1,1,110,0,0.462529," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{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(9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 49 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 31 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 39 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(9*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*(9*a*tan(1/2*d*x + 1/2*c)^7 - 49*a*tan(1/2*d*x + 1/2*c)^5 + 31*a*tan(1/2*d*x + 1/2*c)^3 - 39*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
2,1,96,0,0.498717," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(3*a*tan(1/2*d*x + 1/2*c)^5 - 4*a*tan(1/2*d*x + 1/2*c)^3 + 9*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
3,1,80,0,0.434286," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{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*(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","A",0
4,1,63,0,0.370040," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"(a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*a*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","B",0
5,1,49,0,0.338025," ","integrate(a+a*sec(d*x+c),x, algorithm=""giac"")","a x + \frac{a {\left(\log\left({\left| \frac{1}{\sin\left(d x + c\right)} + \sin\left(d x + c\right) + 2 \right|}\right) - \log\left({\left| \frac{1}{\sin\left(d x + c\right)} + \sin\left(d x + c\right) - 2 \right|}\right)\right)}}{4 \, d}"," ",0,"a*x + 1/4*a*(log(abs(1/sin(d*x + c) + sin(d*x + c) + 2)) - log(abs(1/sin(d*x + c) + sin(d*x + c) - 2)))/d","B",0
6,1,39,0,0.391109," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} a + \frac{2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}}{d}"," ",0,"((d*x + c)*a + 2*a*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","B",0
7,1,56,0,0.362880," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} a + \frac{2 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((d*x + c)*a + 2*(a*tan(1/2*d*x + 1/2*c)^3 + 3*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
8,1,72,0,0.389863," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} a + \frac{2 \, {\left(3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(d*x + c)*a + 2*(3*a*tan(1/2*d*x + 1/2*c)^5 + 4*a*tan(1/2*d*x + 1/2*c)^3 + 9*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
9,1,86,0,0.381390," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{9 \, {\left(d x + c\right)} a + \frac{2 \, {\left(9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 49 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 31 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 39 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(9*(d*x + c)*a + 2*(9*a*tan(1/2*d*x + 1/2*c)^7 + 49*a*tan(1/2*d*x + 1/2*c)^5 + 31*a*tan(1/2*d*x + 1/2*c)^3 + 39*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
10,1,138,0,0.473652," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{15 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, 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} - 70 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 144 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 90 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 65 \, 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}}}{20 \, d}"," ",0,"1/20*(15*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*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 - 70*a^2*tan(1/2*d*x + 1/2*c)^7 + 144*a^2*tan(1/2*d*x + 1/2*c)^5 - 90*a^2*tan(1/2*d*x + 1/2*c)^3 + 65*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
11,1,122,0,0.478738," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{21 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 21 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(21 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 77 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 83 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 75 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(21*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 21*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(21*a^2*tan(1/2*d*x + 1/2*c)^7 - 77*a^2*tan(1/2*d*x + 1/2*c)^5 + 83*a^2*tan(1/2*d*x + 1/2*c)^3 - 75*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
12,1,106,0,0.548603," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{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{2 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 8 \, a^{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)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(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)) - 2*(3*a^2*tan(1/2*d*x + 1/2*c)^5 - 8*a^2*tan(1/2*d*x + 1/2*c)^3 + 9*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
13,1,90,0,0.478113," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{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{2 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(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)) - 2*(3*a^2*tan(1/2*d*x + 1/2*c)^3 - 5*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
14,1,79,0,0.375869," ","integrate((a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{{\left(d x + c\right)} a^{2} + 2 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"((d*x + c)*a^2 + 2*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","B",0
15,1,79,0,0.409624," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} a^{2} + a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}}{d}"," ",0,"(2*(d*x + c)*a^2 + a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","B",0
16,1,64,0,0.473308," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} a^{2} + \frac{2 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(3*(d*x + c)*a^2 + 2*(3*a^2*tan(1/2*d*x + 1/2*c)^3 + 5*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
17,1,80,0,1.800170," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} a^{2} + \frac{2 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 8 \, a^{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)\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 + 2*(3*a^2*tan(1/2*d*x + 1/2*c)^5 + 8*a^2*tan(1/2*d*x + 1/2*c)^3 + 9*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
18,1,96,0,3.918480," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{21 \, {\left(d x + c\right)} a^{2} + \frac{2 \, {\left(21 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 77 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 83 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 75 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(21*(d*x + c)*a^2 + 2*(21*a^2*tan(1/2*d*x + 1/2*c)^7 + 77*a^2*tan(1/2*d*x + 1/2*c)^5 + 83*a^2*tan(1/2*d*x + 1/2*c)^3 + 75*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
19,1,112,0,1.220698," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{15 \, {\left(d x + c\right)} a^{2} + \frac{2 \, {\left(15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 70 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 144 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 90 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 65 \, 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}}}{20 \, d}"," ",0,"1/20*(15*(d*x + c)*a^2 + 2*(15*a^2*tan(1/2*d*x + 1/2*c)^9 + 70*a^2*tan(1/2*d*x + 1/2*c)^7 + 144*a^2*tan(1/2*d*x + 1/2*c)^5 + 90*a^2*tan(1/2*d*x + 1/2*c)^3 + 65*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
20,1,138,0,1.660276," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{195 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 195 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(195 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 910 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1664 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1330 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 765 \, 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)}^{5}}}{120 \, d}"," ",0,"1/120*(195*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 195*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(195*a^3*tan(1/2*d*x + 1/2*c)^9 - 910*a^3*tan(1/2*d*x + 1/2*c)^7 + 1664*a^3*tan(1/2*d*x + 1/2*c)^5 - 1330*a^3*tan(1/2*d*x + 1/2*c)^3 + 765*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
21,1,122,0,1.874189," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{15 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 55 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 73 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 49 \, 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*(15*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(15*a^3*tan(1/2*d*x + 1/2*c)^7 - 55*a^3*tan(1/2*d*x + 1/2*c)^5 + 73*a^3*tan(1/2*d*x + 1/2*c)^3 - 49*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
22,1,106,0,3.907568," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{15 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, 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)}^{3}}}{6 \, d}"," ",0,"1/6*(15*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(15*a^3*tan(1/2*d*x + 1/2*c)^5 - 40*a^3*tan(1/2*d*x + 1/2*c)^3 + 33*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
23,1,100,0,1.970748," ","integrate((a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} a^{3} + 7 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 7 \, 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)^{3} - 7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*a^3 + 7*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 7*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)^3 - 7*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
24,1,80,0,2.011571," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} a^{3} + 3 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, 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)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"(3*(d*x + c)*a^3 + 3*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 4*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","A",0
25,1,100,0,0.486058," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{7 \, {\left(d x + c\right)} a^{3} + 2 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, 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)^{3} + 7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(7*(d*x + c)*a^3 + 2*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*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)^3 + 7*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
26,1,80,0,0.480311," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{15 \, {\left(d x + c\right)} a^{3} + \frac{2 \, {\left(15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, 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)}^{3}}}{6 \, d}"," ",0,"1/6*(15*(d*x + c)*a^3 + 2*(15*a^3*tan(1/2*d*x + 1/2*c)^5 + 40*a^3*tan(1/2*d*x + 1/2*c)^3 + 33*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
27,1,96,0,0.690992," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{15 \, {\left(d x + c\right)} a^{3} + \frac{2 \, {\left(15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 55 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 73 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 49 \, 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*(15*(d*x + c)*a^3 + 2*(15*a^3*tan(1/2*d*x + 1/2*c)^7 + 55*a^3*tan(1/2*d*x + 1/2*c)^5 + 73*a^3*tan(1/2*d*x + 1/2*c)^3 + 49*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
28,1,112,0,0.567046," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{195 \, {\left(d x + c\right)} a^{3} + \frac{2 \, {\left(195 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 910 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1664 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1330 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 765 \, 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)}^{5}}}{120 \, d}"," ",0,"1/120*(195*(d*x + c)*a^3 + 2*(195*a^3*tan(1/2*d*x + 1/2*c)^9 + 910*a^3*tan(1/2*d*x + 1/2*c)^7 + 1664*a^3*tan(1/2*d*x + 1/2*c)^5 + 1330*a^3*tan(1/2*d*x + 1/2*c)^3 + 765*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
29,1,128,0,2.026920," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{345 \, {\left(d x + c\right)} a^{3} + \frac{2 \, {\left(345 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1955 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4554 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5814 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3165 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1575 \, 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*(345*(d*x + c)*a^3 + 2*(345*a^3*tan(1/2*d*x + 1/2*c)^11 + 1955*a^3*tan(1/2*d*x + 1/2*c)^9 + 4554*a^3*tan(1/2*d*x + 1/2*c)^7 + 5814*a^3*tan(1/2*d*x + 1/2*c)^5 + 3165*a^3*tan(1/2*d*x + 1/2*c)^3 + 1575*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
30,1,154,0,3.640147," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{735 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 735 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(735 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 4165 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 9702 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 11802 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7355 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3105 \, a^{4} \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*(735*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 735*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(735*a^4*tan(1/2*d*x + 1/2*c)^11 - 4165*a^4*tan(1/2*d*x + 1/2*c)^9 + 9702*a^4*tan(1/2*d*x + 1/2*c)^7 - 11802*a^4*tan(1/2*d*x + 1/2*c)^5 + 7355*a^4*tan(1/2*d*x + 1/2*c)^3 - 3105*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","A",0
31,1,138,0,0.973849," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{105 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(105 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 490 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 896 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 790 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 375 \, a^{4} \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}}}{30 \, d}"," ",0,"1/30*(105*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(105*a^4*tan(1/2*d*x + 1/2*c)^9 - 490*a^4*tan(1/2*d*x + 1/2*c)^7 + 896*a^4*tan(1/2*d*x + 1/2*c)^5 - 790*a^4*tan(1/2*d*x + 1/2*c)^3 + 375*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
32,1,122,0,0.778816," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{105 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(105 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 385 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 511 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 279 \, a^{4} \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*(105*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(105*a^4*tan(1/2*d*x + 1/2*c)^7 - 385*a^4*tan(1/2*d*x + 1/2*c)^5 + 511*a^4*tan(1/2*d*x + 1/2*c)^3 - 279*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
33,1,116,0,0.410160," ","integrate((a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} a^{4} + 18 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 18 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(15 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 38 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 27 \, a^{4} \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^4 + 18*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 18*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(15*a^4*tan(1/2*d*x + 1/2*c)^5 - 38*a^4*tan(1/2*d*x + 1/2*c)^3 + 27*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
34,1,129,0,0.593667," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{8 \, {\left(d x + c\right)} a^{4} + 13 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 13 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{4 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} - \frac{2 \, {\left(7 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(8*(d*x + c)*a^4 + 13*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 13*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 4*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) - 2*(7*a^4*tan(1/2*d*x + 1/2*c)^3 - 9*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
35,1,129,0,0.818400," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{13 \, {\left(d x + c\right)} a^{4} + 8 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 8 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{4 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + \frac{2 \, {\left(7 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(13*(d*x + c)*a^4 + 8*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 8*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 4*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 2*(7*a^4*tan(1/2*d*x + 1/2*c)^3 + 9*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
36,1,116,0,0.456884," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{18 \, {\left(d x + c\right)} a^{4} + 3 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(15 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 38 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 27 \, a^{4} \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*(18*(d*x + c)*a^4 + 3*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*a^4*tan(1/2*d*x + 1/2*c)^5 + 38*a^4*tan(1/2*d*x + 1/2*c)^3 + 27*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
37,1,96,0,1.228889," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{105 \, {\left(d x + c\right)} a^{4} + \frac{2 \, {\left(105 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 385 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 511 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 279 \, a^{4} \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*(105*(d*x + c)*a^4 + 2*(105*a^4*tan(1/2*d*x + 1/2*c)^7 + 385*a^4*tan(1/2*d*x + 1/2*c)^5 + 511*a^4*tan(1/2*d*x + 1/2*c)^3 + 279*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
38,1,112,0,0.621439," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{105 \, {\left(d x + c\right)} a^{4} + \frac{2 \, {\left(105 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 490 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 896 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 790 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 375 \, a^{4} \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}}}{30 \, d}"," ",0,"1/30*(105*(d*x + c)*a^4 + 2*(105*a^4*tan(1/2*d*x + 1/2*c)^9 + 490*a^4*tan(1/2*d*x + 1/2*c)^7 + 896*a^4*tan(1/2*d*x + 1/2*c)^5 + 790*a^4*tan(1/2*d*x + 1/2*c)^3 + 375*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
39,1,128,0,1.241544," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{735 \, {\left(d x + c\right)} a^{4} + \frac{2 \, {\left(735 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 4165 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 9702 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 11802 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7355 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3105 \, a^{4} \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*(735*(d*x + c)*a^4 + 2*(735*a^4*tan(1/2*d*x + 1/2*c)^11 + 4165*a^4*tan(1/2*d*x + 1/2*c)^9 + 9702*a^4*tan(1/2*d*x + 1/2*c)^7 + 11802*a^4*tan(1/2*d*x + 1/2*c)^5 + 7355*a^4*tan(1/2*d*x + 1/2*c)^3 + 3105*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
40,1,144,0,0.644617," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{1155 \, {\left(d x + c\right)} a^{4} + \frac{2 \, {\left(1155 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 7700 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 21791 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 33792 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 31521 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 14700 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5565 \, a^{4} \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}}}{420 \, d}"," ",0,"1/420*(1155*(d*x + c)*a^4 + 2*(1155*a^4*tan(1/2*d*x + 1/2*c)^13 + 7700*a^4*tan(1/2*d*x + 1/2*c)^11 + 21791*a^4*tan(1/2*d*x + 1/2*c)^9 + 33792*a^4*tan(1/2*d*x + 1/2*c)^7 + 31521*a^4*tan(1/2*d*x + 1/2*c)^5 + 14700*a^4*tan(1/2*d*x + 1/2*c)^3 + 5565*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^7)/d","A",0
41,1,170,0,2.236691," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^5,x, algorithm=""giac"")","\frac{9765 \, a^{5} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 9765 \, a^{5} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(9765 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 65100 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 184233 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 285696 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 260183 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 132020 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 43995 \, a^{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)}^{7}}}{1680 \, d}"," ",0,"1/1680*(9765*a^5*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 9765*a^5*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(9765*a^5*tan(1/2*d*x + 1/2*c)^13 - 65100*a^5*tan(1/2*d*x + 1/2*c)^11 + 184233*a^5*tan(1/2*d*x + 1/2*c)^9 - 285696*a^5*tan(1/2*d*x + 1/2*c)^7 + 260183*a^5*tan(1/2*d*x + 1/2*c)^5 - 132020*a^5*tan(1/2*d*x + 1/2*c)^3 + 43995*a^5*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^7)/d","A",0
42,1,114,0,0.930526," ","integrate(sec(d*x+c)^5/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\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{6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} + \frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, \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} a}}{6 \, d}"," ",0,"-1/6*(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 - 6*tan(1/2*d*x + 1/2*c)/a + 2*(15*tan(1/2*d*x + 1/2*c)^5 - 16*tan(1/2*d*x + 1/2*c)^3 + 9*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a))/d","A",0
43,1,101,0,0.852963," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{3 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\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*(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 - 2*tan(1/2*d*x + 1/2*c)/a + 2*(3*tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a))/d","A",0
44,1,84,0,3.706478," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\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{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} + \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}}{d}"," ",0,"-(log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - tan(1/2*d*x + 1/2*c)/a + 2*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a))/d","A",0
45,1,54,0,1.993657," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\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{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a}}{d}"," ",0,"(log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - tan(1/2*d*x + 1/2*c)/a)/d","A",0
46,1,16,0,3.890326," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a d}"," ",0,"tan(1/2*d*x + 1/2*c)/(a*d)","A",0
47,1,28,0,2.130377," ","integrate(1/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{d x + c}{a} - \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a}}{d}"," ",0,"((d*x + c)/a - tan(1/2*d*x + 1/2*c)/a)/d","A",0
48,1,58,0,0.382037," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{d x + c}{a} - \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \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}}{d}"," ",0,"-((d*x + c)/a - tan(1/2*d*x + 1/2*c)/a - 2*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a))/d","A",0
49,1,73,0,0.328163," ","integrate(cos(d*x+c)^2/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(d x + c\right)}}{a} - \frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\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*(3*(d*x + c)/a - 2*tan(1/2*d*x + 1/2*c)/a - 2*(3*tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a))/d","A",0
50,1,88,0,1.928135," ","integrate(cos(d*x+c)^3/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{9 \, {\left(d x + c\right)}}{a} - \frac{6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, \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} a}}{6 \, d}"," ",0,"-1/6*(9*(d*x + c)/a - 6*tan(1/2*d*x + 1/2*c)/a - 2*(15*tan(1/2*d*x + 1/2*c)^5 + 16*tan(1/2*d*x + 1/2*c)^3 + 9*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a))/d","A",0
51,1,101,0,3.916494," ","integrate(cos(d*x+c)^4/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{45 \, {\left(d x + c\right)}}{a} - \frac{24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{2 \, {\left(75 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 115 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 109 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a}}{24 \, d}"," ",0,"1/24*(45*(d*x + c)/a - 24*tan(1/2*d*x + 1/2*c)/a - 2*(75*tan(1/2*d*x + 1/2*c)^7 + 115*tan(1/2*d*x + 1/2*c)^5 + 109*tan(1/2*d*x + 1/2*c)^3 + 21*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a))/d","A",0
52,1,122,0,1.949482," ","integrate(sec(d*x+c)^5/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{21 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{21 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{6 \, {\left(5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{2}} - \frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(21*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 21*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 6*(5*tan(1/2*d*x + 1/2*c)^3 - 3*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^2) - (a^4*tan(1/2*d*x + 1/2*c)^3 + 21*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
53,1,106,0,0.428107," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{12 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{12 \, \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}} - \frac{a^{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)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(12*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 12*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 12*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^2) - (a^4*tan(1/2*d*x + 1/2*c)^3 + 15*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
54,1,77,0,0.826279," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} - \frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 6*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - (a^4*tan(1/2*d*x + 1/2*c)^3 + 9*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
55,1,31,0,0.694982," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{6 \, a^{2} d}"," ",0,"1/6*(tan(1/2*d*x + 1/2*c)^3 + 3*tan(1/2*d*x + 1/2*c))/(a^2*d)","A",0
56,1,31,0,0.495154," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{6 \, a^{2} d}"," ",0,"-1/6*(tan(1/2*d*x + 1/2*c)^3 - 3*tan(1/2*d*x + 1/2*c))/(a^2*d)","A",0
57,1,50,0,0.369934," ","integrate(1/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(d x + c\right)}}{a^{2}} + \frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)/a^2 + (a^4*tan(1/2*d*x + 1/2*c)^3 - 9*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
58,1,79,0,0.343364," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(d x + c\right)}}{a^{2}} - \frac{12 \, \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}} + \frac{a^{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)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(12*(d*x + c)/a^2 - 12*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^2) + (a^4*tan(1/2*d*x + 1/2*c)^3 - 15*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
59,1,95,0,0.385067," ","integrate(cos(d*x+c)^2/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{21 \, {\left(d x + c\right)}}{a^{2}} - \frac{6 \, {\left(5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}} + \frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(21*(d*x + c)/a^2 - 6*(5*tan(1/2*d*x + 1/2*c)^3 + 3*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2) + (a^4*tan(1/2*d*x + 1/2*c)^3 - 21*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
60,1,108,0,0.911651," ","integrate(cos(d*x+c)^3/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{30 \, {\left(d x + c\right)}}{a^{2}} - \frac{4 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 20 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, \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} a^{2}} + \frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 27 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(30*(d*x + c)/a^2 - 4*(15*tan(1/2*d*x + 1/2*c)^5 + 20*tan(1/2*d*x + 1/2*c)^3 + 9*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^2) + (a^4*tan(1/2*d*x + 1/2*c)^3 - 27*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
61,1,139,0,3.531467," ","integrate(sec(d*x+c)^6/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{390 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{390 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{60 \, {\left(7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{3}} - \frac{3 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 465 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(390*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 390*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 60*(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) - (3*a^12*tan(1/2*d*x + 1/2*c)^5 + 40*a^12*tan(1/2*d*x + 1/2*c)^3 + 465*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
62,1,122,0,1.985204," ","integrate(sec(d*x+c)^5/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{60 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{60 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{40 \, \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^{3}} - \frac{a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 85 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{20 \, d}"," ",0,"-1/20*(60*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 60*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 40*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^3) - (a^12*tan(1/2*d*x + 1/2*c)^5 + 10*a^12*tan(1/2*d*x + 1/2*c)^3 + 85*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
