1,1,293,0,24.071548," ","integrate((a+a*sec(d*x+c))*tan(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
2,1,247,0,7.977154," ","integrate((a+a*sec(d*x+c))*tan(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
3,1,201,0,3.087761," ","integrate((a+a*sec(d*x+c))*tan(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
4,1,155,0,0.955349," ","integrate((a+a*sec(d*x+c))*tan(d*x+c)^3,x, algorithm=""giac"")","-\frac{6 \, a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 6 \, a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{19 \, a + \frac{69 \, a {\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{11 \, a {\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} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(6*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 6*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (19*a + 69*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 45*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 11*a*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^3)/d","B",0
5,1,106,0,0.499269," ","integrate((a+a*sec(d*x+c))*tan(d*x+c),x, algorithm=""giac"")","\frac{a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 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) + \frac{3 \, a + \frac{a {\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}}{d}"," ",0,"(a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (3*a + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/d","B",0
6,1,58,0,0.201411," ","integrate(cot(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","B",0
7,1,103,0,0.246234," ","integrate(cot(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","B",0
8,1,149,0,0.301404," ","integrate(cot(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
9,1,197,0,0.421526," ","integrate(cot(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
10,1,174,0,12.223713," ","integrate((a+a*sec(d*x+c))*tan(d*x+c)^8,x, algorithm=""giac"")","\frac{13440 \, {\left(d x + c\right)} a + 3675 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3675 \, 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*(13440*(d*x + c)*a + 3675*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3675*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
11,1,146,0,8.792157," ","integrate((a+a*sec(d*x+c))*tan(d*x+c)^6,x, algorithm=""giac"")","-\frac{240 \, {\left(d x + c\right)} a + 75 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 75 \, 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*(240*(d*x + c)*a + 75*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 75*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
12,1,118,0,1.542596," ","integrate((a+a*sec(d*x+c))*tan(d*x+c)^4,x, algorithm=""giac"")","\frac{24 \, {\left(d x + c\right)} a + 9 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 9 \, 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*(24*(d*x + c)*a + 9*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 9*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
13,1,88,0,0.901792," ","integrate((a+a*sec(d*x+c))*tan(d*x+c)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(d x + c\right)} a + 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{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*(2*(d*x + c)*a + a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 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","B",0
14,1,26,0,0.230544," ","integrate(cot(d*x+c)^2*(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} a + \frac{a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{d}"," ",0,"-((d*x + c)*a + a/tan(1/2*d*x + 1/2*c))/d","A",0
15,1,56,0,0.516030," ","integrate(cot(d*x+c)^4*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{12 \, {\left(d x + c\right)} a - 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*(d*x + c)*a - 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
16,1,83,0,0.305223," ","integrate(cot(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 \, {\left(d x + c\right)} a - 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*(d*x + c)*a - 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
17,1,113,0,0.345426," ","integrate(cot(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 \, {\left(d x + c\right)} a + 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*(d*x + c)*a + 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
18,1,140,0,0.506569," ","integrate(cot(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 \, {\left(d x + c\right)} a - 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*(d*x + c)*a - 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
19,1,342,0,25.567830," ","integrate((a+a*sec(d*x+c))^2*tan(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{11477 \, a^{2} + \frac{119810 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{566865 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1605720 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3031770 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{2995020 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2171610 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{1114200 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{382545 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{78850 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{7381 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{10}}}{2520 \, d}"," ",0,"1/2520*(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)) + (11477*a^2 + 119810*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 566865*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 1605720*a^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 3031770*a^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 2995020*a^2*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 2171610*a^2*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 1114200*a^2*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 + 382545*a^2*(cos(d*x + c) - 1)^8/(cos(d*x + c) + 1)^8 + 78850*a^2*(cos(d*x + c) - 1)^9/(cos(d*x + c) + 1)^9 + 7381*a^2*(cos(d*x + c) - 1)^10/(cos(d*x + c) + 1)^10)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^10)/d","A",0
20,1,292,0,10.996037," ","integrate((a+a*sec(d*x+c))^2*tan(d*x+c)^7,x, algorithm=""giac"")","-\frac{840 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 840 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{3819 \, a^{2} + \frac{32232 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{120372 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{261464 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{258370 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{175448 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{77364 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{19944 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{2283 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{8}}}{840 \, d}"," ",0,"-1/840*(840*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 840*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (3819*a^2 + 32232*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 120372*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 261464*a^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 258370*a^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 175448*a^2*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 77364*a^2*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 19944*a^2*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 + 2283*a^2*(cos(d*x + c) - 1)^8/(cos(d*x + c) + 1)^8)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^8)/d","B",0
21,1,242,0,3.346874," ","integrate((a+a*sec(d*x+c))^2*tan(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{275 \, a^{2} + \frac{1770 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{4845 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{4780 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2925 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1002 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{147 \, a^{2} {\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)}^{6}}}{60 \, d}"," ",0,"1/60*(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)) + (275*a^2 + 1770*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 4845*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 4780*a^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 2925*a^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 1002*a^2*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 147*a^2*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^6)/d","B",0
22,1,192,0,1.427072," ","integrate((a+a*sec(d*x+c))^2*tan(d*x+c)^3,x, algorithm=""giac"")","-\frac{12 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 12 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{57 \, a^{2} + \frac{252 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{246 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{124 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{25 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{4}}}{12 \, d}"," ",0,"-1/12*(12*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 12*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (57*a^2 + 252*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 246*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 124*a^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 25*a^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^4)/d","B",0
23,1,142,0,0.394095," ","integrate((a+a*sec(d*x+c))^2*tan(d*x+c),x, algorithm=""giac"")","\frac{2 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 2 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{11 \, a^{2} + \frac{10 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{2} {\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*(2*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 2*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (11*a^2 + 10*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 3*a^2*(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
24,1,64,0,0.256865," ","integrate(cot(d*x+c)*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, 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{{\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1 \right|}\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)^2/(cos(d*x + c) + 1)^2 - 1)))/d","A",0
25,1,111,0,0.443647," ","integrate(cot(d*x+c)^3*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, a^{2} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 2 \, 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{2 \, a^{2} {\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}}{2 \, d}"," ",0,"-1/2*(2*a^2*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 2*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - (a^2 + 2*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*(cos(d*x + c) + 1)/(cos(d*x + c) - 1))/d","B",0
26,1,138,0,0.559826," ","integrate(cot(d*x+c)^5*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{14 \, a^{2} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 16 \, 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{8 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{21 \, 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}}}{16 \, d}"," ",0,"1/16*(14*a^2*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 16*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - (a^2 + 8*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 21*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)/d","A",0
27,1,186,0,0.423561," ","integrate(cot(d*x+c)^7*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{78 \, a^{2} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 96 \, 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{9 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{48 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{143 \, 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}}}{96 \, d}"," ",0,"-1/96*(78*a^2*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 96*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 + 9*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 48*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 143*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)/d","A",0
28,1,238,0,1.376654," ","integrate(cot(d*x+c)^9*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{1188 \, a^{2} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 1536 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - \frac{96 \, 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{32 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{174 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{768 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2475 \, 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}}}{1536 \, d}"," ",0,"1/1536*(1188*a^2*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 1536*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 96*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 + 32*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 174*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 768*a^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 2475*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)/d","A",0
29,1,180,0,6.009844," ","integrate((a+a*sec(d*x+c))^2*tan(d*x+c)^6,x, algorithm=""giac"")","-\frac{840 \, {\left(d x + c\right)} a^{2} + 525 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 525 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(315 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 2660 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 9863 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 21216 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 29673 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9660 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1365 \, 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)}^{7}}}{840 \, d}"," ",0,"-1/840*(840*(d*x + c)*a^2 + 525*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 525*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(315*a^2*tan(1/2*d*x + 1/2*c)^13 - 2660*a^2*tan(1/2*d*x + 1/2*c)^11 + 9863*a^2*tan(1/2*d*x + 1/2*c)^9 - 21216*a^2*tan(1/2*d*x + 1/2*c)^7 + 29673*a^2*tan(1/2*d*x + 1/2*c)^5 - 9660*a^2*tan(1/2*d*x + 1/2*c)^3 + 1365*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^7)/d","A",0
30,1,148,0,1.815794," ","integrate((a+a*sec(d*x+c))^2*tan(d*x+c)^4,x, algorithm=""giac"")","\frac{60 \, {\left(d x + c\right)} a^{2} + 45 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 45 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 110 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 328 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 530 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{60 \, d}"," ",0,"1/60*(60*(d*x + c)*a^2 + 45*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 45*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*a^2*tan(1/2*d*x + 1/2*c)^9 - 110*a^2*tan(1/2*d*x + 1/2*c)^7 + 328*a^2*tan(1/2*d*x + 1/2*c)^5 - 530*a^2*tan(1/2*d*x + 1/2*c)^3 + 105*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
31,1,99,0,2.329361," ","integrate((a+a*sec(d*x+c))^2*tan(d*x+c)^2,x, algorithm=""giac"")","-\frac{3 \, {\left(d x + c\right)} a^{2} + 3 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{4 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(d*x + c)*a^2 + 3*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 4*(a^2*tan(1/2*d*x + 1/2*c)^3 - 3*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
32,1,31,0,0.248413," ","integrate(cot(d*x+c)^2*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} a^{2} + \frac{2 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{d}"," ",0,"-((d*x + c)*a^2 + 2*a^2/tan(1/2*d*x + 1/2*c))/d","A",0
33,1,50,0,0.433855," ","integrate(cot(d*x+c)^4*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{6 \, {\left(d x + c\right)} a^{2} + \frac{9 \, 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*(6*(d*x + c)*a^2 + (9*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
34,1,80,0,0.348357," ","integrate(cot(d*x+c)^6*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{120 \, {\left(d x + c\right)} a^{2} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{165 \, a^{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} + 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{120 \, d}"," ",0,"-1/120*(120*(d*x + c)*a^2 - 15*a^2*tan(1/2*d*x + 1/2*c) + (165*a^2*tan(1/2*d*x + 1/2*c)^4 - 25*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
35,1,112,0,0.391565," ","integrate(cot(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} + 3360 \, {\left(d x + c\right)} a^{2} - 735 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{4410 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 770 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 147 \, 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 + 3360*(d*x + c)*a^2 - 735*a^2*tan(1/2*d*x + 1/2*c) + (4410*a^2*tan(1/2*d*x + 1/2*c)^6 - 770*a^2*tan(1/2*d*x + 1/2*c)^4 + 147*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
36,1,145,0,0.434298," ","integrate(cot(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} - 945 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40320 \, {\left(d x + c\right)} a^{2} + 11655 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{51345 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 9765 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 2331 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 405 \, 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 - 945*a^2*tan(1/2*d*x + 1/2*c)^3 - 40320*(d*x + c)*a^2 + 11655*a^2*tan(1/2*d*x + 1/2*c) - (51345*a^2*tan(1/2*d*x + 1/2*c)^8 - 9765*a^2*tan(1/2*d*x + 1/2*c)^6 + 2331*a^2*tan(1/2*d*x + 1/2*c)^4 - 405*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
37,1,367,0,19.683882," ","integrate((a+a*sec(d*x+c))^3*tan(d*x+c)^9,x, algorithm=""giac"")","\frac{27720 \, a^{3} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 27720 \, a^{3} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{153343 \, a^{3} + \frac{1742213 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{9043705 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{28369275 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{59954070 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{67458930 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{57997170 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{36975510 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{16879995 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{5213945 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{976261 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{83711 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{11}}}{27720 \, d}"," ",0,"1/27720*(27720*a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 27720*a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (153343*a^3 + 1742213*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 9043705*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 28369275*a^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 59954070*a^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 67458930*a^3*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 57997170*a^3*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 36975510*a^3*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 + 16879995*a^3*(cos(d*x + c) - 1)^8/(cos(d*x + c) + 1)^8 + 5213945*a^3*(cos(d*x + c) - 1)^9/(cos(d*x + c) + 1)^9 + 976261*a^3*(cos(d*x + c) - 1)^10/(cos(d*x + c) + 1)^10 + 83711*a^3*(cos(d*x + c) - 1)^11/(cos(d*x + c) + 1)^11)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^11)/d","A",0
38,1,317,0,28.274715," ","integrate((a+a*sec(d*x+c))^3*tan(d*x+c)^7,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{14297 \, a^{3} + \frac{133713 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{560052 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1384068 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1594782 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1336734 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{781956 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{302004 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{69201 \, 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)) + (14297*a^3 + 133713*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 560052*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 1384068*a^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 1594782*a^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 1336734*a^3*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 781956*a^3*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 302004*a^3*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 + 69201*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
39,1,267,0,3.999843," ","integrate((a+a*sec(d*x+c))^3*tan(d*x+c)^5,x, algorithm=""giac"")","\frac{420 \, a^{3} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 420 \, a^{3} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{2497 \, a^{3} + \frac{18319 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{58317 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{69475 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{56035 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{28749 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{8463 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{1089 \, a^{3} {\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^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 420*a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (2497*a^3 + 18319*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 58317*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 69475*a^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 56035*a^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 28749*a^3*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 8463*a^3*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 1089*a^3*(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
40,1,217,0,1.521106," ","integrate((a+a*sec(d*x+c))^3*tan(d*x+c)^3,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{393 \, a^{3} + \frac{2085 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2610 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1970 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{805 \, 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)) + (393*a^3 + 2085*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2610*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 1970*a^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 805*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
41,1,167,0,0.505393," ","integrate((a+a*sec(d*x+c))^3*tan(d*x+c),x, algorithm=""giac"")","\frac{6 \, a^{3} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 6 \, a^{3} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{51 \, a^{3} + \frac{69 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{45 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{11 \, 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} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 6*a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (51*a^3 + 69*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 45*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 11*a^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^3)/d","B",0
42,1,145,0,0.318346," ","integrate(cot(d*x+c)*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{4 \, a^{3} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - a^{3} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 3 \, a^{3} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{5 \, a^{3} + \frac{3 \, a^{3} {\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}}{d}"," ",0,"(4*a^3*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 3*a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (5*a^3 + 3*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/d","B",0
43,1,109,0,0.365719," ","integrate(cot(d*x+c)^3*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{a^{3} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 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(a^{3} + \frac{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}}{d}"," ",0,"-(a^3*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - (a^3 + a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*(cos(d*x + c) + 1)/(cos(d*x + c) - 1))/d","B",0
44,1,138,0,1.011724," ","integrate(cot(d*x+c)^5*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{8 \, a^{3} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 8 \, 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(a^{3} + \frac{6 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{12 \, a^{3} {\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}}}{8 \, d}"," ",0,"1/8*(8*a^3*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 8*a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - (a^3 + 6*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 12*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)^2/(cos(d*x + c) - 1)^2)/d","B",0
45,1,165,0,1.482783," ","integrate(cot(d*x+c)^7*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{90 \, a^{3} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 96 \, 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{15 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{66 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{165 \, 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}}}{96 \, d}"," ",0,"-1/96*(90*a^3*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 96*a^3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - (2*a^3 + 15*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 66*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 165*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)/d","A",0
46,1,213,0,0.507383," ","integrate(cot(d*x+c)^9*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{684 \, a^{3} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right) - 768 \, 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{28 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{132 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{504 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1425 \, 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}}}{768 \, d}"," ",0,"1/768*(684*a^3*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 768*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 + 28*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 132*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 504*a^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 1425*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)/d","A",0
47,1,196,0,5.201387," ","integrate((a+a*sec(d*x+c))^3*tan(d*x+c)^6,x, algorithm=""giac"")","-\frac{13440 \, {\left(d x + c\right)} a^{3} + 13125 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 13125 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(315 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} - 11375 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 79723 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 269879 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 550089 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 749973 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 212625 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 26565 \, 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*(13440*(d*x + c)*a^3 + 13125*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 13125*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(315*a^3*tan(1/2*d*x + 1/2*c)^15 - 11375*a^3*tan(1/2*d*x + 1/2*c)^13 + 79723*a^3*tan(1/2*d*x + 1/2*c)^11 - 269879*a^3*tan(1/2*d*x + 1/2*c)^9 + 550089*a^3*tan(1/2*d*x + 1/2*c)^7 - 749973*a^3*tan(1/2*d*x + 1/2*c)^5 + 212625*a^3*tan(1/2*d*x + 1/2*c)^3 - 26565*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^8)/d","A",0
48,1,164,0,2.587595," ","integrate((a+a*sec(d*x+c))^3*tan(d*x+c)^4,x, algorithm=""giac"")","\frac{240 \, {\left(d x + c\right)} a^{3} + 285 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 285 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(45 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 95 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 366 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1746 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3135 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 525 \, 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*(240*(d*x + c)*a^3 + 285*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 285*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(45*a^3*tan(1/2*d*x + 1/2*c)^11 - 95*a^3*tan(1/2*d*x + 1/2*c)^9 - 366*a^3*tan(1/2*d*x + 1/2*c)^7 + 1746*a^3*tan(1/2*d*x + 1/2*c)^5 - 3135*a^3*tan(1/2*d*x + 1/2*c)^3 + 525*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","A",0
49,1,132,0,1.044937," ","integrate((a+a*sec(d*x+c))^3*tan(d*x+c)^2,x, algorithm=""giac"")","-\frac{8 \, {\left(d x + c\right)} a^{3} + 13 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 13 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 13 \, a^{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} + 21 \, 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*(8*(d*x + c)*a^3 + 13*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 13*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(5*a^3*tan(1/2*d*x + 1/2*c)^7 - 13*a^3*tan(1/2*d*x + 1/2*c)^5 + 3*a^3*tan(1/2*d*x + 1/2*c)^3 + 21*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
50,1,66,0,0.333456," ","integrate(cot(d*x+c)^2*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} a^{3} - a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{4 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{d}"," ",0,"-((d*x + c)*a^3 - a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 4*a^3/tan(1/2*d*x + 1/2*c))/d","A",0
51,1,50,0,0.318581," ","integrate(cot(d*x+c)^4*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} a^{3} + \frac{6 \, 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)^{3}}}{3 \, d}"," ",0,"1/3*(3*(d*x + c)*a^3 + (6*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
52,1,66,0,0.364326," ","integrate(cot(d*x+c)^6*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{60 \, {\left(d x + c\right)} a^{3} + \frac{105 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 20 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(60*(d*x + c)*a^3 + (105*a^3*tan(1/2*d*x + 1/2*c)^4 - 20*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
53,1,96,0,0.499141," ","integrate(cot(d*x+c)^8*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{1680 \, {\left(d x + c\right)} a^{3} - 105 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{2730 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 560 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 126 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{1680 \, d}"," ",0,"1/1680*(1680*(d*x + c)*a^3 - 105*a^3*tan(1/2*d*x + 1/2*c) + (2730*a^3*tan(1/2*d*x + 1/2*c)^6 - 560*a^3*tan(1/2*d*x + 1/2*c)^4 + 126*a^3*tan(1/2*d*x + 1/2*c)^2 - 15*a^3)/tan(1/2*d*x + 1/2*c)^7)/d","A",0
54,1,128,0,0.534048," ","integrate(cot(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} + 20160 \, {\left(d x + c\right)} a^{3} - 2520 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{31185 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 6720 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1827 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 360 \, 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 + 20160*(d*x + c)*a^3 - 2520*a^3*tan(1/2*d*x + 1/2*c) + (31185*a^3*tan(1/2*d*x + 1/2*c)^8 - 6720*a^3*tan(1/2*d*x + 1/2*c)^6 + 1827*a^3*tan(1/2*d*x + 1/2*c)^4 - 360*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
