6} b - 592 \, a^{4} b^{3} + 800 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} - 30 \, {\left(71 \, a^{5} b^{2} - 48 \, a^{3} b^{4} - 128 \, a b^{6}\right)} \cos\left(d x + c\right) - 480 \, {\left(3 \, a^{4} b^{3} - 20 \, a^{2} b^{5} + 21 \, b^{7} + {\left(3 \, a^{6} b - 20 \, a^{4} b^{3} + 21 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{5} b^{2} - 20 \, a^{3} b^{4} + 21 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{480 \, {\left(a^{10} d \cos\left(d x + c\right)^{2} + 2 \, a^{9} b d \cos\left(d x + c\right) + a^{8} b^{2} d\right)}}"," ",0,"-1/480*(96*a^7*cos(d*x + c)^7 - 168*a^6*b*cos(d*x + c)^6 - 1785*a^4*b^3 + 5520*a^2*b^5 - 3120*b^7 - 16*(20*a^7 - 21*a^5*b^2)*cos(d*x + c)^5 + 40*(20*a^6*b - 21*a^4*b^3)*cos(d*x + c)^4 + 160*(3*a^7 - 20*a^5*b^2 + 21*a^3*b^4)*cos(d*x + c)^3 + 15*(25*a^6*b - 592*a^4*b^3 + 800*a^2*b^5)*cos(d*x + c)^2 - 30*(71*a^5*b^2 - 48*a^3*b^4 - 128*a*b^6)*cos(d*x + c) - 480*(3*a^4*b^3 - 20*a^2*b^5 + 21*b^7 + (3*a^6*b - 20*a^4*b^3 + 21*a^2*b^5)*cos(d*x + c)^2 + 2*(3*a^5*b^2 - 20*a^3*b^4 + 21*a*b^6)*cos(d*x + c))*log(a*cos(d*x + c) + b))/(a^10*d*cos(d*x + c)^2 + 2*a^9*b*d*cos(d*x + c) + a^8*b^2*d)","A",0
223,1,226,0,0.548730," ","integrate(sin(d*x+c)^3/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, a^{5} \cos\left(d x + c\right)^{5} - 10 \, a^{4} b \cos\left(d x + c\right)^{4} + 39 \, a^{2} b^{3} - 54 \, b^{5} - 4 \, {\left(3 \, a^{5} - 10 \, a^{3} b^{2}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{4} b - 42 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(7 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \cos\left(d x + c\right) + 12 \, {\left(3 \, a^{2} b^{3} - 10 \, b^{5} + {\left(3 \, a^{4} b - 10 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} - 10 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{12 \, {\left(a^{8} d \cos\left(d x + c\right)^{2} + 2 \, a^{7} b d \cos\left(d x + c\right) + a^{6} b^{2} d\right)}}"," ",0,"1/12*(4*a^5*cos(d*x + c)^5 - 10*a^4*b*cos(d*x + c)^4 + 39*a^2*b^3 - 54*b^5 - 4*(3*a^5 - 10*a^3*b^2)*cos(d*x + c)^3 - 3*(5*a^4*b - 42*a^2*b^3)*cos(d*x + c)^2 + 6*(7*a^3*b^2 + 2*a*b^4)*cos(d*x + c) + 12*(3*a^2*b^3 - 10*b^5 + (3*a^4*b - 10*a^2*b^3)*cos(d*x + c)^2 + 2*(3*a^3*b^2 - 10*a*b^4)*cos(d*x + c))*log(a*cos(d*x + c) + b))/(a^8*d*cos(d*x + c)^2 + 2*a^7*b*d*cos(d*x + c) + a^6*b^2*d)","A",0
224,1,126,0,0.593310," ","integrate(sin(d*x+c)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, a^{3} \cos\left(d x + c\right)^{3} + 4 \, a^{2} b \cos\left(d x + c\right)^{2} - 4 \, a b^{2} \cos\left(d x + c\right) - 5 \, b^{3} - 6 \, {\left(a^{2} b \cos\left(d x + c\right)^{2} + 2 \, a b^{2} \cos\left(d x + c\right) + b^{3}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{2 \, {\left(a^{6} d \cos\left(d x + c\right)^{2} + 2 \, a^{5} b d \cos\left(d x + c\right) + a^{4} b^{2} d\right)}}"," ",0,"-1/2*(2*a^3*cos(d*x + c)^3 + 4*a^2*b*cos(d*x + c)^2 - 4*a*b^2*cos(d*x + c) - 5*b^3 - 6*(a^2*b*cos(d*x + c)^2 + 2*a*b^2*cos(d*x + c) + b^3)*log(a*cos(d*x + c) + b))/(a^6*d*cos(d*x + c)^2 + 2*a^5*b*d*cos(d*x + c) + a^4*b^2*d)","A",0
225,1,474,0,0.597355," ","integrate(csc(d*x+c)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{5 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7} + 2 \, {\left(3 \, a^{5} b^{2} - 4 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + 2 \, {\left(3 \, a^{4} b^{3} + a^{2} b^{5} + {\left(3 \, a^{6} b + a^{4} b^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{5} b^{2} + a^{3} b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right) - {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} + a^{2} b^{5} + {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b + 3 \, a^{5} b^{2} + 3 \, a^{4} b^{3} + a^{3} b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5} + {\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b - 3 \, a^{5} b^{2} + 3 \, a^{4} b^{3} - a^{3} b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left({\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b - 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - a^{3} b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{2} - 3 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - a^{2} b^{8}\right)} d\right)}}"," ",0,"1/2*(5*a^4*b^3 - 6*a^2*b^5 + b^7 + 2*(3*a^5*b^2 - 4*a^3*b^4 + a*b^6)*cos(d*x + c) + 2*(3*a^4*b^3 + a^2*b^5 + (3*a^6*b + a^4*b^3)*cos(d*x + c)^2 + 2*(3*a^5*b^2 + a^3*b^4)*cos(d*x + c))*log(a*cos(d*x + c) + b) - (a^5*b^2 + 3*a^4*b^3 + 3*a^3*b^4 + a^2*b^5 + (a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*cos(d*x + c)^2 + 2*(a^6*b + 3*a^5*b^2 + 3*a^4*b^3 + a^3*b^4)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5 + (a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*cos(d*x + c)^2 + 2*(a^6*b - 3*a^5*b^2 + 3*a^4*b^3 - a^3*b^4)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*d*cos(d*x + c)^2 + 2*(a^9*b - 3*a^7*b^3 + 3*a^5*b^5 - a^3*b^7)*d*cos(d*x + c) + (a^8*b^2 - 3*a^6*b^4 + 3*a^4*b^6 - a^2*b^8)*d)","B",0
226,1,1071,0,0.894291," ","integrate(csc(d*x+c)^3/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{16 \, a^{4} b^{3} - 8 \, a^{2} b^{5} - 8 \, b^{7} - 2 \, {\left(a^{7} + 8 \, a^{5} b^{2} - 7 \, a^{3} b^{4} - 2 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{6} b - 11 \, a^{4} b^{3} + 7 \, a^{2} b^{5} + 3 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, a^{5} b^{2} - 10 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right) + 4 \, {\left(3 \, a^{4} b^{3} + 8 \, a^{2} b^{5} + b^{7} - {\left(3 \, a^{6} b + 8 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} b^{2} + 8 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, a^{6} b + 5 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{5} b^{2} + 8 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right) - {\left(a^{5} b^{2} + 6 \, a^{4} b^{3} + 14 \, a^{3} b^{4} + 16 \, a^{2} b^{5} + 9 \, a b^{6} + 2 \, b^{7} - {\left(a^{7} + 6 \, a^{6} b + 14 \, a^{5} b^{2} + 16 \, a^{4} b^{3} + 9 \, a^{3} b^{4} + 2 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b + 6 \, a^{5} b^{2} + 14 \, a^{4} b^{3} + 16 \, a^{3} b^{4} + 9 \, a^{2} b^{5} + 2 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{7} + 6 \, a^{6} b + 13 \, a^{5} b^{2} + 10 \, a^{4} b^{3} - 5 \, a^{3} b^{4} - 14 \, a^{2} b^{5} - 9 \, a b^{6} - 2 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b + 6 \, a^{5} b^{2} + 14 \, a^{4} b^{3} + 16 \, a^{3} b^{4} + 9 \, a^{2} b^{5} + 2 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{5} b^{2} - 6 \, a^{4} b^{3} + 14 \, a^{3} b^{4} - 16 \, a^{2} b^{5} + 9 \, a b^{6} - 2 \, b^{7} - {\left(a^{7} - 6 \, a^{6} b + 14 \, a^{5} b^{2} - 16 \, a^{4} b^{3} + 9 \, a^{3} b^{4} - 2 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b - 6 \, a^{5} b^{2} + 14 \, a^{4} b^{3} - 16 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 2 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{7} - 6 \, a^{6} b + 13 \, a^{5} b^{2} - 10 