63,1,94,0,1.934367," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{60 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{3 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 20 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 60*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - (3*a^12*tan(1/2*d*x + 1/2*c)^5 + 20*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
64,1,46,0,1.572403," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, \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)}{60 \, a^{3} d}"," ",0,"1/60*(3*tan(1/2*d*x + 1/2*c)^5 + 10*tan(1/2*d*x + 1/2*c)^3 + 15*tan(1/2*d*x + 1/2*c))/(a^3*d)","A",0
65,1,31,0,1.254981," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{20 \, a^{3} d}"," ",0,"-1/20*(tan(1/2*d*x + 1/2*c)^5 - 5*tan(1/2*d*x + 1/2*c))/(a^3*d)","A",0
66,1,46,0,0.999753," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, \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)}{60 \, a^{3} d}"," ",0,"1/60*(3*tan(1/2*d*x + 1/2*c)^5 - 10*tan(1/2*d*x + 1/2*c)^3 + 15*tan(1/2*d*x + 1/2*c))/(a^3*d)","A",0
67,1,68,0,0.510429," ","integrate(1/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(d x + c\right)}}{a^{3}} - \frac{3 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 20 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*(d*x + c)/a^3 - (3*a^12*tan(1/2*d*x + 1/2*c)^5 - 20*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
68,1,96,0,4.362962," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{60 \, {\left(d x + c\right)}}{a^{3}} - \frac{40 \, \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^{3}} - \frac{a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 85 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{20 \, d}"," ",0,"-1/20*(60*(d*x + c)/a^3 - 40*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^3) - (a^12*tan(1/2*d*x + 1/2*c)^5 - 10*a^12*tan(1/2*d*x + 1/2*c)^3 + 85*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
69,1,113,0,1.814143," ","integrate(cos(d*x+c)^2/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{390 \, {\left(d x + c\right)}}{a^{3}} - \frac{60 \, {\left(7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}} - \frac{3 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 465 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(390*(d*x + c)/a^3 - 60*(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) - (3*a^12*tan(1/2*d*x + 1/2*c)^5 - 40*a^12*tan(1/2*d*x + 1/2*c)^3 + 465*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
70,1,155,0,0.499632," ","integrate(sec(d*x+c)^7/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{2940 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{2940 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{280 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{4}} - \frac{5 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 63 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 455 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3885 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{280 \, d}"," ",0,"1/280*(2940*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 2940*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 280*(9*tan(1/2*d*x + 1/2*c)^3 - 7*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^4) - (5*a^24*tan(1/2*d*x + 1/2*c)^7 + 63*a^24*tan(1/2*d*x + 1/2*c)^5 + 455*a^24*tan(1/2*d*x + 1/2*c)^3 + 3885*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
71,1,139,0,0.496034," ","integrate(sec(d*x+c)^6/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3360 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{3360 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{1680 \, \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^{4}} - \frac{15 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 147 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 805 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5145 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"-1/840*(3360*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 3360*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 1680*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^4) - (15*a^24*tan(1/2*d*x + 1/2*c)^7 + 147*a^24*tan(1/2*d*x + 1/2*c)^5 + 805*a^24*tan(1/2*d*x + 1/2*c)^3 + 5145*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
72,1,110,0,2.867815," ","integrate(sec(d*x+c)^5/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{168 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{168 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} - \frac{3 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 21 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 77 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 315 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{168 \, d}"," ",0,"1/168*(168*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 168*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 - (3*a^24*tan(1/2*d*x + 1/2*c)^7 + 21*a^24*tan(1/2*d*x + 1/2*c)^5 + 77*a^24*tan(1/2*d*x + 1/2*c)^3 + 315*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
73,1,59,0,2.872102," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 35 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{280 \, a^{4} d}"," ",0,"1/280*(5*tan(1/2*d*x + 1/2*c)^7 + 21*tan(1/2*d*x + 1/2*c)^5 + 35*tan(1/2*d*x + 1/2*c)^3 + 35*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
74,1,59,0,0.878592," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{840 \, a^{4} d}"," ",0,"-1/840*(15*tan(1/2*d*x + 1/2*c)^7 + 21*tan(1/2*d*x + 1/2*c)^5 - 35*tan(1/2*d*x + 1/2*c)^3 - 105*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
75,1,59,0,0.586304," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{840 \, a^{4} d}"," ",0,"1/840*(15*tan(1/2*d*x + 1/2*c)^7 - 21*tan(1/2*d*x + 1/2*c)^5 - 35*tan(1/2*d*x + 1/2*c)^3 + 105*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
76,1,59,0,0.503666," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 35 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 35 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{280 \, a^{4} d}"," ",0,"-1/280*(5*tan(1/2*d*x + 1/2*c)^7 - 21*tan(1/2*d*x + 1/2*c)^5 + 35*tan(1/2*d*x + 1/2*c)^3 - 35*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
77,1,83,0,0.413106," ","integrate(1/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{168 \, {\left(d x + c\right)}}{a^{4}} + \frac{3 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 21 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 77 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 315 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{168 \, d}"," ",0,"1/168*(168*(d*x + c)/a^4 + (3*a^24*tan(1/2*d*x + 1/2*c)^7 - 21*a^24*tan(1/2*d*x + 1/2*c)^5 + 77*a^24*tan(1/2*d*x + 1/2*c)^3 - 315*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
78,1,112,0,0.504505," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3360 \, {\left(d x + c\right)}}{a^{4}} - \frac{1680 \, \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^{4}} + \frac{15 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 147 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 805 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5145 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"-1/840*(3360*(d*x + c)/a^4 - 1680*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^4) + (15*a^24*tan(1/2*d*x + 1/2*c)^7 - 147*a^24*tan(1/2*d*x + 1/2*c)^5 + 805*a^24*tan(1/2*d*x + 1/2*c)^3 - 5145*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
79,1,128,0,0.453531," ","integrate(cos(d*x+c)^2/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{2940 \, {\left(d x + c\right)}}{a^{4}} - \frac{280 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{4}} + \frac{5 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 63 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 455 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3885 \, a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{280 \, d}"," ",0,"1/280*(2940*(d*x + c)/a^4 - 280*(9*tan(1/2*d*x + 1/2*c)^3 + 7*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^4) + (5*a^24*tan(1/2*d*x + 1/2*c)^7 - 63*a^24*tan(1/2*d*x + 1/2*c)^5 + 455*a^24*tan(1/2*d*x + 1/2*c)^3 - 3885*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
80,1,155,0,0.977479," ","integrate(sec(d*x+c)^7/(a+a*sec(d*x+c))^5,x, algorithm=""giac"")","-\frac{\frac{5040 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{5}} - \frac{5040 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{5}} + \frac{2016 \, \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^{5}} - \frac{7 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 72 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 378 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1512 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8127 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{45}}}{1008 \, d}"," ",0,"-1/1008*(5040*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^5 - 5040*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^5 + 2016*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^5) - (7*a^40*tan(1/2*d*x + 1/2*c)^9 + 72*a^40*tan(1/2*d*x + 1/2*c)^7 + 378*a^40*tan(1/2*d*x + 1/2*c)^5 + 1512*a^40*tan(1/2*d*x + 1/2*c)^3 + 8127*a^40*tan(1/2*d*x + 1/2*c))/a^45)/d","A",0
81,1,126,0,0.875786," ","integrate(sec(d*x+c)^6/(a+a*sec(d*x+c))^5,x, algorithm=""giac"")","\frac{\frac{5040 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{5}} - \frac{5040 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{5}} - \frac{35 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 270 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1008 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2730 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9765 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{45}}}{5040 \, d}"," ",0,"1/5040*(5040*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^5 - 5040*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^5 - (35*a^40*tan(1/2*d*x + 1/2*c)^9 + 270*a^40*tan(1/2*d*x + 1/2*c)^7 + 1008*a^40*tan(1/2*d*x + 1/2*c)^5 + 2730*a^40*tan(1/2*d*x + 1/2*c)^3 + 9765*a^40*tan(1/2*d*x + 1/2*c))/a^45)/d","A",0
82,1,72,0,1.461573," ","integrate(sec(d*x+c)^5/(a+a*sec(d*x+c))^5,x, algorithm=""giac"")","\frac{35 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 180 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 378 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 420 \, \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)}{5040 \, a^{5} d}"," ",0,"1/5040*(35*tan(1/2*d*x + 1/2*c)^9 + 180*tan(1/2*d*x + 1/2*c)^7 + 378*tan(1/2*d*x + 1/2*c)^5 + 420*tan(1/2*d*x + 1/2*c)^3 + 315*tan(1/2*d*x + 1/2*c))/(a^5*d)","A",0
83,1,59,0,1.426785," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^5,x, algorithm=""giac"")","-\frac{7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 18 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 42 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 63 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{1008 \, a^{5} d}"," ",0,"-1/1008*(7*tan(1/2*d*x + 1/2*c)^9 + 18*tan(1/2*d*x + 1/2*c)^7 - 42*tan(1/2*d*x + 1/2*c)^3 - 63*tan(1/2*d*x + 1/2*c))/(a^5*d)","A",0
84,1,46,0,0.529472," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^5,x, algorithm=""giac"")","\frac{5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 18 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{720 \, a^{5} d}"," ",0,"1/720*(5*tan(1/2*d*x + 1/2*c)^9 - 18*tan(1/2*d*x + 1/2*c)^5 + 45*tan(1/2*d*x + 1/2*c))/(a^5*d)","A",0
85,1,59,0,3.301366," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^5,x, algorithm=""giac"")","-\frac{7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 18 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 42 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 63 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{1008 \, a^{5} d}"," ",0,"-1/1008*(7*tan(1/2*d*x + 1/2*c)^9 - 18*tan(1/2*d*x + 1/2*c)^7 + 42*tan(1/2*d*x + 1/2*c)^3 - 63*tan(1/2*d*x + 1/2*c))/(a^5*d)","A",0
86,1,72,0,0.821844," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^5,x, algorithm=""giac"")","\frac{35 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 180 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 378 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 420 \, \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)}{5040 \, a^{5} d}"," ",0,"1/5040*(35*tan(1/2*d*x + 1/2*c)^9 - 180*tan(1/2*d*x + 1/2*c)^7 + 378*tan(1/2*d*x + 1/2*c)^5 - 420*tan(1/2*d*x + 1/2*c)^3 + 315*tan(1/2*d*x + 1/2*c))/(a^5*d)","A",0
87,1,100,0,1.014214," ","integrate(1/(a+a*sec(d*x+c))^5,x, algorithm=""giac"")","\frac{\frac{5040 \, {\left(d x + c\right)}}{a^{5}} - \frac{35 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 270 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1008 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2730 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9765 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{45}}}{5040 \, d}"," ",0,"1/5040*(5040*(d*x + c)/a^5 - (35*a^40*tan(1/2*d*x + 1/2*c)^9 - 270*a^40*tan(1/2*d*x + 1/2*c)^7 + 1008*a^40*tan(1/2*d*x + 1/2*c)^5 - 2730*a^40*tan(1/2*d*x + 1/2*c)^3 + 9765*a^40*tan(1/2*d*x + 1/2*c))/a^45)/d","A",0
88,1,129,0,2.122550," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^5,x, algorithm=""giac"")","-\frac{\frac{5040 \, {\left(d x + c\right)}}{a^{5}} - \frac{2016 \, \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^{5}} - \frac{7 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 72 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 378 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1512 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8127 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{45}}}{1008 \, d}"," ",0,"-1/1008*(5040*(d*x + c)/a^5 - 2016*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^5) - (7*a^40*tan(1/2*d*x + 1/2*c)^9 - 72*a^40*tan(1/2*d*x + 1/2*c)^7 + 378*a^40*tan(1/2*d*x + 1/2*c)^5 - 1512*a^40*tan(1/2*d*x + 1/2*c)^3 + 8127*a^40*tan(1/2*d*x + 1/2*c))/a^45)/d","A",0
89,1,145,0,0.864206," ","integrate(cos(d*x+c)^2/(a+a*sec(d*x+c))^5,x, algorithm=""giac"")","\frac{\frac{78120 \, {\left(d x + c\right)}}{a^{5}} - \frac{5040 \, {\left(11 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, \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^{5}} - \frac{35 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 450 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3024 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15750 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 110565 \, a^{40} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{45}}}{5040 \, d}"," ",0,"1/5040*(78120*(d*x + c)/a^5 - 5040*(11*tan(1/2*d*x + 1/2*c)^3 + 9*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^5) - (35*a^40*tan(1/2*d*x + 1/2*c)^9 - 450*a^40*tan(1/2*d*x + 1/2*c)^7 + 3024*a^40*tan(1/2*d*x + 1/2*c)^5 - 15750*a^40*tan(1/2*d*x + 1/2*c)^3 + 110565*a^40*tan(1/2*d*x + 1/2*c))/a^45)/d","A",0
90,1,120,0,20.570095," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{2} {\left(35 \, a^{4} - {\left(35 \, a^{4} + {\left(9 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 49 \, 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)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{35 \, {\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} d}"," ",0,"-2/35*sqrt(2)*(35*a^4 - (35*a^4 + (9*a^4*tan(1/2*d*x + 1/2*c)^2 - 49*a^4)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*sgn(cos(d*x + c))*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
91,1,101,0,3.671911," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{2} {\left(15 \, a^{3} + {\left(7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, a^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{15 \, {\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} d}"," ",0,"2/15*sqrt(2)*(15*a^3 + (7*a^3*tan(1/2*d*x + 1/2*c)^2 - 10*a^3)*tan(1/2*d*x + 1/2*c)^2)*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
92,1,82,0,3.109610," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{2} {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{3 \, {\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} d}"," ",0,"2/3*sqrt(2)*(a^2*tan(1/2*d*x + 1/2*c)^2 - 3*a^2)*sgn(cos(d*x + c))*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)","A",0
93,1,62,0,7.084286," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 \, \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)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} d}"," ",0,"-2*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)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*d)","B",0
94,1,130,0,9.016418," ","integrate((a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\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) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{d {\left| a \right|}}"," ",0,"-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))*sgn(cos(d*x + c))/(d*abs(a))","B",0
95,1,282,0,3.323235," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{\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{8 \, {\left(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{-a} a - \sqrt{-a} a^{2}\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)}^{4} - 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)}^{2} a + a^{2}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{4 \, d}"," ",0,"-1/4*sqrt(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) + 8*(3*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(-a)*a - 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))^4 - 6*(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^2))*sgn(cos(d*x + c))/d","B",0
96,1,378,0,13.769773," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(1/2),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{8 \, {\left(5 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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 + 19 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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} - 17 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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} + \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)}^{4} - 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)}^{2} a + a^{2}\right)}^{2}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{16 \, d}"," ",0,"-1/16*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) - 8*(5*(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 + 19*(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 - 17*(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 + 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))^4 - 6*(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^2)^2)*sgn(cos(d*x + c))/d","B",0
97,1,475,0,4.278645," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{15 \, \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{8 \, {\left(63 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} \sqrt{-a} a - 369 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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} + 1638 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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} - 1074 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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} + 171 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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} - 13 \, \sqrt{-a} a^{6}\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)}^{4} - 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)}^{2} a + a^{2}\right)}^{3}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{96 \, d}"," ",0,"-1/96*sqrt(2)*(15*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) + 8*(63*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*sqrt(-a)*a - 369*(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 + 1638*(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 - 1074*(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 + 171*(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 - 13*sqrt(-a)*a^6)/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(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^2)^3)*sgn(cos(d*x + c))/d","B",0
98,1,571,0,4.458773," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(1/2),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{8 \, {\left(279 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} \sqrt{-a} a + 285 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} \sqrt{-a} a^{2} - 4605 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} \sqrt{-a} a^{3} + 37281 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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^{4} - 35643 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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^{5} + 9175 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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^{6} - 1311 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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^{7} + 43 \, \sqrt{-a} a^{8}\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)}^{4} - 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)}^{2} a + a^{2}\right)}^{4}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{768 \, d}"," ",0,"-1/768*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) - 8*(279*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*sqrt(-a)*a + 285*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*sqrt(-a)*a^2 - 4605*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*sqrt(-a)*a^3 + 37281*(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^4 - 35643*(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^5 + 9175*(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^6 - 1311*(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^7 + 43*sqrt(-a)*a^8)/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(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^2)^4)*sgn(cos(d*x + c))/d","B",0
99,1,180,0,8.342658," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{4 \, {\left(315 \, \sqrt{2} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(525 \, \sqrt{2} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(819 \, \sqrt{2} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 47 \, {\left(2 \, \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} - 9 \, \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)}{315 \, {\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} d}"," ",0,"4/315*(315*sqrt(2)*a^6*sgn(cos(d*x + c)) - (525*sqrt(2)*a^6*sgn(cos(d*x + c)) - (819*sqrt(2)*a^6*sgn(cos(d*x + c)) + 47*(2*sqrt(2)*a^6*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^2 - 9*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
100,1,151,0,9.719337," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{4 \, {\left(105 \, \sqrt{2} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(140 \, \sqrt{2} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 19 \, {\left(2 \, \sqrt{2} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7 \, \sqrt{2} a^{5} \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)}{105 \, {\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} d}"," ",0,"-4/105*(105*sqrt(2)*a^5*sgn(cos(d*x + c)) - (140*sqrt(2)*a^5*sgn(cos(d*x + c)) + 19*(2*sqrt(2)*a^5*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^2 - 7*sqrt(2)*a^5*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
101,1,121,0,7.765573," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{4 \, {\left(5 \, \sqrt{2} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + {\left(2 \, \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)^{2} - 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)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{5 \, {\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} d}"," ",0,"4/5*(5*sqrt(2)*a^4*sgn(cos(d*x + c)) + (2*sqrt(2)*a^4*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^2 - 5*sqrt(2)*a^4*sgn(cos(d*x + c)))*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)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
102,1,93,0,9.427041," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{4 \, {\left(2 \, \sqrt{2} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \sqrt{2} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{3 \, {\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} d}"," ",0,"4/3*(2*sqrt(2)*a^3*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^2 - 3*sqrt(2)*a^3*sgn(cos(d*x + c)))*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)","A",0
103,1,195,0,16.034182," ","integrate((a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{2 \, \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)}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} + \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|}}}{d}"," ",0,"-(2*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)/(a*tan(1/2*d*x + 1/2*c)^2 - a) + 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))/d","B",0
104,1,278,0,7.161556," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \sqrt{-a} a^{3} {\left(\frac{3 \, \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(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 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)}^{2} a + a^{2}\right)} a}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{4 \, d}"," ",0,"-1/4*sqrt(2)*sqrt(-a)*a^3*(3*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*(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)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(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^2)*a))*sgn(cos(d*x + c))/d","B",0
105,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+a*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*x+c))]Warning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableEvaluation time: 0.94Unable to divide, perhaps due to rounding error%%%{%%{[%%%{%%{[469762048,0]:[1,0,-2]%%},[14]%%%},0]:[1,0,%%%{1,[1]%%%}]%%},[0,1]%%%} / %%%{%%%{%%{[67108864,0]:[1,0,-2]%%},[12]%%%},[0,0]%%%} Error: Bad Argument Value","F(-2)",0
106,1,535,0,6.919565," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{33 \, \sqrt{-a} a \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) \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 33 \, \sqrt{-a} a \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) \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + \frac{4 \, {\left(33 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 303 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2394 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1806 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 309 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 19 \, \sqrt{2} \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)}^{4} - 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)}^{2} a + a^{2}\right)}^{3}}}{48 \, d}"," ",0,"-1/48*(33*sqrt(-a)*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)))*sgn(cos(d*x + c)) - 33*sqrt(-a)*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)))*sgn(cos(d*x + c)) + 4*(33*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 303*sqrt(2)*(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)) + 2394*sqrt(2)*(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)) - 1806*sqrt(2)*(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)) + 309*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*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 19*sqrt(2)*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))^4 - 6*(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^2)^3)/d","B",0
107,1,209,0,6.219312," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{8 \, {\left(693 \, \sqrt{2} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(1617 \, \sqrt{2} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(3003 \, \sqrt{2} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 25 \, {\left(99 \, \sqrt{2} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, {\left(2 \, \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} - 11 \, \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)}{693 \, {\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} d}"," ",0,"-8/693*(693*sqrt(2)*a^8*sgn(cos(d*x + c)) - (1617*sqrt(2)*a^8*sgn(cos(d*x + c)) - (3003*sqrt(2)*a^8*sgn(cos(d*x + c)) - 25*(99*sqrt(2)*a^8*sgn(cos(d*x + c)) + 4*(2*sqrt(2)*a^8*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^2 - 11*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
108,1,180,0,5.908467," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{8 \, {\left(315 \, \sqrt{2} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(630 \, \sqrt{2} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 13 \, {\left(63 \, \sqrt{2} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, {\left(2 \, \sqrt{2} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \sqrt{2} a^{7} \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)}{315 \, {\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} d}"," ",0,"8/315*(315*sqrt(2)*a^7*sgn(cos(d*x + c)) - (630*sqrt(2)*a^7*sgn(cos(d*x + c)) - 13*(63*sqrt(2)*a^7*sgn(cos(d*x + c)) + 4*(2*sqrt(2)*a^7*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^2 - 9*sqrt(2)*a^7*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
109,1,151,0,5.110419," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{8 \, {\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) + 4 \, {\left(2 \, \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} - 7 \, \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)}{21 \, {\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} d}"," ",0,"-8/21*(21*sqrt(2)*a^6*sgn(cos(d*x + c)) - (35*sqrt(2)*a^6*sgn(cos(d*x + c)) + 4*(2*sqrt(2)*a^6*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^2 - 7*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
110,1,122,0,6.116481," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{8 \, {\left(15 \, \sqrt{2} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, {\left(2 \, \sqrt{2} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 5 \, \sqrt{2} a^{5} \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)}{15 \, {\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} d}"," ",0,"8/15*(15*sqrt(2)*a^5*sgn(cos(d*x + c)) + 4*(2*sqrt(2)*a^5*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^2 - 5*sqrt(2)*a^5*sgn(cos(d*x + c)))*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)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