55,1,161,0,0.652062," ","integrate(cot(d*x+c)^12*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{693 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 11550 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 887040 \, {\left(d x + c\right)} a^{3} + 159390 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{5 \, {\left(264726 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 59136 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 18018 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 4554 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 770 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 63 \, a^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11}}}{887040 \, d}"," ",0,"-1/887040*(693*a^3*tan(1/2*d*x + 1/2*c)^5 - 11550*a^3*tan(1/2*d*x + 1/2*c)^3 - 887040*(d*x + c)*a^3 + 159390*a^3*tan(1/2*d*x + 1/2*c) - 5*(264726*a^3*tan(1/2*d*x + 1/2*c)^10 - 59136*a^3*tan(1/2*d*x + 1/2*c)^8 + 18018*a^3*tan(1/2*d*x + 1/2*c)^6 - 4554*a^3*tan(1/2*d*x + 1/2*c)^4 + 770*a^3*tan(1/2*d*x + 1/2*c)^2 - 63*a^3)/tan(1/2*d*x + 1/2*c)^11)/d","A",0
56,1,245,0,17.819592," ","integrate(tan(d*x+c)^9/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{420 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a} - \frac{420 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right)}{a} + \frac{\frac{5775 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{20685 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{42595 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{56035 \, {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{28749 \, {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{8463 \, {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{1089 \, {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + 705}{a {\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*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a - 420*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/a + (5775*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 20685*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 42595*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 56035*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 28749*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 8463*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 1089*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 + 705)/(a*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^7))/d","A",0
57,1,201,0,6.785744," ","integrate(tan(d*x+c)^7/(a+a*sec(d*x+c)),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} - \frac{60 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right)}{a} + \frac{\frac{485 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{1330 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1970 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{805 \, {\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}} + 73}{a {\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*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a - 60*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/a + (485*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1330*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 1970*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 805*(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 + 73)/(a*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^5))/d","B",0
58,1,157,0,4.199682," ","integrate(tan(d*x+c)^5/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{6 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a} - \frac{6 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right)}{a} + \frac{\frac{21 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{45 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{11 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + 3}{a {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a - 6*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/a + (21*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 45*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 11*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 3)/(a*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^3))/d","B",0
59,1,111,0,1.121072," ","integrate(tan(d*x+c)^3/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{\log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a} - \frac{\log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right)}{a} + \frac{\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1}{a {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}}}{d}"," ",0,"-(log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a - log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/a + ((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)/(a*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)))/d","B",0
60,1,31,0,0.281586," ","integrate(tan(d*x+c)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a d}"," ",0,"log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/(a*d)","A",0
61,1,86,0,1.237750," ","integrate(cot(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{4 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 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 - 4*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a - (cos(d*x + c) - 1)/(a*(cos(d*x + c) + 1)))/d","A",0
62,1,157,0,0.252681," ","integrate(cot(d*x+c)^3/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(\frac{5 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\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{10 \, \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a} + \frac{32 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a} + \frac{\frac{10 \, 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*(5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)*(cos(d*x + c) + 1)/(a*(cos(d*x + c) - 1)) - 10*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/a + 32*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) + a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/a^2)/d","A",0
63,1,211,0,0.335467," ","integrate(cot(d*x+c)^5/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(\frac{14 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{66 \, {\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{132 \, \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a} + \frac{384 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a} + \frac{\frac{132 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{21 \, 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*(14*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 66*(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) - 132*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/a + 384*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a + (132*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 21*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
64,1,149,0,9.293513," ","integrate(tan(d*x+c)^8/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{240 \, {\left(d x + c\right)}}{a} - \frac{75 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} + \frac{75 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} + \frac{2 \, {\left(315 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1945 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 5118 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3138 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1095 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 165 \, \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*(240*(d*x + c)/a - 75*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a + 75*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a + 2*(315*tan(1/2*d*x + 1/2*c)^11 - 1945*tan(1/2*d*x + 1/2*c)^9 + 5118*tan(1/2*d*x + 1/2*c)^7 - 3138*tan(1/2*d*x + 1/2*c)^5 + 1095*tan(1/2*d*x + 1/2*c)^3 - 165*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^6*a))/d","A",0
65,1,123,0,4.101513," ","integrate(tan(d*x+c)^6/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{24 \, {\left(d x + c\right)}}{a} - \frac{9 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} + \frac{9 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} + \frac{2 \, {\left(33 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 137 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 71 \, \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)}^{4} a}}{24 \, d}"," ",0,"-1/24*(24*(d*x + c)/a - 9*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a + 9*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a + 2*(33*tan(1/2*d*x + 1/2*c)^7 - 137*tan(1/2*d*x + 1/2*c)^5 + 71*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)^4*a))/d","A",0
66,1,96,0,2.266525," ","integrate(tan(d*x+c)^4/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(d x + c\right)}}{a} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{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*(2*(d*x + c)/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 + 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","B",0
67,1,50,0,0.565327," ","integrate(tan(d*x+c)^2/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{d x + c}{a} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a}}{d}"," ",0,"-((d*x + c)/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)/d","B",0
68,1,66,0,0.240274," ","integrate(cot(d*x+c)^2/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(d x + c\right)}}{a} + \frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} + \frac{3}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{12 \, d}"," ",0,"-1/12*(12*(d*x + c)/a + (a^2*tan(1/2*d*x + 1/2*c)^3 - 12*a^2*tan(1/2*d*x + 1/2*c))/a^3 + 3/(a*tan(1/2*d*x + 1/2*c)))/d","A",0
69,1,98,0,0.669085," ","integrate(cot(d*x+c)^4/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{240 \, {\left(d x + c\right)}}{a} + \frac{5 \, {\left(18 \, \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 \, {\left(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} + 80 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{5}}}{240 \, d}"," ",0,"1/240*(240*(d*x + c)/a + 5*(18*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 + 80*a^4*tan(1/2*d*x + 1/2*c))/a^5)/d","A",0
70,1,127,0,0.394404," ","integrate(cot(d*x+c)^6/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{6720 \, {\left(d x + c\right)}}{a} + \frac{7 \, {\left(435 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 40 \, \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} - 168 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1015 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6720 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{7}}}{6720 \, d}"," ",0,"-1/6720*(6720*(d*x + c)/a + 7*(435*tan(1/2*d*x + 1/2*c)^4 - 40*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 - 168*a^6*tan(1/2*d*x + 1/2*c)^5 + 1015*a^6*tan(1/2*d*x + 1/2*c)^3 - 6720*a^6*tan(1/2*d*x + 1/2*c))/a^7)/d","A",0
71,1,223,0,26.200669," ","integrate(tan(d*x+c)^9/(a+a*sec(d*x+c))^2,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^{2}} - \frac{60 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right)}{a^{2}} + \frac{\frac{234 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{1005 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2220 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2925 \, {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1002 \, {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{147 \, {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + 19}{a^{2} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{6}}}{60 \, d}"," ",0,"1/60*(60*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^2 - 60*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/a^2 + (234*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1005*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 2220*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 2925*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 1002*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 147*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 19)/(a^2*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^6))/d","B",0
72,1,180,0,8.972011," ","integrate(tan(d*x+c)^7/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{2}} - \frac{12 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right)}{a^{2}} - \frac{\frac{4 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{54 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{124 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{25 \, {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 7}{a^{2} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{4}}}{12 \, d}"," ",0,"-1/12*(12*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^2 - 12*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/a^2 - (4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 54*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 124*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 25*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 7)/(a^2*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^4))/d","B",0
73,1,136,0,8.111562," ","integrate(tan(d*x+c)^5/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{2}} - \frac{2 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right)}{a^{2}} - \frac{\frac{6 \, {\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}} + 5}{a^{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*(2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^2 - 2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/a^2 - (6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 5)/(a^2*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^2))/d","B",0
74,1,33,0,0.982234," ","integrate(tan(d*x+c)^3/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\log\left({\left| \frac{{\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1 \right|}\right)}{a^{2} d}"," ",0,"-log(abs((cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 1))/(a^2*d)","A",0
75,1,57,0,0.466863," ","integrate(tan(d*x+c)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{2}} + \frac{\cos\left(d x + c\right) - 1}{a^{2} {\left(\cos\left(d x + c\right) + 1\right)}}}{2 \, d}"," ",0,"1/2*(2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^2 + (cos(d*x + c) - 1)/(a^2*(cos(d*x + c) + 1)))/d","A",0
76,1,117,0,0.256869," ","integrate(cot(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{16 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{2}} - \frac{\frac{8 \, 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 - 16*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^2 - (8*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
77,1,186,0,0.353202," ","integrate(cot(d*x+c)^3/(a+a*sec(d*x+c))^2,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} + 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}}{a^{2} {\left(\cos\left(d x + c\right) - 1\right)}} - \frac{18 \, \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{96 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{2}} + \frac{\frac{48 \, a^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{9 \, a^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \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*(6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)*(cos(d*x + c) + 1)/(a^2*(cos(d*x + c) - 1)) - 18*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/a^2 + 96*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^2 + (48*a^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 9*a^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + a^4*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3)/a^6)/d","A",0
78,1,236,0,0.412796," ","integrate(cot(d*x+c)^5/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(\frac{16 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{87 \, {\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{348 \, \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{1536 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{2}} + \frac{\frac{768 \, a^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{174 \, a^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{32 \, 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*(16*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 87*(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) - 348*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/a^2 + 1536*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^2 + (768*a^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 174*a^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 32*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
79,1,136,0,13.721793," ","integrate(tan(d*x+c)^8/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(d x + c\right)}}{a^{2}} - \frac{45 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} + \frac{45 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{2 \, {\left(105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 530 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 328 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 110 \, \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)}^{5} a^{2}}}{60 \, d}"," ",0,"1/60*(60*(d*x + c)/a^2 - 45*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 + 45*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 2*(105*tan(1/2*d*x + 1/2*c)^9 - 530*tan(1/2*d*x + 1/2*c)^7 + 328*tan(1/2*d*x + 1/2*c)^5 - 110*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)^5*a^2))/d","A",0
80,1,99,0,4.132292," ","integrate(tan(d*x+c)^6/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)}}{a^{2}} - \frac{3 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} + \frac{3 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{4 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - \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)^{2} - 1\right)}^{3} a^{2}}}{3 \, d}"," ",0,"-1/3*(3*(d*x + c)/a^2 - 3*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 + 3*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 4*(3*tan(1/2*d*x + 1/2*c)^5 - tan(1/2*d*x + 1/2*c)^3)/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^2))/d","A",0
81,1,79,0,2.655865," ","integrate(tan(d*x+c)^4/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{d x + c}{a^{2}} - \frac{2 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} + \frac{2 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} - \frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{2}}}{d}"," ",0,"((d*x + c)/a^2 - 2*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 + 2*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - 2*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^2))/d","B",0
82,1,29,0,2.819822," ","integrate(tan(d*x+c)^2/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{d x + c}{a^{2}} - \frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}}}{d}"," ",0,"-((d*x + c)/a^2 - 2*tan(1/2*d*x + 1/2*c)/a^2)/d","A",0
83,1,84,0,0.355327," ","integrate(cot(d*x+c)^2/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{120 \, {\left(d x + c\right)}}{a^{2}} + \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} - 25 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 165 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{10}}}{120 \, d}"," ",0,"-1/120*(120*(d*x + c)/a^2 + 15/(a^2*tan(1/2*d*x + 1/2*c)) - (3*a^8*tan(1/2*d*x + 1/2*c)^5 - 25*a^8*tan(1/2*d*x + 1/2*c)^3 + 165*a^8*tan(1/2*d*x + 1/2*c))/a^10)/d","A",0
84,1,114,0,0.312773," ","integrate(cot(d*x+c)^4/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3360 \, {\left(d x + c\right)}}{a^{2}} + \frac{35 \, {\left(21 \, \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} - 147 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 770 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4410 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{14}}}{3360 \, d}"," ",0,"1/3360*(3360*(d*x + c)/a^2 + 35*(21*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 - 147*a^12*tan(1/2*d*x + 1/2*c)^5 + 770*a^12*tan(1/2*d*x + 1/2*c)^3 - 4410*a^12*tan(1/2*d*x + 1/2*c))/a^14)/d","A",0
85,1,144,0,0.453225," ","integrate(cot(d*x+c)^6/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{40320 \, {\left(d x + c\right)}}{a^{2}} + \frac{63 \, {\left(185 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 15 \, \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} - 405 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2331 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9765 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 51345 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{18}}}{40320 \, d}"," ",0,"-1/40320*(40320*(d*x + c)/a^2 + 63*(185*tan(1/2*d*x + 1/2*c)^4 - 15*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 - 405*a^16*tan(1/2*d*x + 1/2*c)^7 + 2331*a^16*tan(1/2*d*x + 1/2*c)^5 - 9765*a^16*tan(1/2*d*x + 1/2*c)^3 + 51345*a^16*tan(1/2*d*x + 1/2*c))/a^18)/d","A",0
86,1,246,0,93.139308," ","integrate(tan(d*x+c)^11/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{420 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{3}} - \frac{420 \, \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{1393 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{819 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6755 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{20195 \, {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{28749 \, {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{8463 \, {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{1089 \, {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + 319}{a^{3} {\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*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^3 - 420*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/a^3 - (1393*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 819*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 6755*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 20195*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 28749*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 8463*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 1089*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 + 319)/(a^3*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^7))/d","A",0
87,1,202,0,20.746571," ","integrate(tan(d*x+c)^9/(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{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{475 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{590 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{50 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{805 \, {\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}} + 119}{a^{3} {\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*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^3 - 60*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/a^3 - (475*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 590*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 50*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 805*(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 + 119)/(a^3*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^5))/d","B",0
88,1,158,0,9.285046," ","integrate(tan(d*x+c)^7/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{6 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{3}} - \frac{6 \, \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{75 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{51 \, {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{11 \, {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + 29}{a^{3} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(6*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^3 - 6*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/a^3 - (75*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 51*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 11*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 29)/(a^3*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^3))/d","B",0
89,1,112,0,5.493971," ","integrate(tan(d*x+c)^5/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{\log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{3}} + \frac{3 \, \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{3 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + 1}{a^{3} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}}}{d}"," ",0,"(log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^3 + 3*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/a^3 - (3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)/(a^3*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)))/d","B",0
90,1,56,0,1.900506," ","integrate(tan(d*x+c)^3/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{\log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{3}} + \frac{\cos\left(d x + c\right) - 1}{a^{3} {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"-(log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^3 + (cos(d*x + c) - 1)/(a^3*(cos(d*x + c) + 1)))/d","A",0
91,1,87,0,0.513674," ","integrate(tan(d*x+c)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{8 \, \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{6 \, a^{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}}}{a^{6}}}{8 \, d}"," ",0,"1/8*(8*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^3 + (6*a^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)/a^6)/d","A",0
92,1,143,0,0.335124," ","integrate(cot(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{96 \, \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{66 \, a^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{15 \, 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 - 96*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^3 - (66*a^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 15*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
93,1,212,0,0.394418," ","integrate(cot(d*x+c)^3/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{12 \, {\left(\frac{7 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\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{84 \, \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{768 \, \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{504 \, a^{9} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{132 \, a^{9} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{28 \, 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*(7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)*(cos(d*x + c) + 1)/(a^3*(cos(d*x + c) - 1)) - 84*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/a^3 + 768*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^3 + (504*a^9*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 132*a^9*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 28*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
94,1,261,0,1.909817," ","integrate(cot(d*x+c)^5/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{30 \, {\left(\frac{18 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{111 \, {\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{2220 \, \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{15360 \, \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{9780 \, a^{12} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2790 \, a^{12} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{740 \, a^{12} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{135 \, a^{12} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{12 \, a^{12} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{15}}}{15360 \, d}"," ",0,"-1/15360*(30*(18*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 111*(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) - 2220*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/a^3 + 15360*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^3 + (9780*a^12*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2790*a^12*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 740*a^12*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 135*a^12*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 12*a^12*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5)/a^15)/d","A",0
95,1,175,0,116.124224," ","integrate(tan(d*x+c)^12/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{13440 \, {\left(d x + c\right)}}{a^{3}} - \frac{13125 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} + \frac{13125 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{2 \, {\left(26565 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} - 212625 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 749973 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 550089 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 269879 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 79723 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 11375 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 315 \, \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*(13440*(d*x + c)/a^3 - 13125*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 + 13125*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 2*(26565*tan(1/2*d*x + 1/2*c)^15 - 212625*tan(1/2*d*x + 1/2*c)^13 + 749973*tan(1/2*d*x + 1/2*c)^11 - 550089*tan(1/2*d*x + 1/2*c)^9 + 269879*tan(1/2*d*x + 1/2*c)^7 - 79723*tan(1/2*d*x + 1/2*c)^5 + 11375*tan(1/2*d*x + 1/2*c)^3 - 315*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^8*a^3))/d","A",0
96,1,149,0,64.838400," ","integrate(tan(d*x+c)^10/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{240 \, {\left(d x + c\right)}}{a^{3}} - \frac{285 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} + \frac{285 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{2 \, {\left(525 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 3135 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1746 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 366 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 95 \, \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^{3}}}{240 \, d}"," ",0,"-1/240*(240*(d*x + c)/a^3 - 285*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 + 285*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 2*(525*tan(1/2*d*x + 1/2*c)^11 - 3135*tan(1/2*d*x + 1/2*c)^9 + 1746*tan(1/2*d*x + 1/2*c)^7 - 366*tan(1/2*d*x + 1/2*c)^5 - 95*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^3))/d","A",0
97,1,123,0,11.182190," ","integrate(tan(d*x+c)^8/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{8 \, {\left(d x + c\right)}}{a^{3}} - \frac{13 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} + \frac{13 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{2 \, {\left(21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 13 \, \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)}^{4} a^{3}}}{8 \, d}"," ",0,"1/8*(8*(d*x + c)/a^3 - 13*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 + 13*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 2*(21*tan(1/2*d*x + 1/2*c)^7 + 3*tan(1/2*d*x + 1/2*c)^5 - 13*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)^4*a^3))/d","A",0
98,1,97,0,7.541020," ","integrate(tan(d*x+c)^6/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(d x + c\right)}}{a^{3}} - \frac{7 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} + \frac{7 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{2 \, {\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}}}{2 \, d}"," ",0,"-1/2*(2*(d*x + c)/a^3 - 7*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 + 7*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - 2*(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))/d","A",0
