1,1,293,0,0.252112," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^9,x, algorithm=""giac"")","\frac{2520 \, a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 2520 \, a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{9177 \, a - \frac{87633 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{375732 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{953988 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1594782 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{1336734 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{781956 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{302004 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{69201 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{7129 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{9}}}{2520 \, d}"," ",0,"1/2520*(2520*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 2520*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (9177*a - 87633*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 375732*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 953988*a*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 1594782*a*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 1336734*a*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 781956*a*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 302004*a*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 + 69201*a*(cos(d*x + c) - 1)^8/(cos(d*x + c) + 1)^8 - 7129*a*(cos(d*x + c) - 1)^9/(cos(d*x + c) + 1)^9)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^9)/d","B",0
2,1,247,0,0.241657," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^7,x, algorithm=""giac"")","\frac{420 \, a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 420 \, a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{1473 \, a - \frac{11151 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{36813 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{69475 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{56035 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{28749 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{8463 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{1089 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{7}}}{420 \, d}"," ",0,"1/420*(420*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 420*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (1473*a - 11151*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 36813*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 69475*a*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 56035*a*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 28749*a*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 8463*a*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 1089*a*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^7)/d","B",0
3,1,201,0,0.582989," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^5,x, algorithm=""giac"")","\frac{60 \, a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 60 \, a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{201 \, a - \frac{1125 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2610 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1970 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{805 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{137 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{5}}}{60 \, d}"," ",0,"1/60*(60*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 60*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (201*a - 1125*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2610*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 1970*a*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 805*a*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 137*a*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^5)/d","B",0
4,1,66,0,0.357090," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^3,x, algorithm=""giac"")","-\frac{a \log\left(\frac{{\left| \cos\left(d x + c\right) \right|}}{{\left| d \right|}}\right)}{d} + \frac{2 \, a d^{2} \cos\left(d x + c\right)^{3} + 3 \, a d^{2} \cos\left(d x + c\right)^{2} - 6 \, a d^{2} \cos\left(d x + c\right)}{6 \, d^{3}}"," ",0,"-a*log(abs(cos(d*x + c))/abs(d))/d + 1/6*(2*a*d^2*cos(d*x + c)^3 + 3*a*d^2*cos(d*x + c)^2 - 6*a*d^2*cos(d*x + c))/d^3","A",0
5,1,32,0,1.451627," ","integrate((a+a*sec(d*x+c))*sin(d*x+c),x, algorithm=""giac"")","-\frac{a \cos\left(d x + c\right)}{d} - \frac{a \log\left(\frac{{\left| \cos\left(d x + c\right) \right|}}{{\left| d \right|}}\right)}{d}"," ",0,"-a*cos(d*x + c)/d - a*log(abs(cos(d*x + c))/abs(d))/d","A",0
6,1,58,0,0.500238," ","integrate(csc(d*x+c)*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{a \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right)}{d}"," ",0,"(a*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)))/d","A",0
7,1,102,0,0.425436," ","integrate(csc(d*x+c)^3*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 4 \, a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{{\left(a - \frac{3 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}{\cos\left(d x + c\right) - 1}}{4 \, d}"," ",0,"1/4*(3*a*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 4*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (a - 3*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*(cos(d*x + c) + 1)/(cos(d*x + c) - 1))/d","A",0
8,1,149,0,0.306873," ","integrate(csc(d*x+c)^5*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{22 \, a \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 32 \, a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) - \frac{{\left(a - \frac{10 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{33 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}{{\left(\cos\left(d x + c\right) - 1\right)}^{2}} + \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}}{32 \, d}"," ",0,"1/32*(22*a*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 32*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) - (a - 10*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 33*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)^2/(cos(d*x + c) - 1)^2 + 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/d","A",0
9,1,196,0,0.315123," ","integrate(csc(d*x+c)^7*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{252 \, a \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 384 \, a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{{\left(2 \, a - \frac{21 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{132 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{462 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{3}}{{\left(\cos\left(d x + c\right) - 1\right)}^{3}} + \frac{42 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{3 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{384 \, d}"," ",0,"1/384*(252*a*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 384*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (2*a - 21*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 132*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 462*a*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3)*(cos(d*x + c) + 1)^3/(cos(d*x + c) - 1)^3 + 42*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 3*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/d","A",0
10,1,174,0,2.319761," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^8,x, algorithm=""giac"")","\frac{3675 \, {\left(d x + c\right)} a + 13440 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 13440 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(9765 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 83825 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 321013 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 724649 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1078359 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 508683 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 140175 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 17115 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{8}}}{13440 \, d}"," ",0,"1/13440*(3675*(d*x + c)*a + 13440*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 13440*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(9765*a*tan(1/2*d*x + 1/2*c)^15 + 83825*a*tan(1/2*d*x + 1/2*c)^13 + 321013*a*tan(1/2*d*x + 1/2*c)^11 + 724649*a*tan(1/2*d*x + 1/2*c)^9 + 1078359*a*tan(1/2*d*x + 1/2*c)^7 + 508683*a*tan(1/2*d*x + 1/2*c)^5 + 140175*a*tan(1/2*d*x + 1/2*c)^3 + 17115*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^8)/d","A",0
11,1,146,0,0.843256," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^6,x, algorithm=""giac"")","\frac{75 \, {\left(d x + c\right)} a + 240 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 240 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(165 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1095 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3138 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5118 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1945 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 315 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(75*(d*x + c)*a + 240*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 240*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(165*a*tan(1/2*d*x + 1/2*c)^11 + 1095*a*tan(1/2*d*x + 1/2*c)^9 + 3138*a*tan(1/2*d*x + 1/2*c)^7 + 5118*a*tan(1/2*d*x + 1/2*c)^5 + 1945*a*tan(1/2*d*x + 1/2*c)^3 + 315*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
12,1,118,0,0.963481," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^4,x, algorithm=""giac"")","\frac{9 \, {\left(d x + c\right)} a + 24 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 24 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 71 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 137 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(9*(d*x + c)*a + 24*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 24*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(15*a*tan(1/2*d*x + 1/2*c)^7 + 71*a*tan(1/2*d*x + 1/2*c)^5 + 137*a*tan(1/2*d*x + 1/2*c)^3 + 33*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
13,1,88,0,0.267491," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(d x + c\right)} a + 2 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((d*x + c)*a + 2*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(a*tan(1/2*d*x + 1/2*c)^3 + 3*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
14,1,50,0,0.341192," ","integrate(csc(d*x+c)^2*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{d}"," ",0,"(a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - a/tan(1/2*d*x + 1/2*c))/d","A",0
15,1,79,0,0.237975," ","integrate(csc(d*x+c)^4*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{12 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 12 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{12 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{12 \, d}"," ",0,"1/12*(12*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 12*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 3*a*tan(1/2*d*x + 1/2*c) - (12*a*tan(1/2*d*x + 1/2*c)^2 + a)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
16,1,107,0,0.279874," ","integrate(csc(d*x+c)^6*(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{5 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 240 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 90 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{3 \, {\left(80 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 10 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{240 \, d}"," ",0,"-1/240*(5*a*tan(1/2*d*x + 1/2*c)^3 - 240*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 240*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 90*a*tan(1/2*d*x + 1/2*c) + 3*(80*a*tan(1/2*d*x + 1/2*c)^4 + 10*a*tan(1/2*d*x + 1/2*c)^2 + a)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
17,1,136,0,0.619966," ","integrate(csc(d*x+c)^8*(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{21 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 280 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6720 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 6720 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3045 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{6720 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1015 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 168 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{6720 \, d}"," ",0,"-1/6720*(21*a*tan(1/2*d*x + 1/2*c)^5 + 280*a*tan(1/2*d*x + 1/2*c)^3 - 6720*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 6720*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3045*a*tan(1/2*d*x + 1/2*c) + (6720*a*tan(1/2*d*x + 1/2*c)^6 + 1015*a*tan(1/2*d*x + 1/2*c)^4 + 168*a*tan(1/2*d*x + 1/2*c)^2 + 15*a)/tan(1/2*d*x + 1/2*c)^7)/d","A",0
18,1,164,0,0.274891," ","integrate(csc(d*x+c)^10*(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{45 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 630 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4830 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80640 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 80640 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 40950 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{80640 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 13650 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 2898 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 450 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9}}}{80640 \, d}"," ",0,"-1/80640*(45*a*tan(1/2*d*x + 1/2*c)^7 + 630*a*tan(1/2*d*x + 1/2*c)^5 + 4830*a*tan(1/2*d*x + 1/2*c)^3 - 80640*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 80640*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 40950*a*tan(1/2*d*x + 1/2*c) + (80640*a*tan(1/2*d*x + 1/2*c)^8 + 13650*a*tan(1/2*d*x + 1/2*c)^6 + 2898*a*tan(1/2*d*x + 1/2*c)^4 + 450*a*tan(1/2*d*x + 1/2*c)^2 + 35*a)/tan(1/2*d*x + 1/2*c)^9)/d","A",0
19,1,370,0,1.926554," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^9,x, algorithm=""giac"")","\frac{2520 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 2520 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{2520 \, {\left(2 \, a^{2} + \frac{a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1} + \frac{1457 \, a^{2} - \frac{20673 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{123012 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{421428 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{949662 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{1009134 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{666036 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{276804 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{66681 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{7129 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{9}}}{1260 \, d}"," ",0,"1/1260*(2520*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 2520*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + 2520*(2*a^2 + a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1) + (1457*a^2 - 20673*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 123012*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 421428*a^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 949662*a^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 1009134*a^2*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 666036*a^2*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 276804*a^2*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 + 66681*a^2*(cos(d*x + c) - 1)^8/(cos(d*x + c) + 1)^8 - 7129*a^2*(cos(d*x + c) - 1)^9/(cos(d*x + c) + 1)^9)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^9)/d","B",0
20,1,320,0,0.361430," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^7,x, algorithm=""giac"")","\frac{420 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 420 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{420 \, {\left(2 \, a^{2} + \frac{a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1} + \frac{357 \, a^{2} - \frac{3759 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{16737 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{42595 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{43855 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{25389 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{8043 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{1089 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{7}}}{210 \, d}"," ",0,"1/210*(420*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 420*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + 420*(2*a^2 + a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1) + (357*a^2 - 3759*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 16737*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 42595*a^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 43855*a^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 25389*a^2*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 8043*a^2*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 1089*a^2*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^7)/d","B",0
21,1,270,0,0.377646," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^5,x, algorithm=""giac"")","\frac{60 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 60 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{60 \, {\left(2 \, a^{2} + \frac{a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1} + \frac{69 \, a^{2} - \frac{525 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{1650 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1610 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{745 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{137 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{5}}}{30 \, d}"," ",0,"1/30*(60*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 60*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + 60*(2*a^2 + a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1) + (69*a^2 - 525*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1650*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 1610*a^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 745*a^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 137*a^2*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^5)/d","B",0
22,1,74,0,0.294819," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^3,x, algorithm=""giac"")","-\frac{2 \, a^{2} \log\left(\frac{{\left| \cos\left(d x + c\right) \right|}}{{\left| d \right|}}\right)}{d} + \frac{a^{2}}{d \cos\left(d x + c\right)} + \frac{a^{2} d^{5} \cos\left(d x + c\right)^{3} + 3 \, a^{2} d^{5} \cos\left(d x + c\right)^{2}}{3 \, d^{6}}"," ",0,"-2*a^2*log(abs(cos(d*x + c))/abs(d))/d + a^2/(d*cos(d*x + c)) + 1/3*(a^2*d^5*cos(d*x + c)^3 + 3*a^2*d^5*cos(d*x + c)^2)/d^6","A",0
23,1,51,0,0.494232," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c),x, algorithm=""giac"")","-\frac{a^{2} \cos\left(d x + c\right)}{d} - \frac{2 \, a^{2} \log\left(\frac{{\left| \cos\left(d x + c\right) \right|}}{{\left| d \right|}}\right)}{d} + \frac{a^{2}}{d \cos\left(d x + c\right)}"," ",0,"-a^2*cos(d*x + c)/d - 2*a^2*log(abs(cos(d*x + c))/abs(d))/d + a^2/(d*cos(d*x + c))","A",0
24,1,115,0,0.280556," ","integrate(csc(d*x+c)*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(a^{2} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{2 \, a^{2} + \frac{a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}}{\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1}\right)}}{d}"," ",0,"2*(a^2*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (2*a^2 + a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/d","B",0
25,1,135,0,0.671878," ","integrate(csc(d*x+c)^3*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{4 \, a^{2} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 4 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{a^{2} + \frac{5 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}}{\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + \frac{{\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}}{2 \, d}"," ",0,"1/2*(4*a^2*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 4*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (a^2 + 5*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + (cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2))/d","A",0
26,1,191,0,0.494087," ","integrate(csc(d*x+c)^5*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{34 \, a^{2} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 32 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) - \frac{{\left(a^{2} - \frac{12 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{51 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}{{\left(\cos\left(d x + c\right) - 1\right)}^{2}} + \frac{32 \, {\left(2 \, a^{2} + \frac{a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1}}{16 \, d}"," ",0,"1/16*(34*a^2*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 32*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) - (a^2 - 12*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 51*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)^2/(cos(d*x + c) - 1)^2 + 32*(2*a^2 + a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/d","A",0
27,1,238,0,0.396908," ","integrate(csc(d*x+c)^7*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{216 \, a^{2} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 192 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) - \frac{3 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{{\left(a^{2} - \frac{12 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{90 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{396 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{3}}{{\left(\cos\left(d x + c\right) - 1\right)}^{3}} + \frac{192 \, {\left(2 \, a^{2} + \frac{a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1}}{96 \, d}"," ",0,"1/96*(216*a^2*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 192*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) - 3*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + (a^2 - 12*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 90*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 396*a^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3)*(cos(d*x + c) + 1)^3/(cos(d*x + c) - 1)^3 + 192*(2*a^2 + a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/d","A",0
28,1,291,0,0.382009," ","integrate(csc(d*x+c)^9*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{3636 \, a^{2} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 3072 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) - \frac{120 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{6 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{{\left(3 \, a^{2} - \frac{40 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{282 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1680 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{7575 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{4}}{{\left(\cos\left(d x + c\right) - 1\right)}^{4}} + \frac{3072 \, {\left(2 \, a^{2} + \frac{a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1}}{1536 \, d}"," ",0,"1/1536*(3636*a^2*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 3072*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) - 120*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 6*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - (3*a^2 - 40*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 282*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 1680*a^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 7575*a^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4)*(cos(d*x + c) + 1)^4/(cos(d*x + c) - 1)^4 + 3072*(2*a^2 + a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/d","A",0
29,1,225,0,0.786266," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^8,x, algorithm=""giac"")","-\frac{25725 \, {\left(d x + c\right)} a^{2} - 26880 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 26880 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{26880 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + \frac{2 \, {\left(39165 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 300265 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 989261 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1791073 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1814943 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 670131 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 147735 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 14595 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{8}}}{13440 \, d}"," ",0,"-1/13440*(25725*(d*x + c)*a^2 - 26880*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 26880*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 26880*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 2*(39165*a^2*tan(1/2*d*x + 1/2*c)^15 + 300265*a^2*tan(1/2*d*x + 1/2*c)^13 + 989261*a^2*tan(1/2*d*x + 1/2*c)^11 + 1791073*a^2*tan(1/2*d*x + 1/2*c)^9 + 1814943*a^2*tan(1/2*d*x + 1/2*c)^7 + 670131*a^2*tan(1/2*d*x + 1/2*c)^5 + 147735*a^2*tan(1/2*d*x + 1/2*c)^3 + 14595*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^8)/d","A",0
30,1,193,0,0.505342," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^6,x, algorithm=""giac"")","-\frac{375 \, {\left(d x + c\right)} a^{2} - 480 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 480 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{480 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + \frac{2 \, {\left(615 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3485 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 7926 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 8586 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2595 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 345 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"-1/240*(375*(d*x + c)*a^2 - 480*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 480*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 480*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 2*(615*a^2*tan(1/2*d*x + 1/2*c)^11 + 3485*a^2*tan(1/2*d*x + 1/2*c)^9 + 7926*a^2*tan(1/2*d*x + 1/2*c)^7 + 8586*a^2*tan(1/2*d*x + 1/2*c)^5 + 2595*a^2*tan(1/2*d*x + 1/2*c)^3 + 345*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
31,1,161,0,1.213470," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^4,x, algorithm=""giac"")","-\frac{27 \, {\left(d x + c\right)} a^{2} - 48 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 48 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{48 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + \frac{2 \, {\left(51 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 187 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 229 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 45 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"-1/24*(27*(d*x + c)*a^2 - 48*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 48*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 48*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 2*(51*a^2*tan(1/2*d*x + 1/2*c)^7 + 187*a^2*tan(1/2*d*x + 1/2*c)^5 + 229*a^2*tan(1/2*d*x + 1/2*c)^3 + 45*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
32,1,128,0,0.293768," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^2,x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} a^{2} - 4 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 4 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{4 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + \frac{2 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*((d*x + c)*a^2 - 4*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 4*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 4*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 2*(3*a^2*tan(1/2*d*x + 1/2*c)^3 + 5*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
33,1,90,0,0.535327," ","integrate(csc(d*x+c)^2*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}\right)}}{d}"," ",0,"2*(a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - (2*a^2*tan(1/2*d*x + 1/2*c)^2 - a^2)/(tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c)))/d","A",0
34,1,104,0,0.303992," ","integrate(csc(d*x+c)^4*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{12 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 12 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - \frac{15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{6 \, d}"," ",0,"1/6*(12*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 12*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 12*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (15*a^2*tan(1/2*d*x + 1/2*c)^2 + a^2)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
35,1,136,0,0.695158," ","integrate(csc(d*x+c)^6*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{240 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 240 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{240 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - \frac{345 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 35 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{120 \, d}"," ",0,"1/120*(240*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 240*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 15*a^2*tan(1/2*d*x + 1/2*c) - 240*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (345*a^2*tan(1/2*d*x + 1/2*c)^4 + 35*a^2*tan(1/2*d*x + 1/2*c)^2 + 3*a^2)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
36,1,168,0,0.320560," ","integrate(csc(d*x+c)^8*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{35 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6720 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 6720 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 945 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{6720 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - \frac{10710 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1330 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 189 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{3360 \, d}"," ",0,"1/3360*(35*a^2*tan(1/2*d*x + 1/2*c)^3 + 6720*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 6720*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 945*a^2*tan(1/2*d*x + 1/2*c) - 6720*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (10710*a^2*tan(1/2*d*x + 1/2*c)^6 + 1330*a^2*tan(1/2*d*x + 1/2*c)^4 + 189*a^2*tan(1/2*d*x + 1/2*c)^2 + 15*a^2)/tan(1/2*d*x + 1/2*c)^7)/d","A",0