111,1,225,0,8.773276," ","integrate((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{2 \, {\left(7 \, \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)^{2} - 9 \, \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)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{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) - 2*(7*sqrt(2)*a^4*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)^2 - 9*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)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
112,1,368,0,7.650613," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{4 \, \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) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} + 5 \, \sqrt{-a} a^{2} \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) \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 5 \, \sqrt{-a} a^{2} \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) \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + \frac{4 \, {\left(3 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - \sqrt{2} \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\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)}^{4} - 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)}^{2} a + a^{2}}}{2 \, d}"," ",0,"-1/2*(4*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*a^3*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 - a) + 5*sqrt(-a)*a^2*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)))*sgn(cos(d*x + c)) - 5*sqrt(-a)*a^2*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)))*sgn(cos(d*x + c)) + 4*(3*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*sqrt(-a)*a^3*sgn(cos(d*x + c)) - sqrt(2)*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))^4 - 6*(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^2))/d","B",0
113,1,364,0,8.775070," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \sqrt{-a} a^{5} {\left(\frac{19 \, \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^{2} {\left| a \right|}} + \frac{8 \, {\left(19 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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} - 171 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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 + 89 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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^{2} - 9 \, 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)}^{4} - 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)}^{2} a + a^{2}\right)}^{2} a^{2}}\right)} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{16 \, d}"," ",0,"-1/16*sqrt(2)*sqrt(-a)*a^5*(19*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^2*abs(a)) + 8*(19*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6 - 171*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a + 89*(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 - 9*a^3)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(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^2)^2*a^2))*sgn(cos(d*x + c))/d","B",0
114,1,539,0,7.322522," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{75 \, \sqrt{-a} a^{2} \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) \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 75 \, \sqrt{-a} a^{2} \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) \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + \frac{4 \, {\left(75 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1125 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6174 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4314 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 807 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 49 \, \sqrt{2} \sqrt{-a} a^{8} \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)}^{4} - 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)}^{2} a + a^{2}\right)}^{3}}}{48 \, d}"," ",0,"-1/48*(75*sqrt(-a)*a^2*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)))*sgn(cos(d*x + c)) - 75*sqrt(-a)*a^2*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)))*sgn(cos(d*x + c)) + 4*(75*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 1125*sqrt(2)*(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^4*sgn(cos(d*x + c)) + 6174*sqrt(2)*(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^5*sgn(cos(d*x + c)) - 4314*sqrt(2)*(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^6*sgn(cos(d*x + c)) + 807*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*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 49*sqrt(2)*sqrt(-a)*a^8*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))^4 - 6*(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^2)^3)/d","B",0
115,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*x+c))]Warning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableEvaluation time: 1.43Unable to divide, perhaps due to rounding error%%%{%%{[%%%{%%{[-2309237210123256509497344,0]:[1,0,-2]%%},[35]%%%},0]:[1,0,%%%{1,[1]%%%}]%%},[0,1]%%%} / %%%{%%%{%%{[-14167099448608935641088,0]:[1,0,-2]%%},[32]%%%},[0,0]%%%} Error: Bad Argument Value","F(-2)",0
116,1,57,0,1.444499," ","integrate(sec(d*x+c)*(a-a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{2} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} d}"," ",0,"-2*sqrt(2)*a*sgn(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))*sgn(cos(d*x + c))/(sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)*d)","B",0
117,1,65,0,1.472304," ","integrate((a-a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{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) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{d}"," ",0,"-2*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))*sgn(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))*sgn(cos(d*x + c))/d","B",0
118,1,134,0,0.785673," ","integrate(cos(d*x+c)*(a-a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{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) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - \frac{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)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{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)}{2 \, d}"," ",0,"1/2*sqrt(2)*(sqrt(2)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))*sgn(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c)) - 2*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)*a*sgn(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))/(a*tan(1/2*d*x + 1/2*c)^2 + a))*sgn(cos(d*x + c))/d","B",0
119,1,205,0,9.895981," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{15 \, \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|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{2 \, {\left({\left(\frac{17 \, 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{20 \, 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)}}{15 \, d}"," ",0,"-1/15*sqrt(2)*(15*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 2*((17*a^2*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 20*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","A",0
120,1,136,0,5.133734," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\frac{4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}{{\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)} + \frac{3 \, \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|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{3 \, d}"," ",0,"1/3*sqrt(2)*(4*a*tan(1/2*d*x + 1/2*c)^3/((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)) + 3*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
121,1,132,0,6.770103," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{\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|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{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)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{d}"," ",0,"-sqrt(2)*(log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 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)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
122,1,65,0,6.410707," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{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|}\right)}{\sqrt{-a} d \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}"," ",0,"sqrt(2)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*d*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))","A",0
123,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(a*sec(d*x + c) + a), x)","F",0
124,1,365,0,6.021678," ","integrate(cos(d*x+c)/(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{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)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{8 \, {\left(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{-a} - \sqrt{-a} a\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 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)}^{2} a + a^{2}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{4 \, d}"," ",0,"-1/4*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)) - 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)/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 8*(3*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(-a) - sqrt(-a)*a)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(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^2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
125,1,462,0,4.707713," ","integrate(cos(d*x+c)^2/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\frac{7 \, \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{8 \, \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)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{8 \, {\left(17 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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} - 57 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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 + 19 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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} - 3 \, \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)}^{4} - 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)}^{2} a + a^{2}\right)}^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)}}{16 \, d}"," ",0,"1/16*sqrt(2)*(7*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)) - 8*log((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)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 8*(17*(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) - 57*(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 + 19*(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 - 3*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))^4 - 6*(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^2)^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
126,1,245,0,8.534961," ","integrate(sec(d*x+c)^5/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left({\left({\left(\frac{5 \, \sqrt{2} a \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{127 \, \sqrt{2} 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{175 \, \sqrt{2} 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{85 \, \sqrt{2} 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)}{{\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}} - \frac{75 \, \sqrt{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|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{20 \, d}"," ",0,"1/20*((((5*sqrt(2)*a*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 127*sqrt(2)*a/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2 + 175*sqrt(2)*a/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2 - 85*sqrt(2)*a/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)) - 75*sqrt(2)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
127,1,207,0,5.766693," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{{\left({\left(\frac{3 \, \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{46 \, \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{27 \, \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}} - \frac{33 \, \sqrt{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|}\right)}{\sqrt{-a} a \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)*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 46*sqrt(2)/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2 + 27*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)) - 33*sqrt(2)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
128,1,159,0,20.501987," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(\frac{\sqrt{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{9 \, \sqrt{2}}{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)}{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{7 \, \sqrt{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|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{4 \, d}"," ",0,"1/4*((sqrt(2)*tan(1/2*d*x + 1/2*c)^2/(a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 9*sqrt(2)/(a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)/sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a) - 7*sqrt(2)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
129,1,122,0,8.560940," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{3 \, \sqrt{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|}\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} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{4 \, d}"," ",0,"1/4*(3*sqrt(2)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
130,1,122,0,8.757948," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{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|}\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} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{4 \, d}"," ",0,"1/4*(sqrt(2)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
131,1,54,0,2.997629," ","integrate(1/(a+a*sec(d*x+c))^(3/2),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)}{4 \, a^{2} d \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}"," ",0,"1/4*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/(a^2*d*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))","A",0
132,1,415,0,4.291370," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{16 \, \sqrt{2} {\left(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 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)}^{2} a + a^{2}\right)} \sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{9 \, \sqrt{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)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \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)}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{12 \, \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)}{\sqrt{-a} {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{8 \, d}"," ",0,"-1/8*(16*sqrt(2)*(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)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(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^2)*sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 9*sqrt(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)/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 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^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 12*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))/(sqrt(-a)*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
133,1,501,0,6.461515," ","integrate(cos(d*x+c)^2/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{13 \, \sqrt{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)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \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)}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{19 \, \log\left(\frac{{\left| -8 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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} - 16 \, \sqrt{2} {\left| a \right|} + 24 \, a \right|}}{{\left| -8 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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} + 16 \, \sqrt{2} {\left| a \right|} + 24 \, a \right|}}\right)}{\sqrt{-a} {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{4 \, \sqrt{2} {\left(29 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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} - 133 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, 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 + 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)}^{2} a^{2} - 7 \, 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)}^{4} - 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)}^{2} a + a^{2}\right)}^{2} \sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{8 \, d}"," ",0,"-1/8*(13*sqrt(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)/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 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^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 19*log(abs(-8*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 16*sqrt(2)*abs(a) + 24*a)/abs(-8*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 16*sqrt(2)*abs(a) + 24*a))/(sqrt(-a)*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 4*sqrt(2)*(29*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6 - 133*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a + 55*(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 - 7*a^3)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(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^2)^2*sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
134,1,254,0,5.423981," ","integrate(sec(d*x+c)^5/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{{\left({\left(3 \, {\left(\frac{2 \, \sqrt{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{23 \, \sqrt{2}}{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{668 \, \sqrt{2}}{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{465 \, \sqrt{2}}{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)}{{\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}} - \frac{489 \, \sqrt{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|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{96 \, d}"," ",0,"-1/96*(((3*(2*sqrt(2)*tan(1/2*d*x + 1/2*c)^2/(a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 23*sqrt(2)/(a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 - 668*sqrt(2)/(a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 + 465*sqrt(2)/(a*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)) - 489*sqrt(2)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
135,1,216,0,10.269532," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left({\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)^{2} - \frac{83 \, \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)}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} + \frac{75 \, \sqrt{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|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{32 \, d}"," ",0,"-1/32*(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)^2 - 83*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) + 75*sqrt(2)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
136,1,160,0,7.536075," ","integrate(sec(d*x+c)^3/(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(\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{11 \, \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{19 \, \sqrt{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|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{32 \, d}"," ",0,"1/32*(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^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 11*sqrt(2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) + 19*sqrt(2)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
137,1,160,0,10.299368," ","integrate(sec(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(\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{3 \, \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{5 \, \sqrt{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|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{32 \, d}"," ",0,"-1/32*(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^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 3*sqrt(2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) - 5*sqrt(2)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
138,1,160,0,22.798771," ","integrate(sec(d*x+c)/(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(\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{5 \, \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{3 \, \sqrt{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|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{32 \, d}"," ",0,"1/32*(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^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 5*sqrt(2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) + 3*sqrt(2)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
139,1,92,0,2.692941," ","integrate(1/(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(\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{13 \, \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)}{32 \, d}"," ",0,"-1/32*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^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 13*sqrt(2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)/d","A",0
140,1,459,0,22.078509," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{2 \, \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^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{21 \, \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{128 \, \sqrt{2} {\left(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 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)}^{2} a + a^{2}\right)} \sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{115 \, \sqrt{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)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{160 \, \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)}{\sqrt{-a} a {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{64 \, d}"," ",0,"1/64*(2*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^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 21*sqrt(2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) - 128*sqrt(2)*(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)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(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^2)*sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 115*sqrt(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)/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 160*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))/(sqrt(-a)*a*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
141,1,81,0,2.195715," ","integrate(sec(d*x+c)/(a-a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{\arctan\left(-i\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{\sqrt{a}} + \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) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}\right)}}{d}"," ",0,"-sqrt(2)*(arctan(-I)*sgn(tan(1/2*d*x + 1/2*c))/sqrt(a) + 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)*sgn(tan(1/2*d*x + 1/2*c))))/d","C",0
142,0,0,0,0.000000," ","integrate(1/(a-a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(-a*sec(d*x + c) + a), x)","F",0
143,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^3, x)","F",0
144,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^2, x)","F",0
145,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(2/3)*sec(d*x + c), x)","F",0
146,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(2/3), x)","F",0
147,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(2/3)*cos(d*x + c), x)","F",0
148,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/3)*sec(d*x + c)^3, x)","F",0
149,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/3)*sec(d*x + c)^2, x)","F",0
150,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/3)*sec(d*x + c), x)","F",0
151,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/3), x)","F",0
152,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/3)*cos(d*x + c), x)","F",0
153,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{4}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/(a*sec(d*x + c) + a)^(1/3), x)","F",0
154,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{3}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(a*sec(d*x + c) + a)^(1/3), x)","F",0
155,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(a*sec(d*x + c) + a)^(1/3), x)","F",0
156,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(a*sec(d*x + c) + a)^(1/3), x)","F",0
157,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(-1/3), x)","F",0
158,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(a*sec(d*x + c) + a)^(1/3), x)","F",0
159,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{4}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/(a*sec(d*x + c) + a)^(5/3), x)","F",0
160,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{3}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(a*sec(d*x + c) + a)^(5/3), x)","F",0
161,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(a*sec(d*x + c) + a)^(5/3), x)","F",0
162,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(a*sec(d*x + c) + a)^(5/3), x)","F",0
163,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(-5/3), x)","F",0
164,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(a*sec(d*x + c) + a)^(5/3), x)","F",0
165,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
166,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
167,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
168,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
169,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
170,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
171,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
172,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*sec(d*x + c)^(5/2), x)","F",0
173,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
174,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
175,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
176,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
177,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/sec(d*x + c)^(5/2), x)","F",0
178,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/sec(d*x + c)^(7/2), x)","F",0
179,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
180,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
181,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
182,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
183,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3/sec(d*x + c)^(5/2), x)","F",0
184,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3/sec(d*x + c)^(7/2), x)","F",0
185,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3/sec(d*x + c)^(9/2), x)","F",0
186,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^4*sec(d*x + c)^(3/2), x)","F",0
187,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{4} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^4*sqrt(sec(d*x + c)), x)","F",0
188,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{4}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^4/sqrt(sec(d*x + c)), x)","F",0
189,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^4/sec(d*x + c)^(3/2), x)","F",0
190,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^4/sec(d*x + c)^(5/2), x)","F",0
191,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^4/sec(d*x + c)^(7/2), x)","F",0
192,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^4/sec(d*x + c)^(9/2), x)","F",0
193,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^4/sec(d*x + c)^(11/2), x)","F",0
194,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/2)/(a*sec(d*x + c) + a), x)","F",0
195,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a), x)","F",0
196,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a), x)","F",0
197,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
198,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
199,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
200,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
201,0,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{9}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(9/2)/(a*sec(d*x + c) + a)^2, x)","F",0
202,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/2)/(a*sec(d*x + c) + a)^2, x)","F",0
203,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^2, x)","F",0
204,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^2, x)","F",0
205,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
206,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
207,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
208,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
209,0,0,0,0.000000," ","integrate(sec(d*x+c)^(11/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{11}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(11/2)/(a*sec(d*x + c) + a)^3, x)","F",0
210,0,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{9}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(9/2)/(a*sec(d*x + c) + a)^3, x)","F",0
211,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/2)/(a*sec(d*x + c) + a)^3, x)","F",0
212,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^3, x)","F",0
213,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^3, x)","F",0
214,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^3, x)","F",0
215,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
216,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
217,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^3*sec(d*x + c)^(5/2)), x)","F",0
218,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
219,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
220,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
221,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a \sec\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
222,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{a \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