99,1,63,0,3.668987," ","integrate(tan(d*x+c)^4/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{d x + c}{a^{3}} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}}}{d}"," ",0,"((d*x + c)/a^3 + log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - 4*tan(1/2*d*x + 1/2*c)/a^3)/d","A",0
100,1,50,0,0.785393," ","integrate(tan(d*x+c)^2/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)}}{a^{3}} + \frac{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{9}}}{3 \, d}"," ",0,"-1/3*(3*(d*x + c)/a^3 + (a^6*tan(1/2*d*x + 1/2*c)^3 - 6*a^6*tan(1/2*d*x + 1/2*c))/a^9)/d","A",0
101,1,99,0,0.486355," ","integrate(cot(d*x+c)^2/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{1680 \, {\left(d x + c\right)}}{a^{3}} + \frac{105}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \frac{15 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 126 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 560 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2730 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{21}}}{1680 \, d}"," ",0,"-1/1680*(1680*(d*x + c)/a^3 + 105/(a^3*tan(1/2*d*x + 1/2*c)) + (15*a^18*tan(1/2*d*x + 1/2*c)^7 - 126*a^18*tan(1/2*d*x + 1/2*c)^5 + 560*a^18*tan(1/2*d*x + 1/2*c)^3 - 2730*a^18*tan(1/2*d*x + 1/2*c))/a^21)/d","A",0
102,1,131,0,0.468623," ","integrate(cot(d*x+c)^4/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{20160 \, {\left(d x + c\right)}}{a^{3}} + \frac{105 \, {\left(24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} - \frac{35 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1827 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6720 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 31185 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{27}}}{20160 \, d}"," ",0,"1/20160*(20160*(d*x + c)/a^3 + 105*(24*tan(1/2*d*x + 1/2*c)^2 - 1)/(a^3*tan(1/2*d*x + 1/2*c)^3) - (35*a^24*tan(1/2*d*x + 1/2*c)^9 - 360*a^24*tan(1/2*d*x + 1/2*c)^7 + 1827*a^24*tan(1/2*d*x + 1/2*c)^5 - 6720*a^24*tan(1/2*d*x + 1/2*c)^3 + 31185*a^24*tan(1/2*d*x + 1/2*c))/a^27)/d","A",0
103,1,160,0,1.467972," ","integrate(cot(d*x+c)^6/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{887040 \, {\left(d x + c\right)}}{a^{3}} + \frac{231 \, {\left(690 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 50 \, \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{5 \, {\left(63 \, 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} + 4554 \, a^{30} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18018 \, a^{30} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 59136 \, a^{30} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 264726 \, a^{30} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{33}}}{887040 \, d}"," ",0,"-1/887040*(887040*(d*x + c)/a^3 + 231*(690*tan(1/2*d*x + 1/2*c)^4 - 50*tan(1/2*d*x + 1/2*c)^2 + 3)/(a^3*tan(1/2*d*x + 1/2*c)^5) + 5*(63*a^30*tan(1/2*d*x + 1/2*c)^11 - 770*a^30*tan(1/2*d*x + 1/2*c)^9 + 4554*a^30*tan(1/2*d*x + 1/2*c)^7 - 18018*a^30*tan(1/2*d*x + 1/2*c)^5 + 59136*a^30*tan(1/2*d*x + 1/2*c)^3 - 264726*a^30*tan(1/2*d*x + 1/2*c))/a^33)/d","A",0
104,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(e*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \left(e \tan\left(d x + c\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*(e*tan(d*x + c))^(5/2), x)","F",0
105,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(e*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*(e*tan(d*x + c))^(3/2), x)","F",0
106,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(e*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \sqrt{e \tan\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*sqrt(e*tan(d*x + c)), x)","F",0
107,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\sqrt{e \tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/sqrt(e*tan(d*x + c)), x)","F",0
108,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/(e*tan(d*x + c))^(3/2), x)","F",0
109,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\left(e \tan\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/(e*tan(d*x + c))^(5/2), x)","F",0
110,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\left(e \tan\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/(e*tan(d*x + c))^(7/2), x)","F",0
111,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(e*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \left(e \tan\left(d x + c\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*(e*tan(d*x + c))^(5/2), x)","F",0
112,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(e*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*(e*tan(d*x + c))^(3/2), x)","F",0
113,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(e*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{e \tan\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*sqrt(e*tan(d*x + c)), x)","F",0
114,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{e \tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/sqrt(e*tan(d*x + c)), x)","F",0
115,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/(e*tan(d*x + c))^(3/2), x)","F",0
116,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\left(e \tan\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/(e*tan(d*x + c))^(5/2), x)","F",0
117,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\left(e \tan\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/(e*tan(d*x + c))^(7/2), x)","F",0
118,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(11/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{\frac{11}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^(11/2)/(a*sec(d*x + c) + a), x)","F",0
119,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(9/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{\frac{9}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^(9/2)/(a*sec(d*x + c) + a), x)","F",0
120,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{\frac{7}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^(7/2)/(a*sec(d*x + c) + a), x)","F",0
121,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^(5/2)/(a*sec(d*x + c) + a), x)","F",0
122,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^(3/2)/(a*sec(d*x + c) + a), x)","F",0
123,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sqrt{e \tan\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*tan(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*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{e \tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*sqrt(e*tan(d*x + c))), x)","F",0
125,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))/(e*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*(e*tan(d*x + c))^(3/2)), x)","F",0
126,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))/(e*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \left(e \tan\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*(e*tan(d*x + c))^(5/2)), x)","F",0
127,-1,0,0,0.000000," ","integrate((e*tan(d*x+c))^(13/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(11/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{\frac{11}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^(11/2)/(a*sec(d*x + c) + a)^2, x)","F",0
129,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(9/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{\frac{9}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^(9/2)/(a*sec(d*x + c) + a)^2, x)","F",0
130,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \tan\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*tan(d*x + c))^(7/2)/(a*sec(d*x + c) + a)^2, x)","F",0
131,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \tan\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*tan(d*x + c))^(5/2)/(a*sec(d*x + c) + a)^2, x)","F",0
132,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \tan\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*tan(d*x + c))^(3/2)/(a*sec(d*x + c) + a)^2, x)","F",0
133,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sqrt{e \tan\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(e*tan(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
134,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^2/(e*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{e \tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^2*sqrt(e*tan(d*x + c))), x)","F",0
135,1,193,0,4.820081," ","integrate((a+a*sec(d*x+c))^(1/2)*tan(d*x+c)^5,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\frac{315 \, \sqrt{2} a \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} + \frac{2 \, {\left(315 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} a - 210 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} a^{2} + 252 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} a^{3} + 1080 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} a^{4} + 560 \, a^{5}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{315 \, d}"," ",0,"1/315*sqrt(2)*(315*sqrt(2)*a*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a) + 2*(315*(a*tan(1/2*d*x + 1/2*c)^2 - a)^4*a - 210*(a*tan(1/2*d*x + 1/2*c)^2 - a)^3*a^2 + 252*(a*tan(1/2*d*x + 1/2*c)^2 - a)^2*a^3 + 1080*(a*tan(1/2*d*x + 1/2*c)^2 - a)*a^4 + 560*a^5)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))*sgn(cos(d*x + c))/d","A",0
136,1,152,0,2.506954," ","integrate((a+a*sec(d*x+c))^(1/2)*tan(d*x+c)^3,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{15 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} + \frac{2 \, {\left(15 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} a^{2} - 10 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} a^{3} - 12 \, a^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{15 \, a d}"," ",0,"-1/15*sqrt(2)*(15*sqrt(2)*a^2*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a) + 2*(15*(a*tan(1/2*d*x + 1/2*c)^2 - a)^2*a^2 - 10*(a*tan(1/2*d*x + 1/2*c)^2 - a)*a^3 - 12*a^4)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))*sgn(cos(d*x + c))/(a*d)","A",0
137,1,75,0,0.733244," ","integrate((a+a*sec(d*x+c))^(1/2)*tan(d*x+c),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\frac{\sqrt{2} a \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} + \frac{2 \, a}{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{d}"," ",0,"sqrt(2)*(sqrt(2)*a*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a) + 2*a/sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))*sgn(cos(d*x + c))/d","A",0
138,1,88,0,2.114177," ","integrate(cot(d*x+c)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{\sqrt{2} a \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} - \frac{a \arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{d}"," ",0,"-sqrt(2)*(sqrt(2)*a*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a) - a*arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a))*sgn(cos(d*x + c))/d","A",0
139,1,140,0,0.786984," ","integrate(cot(d*x+c)^3*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\frac{8 \, \sqrt{2} a \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} - \frac{7 \, a \arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} + 2 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} - \frac{\sqrt{-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)^{2}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{8 \, d}"," ",0,"1/8*sqrt(2)*(8*sqrt(2)*a*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a) - 7*a*arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a) + 2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/tan(1/2*d*x + 1/2*c)^2)*sgn(cos(d*x + c))/d","A",0
140,1,201,0,0.878497," ","integrate(cot(d*x+c)^5*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{384 \, \sqrt{2} a \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} - \frac{321 \, a \arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} + \frac{8 \, {\left({\left(-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}} a^{2} + 15 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{3}\right)}}{a^{3}} + \frac{3 \, {\left(21 \, {\left(-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}} a - 19 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{2}\right)}}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{384 \, d}"," ",0,"-1/384*sqrt(2)*(384*sqrt(2)*a*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a) - 321*a*arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a) + 8*((-a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2)*a^2 + 15*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^3)/a^3 + 3*(21*(-a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2)*a - 19*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^2)/(a^2*tan(1/2*d*x + 1/2*c)^4))*sgn(cos(d*x + c))/d","A",0
141,1,284,0,10.327272," ","integrate((a+a*sec(d*x+c))^(1/2)*tan(d*x+c)^6,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\frac{495 \, \sqrt{2} \sqrt{-a} a \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right)}{{\left| a \right|}} - \frac{4 \, {\left(495 \, a^{6} - {\left(2805 \, a^{6} - {\left(6666 \, a^{6} - {\left(4158 \, a^{6} + {\left(221 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1463 \, a^{6}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{5} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{990 \, d}"," ",0,"1/990*sqrt(2)*(495*sqrt(2)*sqrt(-a)*a*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))/abs(a) - 4*(495*a^6 - (2805*a^6 - (6666*a^6 - (4158*a^6 + (221*a^6*tan(1/2*d*x + 1/2*c)^2 - 1463*a^6)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^5*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))*sgn(cos(d*x + c))/d","A",0
142,1,246,0,5.440647," ","integrate((a+a*sec(d*x+c))^(1/2)*tan(d*x+c)^4,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{105 \, \sqrt{2} \sqrt{-a} a \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right)}{{\left| a \right|}} - \frac{4 \, {\left(105 \, a^{4} - {\left(385 \, a^{4} + {\left(43 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 203 \, a^{4}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{210 \, d}"," ",0,"-1/210*sqrt(2)*(105*sqrt(2)*sqrt(-a)*a*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))/abs(a) - 4*(105*a^4 - (385*a^4 + (43*a^4*tan(1/2*d*x + 1/2*c)^2 - 203*a^4)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))*sgn(cos(d*x + c))/d","A",0
143,1,208,0,4.776124," ","integrate((a+a*sec(d*x+c))^(1/2)*tan(d*x+c)^2,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\frac{3 \, \sqrt{2} \sqrt{-a} a \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right)}{{\left| a \right|}} + \frac{4 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{6 \, d}"," ",0,"1/6*sqrt(2)*(3*sqrt(2)*sqrt(-a)*a*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))/abs(a) + 4*(a^2*tan(1/2*d*x + 1/2*c)^2 - 3*a^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))*sgn(cos(d*x + c))/d","B",0
144,1,236,0,1.179495," ","integrate(cot(d*x+c)^2*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\frac{2 \, \sqrt{2} \sqrt{-a} a \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right)}{{\left| a \right|}} + \sqrt{-a} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right) + \frac{4 \, \sqrt{-a} a}{{\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{4 \, d}"," ",0,"1/4*sqrt(2)*(2*sqrt(2)*sqrt(-a)*a*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))/abs(a) + sqrt(-a)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2) + 4*sqrt(-a)*a/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a))*sgn(cos(d*x + c))/d","B",0
145,1,365,0,4.654549," ","integrate(cot(d*x+c)^4*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{48 \, \sqrt{2} \sqrt{-a} a \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right)}{{\left| a \right|}} + 27 \, \sqrt{-a} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right) + 6 \, \sqrt{-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) + \frac{8 \, {\left(15 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{-a} a - 24 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{-a} a^{2} + 13 \, \sqrt{-a} a^{3}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{3}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{96 \, d}"," ",0,"-1/96*sqrt(2)*(48*sqrt(2)*sqrt(-a)*a*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))/abs(a) + 27*sqrt(-a)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2) + 6*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c) + 8*(15*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(-a)*a - 24*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(-a)*a^2 + 13*sqrt(-a)*a^3)/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^3)*sgn(cos(d*x + c))/d","B",0
146,1,476,0,3.906707," ","integrate(cot(d*x+c)^6*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(30 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 25\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{3840 \, \sqrt{2} \sqrt{-a} a \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right)}{{\left| a \right|}} - 2265 \, \sqrt{-a} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right) - \frac{64 \, {\left(165 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} \sqrt{-a} a - 555 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{-a} a^{2} + 785 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{-a} a^{3} - 505 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{-a} a^{4} + 134 \, \sqrt{-a} a^{5}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{5}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{7680 \, d}"," ",0,"-1/7680*sqrt(2)*(30*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*tan(1/2*d*x + 1/2*c)^2 - 25)*tan(1/2*d*x + 1/2*c) - 3840*sqrt(2)*sqrt(-a)*a*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))/abs(a) - 2265*sqrt(-a)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2) - 64*(165*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*sqrt(-a)*a - 555*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(-a)*a^2 + 785*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(-a)*a^3 - 505*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(-a)*a^4 + 134*sqrt(-a)*a^5)/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^5)*sgn(cos(d*x + c))/d","A",0
147,1,218,0,4.764823," ","integrate((a+a*sec(d*x+c))^(3/2)*tan(d*x+c)^5,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\frac{1155 \, \sqrt{2} a \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} + \frac{2 \, {\left(1155 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{5} a - 770 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} a^{2} + 924 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} a^{3} - 1320 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} a^{4} - 6160 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} a^{5} - 3360 \, a^{6}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{5} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}\right)} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{1155 \, d}"," ",0,"1/1155*sqrt(2)*(1155*sqrt(2)*a*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a) + 2*(1155*(a*tan(1/2*d*x + 1/2*c)^2 - a)^5*a - 770*(a*tan(1/2*d*x + 1/2*c)^2 - a)^4*a^2 + 924*(a*tan(1/2*d*x + 1/2*c)^2 - a)^3*a^3 - 1320*(a*tan(1/2*d*x + 1/2*c)^2 - a)^2*a^4 - 6160*(a*tan(1/2*d*x + 1/2*c)^2 - a)*a^5 - 3360*a^6)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^5*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))*a*sgn(cos(d*x + c))/d","A",0
148,1,173,0,2.126299," ","integrate((a+a*sec(d*x+c))^(3/2)*tan(d*x+c)^3,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{105 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} + \frac{2 \, {\left(105 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} a^{2} - 70 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} a^{3} + 84 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} a^{4} + 120 \, a^{5}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{105 \, d}"," ",0,"-1/105*sqrt(2)*(105*sqrt(2)*a^2*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a) + 2*(105*(a*tan(1/2*d*x + 1/2*c)^2 - a)^3*a^2 - 70*(a*tan(1/2*d*x + 1/2*c)^2 - a)^2*a^3 + 84*(a*tan(1/2*d*x + 1/2*c)^2 - a)*a^4 + 120*a^5)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))*sgn(cos(d*x + c))/d","A",0
149,1,122,0,1.134491," ","integrate((a+a*sec(d*x+c))^(3/2)*tan(d*x+c),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\frac{3 \, \sqrt{2} a \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} + \frac{2 \, {\left(3 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} a - 2 \, a^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}\right)} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{3 \, d}"," ",0,"1/3*sqrt(2)*(3*sqrt(2)*a*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a) + 2*(3*(a*tan(1/2*d*x + 1/2*c)^2 - a)*a - 2*a^2)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))*a*sgn(cos(d*x + c))/d","A",0
150,1,89,0,1.214748," ","integrate(cot(d*x+c)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{\sqrt{2} a \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} - \frac{2 \, a \arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}}\right)} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{d}"," ",0,"-sqrt(2)*(sqrt(2)*a*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a) - 2*a*arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a))*a*sgn(cos(d*x + c))/d","A",0
151,1,138,0,0.908321," ","integrate(cot(d*x+c)^3*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{5 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{\sqrt{-a}} - \frac{8 \, a^{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{\sqrt{-a}} + \frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{4 \, d}"," ",0,"-1/4*(5*sqrt(2)*a^2*arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))*sgn(cos(d*x + c))/sqrt(-a) - 8*a^2*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))*sgn(cos(d*x + c))/sqrt(-a) + sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a*sgn(cos(d*x + c))/tan(1/2*d*x + 1/2*c)^2)/d","A",0
152,1,211,0,1.160819," ","integrate(cot(d*x+c)^5*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{71 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{\sqrt{-a}} - \frac{128 \, a^{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{\sqrt{-a}} - 8 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - \frac{17 \, \sqrt{2} {\left(-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 15 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{64 \, d}"," ",0,"1/64*(71*sqrt(2)*a^2*arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))*sgn(cos(d*x + c))/sqrt(-a) - 128*a^2*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))*sgn(cos(d*x + c))/sqrt(-a) - 8*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a*sgn(cos(d*x + c)) - (17*sqrt(2)*(-a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2)*a^2*sgn(cos(d*x + c)) - 15*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^3*sgn(cos(d*x + c)))/(a^2*tan(1/2*d*x + 1/2*c)^4))/d","A",0
153,1,369,0,6.468239," ","integrate((a+a*sec(d*x+c))^(3/2)*tan(d*x+c)^6,x, algorithm=""giac"")","\frac{\frac{45045 \, \sqrt{-a} a^{2} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} + \frac{2 \, {\left(45045 \, \sqrt{2} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(300300 \, \sqrt{2} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(861861 \, \sqrt{2} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(573144 \, \sqrt{2} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(236951 \, \sqrt{2} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + {\left(4751 \, \sqrt{2} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 53404 \, \sqrt{2} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{6} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{45045 \, d}"," ",0,"1/45045*(45045*sqrt(-a)*a^2*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) + 2*(45045*sqrt(2)*a^8*sgn(cos(d*x + c)) - (300300*sqrt(2)*a^8*sgn(cos(d*x + c)) - (861861*sqrt(2)*a^8*sgn(cos(d*x + c)) - (573144*sqrt(2)*a^8*sgn(cos(d*x + c)) - (236951*sqrt(2)*a^8*sgn(cos(d*x + c)) + (4751*sqrt(2)*a^8*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^2 - 53404*sqrt(2)*a^8*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^6*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
154,1,310,0,3.383795," ","integrate((a+a*sec(d*x+c))^(3/2)*tan(d*x+c)^4,x, algorithm=""giac"")","-\frac{\frac{315 \, \sqrt{-a} a^{2} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} + \frac{2 \, {\left(315 \, \sqrt{2} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(1470 \, \sqrt{2} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(756 \, \sqrt{2} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + {\left(\sqrt{2} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 162 \, \sqrt{2} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{315 \, d}"," ",0,"-1/315*(315*sqrt(-a)*a^2*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) + 2*(315*sqrt(2)*a^6*sgn(cos(d*x + c)) - (1470*sqrt(2)*a^6*sgn(cos(d*x + c)) - (756*sqrt(2)*a^6*sgn(cos(d*x + c)) + (sqrt(2)*a^6*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^2 - 162*sqrt(2)*a^6*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
155,1,224,0,5.495920," ","integrate((a+a*sec(d*x+c))^(3/2)*tan(d*x+c)^2,x, algorithm=""giac"")","\frac{\frac{5 \, \sqrt{-a} a^{2} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} - \frac{2 \, {\left(\sqrt{2} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 5 \, \sqrt{2} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{5 \, d}"," ",0,"1/5*(5*sqrt(-a)*a^2*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) - 2*(sqrt(2)*a^4*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^4 - 5*sqrt(2)*a^4*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
156,1,197,0,1.437354," ","integrate(cot(d*x+c)^2*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{-a} a^{2} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} + \frac{2 \, \sqrt{2} \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a}}{d}"," ",0,"(sqrt(-a)*a^2*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) + 2*sqrt(2)*sqrt(-a)*a^2*sgn(cos(d*x + c))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a))/d","B",0
157,1,369,0,2.461455," ","integrate(cot(d*x+c)^4*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{3 \, \sqrt{2} \sqrt{-a} a \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + \frac{24 \, \sqrt{-a} a^{2} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} + \frac{8 \, \sqrt{2} {\left(6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 9 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5 \, \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{3}}}{24 \, d}"," ",0,"-1/24*(3*sqrt(2)*sqrt(-a)*a*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)*sgn(cos(d*x + c)) + 24*sqrt(-a)*a^2*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) + 8*sqrt(2)*(6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 9*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 5*sqrt(-a)*a^4*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^3)/d","B",0
158,1,519,0,6.013667," ","integrate(cot(d*x+c)^6*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{165 \, \sqrt{2} \sqrt{-a} a \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 30 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{960 \, \sqrt{-a} a^{2} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} + \frac{32 \, \sqrt{2} {\left(60 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 195 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 275 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 175 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 47 \, \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{5}}}{960 \, d}"," ",0,"1/960*(165*sqrt(2)*sqrt(-a)*a*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)*sgn(cos(d*x + c)) + 30*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c) + 960*sqrt(-a)*a^2*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) + 32*sqrt(2)*(60*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 195*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 275*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 175*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 47*sqrt(-a)*a^6*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^5)/d","B",0
159,1,244,0,9.540768," ","integrate((a+a*sec(d*x+c))^(5/2)*tan(d*x+c)^5,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\frac{45045 \, \sqrt{2} a \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} + \frac{2 \, {\left(45045 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{6} a - 30030 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{5} a^{2} + 36036 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} a^{3} - 51480 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} a^{4} + 80080 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} a^{5} + 393120 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} a^{6} + 221760 \, a^{7}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{6} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}\right)} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{45045 \, d}"," ",0,"1/45045*sqrt(2)*(45045*sqrt(2)*a*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a) + 2*(45045*(a*tan(1/2*d*x + 1/2*c)^2 - a)^6*a - 30030*(a*tan(1/2*d*x + 1/2*c)^2 - a)^5*a^2 + 36036*(a*tan(1/2*d*x + 1/2*c)^2 - a)^4*a^3 - 51480*(a*tan(1/2*d*x + 1/2*c)^2 - a)^3*a^4 + 80080*(a*tan(1/2*d*x + 1/2*c)^2 - a)^2*a^5 + 393120*(a*tan(1/2*d*x + 1/2*c)^2 - a)*a^6 + 221760*a^7)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^6*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))*a^2*sgn(cos(d*x + c))/d","A",0
160,1,198,0,3.923037," ","integrate((a+a*sec(d*x+c))^(5/2)*tan(d*x+c)^3,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{315 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} + \frac{2 \, {\left(315 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} a^{2} - 210 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} a^{3} + 252 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} a^{4} - 360 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} a^{5} - 560 \, a^{6}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}\right)} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{315 \, d}"," ",0,"-1/315*sqrt(2)*(315*sqrt(2)*a^2*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a) + 2*(315*(a*tan(1/2*d*x + 1/2*c)^2 - a)^4*a^2 - 210*(a*tan(1/2*d*x + 1/2*c)^2 - a)^3*a^3 + 252*(a*tan(1/2*d*x + 1/2*c)^2 - a)^2*a^4 - 360*(a*tan(1/2*d*x + 1/2*c)^2 - a)*a^5 - 560*a^6)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))*a*sgn(cos(d*x + c))/d","A",0
161,1,148,0,1.729360," ","integrate((a+a*sec(d*x+c))^(5/2)*tan(d*x+c),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\frac{15 \, \sqrt{2} a \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} + \frac{2 \, {\left(15 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} a - 10 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} a^{2} + 12 \, a^{3}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}\right)} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{15 \, d}"," ",0,"1/15*sqrt(2)*(15*sqrt(2)*a*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a) + 2*(15*(a*tan(1/2*d*x + 1/2*c)^2 - a)^2*a - 10*(a*tan(1/2*d*x + 1/2*c)^2 - a)*a^2 + 12*a^3)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))*a^2*sgn(cos(d*x + c))/d","A",0
162,1,112,0,1.030929," ","integrate(cot(d*x+c)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{\sqrt{2} a \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} - \frac{4 \, a \arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{2 \, a}{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}\right)} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{d}"," ",0,"-sqrt(2)*(sqrt(2)*a*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a) - 4*a*arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/sqrt(-a) - 2*a/sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))*a^2*sgn(cos(d*x + c))/d","A",0