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + 14 \, a^{2} b^{5} - 9 \, a b^{6} + 2 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b - 6 \, a^{5} b^{2} + 14 \, a^{4} b^{3} - 16 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 2 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left({\left(a^{10} - 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} - 4 \, a^{4} b^{6} + a^{2} b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)^{3} - {\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)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) - {\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d\right)}}"," ",0,"-1/4*(16*a^4*b^3 - 8*a^2*b^5 - 8*b^7 - 2*(a^7 + 8*a^5*b^2 - 7*a^3*b^4 - 2*a*b^6)*cos(d*x + c)^3 + 2*(a^6*b - 11*a^4*b^3 + 7*a^2*b^5 + 3*b^7)*cos(d*x + c)^2 + 2*(11*a^5*b^2 - 10*a^3*b^4 - a*b^6)*cos(d*x + c) + 4*(3*a^4*b^3 + 8*a^2*b^5 + b^7 - (3*a^6*b + 8*a^4*b^3 + a^2*b^5)*cos(d*x + c)^4 - 2*(3*a^5*b^2 + 8*a^3*b^4 + a*b^6)*cos(d*x + c)^3 + (3*a^6*b + 5*a^4*b^3 - 7*a^2*b^5 - b^7)*cos(d*x + c)^2 + 2*(3*a^5*b^2 + 8*a^3*b^4 + a*b^6)*cos(d*x + c))*log(a*cos(d*x + c) + b) - (a^5*b^2 + 6*a^4*b^3 + 14*a^3*b^4 + 16*a^2*b^5 + 9*a*b^6 + 2*b^7 - (a^7 + 6*a^6*b + 14*a^5*b^2 + 16*a^4*b^3 + 9*a^3*b^4 + 2*a^2*b^5)*cos(d*x + c)^4 - 2*(a^6*b + 6*a^5*b^2 + 14*a^4*b^3 + 16*a^3*b^4 + 9*a^2*b^5 + 2*a*b^6)*cos(d*x + c)^3 + (a^7 + 6*a^6*b + 13*a^5*b^2 + 10*a^4*b^3 - 5*a^3*b^4 - 14*a^2*b^5 - 9*a*b^6 - 2*b^7)*cos(d*x + c)^2 + 2*(a^6*b + 6*a^5*b^2 + 14*a^4*b^3 + 16*a^3*b^4 + 9*a^2*b^5 + 2*a*b^6)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (a^5*b^2 - 6*a^4*b^3 + 14*a^3*b^4 - 16*a^2*b^5 + 9*a*b^6 - 2*b^7 - (a^7 - 6*a^6*b + 14*a^5*b^2 - 16*a^4*b^3 + 9*a^3*b^4 - 2*a^2*b^5)*cos(d*x + c)^4 - 2*(a^6*b - 6*a^5*b^2 + 14*a^4*b^3 - 16*a^3*b^4 + 9*a^2*b^5 - 2*a*b^6)*cos(d*x + c)^3 + (a^7 - 6*a^6*b + 13*a^5*b^2 - 10*a^4*b^3 - 5*a^3*b^4 + 14*a^2*b^5 - 9*a*b^6 + 2*b^7)*cos(d*x + c)^2 + 2*(a^6*b - 6*a^5*b^2 + 14*a^4*b^3 - 16*a^3*b^4 + 9*a^2*b^5 - 2*a*b^6)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8)*d*cos(d*x + c)^4 + 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)^3 - (a^10 - 5*a^8*b^2 + 10*a^6*b^4 - 10*a^4*b^6 + 5*a^2*b^8 - b^10)*d*cos(d*x + c)^2 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c) - (a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d)","B",0
227,1,1803,0,1.360552," ","integrate(csc(d*x+c)^5/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{76 \, a^{6} b^{3} + 36 \, a^{4} b^{5} - 108 \, a^{2} b^{7} - 4 \, b^{9} + 6 \, {\left(a^{9} + 17 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 13 \, a^{3} b^{6}\right)} \cos\left(d x + c\right)^{5} - 12 \, {\left(a^{8} b - 9 \, a^{6} b^{3} - a^{4} b^{5} + 9 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(5 \, a^{9} + 98 \, a^{7} b^{2} - 12 \, a^{5} b^{4} - 98 \, a^{3} b^{6} + 7 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(2 \, a^{8} b - 25 \, a^{6} b^{3} - 3 \, a^{4} b^{5} + 25 \, a^{2} b^{7} + b^{9}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(55 \, a^{7} b^{2} - 9 \, a^{5} b^{4} - 51 \, a^{3} b^{6} + 5 \, a b^{8}\right)} \cos\left(d x + c\right) + 48 \, {\left(a^{6} b^{3} + 5 \, a^{4} b^{5} + 2 \, a^{2} b^{7} + {\left(a^{8} b + 5 \, a^{6} b^{3} + 2 \, a^{4} b^{5}\right)} \cos\left(d x + c\right)^{6} + 2 \, {\left(a^{7} b^{2} + 5 \, a^{5} b^{4} + 2 \, a^{3} b^{6}\right)} \cos\left(d x + c\right)^{5} - {\left(2 \, a^{8} b + 9 \, a^{6} b^{3} - a^{4} b^{5} - 2 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(a^{7} b^{2} + 5 \, a^{5} b^{4} + 2 \, a^{3} b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{8} b + 3 \, a^{6} b^{3} - 8 \, a^{4} b^{5} - 4 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{2} + 5 \, a^{5} b^{4} + 2 \, a^{3} b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right) - 3 \, {\left(a^{7} b^{2} + 8 \, a^{6} b^{3} + 25 \, a^{5} b^{4} + 40 \, a^{4} b^{5} + 35 \, a^{3} b^{6} + 16 \, a^{2} b^{7} + 3 \, a b^{8} + {\left(a^{9} + 8 \, a^{8} b + 25 \, a^{7} b^{2} + 40 \, a^{6} b^{3} + 35 \, a^{5} b^{4} + 16 \, a^{4} b^{5} + 3 \, a^{3} b^{6}\right)} \cos\left(d x + c\right)^{6} + 2 \, {\left(a^{8} b + 8 \, a^{7} b^{2} + 25 \, a^{6} b^{3} + 40 \, a^{5} b^{4} + 35 \, a^{4} b^{5} + 16 \, a^{3} b^{6} + 3 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{5} - {\left(2 \, a^{9} + 16 \, a^{8} b + 49 \, a^{7} b^{2} + 72 \, a^{6} b^{3} + 45 \, a^{5} b^{4} - 8 \, a^{4} b^{5} - 29 \, a^{3} b^{6} - 16 \, a^{2} b^{7} - 3 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(a^{8} b + 8 \, a^{7} b^{2} + 25 \, a^{6} b^{3} + 40 \, a^{5} b^{4} + 35 \, a^{4} b^{5} + 16 \, a^{3} b^{6} + 3 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{9} + 8 \, a^{8} b + 23 \, a^{7} b^{2} + 24 \, a^{6} b^{3} - 15 \, a^{5} b^{4} - 64 \, a^{4} b^{5} - 67 \, a^{3} b^{6} - 32 \, a^{2} b^{7} - 6 \, a b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b + 8 \, a^{7} b^{2} + 25 \, a^{6} b^{3} + 40 \, a^{5} b^{4} + 35 \, a^{4} b^{5} + 16 \, a^{3} b^{6} + 3 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(a^{7} b^{2} - 8 \, a^{6} b^{3} + 25 \, a^{5} b^{4} - 40 \, a^{4} b^{5} + 35 \, a^{3} b^{6} - 16 \, a^{2} b^{7} + 3 \, a b^{8} + {\left(a^{9} - 8 \, a^{8} b + 25 \, a^{7} b^{2} - 40 \, a^{6} b^{3} + 35 \, a^{5} b^{4} - 16 \, a^{4} b^{5} + 3 \, a^{3} b^{6}\right)} \cos\left(d x + c\right)^{6} + 2 \, {\left(a^{8} b - 8 \, a^{7} b^{2} + 25 \, a^{6} b^{3} - 40 \, a^{5} b^{4} + 35 \, a^{4} b^{5} - 16 \, a^{3} b^{6} + 3 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{5} - {\left(2 \, a^{9} - 16 \, a^{8} b + 49 \, a^{7} b^{2} - 72 \, a^{6} b^{3} + 45 \, a^{5} b^{4} + 8 \, a^{4} b^{5} - 29 \, a^{3} b^{6} + 16 \, a^{2} b^{7} - 3 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(a^{8} b - 8 \, a^{7} b^{2} + 25 \, a^{6} b^{3} - 40 \, a^{5} b^{4} + 35 \, a^{4} b^{5} - 16 \, a^{3} b^{6} + 3 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{9} - 8 \, a^{8} b + 23 \, a^{7} b^{2} - 24 \, a^{6} b^{3} - 15 \, a^{5} b^{4} + 64 \, a^{4} b^{5} - 67 \, a^{3} b^{6} + 32 \, a^{2} b^{7} - 6 \, a b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b - 8 \, a^{7} b^{2} + 25 \, a^{6} b^{3} - 40 \, a^{5} b^{4} + 35 \, a^{4} b^{5} - 16 \, a^{3} b^{6} + 3 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{16 \, {\left({\left(a^{12} - 5 \, a^{10} b^{2} + 10 \, a^{8} b^{4} - 10 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - a^{2} b^{10}\right)} d \cos\left(d x + c\right)^{6} + 2 \, {\left(a^{11} b - 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} - 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right)^{5} - {\left(2 \, a^{12} - 11 \, a^{10} b^{2} + 25 \, a^{8} b^{4} - 30 \, a^{6} b^{6} + 20 \, a^{4} b^{8} - 7 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{4} - 4 \, {\left(a^{11} b - 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} - 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{12} - 7 \, a^{10} b^{2} + 20 \, a^{8} b^{4} - 