1,1,33,0,2.725816," ","integrate(sin(x)^3*(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","\frac{3}{8} \, b x + \frac{1}{32} \, a \cos\left(4 \, x\right) - \frac{1}{8} \, a \cos\left(2 \, x\right) + \frac{1}{32} \, b \sin\left(4 \, x\right) - \frac{1}{4} \, b \sin\left(2 \, x\right)"," ",0,"3/8*b*x + 1/32*a*cos(4*x) - 1/8*a*cos(2*x) + 1/32*b*sin(4*x) - 1/4*b*sin(2*x)","A",0
2,1,25,0,2.961009," ","integrate(sin(x)^2*(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","\frac{1}{12} \, b \cos\left(3 \, x\right) - \frac{3}{4} \, b \cos\left(x\right) - \frac{1}{12} \, a \sin\left(3 \, x\right) + \frac{1}{4} \, a \sin\left(x\right)"," ",0,"1/12*b*cos(3*x) - 3/4*b*cos(x) - 1/12*a*sin(3*x) + 1/4*a*sin(x)","A",0
3,1,19,0,0.168421," ","integrate(sin(x)*(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","\frac{1}{2} \, b x - \frac{1}{4} \, a \cos\left(2 \, x\right) - \frac{1}{4} \, b \sin\left(2 \, x\right)"," ",0,"1/2*b*x - 1/4*a*cos(2*x) - 1/4*b*sin(2*x)","A",0
4,1,10,0,1.828790," ","integrate(a*cos(x)+b*sin(x),x, algorithm=""giac"")","-b \cos\left(x\right) + a \sin\left(x\right)"," ",0,"-b*cos(x) + a*sin(x)","A",0
5,1,24,0,0.206148," ","integrate(csc(x)*(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","b x - a \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) + a \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)"," ",0,"b*x - a*log(tan(1/2*x)^2 + 1) + a*log(abs(tan(1/2*x)))","B",0
6,1,33,0,0.199888," ","integrate(csc(x)^2*(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","b \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right) - \frac{1}{2} \, a \tan\left(\frac{1}{2} \, x\right) - \frac{2 \, b \tan\left(\frac{1}{2} \, x\right) + a}{2 \, \tan\left(\frac{1}{2} \, x\right)}"," ",0,"b*log(abs(tan(1/2*x))) - 1/2*a*tan(1/2*x) - 1/2*(2*b*tan(1/2*x) + a)/tan(1/2*x)","B",0
7,1,13,0,0.227576," ","integrate(csc(x)^3*(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","-\frac{2 \, b \tan\left(x\right) + a}{2 \, \tan\left(x\right)^{2}}"," ",0,"-1/2*(2*b*tan(x) + a)/tan(x)^2","A",0
8,1,148,0,0.213619," ","integrate(sin(x)^3/(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","-\frac{a^{3} b \log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a^{4} b + 2 \, a^{2} b^{3} + b^{5}} + \frac{a^{3} \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}} + \frac{{\left(3 \, a^{2} b + b^{3}\right)} x}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}} - \frac{a^{3} \tan\left(x\right)^{2} + a^{2} b \tan\left(x\right) + b^{3} \tan\left(x\right) - a b^{2}}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(x\right)^{2} + 1\right)}}"," ",0,"-a^3*b*log(abs(b*tan(x) + a))/(a^4*b + 2*a^2*b^3 + b^5) + 1/2*a^3*log(tan(x)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 1/2*(3*a^2*b + b^3)*x/(a^4 + 2*a^2*b^2 + b^4) - 1/2*(a^3*tan(x)^2 + a^2*b*tan(x) + b^3*tan(x) - a*b^2)/((a^4 + 2*a^2*b^2 + b^4)*(tan(x)^2 + 1))","A",0
9,1,94,0,0.258234," ","integrate(sin(x)^2/(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","-\frac{a^{2} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(a \tan\left(\frac{1}{2} \, x\right) + b\right)}}{{\left(a^{2} + b^{2}\right)} {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}}"," ",0,"-a^2*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) - 2*(a*tan(1/2*x) + b)/((a^2 + b^2)*(tan(1/2*x)^2 + 1))","A",0
10,1,55,0,1.455942," ","integrate(sin(x)/(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","-\frac{a b \log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a^{2} b + b^{3}} + \frac{b x}{a^{2} + b^{2}} + \frac{a \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(a^{2} + b^{2}\right)}}"," ",0,"-a*b*log(abs(b*tan(x) + a))/(a^2*b + b^3) + b*x/(a^2 + b^2) + 1/2*a*log(tan(x)^2 + 1)/(a^2 + b^2)","A",0
11,1,61,0,0.413513," ","integrate(1/(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","-\frac{\log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}}}"," ",0,"-log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/sqrt(a^2 + b^2)","A",0
12,1,22,0,1.717850," ","integrate(csc(x)/(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","-\frac{\log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a} + \frac{\log\left({\left| \tan\left(x\right) \right|}\right)}{a}"," ",0,"-log(abs(b*tan(x) + a))/a + log(abs(tan(x)))/a","A",0
13,1,108,0,2.970400," ","integrate(csc(x)^2/(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","-\frac{b \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a^{2}} - \frac{\tan\left(\frac{1}{2} \, x\right)}{2 \, a} - \frac{\sqrt{a^{2} + b^{2}} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{a^{2}} + \frac{2 \, b \tan\left(\frac{1}{2} \, x\right) - a}{2 \, a^{2} \tan\left(\frac{1}{2} \, x\right)}"," ",0,"-b*log(abs(tan(1/2*x)))/a^2 - 1/2*tan(1/2*x)/a - sqrt(a^2 + b^2)*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/a^2 + 1/2*(2*b*tan(1/2*x) - a)/(a^2*tan(1/2*x))","B",0
14,1,78,0,0.187185," ","integrate(csc(x)^3/(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","\frac{{\left(a^{2} + b^{2}\right)} \log\left({\left| \tan\left(x\right) \right|}\right)}{a^{3}} - \frac{{\left(a^{2} b + b^{3}\right)} \log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a^{3} b} - \frac{3 \, a^{2} \tan\left(x\right)^{2} + 3 \, b^{2} \tan\left(x\right)^{2} - 2 \, a b \tan\left(x\right) + a^{2}}{2 \, a^{3} \tan\left(x\right)^{2}}"," ",0,"(a^2 + b^2)*log(abs(tan(x)))/a^3 - (a^2*b + b^3)*log(abs(b*tan(x) + a))/(a^3*b) - 1/2*(3*a^2*tan(x)^2 + 3*b^2*tan(x)^2 - 2*a*b*tan(x) + a^2)/(a^3*tan(x)^2)","A",0
15,1,186,0,4.739991," ","integrate(sin(x)^3/(a*cos(x)+b*sin(x))^2,x, algorithm=""giac"")","-\frac{3 \, a^{2} b \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(3 \, a^{2} b \tan\left(\frac{1}{2} \, x\right)^{3} - 3 \, a b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + a^{2} b \tan\left(\frac{1}{2} \, x\right) - 2 \, b^{3} \tan\left(\frac{1}{2} \, x\right) + 2 \, a^{3} - a b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, b \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, b \tan\left(\frac{1}{2} \, x\right) - a\right)} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}"," ",0,"-3*a^2*b*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2*(3*a^2*b*tan(1/2*x)^3 - 3*a*b^2*tan(1/2*x)^2 + a^2*b*tan(1/2*x) - 2*b^3*tan(1/2*x) + 2*a^3 - a*b^2)/((a*tan(1/2*x)^4 - 2*b*tan(1/2*x)^3 - 2*b*tan(1/2*x) - a)*(a^4 + 2*a^2*b^2 + b^4))","A",0
16,1,139,0,1.981597," ","integrate(sin(x)^2/(a*cos(x)+b*sin(x))^2,x, algorithm=""giac"")","-\frac{2 \, a b^{2} \log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a^{4} b + 2 \, a^{2} b^{3} + b^{5}} + \frac{a b \log\left(\tan\left(x\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(a^{2} - b^{2}\right)} x}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, a b^{3} \tan\left(x\right) - a^{4} + a^{2} b^{2}}{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} {\left(b \tan\left(x\right) + a\right)}}"," ",0,"-2*a*b^2*log(abs(b*tan(x) + a))/(a^4*b + 2*a^2*b^3 + b^5) + a*b*log(tan(x)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - (a^2 - b^2)*x/(a^4 + 2*a^2*b^2 + b^4) + (2*a*b^3*tan(x) - a^4 + a^2*b^2)/((a^4*b + 2*a^2*b^3 + b^5)*(b*tan(x) + a))","B",0
17,1,103,0,0.256722," ","integrate(sin(x)/(a*cos(x)+b*sin(x))^2,x, algorithm=""giac"")","-\frac{b \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, x\right) + a\right)}}{{\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, x\right) - a\right)} {\left(a^{2} + b^{2}\right)}}"," ",0,"-b*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) - 2*(b*tan(1/2*x) + a)/((a*tan(1/2*x)^2 - 2*b*tan(1/2*x) - a)*(a^2 + b^2))","A",0
18,1,13,0,0.182242," ","integrate(1/(a*cos(x)+b*sin(x))^2,x, algorithm=""giac"")","-\frac{1}{{\left(b \tan\left(x\right) + a\right)} b}"," ",0,"-1/((b*tan(x) + a)*b)","A",0
19,1,109,0,4.461238," ","integrate(csc(x)/(a*cos(x)+b*sin(x))^2,x, algorithm=""giac"")","\frac{b \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} a^{2}} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a^{2}} - \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, x\right) + a\right)}}{{\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, x\right) - a\right)} a^{2}}"," ",0,"b*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*a^2) + log(abs(tan(1/2*x)))/a^2 - 2*(b*tan(1/2*x) + a)/((a*tan(1/2*x)^2 - 2*b*tan(1/2*x) - a)*a^2)","A",0
20,1,63,0,0.171480," ","integrate(csc(x)^2/(a*cos(x)+b*sin(x))^2,x, algorithm=""giac"")","\frac{2 \, b \log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a^{3}} - \frac{2 \, b \log\left({\left| \tan\left(x\right) \right|}\right)}{a^{3}} - \frac{a^{2} \tan\left(x\right) + 2 \, b^{2} \tan\left(x\right) + a b}{{\left(b \tan\left(x\right)^{2} + a \tan\left(x\right)\right)} a^{2} b}"," ",0,"2*b*log(abs(b*tan(x) + a))/a^3 - 2*b*log(abs(tan(x)))/a^3 - (a^2*tan(x) + 2*b^2*tan(x) + a*b)/((b*tan(x)^2 + a*tan(x))*a^2*b)","A",0
21,1,215,0,8.783297," ","integrate(csc(x)^3/(a*cos(x)+b*sin(x))^2,x, algorithm=""giac"")","\frac{3 \, {\left(a^{2} + 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{2 \, a^{4}} + \frac{3 \, {\left(a^{2} b + b^{3}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} a^{4}} + \frac{a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 8 \, a b \tan\left(\frac{1}{2} \, x\right)}{8 \, a^{4}} - \frac{2 \, {\left(a^{2} b \tan\left(\frac{1}{2} \, x\right) + b^{3} \tan\left(\frac{1}{2} \, x\right) + a^{3} + a b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, x\right) - a\right)} a^{4}} - \frac{18 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 36 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 8 \, a b \tan\left(\frac{1}{2} \, x\right) + a^{2}}{8 \, a^{4} \tan\left(\frac{1}{2} \, x\right)^{2}}"," ",0,"3/2*(a^2 + 2*b^2)*log(abs(tan(1/2*x)))/a^4 + 3*(a^2*b + b^3)*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*a^4) + 1/8*(a^2*tan(1/2*x)^2 + 8*a*b*tan(1/2*x))/a^4 - 2*(a^2*b*tan(1/2*x) + b^3*tan(1/2*x) + a^3 + a*b^2)/((a*tan(1/2*x)^2 - 2*b*tan(1/2*x) - a)*a^4) - 1/8*(18*a^2*tan(1/2*x)^2 + 36*b^2*tan(1/2*x)^2 - 8*a*b*tan(1/2*x) + a^2)/(a^4*tan(1/2*x)^2)","A",0
22,1,242,0,2.954433," ","integrate(sin(x)^3/(a*cos(x)+b*sin(x))^3,x, algorithm=""giac"")","-\frac{{\left(3 \, a^{2} b - b^{3}\right)} x}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(a^{3} - 3 \, a b^{2}\right)} \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}} + \frac{{\left(a^{3} b - 3 \, a b^{3}\right)} \log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} - \frac{3 \, a^{3} b^{4} \tan\left(x\right)^{2} - 9 \, a b^{6} \tan\left(x\right)^{2} + 2 \, a^{6} b \tan\left(x\right) + 14 \, a^{4} b^{3} \tan\left(x\right) - 12 \, a^{2} b^{5} \tan\left(x\right) + a^{7} + 9 \, a^{5} b^{2} - 4 \, a^{3} b^{4}}{2 \, {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(x\right) + a\right)}^{2}}"," ",0,"-(3*a^2*b - b^3)*x/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 1/2*(a^3 - 3*a*b^2)*log(tan(x)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (a^3*b - 3*a*b^3)*log(abs(b*tan(x) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) - 1/2*(3*a^3*b^4*tan(x)^2 - 9*a*b^6*tan(x)^2 + 2*a^6*b*tan(x) + 14*a^4*b^3*tan(x) - 12*a^2*b^5*tan(x) + a^7 + 9*a^5*b^2 - 4*a^3*b^4)/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*(b*tan(x) + a)^2)","B",0
23,1,197,0,0.280693," ","integrate(sin(x)^2/(a*cos(x)+b*sin(x))^3,x, algorithm=""giac"")","\frac{{\left(a^{2} - 2 \, b^{2}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} + \frac{a^{3} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, a b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 3 \, a^{2} b \tan\left(\frac{1}{2} \, x\right)^{2} + 6 \, b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + a^{3} \tan\left(\frac{1}{2} \, x\right) + 10 \, a b^{2} \tan\left(\frac{1}{2} \, x\right) + 3 \, a^{2} b}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, x\right) - a\right)}^{2}}"," ",0,"1/2*(a^2 - 2*b^2)*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) + (a^3*tan(1/2*x)^3 - 2*a*b^2*tan(1/2*x)^3 - 3*a^2*b*tan(1/2*x)^2 + 6*b^3*tan(1/2*x)^2 + a^3*tan(1/2*x) + 10*a*b^2*tan(1/2*x) + 3*a^2*b)/((a^4 + 2*a^2*b^2 + b^4)*(a*tan(1/2*x)^2 - 2*b*tan(1/2*x) - a)^2)","B",0
24,1,20,0,0.260070," ","integrate(sin(x)/(a*cos(x)+b*sin(x))^3,x, algorithm=""giac"")","-\frac{2 \, b \tan\left(x\right) + a}{2 \, {\left(b \tan\left(x\right) + a\right)}^{2} b^{2}}"," ",0,"-1/2*(2*b*tan(x) + a)/((b*tan(x) + a)^2*b^2)","A",0
25,1,166,0,2.381611," ","integrate(1/(a*cos(x)+b*sin(x))^3,x, algorithm=""giac"")","-\frac{\log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{2 \, {\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} + \frac{a^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, a b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + a^{2} b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + a^{3} \tan\left(\frac{1}{2} \, x\right) - 2 \, a b^{2} \tan\left(\frac{1}{2} \, x\right) - a^{2} b}{{\left(a^{4} + a^{2} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, x\right) - a\right)}^{2}}"," ",0,"-1/2*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) + (a^3*tan(1/2*x)^3 + 2*a*b^2*tan(1/2*x)^3 + a^2*b*tan(1/2*x)^2 - 2*b^3*tan(1/2*x)^2 + a^3*tan(1/2*x) - 2*a*b^2*tan(1/2*x) - a^2*b)/((a^4 + a^2*b^2)*(a*tan(1/2*x)^2 - 2*b*tan(1/2*x) - a)^2)","B",0
26,1,77,0,2.015445," ","integrate(csc(x)/(a*cos(x)+b*sin(x))^3,x, algorithm=""giac"")","-\frac{\log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a^{3}} + \frac{\log\left({\left| \tan\left(x\right) \right|}\right)}{a^{3}} + \frac{3 \, b^{4} \tan\left(x\right)^{2} - 2 \, a^{3} b \tan\left(x\right) + 8 \, a b^{3} \tan\left(x\right) - a^{4} + 6 \, a^{2} b^{2}}{2 \, {\left(b \tan\left(x\right) + a\right)}^{2} a^{3} b^{2}}"," ",0,"-log(abs(b*tan(x) + a))/a^3 + log(abs(tan(x)))/a^3 + 1/2*(3*b^4*tan(x)^2 - 2*a^3*b*tan(x) + 8*a*b^3*tan(x) - a^4 + 6*a^2*b^2)/((b*tan(x) + a)^2*a^3*b^2)","A",0
27,1,212,0,3.963285," ","integrate(csc(x)^2/(a*cos(x)+b*sin(x))^3,x, algorithm=""giac"")","-\frac{3 \, b \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a^{4}} - \frac{\tan\left(\frac{1}{2} \, x\right)}{2 \, a^{3}} - \frac{3 \, {\left(a^{2} + 2 \, b^{2}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{2 \, \sqrt{a^{2} + b^{2}} a^{4}} + \frac{6 \, b \tan\left(\frac{1}{2} \, x\right) - a}{2 \, a^{4} \tan\left(\frac{1}{2} \, x\right)} + \frac{a^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + 6 \, a b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 5 \, a^{2} b \tan\left(\frac{1}{2} \, x\right)^{2} - 10 \, b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + a^{3} \tan\left(\frac{1}{2} \, x\right) - 14 \, a b^{2} \tan\left(\frac{1}{2} \, x\right) - 5 \, a^{2} b}{{\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, x\right) - a\right)}^{2} a^{4}}"," ",0,"-3*b*log(abs(tan(1/2*x)))/a^4 - 1/2*tan(1/2*x)/a^3 - 3/2*(a^2 + 2*b^2)*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*a^4) + 1/2*(6*b*tan(1/2*x) - a)/(a^4*tan(1/2*x)) + (a^3*tan(1/2*x)^3 + 6*a*b^2*tan(1/2*x)^3 + 5*a^2*b*tan(1/2*x)^2 - 10*b^3*tan(1/2*x)^2 + a^3*tan(1/2*x) - 14*a*b^2*tan(1/2*x) - 5*a^2*b)/((a*tan(1/2*x)^2 - 2*b*tan(1/2*x) - a)^2*a^4)","A",0
28,1,146,0,1.896230," ","integrate(csc(x)^3/(a*cos(x)+b*sin(x))^3,x, algorithm=""giac"")","\frac{2 \, {\left(a^{2} + 3 \, b^{2}\right)} \log\left({\left| \tan\left(x\right) \right|}\right)}{a^{5}} - \frac{2 \, {\left(a^{2} b + 3 \, b^{3}\right)} \log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a^{5} b} - \frac{2 \, a^{4} b \tan\left(x\right)^{3} - 4 \, a^{2} b^{3} \tan\left(x\right)^{3} - 12 \, b^{5} \tan\left(x\right)^{3} + a^{5} \tan\left(x\right)^{2} - 6 \, a^{3} b^{2} \tan\left(x\right)^{2} - 18 \, a b^{4} \tan\left(x\right)^{2} - 4 \, a^{2} b^{3} \tan\left(x\right) + a^{3} b^{2}}{2 \, {\left(b \tan\left(x\right)^{2} + a \tan\left(x\right)\right)}^{2} a^{4} b^{2}}"," ",0,"2*(a^2 + 3*b^2)*log(abs(tan(x)))/a^5 - 2*(a^2*b + 3*b^3)*log(abs(b*tan(x) + a))/(a^5*b) - 1/2*(2*a^4*b*tan(x)^3 - 4*a^2*b^3*tan(x)^3 - 12*b^5*tan(x)^3 + a^5*tan(x)^2 - 6*a^3*b^2*tan(x)^2 - 18*a*b^4*tan(x)^2 - 4*a^2*b^3*tan(x) + a^3*b^2)/((b*tan(x)^2 + a*tan(x))^2*a^4*b^2)","A",0
29,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^n/(sin(d*x+c)^n),x, algorithm=""giac"")","\int \frac{{\left(a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right)\right)}^{n}}{\sin\left(d x + c\right)^{n}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + I*a*sin(d*x + c))^n/sin(d*x + c)^n, x)","F",0
30,1,95,0,0.414023," ","integrate(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{5}{16} \, a x - \frac{b \cos\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{b \cos\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{5 \, b \cos\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{a \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{3 \, a \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{15 \, a \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"5/16*a*x - 1/192*b*cos(6*d*x + 6*c)/d - 1/32*b*cos(4*d*x + 4*c)/d - 5/64*b*cos(2*d*x + 2*c)/d + 1/192*a*sin(6*d*x + 6*c)/d + 3/64*a*sin(4*d*x + 4*c)/d + 15/64*a*sin(2*d*x + 2*c)/d","A",0
31,1,85,0,0.934925," ","integrate(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{b \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{b \cos\left(3 \, d x + 3 \, c\right)}{16 \, d} - \frac{b \cos\left(d x + c\right)}{8 \, d} + \frac{a \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{5 \, a \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{5 \, a \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/80*b*cos(5*d*x + 5*c)/d - 1/16*b*cos(3*d*x + 3*c)/d - 1/8*b*cos(d*x + c)/d + 1/80*a*sin(5*d*x + 5*c)/d + 5/48*a*sin(3*d*x + 3*c)/d + 5/8*a*sin(d*x + c)/d","A",0
32,1,65,0,0.980849," ","integrate(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{3}{8} \, a x - \frac{b \cos\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{b \cos\left(2 \, d x + 2 \, c\right)}{8 \, d} + \frac{a \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{a \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"3/8*a*x - 1/32*b*cos(4*d*x + 4*c)/d - 1/8*b*cos(2*d*x + 2*c)/d + 1/32*a*sin(4*d*x + 4*c)/d + 1/4*a*sin(2*d*x + 2*c)/d","A",0
33,1,55,0,3.944995," ","integrate(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{b \cos\left(3 \, d x + 3 \, c\right)}{12 \, d} - \frac{b \cos\left(d x + c\right)}{4 \, d} + \frac{a \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{3 \, a \sin\left(d x + c\right)}{4 \, d}"," ",0,"-1/12*b*cos(3*d*x + 3*c)/d - 1/4*b*cos(d*x + c)/d + 1/12*a*sin(3*d*x + 3*c)/d + 3/4*a*sin(d*x + c)/d","A",0
34,1,35,0,3.986650," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{1}{2} \, a x - \frac{b \cos\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{a \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"1/2*a*x - 1/4*b*cos(2*d*x + 2*c)/d + 1/4*a*sin(2*d*x + 2*c)/d","A",0
35,1,24,0,0.191191," ","integrate(a*cos(d*x+c)+b*sin(d*x+c),x, algorithm=""giac"")","-\frac{b \cos\left(d x + c\right)}{d} + \frac{a \sin\left(d x + c\right)}{d}"," ",0,"-b*cos(d*x + c)/d + a*sin(d*x + c)/d","A",0
36,1,27,0,0.161400," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} a + b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*a + b*log(tan(d*x + c)^2 + 1))/d","A",0
37,1,54,0,0.233987," ","integrate(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(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)^{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)^2 - 1))/d","B",0
38,1,25,0,0.259475," ","integrate(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{b \tan\left(d x + c\right)^{2} + 2 \, a \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(b*tan(d*x + c)^2 + 2*a*tan(d*x + c))/d","A",0
39,1,99,0,4.021305," ","integrate(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(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)^{4} - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b\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)^4 - 3*a*tan(1/2*d*x + 1/2*c) - 2*b)/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
40,1,48,0,0.245638," ","integrate(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, b \tan\left(d x + c\right)^{4} + 4 \, a \tan\left(d x + c\right)^{3} + 6 \, b \tan\left(d x + c\right)^{2} + 12 \, a \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*b*tan(d*x + c)^4 + 4*a*tan(d*x + c)^3 + 6*b*tan(d*x + c)^2 + 12*a*tan(d*x + c))/d","A",0
41,1,141,0,4.686806," ","integrate(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{15 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(25 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 40 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 10 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 80 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 10 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{40 \, d}"," ",0,"1/40*(15*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(25*a*tan(1/2*d*x + 1/2*c)^9 - 40*b*tan(1/2*d*x + 1/2*c)^8 - 10*a*tan(1/2*d*x + 1/2*c)^7 - 80*b*tan(1/2*d*x + 1/2*c)^4 + 10*a*tan(1/2*d*x + 1/2*c)^3 - 25*a*tan(1/2*d*x + 1/2*c) - 8*b)/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
42,1,70,0,0.240854," ","integrate(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{5 \, b \tan\left(d x + c\right)^{6} + 6 \, a \tan\left(d x + c\right)^{5} + 15 \, b \tan\left(d x + c\right)^{4} + 20 \, a \tan\left(d x + c\right)^{3} + 15 \, b \tan\left(d x + c\right)^{2} + 30 \, a \tan\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(5*b*tan(d*x + c)^6 + 6*a*tan(d*x + c)^5 + 15*b*tan(d*x + c)^4 + 20*a*tan(d*x + c)^3 + 15*b*tan(d*x + c)^2 + 30*a*tan(d*x + c))/d","A",0
43,1,155,0,0.865571," ","integrate(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{a b \cos\left(7 \, d x + 7 \, c\right)}{224 \, d} - \frac{a b \cos\left(5 \, d x + 5 \, c\right)}{32 \, d} - \frac{3 \, a b \cos\left(3 \, d x + 3 \, c\right)}{32 \, d} - \frac{5 \, a b \cos\left(d x + c\right)}{32 \, d} + \frac{{\left(a^{2} - b^{2}\right)} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{{\left(7 \, a^{2} - 3 \, b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(21 \, a^{2} - b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{5 \, {\left(7 \, a^{2} + b^{2}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"-1/224*a*b*cos(7*d*x + 7*c)/d - 1/32*a*b*cos(5*d*x + 5*c)/d - 3/32*a*b*cos(3*d*x + 3*c)/d - 5/32*a*b*cos(d*x + c)/d + 1/448*(a^2 - b^2)*sin(7*d*x + 7*c)/d + 1/320*(7*a^2 - 3*b^2)*sin(5*d*x + 5*c)/d + 1/192*(21*a^2 - b^2)*sin(3*d*x + 3*c)/d + 5/64*(7*a^2 + b^2)*sin(d*x + c)/d","A",0