163,1,140,0,6.337087," ","integrate(cot(d*x+c)^3*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{3 \, \sqrt{2} a^{3} \arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{\sqrt{-a}} - \frac{4 \, a^{3} \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{\sqrt{-a}} + \frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(3*sqrt(2)*a^3*arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))*sgn(cos(d*x + c))/sqrt(-a) - 4*a^3*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))*sgn(cos(d*x + c))/sqrt(-a) + sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^2*sgn(cos(d*x + c))/tan(1/2*d*x + 1/2*c)^2)/d","A",0
164,1,177,0,1.763406," ","integrate(cot(d*x+c)^5*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{43 \, \sqrt{2} a^{3} \arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{\sqrt{-a}} - \frac{64 \, a^{3} \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{\sqrt{-a}} - \frac{\sqrt{2} {\left(13 \, {\left(-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 11 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{32 \, d}"," ",0,"1/32*(43*sqrt(2)*a^3*arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))*sgn(cos(d*x + c))/sqrt(-a) - 64*a^3*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))*sgn(cos(d*x + c))/sqrt(-a) - sqrt(2)*(13*(-a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2)*a^3*sgn(cos(d*x + c)) - 11*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^4*sgn(cos(d*x + c)))/(a^2*tan(1/2*d*x + 1/2*c)^4))/d","A",0
165,1,397,0,10.859319," ","integrate((a+a*sec(d*x+c))^(5/2)*tan(d*x+c)^6,x, algorithm=""giac"")","\frac{\frac{45045 \, \sqrt{-a} a^{3} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} - \frac{2 \, {\left(45045 \, \sqrt{2} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(345345 \, \sqrt{2} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(1162161 \, \sqrt{2} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(611325 \, \sqrt{2} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(77935 \, \sqrt{2} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + {\left(109005 \, \sqrt{2} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + {\left(11633 \, \sqrt{2} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 64725 \, \sqrt{2} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{7} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{45045 \, d}"," ",0,"1/45045*(45045*sqrt(-a)*a^3*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) - 2*(45045*sqrt(2)*a^10*sgn(cos(d*x + c)) - (345345*sqrt(2)*a^10*sgn(cos(d*x + c)) - (1162161*sqrt(2)*a^10*sgn(cos(d*x + c)) - (611325*sqrt(2)*a^10*sgn(cos(d*x + c)) - (77935*sqrt(2)*a^10*sgn(cos(d*x + c)) + (109005*sqrt(2)*a^10*sgn(cos(d*x + c)) + (11633*sqrt(2)*a^10*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^2 - 64725*sqrt(2)*a^10*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^7*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
166,1,339,0,4.628664," ","integrate((a+a*sec(d*x+c))^(5/2)*tan(d*x+c)^4,x, algorithm=""giac"")","-\frac{\frac{693 \, \sqrt{-a} a^{3} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} - \frac{2 \, {\left(693 \, \sqrt{2} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(3927 \, \sqrt{2} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(462 \, \sqrt{2} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + {\left(1782 \, \sqrt{2} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + {\left(305 \, \sqrt{2} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1331 \, \sqrt{2} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{5} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{693 \, d}"," ",0,"-1/693*(693*sqrt(-a)*a^3*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) - 2*(693*sqrt(2)*a^8*sgn(cos(d*x + c)) - (3927*sqrt(2)*a^8*sgn(cos(d*x + c)) - (462*sqrt(2)*a^8*sgn(cos(d*x + c)) + (1782*sqrt(2)*a^8*sgn(cos(d*x + c)) + (305*sqrt(2)*a^8*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^2 - 1331*sqrt(2)*a^8*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^5*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
167,1,281,0,12.613004," ","integrate((a+a*sec(d*x+c))^(5/2)*tan(d*x+c)^2,x, algorithm=""giac"")","\frac{\frac{21 \, \sqrt{-a} a^{3} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} - \frac{2 \, {\left(21 \, \sqrt{2} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + {\left(35 \, \sqrt{2} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + {\left(17 \, \sqrt{2} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 49 \, \sqrt{2} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{21 \, d}"," ",0,"1/21*(21*sqrt(-a)*a^3*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) - 2*(21*sqrt(2)*a^6*sgn(cos(d*x + c)) + (35*sqrt(2)*a^6*sgn(cos(d*x + c)) + (17*sqrt(2)*a^6*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^2 - 49*sqrt(2)*a^6*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
168,1,192,0,2.439203," ","integrate(cot(d*x+c)^2*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{2} \sqrt{-a} a^{4} {\left(\frac{\sqrt{2} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right)}{a {\left| a \right|}} + \frac{8}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)} a}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{2 \, d}"," ",0,"1/2*sqrt(2)*sqrt(-a)*a^4*(sqrt(2)*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))/(a*abs(a)) + 8/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)*a))*sgn(cos(d*x + c))/d","B",0
169,1,311,0,5.968667," ","integrate(cot(d*x+c)^4*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{3 \, \sqrt{-a} a^{3} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} + \frac{\sqrt{2} {\left(9 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7 \, \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*sqrt(-a)*a^3*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) + sqrt(2)*(9*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 7*sqrt(-a)*a^5*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^3)/d","B",0
170,1,481,0,12.537296," ","integrate(cot(d*x+c)^6*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{5 \, \sqrt{2} \sqrt{-a} a^{2} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + \frac{80 \, \sqrt{-a} a^{3} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} + \frac{4 \, \sqrt{2} {\left(55 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 170 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 240 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 150 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 41 \, \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{5}}}{80 \, d}"," ",0,"1/80*(5*sqrt(2)*sqrt(-a)*a^2*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)*sgn(cos(d*x + c)) + 80*sqrt(-a)*a^3*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) + 4*sqrt(2)*(55*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 170*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 240*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 150*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 41*sqrt(-a)*a^7*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^5)/d","B",0
171,1,190,0,3.768392," ","integrate(tan(d*x+c)^5/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{105 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{2 \, {\left(105 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} - 70 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} a - 252 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} a^{2} - 120 \, a^{3}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{105 \, d}"," ",0,"-1/105*sqrt(2)*(105*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 2*(105*(a*tan(1/2*d*x + 1/2*c)^2 - a)^3 - 70*(a*tan(1/2*d*x + 1/2*c)^2 - a)^2*a - 252*(a*tan(1/2*d*x + 1/2*c)^2 - a)*a^2 - 120*a^3)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
172,1,149,0,1.747902," ","integrate(tan(d*x+c)^3/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\frac{3 \, \sqrt{2} a \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{2 \, {\left(3 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} a + 2 \, a^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{3 \, a d}"," ",0,"1/3*sqrt(2)*(3*sqrt(2)*a*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 2*(3*(a*tan(1/2*d*x + 1/2*c)^2 - a)*a + 2*a^2)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/(a*d)","B",0
173,1,55,0,4.377156," ","integrate(tan(d*x+c)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 \, \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} d \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}"," ",0,"-2*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*d*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))","B",0
174,1,150,0,1.232823," ","integrate(cot(d*x+c)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{2 \, d}"," ",0,"1/2*sqrt(2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/(a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
175,1,229,0,7.085665," ","integrate(cot(d*x+c)^3/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{48 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{27 \, \arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{3 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} + \frac{2 \, {\left({\left(-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}} a^{4} + 12 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{5}\right)}}{a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{48 \, d}"," ",0,"-1/48*sqrt(2)*(48*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 27*arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/(a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*tan(1/2*d*x + 1/2*c)^2) + 2*((-a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2)*a^4 + 12*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^5)/(a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
176,1,296,0,8.554067," ","integrate(cot(d*x+c)^5/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\frac{3840 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{2265 \, \arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{15 \, {\left(25 \, {\left(-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}} - 23 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a\right)}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}} + \frac{8 \, {\left(3 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{12} + 25 \, {\left(-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}} a^{13} + 240 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{14}\right)}}{a^{15} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{3840 \, d}"," ",0,"1/3840*sqrt(2)*(3840*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 2265*arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 15*(25*(-a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2) - 23*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*tan(1/2*d*x + 1/2*c)^4) + 8*(3*(a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^12 + 25*(-a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2)*a^13 + 240*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^14)/(a^15*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
177,1,353,0,9.449046," ","integrate(tan(d*x+c)^6/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{315 \, \sqrt{2} \sqrt{-a} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right)}{{\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, {\left(\frac{315 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - {\left(\frac{1470 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - {\left(\frac{2772 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + {\left(\frac{257 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{1314 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}\right)}}{630 \, d}"," ",0,"-1/630*sqrt(2)*(315*sqrt(2)*sqrt(-a)*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))/(abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*(315*a^4/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (1470*a^4/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (2772*a^4/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + (257*a^4*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 1314*a^4/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
178,1,283,0,6.153514," ","integrate(tan(d*x+c)^4/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\frac{15 \, \sqrt{2} \sqrt{-a} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right)}{{\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, {\left({\left(\frac{13 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{40 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{15 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}\right)}}{30 \, d}"," ",0,"1/30*sqrt(2)*(15*sqrt(2)*sqrt(-a)*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))/(abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*((13*a^2*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 40*a^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2 + 15*a^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
179,1,191,0,1.906979," ","integrate(tan(d*x+c)^2/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{\sqrt{2} \sqrt{-a} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right)}{{\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{2 \, d}"," ",0,"-1/2*sqrt(2)*(sqrt(2)*sqrt(-a)*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))/(abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*tan(1/2*d*x + 1/2*c)/(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
180,1,123,0,1.424804," ","integrate(cot(d*x+c)^2/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{\sqrt{-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)}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, \sqrt{-a}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{8 \, d}"," ",0,"-1/8*sqrt(2)*(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/(a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*sqrt(-a)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
181,1,256,0,1.556105," ","integrate(cot(d*x+c)^4/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(3 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{21}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{32 \, {\left(9 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{-a} - 15 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{-a} a + 8 \, \sqrt{-a} a^{2}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{384 \, d}"," ",0,"-1/384*sqrt(2)*(3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*tan(1/2*d*x + 1/2*c)^2/(a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 21/(a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) - 32*(9*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(-a) - 15*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(-a)*a + 8*sqrt(-a)*a^2)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
182,1,387,0,1.838190," ","integrate(cot(d*x+c)^6/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(5 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(2 \, {\left(\frac{4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{43}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{567}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{96 \, {\left(145 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} \sqrt{-a} - 500 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{-a} a + 710 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{-a} a^{2} - 460 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{-a} a^{3} + 121 \, \sqrt{-a} a^{4}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{15360 \, d}"," ",0,"-1/15360*sqrt(2)*(5*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*(4*tan(1/2*d*x + 1/2*c)^2/(a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 43/(a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 + 567/(a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) + 96*(145*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*sqrt(-a) - 500*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(-a)*a + 710*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(-a)*a^2 - 460*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(-a)*a^3 + 121*sqrt(-a)*a^4)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^5*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
183,1,168,0,4.901010," ","integrate(tan(d*x+c)^5/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{5 \, \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{\sqrt{2} {\left(5 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} + 10 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} a + 4 \, a^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{5 \, d}"," ",0,"-2/5*(5*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + sqrt(2)*(5*(a*tan(1/2*d*x + 1/2*c)^2 - a)^2 + 10*(a*tan(1/2*d*x + 1/2*c)^2 - a)*a + 4*a^2)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
184,1,99,0,3.199592," ","integrate(tan(d*x+c)^3/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{\arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2}}{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{a d}"," ",0,"2*(arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)/(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/(a*d)","B",0
185,1,102,0,2.723273," ","integrate(tan(d*x+c)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{2 \, \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{d}"," ",0,"-(2*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
186,1,185,0,2.424326," ","integrate(cot(d*x+c)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{3 \, \sqrt{2} \arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{24 \, \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left({\left(-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}} a^{6} + 9 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{7}\right)}}{a^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{12 \, d}"," ",0,"-1/12*(3*sqrt(2)*arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 24*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*((-a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2)*a^6 + 9*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^7)/(a^9*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
187,1,281,0,1.625605," ","integrate(cot(d*x+c)^3/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{165 \, \sqrt{2} \arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{960 \, \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{15 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} - \frac{2 \, \sqrt{2} {\left(3 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{16} + 20 \, {\left(-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}} a^{17} + 165 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{18}\right)}}{a^{20} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{480 \, d}"," ",0,"1/480*(165*sqrt(2)*arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 960*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 15*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*tan(1/2*d*x + 1/2*c)^2) - 2*sqrt(2)*(3*(a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^16 + 20*(-a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2)*a^17 + 165*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^18)/(a^20*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
188,1,350,0,1.895691," ","integrate(cot(d*x+c)^5/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{4263 \, \sqrt{2} \arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{21504 \, \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{21 \, {\left(29 \, \sqrt{2} {\left(-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}} - 27 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a\right)}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}} + \frac{8 \, \sqrt{2} {\left(3 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{30} - 21 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{31} - 112 \, {\left(-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}} a^{32} - 882 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{33}\right)}}{a^{35} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{10752 \, d}"," ",0,"-1/10752*(4263*sqrt(2)*arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 21504*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 21*(29*sqrt(2)*(-a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2) - 27*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*tan(1/2*d*x + 1/2*c)^4) + 8*sqrt(2)*(3*(a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^30 - 21*(a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^31 - 112*(-a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2)*a^32 - 882*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^33)/(a^35*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
189,1,338,0,7.384408," ","integrate(tan(d*x+c)^6/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{105 \, \sqrt{-a} {\left(\frac{\log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} + \frac{2 \, {\left({\left({\left(\frac{139 \, \sqrt{2} a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{539 \, \sqrt{2} a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{385 \, \sqrt{2} a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{105 \, \sqrt{2} a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{105 \, d}"," ",0,"-1/105*(105*sqrt(-a)*(log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))) + 2*(((139*sqrt(2)*a^2*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 539*sqrt(2)*a^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2 + 385*sqrt(2)*a^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2 - 105*sqrt(2)*a^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
190,1,258,0,7.994856," ","integrate(tan(d*x+c)^4/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{3 \, \sqrt{-a} {\left(\frac{\log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} + \frac{2 \, {\left(\frac{5 \, \sqrt{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{3 \, \sqrt{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{3 \, d}"," ",0,"1/3*(3*sqrt(-a)*(log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))) + 2*(5*sqrt(2)*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 3*sqrt(2)/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
191,1,73,0,2.968063," ","integrate(tan(d*x+c)^2/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a + \frac{a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}}{2 \, \sqrt{a}}\right)}{a^{\frac{3}{2}}} - \frac{2 \, \arctan\left(\frac{\sqrt{-a + \frac{a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}}{\sqrt{a}}\right)}{a^{\frac{3}{2}}}\right)}}{d}"," ",0,"-sqrt(2)*(sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a + a/tan(1/2*d*x + 1/2*c)^2)/sqrt(a))/a^(3/2) - 2*arctan(sqrt(-a + a/tan(1/2*d*x + 1/2*c)^2)/sqrt(a))/a^(3/2))/d","A",0
192,1,164,0,1.489042," ","integrate(cot(d*x+c)^2/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{17 \, \sqrt{2}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{16 \, \sqrt{2}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)} \sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{64 \, d}"," ",0,"1/64*(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*tan(1/2*d*x + 1/2*c)^2/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 17*sqrt(2)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) + 16*sqrt(2)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)*sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
193,1,289,0,1.953326," ","integrate(cot(d*x+c)^4/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(2 \, {\left(\frac{4 \, \sqrt{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{37 \, \sqrt{2}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{417 \, \sqrt{2}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{32 \, \sqrt{2} {\left(21 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + 19 \, a^{2}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{3} \sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{1536 \, d}"," ",0,"1/1536*(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*(4*sqrt(2)*tan(1/2*d*x + 1/2*c)^2/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 37*sqrt(2)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 + 417*sqrt(2)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) - 32*sqrt(2)*(21*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + 19*a^2)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^3*sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
194,1,414,0,2.514676," ","integrate(cot(d*x+c)^6/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{5 \, {\left(2 \, {\left(4 \, {\left(\frac{6 \, \sqrt{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{65 \, \sqrt{2}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{1451 \, \sqrt{2}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{13503 \, \sqrt{2}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \sqrt{-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) + \frac{256 \, \sqrt{2} {\left(555 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} - 1950 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} a + 2780 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{2} - 1810 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{3} + 473 \, a^{4}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{5} \sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{245760 \, d}"," ",0,"1/245760*(5*(2*(4*(6*sqrt(2)*tan(1/2*d*x + 1/2*c)^2/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 65*sqrt(2)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 + 1451*sqrt(2)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 - 13503*sqrt(2)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c) + 256*sqrt(2)*(555*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8 - 1950*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*a + 2780*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^2 - 1810*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^3 + 473*a^4)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^5*sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
195,1,140,0,4.512882," ","integrate(tan(d*x+c)^5/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{3 \, \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7 \, a\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{3 \, d}"," ",0,"-2/3*(3*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(9*a*tan(1/2*d*x + 1/2*c)^2 - 7*a)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
196,1,104,0,4.922279," ","integrate(tan(d*x+c)^3/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{\arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{a d}"," ",0,"2*(arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/(a*d)","B",0
197,1,130,0,1.496105," ","integrate(tan(d*x+c)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{12 \, \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{\sqrt{2} {\left({\left(-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}} a^{8} + 6 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{9}\right)}}{a^{12} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{6 \, d}"," ",0,"-1/6*(12*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + sqrt(2)*((-a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2)*a^8 + 6*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^9)/(a^12*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
198,1,227,0,4.290919," ","integrate(cot(d*x+c)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{5 \, \sqrt{2} \arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{80 \, \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left({\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{20} + 5 \, {\left(-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}} a^{21} + 35 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{22}\right)}}{a^{25} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{40 \, d}"," ",0,"-1/40*(5*sqrt(2)*arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 80*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^20 + 5*(-a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2)*a^21 + 35*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^22)/(a^25*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
199,1,323,0,2.021188," ","integrate(cot(d*x+c)^3/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{1365 \, \sqrt{2} \arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{13440 \, \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{105 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} + \frac{2 \, \sqrt{2} {\left(15 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{36} - 84 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{37} - 385 \, {\left(-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}} a^{38} - 2730 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{39}\right)}}{a^{42} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{6720 \, d}"," ",0,"1/6720*(1365*sqrt(2)*arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 13440*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 105*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*tan(1/2*d*x + 1/2*c)^2) + 2*sqrt(2)*(15*(a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^36 - 84*(a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^37 - 385*(-a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2)*a^38 - 2730*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^39)/(a^42*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
200,1,392,0,2.665790," ","integrate(cot(d*x+c)^5/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{82845 \, \sqrt{2} \arctan\left(\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{645120 \, \arctan\left(\frac{\sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{315 \, {\left(33 \, \sqrt{2} {\left(-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}} - 31 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a\right)}}{a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}} - \frac{8 \, \sqrt{2} {\left(35 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{56} - 225 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{57} + 1008 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{58} + 4410 \, {\left(-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}} a^{59} + 31185 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} a^{60}\right)}}{a^{63} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{322560 \, d}"," ",0,"-1/322560*(82845*sqrt(2)*arctan(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 645120*arctan(1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 315*(33*sqrt(2)*(-a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2) - 31*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a)/(a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*tan(1/2*d*x + 1/2*c)^4) - 8*sqrt(2)*(35*(a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^56 - 225*(a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^57 + 1008*(a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^58 + 4410*(-a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2)*a^59 + 31185*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^60)/(a^63*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
201,1,292,0,6.434019," ","integrate(tan(d*x+c)^6/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{15 \, \sqrt{-a} {\left(\frac{\log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} + \frac{2 \, {\left({\left(\frac{37 \, \sqrt{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{40 \, \sqrt{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{15 \, \sqrt{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{15 \, d}"," ",0,"-1/15*(15*sqrt(-a)*(log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))) + 2*((37*sqrt(2)*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 40*sqrt(2)/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2 + 15*sqrt(2)/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