30 \, a^{6} b^{6} + 25 \, a^{4} b^{8} - 11 \, a^{2} b^{10} + 2 \, b^{12}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{11} b - 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} - 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right) + {\left(a^{10} b^{2} - 5 \, a^{8} b^{4} + 10 \, a^{6} b^{6} - 10 \, a^{4} b^{8} + 5 \, a^{2} b^{10} - b^{12}\right)} d\right)}}"," ",0,"1/16*(76*a^6*b^3 + 36*a^4*b^5 - 108*a^2*b^7 - 4*b^9 + 6*(a^9 + 17*a^7*b^2 - 5*a^5*b^4 - 13*a^3*b^6)*cos(d*x + c)^5 - 12*(a^8*b - 9*a^6*b^3 - a^4*b^5 + 9*a^2*b^7)*cos(d*x + c)^4 - 2*(5*a^9 + 98*a^7*b^2 - 12*a^5*b^4 - 98*a^3*b^6 + 7*a*b^8)*cos(d*x + c)^3 + 8*(2*a^8*b - 25*a^6*b^3 - 3*a^4*b^5 + 25*a^2*b^7 + b^9)*cos(d*x + c)^2 + 2*(55*a^7*b^2 - 9*a^5*b^4 - 51*a^3*b^6 + 5*a*b^8)*cos(d*x + c) + 48*(a^6*b^3 + 5*a^4*b^5 + 2*a^2*b^7 + (a^8*b + 5*a^6*b^3 + 2*a^4*b^5)*cos(d*x + c)^6 + 2*(a^7*b^2 + 5*a^5*b^4 + 2*a^3*b^6)*cos(d*x + c)^5 - (2*a^8*b + 9*a^6*b^3 - a^4*b^5 - 2*a^2*b^7)*cos(d*x + c)^4 - 4*(a^7*b^2 + 5*a^5*b^4 + 2*a^3*b^6)*cos(d*x + c)^3 + (a^8*b + 3*a^6*b^3 - 8*a^4*b^5 - 4*a^2*b^7)*cos(d*x + c)^2 + 2*(a^7*b^2 + 5*a^5*b^4 + 2*a^3*b^6)*cos(d*x + c))*log(a*cos(d*x + c) + b) - 3*(a^7*b^2 + 8*a^6*b^3 + 25*a^5*b^4 + 40*a^4*b^5 + 35*a^3*b^6 + 16*a^2*b^7 + 3*a*b^8 + (a^9 + 8*a^8*b + 25*a^7*b^2 + 40*a^6*b^3 + 35*a^5*b^4 + 16*a^4*b^5 + 3*a^3*b^6)*cos(d*x + c)^6 + 2*(a^8*b + 8*a^7*b^2 + 25*a^6*b^3 + 40*a^5*b^4 + 35*a^4*b^5 + 16*a^3*b^6 + 3*a^2*b^7)*cos(d*x + c)^5 - (2*a^9 + 16*a^8*b + 49*a^7*b^2 + 72*a^6*b^3 + 45*a^5*b^4 - 8*a^4*b^5 - 29*a^3*b^6 - 16*a^2*b^7 - 3*a*b^8)*cos(d*x + c)^4 - 4*(a^8*b + 8*a^7*b^2 + 25*a^6*b^3 + 40*a^5*b^4 + 35*a^4*b^5 + 16*a^3*b^6 + 3*a^2*b^7)*cos(d*x + c)^3 + (a^9 + 8*a^8*b + 23*a^7*b^2 + 24*a^6*b^3 - 15*a^5*b^4 - 64*a^4*b^5 - 67*a^3*b^6 - 32*a^2*b^7 - 6*a*b^8)*cos(d*x + c)^2 + 2*(a^8*b + 8*a^7*b^2 + 25*a^6*b^3 + 40*a^5*b^4 + 35*a^4*b^5 + 16*a^3*b^6 + 3*a^2*b^7)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 3*(a^7*b^2 - 8*a^6*b^3 + 25*a^5*b^4 - 40*a^4*b^5 + 35*a^3*b^6 - 16*a^2*b^7 + 3*a*b^8 + (a^9 - 8*a^8*b + 25*a^7*b^2 - 40*a^6*b^3 + 35*a^5*b^4 - 16*a^4*b^5 + 3*a^3*b^6)*cos(d*x + c)^6 + 2*(a^8*b - 8*a^7*b^2 + 25*a^6*b^3 - 40*a^5*b^4 + 35*a^4*b^5 - 16*a^3*b^6 + 3*a^2*b^7)*cos(d*x + c)^5 - (2*a^9 - 16*a^8*b + 49*a^7*b^2 - 72*a^6*b^3 + 45*a^5*b^4 + 8*a^4*b^5 - 29*a^3*b^6 + 16*a^2*b^7 - 3*a*b^8)*cos(d*x + c)^4 - 4*(a^8*b - 8*a^7*b^2 + 25*a^6*b^3 - 40*a^5*b^4 + 35*a^4*b^5 - 16*a^3*b^6 + 3*a^2*b^7)*cos(d*x + c)^3 + (a^9 - 8*a^8*b + 23*a^7*b^2 - 24*a^6*b^3 - 15*a^5*b^4 + 64*a^4*b^5 - 67*a^3*b^6 + 32*a^2*b^7 - 6*a*b^8)*cos(d*x + c)^2 + 2*(a^8*b - 8*a^7*b^2 + 25*a^6*b^3 - 40*a^5*b^4 + 35*a^4*b^5 - 16*a^3*b^6 + 3*a^2*b^7)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^12 - 5*a^10*b^2 + 10*a^8*b^4 - 10*a^6*b^6 + 5*a^4*b^8 - a^2*b^10)*d*cos(d*x + c)^6 + 2*(a^11*b - 5*a^9*b^3 + 10*a^7*b^5 - 10*a^5*b^7 + 5*a^3*b^9 - a*b^11)*d*cos(d*x + c)^5 - (2*a^12 - 11*a^10*b^2 + 25*a^8*b^4 - 30*a^6*b^6 + 20*a^4*b^8 - 7*a^2*b^10 + b^12)*d*cos(d*x + c)^4 - 4*(a^11*b - 5*a^9*b^3 + 10*a^7*b^5 - 10*a^5*b^7 + 5*a^3*b^9 - a*b^11)*d*cos(d*x + c)^3 + (a^12 - 7*a^10*b^2 + 20*a^8*b^4 - 30*a^6*b^6 + 25*a^4*b^8 - 11*a^2*b^10 + 2*b^12)*d*cos(d*x + c)^2 + 2*(a^11*b - 5*a^9*b^3 + 10*a^7*b^5 - 10*a^5*b^7 + 5*a^3*b^9 - a*b^11)*d*cos(d*x + c) + (a^10*b^2 - 5*a^8*b^4 + 10*a^6*b^6 - 10*a^4*b^8 + 5*a^2*b^10 - b^12)*d)","B",0
228,1,1057,0,0.696643," ","integrate(sin(d*x+c)^6/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(5 \, a^{8} - 180 \, a^{6} b^{2} + 600 \, a^{4} b^{4} - 448 \, a^{2} b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 30 \, {\left(5 \, a^{7} b - 180 \, a^{5} b^{3} + 600 \, a^{3} b^{5} - 448 \, a b^{7}\right)} d x \cos\left(d x + c\right) + 15 \, {\left(5 \, a^{6} b^{2} - 180 \, a^{4} b^{4} + 600 \, a^{2} b^{6} - 448 \, b^{8}\right)} d x + 60 \, {\left(6 \, a^{4} b^{3} - 47 \, a^{2} b^{5} + 56 \, b^{7} + {\left(6 \, a^{6} b - 47 \, a^{4} b^{3} + 56 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{5} b^{2} - 47 \, a^{3} b^{4} + 56 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - {\left(40 \, a^{8} \cos\left(d x + c\right)^{7} - 64 \, a^{7} b \cos\left(d x + c\right)^{6} - 1704 \, a^{5} b^{3} + 7880 \, a^{3} b^{5} - 6720 \, a b^{7} - 2 \, {\left(65 \, a^{8} - 56 \, a^{6} b^{2}\right)} \cos\left(d x + c\right)^{5} + 4 \, {\left(67 \, a^{7} b - 56 \, a^{5} b^{3}\right)} \cos\left(d x + c\right)^{4} + {\left(165 \, a^{8} - 694 \, a^{6} b^{2} + 560 \, a^{4} b^{4}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(387 \, a^{7} b - 1444 \, a^{5} b^{3} + 1120 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{2} - {\left(2763 \, a^{6} b^{2} - 12100 \, a^{4} b^{4} + 10080 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(a^{11} d \cos\left(d x + c\right)^{2} + 2 \, a^{10} b d \cos\left(d x + c\right) + a^{9} b^{2} d\right)}}, \frac{15 \, {\left(5 \, a^{8} - 180 \, a^{6} b^{2} + 600 \, a^{4} b^{4} - 448 \, a^{2} b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 30 \, {\left(5 \, a^{7} b - 180 \, a^{5} b^{3} + 600 \, a^{3} b^{5} - 448 \, a b^{7}\right)} d x \cos\left(d x + c\right) + 15 \, {\left(5 \, a^{6} b^{2} - 180 \, a^{4} b^{4} + 600 \, a^{2} b^{6} - 448 \, b^{8}\right)} d x - 120 \, {\left(6 \, a^{4} b^{3} - 47 \, a^{2} b^{5} + 56 \, b^{7} + {\left(6 \, a^{6} b - 47 \, a^{4} b^{3} + 56 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{5} b^{2} - 47 \, a^{3} b^{4} + 56 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(40 \, a^{8} \cos\left(d x + c\right)^{7} - 64 \, a^{7} b \cos\left(d x + c\right)^{6} - 1704 \, a^{5} b^{3} + 7880 \, a^{3} b^{5} - 6720 \, a b^{7} - 2 \, {\left(65 \, a^{8} - 56 \, a^{6} b^{2}\right)} \cos\left(d x + c\right)^{5} + 4 \, {\left(67 \, a^{7} b - 56 \, a^{5} b^{3}\right)} \cos\left(d x + c\right)^{4} + {\left(165 \, a^{8} - 694 \, a^{6} b^{2} + 560 \, a^{4} b^{4}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(387 \, a^{7} b - 1444 \, a^{5} b^{3} + 1120 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{2} - {\left(2763 \, a^{6} b^{2} - 12100 \, a^{4} b^{4} + 10080 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(a^{11} d \cos\left(d x + c\right)^{2} + 2 \, a^{10} b d \cos\left(d x + c\right) + a^{9} b^{2} d\right)}}\right]"," ",0,"[1/240*(15*(5*a^8 - 180*a^6*b^2 + 600*a^4*b^4 - 448*a^2*b^6)*d*x*cos(d*x + c)^2 + 30*(5*a^7*b - 180*a^5*b^3 + 600*a^3*b^5 - 448*a*b^7)*d*x*cos(d*x + c) + 15*(5*a^6*b^2 - 180*a^4*b^4 + 600*a^2*b^6 - 448*b^8)*d*x + 60*(6*a^4*b^3 - 47*a^2*b^5 + 56*b^7 + (6*a^6*b - 47*a^4*b^3 + 56*a^2*b^5)*cos(d*x + c)^2 + 2*(6*a^5*b^2 - 47*a^3*b^4 + 56*a*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - (40*a^8*cos(d*x + c)^7 - 64*a^7*b*cos(d*x + c)^6 - 1704*a^5*b^3 + 7880*a^3*b^5 - 6720*a*b^7 - 2*(65*a^8 - 56*a^6*b^2)*cos(d*x + c)^5 + 4*(67*a^7*b - 56*a^5*b^3)*cos(d*x + c)^4 + (165*a^8 - 694*a^6*b^2 + 560*a^4*b^4)*cos(d*x + c)^3 - 2*(387*a^7*b - 1444*a^5*b^3 + 1120*a^3*b^5)*cos(d*x + c)^2 - (2763*a^6*b^2 - 12100*a^4*b^4 + 10080*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/(a^11*d*cos(d*x + c)^2 + 2*a^10*b*d*cos(d*x + c) + a^9*b^2*d), 1/240*(15*(5*a^8 - 180*a^6*b^2 + 600*a^4*b^4 - 448*a^2*b^6)*d*x*cos(d*x + c)^2 + 30*(5*a^7*b - 180*a^5*b^3 + 600*a^3*b^5 - 448*a*b^7)*d*x*cos(d*x + c) + 15*(5*a^6*b^2 - 180*a^4*b^4 + 600*a^2*b^6 - 448*b^8)*d*x - 120*(6*a^4*b^3 - 47*a^2*b^5 + 56*b^7 + (6*a^6*b - 47*a^4*b^3 + 56*a^2*b^5)*cos(d*x + c)^2 + 2*(6*a^5*b^2 - 47*a^3*b^4 + 56*a*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (40*a^8*cos(d*x + c)^7 - 64*a^7*b*cos(d*x + c)^6 - 1704*a^5*b^3 + 7880*a^3*b^5 - 6720*a*b^7 - 2*(65*a^8 - 56*a^6*b^2)*cos(d*x + c)^5 + 4*(67*a^7*b - 56*a^5*b^3)*cos(d*x + c)^4 + (165*a^8 - 694*a^6*b^2 + 560*a^4*b^4)*cos(d*x + c)^3 - 2*(387*a^7*b - 1444*a^5*b^3 + 1120*a^3*b^5)*cos(d*x + c)^2 - (2763*a^6*b^2 - 12100*a^4*b^4 + 10080*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/(a^11*d*cos(d*x + c)^2 + 2*a^10*b*d*cos(d*x + c) + a^9*b^2*d)]","A",0