44,1,132,0,0.241532," ","integrate(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{16} \, {\left(5 \, a^{2} + b^{2}\right)} x - \frac{a b \cos\left(6 \, d x + 6 \, c\right)}{96 \, d} - \frac{a b \cos\left(4 \, d x + 4 \, c\right)}{16 \, d} - \frac{5 \, a b \cos\left(2 \, d x + 2 \, c\right)}{32 \, d} + \frac{{\left(a^{2} - b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{{\left(3 \, a^{2} - b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(15 \, a^{2} + b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"1/16*(5*a^2 + b^2)*x - 1/96*a*b*cos(6*d*x + 6*c)/d - 1/16*a*b*cos(4*d*x + 4*c)/d - 5/32*a*b*cos(2*d*x + 2*c)/d + 1/192*(a^2 - b^2)*sin(6*d*x + 6*c)/d + 1/64*(3*a^2 - b^2)*sin(4*d*x + 4*c)/d + 1/64*(15*a^2 + b^2)*sin(2*d*x + 2*c)/d","A",0
45,1,114,0,3.510768," ","integrate(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{a b \cos\left(5 \, d x + 5 \, c\right)}{40 \, d} - \frac{a b \cos\left(3 \, d x + 3 \, c\right)}{8 \, d} - \frac{a b \cos\left(d x + c\right)}{4 \, d} + \frac{{\left(a^{2} - b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{{\left(5 \, a^{2} - b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(5 \, a^{2} + b^{2}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/40*a*b*cos(5*d*x + 5*c)/d - 1/8*a*b*cos(3*d*x + 3*c)/d - 1/4*a*b*cos(d*x + c)/d + 1/80*(a^2 - b^2)*sin(5*d*x + 5*c)/d + 1/48*(5*a^2 - b^2)*sin(3*d*x + 3*c)/d + 1/8*(5*a^2 + b^2)*sin(d*x + c)/d","A",0
46,1,85,0,4.967936," ","integrate(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{8} \, {\left(3 \, a^{2} + b^{2}\right)} x - \frac{a b \cos\left(4 \, d x + 4 \, c\right)}{16 \, d} - \frac{a b \cos\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{a^{2} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(a^{2} - b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d}"," ",0,"1/8*(3*a^2 + b^2)*x - 1/16*a*b*cos(4*d*x + 4*c)/d - 1/4*a*b*cos(2*d*x + 2*c)/d + 1/4*a^2*sin(2*d*x + 2*c)/d + 1/32*(a^2 - b^2)*sin(4*d*x + 4*c)/d","A",0
47,1,73,0,0.250973," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{a b \cos\left(3 \, d x + 3 \, c\right)}{6 \, d} - \frac{a b \cos\left(d x + c\right)}{2 \, d} + \frac{{\left(a^{2} - b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(3 \, a^{2} + b^{2}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"-1/6*a*b*cos(3*d*x + 3*c)/d - 1/2*a*b*cos(d*x + c)/d + 1/12*(a^2 - b^2)*sin(3*d*x + 3*c)/d + 1/4*(3*a^2 + b^2)*sin(d*x + c)/d","A",0
48,1,50,0,3.728372," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(a^{2} + b^{2}\right)} x - \frac{a b \cos\left(2 \, d x + 2 \, c\right)}{2 \, d} + \frac{{\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"1/2*(a^2 + b^2)*x - 1/2*a*b*cos(2*d*x + 2*c)/d + 1/4*(a^2 - b^2)*sin(2*d*x + 2*c)/d","A",0
49,1,89,0,4.936533," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{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 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a b\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}}{d}"," ",0,"(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) - b^2*tan(1/2*d*x + 1/2*c) - 2*a*b)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","A",0
50,1,44,0,0.214895," ","integrate(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a b \log\left(\tan\left(d x + c\right)^{2} + 1\right) + b^{2} \tan\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} {\left(d x + c\right)}}{d}"," ",0,"(a*b*log(tan(d*x + c)^2 + 1) + b^2*tan(d*x + c) + (a^2 - b^2)*(d*x + c))/d","A",0
51,1,122,0,4.737778," ","integrate(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(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(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)^{2} + b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a b\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*(b^2*tan(1/2*d*x + 1/2*c)^3 - 4*a*b*tan(1/2*d*x + 1/2*c)^2 + b^2*tan(1/2*d*x + 1/2*c) + 4*a*b)/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
52,1,41,0,0.288604," ","integrate(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{b^{2} \tan\left(d x + c\right)^{3} + 3 \, a b \tan\left(d x + c\right)^{2} + 3 \, a^{2} \tan\left(d x + c\right)}{3 \, d}"," ",0,"1/3*(b^2*tan(d*x + c)^3 + 3*a*b*tan(d*x + c)^2 + 3*a^2*tan(d*x + c))/d","A",0
53,1,249,0,0.326055," ","integrate(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, {\left(4 \, a^{2} - 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} - 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} + 3 \, b^{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)^{6} - 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 48 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a^{2} \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) + 16 \, a b\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 - b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*a^2 - 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 + 3*b^2*tan(1/2*d*x + 1/2*c)^7 - 48*a*b*tan(1/2*d*x + 1/2*c)^6 - 12*a^2*tan(1/2*d*x + 1/2*c)^5 + 21*b^2*tan(1/2*d*x + 1/2*c)^5 + 48*a*b*tan(1/2*d*x + 1/2*c)^4 - 12*a^2*tan(1/2*d*x + 1/2*c)^3 + 21*b^2*tan(1/2*d*x + 1/2*c)^3 - 16*a*b*tan(1/2*d*x + 1/2*c)^2 + 12*a^2*tan(1/2*d*x + 1/2*c) + 3*b^2*tan(1/2*d*x + 1/2*c) + 16*a*b)/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
54,1,80,0,0.583450," ","integrate(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{6 \, b^{2} \tan\left(d x + c\right)^{5} + 15 \, a b \tan\left(d x + c\right)^{4} + 10 \, a^{2} \tan\left(d x + c\right)^{3} + 10 \, b^{2} \tan\left(d x + c\right)^{3} + 30 \, a b \tan\left(d x + c\right)^{2} + 30 \, a^{2} \tan\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(6*b^2*tan(d*x + c)^5 + 15*a*b*tan(d*x + c)^4 + 10*a^2*tan(d*x + c)^3 + 10*b^2*tan(d*x + c)^3 + 30*a*b*tan(d*x + c)^2 + 30*a^2*tan(d*x + c))/d","A",0
55,1,343,0,0.526018," ","integrate(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{15 \, {\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) - 15 \, {\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) + \frac{2 \, {\left(150 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 15 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 480 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 210 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 235 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 60 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 390 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 60 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 390 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 960 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 210 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 235 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 96 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 150 \, a^{2} \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) + 96 \, a b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(6*a^2 - b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(6*a^2 - b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(150*a^2*tan(1/2*d*x + 1/2*c)^11 + 15*b^2*tan(1/2*d*x + 1/2*c)^11 - 480*a*b*tan(1/2*d*x + 1/2*c)^10 - 210*a^2*tan(1/2*d*x + 1/2*c)^9 + 235*b^2*tan(1/2*d*x + 1/2*c)^9 + 480*a*b*tan(1/2*d*x + 1/2*c)^8 + 60*a^2*tan(1/2*d*x + 1/2*c)^7 + 390*b^2*tan(1/2*d*x + 1/2*c)^7 - 960*a*b*tan(1/2*d*x + 1/2*c)^6 + 60*a^2*tan(1/2*d*x + 1/2*c)^5 + 390*b^2*tan(1/2*d*x + 1/2*c)^5 + 960*a*b*tan(1/2*d*x + 1/2*c)^4 - 210*a^2*tan(1/2*d*x + 1/2*c)^3 + 235*b^2*tan(1/2*d*x + 1/2*c)^3 - 96*a*b*tan(1/2*d*x + 1/2*c)^2 + 150*a^2*tan(1/2*d*x + 1/2*c) + 15*b^2*tan(1/2*d*x + 1/2*c) + 96*a*b)/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
56,1,118,0,0.311874," ","integrate(sec(d*x+c)^8*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{15 \, b^{2} \tan\left(d x + c\right)^{7} + 35 \, a b \tan\left(d x + c\right)^{6} + 21 \, a^{2} \tan\left(d x + c\right)^{5} + 42 \, b^{2} \tan\left(d x + c\right)^{5} + 105 \, a b \tan\left(d x + c\right)^{4} + 70 \, a^{2} \tan\left(d x + c\right)^{3} + 35 \, b^{2} \tan\left(d x + c\right)^{3} + 105 \, a b \tan\left(d x + c\right)^{2} + 105 \, a^{2} \tan\left(d x + c\right)}{105 \, d}"," ",0,"1/105*(15*b^2*tan(d*x + c)^7 + 35*a*b*tan(d*x + c)^6 + 21*a^2*tan(d*x + c)^5 + 42*b^2*tan(d*x + c)^5 + 105*a*b*tan(d*x + c)^4 + 70*a^2*tan(d*x + c)^3 + 35*b^2*tan(d*x + c)^3 + 105*a*b*tan(d*x + c)^2 + 105*a^2*tan(d*x + c))/d","A",0
57,1,218,0,0.348205," ","integrate(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{5}{128} \, {\left(7 \, a^{3} + 3 \, a b^{2}\right)} x - \frac{{\left(3 \, a^{2} b - b^{3}\right)} \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{{\left(9 \, a^{2} b - b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)}{384 \, d} - \frac{{\left(21 \, a^{2} b + b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{3 \, {\left(7 \, a^{2} b + b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} + \frac{{\left(a^{3} - 3 \, a b^{2}\right)} \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{{\left(2 \, a^{3} - 3 \, a b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{{\left(7 \, a^{3} - 3 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{{\left(14 \, a^{3} + 3 \, a b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"5/128*(7*a^3 + 3*a*b^2)*x - 1/1024*(3*a^2*b - b^3)*cos(8*d*x + 8*c)/d - 1/384*(9*a^2*b - b^3)*cos(6*d*x + 6*c)/d - 1/256*(21*a^2*b + b^3)*cos(4*d*x + 4*c)/d - 3/128*(7*a^2*b + b^3)*cos(2*d*x + 2*c)/d + 1/1024*(a^3 - 3*a*b^2)*sin(8*d*x + 8*c)/d + 1/192*(2*a^3 - 3*a*b^2)*sin(6*d*x + 6*c)/d + 1/128*(7*a^3 - 3*a*b^2)*sin(4*d*x + 4*c)/d + 1/64*(14*a^3 + 3*a*b^2)*sin(2*d*x + 2*c)/d","A",0
58,1,197,0,0.316746," ","integrate(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{{\left(3 \, a^{2} b - b^{3}\right)} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{{\left(15 \, a^{2} b - b^{3}\right)} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{{\left(9 \, a^{2} b + b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{3 \, {\left(5 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)}{64 \, d} + \frac{{\left(a^{3} - 3 \, a b^{2}\right)} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{{\left(7 \, a^{3} - 9 \, a b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(7 \, a^{3} - a b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{64 \, d} + \frac{5 \, {\left(7 \, a^{3} + 3 \, a b^{2}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"-1/448*(3*a^2*b - b^3)*cos(7*d*x + 7*c)/d - 1/320*(15*a^2*b - b^3)*cos(5*d*x + 5*c)/d - 1/64*(9*a^2*b + b^3)*cos(3*d*x + 3*c)/d - 3/64*(5*a^2*b + b^3)*cos(d*x + c)/d + 1/448*(a^3 - 3*a*b^2)*sin(7*d*x + 7*c)/d + 1/320*(7*a^3 - 9*a*b^2)*sin(5*d*x + 5*c)/d + 1/64*(7*a^3 - a*b^2)*sin(3*d*x + 3*c)/d + 5/64*(7*a^3 + 3*a*b^2)*sin(d*x + c)/d","A",0
59,1,157,0,0.356227," ","integrate(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{3 \, a^{2} b \cos\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{1}{16} \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} x - \frac{{\left(3 \, a^{2} b - b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{3 \, {\left(5 \, a^{2} b + b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(a^{3} - 3 \, a b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{3 \, {\left(a^{3} - a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{3 \, {\left(5 \, a^{3} + a b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"-3/32*a^2*b*cos(4*d*x + 4*c)/d + 1/16*(5*a^3 + 3*a*b^2)*x - 1/192*(3*a^2*b - b^3)*cos(6*d*x + 6*c)/d - 3/64*(5*a^2*b + b^3)*cos(2*d*x + 2*c)/d + 1/192*(a^3 - 3*a*b^2)*sin(6*d*x + 6*c)/d + 3/64*(a^3 - a*b^2)*sin(4*d*x + 4*c)/d + 3/64*(5*a^3 + a*b^2)*sin(2*d*x + 2*c)/d","A",0
60,1,145,0,0.483385," ","integrate(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{{\left(3 \, a^{2} b - b^{3}\right)} \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{{\left(9 \, a^{2} b + b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{{\left(3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)}{8 \, d} + \frac{{\left(a^{3} - 3 \, a b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{{\left(5 \, a^{3} - 3 \, a b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(5 \, a^{3} + 3 \, a b^{2}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/80*(3*a^2*b - b^3)*cos(5*d*x + 5*c)/d - 1/48*(9*a^2*b + b^3)*cos(3*d*x + 3*c)/d - 1/8*(3*a^2*b + b^3)*cos(d*x + c)/d + 1/80*(a^3 - 3*a*b^2)*sin(5*d*x + 5*c)/d + 1/48*(5*a^3 - 3*a*b^2)*sin(3*d*x + 3*c)/d + 1/8*(5*a^3 + 3*a*b^2)*sin(d*x + c)/d","A",0
61,1,104,0,0.244133," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{3}{8} \, {\left(a^{3} + a b^{2}\right)} x - \frac{{\left(3 \, a^{2} b - b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{{\left(3 \, a^{2} b + b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)}{8 \, d} + \frac{{\left(a^{3} - 3 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d}"," ",0,"1/4*a^3*sin(2*d*x + 2*c)/d + 3/8*(a^3 + a*b^2)*x - 1/32*(3*a^2*b - b^3)*cos(4*d*x + 4*c)/d - 1/8*(3*a^2*b + b^3)*cos(2*d*x + 2*c)/d + 1/32*(a^3 - 3*a*b^2)*sin(4*d*x + 4*c)/d","A",0
62,1,91,0,0.203700," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{{\left(3 \, a^{2} b - b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right)}{12 \, d} - \frac{3 \, {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right)}{4 \, d} + \frac{{\left(a^{3} - 3 \, a b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{3 \, {\left(a^{3} + a b^{2}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"-1/12*(3*a^2*b - b^3)*cos(3*d*x + 3*c)/d - 3/4*(a^2*b + b^3)*cos(d*x + c)/d + 1/12*(a^3 - 3*a*b^2)*sin(3*d*x + 3*c)/d + 3/4*(a^3 + a*b^2)*sin(d*x + c)/d","A",0
63,1,93,0,0.251920," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{b^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + {\left(a^{3} + 3 \, a b^{2}\right)} {\left(d x + c\right)} - \frac{b^{3} \tan\left(d x + c\right)^{2} - a^{3} \tan\left(d x + c\right) + 3 \, a b^{2} \tan\left(d x + c\right) + 3 \, a^{2} b}{\tan\left(d x + c\right)^{2} + 1}}{2 \, d}"," ",0,"1/2*(b^3*log(tan(d*x + c)^2 + 1) + (a^3 + 3*a*b^2)*(d*x + c) - (b^3*tan(d*x + c)^2 - a^3*tan(d*x + c) + 3*a*b^2*tan(d*x + c) + 3*a^2*b)/(tan(d*x + c)^2 + 1))/d","A",0
64,1,150,0,0.292561," ","integrate(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{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} - 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2} b - 2 \, b^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"(3*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 - 3*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 3*a^2*b*tan(1/2*d*x + 1/2*c)^2 - a^3*tan(1/2*d*x + 1/2*c) + 3*a*b^2*tan(1/2*d*x + 1/2*c) + 3*a^2*b - 2*b^3)/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","A",0
65,1,71,0,0.322822," ","integrate(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{b^{3} \tan\left(d x + c\right)^{2} + 6 \, a b^{2} \tan\left(d x + c\right) + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)} + {\left(3 \, a^{2} b - b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(b^3*tan(d*x + c)^2 + 6*a*b^2*tan(d*x + c) + 2*(a^3 - 3*a*b^2)*(d*x + c) + (3*a^2*b - b^3)*log(tan(d*x + c)^2 + 1))/d","A",0
66,1,171,0,0.329000," ","integrate(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(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(9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, a^{2} b + 4 \, b^{3}\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*(9*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 18*a^2*b*tan(1/2*d*x + 1/2*c)^4 + 36*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 12*b^3*tan(1/2*d*x + 1/2*c)^2 - 9*a*b^2*tan(1/2*d*x + 1/2*c) - 18*a^2*b + 4*b^3)/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
67,1,57,0,0.598315," ","integrate(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{b^{3} \tan\left(d x + c\right)^{4} + 4 \, a b^{2} \tan\left(d x + c\right)^{3} + 6 \, a^{2} b \tan\left(d x + c\right)^{2} + 4 \, a^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(b^3*tan(d*x + c)^4 + 4*a*b^2*tan(d*x + c)^3 + 6*a^2*b*tan(d*x + c)^2 + 4*a^3*tan(d*x + c))/d","B",0
68,1,333,0,0.519260," ","integrate(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{15 \, {\left(4 \, 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) - 15 \, {\left(4 \, 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(60 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 45 \, a b^{2} \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)^{8} - 120 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 270 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 240 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 480 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 80 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 120 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 270 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 80 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 60 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, a^{2} b + 16 \, b^{3}\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 - 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*a^3 - 3*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 + 45*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 360*a^2*b*tan(1/2*d*x + 1/2*c)^8 - 120*a^3*tan(1/2*d*x + 1/2*c)^7 + 270*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 720*a^2*b*tan(1/2*d*x + 1/2*c)^6 - 240*b^3*tan(1/2*d*x + 1/2*c)^6 - 480*a^2*b*tan(1/2*d*x + 1/2*c)^4 - 80*b^3*tan(1/2*d*x + 1/2*c)^4 + 120*a^3*tan(1/2*d*x + 1/2*c)^3 - 270*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 240*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 80*b^3*tan(1/2*d*x + 1/2*c)^2 - 60*a^3*tan(1/2*d*x + 1/2*c) - 45*a*b^2*tan(1/2*d*x + 1/2*c) - 120*a^2*b + 16*b^3)/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
69,1,112,0,0.342131," ","integrate(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{10 \, b^{3} \tan\left(d x + c\right)^{6} + 36 \, a b^{2} \tan\left(d x + c\right)^{5} + 45 \, a^{2} b \tan\left(d x + c\right)^{4} + 15 \, b^{3} \tan\left(d x + c\right)^{4} + 20 \, a^{3} \tan\left(d x + c\right)^{3} + 60 \, a b^{2} \tan\left(d x + c\right)^{3} + 90 \, a^{2} b \tan\left(d x + c\right)^{2} + 60 \, a^{3} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(10*b^3*tan(d*x + c)^6 + 36*a*b^2*tan(d*x + c)^5 + 45*a^2*b*tan(d*x + c)^4 + 15*b^3*tan(d*x + c)^4 + 20*a^3*tan(d*x + c)^3 + 60*a*b^2*tan(d*x + c)^3 + 90*a^2*b*tan(d*x + c)^2 + 60*a^3*tan(d*x + c))/d","A",0
70,1,465,0,0.384537," ","integrate(sec(d*x+c)^8*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{105 \, {\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) - 105 \, {\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) + \frac{2 \, {\left(350 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 105 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1680 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 840 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1540 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3360 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 1120 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 630 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1085 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 5040 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1120 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 6720 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 2240 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 630 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1085 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3696 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 448 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 840 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1540 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 672 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 224 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 350 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 336 \, a^{2} b + 32 \, b^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{7}}}{560 \, d}"," ",0,"1/560*(105*(2*a^3 - a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(2*a^3 - a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(350*a^3*tan(1/2*d*x + 1/2*c)^13 + 105*a*b^2*tan(1/2*d*x + 1/2*c)^13 - 1680*a^2*b*tan(1/2*d*x + 1/2*c)^12 - 840*a^3*tan(1/2*d*x + 1/2*c)^11 + 1540*a*b^2*tan(1/2*d*x + 1/2*c)^11 + 3360*a^2*b*tan(1/2*d*x + 1/2*c)^10 - 1120*b^3*tan(1/2*d*x + 1/2*c)^10 + 630*a^3*tan(1/2*d*x + 1/2*c)^9 + 1085*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 5040*a^2*b*tan(1/2*d*x + 1/2*c)^8 - 1120*b^3*tan(1/2*d*x + 1/2*c)^8 + 6720*a^2*b*tan(1/2*d*x + 1/2*c)^6 - 2240*b^3*tan(1/2*d*x + 1/2*c)^6 - 630*a^3*tan(1/2*d*x + 1/2*c)^5 - 1085*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 3696*a^2*b*tan(1/2*d*x + 1/2*c)^4 - 448*b^3*tan(1/2*d*x + 1/2*c)^4 + 840*a^3*tan(1/2*d*x + 1/2*c)^3 - 1540*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 672*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 224*b^3*tan(1/2*d*x + 1/2*c)^2 - 350*a^3*tan(1/2*d*x + 1/2*c) - 105*a*b^2*tan(1/2*d*x + 1/2*c) - 336*a^2*b + 32*b^3)/(tan(1/2*d*x + 1/2*c)^2 - 1)^7)/d","B",0
71,1,166,0,0.428848," ","integrate(sec(d*x+c)^9*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{105 \, b^{3} \tan\left(d x + c\right)^{8} + 360 \, a b^{2} \tan\left(d x + c\right)^{7} + 420 \, a^{2} b \tan\left(d x + c\right)^{6} + 280 \, b^{3} \tan\left(d x + c\right)^{6} + 168 \, a^{3} \tan\left(d x + c\right)^{5} + 1008 \, a b^{2} \tan\left(d x + c\right)^{5} + 1260 \, a^{2} b \tan\left(d x + c\right)^{4} + 210 \, b^{3} \tan\left(d x + c\right)^{4} + 560 \, a^{3} \tan\left(d x + c\right)^{3} + 840 \, a b^{2} \tan\left(d x + c\right)^{3} + 1260 \, a^{2} b \tan\left(d x + c\right)^{2} + 840 \, a^{3} \tan\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(105*b^3*tan(d*x + c)^8 + 360*a*b^2*tan(d*x + c)^7 + 420*a^2*b*tan(d*x + c)^6 + 280*b^3*tan(d*x + c)^6 + 168*a^3*tan(d*x + c)^5 + 1008*a*b^2*tan(d*x + c)^5 + 1260*a^2*b*tan(d*x + c)^4 + 210*b^3*tan(d*x + c)^4 + 560*a^3*tan(d*x + c)^3 + 840*a*b^2*tan(d*x + c)^3 + 1260*a^2*b*tan(d*x + c)^2 + 840*a^3*tan(d*x + c))/d","A",0