223,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{a \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
224,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{a \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
225,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
226,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2), x)","F",0
227,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
228,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)/sqrt(sec(d*x + c)), x)","F",0
229,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(3/2), x)","F",0
230,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(5/2), x)","F",0
231,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(7/2), x)","F",0
232,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(9/2), x)","F",0
233,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
234,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2), x)","F",0
235,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
236,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)/sqrt(sec(d*x + c)), x)","F",0
237,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(3/2), x)","F",0
238,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(5/2), x)","F",0
239,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(7/2), x)","F",0
240,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(9/2), x)","F",0
241,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(11/2), x)","F",0
242,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/4),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,0,0,0,0.000000," ","integrate(sec(f*x+e)^(1/2)*(a+a*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(f x + e\right) + a} \sqrt{\sec\left(f x + e\right)}\,{d x}"," ",0,"integrate(sqrt(a*sec(f*x + e) + a)*sqrt(sec(f*x + e)), x)","F",0
244,-2,0,0,0.000000," ","integrate((-sec(f*x+e))^(1/2)*(a-a*sec(f*x+e))^(1/2),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: (2*pi/x/2)>(-2*pi/x/2)2*sqrt(2)*(-a^2*atan(sqrt(a)/sqrt(-a))/sqrt(2)/sqrt(-a)+a^2*atan(sqrt(a*tan(1/2*(f*x+exp(1)))^2+a)/sqrt(2)/sqrt(-a))/sqrt(2)/sqrt(-a))*abs(a)*sign(tan(1/2*(f*x+exp(1)))^3+tan(1/2*(f*x+exp(1))))/a^2/f","F(-2)",0
245,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
246,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
247,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(a*sec(d*x + c) + a), x)","F",0
248,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
249,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
250,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
251,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/2)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
252,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
253,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
254,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^(3/2), x)","F",0
255,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c))), x)","F",0
256,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2)), x)","F",0
257,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/2)), x)","F",0
258,0,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{9}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(9/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
259,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
260,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
261,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
262,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^(5/2), x)","F",0
263,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c))), x)","F",0
264,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2)), x)","F",0
265,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{\sec\left(d x + c\right) + 1}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/2)/sqrt(sec(d*x + c) + 1), x)","F",0
266,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{\sec\left(d x + c\right) + 1}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/sqrt(sec(d*x + c) + 1), x)","F",0
267,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{\sec\left(d x + c\right) + 1}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/sqrt(sec(d*x + c) + 1), x)","F",0
268,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{\sec\left(d x + c\right) + 1}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(sec(d*x + c) + 1), x)","F",0
269,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\sec\left(d x + c\right) + 1} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(sec(d*x + c) + 1)*sqrt(sec(d*x + c))), x)","F",0
270,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\sec\left(d x + c\right) + 1} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(sec(d*x + c) + 1)*sec(d*x + c)^(3/2)), x)","F",0
271,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\sec\left(d x + c\right) + 1} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(sec(d*x + c) + 1)*sec(d*x + c)^(5/2)), x)","F",0
272,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(4/3)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(4/3), x)","F",0
273,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/3)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(1/3), x)","F",0
274,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)/(e*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{\sqrt{a \sec\left(d x + c\right) + a}}{\left(e \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)/(e*sec(d*x + c))^(2/3), x)","F",0
275,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(8/3)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{8}{3}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(8/3), x)","F",0
276,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5/3)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{5}{3}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(5/3), x)","F",0
277,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(2/3)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(2/3), x)","F",0
278,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)/(e*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\sqrt{a \sec\left(d x + c\right) + a}}{\left(e \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)/(e*sec(d*x + c))^(1/3), x)","F",0
279,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)/(e*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{\sqrt{a \sec\left(d x + c\right) + a}}{\left(e \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)/(e*sec(d*x + c))^(4/3), x)","F",0
280,-1,0,0,0.000000," ","integrate((e*sec(d*x+c))^(2/3)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,-1,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/3)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,-1,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(1/3)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
283,-1,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(2/3)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
284,0,0,0,0.000000," ","integrate(sec(d*x+c)^(4/3)*(a+a*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}} \sec\left(d x + c\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(1/3)*sec(d*x + c)^(4/3), x)","F",0
285,0,0,0,0.000000," ","integrate(sec(d*x+c)^(4/3)*(a+a*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^(4/3), x)","F",0
286,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/3)*(a+a*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{\frac{5}{3}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^(5/3), x)","F",0
287,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(4/3)/sec(d*x+c)^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
288,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^4,x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{4} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^4*sec(f*x + e)^n, x)","F",0
289,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^3,x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{3} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^3*sec(f*x + e)^n, x)","F",0
290,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^2,x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{2} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^2*sec(f*x + e)^n, x)","F",0
291,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e)),x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)*sec(f*x + e)^n, x)","F",0
292,0,0,0,0.000000," ","integrate(sec(f*x+e)^n/(a+a*sec(f*x+e)),x, algorithm=""giac"")","\int \frac{\sec\left(f x + e\right)^{n}}{a \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sec(f*x + e)^n/(a*sec(f*x + e) + a), x)","F",0
293,0,0,0,0.000000," ","integrate(sec(f*x+e)^n/(a+a*sec(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\sec\left(f x + e\right)^{n}}{{\left(a \sec\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sec(f*x + e)^n/(a*sec(f*x + e) + a)^2, x)","F",0
294,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(1+sec(f*x+e))^(5/2),x, algorithm=""giac"")","\int \sec\left(f x + e\right)^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sec(f*x + e)^n*(sec(f*x + e) + 1)^(5/2), x)","F",0
295,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(1+sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int \sec\left(f x + e\right)^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sec(f*x + e)^n*(sec(f*x + e) + 1)^(3/2), x)","F",0
296,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(1+sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sec\left(f x + e\right)^{n} \sqrt{\sec\left(f x + e\right) + 1}\,{d x}"," ",0,"integrate(sec(f*x + e)^n*sqrt(sec(f*x + e) + 1), x)","F",0
297,0,0,0,0.000000," ","integrate(sec(f*x+e)^n/(1+sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(f x + e\right)^{n}}{\sqrt{\sec\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate(sec(f*x + e)^n/sqrt(sec(f*x + e) + 1), x)","F",0
298,0,0,0,0.000000," ","integrate(sec(f*x+e)^n/(1+sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(f x + e\right)^{n}}{{\left(\sec\left(f x + e\right) + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)^n/(sec(f*x + e) + 1)^(3/2), x)","F",0
299,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(1+sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int \left(-\sec\left(f x + e\right)\right)^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n*(sec(f*x + e) + 1)^(3/2), x)","F",0
300,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(1+sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \left(-\sec\left(f x + e\right)\right)^{n} \sqrt{\sec\left(f x + e\right) + 1}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n*sqrt(sec(f*x + e) + 1), x)","F",0
301,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n/(1+sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(-\sec\left(f x + e\right)\right)^{n}}{\sqrt{\sec\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n/sqrt(sec(f*x + e) + 1), x)","F",0
302,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n/(1+sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\left(-\sec\left(f x + e\right)\right)^{n}}{{\left(\sec\left(f x + e\right) + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n/(sec(f*x + e) + 1)^(3/2), x)","F",0
303,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(1+sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n*(sec(f*x + e) + 1)^(3/2), x)","F",0
304,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(1+sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{n} \sqrt{\sec\left(f x + e\right) + 1}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n*sqrt(sec(f*x + e) + 1), x)","F",0
305,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n/(1+sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{n}}{\sqrt{\sec\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n/sqrt(sec(f*x + e) + 1), x)","F",0
306,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n/(1+sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{n}}{{\left(\sec\left(f x + e\right) + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n/(sec(f*x + e) + 1)^(3/2), x)","F",0
307,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^(5/2),x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^(5/2)*sec(f*x + e)^n, x)","F",0
308,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^(3/2)*sec(f*x + e)^n, x)","F",0
309,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(f x + e\right) + a} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate(sqrt(a*sec(f*x + e) + a)*sec(f*x + e)^n, x)","F",0
310,0,0,0,0.000000," ","integrate(sec(f*x+e)^n/(a+a*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(f x + e\right)^{n}}{\sqrt{a \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(sec(f*x + e)^n/sqrt(a*sec(f*x + e) + a), x)","F",0
311,0,0,0,0.000000," ","integrate(sec(f*x+e)^n/(a+a*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(f x + e\right)^{n}}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)^n/(a*sec(f*x + e) + a)^(3/2), x)","F",0
312,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(a+a*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(-\sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^(3/2)*(-sec(f*x + e))^n, x)","F",0
313,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(a+a*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(f x + e\right) + a} \left(-\sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate(sqrt(a*sec(f*x + e) + a)*(-sec(f*x + e))^n, x)","F",0
314,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n/(a+a*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(-\sec\left(f x + e\right)\right)^{n}}{\sqrt{a \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n/sqrt(a*sec(f*x + e) + a), x)","F",0
315,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n/(a+a*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\left(-\sec\left(f x + e\right)\right)^{n}}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n/(a*sec(f*x + e) + a)^(3/2), x)","F",0
316,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+a*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^(3/2)*(d*sec(f*x + e))^n, x)","F",0
317,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+a*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(f x + e\right) + a} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate(sqrt(a*sec(f*x + e) + a)*(d*sec(f*x + e))^n, x)","F",0
318,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n/(a+a*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{n}}{\sqrt{a \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n/sqrt(a*sec(f*x + e) + a), x)","F",0
319,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n/(a+a*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{n}}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n/(a*sec(f*x + e) + a)^(3/2), x)","F",0
320,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(a-a*sec(f*x+e))^(5/2),x, algorithm=""giac"")","\int {\left(-a \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}} \left(-\sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((-a*sec(f*x + e) + a)^(5/2)*(-sec(f*x + e))^n, x)","F",0
321,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(a-a*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(-a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(-\sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((-a*sec(f*x + e) + a)^(3/2)*(-sec(f*x + e))^n, x)","F",0
322,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(a-a*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{-a \sec\left(f x + e\right) + a} \left(-\sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate(sqrt(-a*sec(f*x + e) + a)*(-sec(f*x + e))^n, x)","F",0
323,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n/(a-a*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(-\sec\left(f x + e\right)\right)^{n}}{\sqrt{-a \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n/sqrt(-a*sec(f*x + e) + a), x)","F",0
324,-2,0,0,0.000000," ","integrate((-sec(f*x+e))^n/(a-a*sec(f*x+e))^(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/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(f*t_nostep+exp(1)))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^3+t_nostep)]Discontinuities at zeroes of t_nostep^3+t_nostep were not checkedUnable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^3+t_nostep)]Discontinuities at zeroes of t_nostep^3+t_nostep were not checkedUnable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^3+t_nostep)]Discontinuities at zeroes of t_nostep^3+t_nostep were not checkedDiscontinuities at zeroes of cos(f*t_nostep+exp(1)) were not checkedUnable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/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(t_nostep),abs(t_nostep^2-1)]Evaluation time: 1.61Unable to divide, perhaps due to rounding error%%%{1,[0,4,1,0]%%%}+%%%{2,[0,2,1,1]%%%}+%%%{1,[0,0,1,2]%%%} / %%%{1,[0,0,0,2]%%%} Error: Bad Argument Value","F(-2)",0
325,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a-a*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(-a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((-a*sec(f*x + e) + a)^(3/2)*sec(f*x + e)^n, x)","F",0
326,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a-a*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{-a \sec\left(f x + e\right) + a} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate(sqrt(-a*sec(f*x + e) + a)*sec(f*x + e)^n, x)","F",0
327,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a-a*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(-a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((-a*sec(f*x + e) + a)^(3/2)*(d*sec(f*x + e))^n, x)","F",0
328,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a-a*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{-a \sec\left(f x + e\right) + a} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate(sqrt(-a*sec(f*x + e) + a)*(d*sec(f*x + e))^n, x)","F",0
329,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(1+sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(\sec\left(f x + e\right) + 1\right)}^{m} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((sec(f*x + e) + 1)^m*sec(f*x + e)^n, x)","F",0
330,0,0,0,0.000000," ","integrate((1-sec(f*x+e))^m*sec(f*x+e)^n,x, algorithm=""giac"")","\int {\left(-\sec\left(f x + e\right) + 1\right)}^{m} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((-sec(f*x + e) + 1)^m*sec(f*x + e)^n, x)","F",0
331,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*sec(f*x + e)^n, x)","F",0
332,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a-a*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(-a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((-a*sec(f*x + e) + a)^m*sec(f*x + e)^n, x)","F",0
333,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(1+sec(f*x+e))^m,x, algorithm=""giac"")","\int \left(-\sec\left(f x + e\right)\right)^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n*(sec(f*x + e) + 1)^m, x)","F",0
334,0,0,0,0.000000," ","integrate((1-sec(f*x+e))^m*(-sec(f*x+e))^n,x, algorithm=""giac"")","\int \left(-\sec\left(f x + e\right)\right)^{n} {\left(-\sec\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n*(-sec(f*x + e) + 1)^m, x)","F",0
335,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(a+a*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m} \left(-\sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*(-sec(f*x + e))^n, x)","F",0
336,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(a-a*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(-a \sec\left(f x + e\right) + a\right)}^{m} \left(-\sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((-a*sec(f*x + e) + a)^m*(-sec(f*x + e))^n, x)","F",0
337,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(1+sec(f*x+e))^m,x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n*(sec(f*x + e) + 1)^m, x)","F",0
338,0,0,0,0.000000," ","integrate((1-sec(f*x+e))^m*(d*sec(f*x+e))^n,x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{n} {\left(-\sec\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n*(-sec(f*x + e) + 1)^m, x)","F",0
339,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+a*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*(d*sec(f*x + e))^n, x)","F",0
340,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a-a*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(-a \sec\left(f x + e\right) + a\right)}^{m} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((-a*sec(f*x + e) + a)^m*(d*sec(f*x + e))^n, x)","F",0
341,0,0,0,0.000000," ","integrate(sec(f*x+e)^4*(a+a*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*sec(f*x + e)^4, x)","F",0
342,0,0,0,0.000000," ","integrate(sec(f*x+e)^3*(a+a*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*sec(f*x + e)^3, x)","F",0
343,0,0,0,0.000000," ","integrate(sec(f*x+e)^2*(a+a*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*sec(f*x + e)^2, x)","F",0
344,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*sec(f*x + e), x)","F",0
345,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m, x)","F",0
346,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+a*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*cos(f*x + e), x)","F",0
347,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(3/2)*(a+a*sec(f*x+e))^m,x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sec\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(3/2)*(a*sec(f*x + e) + a)^m, x)","F",0
348,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/2)*(a+a*sec(f*x+e))^m,x, algorithm=""giac"")","\int \sqrt{d \sec\left(f x + e\right)} {\left(a \sec\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e))*(a*sec(f*x + e) + a)^m, x)","F",0
349,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^m/(d*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(f x + e\right) + a\right)}^{m}}{\sqrt{d \sec\left(f x + e\right)}}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m/sqrt(d*sec(f*x + e)), x)","F",0
350,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^m/(d*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(f x + e\right) + a\right)}^{m}}{\left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m/(d*sec(f*x + e))^(3/2), x)","F",0
351,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
352,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
353,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
354,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
355,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
356,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
357,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
358,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{a \sec\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
359,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*cos(d*x + c)^(9/2), x)","F",0
360,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*cos(d*x + c)^(7/2), x)","F",0
361,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2), x)","F",0
362,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
363,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
364,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
365,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
366,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/cos(d*x + c)^(5/2), x)","F",0
367,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3*cos(d*x + c)^(9/2), x)","F",0
368,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3*cos(d*x + c)^(7/2), x)","F",0
369,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3*cos(d*x + c)^(5/2), x)","F",0
370,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3*cos(d*x + c)^(3/2), x)","F",0
371,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
372,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
373,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3/cos(d*x + c)^(3/2), x)","F",0
374,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a), x)","F",0
375,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a), x)","F",0
376,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
377,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
378,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
379,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
380,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
381,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^2, x)","F",0
382,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^2, x)","F",0
383,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
384,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
385,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2)), x)","F",0
386,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2)), x)","F",0
387,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^2*cos(d*x + c)^(7/2)), x)","F",0
388,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(9/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^2*cos(d*x + c)^(9/2)), x)","F",0
389,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^3, x)","F",0
390,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^3, x)","F",0
391,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^3, x)","F",0
392,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^3*sqrt(cos(d*x + c))), x)","F",0
393,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^3*cos(d*x + c)^(3/2)), x)","F",0
394,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^3*cos(d*x + c)^(5/2)), x)","F",0
395,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^3*cos(d*x + c)^(7/2)), x)","F",0
396,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(9/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^3*cos(d*x + c)^(9/2)), x)","F",0
397,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(11/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^3*cos(d*x + c)^(11/2)), x)","F",0
398,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
399,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
400,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
401,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
402,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a \sec\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
403,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{a \sec\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
404,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{a \sec\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
405,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2), x)","F",0
406,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2), x)","F",0
407,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2), x)","F",0
408,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
409,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)/sqrt(cos(d*x + c)), x)","F",0
410,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)/cos(d*x + c)^(3/2), x)","F",0
411,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)/cos(d*x + c)^(5/2), x)","F",0
412,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(9/2), x)","F",0
413,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(7/2), x)","F",0
414,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2), x)","F",0
415,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2), x)","F",0
416,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c)), x)","F",0
417,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)/sqrt(cos(d*x + c)), x)","F",0
418,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)/cos(d*x + c)^(3/2), x)","F",0
419,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)/cos(d*x + c)^(5/2), x)","F",0
420,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
421,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
422,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/sqrt(a*sec(d*x + c) + a), x)","F",0
423,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
424,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
425,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
426,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
427,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
428,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
429,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^(3/2), x)","F",0
430,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
431,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
432,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
433,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2)), x)","F",0
434,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
435,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^(5/2), x)","F",0
436,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
437,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
438,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
439,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(7/2)), x)","F",0
440,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(9/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(9/2)), x)","F",0
441,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n*(a+a*sec(f*x+e))^3,x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{3} \left(d \cos\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^3*(d*cos(f*x + e))^n, x)","F",0
442,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n*(a+a*sec(f*x+e))^2,x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{2} \left(d \cos\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^2*(d*cos(f*x + e))^n, x)","F",0
443,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n*(a+a*sec(f*x+e)),x, algorithm=""giac"")","\int {\left(a \sec\left(f x + e\right) + a\right)} \left(d \cos\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)*(d*cos(f*x + e))^n, x)","F",0
444,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n/(a+a*sec(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \cos\left(f x + e\right)\right)^{n}}{a \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*cos(f*x + e))^n/(a*sec(f*x + e) + a), x)","F",0
445,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n/(a+a*sec(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \cos\left(f x + e\right)\right)^{n}}{{\left(a \sec\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*cos(f*x + e))^n/(a*sec(f*x + e) + a)^2, x)","F",0