229,1,1041,0,0.688405," ","integrate(sin(d*x+c)^4/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{8} - 25 \, a^{6} b^{2} + 64 \, a^{4} b^{4} - 40 \, a^{2} b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(a^{7} b - 25 \, a^{5} b^{3} + 64 \, a^{3} b^{5} - 40 \, a b^{7}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(a^{6} b^{2} - 25 \, a^{4} b^{4} + 64 \, a^{2} b^{6} - 40 \, b^{8}\right)} d x + 6 \, {\left(2 \, a^{4} b^{3} - 11 \, a^{2} b^{5} + 10 \, b^{7} + {\left(2 \, a^{6} b - 11 \, a^{4} b^{3} + 10 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 10 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + {\left(52 \, a^{5} b^{3} - 172 \, a^{3} b^{5} + 120 \, a b^{7} + 2 \, {\left(a^{8} - a^{6} b^{2}\right)} \cos\left(d x + c\right)^{5} - 4 \, {\left(a^{7} b - a^{5} b^{3}\right)} \cos\left(d x + c\right)^{4} - 5 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 2 \, a^{4} b^{4}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(11 \, a^{7} b - 31 \, a^{5} b^{3} + 20 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(83 \, a^{6} b^{2} - 263 \, a^{4} b^{4} + 180 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, {\left({\left(a^{11} - a^{9} b^{2}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{10} b - a^{8} b^{3}\right)} d \cos\left(d x + c\right) + {\left(a^{9} b^{2} - a^{7} b^{4}\right)} d\right)}}, \frac{3 \, {\left(a^{8} - 25 \, a^{6} b^{2} + 64 \, a^{4} b^{4} - 40 \, a^{2} b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(a^{7} b - 25 \, a^{5} b^{3} + 64 \, a^{3} b^{5} - 40 \, a b^{7}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(a^{6} b^{2} - 25 \, a^{4} b^{4} + 64 \, a^{2} b^{6} - 40 \, b^{8}\right)} d x - 12 \, {\left(2 \, a^{4} b^{3} - 11 \, a^{2} b^{5} + 10 \, b^{7} + {\left(2 \, a^{6} b - 11 \, a^{4} b^{3} + 10 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 10 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(52 \, a^{5} b^{3} - 172 \, a^{3} b^{5} + 120 \, a b^{7} + 2 \, {\left(a^{8} - a^{6} b^{2}\right)} \cos\left(d x + c\right)^{5} - 4 \, {\left(a^{7} b - a^{5} b^{3}\right)} \cos\left(d x + c\right)^{4} - 5 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 2 \, a^{4} b^{4}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(11 \, a^{7} b - 31 \, a^{5} b^{3} + 20 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(83 \, a^{6} b^{2} - 263 \, a^{4} b^{4} + 180 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, {\left({\left(a^{11} - a^{9} b^{2}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{10} b - a^{8} b^{3}\right)} d \cos\left(d x + c\right) + {\left(a^{9} b^{2} - a^{7} b^{4}\right)} d\right)}}\right]"," ",0,"[1/8*(3*(a^8 - 25*a^6*b^2 + 64*a^4*b^4 - 40*a^2*b^6)*d*x*cos(d*x + c)^2 + 6*(a^7*b - 25*a^5*b^3 + 64*a^3*b^5 - 40*a*b^7)*d*x*cos(d*x + c) + 3*(a^6*b^2 - 25*a^4*b^4 + 64*a^2*b^6 - 40*b^8)*d*x + 6*(2*a^4*b^3 - 11*a^2*b^5 + 10*b^7 + (2*a^6*b - 11*a^4*b^3 + 10*a^2*b^5)*cos(d*x + c)^2 + 2*(2*a^5*b^2 - 11*a^3*b^4 + 10*a*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + (52*a^5*b^3 - 172*a^3*b^5 + 120*a*b^7 + 2*(a^8 - a^6*b^2)*cos(d*x + c)^5 - 4*(a^7*b - a^5*b^3)*cos(d*x + c)^4 - 5*(a^8 - 3*a^6*b^2 + 2*a^4*b^4)*cos(d*x + c)^3 + 2*(11*a^7*b - 31*a^5*b^3 + 20*a^3*b^5)*cos(d*x + c)^2 + (83*a^6*b^2 - 263*a^4*b^4 + 180*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^11 - a^9*b^2)*d*cos(d*x + c)^2 + 2*(a^10*b - a^8*b^3)*d*cos(d*x + c) + (a^9*b^2 - a^7*b^4)*d), 1/8*(3*(a^8 - 25*a^6*b^2 + 64*a^4*b^4 - 40*a^2*b^6)*d*x*cos(d*x + c)^2 + 6*(a^7*b - 25*a^5*b^3 + 64*a^3*b^5 - 40*a*b^7)*d*x*cos(d*x + c) + 3*(a^6*b^2 - 25*a^4*b^4 + 64*a^2*b^6 - 40*b^8)*d*x - 12*(2*a^4*b^3 - 11*a^2*b^5 + 10*b^7 + (2*a^6*b - 11*a^4*b^3 + 10*a^2*b^5)*cos(d*x + c)^2 + 2*(2*a^5*b^2 - 11*a^3*b^4 + 10*a*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (52*a^5*b^3 - 172*a^3*b^5 + 120*a*b^7 + 2*(a^8 - a^6*b^2)*cos(d*x + c)^5 - 4*(a^7*b - a^5*b^3)*cos(d*x + c)^4 - 5*(a^8 - 3*a^6*b^2 + 2*a^4*b^4)*cos(d*x + c)^3 + 2*(11*a^7*b - 31*a^5*b^3 + 20*a^3*b^5)*cos(d*x + c)^2 + (83*a^6*b^2 - 263*a^4*b^4 + 180*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^11 - a^9*b^2)*d*cos(d*x + c)^2 + 2*(a^10*b - a^8*b^3)*d*cos(d*x + c) + (a^9*b^2 - a^7*b^4)*d)]","A",0
230,1,984,0,0.610883," ","integrate(sin(d*x+c)^2/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{8} - 14 \, a^{6} b^{2} + 25 \, a^{4} b^{4} - 12 \, a^{2} b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(a^{7} b - 14 \, a^{5} b^{3} + 25 \, a^{3} b^{5} - 12 \, a b^{7}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(a^{6} b^{2} - 14 \, a^{4} b^{4} + 25 \, a^{2} b^{6} - 12 \, b^{8}\right)} d x - {\left(6 \, a^{4} b^{3} - 19 \, a^{2} b^{5} + 12 \, b^{7} + {\left(6 \, a^{6} b - 19 \, a^{4} b^{3} + 12 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{5} b^{2} - 19 \, a^{3} b^{4} + 12 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(11 \, a^{5} b^{3} - 23 \, a^{3} b^{5} + 12 \, a b^{7} - {\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(17 \, a^{6} b^{2} - 35 \, a^{4} b^{4} + 18 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{11} - 2 \, a^{9} b^{2} + a^{7} b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{10} b - 2 \, a^{8} b^{3} + a^{6} b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{9} b^{2} - 2 \, a^{7} b^{4} + a^{5} b^{6}\right)} d\right)}}, \frac{{\left(a^{8} - 14 \, a^{6} b^{2} + 25 \, a^{4} b^{4} - 12 \, a^{2} b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 14 \, a^{5} b^{3} + 25 \, a^{3} b^{5} - 12 \, a b^{7}\right)} d x \cos\left(d x + c\right) + {\left(a^{6} b^{2} - 14 \, a^{4} b^{4} + 25 \, a^{2} b^{6} - 12 \, b^{8}\right)} d x - {\left(6 \, a^{4} b^{3} - 19 \, a^{2} b^{5} + 12 \, b^{7} + {\left(6 \, a^{6} b - 19 \, a^{4} b^{3} + 12 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{5} b^{2} - 19 \, a^{3} b^{4} + 12 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(11 \, a^{5} b^{3} - 