72,1,597,0,0.906428," ","integrate(sec(d*x+c)^10*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{315 \, {\left(8 \, 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) - 315 \, {\left(8 \, 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(5544 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} + 945 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} - 24192 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{16} - 15792 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 24066 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 48384 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} - 16128 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} + 29232 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 31374 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 145152 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 26880 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 33264 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 54810 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 241920 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 80640 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 193536 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 48384 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 33264 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 54810 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 145152 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 48384 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 29232 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 31374 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 76032 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 6912 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 15792 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24066 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6912 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2304 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 5544 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 945 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3456 \, a^{2} b + 256 \, b^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{9}}}{8064 \, d}"," ",0,"1/8064*(315*(8*a^3 - 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 315*(8*a^3 - 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(5544*a^3*tan(1/2*d*x + 1/2*c)^17 + 945*a*b^2*tan(1/2*d*x + 1/2*c)^17 - 24192*a^2*b*tan(1/2*d*x + 1/2*c)^16 - 15792*a^3*tan(1/2*d*x + 1/2*c)^15 + 24066*a*b^2*tan(1/2*d*x + 1/2*c)^15 + 48384*a^2*b*tan(1/2*d*x + 1/2*c)^14 - 16128*b^3*tan(1/2*d*x + 1/2*c)^14 + 29232*a^3*tan(1/2*d*x + 1/2*c)^13 + 31374*a*b^2*tan(1/2*d*x + 1/2*c)^13 - 145152*a^2*b*tan(1/2*d*x + 1/2*c)^12 - 26880*b^3*tan(1/2*d*x + 1/2*c)^12 - 33264*a^3*tan(1/2*d*x + 1/2*c)^11 + 54810*a*b^2*tan(1/2*d*x + 1/2*c)^11 + 241920*a^2*b*tan(1/2*d*x + 1/2*c)^10 - 80640*b^3*tan(1/2*d*x + 1/2*c)^10 - 193536*a^2*b*tan(1/2*d*x + 1/2*c)^8 - 48384*b^3*tan(1/2*d*x + 1/2*c)^8 + 33264*a^3*tan(1/2*d*x + 1/2*c)^7 - 54810*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 145152*a^2*b*tan(1/2*d*x + 1/2*c)^6 - 48384*b^3*tan(1/2*d*x + 1/2*c)^6 - 29232*a^3*tan(1/2*d*x + 1/2*c)^5 - 31374*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 76032*a^2*b*tan(1/2*d*x + 1/2*c)^4 - 6912*b^3*tan(1/2*d*x + 1/2*c)^4 + 15792*a^3*tan(1/2*d*x + 1/2*c)^3 - 24066*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 6912*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 2304*b^3*tan(1/2*d*x + 1/2*c)^2 - 5544*a^3*tan(1/2*d*x + 1/2*c) - 945*a*b^2*tan(1/2*d*x + 1/2*c) - 3456*a^2*b + 256*b^3)/(tan(1/2*d*x + 1/2*c)^2 - 1)^9)/d","B",0
73,1,220,0,0.447890," ","integrate(sec(d*x+c)^11*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{84 \, b^{3} \tan\left(d x + c\right)^{10} + 280 \, a b^{2} \tan\left(d x + c\right)^{9} + 315 \, a^{2} b \tan\left(d x + c\right)^{8} + 315 \, b^{3} \tan\left(d x + c\right)^{8} + 120 \, a^{3} \tan\left(d x + c\right)^{7} + 1080 \, a b^{2} \tan\left(d x + c\right)^{7} + 1260 \, a^{2} b \tan\left(d x + c\right)^{6} + 420 \, b^{3} \tan\left(d x + c\right)^{6} + 504 \, a^{3} \tan\left(d x + c\right)^{5} + 1512 \, a b^{2} \tan\left(d x + c\right)^{5} + 1890 \, a^{2} b \tan\left(d x + c\right)^{4} + 210 \, b^{3} \tan\left(d x + c\right)^{4} + 840 \, a^{3} \tan\left(d x + c\right)^{3} + 840 \, a b^{2} \tan\left(d x + c\right)^{3} + 1260 \, a^{2} b \tan\left(d x + c\right)^{2} + 840 \, a^{3} \tan\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(84*b^3*tan(d*x + c)^10 + 280*a*b^2*tan(d*x + c)^9 + 315*a^2*b*tan(d*x + c)^8 + 315*b^3*tan(d*x + c)^8 + 120*a^3*tan(d*x + c)^7 + 1080*a*b^2*tan(d*x + c)^7 + 1260*a^2*b*tan(d*x + c)^6 + 420*b^3*tan(d*x + c)^6 + 504*a^3*tan(d*x + c)^5 + 1512*a*b^2*tan(d*x + c)^5 + 1890*a^2*b*tan(d*x + c)^4 + 210*b^3*tan(d*x + c)^4 + 840*a^3*tan(d*x + c)^3 + 840*a*b^2*tan(d*x + c)^3 + 1260*a^2*b*tan(d*x + c)^2 + 840*a^3*tan(d*x + c))/d","A",0
74,1,269,0,0.702115," ","integrate(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{a^{3} b \cos\left(5 \, d x + 5 \, c\right)}{16 \, d} - \frac{{\left(a^{3} b - a b^{3}\right)} \cos\left(9 \, d x + 9 \, c\right)}{576 \, d} - \frac{{\left(7 \, a^{3} b - 3 \, a b^{3}\right)} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{{\left(7 \, a^{3} b + 2 \, a b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{{\left(7 \, a^{3} b + 3 \, a b^{3}\right)} \cos\left(d x + c\right)}{32 \, d} + \frac{{\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \sin\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{{\left(9 \, a^{4} - 30 \, a^{2} b^{2} + b^{4}\right)} \sin\left(7 \, d x + 7 \, c\right)}{1792 \, d} + \frac{{\left(9 \, a^{4} - 12 \, a^{2} b^{2} - b^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(21 \, a^{4} - b^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{3 \, {\left(21 \, a^{4} + 14 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{128 \, d}"," ",0,"-1/16*a^3*b*cos(5*d*x + 5*c)/d - 1/576*(a^3*b - a*b^3)*cos(9*d*x + 9*c)/d - 1/448*(7*a^3*b - 3*a*b^3)*cos(7*d*x + 7*c)/d - 1/48*(7*a^3*b + 2*a*b^3)*cos(3*d*x + 3*c)/d - 1/32*(7*a^3*b + 3*a*b^3)*cos(d*x + c)/d + 1/2304*(a^4 - 6*a^2*b^2 + b^4)*sin(9*d*x + 9*c)/d + 1/1792*(9*a^4 - 30*a^2*b^2 + b^4)*sin(7*d*x + 7*c)/d + 1/320*(9*a^4 - 12*a^2*b^2 - b^4)*sin(5*d*x + 5*c)/d + 1/192*(21*a^4 - b^4)*sin(3*d*x + 3*c)/d + 3/128*(21*a^4 + 14*a^2*b^2 + b^4)*sin(d*x + c)/d","A",0
75,1,245,0,0.670636," ","integrate(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{1}{128} \, {\left(35 \, a^{4} + 30 \, a^{2} b^{2} + 3 \, b^{4}\right)} x - \frac{{\left(a^{3} b - a b^{3}\right)} \cos\left(8 \, d x + 8 \, c\right)}{256 \, d} - \frac{{\left(3 \, a^{3} b - a b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)}{96 \, d} - \frac{{\left(7 \, a^{3} b + a b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)}{64 \, d} - \frac{{\left(7 \, a^{3} b + 3 \, a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)}{32 \, d} + \frac{{\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{{\left(a^{4} - 3 \, a^{2} b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right)}{96 \, d} + \frac{{\left(7 \, a^{4} - 6 \, a^{2} b^{2} - b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{{\left(7 \, a^{4} + 3 \, a^{2} b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{32 \, d}"," ",0,"1/128*(35*a^4 + 30*a^2*b^2 + 3*b^4)*x - 1/256*(a^3*b - a*b^3)*cos(8*d*x + 8*c)/d - 1/96*(3*a^3*b - a*b^3)*cos(6*d*x + 6*c)/d - 1/64*(7*a^3*b + a*b^3)*cos(4*d*x + 4*c)/d - 1/32*(7*a^3*b + 3*a*b^3)*cos(2*d*x + 2*c)/d + 1/1024*(a^4 - 6*a^2*b^2 + b^4)*sin(8*d*x + 8*c)/d + 1/96*(a^4 - 3*a^2*b^2)*sin(6*d*x + 6*c)/d + 1/128*(7*a^4 - 6*a^2*b^2 - b^4)*sin(4*d*x + 4*c)/d + 1/32*(7*a^4 + 3*a^2*b^2)*sin(2*d*x + 2*c)/d","A",0
76,1,229,0,0.491199," ","integrate(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{{\left(a^{3} b - a b^{3}\right)} \cos\left(7 \, d x + 7 \, c\right)}{112 \, d} - \frac{{\left(5 \, a^{3} b - a b^{3}\right)} \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{{\left(3 \, a^{3} b + a b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right)}{16 \, d} - \frac{{\left(5 \, a^{3} b + 3 \, a b^{3}\right)} \cos\left(d x + c\right)}{16 \, d} + \frac{{\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{{\left(7 \, a^{4} - 18 \, a^{2} b^{2} - b^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(7 \, a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{64 \, d} + \frac{{\left(35 \, a^{4} + 30 \, a^{2} b^{2} + 3 \, b^{4}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"-1/112*(a^3*b - a*b^3)*cos(7*d*x + 7*c)/d - 1/80*(5*a^3*b - a*b^3)*cos(5*d*x + 5*c)/d - 1/16*(3*a^3*b + a*b^3)*cos(3*d*x + 3*c)/d - 1/16*(5*a^3*b + 3*a*b^3)*cos(d*x + c)/d + 1/448*(a^4 - 6*a^2*b^2 + b^4)*sin(7*d*x + 7*c)/d + 1/320*(7*a^4 - 18*a^2*b^2 - b^4)*sin(5*d*x + 5*c)/d + 1/64*(7*a^4 - 2*a^2*b^2 - b^4)*sin(3*d*x + 3*c)/d + 1/64*(35*a^4 + 30*a^2*b^2 + 3*b^4)*sin(d*x + c)/d","A",0
77,1,187,0,2.017103," ","integrate(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{a^{3} b \cos\left(4 \, d x + 4 \, c\right)}{8 \, d} + \frac{1}{16} \, {\left(5 \, a^{4} + 6 \, a^{2} b^{2} + b^{4}\right)} x - \frac{{\left(a^{3} b - a b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)}{48 \, d} - \frac{{\left(5 \, a^{3} b + 3 \, a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)}{16 \, d} + \frac{{\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{{\left(3 \, a^{4} - 6 \, a^{2} b^{2} - b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(15 \, a^{4} + 6 \, a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"-1/8*a^3*b*cos(4*d*x + 4*c)/d + 1/16*(5*a^4 + 6*a^2*b^2 + b^4)*x - 1/48*(a^3*b - a*b^3)*cos(6*d*x + 6*c)/d - 1/16*(5*a^3*b + 3*a*b^3)*cos(2*d*x + 2*c)/d + 1/192*(a^4 - 6*a^2*b^2 + b^4)*sin(6*d*x + 6*c)/d + 1/64*(3*a^4 - 6*a^2*b^2 - b^4)*sin(4*d*x + 4*c)/d + 1/64*(15*a^4 + 6*a^2*b^2 - b^4)*sin(2*d*x + 2*c)/d","A",0
78,1,165,0,2.940714," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{{\left(a^{3} b - a b^{3}\right)} \cos\left(5 \, d x + 5 \, c\right)}{20 \, d} - \frac{{\left(3 \, a^{3} b + a b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right)}{12 \, d} - \frac{{\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)}{2 \, d} + \frac{{\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{{\left(5 \, a^{4} - 6 \, a^{2} b^{2} - 3 \, b^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(5 \, a^{4} + 6 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/20*(a^3*b - a*b^3)*cos(5*d*x + 5*c)/d - 1/12*(3*a^3*b + a*b^3)*cos(3*d*x + 3*c)/d - 1/2*(a^3*b + a*b^3)*cos(d*x + c)/d + 1/80*(a^4 - 6*a^2*b^2 + b^4)*sin(5*d*x + 5*c)/d + 1/48*(5*a^4 - 6*a^2*b^2 - 3*b^4)*sin(3*d*x + 3*c)/d + 1/8*(5*a^4 + 6*a^2*b^2 + b^4)*sin(d*x + c)/d","A",0
79,1,122,0,2.922094," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{3}{8} \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} x - \frac{{\left(a^{3} b - a b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)}{8 \, d} - \frac{{\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)}{2 \, d} + \frac{{\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(a^{4} - b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"3/8*(a^4 + 2*a^2*b^2 + b^4)*x - 1/8*(a^3*b - a*b^3)*cos(4*d*x + 4*c)/d - 1/2*(a^3*b + a*b^3)*cos(2*d*x + 2*c)/d + 1/32*(a^4 - 6*a^2*b^2 + b^4)*sin(4*d*x + 4*c)/d + 1/4*(a^4 - b^4)*sin(2*d*x + 2*c)/d","A",0
80,1,217,0,0.396445," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(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) + \frac{2 \, {\left(3 \, a^{4} \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} - 12 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{3} b - 8 \, a b^{3}\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)) + 2*(3*a^4*tan(1/2*d*x + 1/2*c)^5 - 3*b^4*tan(1/2*d*x + 1/2*c)^5 - 12*a^3*b*tan(1/2*d*x + 1/2*c)^4 + 2*a^4*tan(1/2*d*x + 1/2*c)^3 + 24*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 10*b^4*tan(1/2*d*x + 1/2*c)^3 - 24*a*b^3*tan(1/2*d*x + 1/2*c)^2 + 3*a^4*tan(1/2*d*x + 1/2*c) - 3*b^4*tan(1/2*d*x + 1/2*c) - 4*a^3*b - 8*a*b^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
81,1,128,0,3.521543," ","integrate(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{4 \, a b^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, b^{4} \tan\left(d x + c\right) + {\left(a^{4} + 6 \, a^{2} b^{2} - 3 \, b^{4}\right)} {\left(d x + c\right)} - \frac{4 \, a b^{3} \tan\left(d x + c\right)^{2} - a^{4} \tan\left(d x + c\right) + 6 \, a^{2} b^{2} \tan\left(d x + c\right) - b^{4} \tan\left(d x + c\right) + 4 \, a^{3} b}{\tan\left(d x + c\right)^{2} + 1}}{2 \, d}"," ",0,"1/2*(4*a*b^3*log(tan(d*x + c)^2 + 1) + 2*b^4*tan(d*x + c) + (a^4 + 6*a^2*b^2 - 3*b^4)*(d*x + c) - (4*a*b^3*tan(d*x + c)^2 - a^4*tan(d*x + c) + 6*a^2*b^2*tan(d*x + c) - b^4*tan(d*x + c) + 4*a^3*b)/(tan(d*x + c)^2 + 1))/d","A",0
82,1,206,0,0.399064," ","integrate(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, {\left(4 \, 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) - 3 \, {\left(4 \, 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{4 \, {\left(a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{3} b + 4 \, a b^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + \frac{2 \, {\left(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)^{2} + b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, a b^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(3*(4*a^2*b^2 - b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*a^2*b^2 - b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 4*(a^4*tan(1/2*d*x + 1/2*c) - 6*a^2*b^2*tan(1/2*d*x + 1/2*c) + b^4*tan(1/2*d*x + 1/2*c) - 4*a^3*b + 4*a*b^3)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 2*(b^4*tan(1/2*d*x + 1/2*c)^3 - 8*a*b^3*tan(1/2*d*x + 1/2*c)^2 + b^4*tan(1/2*d*x + 1/2*c) + 8*a*b^3)/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
83,1,104,0,0.375654," ","integrate(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{b^{4} \tan\left(d x + c\right)^{3} + 6 \, a b^{3} \tan\left(d x + c\right)^{2} + 18 \, a^{2} b^{2} \tan\left(d x + c\right) - 3 \, b^{4} \tan\left(d x + c\right) + 3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} {\left(d x + c\right)} + 6 \, {\left(a^{3} b - a b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{3 \, d}"," ",0,"1/3*(b^4*tan(d*x + c)^3 + 6*a*b^3*tan(d*x + c)^2 + 18*a^2*b^2*tan(d*x + c) - 3*b^4*tan(d*x + c) + 3*(a^4 - 6*a^2*b^2 + b^4)*(d*x + c) + 6*(a^3*b - a*b^3)*log(tan(d*x + c)^2 + 1))/d","A",0
84,1,325,0,0.477755," ","integrate(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(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(72 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, b^{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)^{6} - 72 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 33 \, 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)^{4} - 192 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 72 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 288 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 256 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 72 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, a^{3} b - 64 \, a b^{3}\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*(72*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 9*b^4*tan(1/2*d*x + 1/2*c)^7 - 96*a^3*b*tan(1/2*d*x + 1/2*c)^6 - 72*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 33*b^4*tan(1/2*d*x + 1/2*c)^5 + 288*a^3*b*tan(1/2*d*x + 1/2*c)^4 - 192*a*b^3*tan(1/2*d*x + 1/2*c)^4 - 72*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 33*b^4*tan(1/2*d*x + 1/2*c)^3 - 288*a^3*b*tan(1/2*d*x + 1/2*c)^2 + 256*a*b^3*tan(1/2*d*x + 1/2*c)^2 + 72*a^2*b^2*tan(1/2*d*x + 1/2*c) - 9*b^4*tan(1/2*d*x + 1/2*c) + 96*a^3*b - 64*a*b^3)/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
85,1,73,0,0.655536," ","integrate(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{b^{4} \tan\left(d x + c\right)^{5} + 5 \, a b^{3} \tan\left(d x + c\right)^{4} + 10 \, a^{2} b^{2} \tan\left(d x + c\right)^{3} + 10 \, a^{3} b \tan\left(d x + c\right)^{2} + 5 \, a^{4} \tan\left(d x + c\right)}{5 \, d}"," ",0,"1/5*(b^4*tan(d*x + c)^5 + 5*a*b^3*tan(d*x + c)^4 + 10*a^2*b^2*tan(d*x + c)^3 + 10*a^3*b*tan(d*x + c)^2 + 5*a^4*tan(d*x + c))/d","B",0
86,1,536,0,0.486071," ","integrate(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{15 \, {\left(8 \, a^{4} - 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) - 15 \, {\left(8 \, a^{4} - 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(120 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 180 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 15 \, b^{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)^{10} - 360 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 900 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 85 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2880 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1920 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 240 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1080 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 570 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3200 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1280 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 240 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1080 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 570 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1920 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 360 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 900 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 85 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 960 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 768 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, a^{4} \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) - 15 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 320 \, a^{3} b - 128 \, a b^{3}\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 - 12*a^2*b^2 + b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(8*a^4 - 12*a^2*b^2 + 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 + 180*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 15*b^4*tan(1/2*d*x + 1/2*c)^11 - 960*a^3*b*tan(1/2*d*x + 1/2*c)^10 - 360*a^4*tan(1/2*d*x + 1/2*c)^9 + 900*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 85*b^4*tan(1/2*d*x + 1/2*c)^9 + 2880*a^3*b*tan(1/2*d*x + 1/2*c)^8 - 1920*a*b^3*tan(1/2*d*x + 1/2*c)^8 + 240*a^4*tan(1/2*d*x + 1/2*c)^7 - 1080*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 570*b^4*tan(1/2*d*x + 1/2*c)^7 - 3200*a^3*b*tan(1/2*d*x + 1/2*c)^6 + 1280*a*b^3*tan(1/2*d*x + 1/2*c)^6 + 240*a^4*tan(1/2*d*x + 1/2*c)^5 - 1080*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 570*b^4*tan(1/2*d*x + 1/2*c)^5 + 1920*a^3*b*tan(1/2*d*x + 1/2*c)^4 - 360*a^4*tan(1/2*d*x + 1/2*c)^3 + 900*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 85*b^4*tan(1/2*d*x + 1/2*c)^3 - 960*a^3*b*tan(1/2*d*x + 1/2*c)^2 + 768*a*b^3*tan(1/2*d*x + 1/2*c)^2 + 120*a^4*tan(1/2*d*x + 1/2*c) + 180*a^2*b^2*tan(1/2*d*x + 1/2*c) - 15*b^4*tan(1/2*d*x + 1/2*c) + 320*a^3*b - 128*a*b^3)/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
87,1,144,0,0.434722," ","integrate(sec(d*x+c)^8*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{15 \, b^{4} \tan\left(d x + c\right)^{7} + 70 \, a b^{3} \tan\left(d x + c\right)^{6} + 126 \, a^{2} b^{2} \tan\left(d x + c\right)^{5} + 21 \, b^{4} \tan\left(d x + c\right)^{5} + 105 \, a^{3} b \tan\left(d x + c\right)^{4} + 105 \, a b^{3} \tan\left(d x + c\right)^{4} + 35 \, a^{4} \tan\left(d x + c\right)^{3} + 210 \, a^{2} b^{2} \tan\left(d x + c\right)^{3} + 210 \, a^{3} b \tan\left(d x + c\right)^{2} + 105 \, a^{4} \tan\left(d x + c\right)}{105 \, d}"," ",0,"1/105*(15*b^4*tan(d*x + c)^7 + 70*a*b^3*tan(d*x + c)^6 + 126*a^2*b^2*tan(d*x + c)^5 + 21*b^4*tan(d*x + c)^5 + 105*a^3*b*tan(d*x + c)^4 + 105*a*b^3*tan(d*x + c)^4 + 35*a^4*tan(d*x + c)^3 + 210*a^2*b^2*tan(d*x + c)^3 + 210*a^3*b*tan(d*x + c)^2 + 105*a^4*tan(d*x + c))/d","A",0
88,1,706,0,0.506871," ","integrate(sec(d*x+c)^9*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{105 \, {\left(16 \, a^{4} - 16 \, 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) - 105 \, {\left(16 \, a^{4} - 16 \, 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(2800 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 1680 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} - 105 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} - 17920 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} - 9520 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 22960 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 805 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 53760 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 35840 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 11760 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 7280 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 11655 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 89600 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 5040 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 17360 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 23485 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 125440 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 35840 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 5040 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 17360 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 23485 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 111104 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 57344 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 11760 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 7280 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 11655 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 46592 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 7168 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 9520 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 22960 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 805 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10752 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8192 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2800 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1680 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3584 \, a^{3} b - 1024 \, a b^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{8}}}{4480 \, d}"," ",0,"1/4480*(105*(16*a^4 - 16*a^2*b^2 + b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(16*a^4 - 16*a^2*b^2 + b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(2800*a^4*tan(1/2*d*x + 1/2*c)^15 + 1680*a^2*b^2*tan(1/2*d*x + 1/2*c)^15 - 105*b^4*tan(1/2*d*x + 1/2*c)^15 - 17920*a^3*b*tan(1/2*d*x + 1/2*c)^14 - 9520*a^4*tan(1/2*d*x + 1/2*c)^13 + 22960*a^2*b^2*tan(1/2*d*x + 1/2*c)^13 + 805*b^4*tan(1/2*d*x + 1/2*c)^13 + 53760*a^3*b*tan(1/2*d*x + 1/2*c)^12 - 35840*a*b^3*tan(1/2*d*x + 1/2*c)^12 + 11760*a^4*tan(1/2*d*x + 1/2*c)^11 - 7280*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 + 11655*b^4*tan(1/2*d*x + 1/2*c)^11 - 89600*a^3*b*tan(1/2*d*x + 1/2*c)^10 - 5040*a^4*tan(1/2*d*x + 1/2*c)^9 - 17360*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 23485*b^4*tan(1/2*d*x + 1/2*c)^9 + 125440*a^3*b*tan(1/2*d*x + 1/2*c)^8 - 35840*a*b^3*tan(1/2*d*x + 1/2*c)^8 - 5040*a^4*tan(1/2*d*x + 1/2*c)^7 - 17360*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 23485*b^4*tan(1/2*d*x + 1/2*c)^7 - 111104*a^3*b*tan(1/2*d*x + 1/2*c)^6 + 57344*a*b^3*tan(1/2*d*x + 1/2*c)^6 + 11760*a^4*tan(1/2*d*x + 1/2*c)^5 - 7280*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 11655*b^4*tan(1/2*d*x + 1/2*c)^5 + 46592*a^3*b*tan(1/2*d*x + 1/2*c)^4 + 7168*a*b^3*tan(1/2*d*x + 1/2*c)^4 - 9520*a^4*tan(1/2*d*x + 1/2*c)^3 + 22960*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 805*b^4*tan(1/2*d*x + 1/2*c)^3 - 10752*a^3*b*tan(1/2*d*x + 1/2*c)^2 + 8192*a*b^3*tan(1/2*d*x + 1/2*c)^2 + 2800*a^4*tan(1/2*d*x + 1/2*c) + 1680*a^2*b^2*tan(1/2*d*x + 1/2*c) - 105*b^4*tan(1/2*d*x + 1/2*c) + 3584*a^3*b - 1024*a*b^3)/(tan(1/2*d*x + 1/2*c)^2 - 1)^8)/d","B",0