202,1,73,0,3.049595," ","integrate(tan(d*x+c)^4/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{2} \sqrt{-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)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} a^{2} d \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}"," ",0,"2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*a^2*d*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))","A",0
203,1,54,0,10.292046," ","integrate(tan(d*x+c)^2/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \sqrt{-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)}{2 \, a^{3} d \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}"," ",0,"-1/2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/(a^3*d*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))","A",0
204,1,205,0,5.576932," ","integrate(cot(d*x+c)^2/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(2 \, {\left(\frac{4 \, \sqrt{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{31 \, \sqrt{2}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{291 \, \sqrt{2}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{96 \, \sqrt{2}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)} \sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{768 \, d}"," ",0,"-1/768*(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*(4*sqrt(2)*tan(1/2*d*x + 1/2*c)^2/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 31*sqrt(2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 + 291*sqrt(2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) - 96*sqrt(2)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)*sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
205,1,331,0,2.689945," ","integrate(cot(d*x+c)^4/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{3 \, {\left(2 \, {\left(4 \, {\left(\frac{2 \, \sqrt{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{19 \, \sqrt{2}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{369 \, \sqrt{2}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{2989 \, \sqrt{2}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \sqrt{-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) + \frac{512 \, \sqrt{2} {\left(12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 21 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + 11 \, a^{2}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{3} \sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{24576 \, d}"," ",0,"-1/24576*(3*(2*(4*(2*sqrt(2)*tan(1/2*d*x + 1/2*c)^2/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 19*sqrt(2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 + 369*sqrt(2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 - 2989*sqrt(2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c) + 512*sqrt(2)*(12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 21*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + 11*a^2)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^3*sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
206,1,454,0,3.673862," ","integrate(cot(d*x+c)^6/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{{\left(2 \, {\left(4 \, {\left(6 \, {\left(\frac{8 \, \sqrt{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{91 \, \sqrt{2}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{3043 \, \sqrt{2}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{47185 \, \sqrt{2}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{349965 \, \sqrt{2}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \sqrt{-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) - \frac{1024 \, \sqrt{2} {\left(345 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} - 1230 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} a + 1760 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{2} - 1150 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{3} + 299 \, a^{4}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{5} \sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{983040 \, d}"," ",0,"-1/983040*((2*(4*(6*(8*sqrt(2)*tan(1/2*d*x + 1/2*c)^2/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 91*sqrt(2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 + 3043*sqrt(2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 - 47185*sqrt(2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 + 349965*sqrt(2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c) - 1024*sqrt(2)*(345*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8 - 1230*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*a + 1760*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^2 - 1150*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^3 + 299*a^4)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^5*sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
207,-2,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+a*sec(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*2*tan((f*x+exp(1))/2)*sqrt(-a*tan((f*x+exp(1))/2)^2+a)*(-37/256*sqrt(2)/a^5/sign(tan((f*x+exp(1))/2)^2-1)+tan((f*x+exp(1))/2)^2*(19/384*sqrt(2)/a^5/sign(tan((f*x+exp(1))/2)^2-1)-1/96*sqrt(2)*tan((f*x+exp(1))/2)^2/a^5/sign(tan((f*x+exp(1))/2)^2-1)))","F(-2)",0
208,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*(e*tan(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*(e*tan(d*x + c))^m, x)","F",0
209,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(e*tan(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{3} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3*(e*tan(d*x + c))^m, x)","F",0
210,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(e*tan(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*(e*tan(d*x + c))^m, x)","F",0
211,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(e*tan(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*(e*tan(d*x + c))^m, x)","F",0
212,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^m/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{m}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^m/(a*sec(d*x + c) + a), x)","F",0
213,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^m/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{m}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^m/(a*sec(d*x + c) + a)^2, x)","F",0
214,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^m/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{m}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^m/(a*sec(d*x + c) + a)^3, x)","F",0
215,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(e*tan(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)*(e*tan(d*x + c))^m, x)","F",0
216,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)*(e*tan(d*x+c))^m,x, algorithm=""giac"")","\int \sqrt{a \sec\left(d x + c\right) + a} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*(e*tan(d*x + c))^m, x)","F",0
217,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^m/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{m}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^m/sqrt(a*sec(d*x + c) + a), x)","F",0
218,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^m/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\left(e \tan\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*tan(d*x + c))^m/(a*sec(d*x + c) + a)^(3/2), x)","F",0
219,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*tan(d*x+c)^7,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{7}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*tan(d*x + c)^7, x)","F",0
220,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*tan(d*x+c)^5,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*tan(d*x + c)^5, x)","F",0
221,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*tan(d*x+c)^3,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*tan(d*x + c)^3, x)","F",0
222,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*tan(d*x+c),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*tan(d*x + c), x)","F",0
223,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*cot(d*x + c), x)","F",0
224,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*cot(d*x + c)^3, x)","F",0
225,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*tan(d*x+c)^4,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*tan(d*x + c)^4, x)","F",0
226,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*tan(d*x+c)^2,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*tan(d*x + c)^2, x)","F",0
227,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*cot(d*x + c)^2, x)","F",0
228,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*cot(d*x + c)^4, x)","F",0
229,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*tan(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*tan(d*x + c)^(3/2), x)","F",0
230,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*tan(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sqrt{\tan\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*sqrt(tan(d*x + c)), x)","F",0
231,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n/tan(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{n}}{\sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n/sqrt(tan(d*x + c)), x)","F",0
232,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n/tan(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{n}}{\tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n/tan(d*x + c)^(3/2), x)","F",0
233,0,0,0,0.000000," ","integrate((e*cot(d*x+c))^(5/2)*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \left(e \cot\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sec\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cot(d*x + c))^(5/2)*(a*sec(d*x + c) + a), x)","F",0
234,0,0,0,0.000000," ","integrate((e*cot(d*x+c))^(3/2)*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \left(e \cot\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sec\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cot(d*x + c))^(3/2)*(a*sec(d*x + c) + a), x)","F",0
235,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(e*cot(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{e \cot\left(d x + c\right)} {\left(a \sec\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(e*cot(d*x + c))*(a*sec(d*x + c) + a), x)","F",0
236,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*cot(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\sqrt{e \cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/sqrt(e*cot(d*x + c)), x)","F",0
237,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*cot(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\left(e \cot\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/(e*cot(d*x + c))^(3/2), x)","F",0
238,0,0,0,0.000000," ","integrate((e*cot(d*x+c))^(5/2)*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \left(e \cot\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*cot(d*x + c))^(5/2)*(a*sec(d*x + c) + a)^2, x)","F",0
239,0,0,0,0.000000," ","integrate((e*cot(d*x+c))^(3/2)*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \left(e \cot\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*cot(d*x + c))^(3/2)*(a*sec(d*x + c) + a)^2, x)","F",0
240,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(e*cot(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{e \cot\left(d x + c\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(e*cot(d*x + c))*(a*sec(d*x + c) + a)^2, x)","F",0
241,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*cot(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{e \cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/sqrt(e*cot(d*x + c)), x)","F",0
242,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*cot(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\left(e \cot\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/(e*cot(d*x + c))^(3/2), x)","F",0
243,0,0,0,0.000000," ","integrate((e*cot(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \cot\left(d x + c\right)\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cot(d*x + c))^(3/2)/(a*sec(d*x + c) + a), x)","F",0
244,0,0,0,0.000000," ","integrate((e*cot(d*x+c))^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sqrt{e \cot\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*cot(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
245,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))/(e*cot(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \cot\left(d x + c\right)} {\left(a \sec\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cot(d*x + c))*(a*sec(d*x + c) + a)), x)","F",0
246,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{\left(e \cot\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*cot(d*x + c))^(3/2)*(a*sec(d*x + c) + a)), x)","F",0
247,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{\left(e \cot\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*cot(d*x + c))^(5/2)*(a*sec(d*x + c) + a)), x)","F",0
248,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{\left(e \cot\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*cot(d*x + c))^(7/2)*(a*sec(d*x + c) + a)), x)","F",0
249,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(9/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{\left(e \cot\left(d x + c\right)\right)^{\frac{9}{2}} {\left(a \sec\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*cot(d*x + c))^(9/2)*(a*sec(d*x + c) + a)), x)","F",0
250,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^2/(e*cot(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \cot\left(d x + c\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cot(d*x + c))*(a*sec(d*x + c) + a)^2), x)","F",0
251,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \cot\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*cot(d*x + c))^(3/2)*(a*sec(d*x + c) + a)^2), x)","F",0
252,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \cot\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*cot(d*x + c))^(5/2)*(a*sec(d*x + c) + a)^2), x)","F",0
253,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \cot\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*cot(d*x + c))^(7/2)*(a*sec(d*x + c) + a)^2), x)","F",0
254,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(9/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \cot\left(d x + c\right)\right)^{\frac{9}{2}} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cot(d*x + c))^(9/2)*(a*sec(d*x + c) + a)^2), x)","F",0
255,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(11/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \cot\left(d x + c\right)\right)^{\frac{11}{2}} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cot(d*x + c))^(11/2)*(a*sec(d*x + c) + a)^2), x)","F",0
256,1,317,0,11.584024," ","integrate((a+b*sec(d*x+c))*tan(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{1089 \, a + 384 \, b + \frac{8463 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2688 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{28749 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{8064 \, b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{56035 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{13440 \, b {\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)) + (1089*a + 384*b + 8463*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2688*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 28749*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 8064*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 56035*a*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 13440*b*(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
257,1,248,0,3.013187," ","integrate((a+b*sec(d*x+c))*tan(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{137 \, a + 64 \, b + \frac{805 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{320 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{1970 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{640 \, b {\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)) + (137*a + 64*b + 805*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 320*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1970*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 640*b*(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
258,1,179,0,0.950501," ","integrate((a+b*sec(d*x+c))*tan(d*x+c)^3,x, algorithm=""giac"")","-\frac{6 \, a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 6 \, a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{11 \, a + 8 \, b + \frac{45 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{24 \, 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{11 \, a {\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} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(6*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 6*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (11*a + 8*b + 45*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 24*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 + 11*a*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^3)/d","B",0
259,1,107,0,1.033763," ","integrate((a+b*sec(d*x+c))*tan(d*x+c),x, algorithm=""giac"")","\frac{a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 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) + \frac{a + 2 \, b + \frac{a {\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}}{d}"," ",0,"(a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (a + 2*b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/d","B",0
260,1,61,0,0.257155," ","integrate(cot(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 \, a \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*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)))/d","A",0
261,1,170,0,2.500751," ","integrate(cot(d*x+c)^3*(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, {\left(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) - 8 \, 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 + b + \frac{4 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2 \, 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*(2*a + b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 8*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - (a + b + 4*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*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
262,1,266,0,0.968161," ","integrate(cot(d*x+c)^5*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{4 \, {\left(8 \, a + 3 \, 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 \, 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 + b + \frac{12 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{8 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{48 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{18 \, 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{12 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{8 \, 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*(8*a + 3*b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) - 64*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - (a + b + 12*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 8*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 48*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 18*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 - 12*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 8*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
263,1,358,0,0.566512," ","integrate(cot(d*x+c)^7*(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{12 \, {\left(16 \, a + 5 \, 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 \, 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 + b + \frac{12 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{9 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{87 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{45 \, b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{352 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{110 \, 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{87 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{45 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{12 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{9 \, 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*(16*a + 5*b)*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)) - (a + b + 12*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 9*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 87*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 45*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 352*a*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 110*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 - 87*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 45*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 12*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 9*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
264,1,228,0,4.536795," ","integrate((a+b*sec(d*x+c))*tan(d*x+c)^6,x, algorithm=""giac"")","-\frac{240 \, {\left(d x + c\right)} a + 75 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 75 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(240 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 75 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1520 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 425 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4128 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 990 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4128 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 990 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1520 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 425 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 75 \, 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*(240*(d*x + c)*a + 75*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 75*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(240*a*tan(1/2*d*x + 1/2*c)^11 - 75*b*tan(1/2*d*x + 1/2*c)^11 - 1520*a*tan(1/2*d*x + 1/2*c)^9 + 425*b*tan(1/2*d*x + 1/2*c)^9 + 4128*a*tan(1/2*d*x + 1/2*c)^7 - 990*b*tan(1/2*d*x + 1/2*c)^7 - 4128*a*tan(1/2*d*x + 1/2*c)^5 - 990*b*tan(1/2*d*x + 1/2*c)^5 + 1520*a*tan(1/2*d*x + 1/2*c)^3 + 425*b*tan(1/2*d*x + 1/2*c)^3 - 240*a*tan(1/2*d*x + 1/2*c) - 75*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
265,1,172,0,1.575897," ","integrate((a+b*sec(d*x+c))*tan(d*x+c)^4,x, algorithm=""giac"")","\frac{24 \, {\left(d x + c\right)} a + 9 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 9 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(24 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 104 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 33 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 104 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, 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*(24*(d*x + c)*a + 9*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 9*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(24*a*tan(1/2*d*x + 1/2*c)^7 - 9*b*tan(1/2*d*x + 1/2*c)^7 - 104*a*tan(1/2*d*x + 1/2*c)^5 + 33*b*tan(1/2*d*x + 1/2*c)^5 + 104*a*tan(1/2*d*x + 1/2*c)^3 + 33*b*tan(1/2*d*x + 1/2*c)^3 - 24*a*tan(1/2*d*x + 1/2*c) - 9*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
266,1,115,0,1.524435," ","integrate((a+b*sec(d*x+c))*tan(d*x+c)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(d x + c\right)} a + b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(2 \, 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} - 2 \, 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)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(2*(d*x + c)*a + b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(2*a*tan(1/2*d*x + 1/2*c)^3 - b*tan(1/2*d*x + 1/2*c)^3 - 2*a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
267,1,52,0,0.207904," ","integrate(cot(d*x+c)^2*(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, {\left(d x + c\right)} a - 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*(d*x + c)*a - 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","A",0
268,1,112,0,0.260790," ","integrate(cot(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 \, {\left(d x + c\right)} a - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{15 \, 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}{\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*(d*x + c)*a - 15*a*tan(1/2*d*x + 1/2*c) + 9*b*tan(1/2*d*x + 1/2*c) + (15*a*tan(1/2*d*x + 1/2*c)^2 + 9*b*tan(1/2*d*x + 1/2*c)^2 - a - b)/tan(1/2*d*x + 1/2*c)^3)/d","B",0
269,1,170,0,0.372290," ","integrate(cot(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} - 35 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 25 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, {\left(d x + c\right)} a + 330 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 150 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{330 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 150 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 35 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 25 \, 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 - 35*a*tan(1/2*d*x + 1/2*c)^3 + 25*b*tan(1/2*d*x + 1/2*c)^3 - 480*(d*x + c)*a + 330*a*tan(1/2*d*x + 1/2*c) - 150*b*tan(1/2*d*x + 1/2*c) - (330*a*tan(1/2*d*x + 1/2*c)^4 + 150*b*tan(1/2*d*x + 1/2*c)^4 - 35*a*tan(1/2*d*x + 1/2*c)^2 - 25*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
270,1,225,0,0.350253," ","integrate(cot(d*x+c)^8*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 189 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 147 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1295 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 735 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 13440 \, {\left(d x + c\right)} a - 9765 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3675 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{9765 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3675 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1295 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 735 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 189 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 147 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a - 15 \, b}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{13440 \, d}"," ",0,"1/13440*(15*a*tan(1/2*d*x + 1/2*c)^7 - 15*b*tan(1/2*d*x + 1/2*c)^7 - 189*a*tan(1/2*d*x + 1/2*c)^5 + 147*b*tan(1/2*d*x + 1/2*c)^5 + 1295*a*tan(1/2*d*x + 1/2*c)^3 - 735*b*tan(1/2*d*x + 1/2*c)^3 + 13440*(d*x + c)*a - 9765*a*tan(1/2*d*x + 1/2*c) + 3675*b*tan(1/2*d*x + 1/2*c) + (9765*a*tan(1/2*d*x + 1/2*c)^6 + 3675*b*tan(1/2*d*x + 1/2*c)^6 - 1295*a*tan(1/2*d*x + 1/2*c)^4 - 735*b*tan(1/2*d*x + 1/2*c)^4 + 189*a*tan(1/2*d*x + 1/2*c)^2 + 147*b*tan(1/2*d*x + 1/2*c)^2 - 15*a - 15*b)/tan(1/2*d*x + 1/2*c)^7)/d","B",0
271,1,489,0,19.613704," ","integrate((a+b*sec(d*x+c))^2*tan(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{7381 \, a^{2} + 4096 \, a b + \frac{78850 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{40960 \, a b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{382545 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{184320 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1114200 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{491520 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2171610 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{860160 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{2736972 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{516096 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{258048 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2171610 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{1114200 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{382545 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{78850 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{7381 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{10}}}{2520 \, d}"," ",0,"1/2520*(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)) + (7381*a^2 + 4096*a*b + 78850*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 40960*a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 382545*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 184320*a*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 1114200*a^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 491520*a*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 2171610*a^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 860160*a*b*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 2736972*a^2*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 516096*a*b*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 258048*b^2*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 2171610*a^2*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 1114200*a^2*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 + 382545*a^2*(cos(d*x + c) - 1)^8/(cos(d*x + c) + 1)^8 + 78850*a^2*(cos(d*x + c) - 1)^9/(cos(d*x + c) + 1)^9 + 7381*a^2*(cos(d*x + c) - 1)^10/(cos(d*x + c) + 1)^10)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^10)/d","B",0
272,1,415,0,8.885160," ","integrate((a+b*sec(d*x+c))^2*tan(d*x+c)^7,x, algorithm=""giac"")","-\frac{840 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 840 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{2283 \, a^{2} + 1536 \, a b + \frac{19944 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{12288 \, a b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{77364 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{43008 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{175448 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{86016 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{231490 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{53760 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{26880 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{175448 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{77364 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{19944 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{2283 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{8}}}{840 \, d}"," ",0,"-1/840*(840*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 840*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (2283*a^2 + 1536*a*b + 19944*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 12288*a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 77364*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 43008*a*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 175448*a^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 86016*a*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 231490*a^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 53760*a*b*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 26880*b^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 175448*a^2*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 77364*a^2*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 19944*a^2*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 + 2283*a^2*(cos(d*x + c) - 1)^8/(cos(d*x + c) + 1)^8)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^8)/d","B",0