23 \, a^{3} b^{5} + 12 \, a b^{7} - {\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(17 \, a^{6} b^{2} - 35 \, a^{4} b^{4} + 18 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{11} - 2 \, a^{9} b^{2} + a^{7} b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{10} b - 2 \, a^{8} b^{3} + a^{6} b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{9} b^{2} - 2 \, a^{7} b^{4} + a^{5} b^{6}\right)} d\right)}}\right]"," ",0,"[1/4*(2*(a^8 - 14*a^6*b^2 + 25*a^4*b^4 - 12*a^2*b^6)*d*x*cos(d*x + c)^2 + 4*(a^7*b - 14*a^5*b^3 + 25*a^3*b^5 - 12*a*b^7)*d*x*cos(d*x + c) + 2*(a^6*b^2 - 14*a^4*b^4 + 25*a^2*b^6 - 12*b^8)*d*x - (6*a^4*b^3 - 19*a^2*b^5 + 12*b^7 + (6*a^6*b - 19*a^4*b^3 + 12*a^2*b^5)*cos(d*x + c)^2 + 2*(6*a^5*b^2 - 19*a^3*b^4 + 12*a*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(11*a^5*b^3 - 23*a^3*b^5 + 12*a*b^7 - (a^8 - 2*a^6*b^2 + a^4*b^4)*cos(d*x + c)^3 + 4*(a^7*b - 2*a^5*b^3 + a^3*b^5)*cos(d*x + c)^2 + (17*a^6*b^2 - 35*a^4*b^4 + 18*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^11 - 2*a^9*b^2 + a^7*b^4)*d*cos(d*x + c)^2 + 2*(a^10*b - 2*a^8*b^3 + a^6*b^5)*d*cos(d*x + c) + (a^9*b^2 - 2*a^7*b^4 + a^5*b^6)*d), 1/2*((a^8 - 14*a^6*b^2 + 25*a^4*b^4 - 12*a^2*b^6)*d*x*cos(d*x + c)^2 + 2*(a^7*b - 14*a^5*b^3 + 25*a^3*b^5 - 12*a*b^7)*d*x*cos(d*x + c) + (a^6*b^2 - 14*a^4*b^4 + 25*a^2*b^6 - 12*b^8)*d*x - (6*a^4*b^3 - 19*a^2*b^5 + 12*b^7 + (6*a^6*b - 19*a^4*b^3 + 12*a^2*b^5)*cos(d*x + c)^2 + 2*(6*a^5*b^2 - 19*a^3*b^4 + 12*a*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (11*a^5*b^3 - 23*a^3*b^5 + 12*a*b^7 - (a^8 - 2*a^6*b^2 + a^4*b^4)*cos(d*x + c)^3 + 4*(a^7*b - 2*a^5*b^3 + a^3*b^5)*cos(d*x + c)^2 + (17*a^6*b^2 - 35*a^4*b^4 + 18*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^11 - 2*a^9*b^2 + a^7*b^4)*d*cos(d*x + c)^2 + 2*(a^10*b - 2*a^8*b^3 + a^6*b^5)*d*cos(d*x + c) + (a^9*b^2 - 2*a^7*b^4 + a^5*b^6)*d)]","A",0
231,1,841,0,0.737254," ","integrate(csc(d*x+c)^2/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{22 \, a^{4} b^{3} - 14 \, a^{2} b^{5} - 8 \, b^{7} - 2 \, {\left(2 \, a^{7} + 10 \, a^{5} b^{2} - 11 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{3} b^{3} + 3 \, a b^{5} + {\left(2 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) \sin\left(d x + c\right) + 2 \, {\left(2 \, a^{6} b - 17 \, a^{4} b^{3} + 13 \, a^{2} b^{5} + 2 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(16 \, a^{5} b^{2} - 17 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)}{4 \, {\left({\left(a^{10} - 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} - 4 \, a^{4} b^{6} + a^{2} b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d\right)} \sin\left(d x + c\right)}, \frac{11 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - 4 \, b^{7} - {\left(2 \, a^{7} + 10 \, a^{5} b^{2} - 11 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{3} b^{3} + 3 \, a b^{5} + {\left(2 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + {\left(2 \, a^{6} b - 17 \, a^{4} b^{3} + 13 \, a^{2} b^{5} + 2 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(16 \, a^{5} b^{2} - 17 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)}{2 \, {\left({\left(a^{10} - 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} - 4 \, a^{4} b^{6} + a^{2} b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[1/4*(22*a^4*b^3 - 14*a^2*b^5 - 8*b^7 - 2*(2*a^7 + 10*a^5*b^2 - 11*a^3*b^4 - a*b^6)*cos(d*x + c)^3 - 3*(2*a^3*b^3 + 3*a*b^5 + (2*a^5*b + 3*a^3*b^3)*cos(d*x + c)^2 + 2*(2*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2))*sin(d*x + c) + 2*(2*a^6*b - 17*a^4*b^3 + 13*a^2*b^5 + 2*b^7)*cos(d*x + c)^2 + 2*(16*a^5*b^2 - 17*a^3*b^4 + a*b^6)*cos(d*x + c))/(((a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8)*d*cos(d*x + c)^2 + 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c) + (a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d)*sin(d*x + c)), 1/2*(11*a^4*b^3 - 7*a^2*b^5 - 4*b^7 - (2*a^7 + 10*a^5*b^2 - 11*a^3*b^4 - a*b^6)*cos(d*x + c)^3 - 3*(2*a^3*b^3 + 3*a*b^5 + (2*a^5*b + 3*a^3*b^3)*cos(d*x + c)^2 + 2*(2*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*sin(d*x + c) + (2*a^6*b - 17*a^4*b^3 + 13*a^2*b^5 + 2*b^7)*cos(d*x + c)^2 + (16*a^5*b^2 - 17*a^3*b^4 + a*b^6)*cos(d*x + c))/(((a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8)*d*cos(d*x + c)^2 + 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c) + (a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d)*sin(d*x + c))]","A",0
232,1,1550,0,0.831547," ","integrate(csc(d*x+c)^4/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{78 \, a^{6} b^{3} + 46 \, a^{4} b^{5} - 116 \, a^{2} b^{7} - 8 \, b^{9} + 2 \, {\left(4 \, a^{9} + 58 \, a^{7} b^{2} - 23 \, a^{5} b^{4} - 39 \, a^{3} b^{6}\right)} \cos\left(d x + c\right)^{5} - 10 \, {\left(2 \, a^{8} b - 13 \, a^{6} b^{3} - a^{4} b^{5} + 12 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(3 \, a^{9} + 55 \, a^{7} b^{2} - 8 \, a^{5} b^{4} - 56 \, a^{3} b^{6} + 6 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{5} b^{3} + 23 \, a^{3} b^{5} + 6 \, a b^{7} - {\left(6 \, a^{7} b + 23 \, a^{5} b^{3} + 6 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(6 \, a^{6} b^{2} + 23 \, a^{4} b^{4} + 6 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, a^{7} b + 17 \, a^{5} b^{3} - 17 \, a^{3} b^{5} - 6 \, a b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{6} b^{2} + 23 \, a^{4} b^{4} + 6 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) \sin\left(d x + c\right) + 4 \, {\left(6 \, a^{8} b - 56 \, a^{6} b^{3} - 8 \, a^{4} b^{5} + 55 \, a^{2} b^{7} + 3 \, b^{9}\right)} \cos\left(d x + c\right)^{2} + 10 \, {\left(12 \, a^{7} b^{2} - a^{5} b^{4} - 13 \, a^{3} b^{6} + 2 \, a b^{8}\right)} \cos\left(d x + c\right)}{12 \, {\left({\left(a^{12} - 5 \, a^{10} b^{2} + 10 \, a^{8} b^{4} - 10 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - a^{2} b^{10}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{11} b - 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} - 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right)^{3} - {\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)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{11} b - 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} - 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right) - {\left(a^{10} b^{2} - 5 \, a^{8} b^{4} + 10 \, a^{6} b^{6} - 10 \, a^{4} b^{8} + 5 \, a^{2} b^{10} - b^{12}\right)} d\right)} \sin\left(d x + c\right)}, -\frac{39 \, a^{6} b^{3} + 23 \, a^{4} b^{5} - 58 \, a^{2} b^{7} - 4 \, b^{9} + {\left(4 \, a^{9} + 58 \, a^{7} b^{2} - 23 \, a^{5} b^{4} - 39 \, a^{3} b^{6}\right)} \cos\left(d x + c\right)^{5} - 5 \, {\left(2 \, a^{8} b - 13 \, a^{6} b^{3} - a^{4} b^{5} + 12 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{9} + 55 \, a^{7} b^{2} - 8 \, a^{5} b^{4} - 56 \, a^{3} b^{6} + 6 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(6 \, a^{5} b^{3} + 23 \, a^{3} b^{5} + 6 \, a b^{7} - {\left(6 \, a^{7} b + 23 \, a^{5} b^{3} + 6 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(6 \, a^{6} b^{2} + 23 \, a^{4} b^{4} + 6 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, a^{7} b + 17 \, a^{5} b^{3} - 17 \, a^{3} b^{5} - 6 \, a b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{6} b^{2} + 23 \, a^{4} b^{4} + 6 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 2 \, {\left(6 \, a^{8} b - 56 \, a^{6} b^{3} - 8 \, a^{4} b^{5} + 55 \, a^{2} b^{7} + 3 \, b^{9}\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(12 \, a^{7} b^{2} - a^{5} b^{4} - 13 \, a^{3} b^{6} + 2 \, a b^{8}\right)} \cos\left(d x + c\right)}{6 \, {\left({\left(a^{12} - 5 \, a^{10} b^{2} + 10 \, a^{8} b^{4} - 10 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - a^{2} b^{10}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{11} b - 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} - 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right)^{3} - {\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)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{11} b - 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} - 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right) - {\left(a^{10} b^{2} - 5 \, a^{8} b^{4} + 10 \, a^{6} b^{6} - 10 \, a^{4} b^{8} + 5 \, a^{2} b^{10} - b^{12}\right)} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/12*(78*a^6*b^3 + 46*a^4*b^5 - 116*a^2*b^7 - 8*b^9 + 2*(4*a^9 + 58*a^7*b^2 - 23*a^5*b^4 - 39*a^3*b^6)*cos(d*x + c)^5 - 10*(2*a^8*b - 13*a^6*b^3 - a^4*b^5 + 12*a^2*b^7)*cos(d*x + c)^4 - 4*(3*a^9 + 55*a^7*b^2 - 8*a^5*b^4 - 56*a^3*b^6 + 6*a*b^8)*cos(d*x + c)^3 + 3*(6*a^5*b^3 + 23*a^3*b^5 + 6*a*b^7 - (6*a^7*b + 23*a^5*b^3 + 6*a^3*b^5)*cos(d*x + c)^4 - 2*(6*a^6*b^2 + 23*a^4*b^4 + 6*a^2*b^6)*cos(d*x + c)^3 + (6*a^7*b + 17*a^5*b^3 - 17*a^3*b^5 - 6*a*b^7)*cos(d*x + c)^2 + 2*(6*a^6*b^2 + 23*a^4*b^4 + 6*a^2*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2))*sin(d*x + c) + 4*(6*a^8*b - 56*a^6*b^3 - 8*a^4*b^5 + 55*a^2*b^7 + 3*b^9)*cos(d*x + c)^2 + 10*(12*a^7*b^2 - a^5*b^4 - 13*a^3*b^6 + 2*a*b^8)*cos(d*x + c))/(((a^12 - 5*a^10*b^2 + 10*a^8*b^4 - 10*a^6*b^6 + 5*a^4*b^8 - a^2*b^10)*d*cos(d*x + c)^4 + 2*(a^11*b - 5*a^9*b^3 + 10*a^7*b^5 - 10*a^5*b^7 + 5*a^3*b^9 - a*b^11)*d*cos(d*x + c)^3 - (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)*d*cos(d*x + c)^2 - 2*(a^11*b - 5*a^9*b^3 + 10*a^7*b^5 - 10*a^5*b^7 + 5*a^3*b^9 - a*b^11)*d*cos(d*x + c) - (a^10*b^2 - 5*a^8*b^4 + 10*a^6*b^6 - 10*a^4*b^8 + 5*a^2*b^10 - b^12)*d)*sin(d*x + c)), -1/6*(39*a^6*b^3 + 23*a^4*b^5 - 58*a^2*b^7 - 4*b^9 + (4*a^9 + 58*a^7*b^2 - 23*a^5*b^4 - 39*a^3*b^6)*cos(d*x + c)^5 - 5*(2*a^8*b - 13*a^6*b^3 - a^4*b^5 + 12*a^2*b^7)*cos(d*x + c)^4 - 2*(3*a^9 + 55*a^7*b^2 - 8*a^5*b^4 - 56*a^3*b^6 + 6*a*b^8)*cos(d*x + c)^3 - 3*(6*a^5*b^3 + 23*a^3*b^5 + 6*a*b^7 - (6*a^7*b + 23*a^5*b^3 + 6*a^3*b^5)*cos(d*x + c)^4 - 2*(6*a^6*b^2 + 23*a^4*b^4 + 6*a^2*b^6)*cos(d*x + c)^3 + (6*a^7*b + 17*a^5*b^3 - 17*a^3*b^5 - 6*a*b^7)*cos(d*x + c)^2 + 2*(6*a^6*b^2 + 23*a^4*b^4 + 6*a^2*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*sin(d*x + c) + 2*(6*a^8*b - 56*a^6*b^3 - 8*a^4*b^5 + 55*a^2*b^7 + 3*b^9)*cos(d*x + c)^2 + 5*(12*a^7*b^2 - a^5*b^4 - 13*a^3*b^6 + 2*a*b^8)*cos(d*x + c))/(((a^12 - 5*a^10*b^2 + 10*a^8*b^4 - 10*a^6*b^6 + 5*a^4*b^8 - a^2*b^10)*d*cos(d*x + c)^4 + 2*(a^11*b - 5*a^9*b^3 + 10*a^7*b^5 - 10*a^5*b^7 + 5*a^3*b^9 - a*b^11)*d*cos(d*x + c)^3 - (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)*d*cos(d*x + c)^2 - 2*(a^11*b - 5*a^9*b^3 + 10*a^7*b^5 - 10*a^5*b^7 + 5*a^3*b^9 - a*b^11)*d*cos(d*x + c) - (a^10*b^2 - 5*a^8*b^4 + 10*a^6*b^6 - 10*a^4*b^8 + 5*a^2*b^10 - b^12)*d)*sin(d*x + c))]","A",0
233,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(7/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
234,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
235,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
236,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
237,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
238,0,0,0,175.618144," ","integrate(1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \sin\left(d x + c\right)}}{a e^{2} \cos\left(d x + c\right)^{2} - a e^{2} + {\left(b e^{2} \cos\left(d x + c\right)^{2} - b e^{2}\right)} \sec\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(e*sin(d*x + c))/(a*e^2*cos(d*x + c)^2 - a*e^2 + (b*e^2*cos(d*x + c)^2 - b*e^2)*sec(d*x + c)), x)","F",0
239,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
240,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
241,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(9/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
242,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(7/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(5/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
245,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
246,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^2/(e*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
247,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^2/(e*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
248,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^2/(e*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
249,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,0,0,0,0.984038," ","integrate(csc(f*x+e)^2*(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right) + a} \csc\left(f x + e\right)^{2}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e) + a)*csc(f*x + e)^2, x)","F",0
251,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
252,0,0,0,0.650589," ","integrate(csc(f*x+e)^2*(a+b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \csc\left(f x + e\right)^{2} \sec\left(f x + e\right) + a \csc\left(f x + e\right)^{2}\right)} \sqrt{b \sec\left(f x + e\right) + a}, x\right)"," ",0,"integral((b*csc(f*x + e)^2*sec(f*x + e) + a*csc(f*x + e)^2)*sqrt(b*sec(f*x + e) + a), x)","F",0
253,0,0,0,31.823328," ","integrate(1/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral(1/sqrt(b*sec(f*x + e) + a), x)","F",0
254,0,0,0,0.539333," ","integrate(csc(f*x+e)^2/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(f x + e\right)^{2}}{\sqrt{b \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral(csc(f*x + e)^2/sqrt(b*sec(f*x + e) + a), x)","F",0
255,0,0,0,26.217192," ","integrate(1/(a+b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right) + a}}{b^{2} \sec\left(f x + e\right)^{2} + 2 \, a b \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e) + a)/(b^2*sec(f*x + e)^2 + 2*a*b*sec(f*x + e) + a^2), x)","F",0
256,0,0,0,0.499505," ","integrate(csc(f*x+e)^2/(a+b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right) + a} \csc\left(f x + e\right)^{2}}{b^{2} \sec\left(f x + e\right)^{2} + 2 \, a b \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e) + a)*csc(f*x + e)^2/(b^2*sec(f*x + e)^2 + 2*a*b*sec(f*x + e) + a^2), x)","F",0