89,1,214,0,0.434597," ","integrate(sec(d*x+c)^10*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{70 \, b^{4} \tan\left(d x + c\right)^{9} + 315 \, a b^{3} \tan\left(d x + c\right)^{8} + 540 \, a^{2} b^{2} \tan\left(d x + c\right)^{7} + 180 \, b^{4} \tan\left(d x + c\right)^{7} + 420 \, a^{3} b \tan\left(d x + c\right)^{6} + 840 \, a b^{3} \tan\left(d x + c\right)^{6} + 126 \, a^{4} \tan\left(d x + c\right)^{5} + 1512 \, a^{2} b^{2} \tan\left(d x + c\right)^{5} + 126 \, b^{4} \tan\left(d x + c\right)^{5} + 1260 \, a^{3} b \tan\left(d x + c\right)^{4} + 630 \, a b^{3} \tan\left(d x + c\right)^{4} + 420 \, a^{4} \tan\left(d x + c\right)^{3} + 1260 \, a^{2} b^{2} \tan\left(d x + c\right)^{3} + 1260 \, a^{3} b \tan\left(d x + c\right)^{2} + 630 \, a^{4} \tan\left(d x + c\right)}{630 \, d}"," ",0,"1/630*(70*b^4*tan(d*x + c)^9 + 315*a*b^3*tan(d*x + c)^8 + 540*a^2*b^2*tan(d*x + c)^7 + 180*b^4*tan(d*x + c)^7 + 420*a^3*b*tan(d*x + c)^6 + 840*a*b^3*tan(d*x + c)^6 + 126*a^4*tan(d*x + c)^5 + 1512*a^2*b^2*tan(d*x + c)^5 + 126*b^4*tan(d*x + c)^5 + 1260*a^3*b*tan(d*x + c)^4 + 630*a*b^3*tan(d*x + c)^4 + 420*a^4*tan(d*x + c)^3 + 1260*a^2*b^2*tan(d*x + c)^3 + 1260*a^3*b*tan(d*x + c)^2 + 630*a^4*tan(d*x + c))/d","A",0
90,1,880,0,0.523912," ","integrate(sec(d*x+c)^11*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{315 \, {\left(80 \, a^{4} - 60 \, 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) - 315 \, {\left(80 \, a^{4} - 60 \, 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(55440 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{19} + 18900 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{19} - 945 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{19} - 322560 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{18} - 213360 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} + 462420 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} + 9135 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} + 967680 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{16} - 645120 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{16} + 450240 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 146160 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 218484 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} - 2580480 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} - 430080 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} - 624960 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 468720 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 653940 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 5160960 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 2150400 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 332640 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1096200 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1183770 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 5806080 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 1290240 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 332640 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1096200 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1183770 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4515840 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 624960 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 468720 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 653940 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2949120 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1658880 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 450240 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 146160 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 218484 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1105920 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 184320 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 213360 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 462420 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9135 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 138240 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 102400 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 55440 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18900 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 945 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 46080 \, a^{3} b - 10240 \, a b^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{10}}}{80640 \, d}"," ",0,"1/80640*(315*(80*a^4 - 60*a^2*b^2 + 3*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 315*(80*a^4 - 60*a^2*b^2 + 3*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(55440*a^4*tan(1/2*d*x + 1/2*c)^19 + 18900*a^2*b^2*tan(1/2*d*x + 1/2*c)^19 - 945*b^4*tan(1/2*d*x + 1/2*c)^19 - 322560*a^3*b*tan(1/2*d*x + 1/2*c)^18 - 213360*a^4*tan(1/2*d*x + 1/2*c)^17 + 462420*a^2*b^2*tan(1/2*d*x + 1/2*c)^17 + 9135*b^4*tan(1/2*d*x + 1/2*c)^17 + 967680*a^3*b*tan(1/2*d*x + 1/2*c)^16 - 645120*a*b^3*tan(1/2*d*x + 1/2*c)^16 + 450240*a^4*tan(1/2*d*x + 1/2*c)^15 + 146160*a^2*b^2*tan(1/2*d*x + 1/2*c)^15 + 218484*b^4*tan(1/2*d*x + 1/2*c)^15 - 2580480*a^3*b*tan(1/2*d*x + 1/2*c)^14 - 430080*a*b^3*tan(1/2*d*x + 1/2*c)^14 - 624960*a^4*tan(1/2*d*x + 1/2*c)^13 + 468720*a^2*b^2*tan(1/2*d*x + 1/2*c)^13 + 653940*b^4*tan(1/2*d*x + 1/2*c)^13 + 5160960*a^3*b*tan(1/2*d*x + 1/2*c)^12 - 2150400*a*b^3*tan(1/2*d*x + 1/2*c)^12 + 332640*a^4*tan(1/2*d*x + 1/2*c)^11 - 1096200*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 + 1183770*b^4*tan(1/2*d*x + 1/2*c)^11 - 5806080*a^3*b*tan(1/2*d*x + 1/2*c)^10 + 1290240*a*b^3*tan(1/2*d*x + 1/2*c)^10 + 332640*a^4*tan(1/2*d*x + 1/2*c)^9 - 1096200*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 1183770*b^4*tan(1/2*d*x + 1/2*c)^9 + 4515840*a^3*b*tan(1/2*d*x + 1/2*c)^8 - 624960*a^4*tan(1/2*d*x + 1/2*c)^7 + 468720*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 653940*b^4*tan(1/2*d*x + 1/2*c)^7 - 2949120*a^3*b*tan(1/2*d*x + 1/2*c)^6 + 1658880*a*b^3*tan(1/2*d*x + 1/2*c)^6 + 450240*a^4*tan(1/2*d*x + 1/2*c)^5 + 146160*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 218484*b^4*tan(1/2*d*x + 1/2*c)^5 + 1105920*a^3*b*tan(1/2*d*x + 1/2*c)^4 + 184320*a*b^3*tan(1/2*d*x + 1/2*c)^4 - 213360*a^4*tan(1/2*d*x + 1/2*c)^3 + 462420*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 9135*b^4*tan(1/2*d*x + 1/2*c)^3 - 138240*a^3*b*tan(1/2*d*x + 1/2*c)^2 + 102400*a*b^3*tan(1/2*d*x + 1/2*c)^2 + 55440*a^4*tan(1/2*d*x + 1/2*c) + 18900*a^2*b^2*tan(1/2*d*x + 1/2*c) - 945*b^4*tan(1/2*d*x + 1/2*c) + 46080*a^3*b - 10240*a*b^3)/(tan(1/2*d*x + 1/2*c)^2 - 1)^10)/d","B",0
91,1,284,0,0.535011," ","integrate(sec(d*x+c)^12*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{210 \, b^{4} \tan\left(d x + c\right)^{11} + 924 \, a b^{3} \tan\left(d x + c\right)^{10} + 1540 \, a^{2} b^{2} \tan\left(d x + c\right)^{9} + 770 \, b^{4} \tan\left(d x + c\right)^{9} + 1155 \, a^{3} b \tan\left(d x + c\right)^{8} + 3465 \, a b^{3} \tan\left(d x + c\right)^{8} + 330 \, a^{4} \tan\left(d x + c\right)^{7} + 5940 \, a^{2} b^{2} \tan\left(d x + c\right)^{7} + 990 \, b^{4} \tan\left(d x + c\right)^{7} + 4620 \, a^{3} b \tan\left(d x + c\right)^{6} + 4620 \, a b^{3} \tan\left(d x + c\right)^{6} + 1386 \, a^{4} \tan\left(d x + c\right)^{5} + 8316 \, a^{2} b^{2} \tan\left(d x + c\right)^{5} + 462 \, b^{4} \tan\left(d x + c\right)^{5} + 6930 \, a^{3} b \tan\left(d x + c\right)^{4} + 2310 \, a b^{3} \tan\left(d x + c\right)^{4} + 2310 \, a^{4} \tan\left(d x + c\right)^{3} + 4620 \, a^{2} b^{2} \tan\left(d x + c\right)^{3} + 4620 \, a^{3} b \tan\left(d x + c\right)^{2} + 2310 \, a^{4} \tan\left(d x + c\right)}{2310 \, d}"," ",0,"1/2310*(210*b^4*tan(d*x + c)^11 + 924*a*b^3*tan(d*x + c)^10 + 1540*a^2*b^2*tan(d*x + c)^9 + 770*b^4*tan(d*x + c)^9 + 1155*a^3*b*tan(d*x + c)^8 + 3465*a*b^3*tan(d*x + c)^8 + 330*a^4*tan(d*x + c)^7 + 5940*a^2*b^2*tan(d*x + c)^7 + 990*b^4*tan(d*x + c)^7 + 4620*a^3*b*tan(d*x + c)^6 + 4620*a*b^3*tan(d*x + c)^6 + 1386*a^4*tan(d*x + c)^5 + 8316*a^2*b^2*tan(d*x + c)^5 + 462*b^4*tan(d*x + c)^5 + 6930*a^3*b*tan(d*x + c)^4 + 2310*a*b^3*tan(d*x + c)^4 + 2310*a^4*tan(d*x + c)^3 + 4620*a^2*b^2*tan(d*x + c)^3 + 4620*a^3*b*tan(d*x + c)^2 + 2310*a^4*tan(d*x + c))/d","A",0
92,1,342,0,0.862591," ","integrate(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","\frac{1}{256} \, {\left(63 \, a^{5} + 70 \, a^{3} b^{2} + 15 \, a b^{4}\right)} x - \frac{{\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(10 \, d x + 10 \, c\right)}{5120 \, d} - \frac{5 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(8 \, d x + 8 \, c\right)}{512 \, d} - \frac{5 \, {\left(27 \, a^{4} b - 6 \, a^{2} b^{3} - b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right)}{3072 \, d} - \frac{5 \, {\left(3 \, a^{4} b + a^{2} b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)}{128 \, d} - \frac{5 \, {\left(21 \, a^{4} b + 14 \, a^{2} b^{3} + b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)}{512 \, d} + \frac{{\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{5 \, {\left(a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right)}{2048 \, d} + \frac{5 \, {\left(9 \, a^{5} - 26 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right)}{3072 \, d} + \frac{5 \, {\left(3 \, a^{5} - 2 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{256 \, d} + \frac{5 \, {\left(21 \, a^{5} + 14 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"1/256*(63*a^5 + 70*a^3*b^2 + 15*a*b^4)*x - 1/5120*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(10*d*x + 10*c)/d - 5/512*(a^4*b - a^2*b^3)*cos(8*d*x + 8*c)/d - 5/3072*(27*a^4*b - 6*a^2*b^3 - b^5)*cos(6*d*x + 6*c)/d - 5/128*(3*a^4*b + a^2*b^3)*cos(4*d*x + 4*c)/d - 5/512*(21*a^4*b + 14*a^2*b^3 + b^5)*cos(2*d*x + 2*c)/d + 1/5120*(a^5 - 10*a^3*b^2 + 5*a*b^4)*sin(10*d*x + 10*c)/d + 5/2048*(a^5 - 6*a^3*b^2 + a*b^4)*sin(8*d*x + 8*c)/d + 5/3072*(9*a^5 - 26*a^3*b^2 - 3*a*b^4)*sin(6*d*x + 6*c)/d + 5/256*(3*a^5 - 2*a^3*b^2 - a*b^4)*sin(4*d*x + 4*c)/d + 5/512*(21*a^5 + 14*a^3*b^2 + a*b^4)*sin(2*d*x + 2*c)/d","A",0
93,1,313,0,0.699998," ","integrate(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","-\frac{{\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(9 \, d x + 9 \, c\right)}{2304 \, d} - \frac{{\left(35 \, a^{4} b - 30 \, a^{2} b^{3} - b^{5}\right)} \cos\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{{\left(25 \, a^{4} b - b^{5}\right)} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{{\left(35 \, a^{4} b + 20 \, a^{2} b^{3} + b^{5}\right)} \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{{\left(35 \, a^{4} b + 30 \, a^{2} b^{3} + 3 \, b^{5}\right)} \cos\left(d x + c\right)}{128 \, d} + \frac{{\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \sin\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{{\left(9 \, a^{5} - 50 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \sin\left(7 \, d x + 7 \, c\right)}{1792 \, d} + \frac{{\left(9 \, a^{5} - 20 \, a^{3} b^{2} - 5 \, a b^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(21 \, a^{5} - 5 \, a b^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{{\left(63 \, a^{5} + 70 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \sin\left(d x + c\right)}{128 \, d}"," ",0,"-1/2304*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(9*d*x + 9*c)/d - 1/1792*(35*a^4*b - 30*a^2*b^3 - b^5)*cos(7*d*x + 7*c)/d - 1/320*(25*a^4*b - b^5)*cos(5*d*x + 5*c)/d - 1/192*(35*a^4*b + 20*a^2*b^3 + b^5)*cos(3*d*x + 3*c)/d - 1/128*(35*a^4*b + 30*a^2*b^3 + 3*b^5)*cos(d*x + c)/d + 1/2304*(a^5 - 10*a^3*b^2 + 5*a*b^4)*sin(9*d*x + 9*c)/d + 1/1792*(9*a^5 - 50*a^3*b^2 + 5*a*b^4)*sin(7*d*x + 7*c)/d + 1/320*(9*a^5 - 20*a^3*b^2 - 5*a*b^4)*sin(5*d*x + 5*c)/d + 1/192*(21*a^5 - 5*a*b^4)*sin(3*d*x + 3*c)/d + 1/128*(63*a^5 + 70*a^3*b^2 + 15*a*b^4)*sin(d*x + c)/d","A",0
94,1,278,0,0.643873," ","integrate(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","\frac{5}{128} \, {\left(7 \, a^{5} + 10 \, a^{3} b^{2} + 3 \, a b^{4}\right)} x - \frac{{\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{{\left(15 \, a^{4} b - 10 \, a^{2} b^{3} - b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right)}{384 \, d} - \frac{{\left(35 \, a^{4} b + 10 \, a^{2} b^{3} - b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{{\left(35 \, a^{4} b + 30 \, a^{2} b^{3} + 3 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} + \frac{{\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{{\left(a^{5} - 5 \, a^{3} b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right)}{96 \, d} + \frac{{\left(7 \, a^{5} - 10 \, a^{3} b^{2} - 5 \, a b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{{\left(7 \, a^{5} + 5 \, a^{3} b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{32 \, d}"," ",0,"5/128*(7*a^5 + 10*a^3*b^2 + 3*a*b^4)*x - 1/1024*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(8*d*x + 8*c)/d - 1/384*(15*a^4*b - 10*a^2*b^3 - b^5)*cos(6*d*x + 6*c)/d - 1/256*(35*a^4*b + 10*a^2*b^3 - b^5)*cos(4*d*x + 4*c)/d - 1/128*(35*a^4*b + 30*a^2*b^3 + 3*b^5)*cos(2*d*x + 2*c)/d + 1/1024*(a^5 - 10*a^3*b^2 + 5*a*b^4)*sin(8*d*x + 8*c)/d + 1/96*(a^5 - 5*a^3*b^2)*sin(6*d*x + 6*c)/d + 1/128*(7*a^5 - 10*a^3*b^2 - 5*a*b^4)*sin(4*d*x + 4*c)/d + 1/32*(7*a^5 + 5*a^3*b^2)*sin(2*d*x + 2*c)/d","A",0
95,1,259,0,0.596806," ","integrate(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","-\frac{{\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{{\left(25 \, a^{4} b - 10 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{{\left(45 \, a^{4} b + 30 \, a^{2} b^{3} + b^{5}\right)} \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{5 \, {\left(5 \, a^{4} b + 6 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)}{64 \, d} + \frac{{\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{{\left(7 \, a^{5} - 30 \, a^{3} b^{2} - 5 \, a b^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(21 \, a^{5} - 10 \, a^{3} b^{2} - 15 \, a b^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{5 \, {\left(7 \, a^{5} + 10 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"-1/448*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(7*d*x + 7*c)/d - 1/320*(25*a^4*b - 10*a^2*b^3 - 3*b^5)*cos(5*d*x + 5*c)/d - 1/192*(45*a^4*b + 30*a^2*b^3 + b^5)*cos(3*d*x + 3*c)/d - 5/64*(5*a^4*b + 6*a^2*b^3 + b^5)*cos(d*x + c)/d + 1/448*(a^5 - 10*a^3*b^2 + 5*a*b^4)*sin(7*d*x + 7*c)/d + 1/320*(7*a^5 - 30*a^3*b^2 - 5*a*b^4)*sin(5*d*x + 5*c)/d + 1/192*(21*a^5 - 10*a^3*b^2 - 15*a*b^4)*sin(3*d*x + 3*c)/d + 5/64*(7*a^5 + 10*a^3*b^2 + 3*a*b^4)*sin(d*x + c)/d","A",0
96,1,211,0,0.528315," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","\frac{5}{16} \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} x - \frac{{\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{{\left(5 \, a^{4} b - b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{5 \, {\left(5 \, a^{4} b + 6 \, a^{2} b^{3} + b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{{\left(3 \, a^{5} - 10 \, a^{3} b^{2} - 5 \, a b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{5 \, {\left(3 \, a^{5} + 2 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"5/16*(a^5 + 2*a^3*b^2 + a*b^4)*x - 1/192*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(6*d*x + 6*c)/d - 1/32*(5*a^4*b - b^5)*cos(4*d*x + 4*c)/d - 5/64*(5*a^4*b + 6*a^2*b^3 + b^5)*cos(2*d*x + 2*c)/d + 1/192*(a^5 - 10*a^3*b^2 + 5*a*b^4)*sin(6*d*x + 6*c)/d + 1/64*(3*a^5 - 10*a^3*b^2 - 5*a*b^4)*sin(4*d*x + 4*c)/d + 5/64*(3*a^5 + 2*a^3*b^2 - a*b^4)*sin(2*d*x + 2*c)/d","A",0
97,1,187,0,0.328125," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","-\frac{{\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{5 \, {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{5 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)}{8 \, d} + \frac{{\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{5 \, {\left(a^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{5 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/80*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(5*d*x + 5*c)/d - 5/48*(3*a^4*b + 2*a^2*b^3 - b^5)*cos(3*d*x + 3*c)/d - 5/8*(a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)/d + 1/80*(a^5 - 10*a^3*b^2 + 5*a*b^4)*sin(5*d*x + 5*c)/d + 5/48*(a^5 - 2*a^3*b^2 - 3*a*b^4)*sin(3*d*x + 3*c)/d + 5/8*(a^5 + 2*a^3*b^2 + a*b^4)*sin(d*x + c)/d","B",0
98,1,199,0,4.847812," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","\frac{4 \, b^{5} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + {\left(3 \, a^{5} + 10 \, a^{3} b^{2} + 15 \, a b^{4}\right)} {\left(d x + c\right)} - \frac{6 \, b^{5} \tan\left(d x + c\right)^{4} - 3 \, a^{5} \tan\left(d x + c\right)^{3} - 10 \, a^{3} b^{2} \tan\left(d x + c\right)^{3} + 25 \, a b^{4} \tan\left(d x + c\right)^{3} + 40 \, a^{2} b^{3} \tan\left(d x + c\right)^{2} + 4 \, b^{5} \tan\left(d x + c\right)^{2} - 5 \, a^{5} \tan\left(d x + c\right) + 10 \, a^{3} b^{2} \tan\left(d x + c\right) + 15 \, a b^{4} \tan\left(d x + c\right) + 10 \, a^{4} b + 20 \, a^{2} b^{3}}{{\left(\tan\left(d x + c\right)^{2} + 1\right)}^{2}}}{8 \, d}"," ",0,"1/8*(4*b^5*log(tan(d*x + c)^2 + 1) + (3*a^5 + 10*a^3*b^2 + 15*a*b^4)*(d*x + c) - (6*b^5*tan(d*x + c)^4 - 3*a^5*tan(d*x + c)^3 - 10*a^3*b^2*tan(d*x + c)^3 + 25*a*b^4*tan(d*x + c)^3 + 40*a^2*b^3*tan(d*x + c)^2 + 4*b^5*tan(d*x + c)^2 - 5*a^5*tan(d*x + c) + 10*a^3*b^2*tan(d*x + c) + 15*a*b^4*tan(d*x + c) + 10*a^4*b + 20*a^2*b^3)/(tan(d*x + c)^2 + 1)^2)/d","A",0
99,1,283,0,0.559384," ","integrate(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","\frac{15 \, a b^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, a b^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{6 \, b^{5}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + \frac{2 \, {\left(3 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 50 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 60 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{4} b - 20 \, a^{2} b^{3} + 5 \, b^{5}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(15*a*b^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*a*b^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 6*b^5/(tan(1/2*d*x + 1/2*c)^2 - 1) + 2*(3*a^5*tan(1/2*d*x + 1/2*c)^5 - 15*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 15*a^4*b*tan(1/2*d*x + 1/2*c)^4 + 3*b^5*tan(1/2*d*x + 1/2*c)^4 + 2*a^5*tan(1/2*d*x + 1/2*c)^3 + 40*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 50*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 60*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 + 12*b^5*tan(1/2*d*x + 1/2*c)^2 + 3*a^5*tan(1/2*d*x + 1/2*c) - 15*a*b^4*tan(1/2*d*x + 1/2*c) - 5*a^4*b - 20*a^2*b^3 + 5*b^5)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
100,1,173,0,0.578123," ","integrate(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","\frac{b^{5} \tan\left(d x + c\right)^{2} + 10 \, a b^{4} \tan\left(d x + c\right) + {\left(a^{5} + 10 \, a^{3} b^{2} - 15 \, a b^{4}\right)} {\left(d x + c\right)} + 2 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - \frac{10 \, a^{2} b^{3} \tan\left(d x + c\right)^{2} - 2 \, b^{5} \tan\left(d x + c\right)^{2} - a^{5} \tan\left(d x + c\right) + 10 \, a^{3} b^{2} \tan\left(d x + c\right) - 5 \, a b^{4} \tan\left(d x + c\right) + 5 \, a^{4} b - b^{5}}{\tan\left(d x + c\right)^{2} + 1}}{2 \, d}"," ",0,"1/2*(b^5*tan(d*x + c)^2 + 10*a*b^4*tan(d*x + c) + (a^5 + 10*a^3*b^2 - 15*a*b^4)*(d*x + c) + 2*(5*a^2*b^3 - b^5)*log(tan(d*x + c)^2 + 1) - (10*a^2*b^3*tan(d*x + c)^2 - 2*b^5*tan(d*x + c)^2 - a^5*tan(d*x + c) + 10*a^3*b^2*tan(d*x + c) - 5*a*b^4*tan(d*x + c) + 5*a^4*b - b^5)/(tan(d*x + c)^2 + 1))/d","A",0
101,1,281,0,0.599156," ","integrate(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","\frac{15 \, {\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\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^{2} - 3 \, a b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{12 \, {\left(a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 10 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{4} b + 10 \, a^{2} b^{3} - b^{5}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + \frac{2 \, {\left(15 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 120 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, a^{2} b^{3} + 10 \, b^{5}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(15*(4*a^3*b^2 - 3*a*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*a^3*b^2 - 3*a*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 12*(a^5*tan(1/2*d*x + 1/2*c) - 10*a^3*b^2*tan(1/2*d*x + 1/2*c) + 5*a*b^4*tan(1/2*d*x + 1/2*c) - 5*a^4*b + 10*a^2*b^3 - b^5)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 2*(15*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 60*a^2*b^3*tan(1/2*d*x + 1/2*c)^4 + 6*b^5*tan(1/2*d*x + 1/2*c)^4 + 120*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 - 24*b^5*tan(1/2*d*x + 1/2*c)^2 - 15*a*b^4*tan(1/2*d*x + 1/2*c) - 60*a^2*b^3 + 10*b^5)/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
102,1,144,0,0.622642," ","integrate(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","\frac{3 \, b^{5} \tan\left(d x + c\right)^{4} + 20 \, a b^{4} \tan\left(d x + c\right)^{3} + 60 \, a^{2} b^{3} \tan\left(d x + c\right)^{2} - 6 \, b^{5} \tan\left(d x + c\right)^{2} + 120 \, a^{3} b^{2} \tan\left(d x + c\right) - 60 \, a b^{4} \tan\left(d x + c\right) + 12 \, {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} {\left(d x + c\right)} + 6 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{12 \, d}"," ",0,"1/12*(3*b^5*tan(d*x + c)^4 + 20*a*b^4*tan(d*x + c)^3 + 60*a^2*b^3*tan(d*x + c)^2 - 6*b^5*tan(d*x + c)^2 + 120*a^3*b^2*tan(d*x + c) - 60*a*b^4*tan(d*x + c) + 12*(a^5 - 10*a^3*b^2 + 5*a*b^4)*(d*x + c) + 6*(5*a^4*b - 10*a^2*b^3 + b^5)*log(tan(d*x + c)^2 + 1))/d","A",0