37,1,200,0,0.609957," ","integrate(csc(d*x+c)^10*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{63 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1155 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80640 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 80640 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 17955 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{80640 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - \frac{139545 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 19635 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3591 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 495 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9}}}{40320 \, d}"," ",0,"1/40320*(63*a^2*tan(1/2*d*x + 1/2*c)^5 + 1155*a^2*tan(1/2*d*x + 1/2*c)^3 + 80640*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 80640*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 17955*a^2*tan(1/2*d*x + 1/2*c) - 80640*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (139545*a^2*tan(1/2*d*x + 1/2*c)^8 + 19635*a^2*tan(1/2*d*x + 1/2*c)^6 + 3591*a^2*tan(1/2*d*x + 1/2*c)^4 + 495*a^2*tan(1/2*d*x + 1/2*c)^2 + 35*a^2)/tan(1/2*d*x + 1/2*c)^9)/d","A",0
38,1,396,0,0.545753," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^9,x, algorithm=""giac"")","-\frac{2520 \, a^{3} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 2520 \, a^{3} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) - \frac{1260 \, {\left(9 \, a^{3} + \frac{2 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{3 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{2}} + \frac{45257 \, a^{3} - \frac{392193 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{1467972 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{3001908 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3232782 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{2359854 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{1190196 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{397764 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{79281 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{7129 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{9}}}{2520 \, d}"," ",0,"-1/2520*(2520*a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 2520*a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) - 1260*(9*a^3 + 2*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 3*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^2 + (45257*a^3 - 392193*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1467972*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 3001908*a^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 3232782*a^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 2359854*a^3*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 1190196*a^3*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 397764*a^3*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 + 79281*a^3*(cos(d*x + c) - 1)^8/(cos(d*x + c) + 1)^8 - 7129*a^3*(cos(d*x + c) - 1)^9/(cos(d*x + c) + 1)^9)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^9)/d","B",0
39,1,239,0,1.111862," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^7,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{7 \, {\left(3 \, a^{3} + \frac{2 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{2}} - \frac{43 \, a^{3} - \frac{273 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{672 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{630 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{343 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{105 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{14 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{7}}\right)}}{7 \, d}"," ",0,"2/7*(7*(3*a^3 + 2*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^2 - (43*a^3 - 273*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 672*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 630*a^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 343*a^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 105*a^3*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 14*a^3*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^7)/d","A",0
40,1,297,0,1.276096," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^5,x, algorithm=""giac"")","\frac{60 \, a^{3} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 60 \, a^{3} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{30 \, {\left(15 \, a^{3} + \frac{14 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{2}} - \frac{399 \, a^{3} - \frac{1395 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{390 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{650 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{565 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{137 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{5}}}{60 \, d}"," ",0,"1/60*(60*a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 60*a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + 30*(15*a^3 + 14*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 3*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^2 - (399*a^3 - 1395*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 390*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 650*a^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 565*a^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 137*a^3*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^5)/d","B",0
41,1,102,0,0.385324," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^3,x, algorithm=""giac"")","-\frac{2 \, a^{3} \log\left(\frac{{\left| \cos\left(d x + c\right) \right|}}{{\left| d \right|}}\right)}{d} + \frac{6 \, a^{3} \cos\left(d x + c\right) + a^{3}}{2 \, d \cos\left(d x + c\right)^{2}} + \frac{2 \, a^{3} d^{8} \cos\left(d x + c\right)^{3} + 9 \, a^{3} d^{8} \cos\left(d x + c\right)^{2} + 12 \, a^{3} d^{8} \cos\left(d x + c\right)}{6 \, d^{9}}"," ",0,"-2*a^3*log(abs(cos(d*x + c))/abs(d))/d + 1/2*(6*a^3*cos(d*x + c) + a^3)/(d*cos(d*x + c)^2) + 1/6*(2*a^3*d^8*cos(d*x + c)^3 + 9*a^3*d^8*cos(d*x + c)^2 + 12*a^3*d^8*cos(d*x + c))/d^9","A",0
42,1,64,0,0.316354," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c),x, algorithm=""giac"")","-\frac{a^{3} \cos\left(d x + c\right)}{d} - \frac{3 \, a^{3} \log\left(\frac{{\left| \cos\left(d x + c\right) \right|}}{{\left| d \right|}}\right)}{d} + \frac{6 \, a^{3} \cos\left(d x + c\right) + a^{3}}{2 \, d \cos\left(d x + c\right)^{2}}"," ",0,"-a^3*cos(d*x + c)/d - 3*a^3*log(abs(cos(d*x + c))/abs(d))/d + 1/2*(6*a^3*cos(d*x + c) + a^3)/(d*cos(d*x + c)^2)","A",0
43,1,142,0,0.311284," ","integrate(csc(d*x+c)*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, {\left(2 \, a^{3} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 2 \, a^{3} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{6 \, a^{3} + \frac{8 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{2}}\right)}}{d}"," ",0,"2*(2*a^3*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 2*a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (6*a^3 + 8*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 3*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^2)/d","B",0
44,1,189,0,0.401387," ","integrate(csc(d*x+c)^3*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{10 \, a^{3} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 10 \, a^{3} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{2 \, {\left(a^{3} - \frac{5 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}{\cos\left(d x + c\right) - 1} + \frac{27 \, a^{3} + \frac{38 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{15 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(10*a^3*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 10*a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + 2*(a^3 - 5*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*(cos(d*x + c) + 1)/(cos(d*x + c) - 1) + (27*a^3 + 38*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 15*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^2)/d","B",0
45,1,186,0,0.468555," ","integrate(csc(d*x+c)^5*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{48 \, a^{3} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 48 \, a^{3} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) - \frac{a^{3} - \frac{12 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{75 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{46 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + \frac{{\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}^{2}}}{8 \, d}"," ",0,"1/8*(48*a^3*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 48*a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) - (a^3 - 12*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 75*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 46*a^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + (cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)^2)/d","A",0
46,1,243,0,0.764837," ","integrate(csc(d*x+c)^7*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{666 \, a^{3} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 672 \, a^{3} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{{\left(2 \, a^{3} - \frac{27 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{234 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1221 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{3}}{{\left(\cos\left(d x + c\right) - 1\right)}^{3}} + \frac{48 \, {\left(33 \, a^{3} + \frac{50 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{21 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{2}}}{96 \, d}"," ",0,"1/96*(666*a^3*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 672*a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (2*a^3 - 27*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 234*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 1221*a^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3)*(cos(d*x + c) + 1)^3/(cos(d*x + c) - 1)^3 + 48*(33*a^3 + 50*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 21*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^2)/d","A",0
47,1,292,0,0.650839," ","integrate(csc(d*x+c)^9*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{6012 \, a^{3} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 6144 \, a^{3} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{12 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{{\left(3 \, a^{3} - \frac{44 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{348 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2376 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{12525 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{4}}{{\left(\cos\left(d x + c\right) - 1\right)}^{4}} + \frac{1536 \, {\left(9 \, a^{3} + \frac{14 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{6 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{2}}}{768 \, d}"," ",0,"1/768*(6012*a^3*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 6144*a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + 12*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - (3*a^3 - 44*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 348*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 2376*a^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 12525*a^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4)*(cos(d*x + c) + 1)^4/(cos(d*x + c) - 1)^4 + 1536*(9*a^3 + 14*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 6*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^2)/d","A",0
48,1,244,0,0.506771," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^8,x, algorithm=""giac"")","-\frac{84525 \, {\left(d x + c\right)} a^{3} + 6720 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 6720 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{13440 \, {\left(5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} + \frac{2 \, {\left(44205 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 303065 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 841981 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1123793 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 487983 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 490749 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 267225 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 44205 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{8}}}{13440 \, d}"," ",0,"-1/13440*(84525*(d*x + c)*a^3 + 6720*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 6720*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 13440*(5*a^3*tan(1/2*d*x + 1/2*c)^3 - 7*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 + 2*(44205*a^3*tan(1/2*d*x + 1/2*c)^15 + 303065*a^3*tan(1/2*d*x + 1/2*c)^13 + 841981*a^3*tan(1/2*d*x + 1/2*c)^11 + 1123793*a^3*tan(1/2*d*x + 1/2*c)^9 + 487983*a^3*tan(1/2*d*x + 1/2*c)^7 - 490749*a^3*tan(1/2*d*x + 1/2*c)^5 - 267225*a^3*tan(1/2*d*x + 1/2*c)^3 - 44205*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^8)/d","A",0
49,1,212,0,0.454688," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^6,x, algorithm=""giac"")","-\frac{1275 \, {\left(d x + c\right)} a^{3} - 120 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 120 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{240 \, {\left(5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} + \frac{2 \, {\left(795 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 4025 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 7614 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5634 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 345 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 315 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"-1/240*(1275*(d*x + c)*a^3 - 120*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 120*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 240*(5*a^3*tan(1/2*d*x + 1/2*c)^3 - 7*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 + 2*(795*a^3*tan(1/2*d*x + 1/2*c)^11 + 4025*a^3*tan(1/2*d*x + 1/2*c)^9 + 7614*a^3*tan(1/2*d*x + 1/2*c)^7 + 5634*a^3*tan(1/2*d*x + 1/2*c)^5 - 345*a^3*tan(1/2*d*x + 1/2*c)^3 - 315*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
50,1,180,0,0.401063," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^4,x, algorithm=""giac"")","-\frac{33 \, {\left(d x + c\right)} a^{3} - 12 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 12 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{8 \, {\left(5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} + \frac{2 \, {\left(25 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 81 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 79 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{8 \, d}"," ",0,"-1/8*(33*(d*x + c)*a^3 - 12*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 12*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 8*(5*a^3*tan(1/2*d*x + 1/2*c)^3 - 7*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 + 2*(25*a^3*tan(1/2*d*x + 1/2*c)^7 + 81*a^3*tan(1/2*d*x + 1/2*c)^5 + 79*a^3*tan(1/2*d*x + 1/2*c)^3 + 7*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
51,1,102,0,0.938067," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^2,x, algorithm=""giac"")","-\frac{5 \, {\left(d x + c\right)} a^{3} - 5 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 5 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{4 \, {\left(5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(5*(d*x + c)*a^3 - 5*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 5*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 4*(5*a^3*tan(1/2*d*x + 1/2*c)^7 - 9*a^3*tan(1/2*d*x + 1/2*c)^3)/(tan(1/2*d*x + 1/2*c)^4 - 1)^2)/d","A",0
52,1,106,0,0.395191," ","integrate(csc(d*x+c)^2*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{9 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 9 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{8 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{2 \, {\left(5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(9*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 9*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 8*a^3/tan(1/2*d*x + 1/2*c) - 2*(5*a^3*tan(1/2*d*x + 1/2*c)^3 - 7*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
53,1,123,0,0.563299," ","integrate(csc(d*x+c)^4*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{33 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 33 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{6 \, {\left(5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} - \frac{2 \, {\left(18 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{6 \, d}"," ",0,"1/6*(33*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 33*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 6*(5*a^3*tan(1/2*d*x + 1/2*c)^3 - 7*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 - 2*(18*a^3*tan(1/2*d*x + 1/2*c)^2 + a^3)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
54,1,141,0,0.401627," ","integrate(csc(d*x+c)^6*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{390 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 390 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{60 \, {\left(5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} - \frac{465 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 40 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{60 \, d}"," ",0,"1/60*(390*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 390*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 60*(5*a^3*tan(1/2*d*x + 1/2*c)^3 - 7*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 - (465*a^3*tan(1/2*d*x + 1/2*c)^4 + 40*a^3*tan(1/2*d*x + 1/2*c)^2 + 3*a^3)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
55,1,169,0,0.687458," ","integrate(csc(d*x+c)^8*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{840 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 840 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - 7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{112 \, {\left(5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} - \frac{1050 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 112 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 14 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{112 \, d}"," ",0,"1/112*(840*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 840*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 7*a^3*tan(1/2*d*x + 1/2*c) - 112*(5*a^3*tan(1/2*d*x + 1/2*c)^3 - 7*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 - (1050*a^3*tan(1/2*d*x + 1/2*c)^6 + 112*a^3*tan(1/2*d*x + 1/2*c)^4 + 14*a^3*tan(1/2*d*x + 1/2*c)^2 + a^3)/tan(1/2*d*x + 1/2*c)^7)/d","A",0
56,1,202,0,0.511851," ","integrate(csc(d*x+c)^10*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{105 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 171360 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 171360 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3780 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{20160 \, {\left(5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} + \frac{220185 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 26880 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 4347 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 540 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9}}}{20160 \, d}"," ",0,"-1/20160*(105*a^3*tan(1/2*d*x + 1/2*c)^3 - 171360*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 171360*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3780*a^3*tan(1/2*d*x + 1/2*c) + 20160*(5*a^3*tan(1/2*d*x + 1/2*c)^3 - 7*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 + (220185*a^3*tan(1/2*d*x + 1/2*c)^8 + 26880*a^3*tan(1/2*d*x + 1/2*c)^6 + 4347*a^3*tan(1/2*d*x + 1/2*c)^4 + 540*a^3*tan(1/2*d*x + 1/2*c)^2 + 35*a^3)/tan(1/2*d*x + 1/2*c)^9)/d","A",0
57,1,141,0,0.275282," ","integrate(sin(d*x+c)^9/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{32 \, {\left(\frac{9 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{36 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{84 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{126 \, {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{630 \, {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 1\right)}}{315 \, a d {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{9}}"," ",0,"32/315*(9*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 36*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 84*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 126*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 630*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 1)/(a*d*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^9)","A",0
58,1,119,0,0.841161," ","integrate(sin(d*x+c)^7/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{16 \, {\left(\frac{7 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{21 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{35 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{140 \, {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - 1\right)}}{105 \, a d {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{7}}"," ",0,"16/105*(7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 21*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 35*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 140*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 1)/(a*d*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^7)","A",0
59,1,97,0,0.220814," ","integrate(sin(d*x+c)^5/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{4 \, {\left(\frac{5 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{10 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{30 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 1\right)}}{15 \, a d {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{5}}"," ",0,"4/15*(5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 10*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 30*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 1)/(a*d*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^5)","A",0
60,1,32,0,1.002472," ","integrate(sin(d*x+c)^3/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, \cos\left(d x + c\right)^{3}}{d} - \frac{3 \, \cos\left(d x + c\right)^{2}}{d}}{6 \, a}"," ",0,"1/6*(2*cos(d*x + c)^3/d - 3*cos(d*x + c)^2/d)/a","A",0
61,1,34,0,0.220217," ","integrate(sin(d*x+c)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\cos\left(d x + c\right)}{a d} + \frac{\log\left({\left| -\cos\left(d x + c\right) - 1 \right|}\right)}{a d}"," ",0,"-cos(d*x + c)/(a*d) + log(abs(-cos(d*x + c) - 1))/(a*d)","A",0
62,1,56,0,0.886467," ","integrate(csc(d*x+c)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{\log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a} + \frac{\cos\left(d x + c\right) - 1}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{4 \, d}"," ",0,"1/4*(log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/a + (cos(d*x + c) - 1)/(a*(cos(d*x + c) + 1)))/d","A",0
63,1,129,0,0.236170," ","integrate(csc(d*x+c)^3/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}}{a {\left(\cos\left(d x + c\right) - 1\right)}} - \frac{2 \, \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a} - \frac{\frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a^{2}}}{32 \, d}"," ",0,"-1/32*(2*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)*(cos(d*x + c) + 1)/(a*(cos(d*x + c) - 1)) - 2*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/a - (2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/a^2)/d","A",0
64,1,182,0,0.291504," ","integrate(csc(d*x+c)^5/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(\frac{6 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{6 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}{a {\left(\cos\left(d x + c\right) - 1\right)}^{2}} + \frac{12 \, \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a} + \frac{\frac{12 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{9 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{3}}}{384 \, d}"," ",0,"1/384*(3*(6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 1)*(cos(d*x + c) + 1)^2/(a*(cos(d*x + c) - 1)^2) + 12*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/a + (12*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 9*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 2*a^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3)/a^3)/d","A",0
65,1,139,0,0.297413," ","integrate(sin(d*x+c)^8/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{105 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 805 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2681 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 44099 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 5053 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2681 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 805 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{8} a}}{2688 \, d}"," ",0,"-1/2688*(105*(d*x + c)/a + 2*(105*tan(1/2*d*x + 1/2*c)^15 + 805*tan(1/2*d*x + 1/2*c)^13 + 2681*tan(1/2*d*x + 1/2*c)^11 - 44099*tan(1/2*d*x + 1/2*c)^9 - 5053*tan(1/2*d*x + 1/2*c)^7 - 2681*tan(1/2*d*x + 1/2*c)^5 - 805*tan(1/2*d*x + 1/2*c)^3 - 105*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^8*a))/d","A",0
66,1,113,0,0.447726," ","integrate(sin(d*x+c)^6/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 85 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1338 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 198 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 85 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} a}}{240 \, d}"," ",0,"-1/240*(15*(d*x + c)/a + 2*(15*tan(1/2*d*x + 1/2*c)^11 + 85*tan(1/2*d*x + 1/2*c)^9 - 1338*tan(1/2*d*x + 1/2*c)^7 - 198*tan(1/2*d*x + 1/2*c)^5 - 85*tan(1/2*d*x + 1/2*c)^3 - 15*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*a))/d","A",0
67,1,87,0,0.199153," ","integrate(sin(d*x+c)^4/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 53 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 11 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a}}{24 \, d}"," ",0,"-1/24*(3*(d*x + c)/a + 2*(3*tan(1/2*d*x + 1/2*c)^7 - 53*tan(1/2*d*x + 1/2*c)^5 - 11*tan(1/2*d*x + 1/2*c)^3 - 3*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a))/d","A",0
68,1,58,0,0.319839," ","integrate(sin(d*x+c)^2/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{d x + c}{a} - \frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a}}{2 \, d}"," ",0,"-1/2*((d*x + c)/a - 2*(3*tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a))/d","A",0
69,1,37,0,0.542834," ","integrate(csc(d*x+c)^2/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}{a} + \frac{3}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{12 \, d}"," ",0,"-1/12*(tan(1/2*d*x + 1/2*c)^3/a + 3/(a*tan(1/2*d*x + 1/2*c)))/d","A",0
70,1,74,0,0.244519," ","integrate(csc(d*x+c)^4/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{5 \, {\left(6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} + \frac{3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}{a^{5}}}{240 \, d}"," ",0,"-1/240*(5*(6*tan(1/2*d*x + 1/2*c)^2 + 1)/(a*tan(1/2*d*x + 1/2*c)^3) + (3*a^4*tan(1/2*d*x + 1/2*c)^5 + 10*a^4*tan(1/2*d*x + 1/2*c)^3)/a^5)/d","A",0
71,1,103,0,0.252844," ","integrate(csc(d*x+c)^6/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{7 \, {\left(75 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 20 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3\right)}}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}} + \frac{15 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 84 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 175 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}{a^{7}}}{6720 \, d}"," ",0,"-1/6720*(7*(75*tan(1/2*d*x + 1/2*c)^4 + 20*tan(1/2*d*x + 1/2*c)^2 + 3)/(a*tan(1/2*d*x + 1/2*c)^5) + (15*a^6*tan(1/2*d*x + 1/2*c)^7 + 84*a^6*tan(1/2*d*x + 1/2*c)^5 + 175*a^6*tan(1/2*d*x + 1/2*c)^3)/a^7)/d","A",0
72,1,132,0,0.276900," ","integrate(csc(d*x+c)^8/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(1470 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 490 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 126 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15\right)}}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}} + \frac{35 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 270 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 882 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1470 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}{a^{9}}}{80640 \, d}"," ",0,"-1/80640*(3*(1470*tan(1/2*d*x + 1/2*c)^6 + 490*tan(1/2*d*x + 1/2*c)^4 + 126*tan(1/2*d*x + 1/2*c)^2 + 15)/(a*tan(1/2*d*x + 1/2*c)^7) + (35*a^8*tan(1/2*d*x + 1/2*c)^9 + 270*a^8*tan(1/2*d*x + 1/2*c)^7 + 882*a^8*tan(1/2*d*x + 1/2*c)^5 + 1470*a^8*tan(1/2*d*x + 1/2*c)^3)/a^9)/d","A",0
73,1,161,0,0.294434," ","integrate(csc(d*x+c)^10/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{11 \, {\left(13230 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 5040 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1701 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 360 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35\right)}}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9}} + \frac{315 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3080 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 13365 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33264 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 48510 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}{a^{11}}}{3548160 \, d}"," ",0,"-1/3548160*(11*(13230*tan(1/2*d*x + 1/2*c)^8 + 5040*tan(1/2*d*x + 1/2*c)^6 + 1701*tan(1/2*d*x + 1/2*c)^4 + 360*tan(1/2*d*x + 1/2*c)^2 + 35)/(a*tan(1/2*d*x + 1/2*c)^9) + (315*a^10*tan(1/2*d*x + 1/2*c)^11 + 3080*a^10*tan(1/2*d*x + 1/2*c)^9 + 13365*a^10*tan(1/2*d*x + 1/2*c)^7 + 33264*a^10*tan(1/2*d*x + 1/2*c)^5 + 48510*a^10*tan(1/2*d*x + 1/2*c)^3)/a^11)/d","A",0