257,0,0,0,0.487208," ","integrate((a+b*sec(d*x+c))^3*(e*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}\right)} \left(e \sin\left(d x + c\right)\right)^{m}, x\right)"," ",0,"integral((b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3)*(e*sin(d*x + c))^m, x)","F",0
258,0,0,0,0.539730," ","integrate((a+b*sec(d*x+c))^2*(e*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}\right)} \left(e \sin\left(d x + c\right)\right)^{m}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)*(e*sin(d*x + c))^m, x)","F",0
259,0,0,0,0.469493," ","integrate((a+b*sec(d*x+c))*(e*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{m}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)*(e*sin(d*x + c))^m, x)","F",0
260,0,0,0,0.497600," ","integrate((e*sin(d*x+c))^m/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \sin\left(d x + c\right)\right)^{m}}{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((e*sin(d*x + c))^m/(b*sec(d*x + c) + a), x)","F",0
261,0,0,0,0.586620," ","integrate((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \sin\left(d x + c\right)\right)^{m}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((e*sin(d*x + c))^m/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
262,0,0,0,0.844397," ","integrate((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \sin\left(d x + c\right)\right)^{m}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((e*sin(d*x + c))^m/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
263,0,0,0,0.840649," ","integrate((a+b*sec(d*x+c))^(3/2)*(e*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \left(e \sin\left(d x + c\right)\right)^{m}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(3/2)*(e*sin(d*x + c))^m, x)","F",0
264,0,0,0,0.634881," ","integrate((e*sin(d*x+c))^m*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(d x + c\right) + a} \left(e \sin\left(d x + c\right)\right)^{m}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*(e*sin(d*x + c))^m, x)","F",0
265,0,0,0,0.683750," ","integrate((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \sin\left(d x + c\right)\right)^{m}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((e*sin(d*x + c))^m/sqrt(b*sec(d*x + c) + a), x)","F",0
266,0,0,0,0.928065," ","integrate((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \left(e \sin\left(d x + c\right)\right)^{m}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*(e*sin(d*x + c))^m/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
267,0,0,0,0.803327," ","integrate((a+b*sec(d*x+c))^n*(e*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)}^{n} \left(e \sin\left(d x + c\right)\right)^{m}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^n*(e*sin(d*x + c))^m, x)","F",0
268,0,0,0,0.694826," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^5,x, algorithm=""fricas"")","{\rm integral}\left({\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right), x\right)"," ",0,"integral((cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*(b*sec(d*x + c) + a)^n*sin(d*x + c), x)","F",0
269,0,0,0,0.546985," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(d x + c\right)^{2} - 1\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right), x\right)"," ",0,"integral(-(cos(d*x + c)^2 - 1)*(b*sec(d*x + c) + a)^n*sin(d*x + c), x)","F",0
270,0,0,0,0.549542," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right), x\right)"," ",0,"integral((b*sec(d*x + c) + a)^n*sin(d*x + c), x)","F",0
271,0,0,0,0.618215," ","integrate(csc(d*x+c)*(a+b*sec(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right), x\right)"," ",0,"integral((b*sec(d*x + c) + a)^n*csc(d*x + c), x)","F",0
272,0,0,0,0.977235," ","integrate(csc(d*x+c)^3*(a+b*sec(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{3}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^n*csc(d*x + c)^3, x)","F",0
273,0,0,0,0.788358," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral((cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*(b*sec(d*x + c) + a)^n, x)","F",0
274,0,0,0,0.631104," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(d x + c\right)^{2} - 1\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral(-(cos(d*x + c)^2 - 1)*(b*sec(d*x + c) + a)^n, x)","F",0
275,0,0,0,0.760521," ","integrate(csc(d*x+c)^2*(a+b*sec(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{2}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^n*csc(d*x + c)^2, x)","F",0
276,0,0,0,1.265342," ","integrate(csc(d*x+c)^4*(a+b*sec(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{4}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^n*csc(d*x + c)^4, x)","F",0
277,0,0,0,0.874068," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^n*sin(d*x + c)^(3/2), x)","F",0
278,0,0,0,0.744001," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)}^{n} \sqrt{\sin\left(d x + c\right)}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^n*sqrt(sin(d*x + c)), x)","F",0
279,0,0,0,0.868801," ","integrate((a+b*sec(d*x+c))^n/sin(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(d x + c\right) + a\right)}^{n}}{\sqrt{\sin\left(d x + c\right)}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^n/sqrt(sin(d*x + c)), x)","F",0
280,0,0,0,1.051081," ","integrate((a+b*sec(d*x+c))^n/sin(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b \sec\left(d x + c\right) + a\right)}^{n} \sqrt{\sin\left(d x + c\right)}}{\cos\left(d x + c\right)^{2} - 1}, x\right)"," ",0,"integral(-(b*sec(d*x + c) + a)^n*sqrt(sin(d*x + c))/(cos(d*x + c)^2 - 1), x)","F",0
281,0,0,0,0.646938," ","integrate((e*csc(d*x+c))^(5/2)*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e^{2} \csc\left(d x + c\right)^{2} \sec\left(d x + c\right) + a e^{2} \csc\left(d x + c\right)^{2}\right)} \sqrt{e \csc\left(d x + c\right)}, x\right)"," ",0,"integral((a*e^2*csc(d*x + c)^2*sec(d*x + c) + a*e^2*csc(d*x + c)^2)*sqrt(e*csc(d*x + c)), x)","F",0
282,0,0,0,1.524799," ","integrate((e*csc(d*x+c))^(3/2)*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e \csc\left(d x + c\right) \sec\left(d x + c\right) + a e \csc\left(d x + c\right)\right)} \sqrt{e \csc\left(d x + c\right)}, x\right)"," ",0,"integral((a*e*csc(d*x + c)*sec(d*x + c) + a*e*csc(d*x + c))*sqrt(e*csc(d*x + c)), x)","F",0
283,0,0,0,0.847984," ","integrate((a+a*sec(d*x+c))*(e*csc(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e \csc\left(d x + c\right)} {\left(a \sec\left(d x + c\right) + a\right)}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))*(a*sec(d*x + c) + a), x)","F",0
284,0,0,0,0.946273," ","integrate((a+a*sec(d*x+c))/(e*csc(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \csc\left(d x + c\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{e \csc\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))*(a*sec(d*x + c) + a)/(e*csc(d*x + c)), x)","F",0
285,0,0,0,1.075214," ","integrate((a+a*sec(d*x+c))/(e*csc(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \csc\left(d x + c\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{e^{2} \csc\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))*(a*sec(d*x + c) + a)/(e^2*csc(d*x + c)^2), x)","F",0