103,1,410,0,0.641790," ","integrate(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","\frac{15 \, {\left(8 \, a^{5} - 40 \, a^{3} b^{2} + 15 \, a 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^{5} - 40 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(600 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 225 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 600 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1200 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1050 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2400 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 2400 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 3600 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 5600 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 640 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1200 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1050 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2400 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4000 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 320 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 600 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 225 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 600 \, a^{4} b + 800 \, a^{2} b^{3} - 64 \, b^{5}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(8*a^5 - 40*a^3*b^2 + 15*a*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(8*a^5 - 40*a^3*b^2 + 15*a*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(600*a^3*b^2*tan(1/2*d*x + 1/2*c)^9 - 225*a*b^4*tan(1/2*d*x + 1/2*c)^9 - 600*a^4*b*tan(1/2*d*x + 1/2*c)^8 - 1200*a^3*b^2*tan(1/2*d*x + 1/2*c)^7 + 1050*a*b^4*tan(1/2*d*x + 1/2*c)^7 + 2400*a^4*b*tan(1/2*d*x + 1/2*c)^6 - 2400*a^2*b^3*tan(1/2*d*x + 1/2*c)^6 - 3600*a^4*b*tan(1/2*d*x + 1/2*c)^4 + 5600*a^2*b^3*tan(1/2*d*x + 1/2*c)^4 - 640*b^5*tan(1/2*d*x + 1/2*c)^4 + 1200*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 1050*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 2400*a^4*b*tan(1/2*d*x + 1/2*c)^2 - 4000*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 + 320*b^5*tan(1/2*d*x + 1/2*c)^2 - 600*a^3*b^2*tan(1/2*d*x + 1/2*c) + 225*a*b^4*tan(1/2*d*x + 1/2*c) - 600*a^4*b + 800*a^2*b^3 - 64*b^5)/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
104,1,89,0,2.262670," ","integrate(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","\frac{b^{5} \tan\left(d x + c\right)^{6} + 6 \, a b^{4} \tan\left(d x + c\right)^{5} + 15 \, a^{2} b^{3} \tan\left(d x + c\right)^{4} + 20 \, a^{3} b^{2} \tan\left(d x + c\right)^{3} + 15 \, a^{4} b \tan\left(d x + c\right)^{2} + 6 \, a^{5} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(b^5*tan(d*x + c)^6 + 6*a*b^4*tan(d*x + c)^5 + 15*a^2*b^3*tan(d*x + c)^4 + 20*a^3*b^2*tan(d*x + c)^3 + 15*a^4*b*tan(d*x + c)^2 + 6*a^5*tan(d*x + c))/d","B",0
105,1,680,0,6.461699," ","integrate(sec(d*x+c)^8*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","\frac{105 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(840 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2100 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 525 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 8400 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 3360 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 8400 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3500 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 33600 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 33600 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 4200 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 23100 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 16975 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 53200 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 56000 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 8960 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 44800 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 22400 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 4480 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 4200 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 23100 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16975 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 25200 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 13440 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2688 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3360 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8400 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3500 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 11200 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15680 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 896 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 840 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2100 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 525 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2800 \, a^{4} b + 2240 \, a^{2} b^{3} - 128 \, b^{5}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{7}}}{1680 \, d}"," ",0,"1/1680*(105*(8*a^5 - 20*a^3*b^2 + 5*a*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(8*a^5 - 20*a^3*b^2 + 5*a*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(840*a^5*tan(1/2*d*x + 1/2*c)^13 + 2100*a^3*b^2*tan(1/2*d*x + 1/2*c)^13 - 525*a*b^4*tan(1/2*d*x + 1/2*c)^13 - 8400*a^4*b*tan(1/2*d*x + 1/2*c)^12 - 3360*a^5*tan(1/2*d*x + 1/2*c)^11 + 8400*a^3*b^2*tan(1/2*d*x + 1/2*c)^11 + 3500*a*b^4*tan(1/2*d*x + 1/2*c)^11 + 33600*a^4*b*tan(1/2*d*x + 1/2*c)^10 - 33600*a^2*b^3*tan(1/2*d*x + 1/2*c)^10 + 4200*a^5*tan(1/2*d*x + 1/2*c)^9 - 23100*a^3*b^2*tan(1/2*d*x + 1/2*c)^9 + 16975*a*b^4*tan(1/2*d*x + 1/2*c)^9 - 53200*a^4*b*tan(1/2*d*x + 1/2*c)^8 + 56000*a^2*b^3*tan(1/2*d*x + 1/2*c)^8 - 8960*b^5*tan(1/2*d*x + 1/2*c)^8 + 44800*a^4*b*tan(1/2*d*x + 1/2*c)^6 - 22400*a^2*b^3*tan(1/2*d*x + 1/2*c)^6 - 4480*b^5*tan(1/2*d*x + 1/2*c)^6 - 4200*a^5*tan(1/2*d*x + 1/2*c)^5 + 23100*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 16975*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 25200*a^4*b*tan(1/2*d*x + 1/2*c)^4 + 13440*a^2*b^3*tan(1/2*d*x + 1/2*c)^4 - 2688*b^5*tan(1/2*d*x + 1/2*c)^4 + 3360*a^5*tan(1/2*d*x + 1/2*c)^3 - 8400*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 3500*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 11200*a^4*b*tan(1/2*d*x + 1/2*c)^2 - 15680*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 + 896*b^5*tan(1/2*d*x + 1/2*c)^2 - 840*a^5*tan(1/2*d*x + 1/2*c) - 2100*a^3*b^2*tan(1/2*d*x + 1/2*c) + 525*a*b^4*tan(1/2*d*x + 1/2*c) - 2800*a^4*b + 2240*a^2*b^3 - 128*b^5)/(tan(1/2*d*x + 1/2*c)^2 - 1)^7)/d","B",0
106,1,176,0,2.941622," ","integrate(sec(d*x+c)^9*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","\frac{21 \, b^{5} \tan\left(d x + c\right)^{8} + 120 \, a b^{4} \tan\left(d x + c\right)^{7} + 280 \, a^{2} b^{3} \tan\left(d x + c\right)^{6} + 28 \, b^{5} \tan\left(d x + c\right)^{6} + 336 \, a^{3} b^{2} \tan\left(d x + c\right)^{5} + 168 \, a b^{4} \tan\left(d x + c\right)^{5} + 210 \, a^{4} b \tan\left(d x + c\right)^{4} + 420 \, a^{2} b^{3} \tan\left(d x + c\right)^{4} + 56 \, a^{5} \tan\left(d x + c\right)^{3} + 560 \, a^{3} b^{2} \tan\left(d x + c\right)^{3} + 420 \, a^{4} b \tan\left(d x + c\right)^{2} + 168 \, a^{5} \tan\left(d x + c\right)}{168 \, d}"," ",0,"1/168*(21*b^5*tan(d*x + c)^8 + 120*a*b^4*tan(d*x + c)^7 + 280*a^2*b^3*tan(d*x + c)^6 + 28*b^5*tan(d*x + c)^6 + 336*a^3*b^2*tan(d*x + c)^5 + 168*a*b^4*tan(d*x + c)^5 + 210*a^4*b*tan(d*x + c)^4 + 420*a^2*b^3*tan(d*x + c)^4 + 56*a^5*tan(d*x + c)^3 + 560*a^3*b^2*tan(d*x + c)^3 + 420*a^4*b*tan(d*x + c)^2 + 168*a^5*tan(d*x + c))/d","A",0
107,1,888,0,0.738526," ","integrate(sec(d*x+c)^10*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","\frac{315 \, {\left(48 \, a^{5} - 80 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 315 \, {\left(48 \, a^{5} - 80 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(25200 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} + 25200 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} - 4725 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} - 201600 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{16} - 110880 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 319200 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 40950 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 806400 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} - 806400 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} + 191520 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 453600 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 488250 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1612800 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 806400 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 215040 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 151200 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 151200 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 532350 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 2419200 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 806400 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 322560 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 2661120 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 2096640 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 451584 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 151200 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 151200 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 532350 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1774080 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1128960 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 129024 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 191520 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 453600 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 488250 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 645120 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 23040 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 36864 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 110880 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 319200 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40950 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 161280 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 207360 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9216 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 25200 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 25200 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4725 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 40320 \, a^{4} b + 23040 \, a^{2} b^{3} - 1024 \, b^{5}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{9}}}{40320 \, d}"," ",0,"1/40320*(315*(48*a^5 - 80*a^3*b^2 + 15*a*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 315*(48*a^5 - 80*a^3*b^2 + 15*a*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(25200*a^5*tan(1/2*d*x + 1/2*c)^17 + 25200*a^3*b^2*tan(1/2*d*x + 1/2*c)^17 - 4725*a*b^4*tan(1/2*d*x + 1/2*c)^17 - 201600*a^4*b*tan(1/2*d*x + 1/2*c)^16 - 110880*a^5*tan(1/2*d*x + 1/2*c)^15 + 319200*a^3*b^2*tan(1/2*d*x + 1/2*c)^15 + 40950*a*b^4*tan(1/2*d*x + 1/2*c)^15 + 806400*a^4*b*tan(1/2*d*x + 1/2*c)^14 - 806400*a^2*b^3*tan(1/2*d*x + 1/2*c)^14 + 191520*a^5*tan(1/2*d*x + 1/2*c)^13 - 453600*a^3*b^2*tan(1/2*d*x + 1/2*c)^13 + 488250*a*b^4*tan(1/2*d*x + 1/2*c)^13 - 1612800*a^4*b*tan(1/2*d*x + 1/2*c)^12 + 806400*a^2*b^3*tan(1/2*d*x + 1/2*c)^12 - 215040*b^5*tan(1/2*d*x + 1/2*c)^12 - 151200*a^5*tan(1/2*d*x + 1/2*c)^11 - 151200*a^3*b^2*tan(1/2*d*x + 1/2*c)^11 + 532350*a*b^4*tan(1/2*d*x + 1/2*c)^11 + 2419200*a^4*b*tan(1/2*d*x + 1/2*c)^10 - 806400*a^2*b^3*tan(1/2*d*x + 1/2*c)^10 - 322560*b^5*tan(1/2*d*x + 1/2*c)^10 - 2661120*a^4*b*tan(1/2*d*x + 1/2*c)^8 + 2096640*a^2*b^3*tan(1/2*d*x + 1/2*c)^8 - 451584*b^5*tan(1/2*d*x + 1/2*c)^8 + 151200*a^5*tan(1/2*d*x + 1/2*c)^7 + 151200*a^3*b^2*tan(1/2*d*x + 1/2*c)^7 - 532350*a*b^4*tan(1/2*d*x + 1/2*c)^7 + 1774080*a^4*b*tan(1/2*d*x + 1/2*c)^6 - 1128960*a^2*b^3*tan(1/2*d*x + 1/2*c)^6 - 129024*b^5*tan(1/2*d*x + 1/2*c)^6 - 191520*a^5*tan(1/2*d*x + 1/2*c)^5 + 453600*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 488250*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 645120*a^4*b*tan(1/2*d*x + 1/2*c)^4 + 23040*a^2*b^3*tan(1/2*d*x + 1/2*c)^4 - 36864*b^5*tan(1/2*d*x + 1/2*c)^4 + 110880*a^5*tan(1/2*d*x + 1/2*c)^3 - 319200*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 40950*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 161280*a^4*b*tan(1/2*d*x + 1/2*c)^2 - 207360*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 + 9216*b^5*tan(1/2*d*x + 1/2*c)^2 - 25200*a^5*tan(1/2*d*x + 1/2*c) - 25200*a^3*b^2*tan(1/2*d*x + 1/2*c) + 4725*a*b^4*tan(1/2*d*x + 1/2*c) - 40320*a^4*b + 23040*a^2*b^3 - 1024*b^5)/(tan(1/2*d*x + 1/2*c)^2 - 1)^9)/d","B",0
108,1,262,0,1.179366," ","integrate(sec(d*x+c)^11*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","\frac{126 \, b^{5} \tan\left(d x + c\right)^{10} + 700 \, a b^{4} \tan\left(d x + c\right)^{9} + 1575 \, a^{2} b^{3} \tan\left(d x + c\right)^{8} + 315 \, b^{5} \tan\left(d x + c\right)^{8} + 1800 \, a^{3} b^{2} \tan\left(d x + c\right)^{7} + 1800 \, a b^{4} \tan\left(d x + c\right)^{7} + 1050 \, a^{4} b \tan\left(d x + c\right)^{6} + 4200 \, a^{2} b^{3} \tan\left(d x + c\right)^{6} + 210 \, b^{5} \tan\left(d x + c\right)^{6} + 252 \, a^{5} \tan\left(d x + c\right)^{5} + 5040 \, a^{3} b^{2} \tan\left(d x + c\right)^{5} + 1260 \, a b^{4} \tan\left(d x + c\right)^{5} + 3150 \, a^{4} b \tan\left(d x + c\right)^{4} + 3150 \, a^{2} b^{3} \tan\left(d x + c\right)^{4} + 840 \, a^{5} \tan\left(d x + c\right)^{3} + 4200 \, a^{3} b^{2} \tan\left(d x + c\right)^{3} + 3150 \, a^{4} b \tan\left(d x + c\right)^{2} + 1260 \, a^{5} \tan\left(d x + c\right)}{1260 \, d}"," ",0,"1/1260*(126*b^5*tan(d*x + c)^10 + 700*a*b^4*tan(d*x + c)^9 + 1575*a^2*b^3*tan(d*x + c)^8 + 315*b^5*tan(d*x + c)^8 + 1800*a^3*b^2*tan(d*x + c)^7 + 1800*a*b^4*tan(d*x + c)^7 + 1050*a^4*b*tan(d*x + c)^6 + 4200*a^2*b^3*tan(d*x + c)^6 + 210*b^5*tan(d*x + c)^6 + 252*a^5*tan(d*x + c)^5 + 5040*a^3*b^2*tan(d*x + c)^5 + 1260*a*b^4*tan(d*x + c)^5 + 3150*a^4*b*tan(d*x + c)^4 + 3150*a^2*b^3*tan(d*x + c)^4 + 840*a^5*tan(d*x + c)^3 + 4200*a^3*b^2*tan(d*x + c)^3 + 3150*a^4*b*tan(d*x + c)^2 + 1260*a^5*tan(d*x + c))/d","A",0
109,1,1096,0,12.982558," ","integrate(sec(d*x+c)^12*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","\frac{3465 \, {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3465 \, {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(121968 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{21} + 69300 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{21} - 10395 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{21} - 887040 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{20} - 591360 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{19} + 1626240 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{19} + 110880 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{19} + 3548160 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{18} - 3548160 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{18} + 1459920 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} - 1159620 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} + 2302839 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} - 9757440 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{16} + 1182720 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{16} - 946176 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{16} - 2365440 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 1182720 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 4790016 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 21288960 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} - 9461760 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} - 2365440 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} + 2106720 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 5738040 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 5828130 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 30159360 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 18923520 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 5203968 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 28385280 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 7096320 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 4257792 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 2106720 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 5738040 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 5828130 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 20528640 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 9123840 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 3041280 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 2365440 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1182720 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4790016 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 11151360 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 8110080 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 608256 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1459920 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1159620 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2302839 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3421440 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 450560 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 112640 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 591360 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1626240 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 110880 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 506880 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 619520 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 22528 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 121968 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 69300 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10395 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 126720 \, a^{4} b + 56320 \, a^{2} b^{3} - 2048 \, b^{5}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{11}}}{177408 \, d}"," ",0,"1/177408*(3465*(16*a^5 - 20*a^3*b^2 + 3*a*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3465*(16*a^5 - 20*a^3*b^2 + 3*a*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(121968*a^5*tan(1/2*d*x + 1/2*c)^21 + 69300*a^3*b^2*tan(1/2*d*x + 1/2*c)^21 - 10395*a*b^4*tan(1/2*d*x + 1/2*c)^21 - 887040*a^4*b*tan(1/2*d*x + 1/2*c)^20 - 591360*a^5*tan(1/2*d*x + 1/2*c)^19 + 1626240*a^3*b^2*tan(1/2*d*x + 1/2*c)^19 + 110880*a*b^4*tan(1/2*d*x + 1/2*c)^19 + 3548160*a^4*b*tan(1/2*d*x + 1/2*c)^18 - 3548160*a^2*b^3*tan(1/2*d*x + 1/2*c)^18 + 1459920*a^5*tan(1/2*d*x + 1/2*c)^17 - 1159620*a^3*b^2*tan(1/2*d*x + 1/2*c)^17 + 2302839*a*b^4*tan(1/2*d*x + 1/2*c)^17 - 9757440*a^4*b*tan(1/2*d*x + 1/2*c)^16 + 1182720*a^2*b^3*tan(1/2*d*x + 1/2*c)^16 - 946176*b^5*tan(1/2*d*x + 1/2*c)^16 - 2365440*a^5*tan(1/2*d*x + 1/2*c)^15 + 1182720*a^3*b^2*tan(1/2*d*x + 1/2*c)^15 + 4790016*a*b^4*tan(1/2*d*x + 1/2*c)^15 + 21288960*a^4*b*tan(1/2*d*x + 1/2*c)^14 - 9461760*a^2*b^3*tan(1/2*d*x + 1/2*c)^14 - 2365440*b^5*tan(1/2*d*x + 1/2*c)^14 + 2106720*a^5*tan(1/2*d*x + 1/2*c)^13 - 5738040*a^3*b^2*tan(1/2*d*x + 1/2*c)^13 + 5828130*a*b^4*tan(1/2*d*x + 1/2*c)^13 - 30159360*a^4*b*tan(1/2*d*x + 1/2*c)^12 + 18923520*a^2*b^3*tan(1/2*d*x + 1/2*c)^12 - 5203968*b^5*tan(1/2*d*x + 1/2*c)^12 + 28385280*a^4*b*tan(1/2*d*x + 1/2*c)^10 - 7096320*a^2*b^3*tan(1/2*d*x + 1/2*c)^10 - 4257792*b^5*tan(1/2*d*x + 1/2*c)^10 - 2106720*a^5*tan(1/2*d*x + 1/2*c)^9 + 5738040*a^3*b^2*tan(1/2*d*x + 1/2*c)^9 - 5828130*a*b^4*tan(1/2*d*x + 1/2*c)^9 - 20528640*a^4*b*tan(1/2*d*x + 1/2*c)^8 + 9123840*a^2*b^3*tan(1/2*d*x + 1/2*c)^8 - 3041280*b^5*tan(1/2*d*x + 1/2*c)^8 + 2365440*a^5*tan(1/2*d*x + 1/2*c)^7 - 1182720*a^3*b^2*tan(1/2*d*x + 1/2*c)^7 - 4790016*a*b^4*tan(1/2*d*x + 1/2*c)^7 + 11151360*a^4*b*tan(1/2*d*x + 1/2*c)^6 - 8110080*a^2*b^3*tan(1/2*d*x + 1/2*c)^6 - 608256*b^5*tan(1/2*d*x + 1/2*c)^6 - 1459920*a^5*tan(1/2*d*x + 1/2*c)^5 + 1159620*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 2302839*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 3421440*a^4*b*tan(1/2*d*x + 1/2*c)^4 - 450560*a^2*b^3*tan(1/2*d*x + 1/2*c)^4 - 112640*b^5*tan(1/2*d*x + 1/2*c)^4 + 591360*a^5*tan(1/2*d*x + 1/2*c)^3 - 1626240*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 110880*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 506880*a^4*b*tan(1/2*d*x + 1/2*c)^2 - 619520*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 + 22528*b^5*tan(1/2*d*x + 1/2*c)^2 - 121968*a^5*tan(1/2*d*x + 1/2*c) - 69300*a^3*b^2*tan(1/2*d*x + 1/2*c) + 10395*a*b^4*tan(1/2*d*x + 1/2*c) - 126720*a^4*b + 56320*a^2*b^3 - 2048*b^5)/(tan(1/2*d*x + 1/2*c)^2 - 1)^11)/d","B",0
110,1,322,0,2.928096," ","integrate(cos(d*x+c)^5/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{8 \, b^{6} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} - \frac{4 \, b^{5} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(3 \, a^{5} + 10 \, a^{3} b^{2} + 15 \, a b^{4}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{6 \, b^{5} \tan\left(d x + c\right)^{4} + 3 \, a^{5} \tan\left(d x + c\right)^{3} + 10 \, a^{3} b^{2} \tan\left(d x + c\right)^{3} + 7 \, a b^{4} \tan\left(d x + c\right)^{3} + 4 \, a^{2} b^{3} \tan\left(d x + c\right)^{2} + 16 \, b^{5} \tan\left(d x + c\right)^{2} + 5 \, a^{5} \tan\left(d x + c\right) + 14 \, a^{3} b^{2} \tan\left(d x + c\right) + 9 \, a b^{4} \tan\left(d x + c\right) + 2 \, a^{4} b + 8 \, a^{2} b^{3} + 12 \, b^{5}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(\tan\left(d x + c\right)^{2} + 1\right)}^{2}}}{8 \, d}"," ",0,"1/8*(8*b^6*log(abs(b*tan(d*x + c) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) - 4*b^5*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (3*a^5 + 10*a^3*b^2 + 15*a*b^4)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (6*b^5*tan(d*x + c)^4 + 3*a^5*tan(d*x + c)^3 + 10*a^3*b^2*tan(d*x + c)^3 + 7*a*b^4*tan(d*x + c)^3 + 4*a^2*b^3*tan(d*x + c)^2 + 16*b^5*tan(d*x + c)^2 + 5*a^5*tan(d*x + c) + 14*a^3*b^2*tan(d*x + c) + 9*a*b^4*tan(d*x + c) + 2*a^4*b + 8*a^2*b^3 + 12*b^5)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(tan(d*x + c)^2 + 1)^2))/d","A",0