446,1,164,0,0.219571," ","integrate(sec(d*x+c)^4*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{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} - 15 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 40 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, 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) - 15 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(9*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 - 15*b*tan(1/2*d*x + 1/2*c)^7 - 40*a*tan(1/2*d*x + 1/2*c)^5 - 9*b*tan(1/2*d*x + 1/2*c)^5 + 40*a*tan(1/2*d*x + 1/2*c)^3 - 9*b*tan(1/2*d*x + 1/2*c)^3 - 24*a*tan(1/2*d*x + 1/2*c) - 15*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
447,1,122,0,0.230051," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, b \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) - 6 \, 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}}}{6 \, d}"," ",0,"1/6*(3*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(3*a*tan(1/2*d*x + 1/2*c)^5 - 6*b*tan(1/2*d*x + 1/2*c)^5 + 4*b*tan(1/2*d*x + 1/2*c)^3 - 3*a*tan(1/2*d*x + 1/2*c) - 6*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
448,1,107,0,0.212634," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{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*(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
449,1,63,0,0.199383," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"(a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*b*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","B",0
450,1,49,0,0.141514," ","integrate(a+b*sec(d*x+c),x, algorithm=""giac"")","a x + \frac{b {\left(\log\left({\left| \frac{1}{\sin\left(d x + c\right)} + \sin\left(d x + c\right) + 2 \right|}\right) - \log\left({\left| \frac{1}{\sin\left(d x + c\right)} + \sin\left(d x + c\right) - 2 \right|}\right)\right)}}{4 \, d}"," ",0,"a*x + 1/4*b*(log(abs(1/sin(d*x + c) + sin(d*x + c) + 2)) - log(abs(1/sin(d*x + c) + sin(d*x + c) - 2)))/d","B",0
451,1,39,0,0.159140," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} b + \frac{2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}}{d}"," ",0,"((d*x + c)*b + 2*a*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","B",0
452,1,82,0,0.164454," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} a - \frac{2 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((d*x + c)*a - 2*(a*tan(1/2*d*x + 1/2*c)^3 - 2*b*tan(1/2*d*x + 1/2*c)^3 - a*tan(1/2*d*x + 1/2*c) - 2*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
453,1,98,0,0.148084," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} b + \frac{2 \, {\left(6 \, 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} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, 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)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(d*x + c)*b + 2*(6*a*tan(1/2*d*x + 1/2*c)^5 - 3*b*tan(1/2*d*x + 1/2*c)^5 + 4*a*tan(1/2*d*x + 1/2*c)^3 + 6*a*tan(1/2*d*x + 1/2*c) + 3*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
454,1,140,0,0.170478," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{9 \, {\left(d x + c\right)} a - \frac{2 \, {\left(15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(9*(d*x + c)*a - 2*(15*a*tan(1/2*d*x + 1/2*c)^7 - 24*b*tan(1/2*d*x + 1/2*c)^7 - 9*a*tan(1/2*d*x + 1/2*c)^5 - 40*b*tan(1/2*d*x + 1/2*c)^5 + 9*a*tan(1/2*d*x + 1/2*c)^3 - 40*b*tan(1/2*d*x + 1/2*c)^3 - 15*a*tan(1/2*d*x + 1/2*c) - 24*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
455,1,154,0,0.180325," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{45 \, {\left(d x + c\right)} b + \frac{2 \, {\left(120 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 160 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, 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)}^{5}}}{120 \, d}"," ",0,"1/120*(45*(d*x + c)*b + 2*(120*a*tan(1/2*d*x + 1/2*c)^9 - 75*b*tan(1/2*d*x + 1/2*c)^9 + 160*a*tan(1/2*d*x + 1/2*c)^7 - 30*b*tan(1/2*d*x + 1/2*c)^7 + 464*a*tan(1/2*d*x + 1/2*c)^5 + 160*a*tan(1/2*d*x + 1/2*c)^3 + 30*b*tan(1/2*d*x + 1/2*c)^3 + 120*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)^5)/d","A",0
456,1,272,0,0.232400," ","integrate(sec(d*x+c)^4*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{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} - 75 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 160 \, 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} - 80 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 200 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 232 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, b^{2} \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) + 75 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, 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)}^{5}}}{60 \, d}"," ",0,"1/60*(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 - 75*a*b*tan(1/2*d*x + 1/2*c)^9 + 60*b^2*tan(1/2*d*x + 1/2*c)^9 - 160*a^2*tan(1/2*d*x + 1/2*c)^7 + 30*a*b*tan(1/2*d*x + 1/2*c)^7 - 80*b^2*tan(1/2*d*x + 1/2*c)^7 + 200*a^2*tan(1/2*d*x + 1/2*c)^5 + 232*b^2*tan(1/2*d*x + 1/2*c)^5 - 160*a^2*tan(1/2*d*x + 1/2*c)^3 - 30*a*b*tan(1/2*d*x + 1/2*c)^3 - 80*b^2*tan(1/2*d*x + 1/2*c)^3 + 60*a^2*tan(1/2*d*x + 1/2*c) + 75*a*b*tan(1/2*d*x + 1/2*c) + 60*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
457,1,258,0,0.270089," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, {\left(4 \, a^{2} + 3 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(4 \, a^{2} + 3 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 80 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, b^{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) + 48 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(4*a^2 + 3*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*a^2 + 3*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(12*a^2*tan(1/2*d*x + 1/2*c)^7 - 48*a*b*tan(1/2*d*x + 1/2*c)^7 + 15*b^2*tan(1/2*d*x + 1/2*c)^7 - 12*a^2*tan(1/2*d*x + 1/2*c)^5 + 80*a*b*tan(1/2*d*x + 1/2*c)^5 + 9*b^2*tan(1/2*d*x + 1/2*c)^5 - 12*a^2*tan(1/2*d*x + 1/2*c)^3 - 80*a*b*tan(1/2*d*x + 1/2*c)^3 + 9*b^2*tan(1/2*d*x + 1/2*c)^3 + 12*a^2*tan(1/2*d*x + 1/2*c) + 48*a*b*tan(1/2*d*x + 1/2*c) + 15*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
458,1,178,0,0.236090," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{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} + 3 \, b^{2} \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} - 2 \, 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) + 3 \, 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}}}{3 \, d}"," ",0,"1/3*(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 + 3*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*a^2*tan(1/2*d*x + 1/2*c)^3 - 2*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) + 3*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
459,1,129,0,0.246073," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{{\left(2 \, a^{2} + b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, a^{2} + b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(4 \, 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} - 4 \, 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(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((2*a^2 + b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*a^2 + b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(4*a*b*tan(1/2*d*x + 1/2*c)^3 - b^2*tan(1/2*d*x + 1/2*c)^3 - 4*a*b*tan(1/2*d*x + 1/2*c) - b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
460,1,77,0,0.189821," ","integrate((a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{{\left(d x + c\right)} a^{2} + 2 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"((d*x + c)*a^2 + 2*a*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*a*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*b^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","B",0
461,1,78,0,0.217472," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} a b + b^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - b^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}}{d}"," ",0,"(2*(d*x + c)*a*b + b^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - b^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","B",0
462,1,96,0,0.198933," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{{\left(a^{2} + 2 \, b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((a^2 + 2*b^2)*(d*x + c) - 2*(a^2*tan(1/2*d*x + 1/2*c)^3 - 4*a*b*tan(1/2*d*x + 1/2*c)^3 - a^2*tan(1/2*d*x + 1/2*c) - 4*a*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
463,1,153,0,0.212144," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} a b + \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} + 3 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, 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) + 3 \, 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}}}{3 \, d}"," ",0,"1/3*(3*(d*x + c)*a*b + 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 + 3*b^2*tan(1/2*d*x + 1/2*c)^5 + 2*a^2*tan(1/2*d*x + 1/2*c)^3 + 6*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) + 3*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
464,1,224,0,0.189611," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, a^{2} + 4 \, b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 80 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*a^2 + 4*b^2)*(d*x + c) - 2*(15*a^2*tan(1/2*d*x + 1/2*c)^7 - 48*a*b*tan(1/2*d*x + 1/2*c)^7 + 12*b^2*tan(1/2*d*x + 1/2*c)^7 - 9*a^2*tan(1/2*d*x + 1/2*c)^5 - 80*a*b*tan(1/2*d*x + 1/2*c)^5 + 12*b^2*tan(1/2*d*x + 1/2*c)^5 + 9*a^2*tan(1/2*d*x + 1/2*c)^3 - 80*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*b^2*tan(1/2*d*x + 1/2*c)^3 - 15*a^2*tan(1/2*d*x + 1/2*c) - 48*a*b*tan(1/2*d*x + 1/2*c) - 12*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
465,1,247,0,0.215561," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{45 \, {\left(d x + c\right)} a b + \frac{2 \, {\left(60 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 80 \, 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} + 160 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 232 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 200 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 80 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, b^{2} \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) + 75 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, 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)}^{5}}}{60 \, d}"," ",0,"1/60*(45*(d*x + c)*a*b + 2*(60*a^2*tan(1/2*d*x + 1/2*c)^9 - 75*a*b*tan(1/2*d*x + 1/2*c)^9 + 60*b^2*tan(1/2*d*x + 1/2*c)^9 + 80*a^2*tan(1/2*d*x + 1/2*c)^7 - 30*a*b*tan(1/2*d*x + 1/2*c)^7 + 160*b^2*tan(1/2*d*x + 1/2*c)^7 + 232*a^2*tan(1/2*d*x + 1/2*c)^5 + 200*b^2*tan(1/2*d*x + 1/2*c)^5 + 80*a^2*tan(1/2*d*x + 1/2*c)^3 + 30*a*b*tan(1/2*d*x + 1/2*c)^3 + 160*b^2*tan(1/2*d*x + 1/2*c)^3 + 60*a^2*tan(1/2*d*x + 1/2*c) + 75*a*b*tan(1/2*d*x + 1/2*c) + 60*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
466,1,367,0,0.295050," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{15 \, {\left(4 \, a^{3} + 9 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(4 \, a^{3} + 9 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(60 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 225 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 960 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 90 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 160 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1200 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 464 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 120 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 960 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 90 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 60 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 360 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 225 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, 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)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(4*a^3 + 9*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*a^3 + 9*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(60*a^3*tan(1/2*d*x + 1/2*c)^9 - 360*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 225*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 120*b^3*tan(1/2*d*x + 1/2*c)^9 - 120*a^3*tan(1/2*d*x + 1/2*c)^7 + 960*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 90*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 160*b^3*tan(1/2*d*x + 1/2*c)^7 - 1200*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 464*b^3*tan(1/2*d*x + 1/2*c)^5 + 120*a^3*tan(1/2*d*x + 1/2*c)^3 + 960*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 90*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 160*b^3*tan(1/2*d*x + 1/2*c)^3 - 60*a^3*tan(1/2*d*x + 1/2*c) - 360*a^2*b*tan(1/2*d*x + 1/2*c) - 225*a*b^2*tan(1/2*d*x + 1/2*c) - 120*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
467,1,330,0,0.279862," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, {\left(4 \, a^{2} b + b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(4 \, a^{2} b + b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(8 \, 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} + 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, 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} - 40 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, 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} + 40 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, 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) - 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{8 \, d}"," ",0,"1/8*(3*(4*a^2*b + b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*a^2*b + b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(8*a^3*tan(1/2*d*x + 1/2*c)^7 - 12*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 24*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 5*b^3*tan(1/2*d*x + 1/2*c)^7 - 24*a^3*tan(1/2*d*x + 1/2*c)^5 + 12*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 40*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 3*b^3*tan(1/2*d*x + 1/2*c)^5 + 24*a^3*tan(1/2*d*x + 1/2*c)^3 + 12*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 40*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 3*b^3*tan(1/2*d*x + 1/2*c)^3 - 8*a^3*tan(1/2*d*x + 1/2*c) - 12*a^2*b*tan(1/2*d*x + 1/2*c) - 24*a*b^2*tan(1/2*d*x + 1/2*c) - 5*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
468,1,205,0,0.275302," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(18 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, 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)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(2*a^3 + 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*a^3 + 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(18*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 9*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*b^3*tan(1/2*d*x + 1/2*c)^5 - 36*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 4*b^3*tan(1/2*d*x + 1/2*c)^3 + 18*a^2*b*tan(1/2*d*x + 1/2*c) + 9*a*b^2*tan(1/2*d*x + 1/2*c) + 6*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
469,1,145,0,0.199444," ","integrate((a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} a^{3} + {\left(6 \, a^{2} b + b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(6 \, a^{2} b + b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*a^3 + (6*a^2*b + b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (6*a^2*b + b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*a*b^2*tan(1/2*d*x + 1/2*c)^3 - b^3*tan(1/2*d*x + 1/2*c)^3 - 6*a*b^2*tan(1/2*d*x + 1/2*c) - b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
470,1,131,0,0.230604," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} a^{2} b + 3 \, a b^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, a b^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"(3*(d*x + c)*a^2*b + 3*a*b^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*a*b^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(a^3*tan(1/2*d*x + 1/2*c)^3 - b^3*tan(1/2*d*x + 1/2*c)^3 - a^3*tan(1/2*d*x + 1/2*c) - b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","A",0
471,1,137,0,0.248420," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, b^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, b^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(a^{3} + 6 \, a b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*b^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*b^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (a^3 + 6*a*b^2)*(d*x + c) - 2*(a^3*tan(1/2*d*x + 1/2*c)^3 - 6*a^2*b*tan(1/2*d*x + 1/2*c)^3 - a^3*tan(1/2*d*x + 1/2*c) - 6*a^2*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
472,1,170,0,0.230403," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, a 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}}}{6 \, d}"," ",0,"1/6*(3*(3*a^2*b + 2*b^3)*(d*x + c) + 2*(6*a^3*tan(1/2*d*x + 1/2*c)^5 - 9*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*a^3*tan(1/2*d*x + 1/2*c)^3 + 36*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*a^3*tan(1/2*d*x + 1/2*c) + 9*a^2*b*tan(1/2*d*x + 1/2*c) + 18*a*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
473,1,297,0,0.245067," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, {\left(a^{3} + 4 \, a b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 8 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{8 \, d}"," ",0,"1/8*(3*(a^3 + 4*a*b^2)*(d*x + c) - 2*(5*a^3*tan(1/2*d*x + 1/2*c)^7 - 24*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 12*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 8*b^3*tan(1/2*d*x + 1/2*c)^7 - 3*a^3*tan(1/2*d*x + 1/2*c)^5 - 40*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 12*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 24*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*a^3*tan(1/2*d*x + 1/2*c)^3 - 40*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 12*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 24*b^3*tan(1/2*d*x + 1/2*c)^3 - 5*a^3*tan(1/2*d*x + 1/2*c) - 24*a^2*b*tan(1/2*d*x + 1/2*c) - 12*a*b^2*tan(1/2*d*x + 1/2*c) - 8*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
474,1,332,0,0.228186," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{15 \, {\left(9 \, a^{2} b + 4 \, b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(120 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 225 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 160 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 90 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 960 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 90 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 960 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 225 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, 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)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(9*a^2*b + 4*b^3)*(d*x + c) + 2*(120*a^3*tan(1/2*d*x + 1/2*c)^9 - 225*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*b^3*tan(1/2*d*x + 1/2*c)^9 + 160*a^3*tan(1/2*d*x + 1/2*c)^7 - 90*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 960*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 120*b^3*tan(1/2*d*x + 1/2*c)^7 + 464*a^3*tan(1/2*d*x + 1/2*c)^5 + 1200*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 160*a^3*tan(1/2*d*x + 1/2*c)^3 + 90*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 960*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*b^3*tan(1/2*d*x + 1/2*c)^3 + 120*a^3*tan(1/2*d*x + 1/2*c) + 225*a^2*b*tan(1/2*d*x + 1/2*c) + 360*a*b^2*tan(1/2*d*x + 1/2*c) + 60*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
475,1,431,0,0.268151," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{15 \, {\left(5 \, a^{3} + 18 \, a b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(165 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 720 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 450 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 25 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1680 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 630 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 880 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 450 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3744 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 180 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1440 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 450 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3744 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 180 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1440 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1680 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 630 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 880 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 165 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 720 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 450 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(5*a^3 + 18*a*b^2)*(d*x + c) - 2*(165*a^3*tan(1/2*d*x + 1/2*c)^11 - 720*a^2*b*tan(1/2*d*x + 1/2*c)^11 + 450*a*b^2*tan(1/2*d*x + 1/2*c)^11 - 240*b^3*tan(1/2*d*x + 1/2*c)^11 - 25*a^3*tan(1/2*d*x + 1/2*c)^9 - 1680*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 630*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 880*b^3*tan(1/2*d*x + 1/2*c)^9 + 450*a^3*tan(1/2*d*x + 1/2*c)^7 - 3744*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 180*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 1440*b^3*tan(1/2*d*x + 1/2*c)^7 - 450*a^3*tan(1/2*d*x + 1/2*c)^5 - 3744*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 180*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 1440*b^3*tan(1/2*d*x + 1/2*c)^5 + 25*a^3*tan(1/2*d*x + 1/2*c)^3 - 1680*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 630*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 880*b^3*tan(1/2*d*x + 1/2*c)^3 - 165*a^3*tan(1/2*d*x + 1/2*c) - 720*a^2*b*tan(1/2*d*x + 1/2*c) - 450*a*b^2*tan(1/2*d*x + 1/2*c) - 240*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","B",0
476,1,592,0,0.309791," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{15 \, {\left(8 \, a^{4} + 36 \, a^{2} b^{2} + 5 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(8 \, a^{4} + 36 \, a^{2} b^{2} + 5 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(120 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 900 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 165 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 360 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3520 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1260 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2240 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 25 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 240 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5760 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4992 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 450 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5760 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 360 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4992 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 450 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 360 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3520 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1260 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2240 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 25 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 960 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 900 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 960 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 165 \, b^{4} \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*(15*(8*a^4 + 36*a^2*b^2 + 5*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(8*a^4 + 36*a^2*b^2 + 5*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(120*a^4*tan(1/2*d*x + 1/2*c)^11 - 960*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 900*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 960*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 165*b^4*tan(1/2*d*x + 1/2*c)^11 - 360*a^4*tan(1/2*d*x + 1/2*c)^9 + 3520*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 1260*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 2240*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 25*b^4*tan(1/2*d*x + 1/2*c)^9 + 240*a^4*tan(1/2*d*x + 1/2*c)^7 - 5760*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 360*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 4992*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 450*b^4*tan(1/2*d*x + 1/2*c)^7 + 240*a^4*tan(1/2*d*x + 1/2*c)^5 + 5760*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 360*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 4992*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 450*b^4*tan(1/2*d*x + 1/2*c)^5 - 360*a^4*tan(1/2*d*x + 1/2*c)^3 - 3520*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 1260*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 2240*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 25*b^4*tan(1/2*d*x + 1/2*c)^3 + 120*a^4*tan(1/2*d*x + 1/2*c) + 960*a^3*b*tan(1/2*d*x + 1/2*c) + 900*a^2*b^2*tan(1/2*d*x + 1/2*c) + 960*a*b^3*tan(1/2*d*x + 1/2*c) + 165*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
477,1,461,0,0.292260," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{15 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(30 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 180 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 30 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 480 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 40 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 180 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 600 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 116 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 120 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 30 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{30 \, d}"," ",0,"1/30*(15*(4*a^3*b + 3*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*a^3*b + 3*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(30*a^4*tan(1/2*d*x + 1/2*c)^9 - 60*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 180*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 75*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 30*b^4*tan(1/2*d*x + 1/2*c)^9 - 120*a^4*tan(1/2*d*x + 1/2*c)^7 + 120*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 480*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 30*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 40*b^4*tan(1/2*d*x + 1/2*c)^7 + 180*a^4*tan(1/2*d*x + 1/2*c)^5 + 600*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 116*b^4*tan(1/2*d*x + 1/2*c)^5 - 120*a^4*tan(1/2*d*x + 1/2*c)^3 - 120*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 480*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 30*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 40*b^4*tan(1/2*d*x + 1/2*c)^3 + 30*a^4*tan(1/2*d*x + 1/2*c) + 60*a^3*b*tan(1/2*d*x + 1/2*c) + 180*a^2*b^2*tan(1/2*d*x + 1/2*c) + 75*a*b^3*tan(1/2*d*x + 1/2*c) + 30*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
478,1,360,0,0.291555," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, {\left(8 \, a^{4} + 24 \, a^{2} b^{2} + 3 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(8 \, a^{4} + 24 \, a^{2} b^{2} + 3 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(96 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 288 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 288 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 96 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, 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) - 15 \, b^{4} \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*(3*(8*a^4 + 24*a^2*b^2 + 3*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(8*a^4 + 24*a^2*b^2 + 3*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(96*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 72*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 96*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 15*b^4*tan(1/2*d*x + 1/2*c)^7 - 288*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 72*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 160*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 9*b^4*tan(1/2*d*x + 1/2*c)^5 + 288*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 72*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 160*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 9*b^4*tan(1/2*d*x + 1/2*c)^3 - 96*a^3*b*tan(1/2*d*x + 1/2*c) - 72*a^2*b^2*tan(1/2*d*x + 1/2*c) - 96*a*b^3*tan(1/2*d*x + 1/2*c) - 15*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
479,1,221,0,0.198320," ","integrate((a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} a^{4} + 6 \, {\left(2 \, a^{3} b + a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 6 \, {\left(2 \, a^{3} b + a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(18 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, 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)\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^4 + 6*(2*a^3*b + a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 6*(2*a^3*b + a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(18*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*b^4*tan(1/2*d*x + 1/2*c)^5 - 36*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 2*b^4*tan(1/2*d*x + 1/2*c)^3 + 18*a^2*b^2*tan(1/2*d*x + 1/2*c) + 6*a*b^3*tan(1/2*d*x + 1/2*c) + 3*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
480,1,179,0,0.259704," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{8 \, {\left(d x + c\right)} a^{3} b + \frac{4 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + {\left(12 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(12 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(8 \, 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} - 8 \, a b^{3} \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(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(8*(d*x + c)*a^3*b + 4*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + (12*a^2*b^2 + b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (12*a^2*b^2 + b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(8*a*b^3*tan(1/2*d*x + 1/2*c)^3 - b^4*tan(1/2*d*x + 1/2*c)^3 - 8*a*b^3*tan(1/2*d*x + 1/2*c) - b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