74,1,185,0,0.894594," ","integrate(sin(d*x+c)^11/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{64 \, {\left(\frac{11 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{55 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{165 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{330 \, {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{462 \, {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{198 \, {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{990 \, {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - 1\right)}}{495 \, a^{2} d {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{11}}"," ",0,"-64/495*(11*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 55*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 165*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 330*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 462*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 198*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 990*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 - 1)/(a^2*d*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^11)","A",0
75,1,141,0,0.294678," ","integrate(sin(d*x+c)^9/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{64 \, {\left(\frac{9 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{36 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{84 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{126 \, {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{210 \, {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - 1\right)}}{315 \, a^{2} d {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{9}}"," ",0,"-64/315*(9*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 36*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 84*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 126*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 210*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 1)/(a^2*d*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^9)","A",0
76,1,141,0,0.281988," ","integrate(sin(d*x+c)^7/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{8 \, {\left(\frac{7 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{21 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{35 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{42 \, {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 1\right)}}{21 \, a^{2} d {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{7}}"," ",0,"-8/21*(7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 21*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 35*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 14*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 42*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 1)/(a^2*d*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^7)","B",0
77,1,119,0,0.254722," ","integrate(sin(d*x+c)^5/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{8 \, {\left(\frac{10 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{20 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{15 \, {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - 2\right)}}{15 \, a^{2} d {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{5}}"," ",0,"-8/15*(10*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 20*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 15*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 15*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 2)/(a^2*d*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^5)","B",0
78,1,75,0,1.423989," ","integrate(sin(d*x+c)^3/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, \log\left({\left| -\cos\left(d x + c\right) - 1 \right|}\right)}{a^{2} d} + \frac{a^{4} d^{2} \cos\left(d x + c\right)^{3} - 3 \, a^{4} d^{2} \cos\left(d x + c\right)^{2} + 6 \, a^{4} d^{2} \cos\left(d x + c\right)}{3 \, a^{6} d^{3}}"," ",0,"-2*log(abs(-cos(d*x + c) - 1))/(a^2*d) + 1/3*(a^4*d^2*cos(d*x + c)^3 - 3*a^4*d^2*cos(d*x + c)^2 + 6*a^4*d^2*cos(d*x + c))/(a^6*d^3)","A",0
79,1,52,0,0.198890," ","integrate(sin(d*x+c)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\cos\left(d x + c\right)}{a^{2} d} + \frac{2 \, \log\left({\left| -\cos\left(d x + c\right) - 1 \right|}\right)}{a^{2} d} + \frac{1}{a^{2} d {\left(\cos\left(d x + c\right) + 1\right)}}"," ",0,"-cos(d*x + c)/(a^2*d) + 2*log(abs(-cos(d*x + c) - 1))/(a^2*d) + 1/(a^2*d*(cos(d*x + c) + 1))","A",0
80,1,87,0,1.135448," ","integrate(csc(d*x+c)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{2}} + \frac{\frac{4 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a^{4}}}{16 \, d}"," ",0,"1/16*(2*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/a^2 + (4*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/a^4)/d","A",0
81,1,82,0,0.295841," ","integrate(csc(d*x+c)^3/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(\cos\left(d x + c\right) + 1\right)}}{a^{2} {\left(\cos\left(d x + c\right) - 1\right)}} + \frac{\frac{6 \, a^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{a^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{6}}}{96 \, d}"," ",0,"1/96*(3*(cos(d*x + c) + 1)/(a^2*(cos(d*x + c) - 1)) + (6*a^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - a^4*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3)/a^6)/d","B",0
82,1,207,0,0.304382," ","integrate(csc(d*x+c)^5/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(\frac{4 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{3 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}{a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}} - \frac{12 \, \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{2}} + \frac{\frac{48 \, a^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{6 \, a^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, a^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, a^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{a^{8}}}{1536 \, d}"," ",0,"1/1536*(6*(4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 1)*(cos(d*x + c) + 1)^2/(a^2*(cos(d*x + c) - 1)^2) - 12*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/a^2 + (48*a^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 6*a^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 8*a^6*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 3*a^6*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4)/a^8)/d","A",0
83,1,139,0,0.257125," ","integrate(sin(d*x+c)^8/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{1155 \, {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(1155 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 8855 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 142541 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 31007 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 55583 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 29491 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 8855 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1155 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{8} a^{2}}}{13440 \, d}"," ",0,"1/13440*(1155*(d*x + c)/a^2 + 2*(1155*tan(1/2*d*x + 1/2*c)^15 + 8855*tan(1/2*d*x + 1/2*c)^13 - 142541*tan(1/2*d*x + 1/2*c)^11 + 31007*tan(1/2*d*x + 1/2*c)^9 - 55583*tan(1/2*d*x + 1/2*c)^7 - 29491*tan(1/2*d*x + 1/2*c)^5 - 8855*tan(1/2*d*x + 1/2*c)^3 - 1155*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^8*a^2))/d","A",0
84,1,113,0,0.259074," ","integrate(sin(d*x+c)^6/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{45 \, {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1025 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 174 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 594 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 255 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} a^{2}}}{240 \, d}"," ",0,"1/240*(45*(d*x + c)/a^2 + 2*(45*tan(1/2*d*x + 1/2*c)^11 - 1025*tan(1/2*d*x + 1/2*c)^9 - 174*tan(1/2*d*x + 1/2*c)^7 - 594*tan(1/2*d*x + 1/2*c)^5 - 255*tan(1/2*d*x + 1/2*c)^3 - 45*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*a^2))/d","A",0
85,1,87,0,0.246640," ","integrate(sin(d*x+c)^4/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{21 \, {\left(d x + c\right)}}{a^{2}} - \frac{2 \, {\left(75 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 83 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 77 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{2}}}{24 \, d}"," ",0,"1/24*(21*(d*x + c)/a^2 - 2*(75*tan(1/2*d*x + 1/2*c)^7 + 83*tan(1/2*d*x + 1/2*c)^5 + 77*tan(1/2*d*x + 1/2*c)^3 + 21*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^2))/d","A",0
86,1,75,0,0.731465," ","integrate(sin(d*x+c)^2/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{5 \, {\left(d x + c\right)}}{a^{2}} - \frac{4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} - \frac{2 \, {\left(5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}}}{2 \, d}"," ",0,"-1/2*(5*(d*x + c)/a^2 - 4*tan(1/2*d*x + 1/2*c)/a^2 - 2*(5*tan(1/2*d*x + 1/2*c)^3 + 3*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2))/d","A",0
87,1,74,0,0.261321," ","integrate(csc(d*x+c)^2/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{15}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{3 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{10}}}{120 \, d}"," ",0,"-1/120*(15/(a^2*tan(1/2*d*x + 1/2*c)) - (3*a^8*tan(1/2*d*x + 1/2*c)^5 - 5*a^8*tan(1/2*d*x + 1/2*c)^3 - 15*a^8*tan(1/2*d*x + 1/2*c))/a^10)/d","A",0
88,1,105,0,0.375021," ","integrate(csc(d*x+c)^4/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{35 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} - \frac{15 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 21 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 70 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 210 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{14}}}{3360 \, d}"," ",0,"-1/3360*(35*(3*tan(1/2*d*x + 1/2*c)^2 + 1)/(a^2*tan(1/2*d*x + 1/2*c)^3) - (15*a^12*tan(1/2*d*x + 1/2*c)^7 + 21*a^12*tan(1/2*d*x + 1/2*c)^5 - 70*a^12*tan(1/2*d*x + 1/2*c)^3 - 210*a^12*tan(1/2*d*x + 1/2*c))/a^14)/d","A",0
89,1,134,0,0.348957," ","integrate(csc(d*x+c)^6/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{63 \, {\left(5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}} - \frac{35 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 135 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 63 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 525 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1575 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{18}}}{40320 \, d}"," ",0,"-1/40320*(63*(5*tan(1/2*d*x + 1/2*c)^4 + 5*tan(1/2*d*x + 1/2*c)^2 + 1)/(a^2*tan(1/2*d*x + 1/2*c)^5) - (35*a^16*tan(1/2*d*x + 1/2*c)^9 + 135*a^16*tan(1/2*d*x + 1/2*c)^7 + 63*a^16*tan(1/2*d*x + 1/2*c)^5 - 525*a^16*tan(1/2*d*x + 1/2*c)^3 - 1575*a^16*tan(1/2*d*x + 1/2*c))/a^18)/d","A",0
90,1,134,0,0.346001," ","integrate(csc(d*x+c)^8/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{33 \, {\left(56 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3\right)}}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}} - \frac{63 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 385 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 792 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3234 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9702 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{22}}}{354816 \, d}"," ",0,"-1/354816*(33*(56*tan(1/2*d*x + 1/2*c)^4 + 21*tan(1/2*d*x + 1/2*c)^2 + 3)/(a^2*tan(1/2*d*x + 1/2*c)^7) - (63*a^20*tan(1/2*d*x + 1/2*c)^11 + 385*a^20*tan(1/2*d*x + 1/2*c)^9 + 792*a^20*tan(1/2*d*x + 1/2*c)^7 - 3234*a^20*tan(1/2*d*x + 1/2*c)^3 - 9702*a^20*tan(1/2*d*x + 1/2*c))/a^22)/d","A",0
91,1,207,0,0.406075," ","integrate(sin(d*x+c)^11/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{32 \, {\left(\frac{209 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{1045 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3135 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{6270 \, {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{8778 \, {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{13398 \, {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{2310 \, {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{9240 \, {\left(\cos\left(d x + c\right) - 1\right)}^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - 19\right)}}{3465 \, a^{3} d {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{11}}"," ",0,"32/3465*(209*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1045*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 3135*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 6270*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 8778*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 13398*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 2310*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 - 9240*(cos(d*x + c) - 1)^8/(cos(d*x + c) + 1)^8 - 19)/(a^3*d*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^11)","A",0
92,1,185,0,0.439053," ","integrate(sin(d*x+c)^9/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{32 \, {\left(\frac{36 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{144 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{336 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{504 \, {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{630 \, {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{105 \, {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{315 \, {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - 4\right)}}{315 \, a^{3} d {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{9}}"," ",0,"32/315*(36*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 144*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 336*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 504*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 630*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 105*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 315*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 - 4)/(a^3*d*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^9)","A",0
93,1,163,0,1.273543," ","integrate(sin(d*x+c)^7/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{4 \, {\left(\frac{91 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{273 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{455 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{490 \, {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{210 \, {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{140 \, {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - 13\right)}}{35 \, a^{3} d {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{7}}"," ",0,"4/35*(91*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 273*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 455*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 490*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 210*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 140*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 13)/(a^3*d*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^7)","B",0
94,1,172,0,0.417675," ","integrate(sin(d*x+c)^5/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{60 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{3}} + \frac{\frac{85 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{20 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{200 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{205 \, {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{137 \, {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 29}{a^{3} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{5}}}{15 \, d}"," ",0,"-1/15*(60*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^3 + (85*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 20*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 200*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 205*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 137*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 29)/(a^3*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^5))/d","A",0
95,1,94,0,0.642629," ","integrate(sin(d*x+c)^3/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{7 \, \log\left({\left| -\cos\left(d x + c\right) - 1 \right|}\right)}{a^{3} d} - \frac{2}{a^{3} d {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{2 \, a^{6} d^{5} \cos\left(d x + c\right)^{3} - 9 \, a^{6} d^{5} \cos\left(d x + c\right)^{2} + 30 \, a^{6} d^{5} \cos\left(d x + c\right)}{6 \, a^{9} d^{6}}"," ",0,"-7*log(abs(-cos(d*x + c) - 1))/(a^3*d) - 2/(a^3*d*(cos(d*x + c) + 1)) + 1/6*(2*a^6*d^5*cos(d*x + c)^3 - 9*a^6*d^5*cos(d*x + c)^2 + 30*a^6*d^5*cos(d*x + c))/(a^9*d^6)","A",0
96,1,63,0,0.291045," ","integrate(sin(d*x+c)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\cos\left(d x + c\right)}{a^{3} d} + \frac{3 \, \log\left({\left| -\cos\left(d x + c\right) - 1 \right|}\right)}{a^{3} d} + \frac{6 \, \cos\left(d x + c\right) + 5}{2 \, a^{3} d {\left(\cos\left(d x + c\right) + 1\right)}^{2}}"," ",0,"-cos(d*x + c)/(a^3*d) + 3*log(abs(-cos(d*x + c) - 1))/(a^3*d) + 1/2*(6*cos(d*x + c) + 5)/(a^3*d*(cos(d*x + c) + 1)^2)","A",0
97,1,113,0,0.296893," ","integrate(csc(d*x+c)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{6 \, \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{3}} + \frac{\frac{18 \, a^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{9 \, a^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, a^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{9}}}{96 \, d}"," ",0,"1/96*(6*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/a^3 + (18*a^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 9*a^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 2*a^6*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3)/a^9)/d","A",0
98,1,182,0,0.693904," ","integrate(csc(d*x+c)^3/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{12 \, {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}}{a^{3} {\left(\cos\left(d x + c\right) - 1\right)}} - \frac{12 \, \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{3}} + \frac{\frac{24 \, a^{9} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{12 \, a^{9} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, a^{9} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{3 \, a^{9} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{a^{12}}}{768 \, d}"," ",0,"1/768*(12*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)*(cos(d*x + c) + 1)/(a^3*(cos(d*x + c) - 1)) - 12*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/a^3 + (24*a^9*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 12*a^9*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 4*a^9*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 3*a^9*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4)/a^12)/d","A",0
99,1,232,0,1.065026," ","integrate(csc(d*x+c)^5/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{10 \, {\left(\frac{2 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{9 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}{a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}} - \frac{60 \, \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{3}} + \frac{\frac{60 \, a^{12} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{30 \, a^{12} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{20 \, a^{12} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{5 \, a^{12} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a^{12} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{15}}}{5120 \, d}"," ",0,"1/5120*(10*(2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 9*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 1)*(cos(d*x + c) + 1)^2/(a^3*(cos(d*x + c) - 1)^2) - 60*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/a^3 + (60*a^12*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 30*a^12*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 20*a^12*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 5*a^12*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 4*a^12*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5)/a^15)/d","A",0
100,1,139,0,0.804593," ","integrate(sin(d*x+c)^8/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{3045 \, {\left(d x + c\right)}}{a^{3}} + \frac{2 \, {\left(3045 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} - 120015 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 36939 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 218007 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 146537 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 77749 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 23345 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3045 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{8} a^{3}}}{13440 \, d}"," ",0,"-1/13440*(3045*(d*x + c)/a^3 + 2*(3045*tan(1/2*d*x + 1/2*c)^15 - 120015*tan(1/2*d*x + 1/2*c)^13 - 36939*tan(1/2*d*x + 1/2*c)^11 - 218007*tan(1/2*d*x + 1/2*c)^9 - 146537*tan(1/2*d*x + 1/2*c)^7 - 77749*tan(1/2*d*x + 1/2*c)^5 - 23345*tan(1/2*d*x + 1/2*c)^3 - 3045*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^8*a^3))/d","A",0
101,1,113,0,0.349874," ","integrate(sin(d*x+c)^6/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{345 \, {\left(d x + c\right)}}{a^{3}} - \frac{2 \, {\left(1575 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3165 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 5814 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4554 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1955 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 345 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} a^{3}}}{240 \, d}"," ",0,"-1/240*(345*(d*x + c)/a^3 - 2*(1575*tan(1/2*d*x + 1/2*c)^11 + 3165*tan(1/2*d*x + 1/2*c)^9 + 5814*tan(1/2*d*x + 1/2*c)^7 + 4554*tan(1/2*d*x + 1/2*c)^5 + 1955*tan(1/2*d*x + 1/2*c)^3 + 345*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*a^3))/d","A",0
102,1,101,0,0.300907," ","integrate(sin(d*x+c)^4/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{51 \, {\left(d x + c\right)}}{a^{3}} - \frac{32 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{2 \, {\left(77 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 149 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 123 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{3}}}{8 \, d}"," ",0,"1/8*(51*(d*x + c)/a^3 - 32*tan(1/2*d*x + 1/2*c)/a^3 - 2*(77*tan(1/2*d*x + 1/2*c)^7 + 149*tan(1/2*d*x + 1/2*c)^5 + 123*tan(1/2*d*x + 1/2*c)^3 + 35*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^3))/d","A",0
103,1,96,0,0.320404," ","integrate(sin(d*x+c)^2/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{33 \, {\left(d x + c\right)}}{a^{3}} - \frac{6 \, {\left(7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}} + \frac{2 \, {\left(a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 18 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{9}}}{6 \, d}"," ",0,"-1/6*(33*(d*x + c)/a^3 - 6*(7*tan(1/2*d*x + 1/2*c)^3 + 5*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3) + 2*(a^6*tan(1/2*d*x + 1/2*c)^3 - 18*a^6*tan(1/2*d*x + 1/2*c))/a^9)/d","A",0
104,1,73,0,0.428555," ","integrate(csc(d*x+c)^2/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{35}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \frac{5 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 14 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 70 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{21}}}{560 \, d}"," ",0,"-1/560*(35/(a^3*tan(1/2*d*x + 1/2*c)) + (5*a^18*tan(1/2*d*x + 1/2*c)^7 - 14*a^18*tan(1/2*d*x + 1/2*c)^5 + 70*a^18*tan(1/2*d*x + 1/2*c))/a^21)/d","A",0
105,1,73,0,0.951694," ","integrate(csc(d*x+c)^4/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{15}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} + \frac{5 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 27 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 135 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{27}}}{2880 \, d}"," ",0,"-1/2880*(15/(a^3*tan(1/2*d*x + 1/2*c)^3) + (5*a^24*tan(1/2*d*x + 1/2*c)^9 - 27*a^24*tan(1/2*d*x + 1/2*c)^5 + 135*a^24*tan(1/2*d*x + 1/2*c))/a^27)/d","A",0
106,1,134,0,0.463730," ","integrate(csc(d*x+c)^6/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{231 \, {\left(30 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3\right)}}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}} - \frac{315 \, a^{30} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 770 \, a^{30} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 990 \, a^{30} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4158 \, a^{30} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 20790 \, a^{30} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{33}}}{887040 \, d}"," ",0,"1/887040*(231*(30*tan(1/2*d*x + 1/2*c)^4 - 10*tan(1/2*d*x + 1/2*c)^2 - 3)/(a^3*tan(1/2*d*x + 1/2*c)^5) - (315*a^30*tan(1/2*d*x + 1/2*c)^11 + 770*a^30*tan(1/2*d*x + 1/2*c)^9 - 990*a^30*tan(1/2*d*x + 1/2*c)^7 - 4158*a^30*tan(1/2*d*x + 1/2*c)^5 + 20790*a^30*tan(1/2*d*x + 1/2*c))/a^33)/d","A",0
107,1,163,0,2.019372," ","integrate(csc(d*x+c)^8/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{429 \, {\left(280 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 35 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 28 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 5\right)}}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}} - \frac{1155 \, a^{36} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 5460 \, a^{36} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 5005 \, a^{36} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 17160 \, a^{36} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 42042 \, a^{36} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 210210 \, a^{36} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{39}}}{15375360 \, d}"," ",0,"1/15375360*(429*(280*tan(1/2*d*x + 1/2*c)^6 - 35*tan(1/2*d*x + 1/2*c)^4 - 28*tan(1/2*d*x + 1/2*c)^2 - 5)/(a^3*tan(1/2*d*x + 1/2*c)^7) - (1155*a^36*tan(1/2*d*x + 1/2*c)^13 + 5460*a^36*tan(1/2*d*x + 1/2*c)^11 + 5005*a^36*tan(1/2*d*x + 1/2*c)^9 - 17160*a^36*tan(1/2*d*x + 1/2*c)^7 - 42042*a^36*tan(1/2*d*x + 1/2*c)^5 + 210210*a^36*tan(1/2*d*x + 1/2*c))/a^39)/d","A",0
108,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(e*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*(e*sin(d*x + c))^(5/2), x)","F",0
109,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(e*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*(e*sin(d*x + c))^(3/2), x)","F",0
110,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(e*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \sqrt{e \sin\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*sqrt(e*sin(d*x + c)), x)","F",0
111,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\sqrt{e \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/sqrt(e*sin(d*x + c)), x)","F",0
112,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/(e*sin(d*x + c))^(3/2), x)","F",0
113,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/(e*sin(d*x + c))^(5/2), x)","F",0
114,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(e*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*(e*sin(d*x + c))^(5/2), x)","F",0
115,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(e*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*(e*sin(d*x + c))^(3/2), x)","F",0
116,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(e*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{e \sin\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*sqrt(e*sin(d*x + c)), x)","F",0
117,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{e \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/sqrt(e*sin(d*x + c)), x)","F",0
118,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/(e*sin(d*x + c))^(3/2), x)","F",0
119,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/(e*sin(d*x + c))^(5/2), x)","F",0
120,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{7}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(7/2)/(a*sec(d*x + c) + a), x)","F",0
121,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(5/2)/(a*sec(d*x + c) + a), x)","F",0
122,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(3/2)/(a*sec(d*x + c) + a), x)","F",0
123,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sqrt{e \sin\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*sin(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
124,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))/(e*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{e \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*sqrt(e*sin(d*x + c))), x)","F",0
125,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))/(e*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*(e*sin(d*x + c))^(3/2)), x)","F",0
126,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))/(e*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*(e*sin(d*x + c))^(5/2)), x)","F",0
127,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{7}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(7/2)/(a*sec(d*x + c) + a)^2, x)","F",0
128,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(5/2)/(a*sec(d*x + c) + a)^2, x)","F",0
129,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(3/2)/(a*sec(d*x + c) + a)^2, x)","F",0
130,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sqrt{e \sin\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(e*sin(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
131,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{e \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^2*sqrt(e*sin(d*x + c))), x)","F",0
132,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^2*(e*sin(d*x + c))^(3/2)), x)","F",0
133,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^2*(e*sin(d*x + c))^(5/2)), x)","F",0
134,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(e*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{3} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3*(e*sin(d*x + c))^m, x)","F",0
135,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(e*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*(e*sin(d*x + c))^m, x)","F",0
136,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(e*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*(e*sin(d*x + c))^m, x)","F",0
137,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/(a*sec(d*x + c) + a), x)","F",0
138,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/(a*sec(d*x + c) + a)^2, x)","F",0
139,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/(a*sec(d*x + c) + a)^3, x)","F",0