273,1,341,0,5.390333," ","integrate((a+b*sec(d*x+c))^2*tan(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{147 \, a^{2} + 128 \, a b + \frac{1002 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{768 \, a b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2925 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1920 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{4140 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1280 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{640 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2925 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1002 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{147 \, a^{2} {\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)}^{6}}}{60 \, d}"," ",0,"1/60*(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)) + (147*a^2 + 128*a*b + 1002*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 768*a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2925*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 1920*a*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 4140*a^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 1280*a*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 640*b^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 2925*a^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 1002*a^2*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 147*a^2*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^6)/d","B",0
274,1,267,0,3.749946," ","integrate((a+b*sec(d*x+c))^2*tan(d*x+c)^3,x, algorithm=""giac"")","-\frac{12 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 12 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{25 \, a^{2} + 32 \, a b + \frac{124 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{128 \, a b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{198 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{96 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{48 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{124 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{25 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{{\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{4}}}{12 \, d}"," ",0,"-1/12*(12*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 12*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (25*a^2 + 32*a*b + 124*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 128*a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 198*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 96*a*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 48*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 124*a^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 25*a^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4)/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^4)/d","B",0
275,1,191,0,0.873167," ","integrate((a+b*sec(d*x+c))^2*tan(d*x+c),x, algorithm=""giac"")","\frac{2 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - 2 \, 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} + 8 \, a b + \frac{6 \, 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{4 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{2} {\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*(2*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - 2*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (3*a^2 + 8*a*b + 6*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) - 4*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 3*a^2*(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
276,1,101,0,0.267845," ","integrate(cot(d*x+c)*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) + 2 \, b^{2} \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)}{2 \, d}"," ",0,"-1/2*(2*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) + 2*b^2*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)))/d","A",0
277,1,209,0,1.566231," ","integrate(cot(d*x+c)^3*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{8 \, 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} {\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} - 4 \, {\left(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) + \frac{{\left(a^{2} + 2 \, a b + b^{2} + \frac{4 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{4 \, a 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}}{8 \, d}"," ",0,"1/8*(8*a^2*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) - 4*(a^2 + a*b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) + (a^2 + 2*a*b + b^2 + 4*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 4*a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*(cos(d*x + c) + 1)/(cos(d*x + c) - 1))/d","B",0
278,1,360,0,0.363430," ","integrate(cot(d*x+c)^5*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{64 \, a^{2} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) + \frac{12 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{16 \, 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{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}} - 8 \, {\left(4 \, 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) + \frac{{\left(a^{2} + 2 \, a b + b^{2} + \frac{12 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{16 \, 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{48 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{36 \, 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(\cos\left(d x + c\right) - 1\right)}^{2}}}{64 \, d}"," ",0,"-1/64*(64*a^2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) + 12*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 16*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) + 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 - 8*(4*a^2 + 3*a*b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1)) + (a^2 + 2*a*b + b^2 + 12*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 16*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) + 48*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 36*a*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)/d","B",0
279,1,282,0,9.200769," ","integrate((a+b*sec(d*x+c))^2*tan(d*x+c)^6,x, algorithm=""giac"")","-\frac{840 \, {\left(d x + c\right)} a^{2} + 525 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 525 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(840 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 525 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 6160 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3500 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 19768 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 9905 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 28896 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 7680 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 19768 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9905 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6160 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3500 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 840 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 525 \, 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)}^{7}}}{840 \, d}"," ",0,"-1/840*(840*(d*x + c)*a^2 + 525*a*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 525*a*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(840*a^2*tan(1/2*d*x + 1/2*c)^13 - 525*a*b*tan(1/2*d*x + 1/2*c)^13 - 6160*a^2*tan(1/2*d*x + 1/2*c)^11 + 3500*a*b*tan(1/2*d*x + 1/2*c)^11 + 19768*a^2*tan(1/2*d*x + 1/2*c)^9 - 9905*a*b*tan(1/2*d*x + 1/2*c)^9 - 28896*a^2*tan(1/2*d*x + 1/2*c)^7 + 7680*b^2*tan(1/2*d*x + 1/2*c)^7 + 19768*a^2*tan(1/2*d*x + 1/2*c)^5 + 9905*a*b*tan(1/2*d*x + 1/2*c)^5 - 6160*a^2*tan(1/2*d*x + 1/2*c)^3 - 3500*a*b*tan(1/2*d*x + 1/2*c)^3 + 840*a^2*tan(1/2*d*x + 1/2*c) + 525*a*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^7)/d","A",0
280,1,220,0,2.388601," ","integrate((a+b*sec(d*x+c))^2*tan(d*x+c)^4,x, algorithm=""giac"")","\frac{60 \, {\left(d x + c\right)} a^{2} + 45 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 45 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(60 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 45 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 320 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 210 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 520 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 192 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 320 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 210 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 45 \, 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)}^{5}}}{60 \, d}"," ",0,"1/60*(60*(d*x + c)*a^2 + 45*a*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 45*a*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(60*a^2*tan(1/2*d*x + 1/2*c)^9 - 45*a*b*tan(1/2*d*x + 1/2*c)^9 - 320*a^2*tan(1/2*d*x + 1/2*c)^7 + 210*a*b*tan(1/2*d*x + 1/2*c)^7 + 520*a^2*tan(1/2*d*x + 1/2*c)^5 - 192*b^2*tan(1/2*d*x + 1/2*c)^5 - 320*a^2*tan(1/2*d*x + 1/2*c)^3 - 210*a*b*tan(1/2*d*x + 1/2*c)^3 + 60*a^2*tan(1/2*d*x + 1/2*c) + 45*a*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
281,1,158,0,1.669439," ","integrate((a+b*sec(d*x+c))^2*tan(d*x+c)^2,x, algorithm=""giac"")","-\frac{3 \, {\left(d x + c\right)} a^{2} + 3 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, 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)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(d*x + c)*a^2 + 3*a*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*a*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(3*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*a*b*tan(1/2*d*x + 1/2*c)^5 - 6*a^2*tan(1/2*d*x + 1/2*c)^3 + 4*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*a^2*tan(1/2*d*x + 1/2*c) + 3*a*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
282,1,80,0,1.034314," ","integrate(cot(d*x+c)^2*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(d x + c\right)} a^{2} - 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} + 2 \, a b + b^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"-1/2*(2*(d*x + c)*a^2 - 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 + 2*a*b + b^2)/tan(1/2*d*x + 1/2*c))/d","A",0
283,1,176,0,0.321133," ","integrate(cot(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} + 24 \, {\left(d x + c\right)} a^{2} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, 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) + \frac{15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 18 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, 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 + 24*(d*x + c)*a^2 - 15*a^2*tan(1/2*d*x + 1/2*c) + 18*a*b*tan(1/2*d*x + 1/2*c) - 3*b^2*tan(1/2*d*x + 1/2*c) + (15*a^2*tan(1/2*d*x + 1/2*c)^2 + 18*a*b*tan(1/2*d*x + 1/2*c)^2 + 3*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
284,1,273,0,1.212874," ","integrate(cot(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} - 35 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 50 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, {\left(d x + c\right)} a^{2} + 330 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 300 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 30 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{330 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 300 \, 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} - 35 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 50 \, 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}}{\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 - 35*a^2*tan(1/2*d*x + 1/2*c)^3 + 50*a*b*tan(1/2*d*x + 1/2*c)^3 - 15*b^2*tan(1/2*d*x + 1/2*c)^3 - 480*(d*x + c)*a^2 + 330*a^2*tan(1/2*d*x + 1/2*c) - 300*a*b*tan(1/2*d*x + 1/2*c) + 30*b^2*tan(1/2*d*x + 1/2*c) - (330*a^2*tan(1/2*d*x + 1/2*c)^4 + 300*a*b*tan(1/2*d*x + 1/2*c)^4 + 30*b^2*tan(1/2*d*x + 1/2*c)^4 - 35*a^2*tan(1/2*d*x + 1/2*c)^2 - 50*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)/tan(1/2*d*x + 1/2*c)^5)/d","B",0
285,1,366,0,0.433909," ","integrate(cot(d*x+c)^8*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 189 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 294 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1295 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1470 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 315 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 13440 \, {\left(d x + c\right)} a^{2} - 9765 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7350 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 525 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{9765 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 7350 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 525 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1295 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1470 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 315 \, b^{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} + 294 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 105 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{2} - 30 \, a b - 15 \, b^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{13440 \, d}"," ",0,"1/13440*(15*a^2*tan(1/2*d*x + 1/2*c)^7 - 30*a*b*tan(1/2*d*x + 1/2*c)^7 + 15*b^2*tan(1/2*d*x + 1/2*c)^7 - 189*a^2*tan(1/2*d*x + 1/2*c)^5 + 294*a*b*tan(1/2*d*x + 1/2*c)^5 - 105*b^2*tan(1/2*d*x + 1/2*c)^5 + 1295*a^2*tan(1/2*d*x + 1/2*c)^3 - 1470*a*b*tan(1/2*d*x + 1/2*c)^3 + 315*b^2*tan(1/2*d*x + 1/2*c)^3 + 13440*(d*x + c)*a^2 - 9765*a^2*tan(1/2*d*x + 1/2*c) + 7350*a*b*tan(1/2*d*x + 1/2*c) - 525*b^2*tan(1/2*d*x + 1/2*c) + (9765*a^2*tan(1/2*d*x + 1/2*c)^6 + 7350*a*b*tan(1/2*d*x + 1/2*c)^6 + 525*b^2*tan(1/2*d*x + 1/2*c)^6 - 1295*a^2*tan(1/2*d*x + 1/2*c)^4 - 1470*a*b*tan(1/2*d*x + 1/2*c)^4 - 315*b^2*tan(1/2*d*x + 1/2*c)^4 + 189*a^2*tan(1/2*d*x + 1/2*c)^2 + 294*a*b*tan(1/2*d*x + 1/2*c)^2 + 105*b^2*tan(1/2*d*x + 1/2*c)^2 - 15*a^2 - 30*a*b - 15*b^2)/tan(1/2*d*x + 1/2*c)^7)/d","B",0
286,1,1768,0,17.338575," ","integrate(tan(d*x+c)^9/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{210 \, {\left(a^{7} - 4 \, a^{5} b^{2} + 6 \, a^{3} b^{4} - 4 \, a b^{6}\right)} \log\left({\left| a + b - \frac{2 \, 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|}\right)}{b^{8}} - \frac{420 \, {\left(a^{7} - 4 \, a^{5} b^{2} + 6 \, a^{3} b^{4} - 4 \, a b^{6}\right)} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right)}{b^{8}} - \frac{210 \, {\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + 2 \, b^{8}\right)} \log\left(\frac{{\left| 2 \, b + \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - 2 \, {\left| a \right|} \right|}}{{\left| 2 \, b + \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + 2 \, {\left| a \right|} \right|}}\right)}{b^{8} {\left| a \right|}} + \frac{1089 \, a^{7} - 840 \, a^{6} b - 4356 \, a^{5} b^{2} + 3080 \, a^{4} b^{3} + 6534 \, a^{3} b^{4} - 4088 \, a^{2} b^{5} - 4356 \, a b^{6} + 2232 \, b^{7} + \frac{7623 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{5040 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{31332 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{19040 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{48258 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{26096 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{33012 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{14784 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{22869 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{12600 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{95676 \, 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{47880 \, 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{151494 \, 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{67368 \, 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{107436 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{40152 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{38115 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{16800 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{160860 \, 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{62720 \, 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{258930 \, 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{86240 \, 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{192220 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{53760 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{38115 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{12600 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{160860 \, 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{45080 \, 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{258930 \, 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{56840 \, 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{192220 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{24360 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{22869 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5040 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{95676 \, 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{16800 \, 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{151494 \, 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{18480 \, 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{107436 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{6720 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{7623 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{840 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{31332 \, 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{2520 \, 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{48258 \, 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{2520 \, 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{33012 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{840 \, 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^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{4356 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{6534 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{4356 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{b^{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*(210*(a^7 - 4*a^5*b^2 + 6*a^3*b^4 - 4*a*b^6)*log(abs(a + b - 2*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))/b^8 - 420*(a^7 - 4*a^5*b^2 + 6*a^3*b^4 - 4*a*b^6)*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/b^8 - 210*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + 2*b^8)*log(abs(2*b + 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*abs(a))/abs(2*b + 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*abs(a)))/(b^8*abs(a)) + (1089*a^7 - 840*a^6*b - 4356*a^5*b^2 + 3080*a^4*b^3 + 6534*a^3*b^4 - 4088*a^2*b^5 - 4356*a*b^6 + 2232*b^7 + 7623*a^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 5040*a^6*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 31332*a^5*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 19040*a^4*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 48258*a^3*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 26096*a^2*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 33012*a*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 14784*b^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 22869*a^7*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 12600*a^6*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 95676*a^5*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 47880*a^4*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 151494*a^3*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 67368*a^2*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 107436*a*b^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 40152*b^7*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 38115*a^7*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 16800*a^6*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 160860*a^5*b^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 62720*a^4*b^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 258930*a^3*b^4*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 86240*a^2*b^5*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 192220*a*b^6*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 53760*b^7*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 38115*a^7*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 12600*a^6*b*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 160860*a^5*b^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 45080*a^4*b^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 258930*a^3*b^4*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 56840*a^2*b^5*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 192220*a*b^6*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 24360*b^7*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 22869*a^7*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 5040*a^6*b*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 95676*a^5*b^2*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 16800*a^4*b^3*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 151494*a^3*b^4*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 18480*a^2*b^5*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 107436*a*b^6*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 6720*b^7*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 7623*a^7*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 840*a^6*b*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 31332*a^5*b^2*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 2520*a^4*b^3*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 48258*a^3*b^4*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 2520*a^2*b^5*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 33012*a*b^6*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 840*b^7*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 1089*a^7*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 - 4356*a^5*b^2*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 + 6534*a^3*b^4*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7 - 4356*a*b^6*(cos(d*x + c) - 1)^7/(cos(d*x + c) + 1)^7)/(b^8*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^7))/d","B",0
287,1,1052,0,11.517342," ","integrate(tan(d*x+c)^7/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{30 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \log\left({\left| a + b - \frac{2 \, 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|}\right)}{b^{6}} - \frac{60 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right)}{b^{6}} - \frac{30 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - 2 \, b^{6}\right)} \log\left(\frac{{\left| 2 \, b + \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - 2 \, {\left| a \right|} \right|}}{{\left| 2 \, b + \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + 2 \, {\left| a \right|} \right|}}\right)}{b^{6} {\left| a \right|}} + \frac{137 \, a^{5} - 120 \, a^{4} b - 411 \, a^{3} b^{2} + 320 \, a^{2} b^{3} + 411 \, a b^{4} - 264 \, b^{5} + \frac{685 \, a^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{480 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2175 \, a^{3} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{1360 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2295 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{1200 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{1370 \, a^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{720 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4470 \, 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{2000 \, 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{5070 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1920 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1370 \, a^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{480 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{4470 \, 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{1200 \, 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{5070 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{720 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{685 \, a^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{120 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{2175 \, 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{240 \, 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{2295 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{120 \, 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^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{411 \, a^{3} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{411 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{b^{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*(30*(a^5 - 3*a^3*b^2 + 3*a*b^4)*log(abs(a + b - 2*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))/b^6 - 60*(a^5 - 3*a^3*b^2 + 3*a*b^4)*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/b^6 - 30*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - 2*b^6)*log(abs(2*b + 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*abs(a))/abs(2*b + 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*abs(a)))/(b^6*abs(a)) + (137*a^5 - 120*a^4*b - 411*a^3*b^2 + 320*a^2*b^3 + 411*a*b^4 - 264*b^5 + 685*a^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 480*a^4*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2175*a^3*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1360*a^2*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2295*a*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1200*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1370*a^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 720*a^4*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 4470*a^3*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 2000*a^2*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 5070*a*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 1920*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 1370*a^5*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 480*a^4*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 4470*a^3*b^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 1200*a^2*b^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 5070*a*b^4*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 720*b^5*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 685*a^5*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 120*a^4*b*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 2175*a^3*b^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 240*a^2*b^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 2295*a*b^4*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 120*b^5*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 137*a^5*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 411*a^3*b^2*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 411*a*b^4*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5)/(b^6*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^5))/d","B",0
288,1,560,0,3.135267," ","integrate(tan(d*x+c)^5/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(a^{3} - 2 \, a b^{2}\right)} \log\left({\left| a + b - \frac{2 \, 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|}\right)}{b^{4}} - \frac{6 \, {\left(a^{3} - 2 \, a b^{2}\right)} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right)}{b^{4}} - \frac{3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + 2 \, b^{4}\right)} \log\left(\frac{{\left| 2 \, b + \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - 2 \, {\left| a \right|} \right|}}{{\left| 2 \, b + \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + 2 \, {\left| a \right|} \right|}}\right)}{b^{4} {\left| a \right|}} + \frac{11 \, a^{3} - 12 \, a^{2} b - 22 \, a b^{2} + 20 \, b^{3} + \frac{33 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{24 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{78 \, a b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{48 \, b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{33 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{12 \, a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{78 \, a b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{12 \, b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{11 \, a^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{22 \, a b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{b^{4} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(3*(a^3 - 2*a*b^2)*log(abs(a + b - 2*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))/b^4 - 6*(a^3 - 2*a*b^2)*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/b^4 - 3*(a^4 - 2*a^2*b^2 + 2*b^4)*log(abs(2*b + 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*abs(a))/abs(2*b + 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*abs(a)))/(b^4*abs(a)) + (11*a^3 - 12*a^2*b - 22*a*b^2 + 20*b^3 + 33*a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 24*a^2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 78*a*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 48*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 33*a^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 12*a^2*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 78*a*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 12*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 11*a^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 22*a*b^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3)/(b^4*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^3))/d","B",0
289,1,289,0,2.071405," ","integrate(tan(d*x+c)^3/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{a \log\left({\left| a + b - \frac{2 \, 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|}\right)}{b^{2}} - \frac{2 \, a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right)}{b^{2}} - \frac{{\left(a^{2} - 2 \, b^{2}\right)} \log\left(\frac{{\left| 2 \, b + \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - 2 \, {\left| a \right|} \right|}}{{\left| 2 \, b + \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + 2 \, {\left| a \right|} \right|}}\right)}{b^{2} {\left| a \right|}} + \frac{2 \, {\left(a - 2 \, b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{b^{2} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}}}{2 \, d}"," ",0,"-1/2*(a*log(abs(a + b - 2*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))/b^2 - 2*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/b^2 - (a^2 - 2*b^2)*log(abs(2*b + 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*abs(a))/abs(2*b + 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*abs(a)))/(b^2*abs(a)) + 2*(a - 2*b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/(b^2*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)))/d","B",0
290,1,114,0,0.349608," ","integrate(tan(d*x+c)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\log\left(\frac{{\left| 2 \, b + \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - 2 \, {\left| a \right|} \right|}}{{\left| 2 \, b + \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + 2 \, {\left| a \right|} \right|}}\right)}{d {\left| a \right|}}"," ",0,"log(abs(2*b + 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*abs(a))/abs(2*b + 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*abs(a)))/(d*abs(a))","B",0
291,1,257,0,0.309615," ","integrate(cot(d*x+c)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{a \log\left({\left| -a - b + \frac{2 \, 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|}\right)}{a^{2} - b^{2}} - \frac{{\left(a^{2} - 2 \, b^{2}\right)} \log\left(\frac{{\left| -2 \, b - \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - 2 \, {\left| a \right|} \right|}}{{\left| -2 \, b - \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + 2 \, {\left| a \right|} \right|}}\right)}{{\left(a^{2} - b^{2}\right)} {\left| a \right|}} - \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*(a*log(abs(-a - b + 2*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 - b^2) - (a^2 - 2*b^2)*log(abs(-2*b - 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*abs(a))/abs(-2*b - 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*abs(a)))/((a^2 - b^2)*abs(a)) - log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a + b))/d","B",0