481,1,170,0,0.269253," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{8 \, a b^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 8 \, a b^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{4 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + {\left(a^{4} + 12 \, a^{2} b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a^{3} 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*(8*a*b^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 8*a*b^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 4*b^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + (a^4 + 12*a^2*b^2)*(d*x + c) - 2*(a^4*tan(1/2*d*x + 1/2*c)^3 - 8*a^3*b*tan(1/2*d*x + 1/2*c)^3 - a^4*tan(1/2*d*x + 1/2*c) - 8*a^3*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
482,1,212,0,0.237943," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, b^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, b^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 6 \, {\left(a^{3} b + 2 \, a b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*b^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*b^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 6*(a^3*b + 2*a*b^3)*(d*x + c) + 2*(3*a^4*tan(1/2*d*x + 1/2*c)^5 - 6*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 18*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 2*a^4*tan(1/2*d*x + 1/2*c)^3 + 36*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*a^4*tan(1/2*d*x + 1/2*c) + 6*a^3*b*tan(1/2*d*x + 1/2*c) + 18*a^2*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
483,1,318,0,0.241702," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, a^{4} + 24 \, a^{2} b^{2} + 8 \, b^{4}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(15 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 288 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 288 \, a b^{3} \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) - 96 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, 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)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*a^4 + 24*a^2*b^2 + 8*b^4)*(d*x + c) - 2*(15*a^4*tan(1/2*d*x + 1/2*c)^7 - 96*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 72*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 96*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 9*a^4*tan(1/2*d*x + 1/2*c)^5 - 160*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 72*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 288*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*a^4*tan(1/2*d*x + 1/2*c)^3 - 160*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 72*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 288*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*a^4*tan(1/2*d*x + 1/2*c) - 96*a^3*b*tan(1/2*d*x + 1/2*c) - 72*a^2*b^2*tan(1/2*d*x + 1/2*c) - 96*a*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
484,1,425,0,0.237904," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{15 \, {\left(3 \, a^{3} b + 4 \, a b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(30 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 180 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 30 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 40 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 116 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 600 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 180 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 30 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{30 \, d}"," ",0,"1/30*(15*(3*a^3*b + 4*a*b^3)*(d*x + c) + 2*(30*a^4*tan(1/2*d*x + 1/2*c)^9 - 75*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 180*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 30*b^4*tan(1/2*d*x + 1/2*c)^9 + 40*a^4*tan(1/2*d*x + 1/2*c)^7 - 30*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 480*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 120*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 120*b^4*tan(1/2*d*x + 1/2*c)^7 + 116*a^4*tan(1/2*d*x + 1/2*c)^5 + 600*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 180*b^4*tan(1/2*d*x + 1/2*c)^5 + 40*a^4*tan(1/2*d*x + 1/2*c)^3 + 30*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 480*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 120*b^4*tan(1/2*d*x + 1/2*c)^3 + 30*a^4*tan(1/2*d*x + 1/2*c) + 75*a^3*b*tan(1/2*d*x + 1/2*c) + 180*a^2*b^2*tan(1/2*d*x + 1/2*c) + 60*a*b^3*tan(1/2*d*x + 1/2*c) + 30*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
485,1,550,0,0.252208," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{15 \, {\left(5 \, a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(165 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 900 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 120 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 25 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2240 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1260 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3520 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 450 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4992 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5760 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 450 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4992 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 360 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5760 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 240 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2240 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1260 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3520 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 165 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 900 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, b^{4} \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*(15*(5*a^4 + 36*a^2*b^2 + 8*b^4)*(d*x + c) - 2*(165*a^4*tan(1/2*d*x + 1/2*c)^11 - 960*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 900*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 960*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 120*b^4*tan(1/2*d*x + 1/2*c)^11 - 25*a^4*tan(1/2*d*x + 1/2*c)^9 - 2240*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 1260*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 3520*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 360*b^4*tan(1/2*d*x + 1/2*c)^9 + 450*a^4*tan(1/2*d*x + 1/2*c)^7 - 4992*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 360*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 5760*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 240*b^4*tan(1/2*d*x + 1/2*c)^7 - 450*a^4*tan(1/2*d*x + 1/2*c)^5 - 4992*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 360*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 5760*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 240*b^4*tan(1/2*d*x + 1/2*c)^5 + 25*a^4*tan(1/2*d*x + 1/2*c)^3 - 2240*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 1260*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 3520*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 360*b^4*tan(1/2*d*x + 1/2*c)^3 - 165*a^4*tan(1/2*d*x + 1/2*c) - 960*a^3*b*tan(1/2*d*x + 1/2*c) - 900*a^2*b^2*tan(1/2*d*x + 1/2*c) - 960*a*b^3*tan(1/2*d*x + 1/2*c) - 120*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","B",0
486,1,380,0,0.221737," ","integrate((a+b*sec(d*x+c))^5,x, algorithm=""giac"")","\frac{24 \, {\left(d x + c\right)} a^{5} + 3 \, {\left(40 \, a^{4} b + 40 \, a^{2} b^{3} + 3 \, b^{5}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(40 \, a^{4} b + 40 \, a^{2} b^{3} + 3 \, b^{5}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(240 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 720 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 120 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 200 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 720 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 200 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(24*(d*x + c)*a^5 + 3*(40*a^4*b + 40*a^2*b^3 + 3*b^5)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(40*a^4*b + 40*a^2*b^3 + 3*b^5)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(240*a^3*b^2*tan(1/2*d*x + 1/2*c)^7 - 120*a^2*b^3*tan(1/2*d*x + 1/2*c)^7 + 120*a*b^4*tan(1/2*d*x + 1/2*c)^7 - 15*b^5*tan(1/2*d*x + 1/2*c)^7 - 720*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 120*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 200*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 9*b^5*tan(1/2*d*x + 1/2*c)^5 + 720*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 200*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 9*b^5*tan(1/2*d*x + 1/2*c)^3 - 240*a^3*b^2*tan(1/2*d*x + 1/2*c) - 120*a^2*b^3*tan(1/2*d*x + 1/2*c) - 120*a*b^4*tan(1/2*d*x + 1/2*c) - 15*b^5*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
487,1,286,0,0.274857," ","integrate(sec(d*x+c)^5/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{12 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)} a^{4}}{\sqrt{-a^{2} + b^{2}} b^{4}} - \frac{3 \, {\left(2 \, a^{3} + a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} + \frac{3 \, {\left(2 \, a^{3} + a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} - \frac{2 \, {\left(6 \, 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} - 12 \, 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} + 6 \, 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^{3}}}{6 \, d}"," ",0,"1/6*(12*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))*a^4/(sqrt(-a^2 + b^2)*b^4) - 3*(2*a^3 + a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 + 3*(2*a^3 + a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 - 2*(6*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 - 12*a^2*tan(1/2*d*x + 1/2*c)^3 - 4*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*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^3))/d","B",0
488,1,211,0,0.258601," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)} a^{3}}{\sqrt{-a^{2} + b^{2}} b^{3}} - \frac{{\left(2 \, a^{2} + 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} + 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*(4*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))*a^3/(sqrt(-a^2 + b^2)*b^3) - (2*a^2 + b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^3 + (2*a^2 + 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","A",0
489,1,152,0,0.295253," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c)),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)} a^{2}}{\sqrt{-a^{2} + b^{2}} b^{2}} - \frac{a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{2}} + \frac{a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{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)} b}}{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)))*a^2/(sqrt(-a^2 + b^2)*b^2) - a*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^2 + a*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^2 - 2*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*b))/d","A",0
490,1,120,0,0.235698," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c)),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)} a}{\sqrt{-a^{2} + b^{2}} b} - \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}}{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)))*a/(sqrt(-a^2 + b^2)*b) - log(abs(tan(1/2*d*x + 1/2*c) + 1))/b + log(abs(tan(1/2*d*x + 1/2*c) - 1))/b)/d","B",0
491,1,77,0,0.206656," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\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)}}{\sqrt{-a^{2} + b^{2}} 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)))/(sqrt(-a^2 + b^2)*d)","A",0
492,1,218,0,0.194307," ","integrate(1/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(\sqrt{-a^{2} + b^{2}} {\left(a - 2 \, b\right)} {\left| -a + b \right|} - \sqrt{-a^{2} + b^{2}} {\left| a \right|} {\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 + \sqrt{{\left(a + b\right)} {\left(a - b\right)} + b^{2}}}{a - b}}}\right)\right)}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} a^{2} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} {\left| a \right|}} + \frac{{\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 - \sqrt{{\left(a + b\right)} {\left(a - b\right)} + b^{2}}}{a - b}}}\right)\right)} {\left(a - 2 \, b + {\left| a \right|}\right)}}{a^{2} - b {\left| a \right|}}}{d}"," ",0,"((sqrt(-a^2 + b^2)*(a - 2*b)*abs(-a + b) - sqrt(-a^2 + b^2)*abs(a)*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(b + sqrt((a + b)*(a - b) + b^2))/(a - b))))/((a^2 - 2*a*b + b^2)*a^2 + (a^2*b - 2*a*b^2 + b^3)*abs(a)) + (pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(b - sqrt((a + b)*(a - b) + b^2))/(a - b))))*(a - 2*b + abs(a))/(a^2 - b*abs(a)))/d","B",0
493,1,126,0,0.216824," ","integrate(cos(d*x+c)/(a+b*sec(d*x+c)),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^{2}}{\sqrt{-a^{2} + b^{2}} a^{2}} - \frac{{\left(d x + c\right)} b}{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}}{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^2/(sqrt(-a^2 + b^2)*a^2) - (d*x + c)*b/a^2 + 2*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a))/d","A",0
494,1,178,0,0.204211," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)} b^{3}}{\sqrt{-a^{2} + b^{2}} a^{3}} - \frac{{\left(a^{2} + 2 \, b^{2}\right)} {\left(d x + c\right)}}{a^{3}} + \frac{2 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}}}{2 \, d}"," ",0,"-1/2*(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)))*b^3/(sqrt(-a^2 + b^2)*a^3) - (a^2 + 2*b^2)*(d*x + c)/a^3 + 2*(a*tan(1/2*d*x + 1/2*c)^3 + 2*b*tan(1/2*d*x + 1/2*c)^3 - a*tan(1/2*d*x + 1/2*c) + 2*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2))/d","A",0
495,1,249,0,0.220726," ","integrate(cos(d*x+c)^3/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{12 \, {\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^{4}}{\sqrt{-a^{2} + b^{2}} a^{4}} - \frac{3 \, {\left(a^{2} b + 2 \, b^{3}\right)} {\left(d x + c\right)}}{a^{4}} + \frac{2 \, {\left(6 \, 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} + 4 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, 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} a^{3}}}{6 \, d}"," ",0,"1/6*(12*(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^4/(sqrt(-a^2 + b^2)*a^4) - 3*(a^2*b + 2*b^3)*(d*x + c)/a^4 + 2*(6*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 + 4*a^2*tan(1/2*d*x + 1/2*c)^3 + 12*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*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*a^3))/d","A",0
496,1,393,0,0.238329," ","integrate(cos(d*x+c)^4/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{48 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)} b^{5}}{\sqrt{-a^{2} + b^{2}} a^{5}} - \frac{3 \, {\left(3 \, a^{4} + 4 \, a^{2} b^{2} + 8 \, b^{4}\right)} {\left(d x + c\right)}}{a^{5}} + \frac{2 \, {\left(15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{4}}}{24 \, d}"," ",0,"-1/24*(48*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))*b^5/(sqrt(-a^2 + b^2)*a^5) - 3*(3*a^4 + 4*a^2*b^2 + 8*b^4)*(d*x + c)/a^5 + 2*(15*a^3*tan(1/2*d*x + 1/2*c)^7 + 24*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 12*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 24*b^3*tan(1/2*d*x + 1/2*c)^7 - 9*a^3*tan(1/2*d*x + 1/2*c)^5 + 40*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 12*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 72*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*a^3*tan(1/2*d*x + 1/2*c)^3 + 40*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 12*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 72*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*a^3*tan(1/2*d*x + 1/2*c) + 24*a^2*b*tan(1/2*d*x + 1/2*c) - 12*a*b^2*tan(1/2*d*x + 1/2*c) + 24*b^3*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^4))/d","B",0
497,1,299,0,0.306282," ","integrate(sec(d*x+c)^5/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{2} b^{3} - b^{5}\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{4 \, {\left(3 \, a^{5} - 4 \, a^{3} b^{2}\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^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{{\left(6 \, a^{2} + b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} - \frac{{\left(6 \, a^{2} + b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} + \frac{2 \, {\left(4 \, 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} - 4 \, 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^{3}}}{2 \, d}"," ",0,"1/2*(4*a^4*tan(1/2*d*x + 1/2*c)/((a^2*b^3 - b^5)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) - 4*(3*a^5 - 4*a^3*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^4 - b^6)*sqrt(-a^2 + b^2)) + (6*a^2 + b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 - (6*a^2 + b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 + 2*(4*a*tan(1/2*d*x + 1/2*c)^3 + b*tan(1/2*d*x + 1/2*c)^3 - 4*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^3))/d","A",0
498,1,331,0,0.296301," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(2 \, a^{4} - 3 \, a^{2} b^{2}\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^{2} b^{3} - b^{5}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\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)} {\left(a^{2} b^{2} - b^{4}\right)}} - \frac{a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{3}} + \frac{a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{3}}\right)}}{d}"," ",0,"2*((2*a^4 - 3*a^2*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^3 - b^5)*sqrt(-a^2 + b^2)) - (2*a^3*tan(1/2*d*x + 1/2*c)^3 - a^2*b*tan(1/2*d*x + 1/2*c)^3 - a*b^2*tan(1/2*d*x + 1/2*c)^3 + b^3*tan(1/2*d*x + 1/2*c)^3 - 2*a^3*tan(1/2*d*x + 1/2*c) - a^2*b*tan(1/2*d*x + 1/2*c) + a*b^2*tan(1/2*d*x + 1/2*c) + b^3*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^2*b^2 - b^4)) - a*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^3 + a*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^3)/d","B",0
499,1,203,0,0.275582," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{2} b - b^{3}\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{2 \, {\left(a^{3} - 2 \, a b^{2}\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^{2} b^{2} - b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{2}} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{2}}}{d}"," ",0,"(2*a^2*tan(1/2*d*x + 1/2*c)/((a^2*b - b^3)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) - 2*(a^3 - 2*a*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 - b^4)*sqrt(-a^2 + b^2)) + log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^2 - log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^2)/d","A",0
500,1,150,0,0.232828," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-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}{{\left(a^{2} - b^{2}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{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} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)} {\left(a^{2} - b^{2}\right)}}\right)}}{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/((a^2 - b^2)*sqrt(-a^2 + b^2)) + a*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^2 - b^2)))/d","A",0
501,1,150,0,0.239192," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)} a}{{\left(a^{2} - b^{2}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{b \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)} {\left(a^{2} - b^{2}\right)}}\right)}}{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)))*a/((a^2 - b^2)*sqrt(-a^2 + b^2)) - b*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^2 - b^2)))/d","A",0
502,1,179,0,0.199008," ","integrate(1/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{3} - a b^{2}\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{2 \, {\left(2 \, a^{2} b - b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} - a^{2} b^{2}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{d x + c}{a^{2}}}{d}"," ",0,"-(2*b^2*tan(1/2*d*x + 1/2*c)/((a^3 - a*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) + 2*(2*a^2*b - b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4 - a^2*b^2)*sqrt(-a^2 + b^2)) - (d*x + c)/a^2)/d","A",0
503,1,837,0,0.387035," ","integrate(cos(d*x+c)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, a^{7} b - 5 \, a^{6} b^{2} - 4 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 2 \, a^{3} b^{5} - 4 \, a^{2} b^{6} - 2 \, a^{2} b {\left| -a^{5} + a^{3} b^{2} \right|} - a b^{2} {\left| -a^{5} + a^{3} b^{2} \right|} + 2 \, b^{3} {\left| -a^{5} + a^{3} 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^{4} b - a^{2} b^{3} + \sqrt{{\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} {\left(a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}\right)} + {\left(a^{4} b - a^{2} b^{3}\right)}^{2}}}{a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}}}}\right)\right)}}{a^{4} b {\left| -a^{5} + a^{3} b^{2} \right|} - a^{2} b^{3} {\left| -a^{5} + a^{3} b^{2} \right|} + {\left(a^{5} - a^{3} b^{2}\right)}^{2}} + \frac{{\left({\left(2 \, a^{2} b + a b^{2} - 2 \, b^{3}\right)} \sqrt{-a^{2} + b^{2}} {\left| -a^{5} + a^{3} b^{2} \right|} {\left| -a + b \right|} + {\left(2 \, a^{7} b - 5 \, a^{6} b^{2} - 4 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 2 \, a^{3} b^{5} - 4 \, a^{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{a^{4} b - a^{2} b^{3} - \sqrt{{\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} {\left(a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}\right)} + {\left(a^{4} b - a^{2} b^{3}\right)}^{2}}}{a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}}}}\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} - {\left(a^{6} b - 2 \, a^{5} b^{2} + 2 \, a^{3} b^{4} - a^{2} b^{5}\right)} {\left| -a^{5} + a^{3} b^{2} \right|}} - \frac{2 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)} {\left(a^{4} - a^{2} b^{2}\right)}}}{d}"," ",0,"-((2*a^7*b - 5*a^6*b^2 - 4*a^5*b^3 + 9*a^4*b^4 + 2*a^3*b^5 - 4*a^2*b^6 - 2*a^2*b*abs(-a^5 + a^3*b^2) - a*b^2*abs(-a^5 + a^3*b^2) + 2*b^3*abs(-a^5 + a^3*b^2))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^4*b - a^2*b^3 + sqrt((a^5 + a^4*b - a^3*b^2 - a^2*b^3)*(a^5 - a^4*b - a^3*b^2 + a^2*b^3) + (a^4*b - a^2*b^3)^2))/(a^5 - a^4*b - a^3*b^2 + a^2*b^3))))/(a^4*b*abs(-a^5 + a^3*b^2) - a^2*b^3*abs(-a^5 + a^3*b^2) + (a^5 - a^3*b^2)^2) + ((2*a^2*b + a*b^2 - 2*b^3)*sqrt(-a^2 + b^2)*abs(-a^5 + a^3*b^2)*abs(-a + b) + (2*a^7*b - 5*a^6*b^2 - 4*a^5*b^3 + 9*a^4*b^4 + 2*a^3*b^5 - 4*a^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(-(a^4*b - a^2*b^3 - sqrt((a^5 + a^4*b - a^3*b^2 - a^2*b^3)*(a^5 - a^4*b - a^3*b^2 + a^2*b^3) + (a^4*b - a^2*b^3)^2))/(a^5 - a^4*b - a^3*b^2 + a^2*b^3))))/((a^5 - a^3*b^2)^2*(a^2 - 2*a*b + b^2) - (a^6*b - 2*a^5*b^2 + 2*a^3*b^4 - a^2*b^5)*abs(-a^5 + a^3*b^2)) - 2*(a^3*tan(1/2*d*x + 1/2*c)^3 - a^2*b*tan(1/2*d*x + 1/2*c)^3 - a*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*b^3*tan(1/2*d*x + 1/2*c)^3 - a^3*tan(1/2*d*x + 1/2*c) - a^2*b*tan(1/2*d*x + 1/2*c) + a*b^2*tan(1/2*d*x + 1/2*c) + 2*b^3*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*b*tan(1/2*d*x + 1/2*c)^2 - a - b)*(a^4 - a^2*b^2)))/d","B",0
504,1,264,0,0.214239," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{5} - a^{3} b^{2}\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{4 \, {\left(4 \, a^{2} b^{3} - 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} - a^{4} b^{2}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{{\left(a^{2} + 6 \, b^{2}\right)} {\left(d x + c\right)}}{a^{4}} + \frac{2 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}}}{2 \, d}"," ",0,"-1/2*(4*b^4*tan(1/2*d*x + 1/2*c)/((a^5 - a^3*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) + 4*(4*a^2*b^3 - 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 - a^4*b^2)*sqrt(-a^2 + b^2)) - (a^2 + 6*b^2)*(d*x + c)/a^4 + 2*(a*tan(1/2*d*x + 1/2*c)^3 + 4*b*tan(1/2*d*x + 1/2*c)^3 - a*tan(1/2*d*x + 1/2*c) + 4*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3))/d","A",0
505,1,335,0,0.243495," ","integrate(cos(d*x+c)^3/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - a^{4} b^{2}\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{6 \, {\left(5 \, a^{2} b^{4} - 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)}}{{\left(a^{7} - a^{5} b^{2}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{3 \, {\left(a^{2} b + 4 \, b^{3}\right)} {\left(d x + c\right)}}{a^{5}} + \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} + 9 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, 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) + 9 \, 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} a^{4}}}{3 \, d}"," ",0,"1/3*(6*b^5*tan(1/2*d*x + 1/2*c)/((a^6 - a^4*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) + 6*(5*a^2*b^4 - 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)))/((a^7 - a^5*b^2)*sqrt(-a^2 + b^2)) - 3*(a^2*b + 4*b^3)*(d*x + c)/a^5 + 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 + 9*b^2*tan(1/2*d*x + 1/2*c)^5 + 2*a^2*tan(1/2*d*x + 1/2*c)^3 + 18*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) + 9*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^4))/d","A",0
506,1,383,0,0.404382," ","integrate(sec(d*x+c)^5/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, a^{6} - 5 \, a^{4} b^{2} + 4 \, a^{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)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{4 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}} + \frac{3 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} - \frac{3 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} + \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)} b^{3}}}{d}"," ",0,"-(3*(2*a^6 - 5*a^4*b^2 + 4*a^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)))/((a^4*b^4 - 2*a^2*b^6 + b^8)*sqrt(-a^2 + b^2)) + (4*a^6*tan(1/2*d*x + 1/2*c)^3 - 5*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 7*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 + 8*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 4*a^6*tan(1/2*d*x + 1/2*c) - 5*a^5*b*tan(1/2*d*x + 1/2*c) + 7*a^4*b^2*tan(1/2*d*x + 1/2*c) + 8*a^3*b^3*tan(1/2*d*x + 1/2*c))/((a^4*b^3 - 2*a^2*b^5 + b^7)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2) + 3*a*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 - 3*a*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 + 2*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*b^3))/d","A",0
507,1,347,0,0.366580," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, a^{5} - 5 \, a^{3} b^{2} + 6 \, a 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)}}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{2 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{3}} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{3}}}{d}"," ",0,"((2*a^5 - 5*a^3*b^2 + 6*a*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)))/((a^4*b^3 - 2*a^2*b^5 + b^7)*sqrt(-a^2 + b^2)) + (2*a^5*tan(1/2*d*x + 1/2*c)^3 - 3*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 5*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*a^5*tan(1/2*d*x + 1/2*c) - 3*a^4*b*tan(1/2*d*x + 1/2*c) + 5*a^3*b^2*tan(1/2*d*x + 1/2*c) + 6*a^2*b^3*tan(1/2*d*x + 1/2*c))/((a^4*b^2 - 2*a^2*b^4 + b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2) + log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^3 - log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^3)/d","A",0
508,1,253,0,0.348042," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\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} + 2 \, b^{2}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"-((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 + 2*b^2)/((a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)) - (a^3*tan(1/2*d*x + 1/2*c)^3 + 3*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 4*a*b^2*tan(1/2*d*x + 1/2*c)^3 + a^3*tan(1/2*d*x + 1/2*c) - 3*a^2*b*tan(1/2*d*x + 1/2*c) - 4*a*b^2*tan(1/2*d*x + 1/2*c))/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","A",0
509,1,277,0,0.318876," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)} a b}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"(3*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))*a*b/((a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)) - (2*a^3*tan(1/2*d*x + 1/2*c)^3 - a^2*b*tan(1/2*d*x + 1/2*c)^3 + a*b^2*tan(1/2*d*x + 1/2*c)^3 - 2*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*a^3*tan(1/2*d*x + 1/2*c) - a^2*b*tan(1/2*d*x + 1/2*c) - a*b^2*tan(1/2*d*x + 1/2*c) - 2*b^3*tan(1/2*d*x + 1/2*c))/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
510,1,254,0,0.330418," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\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(2 \, a^{2} + b^{2}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{4 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"-((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)))*(2*a^2 + b^2)/((a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)) - (4*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 3*a*b^2*tan(1/2*d*x + 1/2*c)^3 - b^3*tan(1/2*d*x + 1/2*c)^3 - 4*a^2*b*tan(1/2*d*x + 1/2*c) - 3*a*b^2*tan(1/2*d*x + 1/2*c) + b^3*tan(1/2*d*x + 1/2*c))/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
511,1,322,0,0.213282," ","integrate(1/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(6 \, a^{4} b - 5 \, a^{2} b^{3} + 2 \, 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^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{6 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}} + \frac{d x + c}{a^{3}}}{d}"," ",0,"((6*a^4*b - 5*a^2*b^3 + 2*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^7 - 2*a^5*b^2 + a^3*b^4)*sqrt(-a^2 + b^2)) - (6*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 3*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 2*b^5*tan(1/2*d*x + 1/2*c)^3 - 6*a^3*b^2*tan(1/2*d*x + 1/2*c) - 5*a^2*b^3*tan(1/2*d*x + 1/2*c) + 3*a*b^4*tan(1/2*d*x + 1/2*c) + 2*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2) + (d*x + c)/a^3)/d","B",0