140,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(e*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)*(e*sin(d*x + c))^m, x)","F",0
141,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)*(e*sin(d*x+c))^m,x, algorithm=""giac"")","\int \sqrt{a \sec\left(d x + c\right) + a} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*(e*sin(d*x + c))^m, x)","F",0
142,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/sqrt(a*sec(d*x + c) + a), x)","F",0
143,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/(a*sec(d*x + c) + a)^(3/2), x)","F",0
144,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*(e*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*(e*sin(d*x + c))^m, x)","F",0
145,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^7,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{7}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*sin(d*x + c)^7, x)","F",0
146,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^5,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*sin(d*x + c)^5, x)","F",0
147,-2,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Evaluation time: 1.35sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
148,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*sin(d*x + c), x)","F",0
149,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sec(d*x+c))^n,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*csc(d*x + c), x)","F",0
150,0,0,0,0.000000," ","integrate(csc(d*x+c)^3*(a+a*sec(d*x+c))^n,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*csc(d*x + c)^3, x)","F",0
151,0,0,0,0.000000," ","integrate(csc(d*x+c)^5*(a+a*sec(d*x+c))^n,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*csc(d*x + c)^5, x)","F",0
152,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^4,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*sin(d*x + c)^4, x)","F",0
153,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^2,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*sin(d*x + c)^2, x)","F",0
154,0,0,0,0.000000," ","integrate(csc(d*x+c)^2*(a+a*sec(d*x+c))^n,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*csc(d*x + c)^2, x)","F",0
155,0,0,0,0.000000," ","integrate(csc(d*x+c)^4*(a+a*sec(d*x+c))^n,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*csc(d*x + c)^4, x)","F",0
156,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*sin(d*x + c)^(3/2), x)","F",0
157,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sqrt{\sin\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*sqrt(sin(d*x + c)), x)","F",0
158,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n/sin(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{n}}{\sqrt{\sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n/sqrt(sin(d*x + c)), x)","F",0
159,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n/sin(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{n}}{\sin\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n/sin(d*x + c)^(3/2), x)","F",0
160,1,317,0,0.258938," ","integrate((a+b*sec(d*x+c))*sin(d*x+c)^7,x, algorithm=""giac"")","\frac{420 \, b \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 420 \, b \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{384 \, a + 1089 \, b - \frac{2688 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{8463 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{8064 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{28749 \, b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{13440 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{56035 \, b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{56035 \, b {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{28749 \, b {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{8463 \, b {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{1089 \, b {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{7}}}{420 \, d}"," ",0,"1/420*(420*b*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 420*b*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (384*a + 1089*b - 2688*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 8463*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 8064*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 28749*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 13440*a*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 56035*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 56035*b*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 28749*b*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 8463*b*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 1089*b*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^7)/d","B",0
161,1,248,0,0.238363," ","integrate((a+b*sec(d*x+c))*sin(d*x+c)^5,x, algorithm=""giac"")","\frac{60 \, b \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 60 \, b \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{64 \, a + 137 \, b - \frac{320 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{805 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{640 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1970 \, b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1970 \, b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{805 \, b {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{137 \, b {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{5}}}{60 \, d}"," ",0,"1/60*(60*b*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 60*b*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (64*a + 137*b - 320*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 805*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 640*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 1970*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 1970*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 805*b*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 137*b*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^5)/d","B",0
162,1,66,0,0.337864," ","integrate((a+b*sec(d*x+c))*sin(d*x+c)^3,x, algorithm=""giac"")","-\frac{b \log\left(\frac{{\left| \cos\left(d x + c\right) \right|}}{{\left| d \right|}}\right)}{d} + \frac{2 \, a d^{2} \cos\left(d x + c\right)^{3} + 3 \, b d^{2} \cos\left(d x + c\right)^{2} - 6 \, a d^{2} \cos\left(d x + c\right)}{6 \, d^{3}}"," ",0,"-b*log(abs(cos(d*x + c))/abs(d))/d + 1/6*(2*a*d^2*cos(d*x + c)^3 + 3*b*d^2*cos(d*x + c)^2 - 6*a*d^2*cos(d*x + c))/d^3","A",0
163,1,32,0,0.235117," ","integrate((a+b*sec(d*x+c))*sin(d*x+c),x, algorithm=""giac"")","-\frac{a \cos\left(d x + c\right)}{d} - \frac{b \log\left(\frac{{\left| \cos\left(d x + c\right) \right|}}{{\left| d \right|}}\right)}{d}"," ",0,"-a*cos(d*x + c)/d - b*log(abs(cos(d*x + c))/abs(d))/d","A",0
164,1,61,0,0.206773," ","integrate(csc(d*x+c)*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(a + b\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 2 \, b \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right)}{2 \, d}"," ",0,"1/2*((a + b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 2*b*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)))/d","B",0
165,1,169,0,0.252596," ","integrate(csc(d*x+c)^3*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(a + 2 \, b\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 8 \, b \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{{\left(a + b - \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{4 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}{\cos\left(d x + c\right) - 1} - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}}{8 \, d}"," ",0,"1/8*(2*(a + 2*b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 8*b*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (a + b - 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 4*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*(cos(d*x + c) + 1)/(cos(d*x + c) - 1) - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/d","B",0
166,1,266,0,0.243328," ","integrate(csc(d*x+c)^5*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{4 \, {\left(3 \, a + 8 \, b\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 64 \, b \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) - \frac{{\left(a + b - \frac{8 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{12 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{18 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{48 \, b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}{{\left(\cos\left(d x + c\right) - 1\right)}^{2}} - \frac{8 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{12 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{64 \, d}"," ",0,"1/64*(4*(3*a + 8*b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 64*b*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) - (a + b - 8*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 12*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 18*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 48*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)^2/(cos(d*x + c) - 1)^2 - 8*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 12*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/d","B",0
167,1,357,0,0.454916," ","integrate(csc(d*x+c)^7*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{12 \, {\left(5 \, a + 16 \, b\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 384 \, b \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{{\left(a + b - \frac{9 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{12 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{45 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{87 \, b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{110 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{352 \, b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{3}}{{\left(\cos\left(d x + c\right) - 1\right)}^{3}} - \frac{45 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{87 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{9 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{12 \, b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{384 \, d}"," ",0,"1/384*(12*(5*a + 16*b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 384*b*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (a + b - 9*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 12*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 45*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 87*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 110*a*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 352*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3)*(cos(d*x + c) + 1)^3/(cos(d*x + c) - 1)^3 - 45*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 87*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 9*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 12*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - a*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3)/d","B",0
168,1,228,0,0.446368," ","integrate((a+b*sec(d*x+c))*sin(d*x+c)^6,x, algorithm=""giac"")","\frac{75 \, {\left(d x + c\right)} a + 240 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 240 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(75 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 425 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1520 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 990 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4128 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 990 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4128 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 425 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1520 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 75 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(75*(d*x + c)*a + 240*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 240*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(75*a*tan(1/2*d*x + 1/2*c)^11 - 240*b*tan(1/2*d*x + 1/2*c)^11 + 425*a*tan(1/2*d*x + 1/2*c)^9 - 1520*b*tan(1/2*d*x + 1/2*c)^9 + 990*a*tan(1/2*d*x + 1/2*c)^7 - 4128*b*tan(1/2*d*x + 1/2*c)^7 - 990*a*tan(1/2*d*x + 1/2*c)^5 - 4128*b*tan(1/2*d*x + 1/2*c)^5 - 425*a*tan(1/2*d*x + 1/2*c)^3 - 1520*b*tan(1/2*d*x + 1/2*c)^3 - 75*a*tan(1/2*d*x + 1/2*c) - 240*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
169,1,172,0,0.239579," ","integrate((a+b*sec(d*x+c))*sin(d*x+c)^4,x, algorithm=""giac"")","\frac{9 \, {\left(d x + c\right)} a + 24 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 24 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 104 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 33 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 104 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(9*(d*x + c)*a + 24*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 24*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(9*a*tan(1/2*d*x + 1/2*c)^7 - 24*b*tan(1/2*d*x + 1/2*c)^7 + 33*a*tan(1/2*d*x + 1/2*c)^5 - 104*b*tan(1/2*d*x + 1/2*c)^5 - 33*a*tan(1/2*d*x + 1/2*c)^3 - 104*b*tan(1/2*d*x + 1/2*c)^3 - 9*a*tan(1/2*d*x + 1/2*c) - 24*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
170,1,114,0,0.195389," ","integrate((a+b*sec(d*x+c))*sin(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(d x + c\right)} a + 2 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((d*x + c)*a + 2*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(a*tan(1/2*d*x + 1/2*c)^3 - 2*b*tan(1/2*d*x + 1/2*c)^3 - a*tan(1/2*d*x + 1/2*c) - 2*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
171,1,77,0,1.282789," ","integrate(csc(d*x+c)^2*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{2 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{a + b}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"1/2*(2*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c) - (a + b)/tan(1/2*d*x + 1/2*c))/d","B",0
172,1,133,0,0.251132," ","integrate(csc(d*x+c)^4*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 24 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a*tan(1/2*d*x + 1/2*c)^3 - b*tan(1/2*d*x + 1/2*c)^3 + 24*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 24*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 9*a*tan(1/2*d*x + 1/2*c) - 15*b*tan(1/2*d*x + 1/2*c) - (9*a*tan(1/2*d*x + 1/2*c)^2 + 15*b*tan(1/2*d*x + 1/2*c)^2 + a + b)/tan(1/2*d*x + 1/2*c)^3)/d","B",0
173,1,194,0,1.721910," ","integrate(csc(d*x+c)^6*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 35 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 480 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 150 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 330 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{150 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 330 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 25 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a + 3 \, b}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{480 \, d}"," ",0,"1/480*(3*a*tan(1/2*d*x + 1/2*c)^5 - 3*b*tan(1/2*d*x + 1/2*c)^5 + 25*a*tan(1/2*d*x + 1/2*c)^3 - 35*b*tan(1/2*d*x + 1/2*c)^3 + 480*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 480*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 150*a*tan(1/2*d*x + 1/2*c) - 330*b*tan(1/2*d*x + 1/2*c) - (150*a*tan(1/2*d*x + 1/2*c)^4 + 330*b*tan(1/2*d*x + 1/2*c)^4 + 25*a*tan(1/2*d*x + 1/2*c)^2 + 35*b*tan(1/2*d*x + 1/2*c)^2 + 3*a + 3*b)/tan(1/2*d*x + 1/2*c)^5)/d","B",0
174,1,418,0,0.427844," ","integrate((a+b*sec(d*x+c))^2*sin(d*x+c)^5,x, algorithm=""giac"")","\frac{60 \, a b \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 60 \, a b \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{60 \, {\left(a b + b^{2} + \frac{a b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1} + \frac{32 \, a^{2} + 137 \, a b - 100 \, b^{2} - \frac{160 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{805 \, a b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{440 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{320 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1970 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{640 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1970 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{360 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{805 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{60 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{137 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{5}}}{30 \, d}"," ",0,"1/30*(60*a*b*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 60*a*b*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + 60*(a*b + b^2 + a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1) + (32*a^2 + 137*a*b - 100*b^2 - 160*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 805*a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 440*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 320*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 1970*a*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 640*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 1970*a*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 360*b^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 805*a*b*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 60*b^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 137*a*b*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^5)/d","B",0
175,1,100,0,0.407750," ","integrate((a+b*sec(d*x+c))^2*sin(d*x+c)^3,x, algorithm=""giac"")","-\frac{2 \, a b \log\left(\frac{{\left| \cos\left(d x + c\right) \right|}}{{\left| d \right|}}\right)}{d} + \frac{b^{2}}{d \cos\left(d x + c\right)} + \frac{a^{2} d^{5} \cos\left(d x + c\right)^{3} + 3 \, a b d^{5} \cos\left(d x + c\right)^{2} - 3 \, a^{2} d^{5} \cos\left(d x + c\right) + 3 \, b^{2} d^{5} \cos\left(d x + c\right)}{3 \, d^{6}}"," ",0,"-2*a*b*log(abs(cos(d*x + c))/abs(d))/d + b^2/(d*cos(d*x + c)) + 1/3*(a^2*d^5*cos(d*x + c)^3 + 3*a*b*d^5*cos(d*x + c)^2 - 3*a^2*d^5*cos(d*x + c) + 3*b^2*d^5*cos(d*x + c))/d^6","A",0
176,1,50,0,0.339136," ","integrate((a+b*sec(d*x+c))^2*sin(d*x+c),x, algorithm=""giac"")","-\frac{a^{2} \cos\left(d x + c\right)}{d} - \frac{2 \, a b \log\left(\frac{{\left| \cos\left(d x + c\right) \right|}}{{\left| d \right|}}\right)}{d} + \frac{b^{2}}{d \cos\left(d x + c\right)}"," ",0,"-a^2*cos(d*x + c)/d - 2*a*b*log(abs(cos(d*x + c))/abs(d))/d + b^2/(d*cos(d*x + c))","A",0
177,1,124,0,0.509542," ","integrate(csc(d*x+c)*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{4 \, a b \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) - {\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - \frac{4 \, {\left(a b + b^{2} + \frac{a b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1}}{2 \, d}"," ",0,"-1/2*(4*a*b*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) - (a^2 + 2*a*b + b^2)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 4*(a*b + b^2 + a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/d","A",0
178,1,314,0,0.289697," ","integrate(csc(d*x+c)^3*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{16 \, a b \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, a b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - 2 \, {\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - \frac{a^{2} + 2 \, a b + b^{2} + \frac{6 \, a b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{14 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{4 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{3 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + \frac{{\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}}{8 \, d}"," ",0,"-1/8*(16*a*b*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*(a^2 + 4*a*b + 3*b^2)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - (a^2 + 2*a*b + b^2 + 6*a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 14*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 4*a*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 3*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + (cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2))/d","B",0
179,1,379,0,0.739896," ","integrate((a+b*sec(d*x+c))^2*sin(d*x+c)^6,x, algorithm=""giac"")","\frac{480 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 480 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 75 \, {\left(a^{2} - 6 \, b^{2}\right)} {\left(d x + c\right)} - \frac{480 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + \frac{2 \, {\left(75 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 480 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 210 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 425 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3040 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 870 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 990 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 8256 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 660 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 990 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 8256 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 660 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 425 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3040 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 870 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 75 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 480 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 210 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(480*a*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 480*a*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 75*(a^2 - 6*b^2)*(d*x + c) - 480*b^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 2*(75*a^2*tan(1/2*d*x + 1/2*c)^11 - 480*a*b*tan(1/2*d*x + 1/2*c)^11 - 210*b^2*tan(1/2*d*x + 1/2*c)^11 + 425*a^2*tan(1/2*d*x + 1/2*c)^9 - 3040*a*b*tan(1/2*d*x + 1/2*c)^9 - 870*b^2*tan(1/2*d*x + 1/2*c)^9 + 990*a^2*tan(1/2*d*x + 1/2*c)^7 - 8256*a*b*tan(1/2*d*x + 1/2*c)^7 - 660*b^2*tan(1/2*d*x + 1/2*c)^7 - 990*a^2*tan(1/2*d*x + 1/2*c)^5 - 8256*a*b*tan(1/2*d*x + 1/2*c)^5 + 660*b^2*tan(1/2*d*x + 1/2*c)^5 - 425*a^2*tan(1/2*d*x + 1/2*c)^3 - 3040*a*b*tan(1/2*d*x + 1/2*c)^3 + 870*b^2*tan(1/2*d*x + 1/2*c)^3 - 75*a^2*tan(1/2*d*x + 1/2*c) - 480*a*b*tan(1/2*d*x + 1/2*c) + 210*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","B",0
180,1,285,0,0.303840," ","integrate((a+b*sec(d*x+c))^2*sin(d*x+c)^4,x, algorithm=""giac"")","\frac{48 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 48 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 9 \, {\left(a^{2} - 4 \, b^{2}\right)} {\left(d x + c\right)} - \frac{48 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + \frac{2 \, {\left(9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 208 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 33 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 208 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(48*a*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 48*a*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 9*(a^2 - 4*b^2)*(d*x + c) - 48*b^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 2*(9*a^2*tan(1/2*d*x + 1/2*c)^7 - 48*a*b*tan(1/2*d*x + 1/2*c)^7 - 12*b^2*tan(1/2*d*x + 1/2*c)^7 + 33*a^2*tan(1/2*d*x + 1/2*c)^5 - 208*a*b*tan(1/2*d*x + 1/2*c)^5 - 12*b^2*tan(1/2*d*x + 1/2*c)^5 - 33*a^2*tan(1/2*d*x + 1/2*c)^3 - 208*a*b*tan(1/2*d*x + 1/2*c)^3 + 12*b^2*tan(1/2*d*x + 1/2*c)^3 - 9*a^2*tan(1/2*d*x + 1/2*c) - 48*a*b*tan(1/2*d*x + 1/2*c) + 12*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
181,1,159,0,0.278482," ","integrate((a+b*sec(d*x+c))^2*sin(d*x+c)^2,x, algorithm=""giac"")","\frac{4 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 4 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(a^{2} - 2 \, b^{2}\right)} {\left(d x + c\right)} - \frac{4 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + \frac{2 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*a*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 4*a*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (a^2 - 2*b^2)*(d*x + c) - 4*b^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 2*(a^2*tan(1/2*d*x + 1/2*c)^3 - 4*a*b*tan(1/2*d*x + 1/2*c)^3 - a^2*tan(1/2*d*x + 1/2*c) - 4*a*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
182,1,167,0,1.222723," ","integrate(csc(d*x+c)^2*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{4 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 4 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} - 2 \, a b - b^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"1/2*(4*a*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 4*a*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + a^2*tan(1/2*d*x + 1/2*c) - 2*a*b*tan(1/2*d*x + 1/2*c) + b^2*tan(1/2*d*x + 1/2*c) - (a^2*tan(1/2*d*x + 1/2*c)^2 + 2*a*b*tan(1/2*d*x + 1/2*c)^2 + 5*b^2*tan(1/2*d*x + 1/2*c)^2 - a^2 - 2*a*b - b^2)/(tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c)))/d","B",0
183,1,226,0,1.127099," ","integrate(csc(d*x+c)^4*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 48 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 48 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 30 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{48 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - \frac{9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 30 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 21 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} + 2 \, a b + b^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a^2*tan(1/2*d*x + 1/2*c)^3 - 2*a*b*tan(1/2*d*x + 1/2*c)^3 + b^2*tan(1/2*d*x + 1/2*c)^3 + 48*a*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 48*a*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 9*a^2*tan(1/2*d*x + 1/2*c) - 30*a*b*tan(1/2*d*x + 1/2*c) + 21*b^2*tan(1/2*d*x + 1/2*c) - 48*b^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (9*a^2*tan(1/2*d*x + 1/2*c)^2 + 30*a*b*tan(1/2*d*x + 1/2*c)^2 + 21*b^2*tan(1/2*d*x + 1/2*c)^2 + a^2 + 2*a*b + b^2)/tan(1/2*d*x + 1/2*c)^3)/d","B",0
184,1,326,0,0.327289," ","integrate(csc(d*x+c)^6*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 70 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 45 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 960 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 960 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 150 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 660 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 570 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{960 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - \frac{150 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 660 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 570 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 25 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 70 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 45 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{2} + 6 \, a b + 3 \, b^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{480 \, d}"," ",0,"1/480*(3*a^2*tan(1/2*d*x + 1/2*c)^5 - 6*a*b*tan(1/2*d*x + 1/2*c)^5 + 3*b^2*tan(1/2*d*x + 1/2*c)^5 + 25*a^2*tan(1/2*d*x + 1/2*c)^3 - 70*a*b*tan(1/2*d*x + 1/2*c)^3 + 45*b^2*tan(1/2*d*x + 1/2*c)^3 + 960*a*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 960*a*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 150*a^2*tan(1/2*d*x + 1/2*c) - 660*a*b*tan(1/2*d*x + 1/2*c) + 570*b^2*tan(1/2*d*x + 1/2*c) - 960*b^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (150*a^2*tan(1/2*d*x + 1/2*c)^4 + 660*a*b*tan(1/2*d*x + 1/2*c)^4 + 570*b^2*tan(1/2*d*x + 1/2*c)^4 + 25*a^2*tan(1/2*d*x + 1/2*c)^2 + 70*a*b*tan(1/2*d*x + 1/2*c)^2 + 45*b^2*tan(1/2*d*x + 1/2*c)^2 + 3*a^2 + 6*a*b + 3*b^2)/tan(1/2*d*x + 1/2*c)^5)/d","B",0
185,1,695,0,0.584873," ","integrate((a+b*sec(d*x+c))^3*sin(d*x+c)^5,x, algorithm=""giac"")","\frac{60 \, {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 60 \, {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{30 \, {\left(9 \, a^{2} b + 12 \, a b^{2} - 6 \, b^{3} + \frac{18 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{12 \, a b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{16 \, b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{9 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{2}} + \frac{64 \, a^{3} + 411 \, a^{2} b - 600 \, a b^{2} - 274 \, b^{3} - \frac{320 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2415 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2640 \, a b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{1490 \, b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{640 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{5910 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{3840 \, a b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{3100 \, b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{5910 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2160 \, a b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3100 \, b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2415 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{360 \, a b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{1490 \, b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{411 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{274 \, b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{5}}}{60 \, d}"," ",0,"1/60*(60*(3*a^2*b - 2*b^3)*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 60*(3*a^2*b - 2*b^3)*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + 30*(9*a^2*b + 12*a*b^2 - 6*b^3 + 18*a^2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 12*a*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 16*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 9*a^2*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 6*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^2 + (64*a^3 + 411*a^2*b - 600*a*b^2 - 274*b^3 - 320*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2415*a^2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2640*a*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1490*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 640*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 5910*a^2*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 3840*a*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 3100*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 5910*a^2*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 2160*a*b^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 3100*b^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 2415*a^2*b*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 360*a*b^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 1490*b^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 411*a^2*b*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 274*b^3*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^5)/d","B",0