292,1,403,0,0.859373," ","integrate(cot(d*x+c)^3/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(2 \, a + 3 \, 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^{2} + 2 \, a b + b^{2}} - \frac{4 \, {\left(a^{3} - 2 \, a b^{2}\right)} \log\left({\left| a + b - \frac{2 \, 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|}\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(a + b + \frac{4 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{6 \, 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^{2} + 2 \, a b + b^{2}\right)} {\left(\cos\left(d x + c\right) - 1\right)}} - \frac{4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + 2 \, b^{4}\right)} \log\left(\frac{{\left| 2 \, b + \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - 2 \, {\left| a \right|} \right|}}{{\left| 2 \, b + \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + 2 \, {\left| a \right|} \right|}}\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left| a \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*(2*(2*a + 3*b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a^2 + 2*a*b + b^2) - 4*(a^3 - 2*a*b^2)*log(abs(a + b - 2*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^4 - 2*a^2*b^2 + b^4) - (a + b + 4*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 6*b*(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)) - 4*(a^4 - 2*a^2*b^2 + 2*b^4)*log(abs(2*b + 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*abs(a))/abs(2*b + 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*abs(a)))/((a^4 - 2*a^2*b^2 + b^4)*abs(a)) - (cos(d*x + c) - 1)/((a - b)*(cos(d*x + c) + 1)))/d","B",0
293,1,649,0,1.138103," ","integrate(cot(d*x+c)^5/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{4 \, {\left(8 \, a^{2} + 21 \, a b + 15 \, 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^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{32 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \log\left({\left| a + b - \frac{2 \, 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|}\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} - \frac{\frac{12 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{16 \, 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{12 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{28 \, a b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{16 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{48 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{126 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{90 \, 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^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} {\left(\cos\left(d x + c\right) - 1\right)}^{2}} - \frac{32 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - 2 \, b^{6}\right)} \log\left(\frac{{\left| 2 \, b + \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - 2 \, {\left| a \right|} \right|}}{{\left| 2 \, b + \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + 2 \, {\left| a \right|} \right|}}\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left| a \right|}}}{64 \, d}"," ",0,"1/64*(4*(8*a^2 + 21*a*b + 15*b^2)*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) - 32*(a^5 - 3*a^3*b^2 + 3*a*b^4)*log(abs(a + b - 2*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^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) - (12*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 16*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 + 12*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 28*a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 16*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 48*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 126*a*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 90*b^2*(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) - 32*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - 2*b^6)*log(abs(2*b + 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*abs(a))/abs(2*b + 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*abs(a)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*abs(a)))/d","B",0
294,1,746,0,4.210366," ","integrate(tan(d*x+c)^6/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{24 \, {\left({\left(a^{4} + a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sqrt{-a^{2} + b^{2}} {\left| a \right|} {\left| -a + b \right|} {\left| b \right|} + {\left(a^{5} b + a^{4} b^{2} - 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5} + 2 \, b^{6}\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{b^{6} + \sqrt{b^{12} + {\left(a b^{5} + b^{6}\right)} {\left(a b^{5} - b^{6}\right)}}}{a b^{5} - b^{6}}}}\right)\right)}}{{\left(a b^{4} - b^{5}\right)} a^{2} b^{2} + {\left(a b^{6} - b^{7}\right)} {\left| a \right|} {\left| b \right|}} + \frac{24 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + a b^{6} - 2 \, b^{7} - a^{5} {\left| a \right|} {\left| b \right|} + 3 \, a^{3} b^{2} {\left| a \right|} {\left| b \right|} - 3 \, a b^{4} {\left| a \right|} {\left| b \right|} + b^{5} {\left| a \right|} {\left| 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{b^{6} - \sqrt{b^{12} + {\left(a b^{5} + b^{6}\right)} {\left(a b^{5} - b^{6}\right)}}}{a b^{5} - b^{6}}}}\right)\right)}}{a^{2} b^{6} - b^{6} {\left| a \right|} {\left| b \right|}} - \frac{3 \, {\left(8 \, a^{4} - 20 \, a^{2} b^{2} + 15 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{5}} + \frac{3 \, {\left(8 \, a^{4} - 20 \, a^{2} b^{2} + 15 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{5}} - \frac{2 \, {\left(24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 21 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 176 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 176 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 45 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 21 \, 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} b^{4}}}{24 \, d}"," ",0,"-1/24*(24*((a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3 + b^4)*sqrt(-a^2 + b^2)*abs(a)*abs(-a + b)*abs(b) + (a^5*b + a^4*b^2 - 2*a^3*b^3 - 2*a^2*b^4 + a*b^5 + 2*b^6)*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(-(b^6 + sqrt(b^12 + (a*b^5 + b^6)*(a*b^5 - b^6)))/(a*b^5 - b^6))))/((a*b^4 - b^5)*a^2*b^2 + (a*b^6 - b^7)*abs(a)*abs(b)) + 24*(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 + a*b^6 - 2*b^7 - a^5*abs(a)*abs(b) + 3*a^3*b^2*abs(a)*abs(b) - 3*a*b^4*abs(a)*abs(b) + b^5*abs(a)*abs(b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(b^6 - sqrt(b^12 + (a*b^5 + b^6)*(a*b^5 - b^6)))/(a*b^5 - b^6))))/(a^2*b^6 - b^6*abs(a)*abs(b)) - 3*(8*a^4 - 20*a^2*b^2 + 15*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^5 + 3*(8*a^4 - 20*a^2*b^2 + 15*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^5 - 2*(24*a^3*tan(1/2*d*x + 1/2*c)^7 + 12*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 48*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 21*b^3*tan(1/2*d*x + 1/2*c)^7 - 72*a^3*tan(1/2*d*x + 1/2*c)^5 - 12*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 176*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 45*b^3*tan(1/2*d*x + 1/2*c)^5 + 72*a^3*tan(1/2*d*x + 1/2*c)^3 - 12*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 176*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 45*b^3*tan(1/2*d*x + 1/2*c)^3 - 24*a^3*tan(1/2*d*x + 1/2*c) + 12*a^2*b*tan(1/2*d*x + 1/2*c) + 48*a*b^2*tan(1/2*d*x + 1/2*c) - 21*b^3*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^4*b^4))/d","B",0
295,1,476,0,1.482664," ","integrate(tan(d*x+c)^4/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left({\left(a^{2} + a b - b^{2}\right)} \sqrt{-a^{2} + b^{2}} {\left| a \right|} {\left| -a + b \right|} {\left| b \right|} + {\left(a^{3} b + a^{2} b^{2} - a b^{3} - 2 \, b^{4}\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{b^{4} + \sqrt{b^{8} + {\left(a b^{3} + b^{4}\right)} {\left(a b^{3} - b^{4}\right)}}}{a b^{3} - b^{4}}}}\right)\right)}}{{\left(a b^{2} - b^{3}\right)} a^{2} b^{2} + {\left(a b^{4} - b^{5}\right)} {\left| a \right|} {\left| b \right|}} + \frac{2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} - a b^{4} + 2 \, b^{5} - a^{3} {\left| a \right|} {\left| b \right|} + 2 \, a b^{2} {\left| a \right|} {\left| b \right|} - b^{3} {\left| a \right|} {\left| 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{b^{4} - \sqrt{b^{8} + {\left(a b^{3} + b^{4}\right)} {\left(a b^{3} - b^{4}\right)}}}{a b^{3} - b^{4}}}}\right)\right)}}{a^{2} b^{4} - b^{4} {\left| a \right|} {\left| b \right|}} - \frac{{\left(2 \, a^{2} - 3 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{3}} + \frac{{\left(2 \, a^{2} - 3 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{3}} - \frac{2 \, {\left(2 \, 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} - 2 \, 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)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} b^{2}}}{2 \, d}"," ",0,"-1/2*(2*((a^2 + a*b - b^2)*sqrt(-a^2 + b^2)*abs(a)*abs(-a + b)*abs(b) + (a^3*b + a^2*b^2 - a*b^3 - 2*b^4)*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(-(b^4 + sqrt(b^8 + (a*b^3 + b^4)*(a*b^3 - b^4)))/(a*b^3 - b^4))))/((a*b^2 - b^3)*a^2*b^2 + (a*b^4 - b^5)*abs(a)*abs(b)) + 2*(a^4*b - 2*a^2*b^3 - a*b^4 + 2*b^5 - a^3*abs(a)*abs(b) + 2*a*b^2*abs(a)*abs(b) - b^3*abs(a)*abs(b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(b^4 - sqrt(b^8 + (a*b^3 + b^4)*(a*b^3 - b^4)))/(a*b^3 - b^4))))/(a^2*b^4 - b^4*abs(a)*abs(b)) - (2*a^2 - 3*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^3 + (2*a^2 - 3*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^3 - 2*(2*a*tan(1/2*d*x + 1/2*c)^3 + b*tan(1/2*d*x + 1/2*c)^3 - 2*a*tan(1/2*d*x + 1/2*c) + b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*b^2))/d","B",0
296,1,140,0,1.468760," ","integrate(tan(d*x+c)^2/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{d x + c}{a} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b} + \frac{2 \, {\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^{2} - b^{2}\right)}}{\sqrt{-a^{2} + b^{2}} a b}}{d}"," ",0,"-((d*x + c)/a - log(abs(tan(1/2*d*x + 1/2*c) + 1))/b + log(abs(tan(1/2*d*x + 1/2*c) - 1))/b + 2*(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^2 - b^2)/(sqrt(-a^2 + b^2)*a*b))/d","B",0
297,1,582,0,0.447140," ","integrate(cot(d*x+c)^2/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 3 \, a^{2} b^{3} + a b^{4} - 2 \, b^{5} - a^{2} {\left| -a^{3} + a b^{2} \right|} + a b {\left| -a^{3} + a b^{2} \right|} + b^{2} {\left| -a^{3} + a 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^{2} b - b^{3} + \sqrt{{\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} + {\left(a^{2} b - b^{3}\right)}^{2}}}{a^{3} - a^{2} b - a b^{2} + b^{3}}}}\right)\right)}}{a^{2} b {\left| -a^{3} + a b^{2} \right|} - b^{3} {\left| -a^{3} + a b^{2} \right|} + {\left(a^{3} - a b^{2}\right)}^{2}} + \frac{2 \, {\left({\left(a^{2} - a b - b^{2}\right)} \sqrt{-a^{2} + b^{2}} {\left| -a^{3} + a b^{2} \right|} {\left| -a + b \right|} + {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 3 \, a^{2} b^{3} + a b^{4} - 2 \, b^{5}\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^{2} b - b^{3} - \sqrt{{\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} + {\left(a^{2} b - b^{3}\right)}^{2}}}{a^{3} - a^{2} b - a b^{2} + b^{3}}}}\right)\right)}}{{\left(a^{3} - a b^{2}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} - {\left(a^{4} b - 2 \, a^{3} b^{2} + 2 \, a b^{4} - b^{5}\right)} {\left| -a^{3} + a b^{2} \right|}} - \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*(2*(a^5 - a^4*b - 2*a^3*b^2 + 3*a^2*b^3 + a*b^4 - 2*b^5 - a^2*abs(-a^3 + a*b^2) + a*b*abs(-a^3 + a*b^2) + b^2*abs(-a^3 + a*b^2))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^2*b - b^3 + sqrt((a^3 + a^2*b - a*b^2 - b^3)*(a^3 - a^2*b - a*b^2 + b^3) + (a^2*b - b^3)^2))/(a^3 - a^2*b - a*b^2 + b^3))))/(a^2*b*abs(-a^3 + a*b^2) - b^3*abs(-a^3 + a*b^2) + (a^3 - a*b^2)^2) + 2*((a^2 - a*b - b^2)*sqrt(-a^2 + b^2)*abs(-a^3 + a*b^2)*abs(-a + b) + (a^5 - a^4*b - 2*a^3*b^2 + 3*a^2*b^3 + a*b^4 - 2*b^5)*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^2*b - b^3 - sqrt((a^3 + a^2*b - a*b^2 - b^3)*(a^3 - a^2*b - a*b^2 + b^3) + (a^2*b - b^3)^2))/(a^3 - a^2*b - a*b^2 + b^3))))/((a^3 - a*b^2)^2*(a^2 - 2*a*b + b^2) - (a^4*b - 2*a^3*b^2 + 2*a*b^4 - b^5)*abs(-a^3 + a*b^2)) - tan(1/2*d*x + 1/2*c)/(a - b) + 1/((a + b)*tan(1/2*d*x + 1/2*c)))/d","B",0
298,1,1073,0,0.607859," ","integrate(cot(d*x+c)^4/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{24 \, {\left({\left(a^{4} - a^{3} b - 2 \, a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \sqrt{-a^{2} + b^{2}} {\left| a^{5} - 2 \, a^{3} b^{2} + a b^{4} \right|} {\left| -a + b \right|} - {\left(a^{9} - a^{8} b - 4 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 7 \, a^{4} b^{5} - 4 \, a^{3} b^{6} + 6 \, a^{2} b^{7} + a b^{8} - 2 \, b^{9}\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^{4} b - 2 \, a^{2} b^{3} + b^{5} + \sqrt{{\left(a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)}^{2}}}{a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}}}}\right)\right)}}{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} + {\left(a^{6} b - 2 \, a^{5} b^{2} - a^{4} b^{3} + 4 \, a^{3} b^{4} - a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} {\left| a^{5} - 2 \, a^{3} b^{2} + a b^{4} \right|}} + \frac{24 \, {\left(a^{9} - a^{8} b - 4 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 7 \, a^{4} b^{5} - 4 \, a^{3} b^{6} + 6 \, a^{2} b^{7} + a b^{8} - 2 \, b^{9} + a^{4} {\left| a^{5} - 2 \, a^{3} b^{2} + a b^{4} \right|} - a^{3} b {\left| a^{5} - 2 \, a^{3} b^{2} + a b^{4} \right|} - 2 \, a^{2} b^{2} {\left| a^{5} - 2 \, a^{3} b^{2} + a b^{4} \right|} + 2 \, a b^{3} {\left| a^{5} - 2 \, a^{3} b^{2} + a b^{4} \right|} + b^{4} {\left| a^{5} - 2 \, a^{3} b^{2} + a b^{4} \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^{4} b - 2 \, a^{2} b^{3} + b^{5} - \sqrt{{\left(a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)}^{2}}}{a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}}}}\right)\right)}}{a^{4} b {\left| a^{5} - 2 \, a^{3} b^{2} + a b^{4} \right|} - 2 \, a^{2} b^{3} {\left| a^{5} - 2 \, a^{3} b^{2} + a b^{4} \right|} + b^{5} {\left| a^{5} - 2 \, a^{3} b^{2} + a b^{4} \right|} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)}^{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} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, 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)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 21 \, 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*(24*((a^4 - a^3*b - 2*a^2*b^2 + 2*a*b^3 + b^4)*sqrt(-a^2 + b^2)*abs(a^5 - 2*a^3*b^2 + a*b^4)*abs(-a + b) - (a^9 - a^8*b - 4*a^7*b^2 + 4*a^6*b^3 + 6*a^5*b^4 - 7*a^4*b^5 - 4*a^3*b^6 + 6*a^2*b^7 + a*b^8 - 2*b^9)*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^4*b - 2*a^2*b^3 + b^5 + sqrt((a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5)*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5) + (a^4*b - 2*a^2*b^3 + b^5)^2))/(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5))))/((a^5 - 2*a^3*b^2 + a*b^4)^2*(a^2 - 2*a*b + b^2) + (a^6*b - 2*a^5*b^2 - a^4*b^3 + 4*a^3*b^4 - a^2*b^5 - 2*a*b^6 + b^7)*abs(a^5 - 2*a^3*b^2 + a*b^4)) + 24*(a^9 - a^8*b - 4*a^7*b^2 + 4*a^6*b^3 + 6*a^5*b^4 - 7*a^4*b^5 - 4*a^3*b^6 + 6*a^2*b^7 + a*b^8 - 2*b^9 + a^4*abs(a^5 - 2*a^3*b^2 + a*b^4) - a^3*b*abs(a^5 - 2*a^3*b^2 + a*b^4) - 2*a^2*b^2*abs(a^5 - 2*a^3*b^2 + a*b^4) + 2*a*b^3*abs(a^5 - 2*a^3*b^2 + a*b^4) + b^4*abs(a^5 - 2*a^3*b^2 + a*b^4))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^4*b - 2*a^2*b^3 + b^5 - sqrt((a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5)*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5) + (a^4*b - 2*a^2*b^3 + b^5)^2))/(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5))))/(a^4*b*abs(a^5 - 2*a^3*b^2 + a*b^4) - 2*a^2*b^3*abs(a^5 - 2*a^3*b^2 + a*b^4) + b^5*abs(a^5 - 2*a^3*b^2 + a*b^4) - (a^5 - 2*a^3*b^2 + a*b^4)^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 - 15*a^2*tan(1/2*d*x + 1/2*c) + 36*a*b*tan(1/2*d*x + 1/2*c) - 21*b^2*tan(1/2*d*x + 1/2*c))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (15*a*tan(1/2*d*x + 1/2*c)^2 + 21*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
299,1,1696,0,21.611065," ","integrate(tan(d*x+c)^9/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(7 \, a^{9} - 7 \, a^{8} b - 20 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 18 \, a^{5} b^{4} - 18 \, a^{4} b^{5} - 4 \, a^{3} b^{6} + 4 \, a^{2} b^{7} - a b^{8} + b^{9}\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^{3} b^{8} - a^{2} b^{9}} + \frac{60 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{2}} - \frac{60 \, {\left(7 \, a^{6} - 20 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - 4 \, b^{6}\right)} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right)}{b^{8}} - \frac{60 \, {\left(7 \, a^{9} + 9 \, a^{8} b - 18 \, a^{7} b^{2} - 26 \, a^{6} b^{3} + 12 \, a^{5} b^{4} + 24 \, a^{4} b^{5} + 2 \, a^{3} b^{6} - 6 \, a^{2} b^{7} - 3 \, a b^{8} - b^{9} + \frac{7 \, a^{9} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{7 \, a^{8} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{20 \, a^{7} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{20 \, a^{6} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{18 \, a^{5} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{18 \, a^{4} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{4 \, a^{3} b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{4 \, a^{2} b^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{a b^{8} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b^{9} {\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^{2} b^{8}} + \frac{1029 \, a^{6} - 720 \, a^{5} b - 2940 \, a^{4} b^{2} + 1760 \, a^{3} b^{3} + 2646 \, a^{2} b^{4} - 1168 \, a b^{5} - 588 \, b^{6} + \frac{6174 \, a^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{3600 \, a^{5} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{18240 \, a^{4} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{9120 \, a^{3} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{16956 \, a^{2} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{6288 \, a b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{3888 \, b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{15435 \, a^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{7200 \, a^{5} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{46500 \, a^{4} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{18240 \, a^{3} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{44730 \, a^{2} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{12960 \, a b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{10740 \, b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{20580 \, a^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{7200 \, a^{5} b {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{62400 \, a^{4} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{17600 \, a^{3} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{60840 \, a^{2} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{11680 \, a b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{15520 \, b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15435 \, a^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{3600 \, a^{5} b {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{46500 \, a^{4} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{8160 \, a^{3} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{44730 \, a^{2} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4560 \, a b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{10740 \, b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{6174 \, a^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{720 \, a^{5} b {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{18240 \, a^{4} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{1440 \, a^{3} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{16956 \, a^{2} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{720 \, a b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3888 \, b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{1029 \, a^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{2940 \, a^{4} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{2646 \, a^{2} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{588 \, b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}}{b^{8} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{6}}}{60 \, d}"," ",0,"1/60*(60*(7*a^9 - 7*a^8*b - 20*a^7*b^2 + 20*a^6*b^3 + 18*a^5*b^4 - 18*a^4*b^5 - 4*a^3*b^6 + 4*a^2*b^7 - a*b^8 + b^9)*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^3*b^8 - a^2*b^9) + 60*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^2 - 60*(7*a^6 - 20*a^4*b^2 + 18*a^2*b^4 - 4*b^6)*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/b^8 - 60*(7*a^9 + 9*a^8*b - 18*a^7*b^2 - 26*a^6*b^3 + 12*a^5*b^4 + 24*a^4*b^5 + 2*a^3*b^6 - 6*a^2*b^7 - 3*a*b^8 - b^9 + 7*a^9*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 7*a^8*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 20*a^7*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 20*a^6*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 18*a^5*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 18*a^4*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 4*a^3*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 4*a^2*b^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - a*b^8*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b^9*(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^2*b^8) + (1029*a^6 - 720*a^5*b - 2940*a^4*b^2 + 1760*a^3*b^3 + 2646*a^2*b^4 - 1168*a*b^5 - 588*b^6 + 6174*a^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 3600*a^5*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 18240*a^4*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 9120*a^3*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 16956*a^2*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 6288*a*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 3888*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 15435*a^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 7200*a^5*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 46500*a^4*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 18240*a^3*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 44730*a^2*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 12960*a*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 10740*b^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 20580*a^6*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 7200*a^5*b*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 62400*a^4*b^2*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 17600*a^3*b^3*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 60840*a^2*b^4*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 11680*a*b^5*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 - 15520*b^6*(cos(d*x + c) - 1)^3/(cos(d*x + c) + 1)^3 + 15435*a^6*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 3600*a^5*b*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 46500*a^4*b^2*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 8160*a^3*b^3*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 44730*a^2*b^4*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 4560*a*b^5*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 - 10740*b^6*(cos(d*x + c) - 1)^4/(cos(d*x + c) + 1)^4 + 6174*a^6*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 720*a^5*b*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 18240*a^4*b^2*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 1440*a^3*b^3*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 16956*a^2*b^4*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 720*a*b^5*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 - 3888*b^6*(cos(d*x + c) - 1)^5/(cos(d*x + c) + 1)^5 + 1029*a^6*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 2940*a^4*b^2*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 + 2646*a^2*b^4*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6 - 588*b^6*(cos(d*x + c) - 1)^6/(cos(d*x + c) + 1)^6)/(b^8*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^6))/d","B",0
300,-2,0,0,0.000000," ","integrate(tan(d*x+c)^7/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Evaluation time: 5.9Unable to divide, perhaps due to rounding error%%%{268435456,[7,8,8]%%%}+%%%{-2147483648,[7,7,9]%%%}+%%%{7516192768,[7,6,10]%%%}+%%%{-15032385536,[7,5,11]%%%}+%%%{18790481920,[7,4,12]%%%}+%%%{-15032385536,[7,3,13]%%%}+%%%{7516192768,[7,2,14]%%%}+%%%{-2147483648,[7,1,15]%%%}+%%%{268435456,[7,0,16]%%%}+%%%{-805306368,[6,8,8]%%%}+%%%{7516192768,[6,7,9]%%%}+%%%{-30064771072,[6,6,10]%%%}+%%%{67645734912,[6,5,11]%%%}+%%%{-93952409600,[6,4,12]%%%}+%%%{82678120448,[6,3,13]%%%}+%%%{-45097156608,[6,2,14]%%%}+%%%{13958643712,[6,1,15]%%%}+%%%{-1879048192,[6,0,16]%%%}+%%%{268435456,[5,8,8]%%%}+%%%{-6442450944,[5,7,9]%%%}+%%%{38654705664,[5,6,10]%%%}+%%%{-111669149696,[5,5,11]%%%}+%%%{185220464640,[5,4,12]%%%}+%%%{-186831077376,[5,3,13]%%%}+%%%{113816633344,[5,2,14]%%%}+%%%{-38654705664,[5,1,15]%%%}+%%%{5637144576,[5,0,16]%%%}+%%%{1342177280,[4,8,8]%%%}+%%%{-5368709120,[4,7,9]%%%}+%%%{-5368709120,[4,6,10]%%%}+%%%{69793218560,[4,5,11]%%%}+%%%{-174483046400,[4,4,12]%%%}+%%%{220117073920,[4,3,13]%%%}+%%%{-155692564480,[4,2,14]%%%}+%%%{59055800320,[4,1,15]%%%}+%%%{-9395240960,[4,0,16]%%%}+%%%{-1342177280,[3,8,8]%%%}+%%%{10737418240,[3,7,9]%%%}+%%%{-26843545600,[3,6,10]%%%}+%%%{10737418240,[3,5,11]%%%}+%%%{67108864000,[3,4,12]%%%}+%%%{-139586437120,[3,3,13]%%%}+%%%{123480309760,[3,2,14]%%%}+%%%{-53687091200,[3,1,15]%%%}+%%%{9395240960,[3,0,16]%%%}+%%%{-268435456,[2,8,8]%%%}+%%%{-3221225472,[2,7,9]%%%}+%%%{19327352832,[2,6,10]%%%}+%%%{-33285996544,[2,5,11]%%%}+%%%{8053063680,[2,4,12]%%%}+%%%{41875931136,[2,3,13]%%%}+%%%{-55834574848,[2,2,14]%%%}+%%%{28991029248,[2,1,15]%%%}+%%%{-5637144576,[2,0,16]%%%}+%%%{805306368,[1,8,8]%%%}+%%%{-2147483648,[1,7,9]%%%}+%%%{-2147483648,[1,6,10]%%%}+%%%{12884901888,[1,5,11]%%%}+%%%{-13421772800,[1,4,12]%%%}+%%%{-2147483648,[1,3,13]%%%}+%%%{12884901888,[1,2,14]%%%}+%%%{-8589934592,[1,1,15]%%%}+%%%{1879048192,[1,0,16]%%%}+%%%{-268435456,[0,8,8]%%%}+%%%{1073741824,[0,7,9]%%%}+%%%{-1073741824,[0,6,10]%%%}+%%%{-1073741824,[0,5,11]%%%}+%%%{2684354560,[0,4,12]%%%}+%%%{-1073741824,[0,3,13]%%%}+%%%{-1073741824,[0,2,14]%%%}+%%%{1073741824,[0,1,15]%%%}+%%%{-268435456,[0,0,16]%%%} / %%%{1,[7,2,0]%%%}+%%%{-2,[7,1,1]%%%}+%%%{1,[7,0,2]%%%}+%%%{-3,[6,2,0]%%%}+%%%{10,[6,1,1]%%%}+%%%{-7,[6,0,2]%%%}+%%%{1,[5,2,0]%%%}+%%%{-18,[5,1,1]%%%}+%%%{21,[5,0,2]%%%}+%%%{5,[4,2,0]%%%}+%%%{10,[4,1,1]%%%}+%%%{-35,[4,0,2]%%%}+%%%{-5,[3,2,0]%%%}+%%%{10,[3,1,1]%%%}+%%%{35,[3,0,2]%%%}+%%%{-1,[2,2,0]%%%}+%%%{-18,[2,1,1]%%%}+%%%{-21,[2,0,2]%%%}+%%%{3,[1,2,0]%%%}+%%%{10,[1,1,1]%%%}+%%%{7,[1,0,2]%%%}+%%%{-1,[0,2,0]%%%}+%%%{-2,[0,1,1]%%%}+%%%{-1,[0,0,2]%%%} Error: Bad Argument Value","F(-2)",0
301,1,568,0,6.544129," ","integrate(tan(d*x+c)^5/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(3 \, a^{5} - 3 \, a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} - a b^{4} + 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^{3} b^{4} - a^{2} b^{5}} + \frac{2 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{2}} - \frac{2 \, {\left(3 \, a^{2} - 2 \, b^{2}\right)} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right)}{b^{4}} + \frac{9 \, a^{2} - 8 \, a b - 6 \, b^{2} + \frac{18 \, 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{16 \, b^{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{6 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{b^{4} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{2}} - \frac{2 \, {\left(3 \, a^{5} + 5 \, a^{4} b - 4 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5} + \frac{3 \, a^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{3 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, a^{3} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b^{5} {\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^{2} b^{4}}}{2 \, d}"," ",0,"1/2*(2*(3*a^5 - 3*a^4*b - 2*a^3*b^2 + 2*a^2*b^3 - a*b^4 + 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^3*b^4 - a^2*b^5) + 2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^2 - 2*(3*a^2 - 2*b^2)*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/b^4 + (9*a^2 - 8*a*b - 6*b^2 + 18*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) - 16*b^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 - 6*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/(b^4*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^2) - 2*(3*a^5 + 5*a^4*b - 4*a^2*b^3 - 3*a*b^4 - b^5 + 3*a^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 3*a^4*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*a^3*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*a^2*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - a*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b^5*(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^2*b^4))/d","B",0
302,1,313,0,1.026508," ","integrate(tan(d*x+c)^3/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{{\left(a^{3} - a^{2} b + a b^{2} - 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^{3} b^{2} - a^{2} b^{3}} - \frac{\log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{2}} - \frac{\log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right)}{b^{2}} - \frac{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + \frac{a^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{a^{2} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{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}}{{\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^{2} b^{2}}}{d}"," ",0,"((a^3 - a^2*b + a*b^2 - 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^3*b^2 - a^2*b^3) - log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^2 - log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/b^2 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3 + a^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - a^2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 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))/((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))/d","B",0
303,1,238,0,1.412070," ","integrate(tan(d*x+c)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{{\left(a - b\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^{3} - a^{2} b} - \frac{a^{2} - 2 \, a b - b^{2} + \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}}{{\left(a^{3} - a^{2} b\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)}} - \frac{\log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{2}}}{d}"," ",0,"-((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^3 - a^2*b) - (a^2 - 2*a*b - b^2 + 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))/((a^3 - a^2*b)*(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))) - log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^2)/d","B",0