512,1,357,0,0.312535," ","integrate(cos(d*x+c)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + 2 \, 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)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{8 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}} + \frac{3 \, {\left(d x + c\right)} b}{a^{4}} - \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^{3}}}{d}"," ",0,"-(3*(4*a^4*b^2 - 5*a^2*b^4 + 2*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)))/((a^8 - 2*a^6*b^2 + a^4*b^4)*sqrt(-a^2 + b^2)) - (8*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 7*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 5*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 4*b^6*tan(1/2*d*x + 1/2*c)^3 - 8*a^3*b^3*tan(1/2*d*x + 1/2*c) - 7*a^2*b^4*tan(1/2*d*x + 1/2*c) + 5*a*b^5*tan(1/2*d*x + 1/2*c) + 4*b^6*tan(1/2*d*x + 1/2*c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2) + 3*(d*x + c)*b/a^4 - 2*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^3))/d","A",0
513,1,1723,0,0.829752," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left({\left(a^{6} - a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} - 23 \, a^{2} b^{4} - 6 \, a b^{5} + 12 \, b^{6}\right)} \sqrt{-a^{2} + b^{2}} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} {\left| -a + b \right|} - {\left(a^{15} - a^{14} b + 8 \, a^{13} b^{2} - 28 \, a^{12} b^{3} - 42 \, a^{11} b^{4} + 111 \, a^{10} b^{5} + 68 \, a^{9} b^{6} - 158 \, a^{8} b^{7} - 47 \, a^{7} b^{8} + 100 \, a^{6} b^{9} + 12 \, a^{5} b^{10} - 24 \, a^{4} b^{11}\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^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5} + \sqrt{{\left(a^{9} + a^{8} b - 2 \, a^{7} b^{2} - 2 \, a^{6} b^{3} + a^{5} b^{4} + a^{4} b^{5}\right)} {\left(a^{9} - a^{8} b - 2 \, a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} - a^{4} b^{5}\right)} + {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)}^{2}}}{a^{9} - a^{8} b - 2 \, a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} - a^{4} b^{5}}}}\right)\right)}}{{\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} + {\left(a^{10} b - 2 \, a^{9} b^{2} - a^{8} b^{3} + 4 \, a^{7} b^{4} - a^{6} b^{5} - 2 \, a^{5} b^{6} + a^{4} b^{7}\right)} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|}} + \frac{{\left(a^{15} - a^{14} b + 8 \, a^{13} b^{2} - 28 \, a^{12} b^{3} - 42 \, a^{11} b^{4} + 111 \, a^{10} b^{5} + 68 \, a^{9} b^{6} - 158 \, a^{8} b^{7} - 47 \, a^{7} b^{8} + 100 \, a^{6} b^{9} + 12 \, a^{5} b^{10} - 24 \, a^{4} b^{11} + a^{6} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - a^{5} b {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 10 \, a^{4} b^{2} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 10 \, a^{3} b^{3} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 23 \, a^{2} b^{4} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 6 \, a b^{5} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 12 \, b^{6} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} 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^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5} - \sqrt{{\left(a^{9} + a^{8} b - 2 \, a^{7} b^{2} - 2 \, a^{6} b^{3} + a^{5} b^{4} + a^{4} b^{5}\right)} {\left(a^{9} - a^{8} b - 2 \, a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} - a^{4} b^{5}\right)} + {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)}^{2}}}{a^{9} - a^{8} b - 2 \, a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} - a^{4} b^{5}}}}\right)\right)}}{a^{8} b {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 2 \, a^{6} b^{3} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + a^{4} b^{5} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - {\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)}^{2}} + \frac{2 \, {\left(a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 13 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 17 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 26 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 29 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 67 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 26 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 29 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 67 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 33 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 17 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(((a^6 - a^5*b + 10*a^4*b^2 + 10*a^3*b^3 - 23*a^2*b^4 - 6*a*b^5 + 12*b^6)*sqrt(-a^2 + b^2)*abs(a^9 - 2*a^7*b^2 + a^5*b^4)*abs(-a + b) - (a^15 - a^14*b + 8*a^13*b^2 - 28*a^12*b^3 - 42*a^11*b^4 + 111*a^10*b^5 + 68*a^9*b^6 - 158*a^8*b^7 - 47*a^7*b^8 + 100*a^6*b^9 + 12*a^5*b^10 - 24*a^4*b^11)*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^8*b - 2*a^6*b^3 + a^4*b^5 + sqrt((a^9 + a^8*b - 2*a^7*b^2 - 2*a^6*b^3 + a^5*b^4 + a^4*b^5)*(a^9 - a^8*b - 2*a^7*b^2 + 2*a^6*b^3 + a^5*b^4 - a^4*b^5) + (a^8*b - 2*a^6*b^3 + a^4*b^5)^2))/(a^9 - a^8*b - 2*a^7*b^2 + 2*a^6*b^3 + a^5*b^4 - a^4*b^5))))/((a^9 - 2*a^7*b^2 + a^5*b^4)^2*(a^2 - 2*a*b + b^2) + (a^10*b - 2*a^9*b^2 - a^8*b^3 + 4*a^7*b^4 - a^6*b^5 - 2*a^5*b^6 + a^4*b^7)*abs(a^9 - 2*a^7*b^2 + a^5*b^4)) + (a^15 - a^14*b + 8*a^13*b^2 - 28*a^12*b^3 - 42*a^11*b^4 + 111*a^10*b^5 + 68*a^9*b^6 - 158*a^8*b^7 - 47*a^7*b^8 + 100*a^6*b^9 + 12*a^5*b^10 - 24*a^4*b^11 + a^6*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - a^5*b*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 10*a^4*b^2*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 10*a^3*b^3*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 23*a^2*b^4*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 6*a*b^5*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 12*b^6*abs(a^9 - 2*a^7*b^2 + a^5*b^4))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^8*b - 2*a^6*b^3 + a^4*b^5 - sqrt((a^9 + a^8*b - 2*a^7*b^2 - 2*a^6*b^3 + a^5*b^4 + a^4*b^5)*(a^9 - a^8*b - 2*a^7*b^2 + 2*a^6*b^3 + a^5*b^4 - a^4*b^5) + (a^8*b - 2*a^6*b^3 + a^4*b^5)^2))/(a^9 - a^8*b - 2*a^7*b^2 + 2*a^6*b^3 + a^5*b^4 - a^4*b^5))))/(a^8*b*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 2*a^6*b^3*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + a^4*b^5*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - (a^9 - 2*a^7*b^2 + a^5*b^4)^2) + 2*(a^7*tan(1/2*d*x + 1/2*c)^7 + 4*a^6*b*tan(1/2*d*x + 1/2*c)^7 - 13*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 2*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 33*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 17*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 - 18*a*b^6*tan(1/2*d*x + 1/2*c)^7 + 12*b^7*tan(1/2*d*x + 1/2*c)^7 - 3*a^7*tan(1/2*d*x + 1/2*c)^5 - 4*a^6*b*tan(1/2*d*x + 1/2*c)^5 - 5*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 + 26*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 29*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 - 67*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 - 18*a*b^6*tan(1/2*d*x + 1/2*c)^5 + 36*b^7*tan(1/2*d*x + 1/2*c)^5 + 3*a^7*tan(1/2*d*x + 1/2*c)^3 - 4*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 5*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 + 26*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 29*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 - 67*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 18*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 36*b^7*tan(1/2*d*x + 1/2*c)^3 - a^7*tan(1/2*d*x + 1/2*c) + 4*a^6*b*tan(1/2*d*x + 1/2*c) + 13*a^5*b^2*tan(1/2*d*x + 1/2*c) - 2*a^4*b^3*tan(1/2*d*x + 1/2*c) - 33*a^3*b^4*tan(1/2*d*x + 1/2*c) - 17*a^2*b^5*tan(1/2*d*x + 1/2*c) + 18*a*b^6*tan(1/2*d*x + 1/2*c) + 12*b^7*tan(1/2*d*x + 1/2*c))/((a^8 - 2*a^6*b^2 + a^4*b^4)*(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
514,1,592,0,0.388903," ","integrate(sec(d*x+c)^6/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(8 \, a^{8} - 28 \, a^{6} b^{2} + 35 \, a^{4} b^{4} - 20 \, a^{2} 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)}}{{\left(a^{6} b^{5} - 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} - b^{11}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{18 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 42 \, a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 117 \, a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 152 \, a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 236 \, a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 42 \, a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 117 \, a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10}\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)}^{3}} + \frac{12 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{5}} - \frac{12 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{5}} + \frac{6 \, \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)} b^{4}}}{3 \, d}"," ",0,"-1/3*(3*(8*a^8 - 28*a^6*b^2 + 35*a^4*b^4 - 20*a^2*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)))/((a^6*b^5 - 3*a^4*b^7 + 3*a^2*b^9 - b^11)*sqrt(-a^2 + b^2)) + (18*a^9*tan(1/2*d*x + 1/2*c)^5 - 42*a^8*b*tan(1/2*d*x + 1/2*c)^5 - 24*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 + 117*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 - 24*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 105*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 60*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 - 36*a^9*tan(1/2*d*x + 1/2*c)^3 + 152*a^7*b^2*tan(1/2*d*x + 1/2*c)^3 - 236*a^5*b^4*tan(1/2*d*x + 1/2*c)^3 + 120*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 + 18*a^9*tan(1/2*d*x + 1/2*c) + 42*a^8*b*tan(1/2*d*x + 1/2*c) - 24*a^7*b^2*tan(1/2*d*x + 1/2*c) - 117*a^6*b^3*tan(1/2*d*x + 1/2*c) - 24*a^5*b^4*tan(1/2*d*x + 1/2*c) + 105*a^4*b^5*tan(1/2*d*x + 1/2*c) + 60*a^3*b^6*tan(1/2*d*x + 1/2*c))/((a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3) + 12*a*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^5 - 12*a*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^5 + 6*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*b^4))/d","A",0
515,1,559,0,0.467838," ","integrate(sec(d*x+c)^5/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, a^{7} - 7 \, a^{5} b^{2} + 8 \, a^{3} b^{4} - 8 \, a 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)}}{{\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{6 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 56 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 116 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\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)}^{3}} + \frac{3 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} - \frac{3 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}}}{3 \, d}"," ",0,"1/3*(3*(2*a^7 - 7*a^5*b^2 + 8*a^3*b^4 - 8*a*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)))/((a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10)*sqrt(-a^2 + b^2)) + (6*a^8*tan(1/2*d*x + 1/2*c)^5 - 15*a^7*b*tan(1/2*d*x + 1/2*c)^5 - 6*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 + 45*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 60*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 + 36*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 - 12*a^8*tan(1/2*d*x + 1/2*c)^3 + 56*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 - 116*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 + 72*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 + 6*a^8*tan(1/2*d*x + 1/2*c) + 15*a^7*b*tan(1/2*d*x + 1/2*c) - 6*a^6*b^2*tan(1/2*d*x + 1/2*c) - 45*a^5*b^3*tan(1/2*d*x + 1/2*c) - 6*a^4*b^4*tan(1/2*d*x + 1/2*c) + 60*a^3*b^5*tan(1/2*d*x + 1/2*c) + 36*a^2*b^6*tan(1/2*d*x + 1/2*c))/((a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3) + 3*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 - 3*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4)/d","B",0
516,1,403,0,0.318041," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{6 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(3*a^2*b + 2*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) + (6*a^5*tan(1/2*d*x + 1/2*c)^5 - 3*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 6*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 27*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 18*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 4*a^5*tan(1/2*d*x + 1/2*c)^3 - 32*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 36*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 6*a^5*tan(1/2*d*x + 1/2*c) + 3*a^4*b*tan(1/2*d*x + 1/2*c) + 6*a^3*b^2*tan(1/2*d*x + 1/2*c) + 27*a^2*b^3*tan(1/2*d*x + 1/2*c) + 18*a*b^4*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","A",0
517,1,431,0,0.376599," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(a^{3} + 4 \, a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{3 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 28 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(a^3 + 4*a*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^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) - (3*a^5*tan(1/2*d*x + 1/2*c)^5 + 12*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 27*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*b^5*tan(1/2*d*x + 1/2*c)^5 - 28*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 16*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 12*b^5*tan(1/2*d*x + 1/2*c)^3 - 3*a^5*tan(1/2*d*x + 1/2*c) + 12*a^4*b*tan(1/2*d*x + 1/2*c) + 27*a^3*b^2*tan(1/2*d*x + 1/2*c) + 12*a^2*b^3*tan(1/2*d*x + 1/2*c) + 6*a*b^4*tan(1/2*d*x + 1/2*c) + 6*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","B",0
518,1,431,0,0.353410," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(4 \, a^{2} b + b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{6 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(4*a^2*b + b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) + (6*a^5*tan(1/2*d*x + 1/2*c)^5 - 6*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 12*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 27*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 12*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*b^5*tan(1/2*d*x + 1/2*c)^5 - 12*a^5*tan(1/2*d*x + 1/2*c)^3 - 16*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 28*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 6*a^5*tan(1/2*d*x + 1/2*c) + 6*a^4*b*tan(1/2*d*x + 1/2*c) + 12*a^3*b^2*tan(1/2*d*x + 1/2*c) + 27*a^2*b^3*tan(1/2*d*x + 1/2*c) + 12*a*b^4*tan(1/2*d*x + 1/2*c) - 3*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","B",0
519,1,403,0,0.355768," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{18 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(2*a^3 + 3*a*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^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) - (18*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 27*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 3*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*b^5*tan(1/2*d*x + 1/2*c)^5 - 36*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 32*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 4*b^5*tan(1/2*d*x + 1/2*c)^3 + 18*a^4*b*tan(1/2*d*x + 1/2*c) + 27*a^3*b^2*tan(1/2*d*x + 1/2*c) + 6*a^2*b^3*tan(1/2*d*x + 1/2*c) + 3*a*b^4*tan(1/2*d*x + 1/2*c) + 6*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","B",0
520,1,532,0,0.265932," ","integrate(1/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(8 \, a^{6} b - 8 \, a^{4} b^{3} + 7 \, a^{2} b^{5} - 2 \, 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^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{36 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 116 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} 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)}^{3}} + \frac{3 \, {\left(d x + c\right)}}{a^{4}}}{3 \, d}"," ",0,"1/3*(3*(8*a^6*b - 8*a^4*b^3 + 7*a^2*b^5 - 2*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^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*sqrt(-a^2 + b^2)) - (36*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 - 60*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 + 45*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 - 15*a*b^7*tan(1/2*d*x + 1/2*c)^5 + 6*b^8*tan(1/2*d*x + 1/2*c)^5 - 72*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 + 116*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 - 56*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 + 12*b^8*tan(1/2*d*x + 1/2*c)^3 + 36*a^6*b^2*tan(1/2*d*x + 1/2*c) + 60*a^5*b^3*tan(1/2*d*x + 1/2*c) - 6*a^4*b^4*tan(1/2*d*x + 1/2*c) - 45*a^3*b^5*tan(1/2*d*x + 1/2*c) - 6*a^2*b^6*tan(1/2*d*x + 1/2*c) + 15*a*b^7*tan(1/2*d*x + 1/2*c) + 6*b^8*tan(1/2*d*x + 1/2*c))/((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3) + 3*(d*x + c)/a^4)/d","B",0
521,1,564,0,0.322577," ","integrate(cos(d*x+c)/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(20 \, a^{6} b^{2} - 35 \, a^{4} b^{4} + 28 \, a^{2} b^{6} - 8 \, b^{8}\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^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{60 \, a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 117 \, a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 42 \, a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 120 \, a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 236 \, a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 152 \, a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 117 \, a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 42 \, a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}} + \frac{12 \, {\left(d x + c\right)} b}{a^{5}} - \frac{6 \, \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^{4}}}{3 \, d}"," ",0,"-1/3*(3*(20*a^6*b^2 - 35*a^4*b^4 + 28*a^2*b^6 - 8*b^8)*(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^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*sqrt(-a^2 + b^2)) - (60*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 - 105*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 24*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 117*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 - 24*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 - 42*a*b^8*tan(1/2*d*x + 1/2*c)^5 + 18*b^9*tan(1/2*d*x + 1/2*c)^5 - 120*a^6*b^3*tan(1/2*d*x + 1/2*c)^3 + 236*a^4*b^5*tan(1/2*d*x + 1/2*c)^3 - 152*a^2*b^7*tan(1/2*d*x + 1/2*c)^3 + 36*b^9*tan(1/2*d*x + 1/2*c)^3 + 60*a^6*b^3*tan(1/2*d*x + 1/2*c) + 105*a^5*b^4*tan(1/2*d*x + 1/2*c) - 24*a^4*b^5*tan(1/2*d*x + 1/2*c) - 117*a^3*b^6*tan(1/2*d*x + 1/2*c) - 24*a^2*b^7*tan(1/2*d*x + 1/2*c) + 42*a*b^8*tan(1/2*d*x + 1/2*c) + 18*b^9*tan(1/2*d*x + 1/2*c))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3) + 12*(d*x + c)*b/a^5 - 6*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^4))/d","A",0
522,1,615,0,0.347756," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(40 \, a^{6} b^{3} - 84 \, a^{4} b^{5} + 69 \, a^{2} b^{7} - 20 \, b^{9}\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^{12} - 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} - a^{6} b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{2 \, {\left(90 \, a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 162 \, a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 213 \, a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 81 \, a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 180 \, a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 392 \, a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 284 \, a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 90 \, a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 162 \, a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 213 \, a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 81 \, a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} 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)}^{3}} + \frac{3 \, {\left(a^{2} + 20 \, b^{2}\right)} {\left(d x + c\right)}}{a^{6}} - \frac{6 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, 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) + 8 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{5}}}{6 \, d}"," ",0,"1/6*(6*(40*a^6*b^3 - 84*a^4*b^5 + 69*a^2*b^7 - 20*b^9)*(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^12 - 3*a^10*b^2 + 3*a^8*b^4 - a^6*b^6)*sqrt(-a^2 + b^2)) - 2*(90*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 - 162*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 - 48*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 + 213*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 - 48*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 - 81*a*b^9*tan(1/2*d*x + 1/2*c)^5 + 36*b^10*tan(1/2*d*x + 1/2*c)^5 - 180*a^6*b^4*tan(1/2*d*x + 1/2*c)^3 + 392*a^4*b^6*tan(1/2*d*x + 1/2*c)^3 - 284*a^2*b^8*tan(1/2*d*x + 1/2*c)^3 + 72*b^10*tan(1/2*d*x + 1/2*c)^3 + 90*a^6*b^4*tan(1/2*d*x + 1/2*c) + 162*a^5*b^5*tan(1/2*d*x + 1/2*c) - 48*a^4*b^6*tan(1/2*d*x + 1/2*c) - 213*a^3*b^7*tan(1/2*d*x + 1/2*c) - 48*a^2*b^8*tan(1/2*d*x + 1/2*c) + 81*a*b^9*tan(1/2*d*x + 1/2*c) + 36*b^10*tan(1/2*d*x + 1/2*c))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3) + 3*(a^2 + 20*b^2)*(d*x + c)/a^6 - 6*(a*tan(1/2*d*x + 1/2*c)^3 + 8*b*tan(1/2*d*x + 1/2*c)^3 - a*tan(1/2*d*x + 1/2*c) + 8*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^5))/d","A",0
523,1,30,0,0.162993," ","integrate(1/(3+5*sec(d*x+c)),x, algorithm=""giac"")","-\frac{d x + c - 10 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 3}\right)}{12 \, d}"," ",0,"-1/12*(d*x + c - 10*arctan(sin(d*x + c)/(cos(d*x + c) + 3)))/d","A",0
524,1,59,0,0.169585," ","integrate(1/(3+5*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{29 \, d x + 29 \, c - \frac{300 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4} + 70 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 3}\right)}{576 \, d}"," ",0,"1/576*(29*d*x + 29*c - 300*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 4) + 70*arctan(sin(d*x + c)/(cos(d*x + c) + 3)))/d","A",0
525,1,75,0,0.176316," ","integrate(1/(3+5*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{1007 \, d x + 1007 \, c - \frac{300 \, {\left(19 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 44 \, \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} + 4\right)}^{2}} - 6110 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 3}\right)}{55296 \, d}"," ",0,"-1/55296*(1007*d*x + 1007*c - 300*(19*tan(1/2*d*x + 1/2*c)^3 - 44*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 4)^2 - 6110*arctan(sin(d*x + c)/(cos(d*x + c) + 3)))/d","A",0
526,1,88,0,0.185983," ","integrate(1/(3+5*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{21553 \, d x + 21553 \, c - \frac{300 \, {\left(1037 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4576 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 11312 \, \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} + 4\right)}^{3}} + 22430 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 3}\right)}{2654208 \, d}"," ",0,"1/2654208*(21553*d*x + 21553*c - 300*(1037*tan(1/2*d*x + 1/2*c)^5 + 4576*tan(1/2*d*x + 1/2*c)^3 + 11312*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 4)^3 + 22430*arctan(sin(d*x + c)/(cos(d*x + c) + 3)))/d","A",0
527,1,43,0,0.213737," ","integrate(1/(5+3*sec(d*x+c)),x, algorithm=""giac"")","\frac{4 \, d x + 4 \, c - 3 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \right|}\right) + 3 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \right|}\right)}{20 \, d}"," ",0,"1/20*(4*d*x + 4*c - 3*log(abs(tan(1/2*d*x + 1/2*c) + 2)) + 3*log(abs(tan(1/2*d*x + 1/2*c) - 2)))/d","A",0
528,1,69,0,0.186388," ","integrate(1/(5+3*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{64 \, d x + 64 \, c - \frac{180 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4} - 123 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \right|}\right) + 123 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \right|}\right)}{1600 \, d}"," ",0,"1/1600*(64*d*x + 64*c - 180*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 4) - 123*log(abs(tan(1/2*d*x + 1/2*c) + 2)) + 123*log(abs(tan(1/2*d*x + 1/2*c) - 2)))/d","A",0
529,1,85,0,0.174721," ","integrate(1/(5+3*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{2048 \, d x + 2048 \, c - \frac{540 \, {\left(49 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 156 \, \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} - 4\right)}^{2}} - 8361 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \right|}\right) + 8361 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \right|}\right)}{256000 \, d}"," ",0,"1/256000*(2048*d*x + 2048*c - 540*(49*tan(1/2*d*x + 1/2*c)^3 - 156*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 4)^2 - 8361*log(abs(tan(1/2*d*x + 1/2*c) + 2)) + 8361*log(abs(tan(1/2*d*x + 1/2*c) - 2)))/d","A",0
530,1,98,0,0.186486," ","integrate(1/(5+3*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{32768 \, d x + 32768 \, c - \frac{540 \, {\left(2559 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16032 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 26384 \, \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} - 4\right)}^{3}} - 278151 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \right|}\right) + 278151 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \right|}\right)}{20480000 \, d}"," ",0,"1/20480000*(32768*d*x + 32768*c - 540*(2559*tan(1/2*d*x + 1/2*c)^5 - 16032*tan(1/2*d*x + 1/2*c)^3 + 26384*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 4)^3 - 278151*log(abs(tan(1/2*d*x + 1/2*c) + 2)) + 278151*log(abs(tan(1/2*d*x + 1/2*c) - 2)))/d","A",0
531,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
532,0,0,0,0.000000," ","integrate(sec(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} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
533,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c), x)","F",0
534,0,0,0,0.000000," ","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
535,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*cos(d*x + c), x)","F",0
536,0,0,0,0.000000," ","integrate(cos(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} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
537,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^4, x)","F",0
538,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^3, x)","F",0
539,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^2, x)","F",0
540,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
541,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\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
542,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
543,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
544,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^4, x)","F",0
545,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^3, x)","F",0
546,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^2, x)","F",0
547,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
548,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2), x)","F",0
549,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c), x)","F",0
550,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
551,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^3, x)","F",0
552,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^4, x)","F",0
553,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(7/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(7/2), x)","F",0
554,0,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{5}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^5/sqrt(b*sec(d*x + c) + a), x)","F",0
555,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{4}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/sqrt(b*sec(d*x + c) + a), x)","F",0
556,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/sqrt(b*sec(d*x + c) + a), x)","F",0
557,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
558,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
559,0,0,0,0.000000," ","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
560,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
561,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
562,0,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{5}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^5/(b*sec(d*x + c) + a)^(3/2), x)","F",0
563,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{4}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/(b*sec(d*x + c) + a)^(3/2), x)","F",0
564,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{3}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(b*sec(d*x + c) + a)^(3/2), x)","F",0
565,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
566,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
567,0,0,0,0.000000," ","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
568,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
569,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
570,0,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{5}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^5/(b*sec(d*x + c) + a)^(5/2), x)","F",0
571,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{4}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/(b*sec(d*x + c) + a)^(5/2), x)","F",0
572,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{3}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(b*sec(d*x + c) + a)^(5/2), x)","F",0
573,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*sec(d*x + c) + a)^(5/2), x)","F",0
574,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
575,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(-5/2), x)","F",0
576,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
577,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*sec(d*x + c) + a)^(5/2), x)","F",0
578,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(-7/2), x)","F",0
579,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
580,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
581,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
582,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{b \sec\left(d x + c\right) + a}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
583,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{b \sec\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
584,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{b \sec\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
585,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{b \sec\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
586,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2*sec(d*x + c)^(5/2), x)","F",0
587,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
588,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
589,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