186,1,128,0,0.402870," ","integrate((a+b*sec(d*x+c))^3*sin(d*x+c)^3,x, algorithm=""giac"")","-\frac{{\left(3 \, a^{2} b - b^{3}\right)} \log\left(\frac{{\left| \cos\left(d x + c\right) \right|}}{{\left| d \right|}}\right)}{d} + \frac{6 \, a b^{2} \cos\left(d x + c\right) + b^{3}}{2 \, d \cos\left(d x + c\right)^{2}} + \frac{2 \, a^{3} d^{8} \cos\left(d x + c\right)^{3} + 9 \, a^{2} b d^{8} \cos\left(d x + c\right)^{2} - 6 \, a^{3} d^{8} \cos\left(d x + c\right) + 18 \, a b^{2} d^{8} \cos\left(d x + c\right)}{6 \, d^{9}}"," ",0,"-(3*a^2*b - b^3)*log(abs(cos(d*x + c))/abs(d))/d + 1/2*(6*a*b^2*cos(d*x + c) + b^3)/(d*cos(d*x + c)^2) + 1/6*(2*a^3*d^8*cos(d*x + c)^3 + 9*a^2*b*d^8*cos(d*x + c)^2 - 6*a^3*d^8*cos(d*x + c) + 18*a*b^2*d^8*cos(d*x + c))/d^9","A",0
187,1,66,0,1.562829," ","integrate((a+b*sec(d*x+c))^3*sin(d*x+c),x, algorithm=""giac"")","-\frac{a^{3} \cos\left(d x + c\right)}{d} - \frac{3 \, a^{2} b \log\left(\frac{{\left| \cos\left(d x + c\right) \right|}}{{\left| d \right|}}\right)}{d} + \frac{6 \, a b^{2} \cos\left(d x + c\right) + b^{3}}{2 \, d \cos\left(d x + c\right)^{2}}"," ",0,"-a^3*cos(d*x + c)/d - 3*a^2*b*log(abs(cos(d*x + c))/abs(d))/d + 1/2*(6*a*b^2*cos(d*x + c) + b^3)/(d*cos(d*x + c)^2)","A",0
188,1,250,0,0.498230," ","integrate(csc(d*x+c)*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{9 \, a^{2} b + 12 \, a b^{2} + 3 \, b^{3} + \frac{18 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{12 \, a b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2 \, b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{9 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 2*(3*a^2*b + b^3)*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (9*a^2*b + 12*a*b^2 + 3*b^3 + 18*a^2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 12*a*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 9*a^2*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 3*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^2)/d","B",0
189,1,482,0,1.261278," ","integrate(csc(d*x+c)^3*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{3 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{3 \, a b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - 2 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) + 8 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) - \frac{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - \frac{2 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{12 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{18 \, a b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{8 \, b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}{\cos\left(d x + c\right) - 1} - \frac{4 \, {\left(9 \, a^{2} b + 12 \, a b^{2} + 6 \, b^{3} + \frac{18 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{12 \, a b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{8 \, b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{9 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{2}}}{8 \, d}"," ",0,"-1/8*(a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 3*a^2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 3*a*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) + 8*(3*a^2*b + 2*b^3)*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) - (a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 12*a^2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 18*a*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 8*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*(cos(d*x + c) + 1)/(cos(d*x + c) - 1) - 4*(9*a^2*b + 12*a*b^2 + 6*b^3 + 18*a^2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 12*a*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 8*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 9*a^2*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 6*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^2)/d","B",0
190,1,563,0,0.463539," ","integrate((a+b*sec(d*x+c))^3*sin(d*x+c)^6,x, algorithm=""giac"")","\frac{75 \, {\left(a^{3} - 18 \, a b^{2}\right)} {\left(d x + c\right)} + 120 \, {\left(6 \, a^{2} b - 5 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 120 \, {\left(6 \, a^{2} b - 5 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{240 \, {\left(6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} + \frac{2 \, {\left(75 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 720 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 630 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 480 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 425 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 4560 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2610 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2720 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 990 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12384 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1980 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5760 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 990 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12384 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1980 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5760 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 425 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4560 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2610 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2720 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 75 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 720 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 630 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(75*(a^3 - 18*a*b^2)*(d*x + c) + 120*(6*a^2*b - 5*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 120*(6*a^2*b - 5*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 240*(6*a*b^2*tan(1/2*d*x + 1/2*c)^3 - b^3*tan(1/2*d*x + 1/2*c)^3 - 6*a*b^2*tan(1/2*d*x + 1/2*c) - b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 + 2*(75*a^3*tan(1/2*d*x + 1/2*c)^11 - 720*a^2*b*tan(1/2*d*x + 1/2*c)^11 - 630*a*b^2*tan(1/2*d*x + 1/2*c)^11 + 480*b^3*tan(1/2*d*x + 1/2*c)^11 + 425*a^3*tan(1/2*d*x + 1/2*c)^9 - 4560*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 2610*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 2720*b^3*tan(1/2*d*x + 1/2*c)^9 + 990*a^3*tan(1/2*d*x + 1/2*c)^7 - 12384*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 1980*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 5760*b^3*tan(1/2*d*x + 1/2*c)^7 - 990*a^3*tan(1/2*d*x + 1/2*c)^5 - 12384*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 1980*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 5760*b^3*tan(1/2*d*x + 1/2*c)^5 - 425*a^3*tan(1/2*d*x + 1/2*c)^3 - 4560*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 2610*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 2720*b^3*tan(1/2*d*x + 1/2*c)^3 - 75*a^3*tan(1/2*d*x + 1/2*c) - 720*a^2*b*tan(1/2*d*x + 1/2*c) + 630*a*b^2*tan(1/2*d*x + 1/2*c) + 480*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","B",0
191,1,431,0,0.403977," ","integrate((a+b*sec(d*x+c))^3*sin(d*x+c)^4,x, algorithm=""giac"")","\frac{3 \, {\left(a^{3} - 12 \, a b^{2}\right)} {\left(d x + c\right)} + 12 \, {\left(2 \, a^{2} b - b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 12 \, {\left(2 \, a^{2} b - b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{8 \, {\left(6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} + \frac{2 \, {\left(3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 8 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 11 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 104 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 11 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 104 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{8 \, d}"," ",0,"1/8*(3*(a^3 - 12*a*b^2)*(d*x + c) + 12*(2*a^2*b - b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 12*(2*a^2*b - b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 8*(6*a*b^2*tan(1/2*d*x + 1/2*c)^3 - b^3*tan(1/2*d*x + 1/2*c)^3 - 6*a*b^2*tan(1/2*d*x + 1/2*c) - b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 + 2*(3*a^3*tan(1/2*d*x + 1/2*c)^7 - 24*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 12*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 8*b^3*tan(1/2*d*x + 1/2*c)^7 + 11*a^3*tan(1/2*d*x + 1/2*c)^5 - 104*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 12*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 24*b^3*tan(1/2*d*x + 1/2*c)^5 - 11*a^3*tan(1/2*d*x + 1/2*c)^3 - 104*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 12*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 24*b^3*tan(1/2*d*x + 1/2*c)^3 - 3*a^3*tan(1/2*d*x + 1/2*c) - 24*a^2*b*tan(1/2*d*x + 1/2*c) + 12*a*b^2*tan(1/2*d*x + 1/2*c) + 8*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
192,1,346,0,0.378963," ","integrate((a+b*sec(d*x+c))^3*sin(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(a^{3} - 6 \, a b^{2}\right)} {\left(d x + c\right)} + {\left(6 \, a^{2} b - b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(6 \, a^{2} b - b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((a^3 - 6*a*b^2)*(d*x + c) + (6*a^2*b - b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (6*a^2*b - b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(a^3*tan(1/2*d*x + 1/2*c)^7 - 6*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 6*a*b^2*tan(1/2*d*x + 1/2*c)^7 + b^3*tan(1/2*d*x + 1/2*c)^7 - 3*a^3*tan(1/2*d*x + 1/2*c)^5 + 6*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 6*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 3*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*a^3*tan(1/2*d*x + 1/2*c)^3 + 6*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 6*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*b^3*tan(1/2*d*x + 1/2*c)^3 - a^3*tan(1/2*d*x + 1/2*c) - 6*a^2*b*tan(1/2*d*x + 1/2*c) + 6*a*b^2*tan(1/2*d*x + 1/2*c) + b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1)^2)/d","B",0
193,1,225,0,0.356027," ","integrate(csc(d*x+c)^2*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, {\left(2 \, a^{2} b + b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, a^{2} b + b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{2 \, {\left(6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(a^3*tan(1/2*d*x + 1/2*c) - 3*a^2*b*tan(1/2*d*x + 1/2*c) + 3*a*b^2*tan(1/2*d*x + 1/2*c) - b^3*tan(1/2*d*x + 1/2*c) + 3*(2*a^2*b + b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*a^2*b + b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)/tan(1/2*d*x + 1/2*c) - 2*(6*a*b^2*tan(1/2*d*x + 1/2*c)^3 - b^3*tan(1/2*d*x + 1/2*c)^3 - 6*a*b^2*tan(1/2*d*x + 1/2*c) - b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
194,1,361,0,0.515511," ","integrate(csc(d*x+c)^4*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 63 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 12 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{24 \, {\left(6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} - \frac{9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 45 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 63 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 27 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a^3*tan(1/2*d*x + 1/2*c)^3 - 3*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 3*a*b^2*tan(1/2*d*x + 1/2*c)^3 - b^3*tan(1/2*d*x + 1/2*c)^3 + 9*a^3*tan(1/2*d*x + 1/2*c) - 45*a^2*b*tan(1/2*d*x + 1/2*c) + 63*a*b^2*tan(1/2*d*x + 1/2*c) - 27*b^3*tan(1/2*d*x + 1/2*c) + 12*(6*a^2*b + 5*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 12*(6*a^2*b + 5*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 24*(6*a*b^2*tan(1/2*d*x + 1/2*c)^3 - b^3*tan(1/2*d*x + 1/2*c)^3 - 6*a*b^2*tan(1/2*d*x + 1/2*c) - b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 - (9*a^3*tan(1/2*d*x + 1/2*c)^2 + 45*a^2*b*tan(1/2*d*x + 1/2*c)^2 + 63*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 27*b^3*tan(1/2*d*x + 1/2*c)^2 + a^3 + 3*a^2*b + 3*a*b^2 + b^3)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
195,1,498,0,0.377109," ","integrate(csc(d*x+c)^6*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 135 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 55 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 150 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 990 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1710 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 870 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, {\left(6 \, a^{2} b + 7 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 240 \, {\left(6 \, a^{2} b + 7 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{480 \, {\left(6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} - \frac{150 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 990 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1710 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 870 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 25 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 105 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 135 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 55 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{3} + 9 \, a^{2} b + 9 \, a b^{2} + 3 \, b^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{480 \, d}"," ",0,"1/480*(3*a^3*tan(1/2*d*x + 1/2*c)^5 - 9*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 9*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 3*b^3*tan(1/2*d*x + 1/2*c)^5 + 25*a^3*tan(1/2*d*x + 1/2*c)^3 - 105*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 135*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 55*b^3*tan(1/2*d*x + 1/2*c)^3 + 150*a^3*tan(1/2*d*x + 1/2*c) - 990*a^2*b*tan(1/2*d*x + 1/2*c) + 1710*a*b^2*tan(1/2*d*x + 1/2*c) - 870*b^3*tan(1/2*d*x + 1/2*c) + 240*(6*a^2*b + 7*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 240*(6*a^2*b + 7*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 480*(6*a*b^2*tan(1/2*d*x + 1/2*c)^3 - b^3*tan(1/2*d*x + 1/2*c)^3 - 6*a*b^2*tan(1/2*d*x + 1/2*c) - b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 - (150*a^3*tan(1/2*d*x + 1/2*c)^4 + 990*a^2*b*tan(1/2*d*x + 1/2*c)^4 + 1710*a*b^2*tan(1/2*d*x + 1/2*c)^4 + 870*b^3*tan(1/2*d*x + 1/2*c)^4 + 25*a^3*tan(1/2*d*x + 1/2*c)^2 + 105*a^2*b*tan(1/2*d*x + 1/2*c)^2 + 135*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 55*b^3*tan(1/2*d*x + 1/2*c)^2 + 3*a^3 + 9*a^2*b + 9*a*b^2 + 3*b^3)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
196,1,1559,0,1.616554," ","integrate(sin(d*x+c)^7/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{420 \, {\left(a^{7} b - a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7} + b^{8}\right)} \log\left({\left| a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{9} - a^{8} b} - \frac{420 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{8}} + \frac{384 \, a^{7} - 1089 \, a^{6} b - 1848 \, a^{5} b^{2} + 3267 \, a^{4} b^{3} + 2240 \, a^{3} b^{4} - 3267 \, a^{2} b^{5} - 840 \, a b^{6} + 1089 \, b^{7} - \frac{2688 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{8463 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{12096 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{24549 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{14000 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{23709 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{5040 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{7623 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{8064 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{28749 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{32088 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{78687 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{35280 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{72807 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{12600 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{22869 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{13440 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{56035 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{40320 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{136185 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{45920 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{122745 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{16800 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{38115 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{56035 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{24360 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{136185 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{32480 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{122745 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{12600 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{38115 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{28749 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{6720 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{78687 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{11760 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{72807 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5040 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{22869 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{8463 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{840 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{24549 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{1680 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{23709 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{840 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{7623 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{1089 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{3267 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{3267 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{1089 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{8} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{7}}}{420 \, d}"," ",0,"1/420*(420*(a^7*b - a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 - 3*a^2*b^6 - a*b^7 + b^8)*log(abs(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^9 - a^8*b) - 420*(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^8 + (384*a^7 - 1089*a^6*b - 1848*a^5*b^2 + 3267*a^4*b^3 + 2240*a^3*b^4 - 3267*a^2*b^5 - 840*a*b^6 + 1089*b^7 - 2688*a^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 8463*a^6*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 12096*a^5*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 24549*a^4*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 14000*a^3*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 23709*a^2*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 5040*a*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 7623*b^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 8064*a^7*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 28749*a^6*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 32088*a^5*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 78687*a^4*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 35280*a^3*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 72807*a^2*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 12600*a*b^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 22869*b^7*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 13440*a^7*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 56035*a^6*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 40320*a^5*b^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 136185*a^4*b^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 45920*a^3*b^4*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 122745*a^2*b^5*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 16800*a*b^6*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 38115*b^7*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 56035*a^6*b*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 24360*a^5*b^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 136185*a^4*b^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 32480*a^3*b^4*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 122745*a^2*b^5*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 12600*a*b^6*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 38115*b^7*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 28749*a^6*b*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 6720*a^5*b^2*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 78687*a^4*b^3*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 11760*a^3*b^4*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 72807*a^2*b^5*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 5040*a*b^6*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 22869*b^7*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 8463*a^6*b*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 840*a^5*b^2*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 24549*a^4*b^3*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 1680*a^3*b^4*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 23709*a^2*b^5*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 840*a*b^6*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 7623*b^7*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 1089*a^6*b*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 - 3267*a^4*b^3*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 + 3267*a^2*b^5*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 - 1089*b^7*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7)/(a^8*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^7))/d","B",0
197,1,867,0,0.442029," ","integrate(sin(d*x+c)^5/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{60 \, {\left(a^{5} b - a^{4} b^{2} - 2 \, a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5} - b^{6}\right)} \log\left({\left| a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{7} - a^{6} b} - \frac{60 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{6}} + \frac{64 \, a^{5} - 137 \, a^{4} b - 200 \, a^{3} b^{2} + 274 \, a^{2} b^{3} + 120 \, a b^{4} - 137 \, b^{5} - \frac{320 \, a^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{805 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{880 \, a^{3} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{1490 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{480 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{685 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{640 \, a^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1970 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1280 \, a^{3} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3100 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{720 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1370 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1970 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{720 \, a^{3} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{3100 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{480 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1370 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{805 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{120 \, a^{3} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1490 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{120 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{685 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{137 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{274 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{137 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{6} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{5}}}{60 \, d}"," ",0,"1/60*(60*(a^5*b - a^4*b^2 - 2*a^3*b^3 + 2*a^2*b^4 + a*b^5 - b^6)*log(abs(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^7 - a^6*b) - 60*(a^4*b - 2*a^2*b^3 + b^5)*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^6 + (64*a^5 - 137*a^4*b - 200*a^3*b^2 + 274*a^2*b^3 + 120*a*b^4 - 137*b^5 - 320*a^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 805*a^4*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 880*a^3*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1490*a^2*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 480*a*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 685*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 640*a^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 1970*a^4*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 1280*a^3*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 3100*a^2*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 720*a*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 1370*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 1970*a^4*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 720*a^3*b^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 3100*a^2*b^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 480*a*b^4*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 1370*b^5*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 805*a^4*b*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 120*a^3*b^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 1490*a^2*b^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 120*a*b^4*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 685*b^5*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 137*a^4*b*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 274*a^2*b^3*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 137*b^5*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5)/(a^6*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^5))/d","B",0
198,1,102,0,0.234161," ","integrate(sin(d*x+c)^3/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(a^{2} b - b^{3}\right)} \log\left({\left| -a \cos\left(d x + c\right) - b \right|}\right)}{a^{4} d} + \frac{2 \, a^{2} d^{2} \cos\left(d x + c\right)^{3} - 3 \, a b d^{2} \cos\left(d x + c\right)^{2} - 6 \, a^{2} d^{2} \cos\left(d x + c\right) + 6 \, b^{2} d^{2} \cos\left(d x + c\right)}{6 \, a^{3} d^{3}}"," ",0,"(a^2*b - b^3)*log(abs(-a*cos(d*x + c) - b))/(a^4*d) + 1/6*(2*a^2*d^2*cos(d*x + c)^3 - 3*a*b*d^2*cos(d*x + c)^2 - 6*a^2*d^2*cos(d*x + c) + 6*b^2*d^2*cos(d*x + c))/(a^3*d^3)","A",0
199,1,38,0,0.240371," ","integrate(sin(d*x+c)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\cos\left(d x + c\right)}{a d} + \frac{b \log\left({\left| -a \cos\left(d x + c\right) - b \right|}\right)}{a^{2} d}"," ",0,"-cos(d*x + c)/(a*d) + b*log(abs(-a*cos(d*x + c) - b))/(a^2*d)","A",0
200,1,100,0,0.300941," ","integrate(csc(d*x+c)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, b \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{2} - b^{2}} + \frac{\log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a + b}}{2 \, d}"," ",0,"1/2*(2*b*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^2 - b^2) + log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a + b))/d","A",0
201,1,202,0,0.399839," ","integrate(csc(d*x+c)^3/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{8 \, a^{2} b \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, a \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{2} + 2 \, a b + b^{2}} + \frac{{\left(a + b - \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}{{\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(\cos\left(d x + c\right) - 1\right)}} - \frac{\cos\left(d x + c\right) - 1}{{\left(a - b\right)} {\left(\cos\left(d x + c\right) + 1\right)}}}{8 \, d}"," ",0,"1/8*(8*a^2*b*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^4 - 2*a^2*b^2 + b^4) + 2*a*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a^2 + 2*a*b + b^2) + (a + b - 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*(cos(d*x + c) + 1)/((a^2 + 2*a*b + b^2)*(cos(d*x + c) - 1)) - (cos(d*x + c) - 1)/((a - b)*(cos(d*x + c) + 1)))/d","A",0
202,1,419,0,0.747512," ","integrate(csc(d*x+c)^5/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{64 \, a^{4} b \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} + \frac{4 \, {\left(3 \, a^{2} + a b\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{\frac{8 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{4 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a^{2} - 2 \, a b + b^{2}} - \frac{{\left(a^{2} + 2 \, a b + b^{2} - \frac{8 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{12 \, a b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{4 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{18 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}}{64 \, d}"," ",0,"1/64*(64*a^4*b*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) + 4*(3*a^2 + a*b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - (8*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 4*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/(a^2 - 2*a*b + b^2) - (a^2 + 2*a*b + b^2 - 8*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 12*a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 4*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 18*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 6*a*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)^2/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*(cos(d*x + c) - 1)^2))/d","B",0