111,1,286,0,0.303001," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, b^{4} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} b + 4 \, b^{3}\right)}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*b^4*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2*(3*a^3*tan(1/2*d*x + 1/2*c)^5 + 6*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 3*a^2*b*tan(1/2*d*x + 1/2*c)^4 + 6*b^3*tan(1/2*d*x + 1/2*c)^4 + 2*a^3*tan(1/2*d*x + 1/2*c)^3 + 8*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*b^3*tan(1/2*d*x + 1/2*c)^2 + 3*a^3*tan(1/2*d*x + 1/2*c) + 6*a*b^2*tan(1/2*d*x + 1/2*c) + a^2*b + 4*b^3)/((a^4 + 2*a^2*b^2 + b^4)*(tan(1/2*d*x + 1/2*c)^2 + 1)^3))/d","A",0
112,1,182,0,0.282075," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, b^{4} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4} b + 2 \, a^{2} b^{3} + b^{5}} - \frac{b^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{3} + 3 \, a b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{b^{3} \tan\left(d x + c\right)^{2} + a^{3} \tan\left(d x + c\right) + a b^{2} \tan\left(d x + c\right) + a^{2} b + 2 \, b^{3}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(d x + c\right)^{2} + 1\right)}}}{2 \, d}"," ",0,"1/2*(2*b^4*log(abs(b*tan(d*x + c) + a))/(a^4*b + 2*a^2*b^3 + b^5) - b^3*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (a^3 + 3*a*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) + (b^3*tan(d*x + c)^2 + a^3*tan(d*x + c) + a*b^2*tan(d*x + c) + a^2*b + 2*b^3)/((a^4 + 2*a^2*b^2 + b^4)*(tan(d*x + c)^2 + 1)))/d","A",0
113,1,118,0,1.325465," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{b^{2} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b\right)}}{{\left(a^{2} + b^{2}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}}}{d}"," ",0,"-(b^2*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) - 2*(a*tan(1/2*d*x + 1/2*c) + b)/((a^2 + b^2)*(tan(1/2*d*x + 1/2*c)^2 + 1)))/d","A",0
114,1,74,0,0.195116," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, b^{2} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{2} b + b^{3}} + \frac{2 \, {\left(d x + c\right)} a}{a^{2} + b^{2}} - \frac{b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}}}{2 \, d}"," ",0,"1/2*(2*b^2*log(abs(b*tan(d*x + c) + a))/(a^2*b + b^3) + 2*(d*x + c)*a/(a^2 + b^2) - b*log(tan(d*x + c)^2 + 1)/(a^2 + b^2))/d","A",0
115,1,74,0,2.751399," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} d}"," ",0,"-log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*d)","A",0
116,1,19,0,1.969352," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b d}"," ",0,"log(abs(b*tan(d*x + c) + a))/(b*d)","A",0
117,1,136,0,0.322153," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\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{\sqrt{a^{2} + b^{2}} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{b^{2}} + \frac{2}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} b}}{d}"," ",0,"-(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 + sqrt(a^2 + b^2)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/b^2 + 2/((tan(1/2*d*x + 1/2*c)^2 - 1)*b))/d","A",0
118,1,54,0,4.587044," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{b \tan\left(d x + c\right)^{2} - 2 \, a \tan\left(d x + c\right)}{b^{2}} + \frac{2 \, {\left(a^{2} + b^{2}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b^{3}}}{2 \, d}"," ",0,"1/2*((b*tan(d*x + c)^2 - 2*a*tan(d*x + c))/b^2 + 2*(a^2 + b^2)*log(abs(b*tan(d*x + c) + a))/b^3)/d","A",0
119,1,278,0,3.037176," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\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)}{b^{4}} - \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)}{b^{4}} + \frac{6 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} b^{4}} + \frac{2 \, {\left(3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{2} + 8 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} b^{3}}}{6 \, d}"," ",0,"-1/6*(3*(2*a^3 + 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 - 3*(2*a^3 + 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 + 6*(a^4 + 2*a^2*b^2 + b^4)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^4) + 2*(3*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*a^2*tan(1/2*d*x + 1/2*c)^4 + 12*b^2*tan(1/2*d*x + 1/2*c)^4 - 12*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*a*b*tan(1/2*d*x + 1/2*c) + 6*a^2 + 8*b^2)/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*b^3))/d","A",0
120,1,120,0,4.893469," ","integrate(sec(d*x+c)^5/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, b^{3} \tan\left(d x + c\right)^{4} - 4 \, a b^{2} \tan\left(d x + c\right)^{3} + 6 \, a^{2} b \tan\left(d x + c\right)^{2} + 12 \, b^{3} \tan\left(d x + c\right)^{2} - 12 \, a^{3} \tan\left(d x + c\right) - 24 \, a b^{2} \tan\left(d x + c\right)}{b^{4}} + \frac{12 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b^{5}}}{12 \, d}"," ",0,"1/12*((3*b^3*tan(d*x + c)^4 - 4*a*b^2*tan(d*x + c)^3 + 6*a^2*b*tan(d*x + c)^2 + 12*b^3*tan(d*x + c)^2 - 12*a^3*tan(d*x + c) - 24*a*b^2*tan(d*x + c))/b^4 + 12*(a^4 + 2*a^2*b^2 + b^4)*log(abs(b*tan(d*x + c) + a))/b^5)/d","A",0
121,1,554,0,0.361900," ","integrate(sec(d*x+c)^6/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(8 \, a^{5} + 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{6}} - \frac{15 \, {\left(8 \, a^{5} + 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{6}} + \frac{120 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} b^{6}} + \frac{2 \, {\left(60 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 135 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 360 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 360 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 120 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 150 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 480 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1200 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 720 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 720 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1600 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1120 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 120 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 150 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1040 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 560 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 60 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 135 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, a^{4} + 280 \, a^{2} b^{2} + 184 \, b^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5} b^{5}}}{120 \, d}"," ",0,"-1/120*(15*(8*a^5 + 20*a^3*b^2 + 15*a*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^6 - 15*(8*a^5 + 20*a^3*b^2 + 15*a*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^6 + 120*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^6) + 2*(60*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 135*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*a^4*tan(1/2*d*x + 1/2*c)^8 + 360*a^2*b^2*tan(1/2*d*x + 1/2*c)^8 + 360*b^4*tan(1/2*d*x + 1/2*c)^8 - 120*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 150*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 480*a^4*tan(1/2*d*x + 1/2*c)^6 - 1200*a^2*b^2*tan(1/2*d*x + 1/2*c)^6 - 720*b^4*tan(1/2*d*x + 1/2*c)^6 + 720*a^4*tan(1/2*d*x + 1/2*c)^4 + 1600*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 1120*b^4*tan(1/2*d*x + 1/2*c)^4 + 120*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 150*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 480*a^4*tan(1/2*d*x + 1/2*c)^2 - 1040*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 560*b^4*tan(1/2*d*x + 1/2*c)^2 - 60*a^3*b*tan(1/2*d*x + 1/2*c) - 135*a*b^3*tan(1/2*d*x + 1/2*c) + 120*a^4 + 280*a^2*b^2 + 184*b^4)/((tan(1/2*d*x + 1/2*c)^2 - 1)^5*b^5))/d","B",0
122,1,250,0,0.198328," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{8 \, a b^{4} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} - \frac{4 \, a b^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(a^{4} + 6 \, a^{2} b^{2} - 3 \, b^{4}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{a^{2} b \tan\left(d x + c\right)^{2} - 3 \, b^{3} \tan\left(d x + c\right)^{2} + a^{3} \tan\left(d x + c\right) + a b^{2} \tan\left(d x + c\right) + 2 \, a^{2} b - 2 \, b^{3}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \tan\left(d x + c\right)^{3} + a \tan\left(d x + c\right)^{2} + b \tan\left(d x + c\right) + a\right)}}}{2 \, d}"," ",0,"1/2*(8*a*b^4*log(abs(b*tan(d*x + c) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) - 4*a*b^3*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (a^4 + 6*a^2*b^2 - 3*b^4)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (a^2*b*tan(d*x + c)^2 - 3*b^3*tan(d*x + c)^2 + a^3*tan(d*x + c) + a*b^2*tan(d*x + c) + 2*a^2*b - 2*b^3)/((a^4 + 2*a^2*b^2 + b^4)*(b*tan(d*x + c)^3 + a*tan(d*x + c)^2 + b*tan(d*x + c) + a)))/d","A",0
123,1,286,0,0.321705," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, a b^{2} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{3} b + a b^{3}\right)}}{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}}}{d}"," ",0,"-(3*a*b^2*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2*(a^4*tan(1/2*d*x + 1/2*c)^3 - a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + b^4*tan(1/2*d*x + 1/2*c)^3 + 3*a*b^3*tan(1/2*d*x + 1/2*c)^2 - a^4*tan(1/2*d*x + 1/2*c) - 3*a^2*b^2*tan(1/2*d*x + 1/2*c) + b^4*tan(1/2*d*x + 1/2*c) - 2*a^3*b + a*b^3)/((a^5 + 2*a^3*b^2 + a*b^4)*(a*tan(1/2*d*x + 1/2*c)^4 - 2*b*tan(1/2*d*x + 1/2*c)^3 - 2*b*tan(1/2*d*x + 1/2*c) - a)))/d","B",0
124,1,159,0,1.961724," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, a b^{2} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4} b + 2 \, a^{2} b^{3} + b^{5}} - \frac{a b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{2} - b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, a b^{2} \tan\left(d x + c\right) + 3 \, a^{2} b + b^{3}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \tan\left(d x + c\right) + a\right)}}}{d}"," ",0,"(2*a*b^2*log(abs(b*tan(d*x + c) + a))/(a^4*b + 2*a^2*b^3 + b^5) - a*b*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (a^2 - b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - (2*a*b^2*tan(d*x + c) + 3*a^2*b + b^3)/((a^4 + 2*a^2*b^2 + b^4)*(b*tan(d*x + c) + a)))/d","A",0
125,1,138,0,0.303346," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{a \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a b\right)}}{{\left(a^{3} + a b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}}}{d}"," ",0,"-(a*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) - 2*(b^2*tan(1/2*d*x + 1/2*c) + a*b)/((a^3 + a*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)))/d","A",0
126,1,20,0,1.613914," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{1}{{\left(b \tan\left(d x + c\right) + a\right)} b d}"," ",0,"-1/((b*tan(d*x + c) + a)*b*d)","A",0
127,1,166,0,0.354686," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{a \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{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}} + \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)} a b}}{d}"," ",0,"(a*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^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 + 2*(b*tan(1/2*d*x + 1/2*c) + a)/((a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)*a*b))/d","A",0
128,1,71,0,0.247056," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, a \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b^{3}} - \frac{\tan\left(d x + c\right)}{b^{2}} - \frac{2 \, a b \tan\left(d x + c\right) + a^{2} - b^{2}}{{\left(b \tan\left(d x + c\right) + a\right)} b^{3}}}{d}"," ",0,"-(2*a*log(abs(b*tan(d*x + c) + a))/b^3 - tan(d*x + c)/b^2 - (2*a*b*tan(d*x + c) + a^2 - b^2)/((b*tan(d*x + c) + a)*b^3))/d","A",0
129,1,280,0,0.343486," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\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^{4}} - \frac{3 \, {\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^{4}} + \frac{6 \, {\left(a^{3} + a b^{2}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} b^{4}} + \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} b^{3}} + \frac{4 \, {\left(a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3} + a b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)} a b^{3}}}{2 \, d}"," ",0,"1/2*(3*(2*a^2 + b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 - 3*(2*a^2 + b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 + 6*(a^3 + a*b^2)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^4) + 2*(b*tan(1/2*d*x + 1/2*c)^3 + 4*a*tan(1/2*d*x + 1/2*c)^2 + b*tan(1/2*d*x + 1/2*c) - 4*a)/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*b^3) + 4*(a^2*b*tan(1/2*d*x + 1/2*c) + b^3*tan(1/2*d*x + 1/2*c) + a^3 + a*b^2)/((a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)*a*b^3))/d","A",0
130,1,149,0,0.248052," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(a^{3} + a b^{2}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b^{5}} - \frac{b^{4} \tan\left(d x + c\right)^{3} - 3 \, a b^{3} \tan\left(d x + c\right)^{2} + 9 \, a^{2} b^{2} \tan\left(d x + c\right) + 6 \, b^{4} \tan\left(d x + c\right)}{b^{6}} - \frac{3 \, {\left(4 \, a^{3} b \tan\left(d x + c\right) + 4 \, a b^{3} \tan\left(d x + c\right) + 3 \, a^{4} + 2 \, a^{2} b^{2} - b^{4}\right)}}{{\left(b \tan\left(d x + c\right) + a\right)} b^{5}}}{3 \, d}"," ",0,"-1/3*(12*(a^3 + a*b^2)*log(abs(b*tan(d*x + c) + a))/b^5 - (b^4*tan(d*x + c)^3 - 3*a*b^3*tan(d*x + c)^2 + 9*a^2*b^2*tan(d*x + c) + 6*b^4*tan(d*x + c))/b^6 - 3*(4*a^3*b*tan(d*x + c) + 4*a*b^3*tan(d*x + c) + 3*a^4 + 2*a^2*b^2 - b^4)/((b*tan(d*x + c) + a)*b^5))/d","A",0
131,1,399,0,0.992164," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(4 \, a^{2} b^{2} - b^{4}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \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{4 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2} b - b^{3}\right)}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}} - \frac{2 \, {\left(9 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 23 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a^{4} b^{3} - a^{2} b^{5}\right)}}{{\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(3*(4*a^2*b^2 - b^4)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a^2 + b^2)) - 4*(a^3*tan(1/2*d*x + 1/2*c) - 3*a*b^2*tan(1/2*d*x + 1/2*c) + 3*a^2*b - b^3)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(tan(1/2*d*x + 1/2*c)^2 + 1)) - 2*(9*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 2*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 8*a^4*b^3*tan(1/2*d*x + 1/2*c)^2 - 15*a^2*b^5*tan(1/2*d*x + 1/2*c)^2 - 2*b^7*tan(1/2*d*x + 1/2*c)^2 - 23*a^3*b^4*tan(1/2*d*x + 1/2*c) - 2*a*b^6*tan(1/2*d*x + 1/2*c) - 8*a^4*b^3 - a^2*b^5)/((a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)^2))/d","A",0
132,1,265,0,0.386945," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(3 \, a^{2} b - b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} - \frac{9 \, a^{2} b^{3} \tan\left(d x + c\right)^{2} - 3 \, b^{5} \tan\left(d x + c\right)^{2} + 22 \, a^{3} b^{2} \tan\left(d x + c\right) - 2 \, a b^{4} \tan\left(d x + c\right) + 14 \, a^{4} b + 3 \, a^{2} b^{3} + b^{5}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(a^3 - 3*a*b^2)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (3*a^2*b - b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(3*a^2*b^2 - b^4)*log(abs(b*tan(d*x + c) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) - (9*a^2*b^3*tan(d*x + c)^2 - 3*b^5*tan(d*x + c)^2 + 22*a^3*b^2*tan(d*x + c) - 2*a*b^4*tan(d*x + c) + 14*a^4*b + 3*a^2*b^3 + b^5)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(b*tan(d*x + c) + a)^2))/d","B",0
133,1,293,0,2.194884," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, a^{2} - b^{2}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(5 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 11 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{4} b - a^{2} b^{3}\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} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}^{2}}}{2 \, d}"," ",0,"-1/2*((2*a^2 - b^2)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2*(5*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*a^4*b*tan(1/2*d*x + 1/2*c)^2 - 7*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 - 2*b^5*tan(1/2*d*x + 1/2*c)^2 - 11*a^3*b^2*tan(1/2*d*x + 1/2*c) - 2*a*b^4*tan(1/2*d*x + 1/2*c) - 4*a^4*b - a^2*b^3)/((a^6 + 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)^2))/d","B",0
134,1,20,0,0.438922," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{1}{2 \, {\left(b \tan\left(d x + c\right) + a\right)}^{2} b d}"," ",0,"-1/2/((b*tan(d*x + c) + a)^2*b*d)","A",0
135,1,221,0,1.589621," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{\log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2} b\right)}}{{\left(a^{4} + a^{2} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) - 2*(a^3*tan(1/2*d*x + 1/2*c)^3 + 2*a*b^2*tan(1/2*d*x + 1/2*c)^3 + a^2*b*tan(1/2*d*x + 1/2*c)^2 - 2*b^3*tan(1/2*d*x + 1/2*c)^2 + a^3*tan(1/2*d*x + 1/2*c) - 2*a*b^2*tan(1/2*d*x + 1/2*c) - a^2*b)/((a^4 + a^2*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)^2))/d","B",0
136,1,62,0,1.832904," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b^{3}} - \frac{3 \, b \tan\left(d x + c\right)^{2} + 2 \, a \tan\left(d x + c\right) + b}{{\left(b \tan\left(d x + c\right) + a\right)}^{2} b^{2}}}{2 \, d}"," ",0,"1/2*(2*log(abs(b*tan(d*x + c) + a))/b^3 - (3*b*tan(d*x + c)^2 + 2*a*tan(d*x + c) + b)/((b*tan(d*x + c) + a)^2*b^2))/d","A",0
137,1,314,0,1.323377," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{6 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} - \frac{6 \, a \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^{2} + b^{2}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} b^{4}} + \frac{4}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} b^{3}} + \frac{2 \, {\left(3 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 13 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{4} + a^{2} b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}^{2} a^{2} b^{3}}}{2 \, d}"," ",0,"-1/2*(6*a*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 - 6*a*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 + 3*(2*a^2 + b^2)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^4) + 4/((tan(1/2*d*x + 1/2*c)^2 - 1)*b^3) + 2*(3*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 2*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 4*a^4*tan(1/2*d*x + 1/2*c)^2 - 9*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 2*b^4*tan(1/2*d*x + 1/2*c)^2 - 13*a^3*b*tan(1/2*d*x + 1/2*c) + 2*a*b^3*tan(1/2*d*x + 1/2*c) - 4*a^4 + a^2*b^2)/((a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)^2*a^2*b^3))/d","A",0
138,1,140,0,0.598458," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(3 \, a^{2} + b^{2}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b^{5}} + \frac{b^{3} \tan\left(d x + c\right)^{2} - 6 \, a b^{2} \tan\left(d x + c\right)}{b^{6}} - \frac{18 \, a^{2} b^{2} \tan\left(d x + c\right)^{2} + 6 \, b^{4} \tan\left(d x + c\right)^{2} + 28 \, a^{3} b \tan\left(d x + c\right) + 4 \, a b^{3} \tan\left(d x + c\right) + 11 \, a^{4} + b^{4}}{{\left(b \tan\left(d x + c\right) + a\right)}^{2} b^{5}}}{2 \, d}"," ",0,"1/2*(4*(3*a^2 + b^2)*log(abs(b*tan(d*x + c) + a))/b^5 + (b^3*tan(d*x + c)^2 - 6*a*b^2*tan(d*x + c))/b^6 - (18*a^2*b^2*tan(d*x + c)^2 + 6*b^4*tan(d*x + c)^2 + 28*a^3*b*tan(d*x + c) + 4*a*b^3*tan(d*x + c) + 11*a^4 + b^4)/((b*tan(d*x + c) + a)^2*b^5))/d","A",0
139,1,510,0,2.074389," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(4 \, 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)}{b^{6}} - \frac{15 \, {\left(4 \, 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)}{b^{6}} + \frac{15 \, {\left(4 \, a^{4} + 5 \, a^{2} b^{2} + b^{4}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} b^{6}} + \frac{2 \, {\left(9 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 18 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 72 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, a^{2} + 14 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} b^{5}} + \frac{6 \, {\left(7 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 25 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 23 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a^{6} - 7 \, a^{4} b^{2} + a^{2} b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}^{2} a^{2} b^{5}}}{6 \, d}"," ",0,"-1/6*(15*(4*a^3 + 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^6 - 15*(4*a^3 + 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^6 + 15*(4*a^4 + 5*a^2*b^2 + b^4)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^6) + 2*(9*a*b*tan(1/2*d*x + 1/2*c)^5 + 36*a^2*tan(1/2*d*x + 1/2*c)^4 + 18*b^2*tan(1/2*d*x + 1/2*c)^4 - 72*a^2*tan(1/2*d*x + 1/2*c)^2 - 24*b^2*tan(1/2*d*x + 1/2*c)^2 - 9*a*b*tan(1/2*d*x + 1/2*c) + 36*a^2 + 14*b^2)/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*b^5) + 6*(7*a^5*b*tan(1/2*d*x + 1/2*c)^3 + 5*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 8*a^6*tan(1/2*d*x + 1/2*c)^2 - 9*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 - 15*a^2*b^4*tan(1/2*d*x + 1/2*c)^2 + 2*b^6*tan(1/2*d*x + 1/2*c)^2 - 25*a^5*b*tan(1/2*d*x + 1/2*c) - 23*a^3*b^3*tan(1/2*d*x + 1/2*c) + 2*a*b^5*tan(1/2*d*x + 1/2*c) - 8*a^6 - 7*a^4*b^2 + a^2*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)^2*a^2*b^5))/d","A",0
140,1,243,0,1.004425," ","integrate(sec(d*x+c)^5/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{12 \, {\left(5 \, a^{4} + 6 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b^{7}} - \frac{2 \, {\left(45 \, a^{4} b^{2} \tan\left(d x + c\right)^{2} + 54 \, a^{2} b^{4} \tan\left(d x + c\right)^{2} + 9 \, b^{6} \tan\left(d x + c\right)^{2} + 78 \, a^{5} b \tan\left(d x + c\right) + 84 \, a^{3} b^{3} \tan\left(d x + c\right) + 6 \, a b^{5} \tan\left(d x + c\right) + 34 \, a^{6} + 33 \, a^{4} b^{2} + b^{6}\right)}}{{\left(b \tan\left(d x + c\right) + a\right)}^{2} b^{7}} + \frac{b^{9} \tan\left(d x + c\right)^{4} - 4 \, a b^{8} \tan\left(d x + c\right)^{3} + 12 \, a^{2} b^{7} \tan\left(d x + c\right)^{2} + 6 \, b^{9} \tan\left(d x + c\right)^{2} - 40 \, a^{3} b^{6} \tan\left(d x + c\right) - 36 \, a b^{8} \tan\left(d x + c\right)}{b^{12}}}{4 \, d}"," ",0,"1/4*(12*(5*a^4 + 6*a^2*b^2 + b^4)*log(abs(b*tan(d*x + c) + a))/b^7 - 2*(45*a^4*b^2*tan(d*x + c)^2 + 54*a^2*b^4*tan(d*x + c)^2 + 9*b^6*tan(d*x + c)^2 + 78*a^5*b*tan(d*x + c) + 84*a^3*b^3*tan(d*x + c) + 6*a*b^5*tan(d*x + c) + 34*a^6 + 33*a^4*b^2 + b^6)/((b*tan(d*x + c) + a)^2*b^7) + (b^9*tan(d*x + c)^4 - 4*a*b^8*tan(d*x + c)^3 + 12*a^2*b^7*tan(d*x + c)^2 + 6*b^9*tan(d*x + c)^2 - 40*a^3*b^6*tan(d*x + c) - 36*a*b^8*tan(d*x + c))/b^12)/d","A",0