304,1,303,0,0.283071," ","integrate(cot(d*x+c)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(3 \, a^{2} b^{2} - b^{4}\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} - 2 \, a^{4} b^{2} + a^{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{2 \, {\left(3 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4} + \frac{3 \, a^{2} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{{\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{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)}} + \frac{2 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{2}}}{2 \, d}"," ",0,"-1/2*(2*(3*a^2*b^2 - b^4)*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 - 2*a^4*b^2 + a^2*b^4) - log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a^2 + 2*a*b + b^2) - 2*(3*a^2*b^2 + 4*a*b^3 + b^4 + 3*a^2*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((a^5 + a^4*b - a^3*b^2 - a^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))) + 2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^2)/d","B",0
305,1,656,0,1.930498," ","integrate(cot(d*x+c)^3/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\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^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{8 \, {\left(5 \, a^{2} b^{4} - 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} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}} - \frac{a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3} + \frac{3 \, a^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{3 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{3 \, a^{3} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{2} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{20 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{4 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2 \, a^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, a^{4} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, 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{12 \, 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{4 \, a b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{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)}} - \frac{8 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{2}}}{8 \, d}"," ",0,"-1/8*(4*(a + 2*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*(5*a^2*b^4 - 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 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6) - (a^5 - a^4*b - a^3*b^2 + a^2*b^3 + 3*a^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 3*a^4*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 3*a^3*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 3*a^2*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 20*a*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 4*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*a^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 4*a^4*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 2*a^3*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 12*a^2*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 4*a*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 4*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((a^6 - 2*a^4*b^2 + a^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)) - 8*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^2)/d","B",0
306,1,795,0,1.192019," ","integrate(cot(d*x+c)^5/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{8 \, {\left(4 \, a^{2} + 13 \, a b + 12 \, 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{64 \, {\left(7 \, a^{2} b^{6} - 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} - 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} - 4 \, a^{4} b^{6} + a^{2} b^{8}} - \frac{\frac{12 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{32 \, a b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{20 \, 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{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{12 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{32 \, a b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{20 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{48 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{156 \, a b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{144 \, 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{64 \, {\left(7 \, a^{3} b^{6} + 5 \, a^{2} b^{7} - 3 \, a b^{8} - b^{9} + \frac{7 \, a^{3} b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{7 \, a^{2} b^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{a b^{8} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b^{9} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{{\left(a^{10} - 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} - 4 \, a^{4} b^{6} + a^{2} b^{8}\right)} {\left(a + 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)}} - \frac{64 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{2}}}{64 \, d}"," ",0,"1/64*(8*(4*a^2 + 13*a*b + 12*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) - 64*(7*a^2*b^6 - 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 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8) - (12*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 32*a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 20*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 - 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 + 12*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 32*a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 20*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 48*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 156*a*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 144*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) + 64*(7*a^3*b^6 + 5*a^2*b^7 - 3*a*b^8 - b^9 + 7*a^3*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 7*a^2*b^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - a*b^8*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b^9*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*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))) - 64*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^2)/d","B",0
307,1,411,0,4.335530," ","integrate(tan(d*x+c)^6/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)}}{a^{2}} + \frac{3 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{5}} - \frac{3 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{5}} + \frac{6 \, {\left(a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, 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 b^{4}} - \frac{6 \, {\left(4 \, a^{6} - 7 \, a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-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^{2} b^{5}} + \frac{2 \, {\left(9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, 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) - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, 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)}^{3} b^{4}}}{3 \, d}"," ",0,"-1/3*(3*(d*x + c)/a^2 + 3*(4*a^3 - 5*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^5 - 3*(4*a^3 - 5*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^5 + 6*(a^4*tan(1/2*d*x + 1/2*c) - 2*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*b^4) - 6*(4*a^6 - 7*a^4*b^2 + 2*a^2*b^4 + b^6)*(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^2*b^5) + 2*(9*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*a*b*tan(1/2*d*x + 1/2*c)^5 - 6*b^2*tan(1/2*d*x + 1/2*c)^5 - 18*a^2*tan(1/2*d*x + 1/2*c)^3 + 16*b^2*tan(1/2*d*x + 1/2*c)^3 + 9*a^2*tan(1/2*d*x + 1/2*c) - 3*a*b*tan(1/2*d*x + 1/2*c) - 6*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*b^4))/d","B",0
308,1,294,0,1.552214," ","integrate(tan(d*x+c)^4/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{d x + c}{a^{2}} - \frac{2 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{3}} + \frac{2 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{3}} - \frac{2 \, {\left(2 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 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} - 2 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 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)\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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} a b^{2}} + \frac{2 \, {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-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^{2} b^{3}}}{d}"," ",0,"((d*x + c)/a^2 - 2*a*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^3 + 2*a*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^3 - 2*(2*a^2*tan(1/2*d*x + 1/2*c)^3 - a*b*tan(1/2*d*x + 1/2*c)^3 - b^2*tan(1/2*d*x + 1/2*c)^3 - 2*a^2*tan(1/2*d*x + 1/2*c) - a*b*tan(1/2*d*x + 1/2*c) + b^2*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b)*a*b^2) + 2*(2*a^4 - a^2*b^2 - b^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)))/(sqrt(-a^2 + b^2)*a^2*b^3))/d","B",0
309,1,144,0,0.663150," ","integrate(tan(d*x+c)^2/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-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)} b}{\sqrt{-a^{2} + b^{2}} a^{2}} - \frac{d x + c}{a^{2}} - \frac{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}}{d}"," ",0,"(2*(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)))*b/(sqrt(-a^2 + b^2)*a^2) - (d*x + c)/a^2 - 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))/d","A",0
310,1,332,0,0.308742," ","integrate(cot(d*x+c)^2/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(4 \, 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)}}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{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^{4} \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)^{2} + 3 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{4} + a^{3} b + a^{2} b^{2} - a b^{3}}{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{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)}} + \frac{2 \, {\left(d x + c\right)}}{a^{2}}}{2 \, d}"," ",0,"-1/2*(4*(4*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)))/((a^6 - 2*a^4*b^2 + a^2*b^4)*sqrt(-a^2 + b^2)) - tan(1/2*d*x + 1/2*c)/(a^2 - 2*a*b + b^2) + (a^4*tan(1/2*d*x + 1/2*c)^2 - 3*a^3*b*tan(1/2*d*x + 1/2*c)^2 + 3*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - a*b^3*tan(1/2*d*x + 1/2*c)^2 + 4*b^4*tan(1/2*d*x + 1/2*c)^2 - a^4 + a^3*b + a^2*b^2 - a*b^3)/((a^5 - 2*a^3*b^2 + a*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))) + 2*(d*x + c)/a^2)/d","A",0
311,1,487,0,0.362648," ","integrate(cot(d*x+c)^4/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{48 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}} - \frac{48 \, {\left(6 \, 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)}}{{\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} 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} - 15 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 126 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, 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{24 \, {\left(d x + c\right)}}{a^{2}} - \frac{15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 27 \, 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*b^6*tan(1/2*d*x + 1/2*c)/((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) - 48*(6*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)))/((a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*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 - 15*a^4*tan(1/2*d*x + 1/2*c) + 72*a^3*b*tan(1/2*d*x + 1/2*c) - 126*a^2*b^2*tan(1/2*d*x + 1/2*c) + 96*a*b^3*tan(1/2*d*x + 1/2*c) - 27*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) - 24*(d*x + c)/a^2 - (15*a*tan(1/2*d*x + 1/2*c)^2 + 27*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
312,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{\frac{5}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^(5/2)/(b*sec(d*x + c) + a), x)","F",0
313,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^(3/2)/(b*sec(d*x + c) + a), x)","F",0
314,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sqrt{e \tan\left(d x + c\right)}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*tan(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
315,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/(e*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{e \tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*sqrt(e*tan(d*x + c))), x)","F",0
316,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/(e*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*(e*tan(d*x + c))^(3/2)), x)","F",0
317,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/(e*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \left(e \tan\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*(e*tan(d*x + c))^(5/2)), x)","F",0
318,1,966,0,3.761418," ","integrate((a+b*sec(d*x+c))^(1/2)*tan(d*x+c)^5,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{315 \, a \arctan\left(-\frac{\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b} + \sqrt{a - b}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} - \frac{2 \, {\left(315 \, {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)}^{8} a - 3150 \, {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)}^{7} \sqrt{a - b} a + 210 \, {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)}^{6} {\left(39 \, a^{2} - 5 \, a b - 32 \, b^{2}\right)} - 630 \, {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)}^{5} {\left(9 \, a^{2} + 15 \, a b - 16 \, b^{2}\right)} \sqrt{a - b} - 252 \, {\left(25 \, a^{3} - 37 \, a^{2} b + 80 \, a b^{2} - 72 \, b^{3}\right)} {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)}^{4} + 945 \, a^{5} + 3864 \, a^{4} b + 2562 \, a^{3} b^{2} + 2448 \, a^{2} b^{3} - 1083 \, a b^{4} + 224 \, b^{5} + 42 \, {\left(255 \, a^{3} + 2 \, a^{2} b + 655 \, a b^{2} - 288 \, b^{3}\right)} {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)}^{3} \sqrt{a - b} - 18 \, {\left(175 \, a^{4} - 483 \, a^{3} b + 1113 \, a^{2} b^{2} - 773 \, a b^{3} + 448 \, b^{4}\right)} {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)}^{2} - 18 \, {\left(105 \, a^{4} + 637 \, a^{3} b + 203 \, a^{2} b^{2} + 447 \, a b^{3} - 112 \, b^{4}\right)} {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)} \sqrt{a - b}\right)}}{{\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b} - \sqrt{a - b}\right)}^{9}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{315 \, d}"," ",0,"2/315*(315*a*arctan(-1/2*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b) + sqrt(a - b))/sqrt(-a))/sqrt(-a) - 2*(315*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))^8*a - 3150*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))^7*sqrt(a - b)*a + 210*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))^6*(39*a^2 - 5*a*b - 32*b^2) - 630*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))^5*(9*a^2 + 15*a*b - 16*b^2)*sqrt(a - b) - 252*(25*a^3 - 37*a^2*b + 80*a*b^2 - 72*b^3)*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))^4 + 945*a^5 + 3864*a^4*b + 2562*a^3*b^2 + 2448*a^2*b^3 - 1083*a*b^4 + 224*b^5 + 42*(255*a^3 + 2*a^2*b + 655*a*b^2 - 288*b^3)*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))^3*sqrt(a - b) - 18*(175*a^4 - 483*a^3*b + 1113*a^2*b^2 - 773*a*b^3 + 448*b^4)*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))^2 - 18*(105*a^4 + 637*a^3*b + 203*a^2*b^2 + 447*a*b^3 - 112*b^4)*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))*sqrt(a - b))/(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b) - sqrt(a - b))^9)*sgn(cos(d*x + c))/d","B",0
319,1,539,0,2.167960," ","integrate((a+b*sec(d*x+c))^(1/2)*tan(d*x+c)^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{15 \, a \arctan\left(-\frac{\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b} + \sqrt{a - b}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} - \frac{2 \, {\left(15 \, {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)}^{4} a - 30 \, {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)}^{3} {\left(a + 2 \, b\right)} \sqrt{a - b} + 20 \, {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)}^{2} {\left(4 \, a b - 3 \, b^{2}\right)} - 15 \, a^{3} - 10 \, a^{2} b - 35 \, a b^{2} + 12 \, b^{3} + 10 \, {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)} {\left(3 \, a^{2} - a b + 6 \, b^{2}\right)} \sqrt{a - b}\right)}}{{\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b} - \sqrt{a - b}\right)}^{5}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{15 \, d}"," ",0,"-2/15*(15*a*arctan(-1/2*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b) + sqrt(a - b))/sqrt(-a))/sqrt(-a) - 2*(15*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))^4*a - 30*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))^3*(a + 2*b)*sqrt(a - b) + 20*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))^2*(4*a*b - 3*b^2) - 15*a^3 - 10*a^2*b - 35*a*b^2 + 12*b^3 + 10*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))*(3*a^2 - a*b + 6*b^2)*sqrt(a - b))/(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b) - sqrt(a - b))^5)*sgn(cos(d*x + c))/d","B",0
320,1,185,0,0.411889," ","integrate((a+b*sec(d*x+c))^(1/2)*tan(d*x+c),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{a \arctan\left(-\frac{\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b} + \sqrt{a - b}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} - \frac{2 \, b}{\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b} - \sqrt{a - b}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{d}"," ",0,"2*(a*arctan(-1/2*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b) + sqrt(a - b))/sqrt(-a))/sqrt(-a) - 2*b/(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b) - sqrt(a - b)))*sgn(cos(d*x + c))/d","B",0
321,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
322,1,514,0,1.886923," ","integrate(cot(d*x+c)^3*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{{\left(\frac{16 \, a \arctan\left(-\frac{\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b} + \sqrt{a - b}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} - \frac{2 \, {\left(4 \, a + 3 \, b\right)} \arctan\left(-\frac{\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}}{\sqrt{-a - b}}\right)}{\sqrt{-a - b}} + \frac{{\left(4 \, a - 3 \, b\right)} \log\left({\left| {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)} {\left(a - b\right)} - \sqrt{a - b} a \right|}\right)}{\sqrt{a - b}} + \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b} - \frac{2 \, {\left({\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)} a - {\left(a + b\right)} \sqrt{a - b}\right)}}{{\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)}^{2} - a - b}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{8 \, d}"," ",0,"1/8*(16*a*arctan(-1/2*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b) + sqrt(a - b))/sqrt(-a))/sqrt(-a) - 2*(4*a + 3*b)*arctan(-(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))/sqrt(-a - b))/sqrt(-a - b) + (4*a - 3*b)*log(abs((sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))*(a - b) - sqrt(a - b)*a))/sqrt(a - b) + sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b) - 2*((sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))*a - (a + b)*sqrt(a - b))/((sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))^2 - a - b))*sgn(cos(d*x + c))/d","B",0
323,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)*tan(d*x+c)^2,x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*tan(d*x + c)^2, x)","F",0
324,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a), x)","F",0
325,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*cot(d*x + c)^2, x)","F",0
326,1,722,0,6.082462," ","integrate(tan(d*x+c)^5/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{105 \, \arctan\left(-\frac{\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b} + \sqrt{a - b}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{2 \, {\left(105 \, {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)}^{6} - 840 \, {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)}^{5} \sqrt{a - b} + 35 \, {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)}^{4} {\left(27 \, a - 23 \, b\right)} + 280 \, {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)}^{3} {\left(3 \, a + 4 \, b\right)} \sqrt{a - b} - 21 \, {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)}^{2} {\left(65 \, a^{2} - 2 \, a b - 15 \, b^{2}\right)} + 315 \, a^{3} + 707 \, a^{2} b - 7 \, a b^{2} - 55 \, b^{3} - 56 \, {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)} {\left(19 \, a b + 5 \, b^{2}\right)} \sqrt{a - b}\right)}}{{\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b} - \sqrt{a - b}\right)}^{7} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{105 \, d}"," ",0,"-2/105*(105*arctan(-1/2*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b) + sqrt(a - b))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 2*(105*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))^6 - 840*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))^5*sqrt(a - b) + 35*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))^4*(27*a - 23*b) + 280*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))^3*(3*a + 4*b)*sqrt(a - b) - 21*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))^2*(65*a^2 - 2*a*b - 15*b^2) + 315*a^3 + 707*a^2*b - 7*a*b^2 - 55*b^3 - 56*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))*(19*a*b + 5*b^2)*sqrt(a - b))/((sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b) - sqrt(a - b))^7*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
327,1,288,0,1.437740," ","integrate(tan(d*x+c)^3/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{3 \, \arctan\left(-\frac{\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b} + \sqrt{a - b}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{2 \, {\left(3 \, {\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}\right)}^{2} - 3 \, a - b\right)}}{{\left(\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b} - \sqrt{a - b}\right)}^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{3 \, d}"," ",0,"2/3*(3*arctan(-1/2*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b) + sqrt(a - b))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 2*(3*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b))^2 - 3*a - b)/((sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b) - sqrt(a - b))^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
328,1,109,0,1.611107," ","integrate(tan(d*x+c)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 \, \arctan\left(-\frac{\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b} + \sqrt{a - b}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} d \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}"," ",0,"-2*arctan(-1/2*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b) + sqrt(a - b))/sqrt(-a))/(sqrt(-a)*d*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))","B",0
329,-2,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*t_nostep+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Discontinuities at zeroes of cos(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Evaluation time: 0.58Error: Bad Argument Type","F(-2)",0
330,-2,0,0,0.000000," ","integrate(cot(d*x+c)^3/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*t_nostep+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Discontinuities at zeroes of cos(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Evaluation time: 1.26Error: Bad Argument Type","F(-2)",0
331,0,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{4}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^4/sqrt(b*sec(d*x + c) + a), x)","F",0
332,0,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
333,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*sec(d*x + c) + a), x)","F",0
334,0,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
335,0,0,0,0.000000," ","integrate(tan(d*x+c)^5/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{5}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^5/(b*sec(d*x + c) + a)^(3/2), x)","F",0
336,1,307,0,2.059033," ","integrate(tan(d*x+c)^3/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{\frac{{\left(2 \, a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - a^{2} b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - a b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{2} b^{2}} - \frac{2 \, a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) + a^{2} b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - a b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}{a^{2} b^{2}}}{\sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b}} + \frac{\arctan\left(-\frac{\sqrt{a - b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{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 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b} + \sqrt{a - b}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{d}"," ",0,"2*(((2*a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - a^2*b*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - a*b^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2/(a^2*b^2) - (2*a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) + a^2*b*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - a*b^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/(a^2*b^2))/sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b) + arctan(-1/2*(sqrt(a - b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b) + sqrt(a - b))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
337,-2,0,0,0.000000," ","integrate(tan(d*x+c)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*t_nostep+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Discontinuities at zeroes of cos(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Evaluation time: 0.8Unable to divide, perhaps due to rounding error%%%{%%%{4,[2,2]%%%}+%%%{-4,[1,3]%%%},[2,1]%%%}+%%%{%%{[%%%{8,[2,2]%%%}+%%%{8,[1,3]%%%},0]:[1,0,%%%{-1,[1,0]%%%}+%%%{1,[0,1]%%%}]%%},[1,1]%%%}+%%%{%%%{4,[3,2]%%%}+%%%{8,[2,3]%%%}+%%%{4,[1,4]%%%},[0,1]%%%} / %%%{%%%{1,[2,0]%%%}+%%%{-2,[1,1]%%%}+%%%{1,[0,2]%%%},[2,0]%%%}+%%%{%%{[%%%{2,[2,0]%%%}+%%%{-2,[0,2]%%%},0]:[1,0,%%%{-1,[1,0]%%%}+%%%{1,[0,1]%%%}]%%},[1,0]%%%}+%%%{%%%{1,[3,0]%%%}+%%%{1,[2,1]%%%}+%%%{-1,[1,2]%%%}+%%%{-1,[0,3]%%%},[0,0]%%%} Error: Bad Argument Value","F(-2)",0
338,-2,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*t_nostep+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Discontinuities at zeroes of cos(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Evaluation time: 0.88Error: Bad Argument Type","F(-2)",0
339,-2,0,0,0.000000," ","integrate(cot(d*x+c)^3/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*t_nostep+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Discontinuities at zeroes of cos(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Evaluation time: 1.2Unable to divide, perhaps due to rounding error%%%{%%%{32,[2,6]%%%}+%%%{-32,[1,7]%%%},[6,1]%%%}+%%%{%%{[%%%{64,[2,6]%%%}+%%%{64,[1,7]%%%},0]:[1,0,%%%{-1,[1,0]%%%}+%%%{1,[0,1]%%%}]%%},[5,1]%%%}+%%%{%%%{-32,[3,6]%%%}+%%%{64,[2,7]%%%}+%%%{96,[1,8]%%%},[4,1]%%%}+%%%{%%{[%%%{-128,[3,6]%%%}+%%%{-256,[2,7]%%%}+%%%{-128,[1,8]%%%},0]:[1,0,%%%{-1,[1,0]%%%}+%%%{1,[0,1]%%%}]%%},[3,1]%%%}+%%%{%%%{-32,[4,6]%%%}+%%%{-160,[3,7]%%%}+%%%{-224,[2,8]%%%}+%%%{-96,[1,9]%%%},[2,1]%%%}+%%%{%%{[%%%{64,[4,6]%%%}+%%%{192,[3,7]%%%}+%%%{192,[2,8]%%%}+%%%{64,[1,9]%%%},0]:[1,0,%%%{-1,[1,0]%%%}+%%%{1,[0,1]%%%}]%%},[1,1]%%%}+%%%{%%%{32,[5,6]%%%}+%%%{128,[4,7]%%%}+%%%{192,[3,8]%%%}+%%%{128,[2,9]%%%}+%%%{32,[1,10]%%%},[0,1]%%%} / %%%{%%%{1,[2,0]%%%}+%%%{-2,[1,1]%%%}+%%%{1,[0,2]%%%},[6,0]%%%}+%%%{%%{[%%%{2,[2,0]%%%}+%%%{-2,[0,2]%%%},0]:[1,0,%%%{-1,[1,0]%%%}+%%%{1,[0,1]%%%}]%%},[5,0]%%%}+%%%{%%%{-1,[3,0]%%%}+%%%{3,[2,1]%%%}+%%%{1,[1,2]%%%}+%%%{-3,[0,3]%%%},[4,0]%%%}+%%%{%%{[%%%{-4,[3,0]%%%}+%%%{-4,[2,1]%%%}+%%%{4,[1,2]%%%}+%%%{4,[0,3]%%%},0]:[1,0,%%%{-1,[1,0]%%%}+%%%{1,[0,1]%%%}]%%},[3,0]%%%}+%%%{%%%{-1,[4,0]%%%}+%%%{-4,[3,1]%%%}+%%%{-2,[2,2]%%%}+%%%{4,[1,3]%%%}+%%%{3,[0,4]%%%},[2,0]%%%}+%%%{%%{[%%%{2,[4,0]%%%}+%%%{4,[3,1]%%%}+%%%{-4,[1,3]%%%}+%%%{-2,[0,4]%%%},0]:[1,0,%%%{-1,[1,0]%%%}+%%%{1,[0,1]%%%}]%%},[1,0]%%%}+%%%{%%%{1,[5,0]%%%}+%%%{3,[4,1]%%%}+%%%{2,[3,2]%%%}+%%%{-2,[2,3]%%%}+%%%{-3,[1,4]%%%}+%%%{-1,[0,5]%%%},[0,0]%%%} Error: Bad Argument Value","F(-2)",0
340,0,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{4}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^4/(b*sec(d*x + c) + a)^(3/2), x)","F",0
341,0,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
342,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(-3/2), x)","F",0
343,0,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
344,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^3*(d*tan(f*x+e))^n,x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{3} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^3*(d*tan(f*x + e))^n, x)","F",0
345,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^2*(d*tan(f*x+e))^n,x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{2} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^2*(d*tan(f*x + e))^n, x)","F",0
346,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))*(d*tan(f*x+e))^n,x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)*(d*tan(f*x + e))^n, x)","F",0
347,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n/(a+b*sec(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \tan\left(f x + e\right)\right)^{n}}{b \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*tan(f*x + e))^n/(b*sec(f*x + e) + a), x)","F",0
348,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(e*tan(d*x+c))^m,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*(e*tan(d*x + c))^m, x)","F",0
349,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)*(e*tan(d*x+c))^m,x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*(e*tan(d*x + c))^m, x)","F",0
350,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^m/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{m}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^m/sqrt(b*sec(d*x + c) + a), x)","F",0
351,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^m/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\left(e \tan\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*tan(d*x + c))^m/(b*sec(d*x + c) + a)^(3/2), x)","F",0
352,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*(e*tan(d*x+c))^m,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*(e*tan(d*x + c))^m, x)","F",0
353,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*tan(d*x+c)^5,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*tan(d*x + c)^5, x)","F",0
354,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*tan(d*x+c)^3,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*tan(d*x + c)^3, x)","F",0
355,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*tan(d*x+c),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*tan(d*x + c), x)","F",0
356,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*cot(d*x + c), x)","F",0
357,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*cot(d*x + c)^3, x)","F",0
358,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*tan(d*x+c)^4,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*tan(d*x + c)^4, x)","F",0
359,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*tan(d*x+c)^2,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*tan(d*x + c)^2, x)","F",0
360,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*cot(d*x + c)^2, x)","F",0
361,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*cot(d*x + c)^4, x)","F",0
362,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*tan(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*tan(d*x + c)^(3/2), x)","F",0
363,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*tan(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \sqrt{\tan\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*sqrt(tan(d*x + c)), x)","F",0
364,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n/tan(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{n}}{\sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n/sqrt(tan(d*x + c)), x)","F",0
365,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n/tan(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{n}}{\tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n/tan(d*x + c)^(3/2), x)","F",0