203,1,781,0,0.289093," ","integrate(sin(d*x+c)^6/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{15 \, {\left(5 \, a^{6} - 30 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 16 \, b^{6}\right)} {\left(d x + c\right)}}{a^{7}} - \frac{480 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{7}} + \frac{2 \, {\left(75 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 240 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 210 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 480 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 120 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 240 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 425 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1520 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 870 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2720 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1200 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 990 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4128 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 660 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5760 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2400 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 990 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4128 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 660 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5760 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 240 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2400 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 425 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1520 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 870 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2720 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1200 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 75 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 210 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 480 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} a^{6}}}{240 \, d}"," ",0,"1/240*(15*(5*a^6 - 30*a^4*b^2 + 40*a^2*b^4 - 16*b^6)*(d*x + c)/a^7 - 480*(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^7) + 2*(75*a^5*tan(1/2*d*x + 1/2*c)^11 + 240*a^4*b*tan(1/2*d*x + 1/2*c)^11 - 210*a^3*b^2*tan(1/2*d*x + 1/2*c)^11 - 480*a^2*b^3*tan(1/2*d*x + 1/2*c)^11 + 120*a*b^4*tan(1/2*d*x + 1/2*c)^11 + 240*b^5*tan(1/2*d*x + 1/2*c)^11 + 425*a^5*tan(1/2*d*x + 1/2*c)^9 + 1520*a^4*b*tan(1/2*d*x + 1/2*c)^9 - 870*a^3*b^2*tan(1/2*d*x + 1/2*c)^9 - 2720*a^2*b^3*tan(1/2*d*x + 1/2*c)^9 + 360*a*b^4*tan(1/2*d*x + 1/2*c)^9 + 1200*b^5*tan(1/2*d*x + 1/2*c)^9 + 990*a^5*tan(1/2*d*x + 1/2*c)^7 + 4128*a^4*b*tan(1/2*d*x + 1/2*c)^7 - 660*a^3*b^2*tan(1/2*d*x + 1/2*c)^7 - 5760*a^2*b^3*tan(1/2*d*x + 1/2*c)^7 + 240*a*b^4*tan(1/2*d*x + 1/2*c)^7 + 2400*b^5*tan(1/2*d*x + 1/2*c)^7 - 990*a^5*tan(1/2*d*x + 1/2*c)^5 + 4128*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 660*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 5760*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 240*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 2400*b^5*tan(1/2*d*x + 1/2*c)^5 - 425*a^5*tan(1/2*d*x + 1/2*c)^3 + 1520*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 870*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 2720*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 360*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 1200*b^5*tan(1/2*d*x + 1/2*c)^3 - 75*a^5*tan(1/2*d*x + 1/2*c) + 240*a^4*b*tan(1/2*d*x + 1/2*c) + 210*a^3*b^2*tan(1/2*d*x + 1/2*c) - 480*a^2*b^3*tan(1/2*d*x + 1/2*c) - 120*a*b^4*tan(1/2*d*x + 1/2*c) + 240*b^5*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*a^6))/d","B",0
204,1,407,0,0.304395," ","integrate(sin(d*x+c)^4/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} {\left(d x + c\right)}}{a^{5}} - \frac{48 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{5}} + \frac{2 \, {\left(9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 104 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 33 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 104 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*a^4 - 12*a^2*b^2 + 8*b^4)*(d*x + c)/a^5 - 48*(a^4*b - 2*a^2*b^3 + b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^5) + 2*(9*a^3*tan(1/2*d*x + 1/2*c)^7 + 24*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 12*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 24*b^3*tan(1/2*d*x + 1/2*c)^7 + 33*a^3*tan(1/2*d*x + 1/2*c)^5 + 104*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 12*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 72*b^3*tan(1/2*d*x + 1/2*c)^5 - 33*a^3*tan(1/2*d*x + 1/2*c)^3 + 104*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 12*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 72*b^3*tan(1/2*d*x + 1/2*c)^3 - 9*a^3*tan(1/2*d*x + 1/2*c) + 24*a^2*b*tan(1/2*d*x + 1/2*c) + 12*a*b^2*tan(1/2*d*x + 1/2*c) - 24*b^3*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^4))/d","B",0
205,1,185,0,0.267231," ","integrate(sin(d*x+c)^2/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(a^{2} - 2 \, b^{2}\right)} {\left(d x + c\right)}}{a^{3}} - \frac{4 \, {\left(a^{2} b - b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{3}} + \frac{2 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}}}{2 \, d}"," ",0,"1/2*((a^2 - 2*b^2)*(d*x + c)/a^3 - 4*(a^2*b - b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^3) + 2*(a*tan(1/2*d*x + 1/2*c)^3 + 2*b*tan(1/2*d*x + 1/2*c)^3 - a*tan(1/2*d*x + 1/2*c) + 2*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2))/d","B",0
206,1,129,0,0.252525," ","integrate(csc(d*x+c)^2/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)} a b}{{\left(a^{2} - b^{2}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a - b} + \frac{1}{{\left(a + b\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"-1/2*(4*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))*a*b/((a^2 - b^2)*sqrt(-a^2 + b^2)) - tan(1/2*d*x + 1/2*c)/(a - b) + 1/((a + b)*tan(1/2*d*x + 1/2*c)))/d","A",0
207,1,269,0,0.271740," ","integrate(csc(d*x+c)^4/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{48 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)} a^{3} b}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(48*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))*a^3*b/((a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)) + (a^2*tan(1/2*d*x + 1/2*c)^3 - 2*a*b*tan(1/2*d*x + 1/2*c)^3 + b^2*tan(1/2*d*x + 1/2*c)^3 + 9*a^2*tan(1/2*d*x + 1/2*c) - 12*a*b*tan(1/2*d*x + 1/2*c) + 3*b^2*tan(1/2*d*x + 1/2*c))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (9*a*tan(1/2*d*x + 1/2*c)^2 + 3*b*tan(1/2*d*x + 1/2*c)^2 + a + b)/((a^2 + 2*a*b + b^2)*tan(1/2*d*x + 1/2*c)^3))/d","B",0
208,1,541,0,0.351413," ","integrate(csc(d*x+c)^6/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{960 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)} a^{5} b}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 90 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 70 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 150 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 420 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 420 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 180 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 30 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}} + \frac{150 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 120 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 30 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 25 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 40 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{2} + 6 \, a b + 3 \, b^{2}}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{480 \, d}"," ",0,"-1/480*(960*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))*a^5*b/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) - (3*a^4*tan(1/2*d*x + 1/2*c)^5 - 12*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 18*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 12*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*b^4*tan(1/2*d*x + 1/2*c)^5 + 25*a^4*tan(1/2*d*x + 1/2*c)^3 - 90*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 120*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 70*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 15*b^4*tan(1/2*d*x + 1/2*c)^3 + 150*a^4*tan(1/2*d*x + 1/2*c) - 420*a^3*b*tan(1/2*d*x + 1/2*c) + 420*a^2*b^2*tan(1/2*d*x + 1/2*c) - 180*a*b^3*tan(1/2*d*x + 1/2*c) + 30*b^4*tan(1/2*d*x + 1/2*c))/(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5) + (150*a^2*tan(1/2*d*x + 1/2*c)^4 + 120*a*b*tan(1/2*d*x + 1/2*c)^4 + 30*b^2*tan(1/2*d*x + 1/2*c)^4 + 25*a^2*tan(1/2*d*x + 1/2*c)^2 + 40*a*b*tan(1/2*d*x + 1/2*c)^2 + 15*b^2*tan(1/2*d*x + 1/2*c)^2 + 3*a^2 + 6*a*b + 3*b^2)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*tan(1/2*d*x + 1/2*c)^5))/d","B",0
209,1,1861,0,0.769886," ","integrate(sin(d*x+c)^7/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{420 \, {\left(a^{7} b - a^{6} b^{2} - 6 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 9 \, a^{2} b^{6} - 4 \, a b^{7} + 4 \, b^{8}\right)} \log\left({\left| a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{10} - a^{9} b} - \frac{420 \, {\left(a^{6} b - 6 \, a^{4} b^{3} + 9 \, a^{2} b^{5} - 4 \, b^{7}\right)} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{9}} - \frac{420 \, {\left(a^{7} b - 7 \, a^{5} b^{3} - 4 \, a^{4} b^{4} + 11 \, a^{3} b^{5} + 8 \, a^{2} b^{6} - 5 \, a b^{7} - 4 \, b^{8} + \frac{a^{7} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{a^{6} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{6 \, a^{5} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{6 \, a^{4} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{9 \, a^{3} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{9 \, a^{2} b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{4 \, a b^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{4 \, b^{8} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{{\left(a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)} a^{9}} + \frac{192 \, a^{7} - 1089 \, a^{6} b - 2772 \, a^{5} b^{2} + 6534 \, a^{4} b^{3} + 5600 \, a^{3} b^{4} - 9801 \, a^{2} b^{5} - 2940 \, a b^{6} + 4356 \, b^{7} - \frac{1344 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{8463 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{18144 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{49098 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{35000 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{71127 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{17640 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{30492 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{4032 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{28749 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{48132 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{157374 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{88200 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{218421 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{44100 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{91476 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6720 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{56035 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{60480 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{272370 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{114800 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{368235 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{58800 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{152460 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{56035 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{36540 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{272370 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{81200 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{368235 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{44100 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{152460 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{28749 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{10080 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{157374 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{29400 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{218421 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{17640 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{91476 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{8463 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{1260 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{49098 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{4200 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{71127 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{2940 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{30492 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{1089 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{6534 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{9801 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{4356 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{9} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{7}}}{210 \, d}"," ",0,"1/210*(420*(a^7*b - a^6*b^2 - 6*a^5*b^3 + 6*a^4*b^4 + 9*a^3*b^5 - 9*a^2*b^6 - 4*a*b^7 + 4*b^8)*log(abs(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^10 - a^9*b) - 420*(a^6*b - 6*a^4*b^3 + 9*a^2*b^5 - 4*b^7)*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^9 - 420*(a^7*b - 7*a^5*b^3 - 4*a^4*b^4 + 11*a^3*b^5 + 8*a^2*b^6 - 5*a*b^7 - 4*b^8 + a^7*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - a^6*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 6*a^5*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 6*a^4*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 9*a^3*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 9*a^2*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 4*a*b^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 4*b^8*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*a^9) + (192*a^7 - 1089*a^6*b - 2772*a^5*b^2 + 6534*a^4*b^3 + 5600*a^3*b^4 - 9801*a^2*b^5 - 2940*a*b^6 + 4356*b^7 - 1344*a^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 8463*a^6*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 18144*a^5*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 49098*a^4*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 35000*a^3*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 71127*a^2*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 17640*a*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 30492*b^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 4032*a^7*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 28749*a^6*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 48132*a^5*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 157374*a^4*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 88200*a^3*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 218421*a^2*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 44100*a*b^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 91476*b^7*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 6720*a^7*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 56035*a^6*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 60480*a^5*b^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 272370*a^4*b^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 114800*a^3*b^4*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 368235*a^2*b^5*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 58800*a*b^6*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 152460*b^7*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 56035*a^6*b*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 36540*a^5*b^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 272370*a^4*b^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 81200*a^3*b^4*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 368235*a^2*b^5*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 44100*a*b^6*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 152460*b^7*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 28749*a^6*b*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 10080*a^5*b^2*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 157374*a^4*b^3*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 29400*a^3*b^4*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 218421*a^2*b^5*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 17640*a*b^6*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 91476*b^7*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 8463*a^6*b*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 1260*a^5*b^2*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 49098*a^4*b^3*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 4200*a^3*b^4*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 71127*a^2*b^5*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 2940*a*b^6*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 30492*b^7*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 1089*a^6*b*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 - 6534*a^4*b^3*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 + 9801*a^2*b^5*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 - 4356*b^7*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7)/(a^9*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^7))/d","B",0
210,1,1102,0,0.368025," ","integrate(sin(d*x+c)^5/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(a^{5} b - a^{4} b^{2} - 4 \, a^{3} b^{3} + 4 \, a^{2} b^{4} + 3 \, a b^{5} - 3 \, b^{6}\right)} \log\left({\left| a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{8} - a^{7} b} - \frac{60 \, {\left(a^{4} b - 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{7}} - \frac{60 \, {\left(a^{5} b - 5 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 4 \, a b^{5} + 3 \, b^{6} + \frac{a^{5} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{a^{4} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{4 \, a^{3} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{4 \, a^{2} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{3 \, a b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{3 \, b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{{\left(a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)} a^{7}} + \frac{32 \, a^{5} - 137 \, a^{4} b - 300 \, a^{3} b^{2} + 548 \, a^{2} b^{3} + 300 \, a b^{4} - 411 \, b^{5} - \frac{160 \, a^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{805 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{1320 \, a^{3} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2980 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{1200 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2055 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{320 \, a^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1970 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1920 \, a^{3} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6200 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1800 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4110 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1970 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1080 \, a^{3} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{6200 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{1200 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{4110 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{805 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{180 \, a^{3} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{2980 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{300 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{2055 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{137 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{548 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{411 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{7} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{5}}}{30 \, d}"," ",0,"1/30*(60*(a^5*b - a^4*b^2 - 4*a^3*b^3 + 4*a^2*b^4 + 3*a*b^5 - 3*b^6)*log(abs(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^8 - a^7*b) - 60*(a^4*b - 4*a^2*b^3 + 3*b^5)*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^7 - 60*(a^5*b - 5*a^3*b^3 - 3*a^2*b^4 + 4*a*b^5 + 3*b^6 + a^5*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - a^4*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 4*a^3*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 4*a^2*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 3*a*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 3*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*a^7) + (32*a^5 - 137*a^4*b - 300*a^3*b^2 + 548*a^2*b^3 + 300*a*b^4 - 411*b^5 - 160*a^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 805*a^4*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1320*a^3*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2980*a^2*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1200*a*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2055*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 320*a^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 1970*a^4*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 1920*a^3*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 6200*a^2*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 1800*a*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 4110*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 1970*a^4*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 1080*a^3*b^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 6200*a^2*b^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 1200*a*b^4*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 4110*b^5*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 805*a^4*b*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 180*a^3*b^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 2980*a^2*b^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 300*a*b^4*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 2055*b^5*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 137*a^4*b*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 548*a^2*b^3*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 411*b^5*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5)/(a^7*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^5))/d","B",0
211,1,139,0,0.257940," ","integrate(sin(d*x+c)^3/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(a^{2} b - 2 \, b^{3}\right)} \log\left({\left| -a \cos\left(d x + c\right) - b \right|}\right)}{a^{5} d} + \frac{a^{2} b^{2} - b^{4}}{{\left(a \cos\left(d x + c\right) + b\right)} a^{5} d} + \frac{a^{4} d^{5} \cos\left(d x + c\right)^{3} - 3 \, a^{3} b d^{5} \cos\left(d x + c\right)^{2} - 3 \, a^{4} d^{5} \cos\left(d x + c\right) + 9 \, a^{2} b^{2} d^{5} \cos\left(d x + c\right)}{3 \, a^{6} d^{6}}"," ",0,"2*(a^2*b - 2*b^3)*log(abs(-a*cos(d*x + c) - b))/(a^5*d) + (a^2*b^2 - b^4)/((a*cos(d*x + c) + b)*a^5*d) + 1/3*(a^4*d^5*cos(d*x + c)^3 - 3*a^3*b*d^5*cos(d*x + c)^2 - 3*a^4*d^5*cos(d*x + c) + 9*a^2*b^2*d^5*cos(d*x + c))/(a^6*d^6)","A",0
212,1,61,0,0.247626," ","integrate(sin(d*x+c)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\cos\left(d x + c\right)}{a^{2} d} + \frac{2 \, b \log\left({\left| -a \cos\left(d x + c\right) - b \right|}\right)}{a^{3} d} + \frac{b^{2}}{{\left(a \cos\left(d x + c\right) + b\right)} a^{3} d}"," ",0,"-cos(d*x + c)/(a^2*d) + 2*b*log(abs(-a*cos(d*x + c) - b))/(a^3*d) + b^2/((a*cos(d*x + c) + b)*a^3*d)","A",0
213,1,213,0,0.268308," ","integrate(csc(d*x+c)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, a b \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} + \frac{\log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{4 \, {\left(a b + b^{2} + \frac{a b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{{\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} {\left(a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}}{2 \, d}"," ",0,"1/2*(4*a*b*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^4 - 2*a^2*b^2 + b^4) + log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a^2 + 2*a*b + b^2) - 4*(a*b + b^2 + a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((a^3 + a^2*b - a*b^2 - b^3)*(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))))/d","B",0
214,1,456,0,0.322799," ","integrate(csc(d*x+c)^3/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a - b\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{16 \, {\left(a^{3} b + a b^{3}\right)} \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} + \frac{a^{3} - a^{2} b - a b^{2} + b^{3} - \frac{8 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{8 \, a b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{3 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{3 \, a b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}} - \frac{\cos\left(d x + c\right) - 1}{{\left(a^{2} - 2 \, a b + b^{2}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}}{8 \, d}"," ",0,"1/8*(2*(a - b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 16*(a^3*b + a*b^3)*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) + (a^3 - a^2*b - a*b^2 + b^3 - 8*a^2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 8*a*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 3*a^2*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 3*a*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((a^4 - 2*a^2*b^2 + b^4)*(a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)) - (cos(d*x + c) - 1)/((a^2 - 2*a*b + b^2)*(cos(d*x + c) + 1)))/d","B",0
215,1,710,0,0.445508," ","integrate(csc(d*x+c)^5/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(3 \, a^{2} - 4 \, a b - b^{2}\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{128 \, {\left(a^{5} b + 2 \, a^{3} b^{3}\right)} \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} - \frac{\frac{8 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{8 \, a b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} - \frac{{\left(a^{2} + 2 \, a b + b^{2} - \frac{8 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{8 \, a b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{18 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{24 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} {\left(\cos\left(d x + c\right) - 1\right)}^{2}} - \frac{128 \, {\left(a^{6} b + a^{4} b^{3} + 2 \, a^{3} b^{4} + \frac{a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}}{64 \, d}"," ",0,"1/64*(4*(3*a^2 - 4*a*b - b^2)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + 128*(a^5*b + 2*a^3*b^3)*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) - (8*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 8*a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 2*a*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) - (a^2 + 2*a*b + b^2 - 8*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 8*a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 18*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 24*a*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 6*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)^2/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*(cos(d*x + c) - 1)^2) - 128*(a^6*b + a^4*b^3 + 2*a^3*b^4 + a^6*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - a^5*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*a^4*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*a^3*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))))/d","B",0
216,1,870,0,0.369900," ","integrate(sin(d*x+c)^6/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(5 \, a^{6} - 90 \, a^{4} b^{2} + 200 \, a^{2} b^{4} - 112 \, b^{6}\right)} {\left(d x + c\right)}}{a^{8}} - \frac{480 \, {\left(2 \, a^{6} b - 11 \, a^{4} b^{3} + 16 \, a^{2} b^{5} - 7 \, b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{8}} - \frac{480 \, {\left(a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)} a^{7}} + \frac{2 \, {\left(75 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 480 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 630 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1920 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 600 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1440 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 425 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3040 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2610 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 10880 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1800 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 7200 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 990 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 8256 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1980 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 23040 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1200 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 14400 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 990 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 8256 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1980 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 23040 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1200 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 14400 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 425 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3040 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2610 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10880 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1800 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7200 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 75 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 630 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1920 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 600 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1440 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} a^{7}}}{240 \, d}"," ",0,"1/240*(15*(5*a^6 - 90*a^4*b^2 + 200*a^2*b^4 - 112*b^6)*(d*x + c)/a^8 - 480*(2*a^6*b - 11*a^4*b^3 + 16*a^2*b^5 - 7*b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^8) - 480*(a^4*b^2*tan(1/2*d*x + 1/2*c) - 2*a^2*b^4*tan(1/2*d*x + 1/2*c) + b^6*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)*a^7) + 2*(75*a^5*tan(1/2*d*x + 1/2*c)^11 + 480*a^4*b*tan(1/2*d*x + 1/2*c)^11 - 630*a^3*b^2*tan(1/2*d*x + 1/2*c)^11 - 1920*a^2*b^3*tan(1/2*d*x + 1/2*c)^11 + 600*a*b^4*tan(1/2*d*x + 1/2*c)^11 + 1440*b^5*tan(1/2*d*x + 1/2*c)^11 + 425*a^5*tan(1/2*d*x + 1/2*c)^9 + 3040*a^4*b*tan(1/2*d*x + 1/2*c)^9 - 2610*a^3*b^2*tan(1/2*d*x + 1/2*c)^9 - 10880*a^2*b^3*tan(1/2*d*x + 1/2*c)^9 + 1800*a*b^4*tan(1/2*d*x + 1/2*c)^9 + 7200*b^5*tan(1/2*d*x + 1/2*c)^9 + 990*a^5*tan(1/2*d*x + 1/2*c)^7 + 8256*a^4*b*tan(1/2*d*x + 1/2*c)^7 - 1980*a^3*b^2*tan(1/2*d*x + 1/2*c)^7 - 23040*a^2*b^3*tan(1/2*d*x + 1/2*c)^7 + 1200*a*b^4*tan(1/2*d*x + 1/2*c)^7 + 14400*b^5*tan(1/2*d*x + 1/2*c)^7 - 990*a^5*tan(1/2*d*x + 1/2*c)^5 + 8256*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 1980*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 23040*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 1200*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 14400*b^5*tan(1/2*d*x + 1/2*c)^5 - 425*a^5*tan(1/2*d*x + 1/2*c)^3 + 3040*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 2610*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 10880*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 1800*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 7200*b^5*tan(1/2*d*x + 1/2*c)^3 - 75*a^5*tan(1/2*d*x + 1/2*c) + 480*a^4*b*tan(1/2*d*x + 1/2*c) + 630*a^3*b^2*tan(1/2*d*x + 1/2*c) - 1920*a^2*b^3*tan(1/2*d*x + 1/2*c) - 600*a*b^4*tan(1/2*d*x + 1/2*c) + 1440*b^5*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*a^7))/d","A",0