141,1,370,0,1.822074," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{6 \, {\left(a^{3} b - a b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{12 \, {\left(a^{3} b^{2} - a b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}} - \frac{22 \, a^{3} b^{4} \tan\left(d x + c\right)^{3} - 22 \, a b^{6} \tan\left(d x + c\right)^{3} + 75 \, a^{4} b^{3} \tan\left(d x + c\right)^{2} - 60 \, a^{2} b^{5} \tan\left(d x + c\right)^{2} - 3 \, b^{7} \tan\left(d x + c\right)^{2} + 87 \, a^{5} b^{2} \tan\left(d x + c\right) - 48 \, a^{3} b^{4} \tan\left(d x + c\right) - 3 \, a b^{6} \tan\left(d x + c\right) + 35 \, a^{6} b - 7 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(a^4 - 6*a^2*b^2 + b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 6*(a^3*b - a*b^3)*log(tan(d*x + c)^2 + 1)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 12*(a^3*b^2 - a*b^4)*log(abs(b*tan(d*x + c) + a))/(a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9) - (22*a^3*b^4*tan(d*x + c)^3 - 22*a*b^6*tan(d*x + c)^3 + 75*a^4*b^3*tan(d*x + c)^2 - 60*a^2*b^5*tan(d*x + c)^2 - 3*b^7*tan(d*x + c)^2 + 87*a^5*b^2*tan(d*x + c) - 48*a^3*b^4*tan(d*x + c) - 3*a*b^6*tan(d*x + c) + 35*a^6*b - 7*a^4*b^3 + 3*a^2*b^5 + b^7)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*(b*tan(d*x + c) + a)^3))/d","B",0
142,1,524,0,0.435321," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(27 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, a^{4} b^{4} \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} + 18 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 81 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 36 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 108 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 42 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 18 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 81 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, a^{4} b^{4} \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) + 18 \, a^{7} b + 5 \, a^{5} b^{3} + 2 \, a^{3} b^{5}\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} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(3*(2*a^3 - 3*a*b^2)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a^2 + b^2)) - 2*(27*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 + 18*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 + 18*a^7*b*tan(1/2*d*x + 1/2*c)^4 - 81*a^5*b^3*tan(1/2*d*x + 1/2*c)^4 - 36*a^3*b^5*tan(1/2*d*x + 1/2*c)^4 - 12*a*b^7*tan(1/2*d*x + 1/2*c)^4 - 108*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 + 42*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 + 8*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 + 8*b^8*tan(1/2*d*x + 1/2*c)^3 - 36*a^7*b*tan(1/2*d*x + 1/2*c)^2 + 120*a^5*b^3*tan(1/2*d*x + 1/2*c)^2 + 18*a^3*b^5*tan(1/2*d*x + 1/2*c)^2 + 12*a*b^7*tan(1/2*d*x + 1/2*c)^2 + 81*a^6*b^2*tan(1/2*d*x + 1/2*c) + 12*a^4*b^4*tan(1/2*d*x + 1/2*c) + 6*a^2*b^6*tan(1/2*d*x + 1/2*c) + 18*a^7*b + 5*a^5*b^3 + 2*a^3*b^5)/((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 - 2*b*tan(1/2*d*x + 1/2*c) - a)^3))/d","B",0
143,1,20,0,1.454800," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{1}{3 \, {\left(b \tan\left(d x + c\right) + a\right)}^{3} b d}"," ",0,"-1/3/((b*tan(d*x + c) + a)^3*b*d)","A",0
144,1,426,0,4.079680," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, a \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(3 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 24 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 30 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 30 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{5} b + 2 \, a^{3} b^{3}\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} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(3*a*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2*(3*a^6*tan(1/2*d*x + 1/2*c)^5 + 12*a^4*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*a^2*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*a^5*b*tan(1/2*d*x + 1/2*c)^4 - 24*a^3*b^3*tan(1/2*d*x + 1/2*c)^4 - 12*a*b^5*tan(1/2*d*x + 1/2*c)^4 - 30*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 + 8*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 + 8*b^6*tan(1/2*d*x + 1/2*c)^3 - 12*a^5*b*tan(1/2*d*x + 1/2*c)^2 + 30*a^3*b^3*tan(1/2*d*x + 1/2*c)^2 + 12*a*b^5*tan(1/2*d*x + 1/2*c)^2 - 3*a^6*tan(1/2*d*x + 1/2*c) + 18*a^4*b^2*tan(1/2*d*x + 1/2*c) + 6*a^2*b^4*tan(1/2*d*x + 1/2*c) + 5*a^5*b + 2*a^3*b^3)/((a^7 + 2*a^5*b^2 + a^3*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)^3))/d","B",0
145,1,50,0,1.898978," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{3 \, b^{2} \tan\left(d x + c\right)^{2} + 3 \, a b \tan\left(d x + c\right) + a^{2} + b^{2}}{3 \, {\left(b \tan\left(d x + c\right) + a\right)}^{3} b^{3} d}"," ",0,"-1/3*(3*b^2*tan(d*x + c)^2 + 3*a*b*tan(d*x + c) + a^2 + b^2)/((b*tan(d*x + c) + a)^3*b^3*d)","A",0
146,1,527,0,4.072082," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} + b^{2}}} + \frac{2 \, {\left(3 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 9 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 36 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 48 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 42 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 33 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{7} + 5 \, a^{5} b^{2} + 2 \, a^{3} b^{4}\right)}}{{\left(a^{5} b^{3} + a^{3} b^{5}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}^{3}} + \frac{6 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} - \frac{6 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}}}{6 \, d}"," ",0,"1/6*(3*(2*a^3 + 3*a*b^2)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/((a^2*b^4 + b^6)*sqrt(a^2 + b^2)) + 2*(3*a^6*b*tan(1/2*d*x + 1/2*c)^5 + 6*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*a^7*tan(1/2*d*x + 1/2*c)^4 - 9*a^5*b^2*tan(1/2*d*x + 1/2*c)^4 - 12*a^3*b^4*tan(1/2*d*x + 1/2*c)^4 - 12*a*b^6*tan(1/2*d*x + 1/2*c)^4 - 36*a^6*b*tan(1/2*d*x + 1/2*c)^3 - 6*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 + 8*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 8*b^7*tan(1/2*d*x + 1/2*c)^3 - 12*a^7*tan(1/2*d*x + 1/2*c)^2 + 48*a^5*b^2*tan(1/2*d*x + 1/2*c)^2 + 42*a^3*b^4*tan(1/2*d*x + 1/2*c)^2 + 12*a*b^6*tan(1/2*d*x + 1/2*c)^2 + 33*a^6*b*tan(1/2*d*x + 1/2*c) + 24*a^4*b^3*tan(1/2*d*x + 1/2*c) + 6*a^2*b^5*tan(1/2*d*x + 1/2*c) + 6*a^7 + 5*a^5*b^2 + 2*a^3*b^4)/((a^5*b^3 + a^3*b^5)*(a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)^3) + 6*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 - 6*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4)/d","B",0
147,1,138,0,4.817322," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{12 \, a \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b^{5}} - \frac{3 \, \tan\left(d x + c\right)}{b^{4}} - \frac{22 \, a b^{3} \tan\left(d x + c\right)^{3} + 48 \, a^{2} b^{2} \tan\left(d x + c\right)^{2} - 6 \, b^{4} \tan\left(d x + c\right)^{2} + 36 \, a^{3} b \tan\left(d x + c\right) - 6 \, a b^{3} \tan\left(d x + c\right) + 9 \, a^{4} - 2 \, a^{2} b^{2} - b^{4}}{{\left(b \tan\left(d x + c\right) + a\right)}^{3} b^{5}}}{3 \, d}"," ",0,"-1/3*(12*a*log(abs(b*tan(d*x + c) + a))/b^5 - 3*tan(d*x + c)/b^4 - (22*a*b^3*tan(d*x + c)^3 + 48*a^2*b^2*tan(d*x + c)^2 - 6*b^4*tan(d*x + c)^2 + 36*a^3*b*tan(d*x + c) - 6*a*b^3*tan(d*x + c) + 9*a^4 - 2*a^2*b^2 - b^4)/((b*tan(d*x + c) + a)^3*b^5))/d","A",0
148,1,548,0,3.103173," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(4 \, a^{2} + b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{6}} - \frac{15 \, {\left(4 \, a^{2} + b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{6}} + \frac{15 \, {\left(4 \, a^{3} + 3 \, a b^{2}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} b^{6}} + \frac{6 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, 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) - 8 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} b^{5}} + \frac{2 \, {\left(27 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 117 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 216 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 114 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 300 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 54 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 189 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 30 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, a^{7} + 5 \, a^{5} b^{2} + 2 \, a^{3} b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}^{3} a^{3} b^{5}}}{6 \, d}"," ",0,"1/6*(15*(4*a^2 + b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^6 - 15*(4*a^2 + b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^6 + 15*(4*a^3 + 3*a*b^2)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^6) + 6*(b*tan(1/2*d*x + 1/2*c)^3 + 8*a*tan(1/2*d*x + 1/2*c)^2 + b*tan(1/2*d*x + 1/2*c) - 8*a)/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*b^5) + 2*(27*a^6*b*tan(1/2*d*x + 1/2*c)^5 + 6*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 36*a^7*tan(1/2*d*x + 1/2*c)^4 - 117*a^5*b^2*tan(1/2*d*x + 1/2*c)^4 - 12*a*b^6*tan(1/2*d*x + 1/2*c)^4 - 216*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 114*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 + 8*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 8*b^7*tan(1/2*d*x + 1/2*c)^3 - 72*a^7*tan(1/2*d*x + 1/2*c)^2 + 300*a^5*b^2*tan(1/2*d*x + 1/2*c)^2 + 54*a^3*b^4*tan(1/2*d*x + 1/2*c)^2 + 12*a*b^6*tan(1/2*d*x + 1/2*c)^2 + 189*a^6*b*tan(1/2*d*x + 1/2*c) + 30*a^4*b^3*tan(1/2*d*x + 1/2*c) + 6*a^2*b^5*tan(1/2*d*x + 1/2*c) + 36*a^7 + 5*a^5*b^2 + 2*a^3*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)^3*a^3*b^5))/d","A",0
149,1,249,0,0.272571," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b^{7}} - \frac{110 \, a^{3} b^{3} \tan\left(d x + c\right)^{3} + 66 \, a b^{5} \tan\left(d x + c\right)^{3} + 285 \, a^{4} b^{2} \tan\left(d x + c\right)^{2} + 144 \, a^{2} b^{4} \tan\left(d x + c\right)^{2} - 9 \, b^{6} \tan\left(d x + c\right)^{2} + 249 \, a^{5} b \tan\left(d x + c\right) + 108 \, a^{3} b^{3} \tan\left(d x + c\right) - 9 \, a b^{5} \tan\left(d x + c\right) + 73 \, a^{6} + 27 \, a^{4} b^{2} - 3 \, a^{2} b^{4} - b^{6}}{{\left(b \tan\left(d x + c\right) + a\right)}^{3} b^{7}} - \frac{b^{8} \tan\left(d x + c\right)^{3} - 6 \, a b^{7} \tan\left(d x + c\right)^{2} + 30 \, a^{2} b^{6} \tan\left(d x + c\right) + 9 \, b^{8} \tan\left(d x + c\right)}{b^{12}}}{3 \, d}"," ",0,"-1/3*(12*(5*a^3 + 3*a*b^2)*log(abs(b*tan(d*x + c) + a))/b^7 - (110*a^3*b^3*tan(d*x + c)^3 + 66*a*b^5*tan(d*x + c)^3 + 285*a^4*b^2*tan(d*x + c)^2 + 144*a^2*b^4*tan(d*x + c)^2 - 9*b^6*tan(d*x + c)^2 + 249*a^5*b*tan(d*x + c) + 108*a^3*b^3*tan(d*x + c) - 9*a*b^5*tan(d*x + c) + 73*a^6 + 27*a^4*b^2 - 3*a^2*b^4 - b^6)/((b*tan(d*x + c) + a)^3*b^7) - (b^8*tan(d*x + c)^3 - 6*a*b^7*tan(d*x + c)^2 + 30*a^2*b^6*tan(d*x + c) + 9*b^8*tan(d*x + c))/b^12)/d","A",0
150,1,116,0,0.239291," ","integrate(cos(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{-\frac{30 i \, \log\left(\tan\left(d x + c\right) + i\right)}{a} + \frac{30 i \, \log\left(\tan\left(d x + c\right) - i\right)}{a} + \frac{3 \, {\left(-15 i \, \tan\left(d x + c\right)^{2} + 38 \, \tan\left(d x + c\right) + 25 i\right)}}{a {\left(-i \, \tan\left(d x + c\right) + 1\right)}^{2}} - \frac{55 i \, \tan\left(d x + c\right)^{3} + 201 \, \tan\left(d x + c\right)^{2} - 255 i \, \tan\left(d x + c\right) - 117}{a {\left(\tan\left(d x + c\right) - i\right)}^{3}}}{192 \, d}"," ",0,"-1/192*(-30*I*log(tan(d*x + c) + I)/a + 30*I*log(tan(d*x + c) - I)/a + 3*(-15*I*tan(d*x + c)^2 + 38*tan(d*x + c) + 25*I)/(a*(-I*tan(d*x + c) + 1)^2) - (55*I*tan(d*x + c)^3 + 201*tan(d*x + c)^2 - 255*I*tan(d*x + c) - 117)/(a*(tan(d*x + c) - I)^3))/d","A",0
151,1,119,0,1.225883," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{5 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 13\right)}}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}^{3}} + \frac{165 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 480 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 650 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 400 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 113}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{5}}}{120 \, d}"," ",0,"1/120*(5*(15*tan(1/2*d*x + 1/2*c)^2 + 24*I*tan(1/2*d*x + 1/2*c) - 13)/(a*(tan(1/2*d*x + 1/2*c) + I)^3) + (165*tan(1/2*d*x + 1/2*c)^4 - 480*I*tan(1/2*d*x + 1/2*c)^3 - 650*tan(1/2*d*x + 1/2*c)^2 + 400*I*tan(1/2*d*x + 1/2*c) + 113)/(a*(tan(1/2*d*x + 1/2*c) - I)^5))/d","A",0
152,1,99,0,0.189049," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{6 i \, \log\left(i \, \tan\left(d x + c\right) + 1\right)}{a} - \frac{6 i \, \log\left(i \, \tan\left(d x + c\right) - 1\right)}{a} + \frac{2 \, {\left(3 \, \tan\left(d x + c\right) + 5 i\right)}}{a {\left(-i \, \tan\left(d x + c\right) + 1\right)}} + \frac{-9 i \, \tan\left(d x + c\right)^{2} - 26 \, \tan\left(d x + c\right) + 21 i}{a {\left(\tan\left(d x + c\right) - i\right)}^{2}}}{32 \, d}"," ",0,"-1/32*(6*I*log(I*tan(d*x + c) + 1)/a - 6*I*log(I*tan(d*x + c) - 1)/a + 2*(3*tan(d*x + c) + 5*I)/(a*(-I*tan(d*x + c) + 1)) + (-9*I*tan(d*x + c)^2 - 26*tan(d*x + c) + 21*I)/(a*(tan(d*x + c) - I)^2))/d","A",0
153,1,67,0,1.795895," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}} + \frac{9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3/(a*(tan(1/2*d*x + 1/2*c) + I)) + (9*tan(1/2*d*x + 1/2*c)^2 - 12*I*tan(1/2*d*x + 1/2*c) - 7)/(a*(tan(1/2*d*x + 1/2*c) - I)^3))/d","A",0
154,1,60,0,2.930769," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{i \, \log\left(\tan\left(d x + c\right) - i\right)}{a} - \frac{i \, \log\left(-i \, \tan\left(d x + c\right) + 1\right)}{a} + \frac{-i \, \tan\left(d x + c\right) - 3}{a {\left(\tan\left(d x + c\right) - i\right)}}}{4 \, d}"," ",0,"-1/4*(I*log(tan(d*x + c) - I)/a - I*log(-I*tan(d*x + c) + 1)/a + (-I*tan(d*x + c) - 3)/(a*(tan(d*x + c) - I)))/d","A",0
155,1,21,0,0.162869," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""giac"")","\frac{2}{a d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}}"," ",0,"2/(a*d*(tan(1/2*d*x + 1/2*c) - I))","A",0
156,1,57,0,0.195117," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{-\frac{i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a} + \frac{2 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}{a} - \frac{i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a}}{d}"," ",0,"-(-I*log(tan(1/2*d*x + 1/2*c) + 1)/a + 2*I*log(tan(1/2*d*x + 1/2*c) - I)/a - I*log(tan(1/2*d*x + 1/2*c) - 1)/a)/d","B",0
157,1,58,0,2.581491," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{\log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a} - \frac{\log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a} + \frac{2 i}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a}}{d}"," ",0,"(log(tan(1/2*d*x + 1/2*c) + 1)/a - log(tan(1/2*d*x + 1/2*c) - 1)/a + 2*I/((tan(1/2*d*x + 1/2*c)^2 - 1)*a))/d","A",0
158,1,27,0,0.233697," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{i \, \tan\left(d x + c\right)^{2} - 2 \, \tan\left(d x + c\right)}{2 \, a d}"," ",0,"-1/2*(I*tan(d*x + c)^2 - 2*tan(d*x + c))/(a*d)","A",0
159,1,99,0,2.724546," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a} - \frac{3 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a} + \frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a}}{6 \, d}"," ",0,"1/6*(3*log(tan(1/2*d*x + 1/2*c) + 1)/a - 3*log(tan(1/2*d*x + 1/2*c) - 1)/a + 2*(3*tan(1/2*d*x + 1/2*c)^5 + 6*I*tan(1/2*d*x + 1/2*c)^4 - 3*tan(1/2*d*x + 1/2*c) + 2*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a))/d","A",0
160,1,47,0,0.229428," ","integrate(sec(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{3 i \, \tan\left(d x + c\right)^{4} - 4 \, \tan\left(d x + c\right)^{3} + 6 i \, \tan\left(d x + c\right)^{2} - 12 \, \tan\left(d x + c\right)}{12 \, a d}"," ",0,"-1/12*(3*I*tan(d*x + c)^4 - 4*tan(d*x + c)^3 + 6*I*tan(d*x + c)^2 - 12*tan(d*x + c))/(a*d)","A",0
161,1,138,0,0.232309," ","integrate(sec(d*x+c)^6/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{15 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a} - \frac{15 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a} + \frac{2 \, {\left(25 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 40 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 80 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5} a}}{40 \, d}"," ",0,"1/40*(15*log(tan(1/2*d*x + 1/2*c) + 1)/a - 15*log(tan(1/2*d*x + 1/2*c) - 1)/a + 2*(25*tan(1/2*d*x + 1/2*c)^9 + 40*I*tan(1/2*d*x + 1/2*c)^8 - 10*tan(1/2*d*x + 1/2*c)^7 + 80*I*tan(1/2*d*x + 1/2*c)^4 + 10*tan(1/2*d*x + 1/2*c)^3 - 25*tan(1/2*d*x + 1/2*c) + 8*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^5*a))/d","A",0
162,1,67,0,0.224093," ","integrate(sec(d*x+c)^7/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{5 i \, \tan\left(d x + c\right)^{6} - 6 \, \tan\left(d x + c\right)^{5} + 15 i \, \tan\left(d x + c\right)^{4} - 20 \, \tan\left(d x + c\right)^{3} + 15 i \, \tan\left(d x + c\right)^{2} - 30 \, \tan\left(d x + c\right)}{30 \, a d}"," ",0,"-1/30*(5*I*tan(d*x + c)^6 - 6*tan(d*x + c)^5 + 15*I*tan(d*x + c)^4 - 20*tan(d*x + c)^3 + 15*I*tan(d*x + c)^2 - 30*tan(d*x + c))/(a*d)","A",0
163,1,145,0,1.204968," ","integrate(cos(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{7 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}^{3}} + \frac{273 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1155 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2450 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2870 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2037 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 791 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 152}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{7}}}{168 \, d}"," ",0,"1/168*(7*(9*tan(1/2*d*x + 1/2*c)^2 + 15*I*tan(1/2*d*x + 1/2*c) - 8)/(a^2*(tan(1/2*d*x + 1/2*c) + I)^3) + (273*tan(1/2*d*x + 1/2*c)^6 - 1155*I*tan(1/2*d*x + 1/2*c)^5 - 2450*tan(1/2*d*x + 1/2*c)^4 + 2870*I*tan(1/2*d*x + 1/2*c)^3 + 2037*tan(1/2*d*x + 1/2*c)^2 - 791*I*tan(1/2*d*x + 1/2*c) - 152)/(a^2*(tan(1/2*d*x + 1/2*c) - I)^7))/d","A",0
164,1,103,0,0.250414," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{-\frac{6 i \, \log\left(\tan\left(d x + c\right) + i\right)}{a^{2}} + \frac{6 i \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{2}} + \frac{3 \, {\left(2 i \, \tan\left(d x + c\right) - 3\right)}}{a^{2} {\left(\tan\left(d x + c\right) + i\right)}} + \frac{-11 i \, \tan\left(d x + c\right)^{3} - 42 \, \tan\left(d x + c\right)^{2} + 57 i \, \tan\left(d x + c\right) + 30}{a^{2} {\left(\tan\left(d x + c\right) - i\right)}^{3}}}{48 \, d}"," ",0,"-1/48*(-6*I*log(tan(d*x + c) + I)/a^2 + 6*I*log(tan(d*x + c) - I)/a^2 + 3*(2*I*tan(d*x + c) - 3)/(a^2*(tan(d*x + c) + I)) + (-11*I*tan(d*x + c)^3 - 42*tan(d*x + c)^2 + 57*I*tan(d*x + c) + 30)/(a^2*(tan(d*x + c) - I)^3))/d","A",0
165,1,93,0,0.234706," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{5}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}} + \frac{35 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 90 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 70 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{5}}}{20 \, d}"," ",0,"1/20*(5/(a^2*(tan(1/2*d*x + 1/2*c) + I)) + (35*tan(1/2*d*x + 1/2*c)^4 - 90*I*tan(1/2*d*x + 1/2*c)^3 - 120*tan(1/2*d*x + 1/2*c)^2 + 70*I*tan(1/2*d*x + 1/2*c) + 21)/(a^2*(tan(1/2*d*x + 1/2*c) - I)^5))/d","A",0
166,1,72,0,0.419079," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 i \, \log\left(i \, \tan\left(d x + c\right) + 1\right)}{a^{2}} - \frac{2 i \, \log\left(i \, \tan\left(d x + c\right) - 1\right)}{a^{2}} + \frac{-3 i \, \tan\left(d x + c\right)^{2} - 10 \, \tan\left(d x + c\right) + 11 i}{a^{2} {\left(\tan\left(d x + c\right) - i\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(2*I*log(I*tan(d*x + c) + 1)/a^2 - 2*I*log(I*tan(d*x + c) - 1)/a^2 + (-3*I*tan(d*x + c)^2 - 10*tan(d*x + c) + 11*I)/(a^2*(tan(d*x + c) - I)^2))/d","A",0
167,1,47,0,1.067899," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2\right)}}{3 \, a^{2} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{3}}"," ",0,"2/3*(3*tan(1/2*d*x + 1/2*c)^2 - 3*I*tan(1/2*d*x + 1/2*c) - 2)/(a^2*d*(tan(1/2*d*x + 1/2*c) - I)^3)","A",0
168,1,30,0,0.189389," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{2}}"," ",0,"-2*tan(1/2*d*x + 1/2*c)/(a^2*d*(tan(1/2*d*x + 1/2*c) - I)^2)","A",0
169,1,57,0,1.682470," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{\log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{2}} - \frac{\log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{2}} - \frac{4}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}}}{d}"," ",0,"-(log(tan(1/2*d*x + 1/2*c) + 1)/a^2 - log(tan(1/2*d*x + 1/2*c) - 1)/a^2 - 4/(a^2*(tan(1/2*d*x + 1/2*c) - I)))/d","A",0
170,1,100,0,2.926309," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{2}} - \frac{2 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}{a^{2}} + \frac{i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{2}} + \frac{-i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{2}}\right)}}{d}"," ",0,"2*(I*log(tan(1/2*d*x + 1/2*c) + 1)/a^2 - 2*I*log(tan(1/2*d*x + 1/2*c) - I)/a^2 + I*log(tan(1/2*d*x + 1/2*c) - 1)/a^2 + (-I*tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) + I)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^2))/d","A",0
171,1,95,0,0.335051," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{2}} - \frac{3 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{2}} - \frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{2}}}{2 \, d}"," ",0,"1/2*(3*log(tan(1/2*d*x + 1/2*c) + 1)/a^2 - 3*log(tan(1/2*d*x + 1/2*c) - 1)/a^2 - 2*(tan(1/2*d*x + 1/2*c)^3 - 4*I*tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) + 4*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^2))/d","A",0
172,1,35,0,1.630306," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\tan\left(d x + c\right)^{3} + 3 i \, \tan\left(d x + c\right)^{2} - 3 \, \tan\left(d x + c\right)}{3 \, a^{2} d}"," ",0,"-1/3*(tan(d*x + c)^3 + 3*I*tan(d*x + c)^2 - 3*tan(d*x + c))/(a^2*d)","A",0