590,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
591,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2/sec(d*x + c)^(5/2), x)","F",0
592,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2/sec(d*x + c)^(7/2), x)","F",0
593,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
594,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
595,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
596,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
597,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3/sec(d*x + c)^(5/2), x)","F",0
598,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3/sec(d*x + c)^(7/2), x)","F",0
599,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3/sec(d*x + c)^(9/2), x)","F",0
600,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^4*sec(d*x + c)^(3/2), x)","F",0
601,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{4} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^4*sqrt(sec(d*x + c)), x)","F",0
602,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{4}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^4/sqrt(sec(d*x + c)), x)","F",0
603,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^4/sec(d*x + c)^(3/2), x)","F",0
604,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^4/sec(d*x + c)^(5/2), x)","F",0
605,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^4/sec(d*x + c)^(7/2), x)","F",0
606,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^4/sec(d*x + c)^(9/2), x)","F",0
607,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^4/sec(d*x + c)^(11/2), x)","F",0
608,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/2)/(b*sec(d*x + c) + a), x)","F",0
609,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a), x)","F",0
610,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a), x)","F",0
611,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
612,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
613,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
614,0,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{9}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(9/2)/(b*sec(d*x + c) + a)^2, x)","F",0
615,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/2)/(b*sec(d*x + c) + a)^2, x)","F",0
616,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^2, x)","F",0
617,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^2, x)","F",0
618,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^2, x)","F",0
619,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
620,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
621,0,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{9}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(9/2)/(b*sec(d*x + c) + a)^3, x)","F",0
622,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/2)/(b*sec(d*x + c) + a)^3, x)","F",0
623,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^3, x)","F",0
624,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^3, x)","F",0
625,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^3, x)","F",0
626,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
627,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
628,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
629,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
630,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
631,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
632,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
633,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
634,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2), x)","F",0
635,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c)), x)","F",0
636,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)/sqrt(sec(d*x + c)), x)","F",0
637,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(3/2), x)","F",0
638,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(5/2), x)","F",0
639,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(7/2), x)","F",0
640,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2), x)","F",0
641,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c)), x)","F",0
642,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)/sqrt(sec(d*x + c)), x)","F",0
643,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(3/2), x)","F",0
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645,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(7/2), x)","F",0
646,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(9/2), x)","F",0
647,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
648,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
649,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
650,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
651,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
652,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
653,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
654,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
655,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
656,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
657,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^(3/2), x)","F",0
658,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(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}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c))), x)","F",0
659,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(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}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2)), x)","F",0
660,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/2)/(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}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/2)), x)","F",0
661,0,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{9}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(9/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
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663,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
664,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
665,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^(5/2), x)","F",0
666,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c))), x)","F",0
667,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2)), x)","F",0
668,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2)), x)","F",0
669,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(2+3*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, \sec\left(d x + c\right) + 2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(3*sec(d*x + c) + 2)*sqrt(sec(d*x + c))), x)","F",0
670,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(-2+3*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, \sec\left(d x + c\right) - 2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(3*sec(d*x + c) - 2)*sqrt(sec(d*x + c))), x)","F",0
671,0,0,0,0.000000," ","integrate(1/(2-3*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, \sec\left(d x + c\right) + 2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-3*sec(d*x + c) + 2)*sqrt(sec(d*x + c))), x)","F",0
672,0,0,0,0.000000," ","integrate(1/(-2-3*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, \sec\left(d x + c\right) - 2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-3*sec(d*x + c) - 2)*sqrt(sec(d*x + c))), x)","F",0
673,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(3+2*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, \sec\left(d x + c\right) + 3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(2*sec(d*x + c) + 3)*sqrt(sec(d*x + c))), x)","F",0
674,0,0,0,0.000000," ","integrate(1/(3-2*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, \sec\left(d x + c\right) + 3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-2*sec(d*x + c) + 3)*sqrt(sec(d*x + c))), x)","F",0
675,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(-3+2*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, \sec\left(d x + c\right) - 3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(2*sec(d*x + c) - 3)*sqrt(sec(d*x + c))), x)","F",0
676,0,0,0,0.000000," ","integrate(1/(-3-2*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, \sec\left(d x + c\right) - 3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-2*sec(d*x + c) - 3)*sqrt(sec(d*x + c))), x)","F",0
677,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(2+3*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{3 \, \sec\left(d x + c\right) + 2}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(3*sec(d*x + c) + 2), x)","F",0
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679,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(2-3*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{-3 \, \sec\left(d x + c\right) + 2}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(-3*sec(d*x + c) + 2), x)","F",0
680,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(-2-3*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{-3 \, \sec\left(d x + c\right) - 2}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(-3*sec(d*x + c) - 2), x)","F",0
681,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(3+2*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{2 \, \sec\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(2*sec(d*x + c) + 3), x)","F",0
682,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(3-2*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{-2 \, \sec\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(-2*sec(d*x + c) + 3), x)","F",0
683,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(-3+2*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{2 \, \sec\left(d x + c\right) - 3}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(2*sec(d*x + c) - 3), x)","F",0
684,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(-3-2*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{-2 \, \sec\left(d x + c\right) - 3}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(-2*sec(d*x + c) - 3), x)","F",0
685,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(1/3)*sec(d*x + c), x)","F",0
686,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(1/3), x)","F",0
687,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^4, x)","F",0
688,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^3, x)","F",0
689,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^2, x)","F",0
690,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(2/3)*sec(d*x + c), x)","F",0
691,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(2/3), x)","F",0
692,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(4/3)*sec(d*x + c), x)","F",0
693,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(4/3), x)","F",0
694,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+b*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/3)*sec(d*x + c)^4, x)","F",0
695,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/3)*sec(d*x + c)^3, x)","F",0
696,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/3)*sec(d*x + c)^2, x)","F",0
697,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/3)*sec(d*x + c), x)","F",0
698,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/3), x)","F",0
699,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{4}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/(b*sec(d*x + c) + a)^(1/3), x)","F",0
700,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{3}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(b*sec(d*x + c) + a)^(1/3), x)","F",0
701,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*sec(d*x + c) + a)^(1/3), x)","F",0
702,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sec(d*x + c) + a)^(1/3), x)","F",0
703,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(-1/3), x)","F",0
704,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sec(d*x + c) + a)^(2/3), x)","F",0
705,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(-2/3), x)","F",0
706,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sec(d*x + c) + a)^(4/3), x)","F",0
707,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(-4/3), x)","F",0
708,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{4}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/(b*sec(d*x + c) + a)^(5/3), x)","F",0
709,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{3}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(b*sec(d*x + c) + a)^(5/3), x)","F",0
710,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*sec(d*x + c) + a)^(5/3), x)","F",0
711,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sec(d*x + c) + a)^(5/3), x)","F",0
712,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(5/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(-5/3), x)","F",0
713,0,0,0,0.000000," ","integrate(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{2}{3}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(2/3)/(b*sec(d*x + c) + a), x)","F",0
714,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{\frac{1}{3}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(1/3)/(b*sec(d*x + c) + a), x)","F",0
715,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*sec(d*x + c)^(1/3)), x)","F",0
716,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*sec(d*x + c)^(2/3)), x)","F",0
717,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/3)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{3}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(7/3), x)","F",0
718,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/3)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{3}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(5/3), x)","F",0
719,0,0,0,0.000000," ","integrate(sec(d*x+c)^(4/3)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(4/3), x)","F",0
720,0,0,0,0.000000," ","integrate(sec(d*x+c)^(2/3)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3), x)","F",0
721,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/3)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(1/3), x)","F",0
722,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/3),x, algorithm=""giac"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(1/3), x)","F",0
723,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(2/3),x, algorithm=""giac"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(2/3), x)","F",0
724,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(4/3),x, algorithm=""giac"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(4/3), x)","F",0
725,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/3),x, algorithm=""giac"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(5/3), x)","F",0
726,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/3),x, algorithm=""giac"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{3}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(7/3), x)","F",0
727,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/3)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{7}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(7/3), x)","F",0
728,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/3)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{5}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/3), x)","F",0
729,0,0,0,0.000000," ","integrate(sec(d*x+c)^(4/3)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(4/3), x)","F",0
730,0,0,0,0.000000," ","integrate(sec(d*x+c)^(2/3)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(2/3), x)","F",0
731,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/3)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(1/3), x)","F",0
732,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
733,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(2/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
734,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(4/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
735,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(5/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
736,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(7/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
737,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/3)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{7}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(7/3), x)","F",0
738,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/3)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/3), x)","F",0
739,0,0,0,0.000000," ","integrate(sec(d*x+c)^(4/3)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(4/3), x)","F",0
740,0,0,0,0.000000," ","integrate(sec(d*x+c)^(2/3)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(2/3), x)","F",0
741,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/3)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(1/3), x)","F",0
742,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
743,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(2/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
744,-2,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(4/3),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*x+c))]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)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)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)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)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)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/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (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: 2.78int()  Error: Bad Argument Value","F(-2)",0
745,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(5/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
746,-2,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(7/3),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*x+c))]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)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)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)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)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)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/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (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: 2.96int()  Error: Bad Argument Value","F(-2)",0
747,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
748,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
749,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
750,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
751,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
752,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
753,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
754,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
755,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
756,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
757,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
758,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
759,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
760,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
761,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
762,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
763,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(2/3)/(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}} \sec\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(2/3)), x)","F",0
764,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
765,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
766,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
767,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
768,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
769,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
770,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
771,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
772,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
773,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(2/3)), x)","F",0
774,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
775,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
776,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
777,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^3,x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{3} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^3*(d*sec(f*x + e))^n, x)","F",0
778,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^2,x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{2} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^2*(d*sec(f*x + e))^n, x)","F",0
779,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e)),x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)*(d*sec(f*x + e))^n, x)","F",0
780,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n/(a+b*sec(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{n}}{b \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n/(b*sec(f*x + e) + a), x)","F",0
781,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n/(a+b*sec(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{n}}{{\left(b \sec\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n/(b*sec(f*x + e) + a)^2, x)","F",0
782,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(3/2)*(d*sec(f*x + e))^n, x)","F",0
783,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(f x + e\right) + a} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a)*(d*sec(f*x + e))^n, x)","F",0
784,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n/(a+b*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{n}}{\sqrt{b \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n/sqrt(b*sec(f*x + e) + a), x)","F",0
785,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n/(a+b*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{n}}{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n/(b*sec(f*x + e) + a)^(3/2), x)","F",0
786,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+b*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^m*sec(f*x + e)^n, x)","F",0
787,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{m} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^m*(d*sec(f*x + e))^n, x)","F",0
788,0,0,0,0.000000," ","integrate(sec(f*x+e)^3*(a+b*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^m*sec(f*x + e)^3, x)","F",0
789,0,0,0,0.000000," ","integrate(sec(f*x+e)^2*(a+b*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^m*sec(f*x + e)^2, x)","F",0
790,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^m*sec(f*x + e), x)","F",0
791,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^m, x)","F",0
792,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+b*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^m*cos(f*x + e), x)","F",0
793,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
794,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)*cos(d*x + c)^(9/2), x)","F",0
795,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
796,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
797,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
798,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
799,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{b \sec\left(d x + c\right) + a}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
800,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{b \sec\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
801,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{b \sec\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
802,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2*cos(d*x + c)^(9/2), x)","F",0
803,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2*cos(d*x + c)^(7/2), x)","F",0
804,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2), x)","F",0
805,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
806,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
807,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
808,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
809,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2/cos(d*x + c)^(5/2), x)","F",0
810,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3*cos(d*x + c)^(9/2), x)","F",0
811,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3*cos(d*x + c)^(7/2), x)","F",0
812,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3*cos(d*x + c)^(5/2), x)","F",0
813,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3*cos(d*x + c)^(3/2), x)","F",0
814,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
815,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
816,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3/cos(d*x + c)^(3/2), x)","F",0
817,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(b*sec(d*x + c) + a), x)","F",0
818,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a), x)","F",0
819,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
820,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
821,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
822,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
823,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
824,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^2, x)","F",0
825,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(b*sec(d*x + c) + a)^2, x)","F",0
826,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
827,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2)), x)","F",0
828,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2)), x)","F",0
829,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^2*cos(d*x + c)^(7/2)), x)","F",0
830,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^3, x)","F",0
831,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(b*sec(d*x + c) + a)^3, x)","F",0
832,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^3*sqrt(cos(d*x + c))), x)","F",0
833,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^3*cos(d*x + c)^(3/2)), x)","F",0
834,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^3*cos(d*x + c)^(5/2)), x)","F",0
835,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^3*cos(d*x + c)^(7/2)), x)","F",0
836,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(9/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^3*cos(d*x + c)^(9/2)), x)","F",0
837,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
838,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
839,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
840,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
841,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
842,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2), x)","F",0
843,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2), x)","F",0
844,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2), x)","F",0
845,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
846,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)/sqrt(cos(d*x + c)), x)","F",0
847,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)/cos(d*x + c)^(3/2), x)","F",0
848,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(9/2), x)","F",0
849,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(7/2), x)","F",0
850,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2), x)","F",0
851,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2), x)","F",0
852,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c)), x)","F",0
853,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)/sqrt(cos(d*x + c)), x)","F",0
854,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)/cos(d*x + c)^(3/2), x)","F",0
855,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
856,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
857,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
858,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
859,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
860,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
861,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
862,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
863,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
864,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(b*sec(d*x + c) + a)^(3/2), x)","F",0
865,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(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}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
866,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(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}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
867,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(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}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
868,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(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}} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2)), x)","F",0
869,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
870,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(b*sec(d*x + c) + a)^(5/2), x)","F",0
871,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
872,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
873,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
874,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(7/2)), x)","F",0
875,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n*(a+b*sec(f*x+e))^3,x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{3} \left(d \cos\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^3*(d*cos(f*x + e))^n, x)","F",0
876,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n*(a+b*sec(f*x+e))^2,x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{2} \left(d \cos\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^2*(d*cos(f*x + e))^n, x)","F",0
877,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n*(a+b*sec(f*x+e)),x, algorithm=""giac"")","\int {\left(b \sec\left(f x + e\right) + a\right)} \left(d \cos\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)*(d*cos(f*x + e))^n, x)","F",0
878,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n/(a+b*sec(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \cos\left(f x + e\right)\right)^{n}}{b \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*cos(f*x + e))^n/(b*sec(f*x + e) + a), x)","F",0
879,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n/(a+b*sec(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \cos\left(f x + e\right)\right)^{n}}{{\left(b \sec\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*cos(f*x + e))^n/(b*sec(f*x + e) + a)^2, x)","F",0