217,1,482,0,0.887337," ","integrate(sin(d*x+c)^4/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(3 \, a^{4} - 36 \, a^{2} b^{2} + 40 \, b^{4}\right)} {\left(d x + c\right)}}{a^{6}} - \frac{48 \, {\left(2 \, a^{4} b - 7 \, a^{2} b^{3} + 5 \, b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{6}} - \frac{48 \, {\left(a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)} a^{5}} + \frac{2 \, {\left(9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 48 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 208 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 288 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 33 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 208 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 288 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{5}}}{24 \, d}"," ",0,"1/24*(3*(3*a^4 - 36*a^2*b^2 + 40*b^4)*(d*x + c)/a^6 - 48*(2*a^4*b - 7*a^2*b^3 + 5*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^6) - 48*(a^2*b^2*tan(1/2*d*x + 1/2*c) - b^4*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)*a^5) + 2*(9*a^3*tan(1/2*d*x + 1/2*c)^7 + 48*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 36*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 96*b^3*tan(1/2*d*x + 1/2*c)^7 + 33*a^3*tan(1/2*d*x + 1/2*c)^5 + 208*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 36*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 288*b^3*tan(1/2*d*x + 1/2*c)^5 - 33*a^3*tan(1/2*d*x + 1/2*c)^3 + 208*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 36*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 288*b^3*tan(1/2*d*x + 1/2*c)^3 - 9*a^3*tan(1/2*d*x + 1/2*c) + 48*a^2*b*tan(1/2*d*x + 1/2*c) + 36*a*b^2*tan(1/2*d*x + 1/2*c) - 96*b^3*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^5))/d","A",0
218,1,240,0,0.257463," ","integrate(sin(d*x+c)^2/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)} a^{3}} - \frac{{\left(a^{2} - 6 \, b^{2}\right)} {\left(d x + c\right)}}{a^{4}} + \frac{4 \, {\left(2 \, a^{2} b - 3 \, b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{4}} - \frac{2 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}}}{2 \, d}"," ",0,"-1/2*(4*b^2*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)*a^3) - (a^2 - 6*b^2)*(d*x + c)/a^4 + 4*(2*a^2*b - 3*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^4) - 2*(a*tan(1/2*d*x + 1/2*c)^3 + 4*b*tan(1/2*d*x + 1/2*c)^3 - a*tan(1/2*d*x + 1/2*c) + 4*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3))/d","A",0
219,1,289,0,0.507705," ","integrate(csc(d*x+c)^2/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(2 \, a^{2} b + b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{3} + a^{2} b + a b^{2} - b^{3}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}}{2 \, d}"," ",0,"1/2*(4*(2*a^2*b + b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)) + tan(1/2*d*x + 1/2*c)/(a^2 - 2*a*b + b^2) - (a^3*tan(1/2*d*x + 1/2*c)^2 - 3*a^2*b*tan(1/2*d*x + 1/2*c)^2 + 7*a*b^2*tan(1/2*d*x + 1/2*c)^2 - b^3*tan(1/2*d*x + 1/2*c)^2 - a^3 + a^2*b + a*b^2 - b^3)/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^3 - b*tan(1/2*d*x + 1/2*c)^3 - a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))))/d","A",0
220,1,457,0,0.360124," ","integrate(csc(d*x+c)^4/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{48 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}} - \frac{48 \, {\left(2 \, a^{4} b + 3 \, a^{2} b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6} - 6 \, a^{5} b + 15 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 15 \, a^{2} b^{4} - 6 \, a b^{5} + b^{6}} + \frac{9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"-1/24*(48*a^3*b^2*tan(1/2*d*x + 1/2*c)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) - 48*(2*a^4*b + 3*a^2*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) - (a^4*tan(1/2*d*x + 1/2*c)^3 - 4*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 6*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*a*b^3*tan(1/2*d*x + 1/2*c)^3 + b^4*tan(1/2*d*x + 1/2*c)^3 + 9*a^4*tan(1/2*d*x + 1/2*c) - 24*a^3*b*tan(1/2*d*x + 1/2*c) + 18*a^2*b^2*tan(1/2*d*x + 1/2*c) - 3*b^4*tan(1/2*d*x + 1/2*c))/(a^6 - 6*a^5*b + 15*a^4*b^2 - 20*a^3*b^3 + 15*a^2*b^4 - 6*a*b^5 + b^6) + (9*a*tan(1/2*d*x + 1/2*c)^2 - 3*b*tan(1/2*d*x + 1/2*c)^2 + a + b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*tan(1/2*d*x + 1/2*c)^3))/d","A",0
221,1,2150,0,2.601776," ","integrate(sin(d*x+c)^7/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{420 \, {\left(a^{7} b - a^{6} b^{2} - 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 21 \, a^{3} b^{5} - 21 \, a^{2} b^{6} - 12 \, a b^{7} + 12 \, b^{8}\right)} \log\left({\left| a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{11} - a^{10} b} - \frac{420 \, {\left(a^{6} b - 10 \, a^{4} b^{3} + 21 \, a^{2} b^{5} - 12 \, b^{7}\right)} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{10}} - \frac{70 \, {\left(9 \, a^{8} b + 6 \, a^{7} b^{2} - 105 \, a^{6} b^{3} - 148 \, a^{5} b^{4} + 187 \, a^{4} b^{5} + 390 \, a^{3} b^{6} + 17 \, a^{2} b^{7} - 248 \, a b^{8} - 108 \, b^{9} + \frac{18 \, a^{8} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{12 \, a^{7} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{202 \, a^{6} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{56 \, a^{5} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{566 \, a^{4} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{76 \, a^{3} b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{598 \, a^{2} b^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{32 \, a b^{8} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{216 \, b^{9} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{9 \, a^{8} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{18 \, a^{7} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{81 \, a^{6} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{180 \, a^{5} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{99 \, a^{4} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{378 \, a^{3} b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{81 \, a^{2} b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{216 \, a b^{8} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{108 \, b^{9} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{{\left(a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}^{2} a^{10}} + \frac{128 \, a^{7} - 1089 \, a^{6} b - 3696 \, a^{5} b^{2} + 10890 \, a^{4} b^{3} + 11200 \, a^{3} b^{4} - 22869 \, a^{2} b^{5} - 7840 \, a b^{6} + 13068 \, b^{7} - \frac{896 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{8463 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{24192 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{81830 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{70000 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{165963 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{47040 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{91476 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2688 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{28749 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{64176 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{262290 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{176400 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{509649 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{117600 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{274428 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4480 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{56035 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{80640 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{453950 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{229600 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{859215 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{156800 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{457380 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{56035 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{48720 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{453950 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{162400 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{859215 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{117600 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{457380 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{28749 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{13440 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{262290 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{58800 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{509649 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{47040 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{274428 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{8463 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{1680 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{81830 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{8400 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{165963 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{7840 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{91476 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{1089 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{10890 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{22869 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{13068 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{10} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{7}}}{140 \, d}"," ",0,"1/140*(420*(a^7*b - a^6*b^2 - 10*a^5*b^3 + 10*a^4*b^4 + 21*a^3*b^5 - 21*a^2*b^6 - 12*a*b^7 + 12*b^8)*log(abs(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^11 - a^10*b) - 420*(a^6*b - 10*a^4*b^3 + 21*a^2*b^5 - 12*b^7)*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^10 - 70*(9*a^8*b + 6*a^7*b^2 - 105*a^6*b^3 - 148*a^5*b^4 + 187*a^4*b^5 + 390*a^3*b^6 + 17*a^2*b^7 - 248*a*b^8 - 108*b^9 + 18*a^8*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 12*a^7*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 202*a^6*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 56*a^5*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 566*a^4*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 76*a^3*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 598*a^2*b^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 32*a*b^8*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 216*b^9*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 9*a^8*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 18*a^7*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 81*a^6*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 180*a^5*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 99*a^4*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 378*a^3*b^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 81*a^2*b^7*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 216*a*b^8*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 108*b^9*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))^2*a^10) + (128*a^7 - 1089*a^6*b - 3696*a^5*b^2 + 10890*a^4*b^3 + 11200*a^3*b^4 - 22869*a^2*b^5 - 7840*a*b^6 + 13068*b^7 - 896*a^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 8463*a^6*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 24192*a^5*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 81830*a^4*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 70000*a^3*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 165963*a^2*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 47040*a*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 91476*b^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2688*a^7*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 28749*a^6*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 64176*a^5*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 262290*a^4*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 176400*a^3*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 509649*a^2*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 117600*a*b^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 274428*b^7*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 4480*a^7*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 56035*a^6*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 80640*a^5*b^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 453950*a^4*b^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 229600*a^3*b^4*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 859215*a^2*b^5*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 156800*a*b^6*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 457380*b^7*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 56035*a^6*b*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 48720*a^5*b^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 453950*a^4*b^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 162400*a^3*b^4*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 859215*a^2*b^5*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 117600*a*b^6*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 457380*b^7*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 28749*a^6*b*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 13440*a^5*b^2*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 262290*a^4*b^3*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 58800*a^3*b^4*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 509649*a^2*b^5*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 47040*a*b^6*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 274428*b^7*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 8463*a^6*b*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 1680*a^5*b^2*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 81830*a^4*b^3*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 8400*a^3*b^4*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 165963*a^2*b^5*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 7840*a*b^6*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 91476*b^7*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 1089*a^6*b*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 - 10890*a^4*b^3*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 + 22869*a^2*b^5*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 - 13068*b^7*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7)/(a^10*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^7))/d","B",0
222,1,1337,0,0.445347," ","integrate(sin(d*x+c)^5/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(3 \, a^{5} b - 3 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 20 \, a^{2} b^{4} + 21 \, a b^{5} - 21 \, b^{6}\right)} \log\left({\left| a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{9} - a^{8} b} - \frac{60 \, {\left(3 \, a^{4} b - 20 \, a^{2} b^{3} + 21 \, b^{5}\right)} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{8}} - \frac{30 \, {\left(9 \, a^{6} b + 6 \, a^{5} b^{2} - 75 \, a^{4} b^{3} - 108 \, a^{3} b^{4} + 51 \, a^{2} b^{5} + 150 \, a b^{6} + 63 \, b^{7} + \frac{18 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{12 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{142 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{36 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{250 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{24 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{126 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{9 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{18 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{51 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{120 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{126 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{63 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{{\left(a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}^{2} a^{8}} + \frac{64 \, a^{5} - 411 \, a^{4} b - 1200 \, a^{3} b^{2} + 2740 \, a^{2} b^{3} + 1800 \, a b^{4} - 2877 \, b^{5} - \frac{320 \, a^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2415 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{5280 \, a^{3} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{14900 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{7200 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{14385 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{640 \, a^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{5910 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{7680 \, a^{3} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{31000 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10800 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{28770 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{5910 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{4320 \, a^{3} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{31000 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{7200 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{28770 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{2415 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{720 \, a^{3} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{14900 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1800 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{14385 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{411 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{2740 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2877 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{8} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{5}}}{60 \, d}"," ",0,"1/60*(60*(3*a^5*b - 3*a^4*b^2 - 20*a^3*b^3 + 20*a^2*b^4 + 21*a*b^5 - 21*b^6)*log(abs(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^9 - a^8*b) - 60*(3*a^4*b - 20*a^2*b^3 + 21*b^5)*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^8 - 30*(9*a^6*b + 6*a^5*b^2 - 75*a^4*b^3 - 108*a^3*b^4 + 51*a^2*b^5 + 150*a*b^6 + 63*b^7 + 18*a^6*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 12*a^5*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 142*a^4*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 36*a^3*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 250*a^2*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 24*a*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 126*b^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 9*a^6*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 18*a^5*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 51*a^4*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 120*a^3*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 3*a^2*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 126*a*b^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 63*b^7*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))^2*a^8) + (64*a^5 - 411*a^4*b - 1200*a^3*b^2 + 2740*a^2*b^3 + 1800*a*b^4 - 2877*b^5 - 320*a^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2415*a^4*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 5280*a^3*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 14900*a^2*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 7200*a*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 14385*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 640*a^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 5910*a^4*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 7680*a^3*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 31000*a^2*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 10800*a*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 28770*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 5910*a^4*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 4320*a^3*b^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 31000*a^2*b^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 7200*a*b^4*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 28770*b^5*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 2415*a^4*b*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 720*a^3*b^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 14900*a^2*b^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 1800*a*b^4*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 14385*b^5*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 411*a^4*b*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 2740*a^2*b^3*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 2877*b^5*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5)/(a^8*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^5))/d","B",0
223,1,170,0,0.504997," ","integrate(sin(d*x+c)^3/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{{\left(3 \, a^{2} b - 10 \, b^{3}\right)} \log\left({\left| -a \cos\left(d x + c\right) - b \right|}\right)}{a^{6} d} + \frac{5 \, a^{2} b^{3} - 9 \, b^{5} + \frac{2 \, {\left(3 \, a^{3} b^{2} d - 5 \, a b^{4} d\right)} \cos\left(d x + c\right)}{d}}{2 \, {\left(a \cos\left(d x + c\right) + b\right)}^{2} a^{6} d} + \frac{2 \, a^{6} d^{8} \cos\left(d x + c\right)^{3} - 9 \, a^{5} b d^{8} \cos\left(d x + c\right)^{2} - 6 \, a^{6} d^{8} \cos\left(d x + c\right) + 36 \, a^{4} b^{2} d^{8} \cos\left(d x + c\right)}{6 \, a^{9} d^{9}}"," ",0,"(3*a^2*b - 10*b^3)*log(abs(-a*cos(d*x + c) - b))/(a^6*d) + 1/2*(5*a^2*b^3 - 9*b^5 + 2*(3*a^3*b^2*d - 5*a*b^4*d)*cos(d*x + c)/d)/((a*cos(d*x + c) + b)^2*a^6*d) + 1/6*(2*a^6*d^8*cos(d*x + c)^3 - 9*a^5*b*d^8*cos(d*x + c)^2 - 6*a^6*d^8*cos(d*x + c) + 36*a^4*b^2*d^8*cos(d*x + c))/(a^9*d^9)","A",0
224,1,77,0,0.347358," ","integrate(sin(d*x+c)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\cos\left(d x + c\right)}{a^{3} d} + \frac{3 \, b \log\left({\left| -a \cos\left(d x + c\right) - b \right|}\right)}{a^{4} d} + \frac{6 \, a b^{2} \cos\left(d x + c\right) + 5 \, b^{3}}{2 \, {\left(a \cos\left(d x + c\right) + b\right)}^{2} a^{4} d}"," ",0,"-cos(d*x + c)/(a^3*d) + 3*b*log(abs(-a*cos(d*x + c) - b))/(a^4*d) + 1/2*(6*a*b^2*cos(d*x + c) + 5*b^3)/((a*cos(d*x + c) + b)^2*a^4*d)","A",0
225,1,452,0,1.508377," ","integrate(csc(d*x+c)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(3 \, a^{2} b + b^{3}\right)} \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} + \frac{\log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{9 \, a^{3} b + 15 \, a^{2} b^{2} + 3 \, a b^{3} - 3 \, b^{4} + \frac{18 \, a^{3} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{6 \, a^{2} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{10 \, a b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2 \, b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{9 \, a^{3} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{9 \, a^{2} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{3 \, b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{{\left(a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} {\left(a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(3*a^2*b + b^3)*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) + log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - (9*a^3*b + 15*a^2*b^2 + 3*a*b^3 - 3*b^4 + 18*a^3*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 6*a^2*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 10*a*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 9*a^3*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 9*a^2*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 3*a*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 3*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5)*(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))^2))/d","B",0
226,1,800,0,2.648238," ","integrate(csc(d*x+c)^3/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a - 2 \, b\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{8 \, {\left(3 \, a^{4} b + 8 \, a^{2} b^{3} + b^{5}\right)} \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} + \frac{{\left(a + b - \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{4 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} {\left(\cos\left(d x + c\right) - 1\right)}} - \frac{\cos\left(d x + c\right) - 1}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{4 \, {\left(9 \, a^{6} b + 6 \, a^{5} b^{2} + 9 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 11 \, a^{2} b^{5} - 2 \, a b^{6} + 3 \, b^{7} + \frac{18 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{12 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{26 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{4 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{38 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{8 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{6 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{9 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{18 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{33 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{48 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{27 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}^{2}}}{8 \, d}"," ",0,"1/8*(2*(a - 2*b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + 8*(3*a^4*b + 8*a^2*b^3 + b^5)*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) + (a + b - 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 4*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*(cos(d*x + c) + 1)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*(cos(d*x + c) - 1)) - (cos(d*x + c) - 1)/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(cos(d*x + c) + 1)) - 4*(9*a^6*b + 6*a^5*b^2 + 9*a^4*b^3 + 28*a^3*b^4 + 11*a^2*b^5 - 2*a*b^6 + 3*b^7 + 18*a^6*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 12*a^5*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 26*a^4*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 4*a^3*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 38*a^2*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 8*a*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 6*b^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 9*a^6*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 18*a^5*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 33*a^4*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 48*a^3*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 27*a^2*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 6*a*b^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 3*b^7*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))^2))/d","B",0