286,0,0,0,1.402433," ","integrate((a+a*sec(d*x+c))/(e*csc(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \csc\left(d x + c\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{e^{3} \csc\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))*(a*sec(d*x + c) + a)/(e^3*csc(d*x + c)^3), x)","F",0
287,0,0,0,0.786172," ","integrate((e*csc(d*x+c))^(5/2)*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} e^{2} \csc\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} e^{2} \csc\left(d x + c\right)^{2} \sec\left(d x + c\right) + a^{2} e^{2} \csc\left(d x + c\right)^{2}\right)} \sqrt{e \csc\left(d x + c\right)}, x\right)"," ",0,"integral((a^2*e^2*csc(d*x + c)^2*sec(d*x + c)^2 + 2*a^2*e^2*csc(d*x + c)^2*sec(d*x + c) + a^2*e^2*csc(d*x + c)^2)*sqrt(e*csc(d*x + c)), x)","F",0
288,0,0,0,1.086930," ","integrate((e*csc(d*x+c))^(3/2)*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} e \csc\left(d x + c\right) \sec\left(d x + c\right)^{2} + 2 \, a^{2} e \csc\left(d x + c\right) \sec\left(d x + c\right) + a^{2} e \csc\left(d x + c\right)\right)} \sqrt{e \csc\left(d x + c\right)}, x\right)"," ",0,"integral((a^2*e*csc(d*x + c)*sec(d*x + c)^2 + 2*a^2*e*csc(d*x + c)*sec(d*x + c) + a^2*e*csc(d*x + c))*sqrt(e*csc(d*x + c)), x)","F",0
289,0,0,0,0.730850," ","integrate((a+a*sec(d*x+c))^2*(e*csc(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}\right)} \sqrt{e \csc\left(d x + c\right)}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)*sqrt(e*csc(d*x + c)), x)","F",0
290,0,0,0,1.470614," ","integrate((a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}\right)} \sqrt{e \csc\left(d x + c\right)}}{e \csc\left(d x + c\right)}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)*sqrt(e*csc(d*x + c))/(e*csc(d*x + c)), x)","F",0
291,0,0,0,1.333255," ","integrate((a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}\right)} \sqrt{e \csc\left(d x + c\right)}}{e^{2} \csc\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)*sqrt(e*csc(d*x + c))/(e^2*csc(d*x + c)^2), x)","F",0
292,0,0,0,1.049128," ","integrate((a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}\right)} \sqrt{e \csc\left(d x + c\right)}}{e^{3} \csc\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)*sqrt(e*csc(d*x + c))/(e^3*csc(d*x + c)^3), x)","F",0
293,0,0,0,0.477831," ","integrate((e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \csc\left(d x + c\right)} e^{2} \csc\left(d x + c\right)^{2}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))*e^2*csc(d*x + c)^2/(a*sec(d*x + c) + a), x)","F",0
294,0,0,0,0.452794," ","integrate((e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \csc\left(d x + c\right)} e \csc\left(d x + c\right)}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))*e*csc(d*x + c)/(a*sec(d*x + c) + a), x)","F",0
295,0,0,0,0.493962," ","integrate((e*csc(d*x+c))^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \csc\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
296,0,0,0,0.478232," ","integrate(1/(a+a*sec(d*x+c))/(e*csc(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \csc\left(d x + c\right)}}{a e \csc\left(d x + c\right) \sec\left(d x + c\right) + a e \csc\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))/(a*e*csc(d*x + c)*sec(d*x + c) + a*e*csc(d*x + c)), x)","F",0
297,0,0,0,0.582573," ","integrate(1/(e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \csc\left(d x + c\right)}}{a e^{2} \csc\left(d x + c\right)^{2} \sec\left(d x + c\right) + a e^{2} \csc\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))/(a*e^2*csc(d*x + c)^2*sec(d*x + c) + a*e^2*csc(d*x + c)^2), x)","F",0
298,0,0,0,0.495491," ","integrate(1/(e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \csc\left(d x + c\right)}}{a e^{3} \csc\left(d x + c\right)^{3} \sec\left(d x + c\right) + a e^{3} \csc\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))/(a*e^3*csc(d*x + c)^3*sec(d*x + c) + a*e^3*csc(d*x + c)^3), x)","F",0
299,0,0,0,0.527409," ","integrate(1/(e*csc(d*x+c))^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \csc\left(d x + c\right)}}{a e^{4} \csc\left(d x + c\right)^{4} \sec\left(d x + c\right) + a e^{4} \csc\left(d x + c\right)^{4}}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))/(a*e^4*csc(d*x + c)^4*sec(d*x + c) + a*e^4*csc(d*x + c)^4), x)","F",0
300,0,0,0,0.476265," ","integrate((e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \csc\left(d x + c\right)} e^{2} \csc\left(d x + c\right)^{2}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))*e^2*csc(d*x + c)^2/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
301,0,0,0,0.612847," ","integrate((e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \csc\left(d x + c\right)} e \csc\left(d x + c\right)}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))*e*csc(d*x + c)/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
302,0,0,0,0.539902," ","integrate((e*csc(d*x+c))^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \csc\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
303,0,0,0,0.500629," ","integrate(1/(a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \csc\left(d x + c\right)}}{a^{2} e \csc\left(d x + c\right) \sec\left(d x + c\right)^{2} + 2 \, a^{2} e \csc\left(d x + c\right) \sec\left(d x + c\right) + a^{2} e \csc\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))/(a^2*e*csc(d*x + c)*sec(d*x + c)^2 + 2*a^2*e*csc(d*x + c)*sec(d*x + c) + a^2*e*csc(d*x + c)), x)","F",0
304,0,0,0,0.505618," ","integrate(1/(e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \csc\left(d x + c\right)}}{a^{2} e^{2} \csc\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} e^{2} \csc\left(d x + c\right)^{2} \sec\left(d x + c\right) + a^{2} e^{2} \csc\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))/(a^2*e^2*csc(d*x + c)^2*sec(d*x + c)^2 + 2*a^2*e^2*csc(d*x + c)^2*sec(d*x + c) + a^2*e^2*csc(d*x + c)^2), x)","F",0
305,0,0,0,0.702596," ","integrate(1/(e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \csc\left(d x + c\right)}}{a^{2} e^{3} \csc\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + 2 \, a^{2} e^{3} \csc\left(d x + c\right)^{3} \sec\left(d x + c\right) + a^{2} e^{3} \csc\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))/(a^2*e^3*csc(d*x + c)^3*sec(d*x + c)^2 + 2*a^2*e^3*csc(d*x + c)^3*sec(d*x + c) + a^2*e^3*csc(d*x + c)^3), x)","F",0
306,0,0,0,0.736989," ","integrate(1/(e*csc(d*x+c))^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \csc\left(d x + c\right)}}{a^{2} e^{4} \csc\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + 2 \, a^{2} e^{4} \csc\left(d x + c\right)^{4} \sec\left(d x + c\right) + a^{2} e^{4} \csc\left(d x + c\right)^{4}}, x\right)"," ",0,"integral(sqrt(e*csc(d*x + c))/(a^2*e^4*csc(d*x + c)^4*sec(d*x + c)^2 + 2*a^2*e^4*csc(d*x + c)^4*sec(d*x + c) + a^2*e^4*csc(d*x + c)^4), x)","F",0