227,1,1551,0,0.542819," ","integrate(csc(d*x+c)^5/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{12 \, {\left(a^{2} - 3 \, a b\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}} + \frac{192 \, {\left(a^{6} b + 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{10} - 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} - 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}} - \frac{\frac{8 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{12 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{4 \, b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{3 \, a b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a^{6} - 6 \, a^{5} b + 15 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 15 \, a^{2} b^{4} - 6 \, a b^{5} + b^{6}} - \frac{a^{8} - 2 \, a^{7} b - 2 \, a^{6} b^{2} + 6 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + 2 \, a^{2} b^{6} + 2 \, a b^{7} - b^{8} - \frac{6 \, a^{8} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{20 \, a^{7} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{12 \, a^{6} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{28 \, a^{5} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{40 \, a^{4} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{4 \, a^{3} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{20 \, a^{2} b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{12 \, a b^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, b^{8} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{6 \, a^{8} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{163 \, a^{7} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{257 \, a^{6} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{339 \, a^{5} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{203 \, a^{4} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{223 \, a^{3} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{309 \, a^{2} b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{23 \, a b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{7 \, b^{8} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{8} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{186 \, a^{7} b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{274 \, a^{6} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{890 \, a^{5} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{894 \, a^{4} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{478 \, a^{3} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{374 \, a^{2} b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{18 \, a b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{4 \, b^{8} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{9 \, a^{8} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{45 \, a^{7} b {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{45 \, a^{6} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{63 \, a^{5} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{117 \, a^{4} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{9 \, a^{3} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{63 \, a^{2} b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{27 \, a b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{{\left(a^{9} - a^{8} b - 4 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 6 \, a^{4} b^{5} - 4 \, a^{3} b^{6} + 4 \, a^{2} b^{7} + a b^{8} - b^{9}\right)} {\left(\frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}^{2}}}{64 \, d}"," ",0,"1/64*(12*(a^2 - 3*a*b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5) + 192*(a^6*b + 5*a^4*b^3 + 2*a^2*b^5)*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^10 - 5*a^8*b^2 + 10*a^6*b^4 - 10*a^4*b^6 + 5*a^2*b^8 - b^10) - (8*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 12*a^2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 4*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 3*a^2*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 3*a*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/(a^6 - 6*a^5*b + 15*a^4*b^2 - 20*a^3*b^3 + 15*a^2*b^4 - 6*a*b^5 + b^6) - (a^8 - 2*a^7*b - 2*a^6*b^2 + 6*a^5*b^3 - 6*a^3*b^5 + 2*a^2*b^6 + 2*a*b^7 - b^8 - 6*a^8*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 20*a^7*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 12*a^6*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 28*a^5*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 40*a^4*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 4*a^3*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 20*a^2*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 12*a*b^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*b^8*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 6*a^8*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 163*a^7*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 257*a^6*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 339*a^5*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 203*a^4*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 223*a^3*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 309*a^2*b^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 23*a*b^7*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 7*b^8*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 10*a^8*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 186*a^7*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 274*a^6*b^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 890*a^5*b^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 894*a^4*b^4*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 478*a^3*b^5*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 374*a^2*b^6*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 18*a*b^7*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 4*b^8*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 9*a^8*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 45*a^7*b*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 45*a^6*b^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 63*a^5*b^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 117*a^4*b^4*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 9*a^3*b^5*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 63*a^2*b^6*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 27*a*b^7*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4)/((a^9 - a^8*b - 4*a^7*b^2 + 4*a^6*b^3 + 6*a^5*b^4 - 6*a^4*b^5 - 4*a^3*b^6 + 4*a^2*b^7 + a*b^8 - b^9)*(a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)^2))/d","B",0
228,1,1030,0,0.809566," ","integrate(sin(d*x+c)^6/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(5 \, a^{6} - 180 \, a^{4} b^{2} + 600 \, a^{2} b^{4} - 448 \, b^{6}\right)} {\left(d x + c\right)}}{a^{9}} - \frac{240 \, {\left(6 \, a^{6} b - 53 \, a^{4} b^{3} + 103 \, a^{2} b^{5} - 56 \, b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{9}} - \frac{240 \, {\left(6 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 19 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 14 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 14 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2} a^{8}} + \frac{2 \, {\left(75 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 720 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1260 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 4800 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1800 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 5040 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 425 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4560 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 5220 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 27200 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 5400 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 25200 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 990 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12384 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3960 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 57600 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3600 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 50400 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 990 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12384 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3960 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 57600 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3600 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 50400 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 425 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4560 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5220 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 27200 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5400 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 25200 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 75 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1260 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4800 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1800 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5040 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} a^{8}}}{240 \, d}"," ",0,"1/240*(15*(5*a^6 - 180*a^4*b^2 + 600*a^2*b^4 - 448*b^6)*(d*x + c)/a^9 - 240*(6*a^6*b - 53*a^4*b^3 + 103*a^2*b^5 - 56*b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^9) - 240*(6*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 21*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 19*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 15*a*b^6*tan(1/2*d*x + 1/2*c)^3 - 14*b^7*tan(1/2*d*x + 1/2*c)^3 - 6*a^5*b^2*tan(1/2*d*x + 1/2*c) - 5*a^4*b^3*tan(1/2*d*x + 1/2*c) + 21*a^3*b^4*tan(1/2*d*x + 1/2*c) + 19*a^2*b^5*tan(1/2*d*x + 1/2*c) - 15*a*b^6*tan(1/2*d*x + 1/2*c) - 14*b^7*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2*a^8) + 2*(75*a^5*tan(1/2*d*x + 1/2*c)^11 + 720*a^4*b*tan(1/2*d*x + 1/2*c)^11 - 1260*a^3*b^2*tan(1/2*d*x + 1/2*c)^11 - 4800*a^2*b^3*tan(1/2*d*x + 1/2*c)^11 + 1800*a*b^4*tan(1/2*d*x + 1/2*c)^11 + 5040*b^5*tan(1/2*d*x + 1/2*c)^11 + 425*a^5*tan(1/2*d*x + 1/2*c)^9 + 4560*a^4*b*tan(1/2*d*x + 1/2*c)^9 - 5220*a^3*b^2*tan(1/2*d*x + 1/2*c)^9 - 27200*a^2*b^3*tan(1/2*d*x + 1/2*c)^9 + 5400*a*b^4*tan(1/2*d*x + 1/2*c)^9 + 25200*b^5*tan(1/2*d*x + 1/2*c)^9 + 990*a^5*tan(1/2*d*x + 1/2*c)^7 + 12384*a^4*b*tan(1/2*d*x + 1/2*c)^7 - 3960*a^3*b^2*tan(1/2*d*x + 1/2*c)^7 - 57600*a^2*b^3*tan(1/2*d*x + 1/2*c)^7 + 3600*a*b^4*tan(1/2*d*x + 1/2*c)^7 + 50400*b^5*tan(1/2*d*x + 1/2*c)^7 - 990*a^5*tan(1/2*d*x + 1/2*c)^5 + 12384*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 3960*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 57600*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 3600*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 50400*b^5*tan(1/2*d*x + 1/2*c)^5 - 425*a^5*tan(1/2*d*x + 1/2*c)^3 + 4560*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 5220*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 27200*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 5400*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 25200*b^5*tan(1/2*d*x + 1/2*c)^3 - 75*a^5*tan(1/2*d*x + 1/2*c) + 720*a^4*b*tan(1/2*d*x + 1/2*c) + 1260*a^3*b^2*tan(1/2*d*x + 1/2*c) - 4800*a^2*b^3*tan(1/2*d*x + 1/2*c) - 1800*a*b^4*tan(1/2*d*x + 1/2*c) + 5040*b^5*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*a^8))/d","B",0
229,1,584,0,3.101095," ","integrate(sin(d*x+c)^4/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(a^{4} - 24 \, a^{2} b^{2} + 40 \, b^{4}\right)} {\left(d x + c\right)}}{a^{7}} - \frac{24 \, {\left(2 \, a^{4} b - 11 \, a^{2} b^{3} + 10 \, b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{7}} - \frac{8 \, {\left(6 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 11 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2} a^{6}} + \frac{2 \, {\left(3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 80 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 11 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 104 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 240 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 11 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 104 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 80 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{6}}}{8 \, d}"," ",0,"1/8*(3*(a^4 - 24*a^2*b^2 + 40*b^4)*(d*x + c)/a^7 - 24*(2*a^4*b - 11*a^2*b^3 + 10*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^7) - 8*(6*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 11*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 10*b^5*tan(1/2*d*x + 1/2*c)^3 - 6*a^3*b^2*tan(1/2*d*x + 1/2*c) - 5*a^2*b^3*tan(1/2*d*x + 1/2*c) + 11*a*b^4*tan(1/2*d*x + 1/2*c) + 10*b^5*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2*a^6) + 2*(3*a^3*tan(1/2*d*x + 1/2*c)^7 + 24*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 24*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 80*b^3*tan(1/2*d*x + 1/2*c)^7 + 11*a^3*tan(1/2*d*x + 1/2*c)^5 + 104*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 24*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 240*b^3*tan(1/2*d*x + 1/2*c)^5 - 11*a^3*tan(1/2*d*x + 1/2*c)^3 + 104*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 24*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 240*b^3*tan(1/2*d*x + 1/2*c)^3 - 3*a^3*tan(1/2*d*x + 1/2*c) + 24*a^2*b*tan(1/2*d*x + 1/2*c) + 24*a*b^2*tan(1/2*d*x + 1/2*c) - 80*b^3*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^6))/d","A",0
230,1,1193,0,0.646731," ","integrate(sin(d*x+c)^2/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(a^{11} - 7 \, a^{10} b - 14 \, a^{9} b^{2} + 39 \, a^{8} b^{3} + 25 \, a^{7} b^{4} - 56 \, a^{6} b^{5} - 12 \, a^{5} b^{6} + 24 \, a^{4} b^{7} - a^{4} {\left| -a^{7} + a^{5} b^{2} \right|} - 5 \, a^{3} b {\left| -a^{7} + a^{5} b^{2} \right|} + 13 \, a^{2} b^{2} {\left| -a^{7} + a^{5} b^{2} \right|} + 6 \, a b^{3} {\left| -a^{7} + a^{5} b^{2} \right|} - 12 \, b^{4} {\left| -a^{7} + a^{5} b^{2} \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a^{6} b - a^{4} b^{3} + \sqrt{{\left(a^{7} + a^{6} b - a^{5} b^{2} - a^{4} b^{3}\right)} {\left(a^{7} - a^{6} b - a^{5} b^{2} + a^{4} b^{3}\right)} + {\left(a^{6} b - a^{4} b^{3}\right)}^{2}}}{a^{7} - a^{6} b - a^{5} b^{2} + a^{4} b^{3}}}}\right)\right)}}{a^{6} b {\left| -a^{7} + a^{5} b^{2} \right|} - a^{4} b^{3} {\left| -a^{7} + a^{5} b^{2} \right|} + {\left(a^{7} - a^{5} b^{2}\right)}^{2}} + \frac{{\left({\left(a^{4} + 5 \, a^{3} b - 13 \, a^{2} b^{2} - 6 \, a b^{3} + 12 \, b^{4}\right)} \sqrt{-a^{2} + b^{2}} {\left| -a^{7} + a^{5} b^{2} \right|} {\left| -a + b \right|} + {\left(a^{11} - 7 \, a^{10} b - 14 \, a^{9} b^{2} + 39 \, a^{8} b^{3} + 25 \, a^{7} b^{4} - 56 \, a^{6} b^{5} - 12 \, a^{5} b^{6} + 24 \, a^{4} b^{7}\right)} \sqrt{-a^{2} + b^{2}} {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a^{6} b - a^{4} b^{3} - \sqrt{{\left(a^{7} + a^{6} b - a^{5} b^{2} - a^{4} b^{3}\right)} {\left(a^{7} - a^{6} b - a^{5} b^{2} + a^{4} b^{3}\right)} + {\left(a^{6} b - a^{4} b^{3}\right)}^{2}}}{a^{7} - a^{6} b - a^{5} b^{2} + a^{4} b^{3}}}}\right)\right)}}{{\left(a^{7} - a^{5} b^{2}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} - {\left(a^{8} b - 2 \, a^{7} b^{2} + 2 \, a^{5} b^{4} - a^{4} b^{5}\right)} {\left| -a^{7} + a^{5} b^{2} \right|}} + \frac{2 \, {\left(a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 7 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 18 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 14 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 37 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 14 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 37 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 18 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{2 \, d}"," ",0,"1/2*((a^11 - 7*a^10*b - 14*a^9*b^2 + 39*a^8*b^3 + 25*a^7*b^4 - 56*a^6*b^5 - 12*a^5*b^6 + 24*a^4*b^7 - a^4*abs(-a^7 + a^5*b^2) - 5*a^3*b*abs(-a^7 + a^5*b^2) + 13*a^2*b^2*abs(-a^7 + a^5*b^2) + 6*a*b^3*abs(-a^7 + a^5*b^2) - 12*b^4*abs(-a^7 + a^5*b^2))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^6*b - a^4*b^3 + sqrt((a^7 + a^6*b - a^5*b^2 - a^4*b^3)*(a^7 - a^6*b - a^5*b^2 + a^4*b^3) + (a^6*b - a^4*b^3)^2))/(a^7 - a^6*b - a^5*b^2 + a^4*b^3))))/(a^6*b*abs(-a^7 + a^5*b^2) - a^4*b^3*abs(-a^7 + a^5*b^2) + (a^7 - a^5*b^2)^2) + ((a^4 + 5*a^3*b - 13*a^2*b^2 - 6*a*b^3 + 12*b^4)*sqrt(-a^2 + b^2)*abs(-a^7 + a^5*b^2)*abs(-a + b) + (a^11 - 7*a^10*b - 14*a^9*b^2 + 39*a^8*b^3 + 25*a^7*b^4 - 56*a^6*b^5 - 12*a^5*b^6 + 24*a^4*b^7)*sqrt(-a^2 + b^2)*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^6*b - a^4*b^3 - sqrt((a^7 + a^6*b - a^5*b^2 - a^4*b^3)*(a^7 - a^6*b - a^5*b^2 + a^4*b^3) + (a^6*b - a^4*b^3)^2))/(a^7 - a^6*b - a^5*b^2 + a^4*b^3))))/((a^7 - a^5*b^2)^2*(a^2 - 2*a*b + b^2) - (a^8*b - 2*a^7*b^2 + 2*a^5*b^4 - a^4*b^5)*abs(-a^7 + a^5*b^2)) + 2*(a^5*tan(1/2*d*x + 1/2*c)^7 + 4*a^4*b*tan(1/2*d*x + 1/2*c)^7 - 18*a^3*b^2*tan(1/2*d*x + 1/2*c)^7 + 7*a^2*b^3*tan(1/2*d*x + 1/2*c)^7 + 18*a*b^4*tan(1/2*d*x + 1/2*c)^7 - 12*b^5*tan(1/2*d*x + 1/2*c)^7 - 3*a^5*tan(1/2*d*x + 1/2*c)^5 - 4*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 14*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 37*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 18*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 36*b^5*tan(1/2*d*x + 1/2*c)^5 + 3*a^5*tan(1/2*d*x + 1/2*c)^3 - 4*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 14*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 37*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 18*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 36*b^5*tan(1/2*d*x + 1/2*c)^3 - a^5*tan(1/2*d*x + 1/2*c) + 4*a^4*b*tan(1/2*d*x + 1/2*c) + 18*a^3*b^2*tan(1/2*d*x + 1/2*c) + 7*a^2*b^3*tan(1/2*d*x + 1/2*c) - 18*a*b^4*tan(1/2*d*x + 1/2*c) - 12*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - a^4*b^2)*(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
231,1,386,0,3.770799," ","integrate(csc(d*x+c)^2/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(2 \, a^{3} b + 3 \, a b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{2 \, {\left(6 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}} - \frac{1}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"1/2*(6*(2*a^3*b + 3*a*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) + tan(1/2*d*x + 1/2*c)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - 2*(6*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + a*b^4*tan(1/2*d*x + 1/2*c)^3 - 2*b^5*tan(1/2*d*x + 1/2*c)^3 - 6*a^3*b^2*tan(1/2*d*x + 1/2*c) - 5*a^2*b^3*tan(1/2*d*x + 1/2*c) - a*b^4*tan(1/2*d*x + 1/2*c) - 2*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2) - 1/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*tan(1/2*d*x + 1/2*c)))/d","A",0
232,1,709,0,0.500907," ","integrate(csc(d*x+c)^4/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{24 \, {\left(6 \, a^{5} b + 23 \, a^{3} b^{3} + 6 \, a b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 20 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 45 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{9} - 9 \, a^{8} b + 36 \, a^{7} b^{2} - 84 \, a^{6} b^{3} + 126 \, a^{5} b^{4} - 126 \, a^{4} b^{5} + 84 \, a^{3} b^{6} - 36 \, a^{2} b^{7} + 9 \, a b^{8} - b^{9}} - \frac{24 \, {\left(6 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}} - \frac{9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(24*(6*a^5*b + 23*a^3*b^3 + 6*a*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*sqrt(-a^2 + b^2)) + (a^6*tan(1/2*d*x + 1/2*c)^3 - 6*a^5*b*tan(1/2*d*x + 1/2*c)^3 + 15*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - 20*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 15*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 6*a*b^5*tan(1/2*d*x + 1/2*c)^3 + b^6*tan(1/2*d*x + 1/2*c)^3 + 9*a^6*tan(1/2*d*x + 1/2*c) - 36*a^5*b*tan(1/2*d*x + 1/2*c) + 45*a^4*b^2*tan(1/2*d*x + 1/2*c) - 45*a^2*b^4*tan(1/2*d*x + 1/2*c) + 36*a*b^5*tan(1/2*d*x + 1/2*c) - 9*b^6*tan(1/2*d*x + 1/2*c))/(a^9 - 9*a^8*b + 36*a^7*b^2 - 84*a^6*b^3 + 126*a^5*b^4 - 126*a^4*b^5 + 84*a^3*b^6 - 36*a^2*b^7 + 9*a*b^8 - b^9) - 24*(6*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 + 5*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 - 6*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 - 6*a^5*b^2*tan(1/2*d*x + 1/2*c) - 5*a^4*b^3*tan(1/2*d*x + 1/2*c) - 5*a^3*b^4*tan(1/2*d*x + 1/2*c) - 6*a^2*b^5*tan(1/2*d*x + 1/2*c))/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2) - (9*a*tan(1/2*d*x + 1/2*c)^2 - 9*b*tan(1/2*d*x + 1/2*c)^2 + a + b)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*tan(1/2*d*x + 1/2*c)^3))/d","A",0
233,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(7/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{7}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(7/2)/(b*sec(d*x + c) + a), x)","F",0
234,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(5/2)/(b*sec(d*x + c) + a), x)","F",0
235,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(3/2)/(b*sec(d*x + c) + a), x)","F",0
236,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sqrt{e \sin\left(d x + c\right)}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*sin(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
237,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{e \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*sqrt(e*sin(d*x + c))), x)","F",0
238,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*(e*sin(d*x + c))^(3/2)), x)","F",0
239,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*(e*sin(d*x + c))^(5/2)), x)","F",0
240,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*(e*sin(d*x + c))^(7/2)), x)","F",0
241,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(9/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(5/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
244,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(3/2)/(b*sec(d*x + c) + a)^2, x)","F",0
245,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sqrt{e \sin\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(e*sin(d*x + c))/(b*sec(d*x + c) + a)^2, x)","F",0
246,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^2/(e*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{e \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^2*sqrt(e*sin(d*x + c))), x)","F",0
247,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^2/(e*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^2*(e*sin(d*x + c))^(3/2)), x)","F",0
248,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^2/(e*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^2*(e*sin(d*x + c))^(5/2)), x)","F",0
249,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a), x)","F",0
250,0,0,0,0.000000," ","integrate(csc(f*x+e)^2*(a+b*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(f x + e\right) + a} \csc\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a)*csc(f*x + e)^2, x)","F",0
251,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(3/2), x)","F",0
252,0,0,0,0.000000," ","integrate(csc(f*x+e)^2*(a+b*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \csc\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(3/2)*csc(f*x + e)^2, x)","F",0
253,0,0,0,0.000000," ","integrate(1/(a+b*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*sec(f*x + e) + a), x)","F",0
254,0,0,0,0.000000," ","integrate(csc(f*x+e)^2/(a+b*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\csc\left(f x + e\right)^{2}}{\sqrt{b \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(csc(f*x + e)^2/sqrt(b*sec(f*x + e) + a), x)","F",0
255,0,0,0,0.000000," ","integrate(1/(a+b*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(-3/2), x)","F",0
256,0,0,0,0.000000," ","integrate(csc(f*x+e)^2/(a+b*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\csc\left(f x + e\right)^{2}}{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(f*x + e)^2/(b*sec(f*x + e) + a)^(3/2), x)","F",0
257,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(e*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{3} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3*(e*sin(d*x + c))^m, x)","F",0
258,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(e*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{2} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2*(e*sin(d*x + c))^m, x)","F",0
259,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(e*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)*(e*sin(d*x + c))^m, x)","F",0
260,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/(b*sec(d*x + c) + a), x)","F",0
261,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/(b*sec(d*x + c) + a)^2, x)","F",0
262,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/(b*sec(d*x + c) + a)^3, x)","F",0
263,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(e*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*(e*sin(d*x + c))^m, x)","F",0
264,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*(e*sin(d*x + c))^m, x)","F",0
265,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/sqrt(b*sec(d*x + c) + a), x)","F",0
266,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/(b*sec(d*x + c) + a)^(3/2), x)","F",0
267,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*(e*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*(e*sin(d*x + c))^m, x)","F",0
268,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^5,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*sin(d*x + c)^5, x)","F",0
269,-2,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Evaluation time: 1.34sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
270,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*sin(d*x + c), x)","F",0
271,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+b*sec(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*csc(d*x + c), x)","F",0
272,0,0,0,0.000000," ","integrate(csc(d*x+c)^3*(a+b*sec(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*csc(d*x + c)^3, x)","F",0
273,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^4,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*sin(d*x + c)^4, x)","F",0
274,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^2,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*sin(d*x + c)^2, x)","F",0
275,0,0,0,0.000000," ","integrate(csc(d*x+c)^2*(a+b*sec(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*csc(d*x + c)^2, x)","F",0
276,0,0,0,0.000000," ","integrate(csc(d*x+c)^4*(a+b*sec(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*csc(d*x + c)^4, x)","F",0
277,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*sin(d*x + c)^(3/2), x)","F",0
278,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \sqrt{\sin\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*sqrt(sin(d*x + c)), x)","F",0
279,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n/sin(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{n}}{\sqrt{\sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n/sqrt(sin(d*x + c)), x)","F",0
280,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n/sin(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{n}}{\sin\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n/sin(d*x + c)^(3/2), x)","F",0
281,0,0,0,0.000000," ","integrate((e*csc(d*x+c))^(5/2)*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \left(e \csc\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sec\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*csc(d*x + c))^(5/2)*(a*sec(d*x + c) + a), x)","F",0
282,0,0,0,0.000000," ","integrate((e*csc(d*x+c))^(3/2)*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \left(e \csc\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sec\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*csc(d*x + c))^(3/2)*(a*sec(d*x + c) + a), x)","F",0
283,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(e*csc(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{e \csc\left(d x + c\right)} {\left(a \sec\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(e*csc(d*x + c))*(a*sec(d*x + c) + a), x)","F",0
284,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*csc(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\sqrt{e \csc\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/sqrt(e*csc(d*x + c)), x)","F",0
285,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*csc(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\left(e \csc\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/(e*csc(d*x + c))^(3/2), x)","F",0
286,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*csc(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\left(e \csc\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/(e*csc(d*x + c))^(5/2), x)","F",0
287,0,0,0,0.000000," ","integrate((e*csc(d*x+c))^(5/2)*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \left(e \csc\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sec\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((e*csc(d*x + c))^(5/2)*(a*sec(d*x + c) + a)^2, x)","F",0
288,0,0,0,0.000000," ","integrate((e*csc(d*x+c))^(3/2)*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \left(e \csc\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sec\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((e*csc(d*x + c))^(3/2)*(a*sec(d*x + c) + a)^2, x)","F",0
289,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(e*csc(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{e \csc\left(d x + c\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(e*csc(d*x + c))*(a*sec(d*x + c) + a)^2, x)","F",0
290,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{e \csc\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/sqrt(e*csc(d*x + c)), x)","F",0
291,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\left(e \csc\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/(e*csc(d*x + c))^(3/2), x)","F",0
292,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\left(e \csc\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/(e*csc(d*x + c))^(5/2), x)","F",0
293,0,0,0,0.000000," ","integrate((e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \csc\left(d x + c\right)\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*csc(d*x + c))^(5/2)/(a*sec(d*x + c) + a), x)","F",0
294,0,0,0,0.000000," ","integrate((e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \csc\left(d x + c\right)\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*csc(d*x + c))^(3/2)/(a*sec(d*x + c) + a), x)","F",0
295,0,0,0,0.000000," ","integrate((e*csc(d*x+c))^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sqrt{e \csc\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*csc(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
296,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))/(e*csc(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \csc\left(d x + c\right)} {\left(a \sec\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(e*csc(d*x + c))*(a*sec(d*x + c) + a)), x)","F",0
297,0,0,0,0.000000," ","integrate(1/(e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{\left(e \csc\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sec\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*csc(d*x + c))^(3/2)*(a*sec(d*x + c) + a)), x)","F",0
298,0,0,0,0.000000," ","integrate(1/(e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{\left(e \csc\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sec\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*csc(d*x + c))^(5/2)*(a*sec(d*x + c) + a)), x)","F",0
299,0,0,0,0.000000," ","integrate(1/(e*csc(d*x+c))^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{\left(e \csc\left(d x + c\right)\right)^{\frac{7}{2}} {\left(a \sec\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*csc(d*x + c))^(7/2)*(a*sec(d*x + c) + a)), x)","F",0
300,0,0,0,0.000000," ","integrate((e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \csc\left(d x + c\right)\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*csc(d*x + c))^(5/2)/(a*sec(d*x + c) + a)^2, x)","F",0
301,0,0,0,0.000000," ","integrate((e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \csc\left(d x + c\right)\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*csc(d*x + c))^(3/2)/(a*sec(d*x + c) + a)^2, x)","F",0
302,0,0,0,0.000000," ","integrate((e*csc(d*x+c))^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sqrt{e \csc\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(e*csc(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
303,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \csc\left(d x + c\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(e*csc(d*x + c))*(a*sec(d*x + c) + a)^2), x)","F",0
304,0,0,0,0.000000," ","integrate(1/(e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \csc\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*csc(d*x + c))^(3/2)*(a*sec(d*x + c) + a)^2), x)","F",0
305,0,0,0,0.000000," ","integrate(1/(e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \csc\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*csc(d*x + c))^(5/2)*(a*sec(d*x + c) + a)^2), x)","F",0
306,0,0,0,0.000000," ","integrate(1/(e*csc(d*x+c))^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \csc\left(d x + c\right)\right)^{\frac{7}{2}} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*csc(d*x + c))^(7/2)*(a*sec(d*x + c) + a)^2), x)","F",0