173,1,151,0,0.260021," ","integrate(sec(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{15 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{2}} - \frac{15 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{2}} + \frac{2 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 48 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 33 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 33 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 16 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4} a^{2}}}{24 \, d}"," ",0,"1/24*(15*log(tan(1/2*d*x + 1/2*c) + 1)/a^2 - 15*log(tan(1/2*d*x + 1/2*c) - 1)/a^2 + 2*(9*tan(1/2*d*x + 1/2*c)^7 + 48*I*tan(1/2*d*x + 1/2*c)^6 - 33*tan(1/2*d*x + 1/2*c)^5 - 48*I*tan(1/2*d*x + 1/2*c)^4 - 33*tan(1/2*d*x + 1/2*c)^3 + 16*I*tan(1/2*d*x + 1/2*c)^2 + 9*tan(1/2*d*x + 1/2*c) - 16*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^4*a^2))/d","B",0
174,1,47,0,0.234599," ","integrate(sec(d*x+c)^6/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, \tan\left(d x + c\right)^{5} + 5 i \, \tan\left(d x + c\right)^{4} + 10 i \, \tan\left(d x + c\right)^{2} - 10 \, \tan\left(d x + c\right)}{10 \, a^{2} d}"," ",0,"-1/10*(2*tan(d*x + c)^5 + 5*I*tan(d*x + c)^4 + 10*I*tan(d*x + c)^2 - 10*tan(d*x + c))/(a^2*d)","A",0
175,1,119,0,0.283326," ","integrate(cos(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{-\frac{60 i \, \log\left(-i \, \tan\left(d x + c\right) + 1\right)}{a^{3}} + \frac{60 i \, \log\left(-i \, \tan\left(d x + c\right) - 1\right)}{a^{3}} - \frac{12 \, {\left(5 \, \tan\left(d x + c\right) + 7 i\right)}}{a^{3} {\left(i \, \tan\left(d x + c\right) - 1\right)}} + \frac{-125 i \, \tan\left(d x + c\right)^{4} - 596 \, \tan\left(d x + c\right)^{3} + 1110 i \, \tan\left(d x + c\right)^{2} + 996 \, \tan\left(d x + c\right) - 405 i}{a^{3} {\left(\tan\left(d x + c\right) - i\right)}^{4}}}{768 \, d}"," ",0,"-1/768*(-60*I*log(-I*tan(d*x + c) + 1)/a^3 + 60*I*log(-I*tan(d*x + c) - 1)/a^3 - 12*(5*tan(d*x + c) + 7*I)/(a^3*(I*tan(d*x + c) - 1)) + (-125*I*tan(d*x + c)^4 - 596*tan(d*x + c)^3 + 1110*I*tan(d*x + c)^2 + 996*tan(d*x + c) - 405*I)/(a^3*(tan(d*x + c) - I)^4))/d","A",0
176,1,119,0,0.264720," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{35}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}} + \frac{525 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1960 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4025 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4480 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3143 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1176 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 243}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{7}}}{280 \, d}"," ",0,"1/280*(35/(a^3*(tan(1/2*d*x + 1/2*c) + I)) + (525*tan(1/2*d*x + 1/2*c)^6 - 1960*I*tan(1/2*d*x + 1/2*c)^5 - 4025*tan(1/2*d*x + 1/2*c)^4 + 4480*I*tan(1/2*d*x + 1/2*c)^3 + 3143*tan(1/2*d*x + 1/2*c)^2 - 1176*I*tan(1/2*d*x + 1/2*c) - 243)/(a^3*(tan(1/2*d*x + 1/2*c) - I)^7))/d","A",0
177,1,80,0,0.254694," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{6 i \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{3}} - \frac{6 i \, \log\left(i \, \tan\left(d x + c\right) - 1\right)}{a^{3}} + \frac{-11 i \, \tan\left(d x + c\right)^{3} - 45 \, \tan\left(d x + c\right)^{2} + 69 i \, \tan\left(d x + c\right) + 51}{a^{3} {\left(\tan\left(d x + c\right) - i\right)}^{3}}}{96 \, d}"," ",0,"-1/96*(6*I*log(tan(d*x + c) - I)/a^3 - 6*I*log(I*tan(d*x + c) - 1)/a^3 + (-11*I*tan(d*x + c)^3 - 45*tan(d*x + c)^2 + 69*I*tan(d*x + c) + 51)/(a^3*(tan(d*x + c) - I)^3))/d","A",0
178,1,73,0,1.504409," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 30 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 20 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7\right)}}{15 \, a^{3} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{5}}"," ",0,"2/15*(15*tan(1/2*d*x + 1/2*c)^4 - 30*I*tan(1/2*d*x + 1/2*c)^3 - 40*tan(1/2*d*x + 1/2*c)^2 + 20*I*tan(1/2*d*x + 1/2*c) + 7)/(a^3*d*(tan(1/2*d*x + 1/2*c) - I)^5)","A",0
179,1,57,0,0.974443," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{3} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{4}}"," ",0,"-2*(tan(1/2*d*x + 1/2*c)^3 - I*tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c))/(a^3*d*(tan(1/2*d*x + 1/2*c) - I)^4)","B",0
180,1,36,0,1.897641," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{3 \, a^{3} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{3}}"," ",0,"2/3*(3*tan(1/2*d*x + 1/2*c)^2 - 1)/(a^3*d*(tan(1/2*d*x + 1/2*c) - I)^3)","A",0
181,1,100,0,0.311255," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{3}} - \frac{2 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}{a^{3}} + \frac{i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{3}} + \frac{3 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 i}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{2}}}{d}"," ",0,"-(I*log(tan(1/2*d*x + 1/2*c) + 1)/a^3 - 2*I*log(tan(1/2*d*x + 1/2*c) - I)/a^3 + I*log(tan(1/2*d*x + 1/2*c) - 1)/a^3 + (3*I*tan(1/2*d*x + 1/2*c)^2 + 10*tan(1/2*d*x + 1/2*c) - 3*I)/(a^3*(tan(1/2*d*x + 1/2*c) - I)^2))/d","A",0
182,1,110,0,0.621787," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{3 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{3}} - \frac{3 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{3}} - \frac{2 \, {\left(4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)} a^{3}}}{d}"," ",0,"-(3*log(tan(1/2*d*x + 1/2*c) + 1)/a^3 - 3*log(tan(1/2*d*x + 1/2*c) - 1)/a^3 - 2*(4*tan(1/2*d*x + 1/2*c)^2 - I*tan(1/2*d*x + 1/2*c) - 5)/((tan(1/2*d*x + 1/2*c)^3 - I*tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c) + I)*a^3))/d","A",0
183,1,128,0,0.295599," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{2 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{3}} - \frac{4 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}{a^{3}} + \frac{2 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{3}} + \frac{-3 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 i}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{3}}\right)}}{d}"," ",0,"2*(2*I*log(tan(1/2*d*x + 1/2*c) + 1)/a^3 - 4*I*log(tan(1/2*d*x + 1/2*c) - I)/a^3 + 2*I*log(tan(1/2*d*x + 1/2*c) - 1)/a^3 + (-3*I*tan(1/2*d*x + 1/2*c)^4 + 3*tan(1/2*d*x + 1/2*c)^3 + 7*I*tan(1/2*d*x + 1/2*c)^2 - 3*tan(1/2*d*x + 1/2*c) - 3*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^3))/d","A",0
184,1,112,0,0.282175," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{15 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{3}} - \frac{15 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{3}} - \frac{2 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 48 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 22 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{3}}}{6 \, d}"," ",0,"1/6*(15*log(tan(1/2*d*x + 1/2*c) + 1)/a^3 - 15*log(tan(1/2*d*x + 1/2*c) - 1)/a^3 - 2*(9*tan(1/2*d*x + 1/2*c)^5 - 18*I*tan(1/2*d*x + 1/2*c)^4 + 48*I*tan(1/2*d*x + 1/2*c)^2 - 9*tan(1/2*d*x + 1/2*c) - 22*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^3))/d","A",0
185,1,47,0,0.406729," ","integrate(sec(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{-i \, \tan\left(d x + c\right)^{4} + 4 \, \tan\left(d x + c\right)^{3} + 6 i \, \tan\left(d x + c\right)^{2} - 4 \, \tan\left(d x + c\right)}{4 \, a^{3} d}"," ",0,"-1/4*(-I*tan(d*x + c)^4 + 4*tan(d*x + c)^3 + 6*I*tan(d*x + c)^2 - 4*tan(d*x + c))/(a^3*d)","A",0
186,1,164,0,1.954655," ","integrate(sec(d*x+c)^6/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{105 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{3}} - \frac{105 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{3}} + \frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 390 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 400 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 390 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 136 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5} a^{3}}}{120 \, d}"," ",0,"1/120*(105*log(tan(1/2*d*x + 1/2*c) + 1)/a^3 - 105*log(tan(1/2*d*x + 1/2*c) - 1)/a^3 + 2*(15*tan(1/2*d*x + 1/2*c)^9 + 360*I*tan(1/2*d*x + 1/2*c)^8 - 390*tan(1/2*d*x + 1/2*c)^7 - 960*I*tan(1/2*d*x + 1/2*c)^6 + 400*I*tan(1/2*d*x + 1/2*c)^4 + 390*tan(1/2*d*x + 1/2*c)^3 - 320*I*tan(1/2*d*x + 1/2*c)^2 - 15*tan(1/2*d*x + 1/2*c) + 136*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^5*a^3))/d","A",0
187,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^n/(cos(d*x+c)^n),x, algorithm=""giac"")","\int \frac{{\left(a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right)\right)}^{n}}{\cos\left(d x + c\right)^{n}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + I*a*sin(d*x + c))^n/cos(d*x + c)^n, x)","F",0
188,1,22,0,5.738781," ","integrate(1/(sec(x)+tan(x)),x, algorithm=""giac"")","-\log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) + 2 \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right)"," ",0,"-log(tan(1/2*x)^2 + 1) + 2*log(abs(tan(1/2*x) + 1))","B",0
189,1,10,0,0.156556," ","integrate(sin(x)/(sec(x)+tan(x)),x, algorithm=""giac"")","-\log\left(\sin\left(x\right) + 1\right) + \sin\left(x\right)"," ",0,"-log(sin(x) + 1) + sin(x)","A",0
190,1,14,0,0.827529," ","integrate(cos(x)/(sec(x)+tan(x)),x, algorithm=""giac"")","x + \frac{2}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}"," ",0,"x + 2/(tan(1/2*x)^2 + 1)","B",0
191,1,12,0,0.959116," ","integrate(tan(x)/(sec(x)+tan(x)),x, algorithm=""giac"")","x + \frac{2}{\tan\left(\frac{1}{2} \, x\right) + 1}"," ",0,"x + 2/(tan(1/2*x) + 1)","A",0
192,1,10,0,3.983503," ","integrate(cot(x)/(sec(x)+tan(x)),x, algorithm=""giac"")","-x + \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)"," ",0,"-x + log(abs(tan(1/2*x)))","A",0
193,1,10,0,0.199999," ","integrate(sec(x)/(sec(x)+tan(x)),x, algorithm=""giac"")","-\frac{2}{\tan\left(\frac{1}{2} \, x\right) + 1}"," ",0,"-2/(tan(1/2*x) + 1)","A",0
194,1,12,0,0.161115," ","integrate(csc(x)/(sec(x)+tan(x)),x, algorithm=""giac"")","-\log\left(\sin\left(x\right) + 1\right) + \log\left({\left| \sin\left(x\right) \right|}\right)"," ",0,"-log(sin(x) + 1) + log(abs(sin(x)))","A",0
195,1,20,0,0.167005," ","integrate(1/(sec(x)-tan(x)),x, algorithm=""giac"")","\log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) - 2 \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right)"," ",0,"log(tan(1/2*x)^2 + 1) - 2*log(abs(tan(1/2*x) - 1))","B",0
196,1,14,0,2.391994," ","integrate(sin(x)/(sec(x)-tan(x)),x, algorithm=""giac"")","-\log\left(-\sin\left(x\right) + 1\right) - \sin\left(x\right)"," ",0,"-log(-sin(x) + 1) - sin(x)","A",0
197,1,14,0,1.025531," ","integrate(cos(x)/(sec(x)-tan(x)),x, algorithm=""giac"")","x - \frac{2}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}"," ",0,"x - 2/(tan(1/2*x)^2 + 1)","B",0
198,1,14,0,1.954125," ","integrate(tan(x)/(sec(x)-tan(x)),x, algorithm=""giac"")","-x - \frac{2}{\tan\left(\frac{1}{2} \, x\right) - 1}"," ",0,"-x - 2/(tan(1/2*x) - 1)","A",0
199,1,8,0,0.200755," ","integrate(cot(x)/(sec(x)-tan(x)),x, algorithm=""giac"")","x + \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)"," ",0,"x + log(abs(tan(1/2*x)))","A",0
200,1,10,0,1.668004," ","integrate(sec(x)/(sec(x)-tan(x)),x, algorithm=""giac"")","-\frac{2}{\tan\left(\frac{1}{2} \, x\right) - 1}"," ",0,"-2/(tan(1/2*x) - 1)","A",0
201,1,14,0,0.184545," ","integrate(csc(x)/(sec(x)-tan(x)),x, algorithm=""giac"")","-\log\left(-\sin\left(x\right) + 1\right) + \log\left({\left| \sin\left(x\right) \right|}\right)"," ",0,"-log(-sin(x) + 1) + log(abs(sin(x)))","A",0
202,1,16,0,0.261443," ","integrate(csc(d*x+c)*(cot(d*x+c)+csc(d*x+c)),x, algorithm=""giac"")","-\frac{1}{d \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}"," ",0,"-1/(d*tan(1/2*d*x + 1/2*c))","A",0
203,1,18,0,0.212270," ","integrate(sin(x)/(cot(x)+csc(x)),x, algorithm=""giac"")","x - \frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}"," ",0,"x - 2*tan(1/2*x)/(tan(1/2*x)^2 + 1)","B",0
204,1,10,0,0.427201," ","integrate(cos(x)/(cot(x)+csc(x)),x, algorithm=""giac"")","-\cos\left(x\right) + \log\left(\cos\left(x\right) + 1\right)"," ",0,"-cos(x) + log(cos(x) + 1)","A",0
205,1,22,0,0.216410," ","integrate(tan(x)/(cot(x)+csc(x)),x, algorithm=""giac"")","-x + \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right) - \log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right)"," ",0,"-x + log(abs(tan(1/2*x) + 1)) - log(abs(tan(1/2*x) - 1))","B",0
206,1,8,0,0.216146," ","integrate(cot(x)/(cot(x)+csc(x)),x, algorithm=""giac"")","x - \tan\left(\frac{1}{2} \, x\right)"," ",0,"x - tan(1/2*x)","A",0
207,1,12,0,0.153044," ","integrate(sec(x)/(cot(x)+csc(x)),x, algorithm=""giac"")","\log\left(\cos\left(x\right) + 1\right) - \log\left({\left| \cos\left(x\right) \right|}\right)"," ",0,"log(cos(x) + 1) - log(abs(cos(x)))","A",0
208,1,4,0,0.214914," ","integrate(csc(x)/(cot(x)+csc(x)),x, algorithm=""giac"")","\tan\left(\frac{1}{2} \, x\right)"," ",0,"tan(1/2*x)","A",0
209,1,18,0,0.199221," ","integrate(sin(x)/(-cot(x)+csc(x)),x, algorithm=""giac"")","x + \frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}"," ",0,"x + 2*tan(1/2*x)/(tan(1/2*x)^2 + 1)","B",0
210,1,10,0,0.196111," ","integrate(cos(x)/(-cot(x)+csc(x)),x, algorithm=""giac"")","\cos\left(x\right) + \log\left(-\cos\left(x\right) + 1\right)"," ",0,"cos(x) + log(-cos(x) + 1)","A",0
211,1,20,0,0.475255," ","integrate(tan(x)/(-cot(x)+csc(x)),x, algorithm=""giac"")","x + \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right) - \log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right)"," ",0,"x + log(abs(tan(1/2*x) + 1)) - log(abs(tan(1/2*x) - 1))","B",0
212,1,12,0,0.157527," ","integrate(cot(x)/(-cot(x)+csc(x)),x, algorithm=""giac"")","-x - \frac{1}{\tan\left(\frac{1}{2} \, x\right)}"," ",0,"-x - 1/tan(1/2*x)","A",0
213,1,14,0,0.256936," ","integrate(sec(x)/(-cot(x)+csc(x)),x, algorithm=""giac"")","\log\left(-\cos\left(x\right) + 1\right) - \log\left({\left| \cos\left(x\right) \right|}\right)"," ",0,"log(-cos(x) + 1) - log(abs(cos(x)))","A",0
214,1,8,0,0.202066," ","integrate(csc(x)/(-cot(x)+csc(x)),x, algorithm=""giac"")","-\frac{1}{\tan\left(\frac{1}{2} \, x\right)}"," ",0,"-1/tan(1/2*x)","A",0
215,1,68,0,1.204617," ","integrate(1/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""giac"")","\frac{\sqrt{2} \log\left(\frac{{\left| -4 \, \sqrt{2} - \frac{2 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + 6 \right|}}{{\left| 4 \, \sqrt{2} - \frac{2 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + 6 \right|}}\right)}{4 \, d}"," ",0,"1/4*sqrt(2)*log(abs(-4*sqrt(2) - 2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 6)/abs(4*sqrt(2) - 2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 6))/d","B",0
216,1,82,0,0.222835," ","integrate(sin(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, d x - \sqrt{2} {\left(d x + c + \arctan\left(-\frac{\sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 2 \, \sin\left(2 \, d x + 2 \, c\right)}{\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 2}\right)\right)} + 2 \, c}{2 \, d}"," ",0,"1/2*(2*d*x - sqrt(2)*(d*x + c + arctan(-(sqrt(2)*sin(2*d*x + 2*c) - 2*sin(2*d*x + 2*c))/(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2) - 2*cos(2*d*x + 2*c) + 2))) + 2*c)/d","A",0
217,1,16,0,0.261319," ","integrate(cos(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""giac"")","\frac{\log\left(\sin\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*log(sin(d*x + c)^2 + 1)/d","A",0
218,1,37,0,0.391089," ","integrate(tan(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, \arctan\left(\sin\left(d x + c\right)\right) - \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{4 \, d}"," ",0,"-1/4*(2*arctan(sin(d*x + c)) - log(abs(sin(d*x + c) + 1)) + log(abs(sin(d*x + c) - 1)))/d","A",0
219,1,11,0,0.252069," ","integrate(cot(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""giac"")","\frac{\arctan\left(\sin\left(d x + c\right)\right)}{d}"," ",0,"arctan(sin(d*x + c))/d","A",0
220,1,79,0,0.277621," ","integrate(sec(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) - \log\left({\left| -\frac{6 \, {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{{\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1 \right|}\right)}{4 \, d}"," ",0,"-1/4*(2*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) - log(abs(-6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + (cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 1)))/d","B",0
221,1,72,0,0.252711," ","integrate(csc(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(d x + c + \arctan\left(-\frac{\sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 2 \, \sin\left(2 \, d x + 2 \, c\right)}{\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 2}\right)\right)}}{2 \, d}"," ",0,"1/2*sqrt(2)*(d*x + c + arctan(-(sqrt(2)*sin(2*d*x + 2*c) - 2*sin(2*d*x + 2*c))/(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2) - 2*cos(2*d*x + 2*c) + 2)))/d","A",0
222,1,28,0,0.191263," ","integrate(1/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""giac"")","\frac{2}{d {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}}"," ",0,"2/(d*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))","B",0
223,1,18,0,0.345250," ","integrate(sin(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""giac"")","-\frac{d x + c - \tan\left(d x + c\right)}{d}"," ",0,"-(d*x + c - tan(d*x + c))/d","A",0
224,1,26,0,0.199435," ","integrate(cos(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""giac"")","-\frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{2 \, d}"," ",0,"-1/2*(log(abs(sin(d*x + c) + 1)) + log(abs(sin(d*x + c) - 1)))/d","B",0
225,1,48,0,0.315502," ","integrate(tan(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{4 \, d}"," ",0,"-1/4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(abs(sin(d*x + c) + 1)) - log(abs(sin(d*x + c) - 1)))/d","A",0
226,1,28,0,0.988492," ","integrate(cot(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""giac"")","\frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{2 \, d}"," ",0,"1/2*(log(abs(sin(d*x + c) + 1)) - log(abs(sin(d*x + c) - 1)))/d","B",0
227,1,46,0,0.231215," ","integrate(sec(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, {\left(\cos\left(d x + c\right) - 1\right)}}{d {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{2} {\left(\cos\left(d x + c\right) + 1\right)}}"," ",0,"-2*(cos(d*x + c) - 1)/(d*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^2*(cos(d*x + c) + 1))","B",0
228,1,10,0,0.204252," ","integrate(csc(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""giac"")","\frac{\tan\left(d x + c\right)}{d}"," ",0,"tan(d*x + c)/d","A",0
229,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)-a*8*d/(8*d)^2*cos(2*c+2*d*x)-a*32*d/(32*d)^2*cos(4*c+4*d*x)+(3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^6+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^4+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^2+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^6+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^4+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^2+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)-3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^6*tan(d*x/2)^6-9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^6*tan(d*x/2)^4-9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^6*tan(d*x/2)^2-3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^6-9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^4*tan(d*x/2)^6-27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^4*tan(d*x/2)^4-27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^4*tan(d*x/2)^2-9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^4-9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^2*tan(d*x/2)^6-27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^2*tan(d*x/2)^4-27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^2*tan(d*x/2)^2-9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^2-3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(d*x/2)^6-9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(d*x/2)^4-9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(d*x/2)^2-3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^6+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^4+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^2+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^6+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^4+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^2+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^6*tan(d*x/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^6*tan(d*x/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^6*tan(d*x/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^4*tan(d*x/2)^6+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^4*tan(d*x/2)^4+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^4*tan(d*x/2)^2+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^2*tan(d*x/2)^6+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^2*tan(d*x/2)^4+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^2*tan(d*x/2)^2+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(d*x/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(d*x/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(d*x/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)-6*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6*tan(d*x/2)^6-18*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6*tan(d*x/2)^4-18*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6*tan(d*x/2)^2-6*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6-18*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4*tan(d*x/2)^6-54*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4*tan(d*x/2)^4-54*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4*tan(d*x/2)^2-18*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4-18*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2*tan(d*x/2)^6-54*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2*tan(d*x/2)^4-54*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2*tan(d*x/2)^2-18*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2-6*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(d*x/2)^6-18*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(d*x/2)^4-18*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(d*x/2)^2-6*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)+6*b*pi*tan(c/2)^6*tan(d*x/2)^6+18*b*pi*tan(c/2)^6*tan(d*x/2)^4+18*b*pi*tan(c/2)^6*tan(d*x/2)^2+6*b*pi*tan(c/2)^6+18*b*pi*tan(c/2)^4*tan(d*x/2)^6+54*b*pi*tan(c/2)^4*tan(d*x/2)^4+54*b*pi*tan(c/2)^4*tan(d*x/2)^2+18*b*pi*tan(c/2)^4+18*b*pi*tan(c/2)^2*tan(d*x/2)^6+54*b*pi*tan(c/2)^2*tan(d*x/2)^4+54*b*pi*tan(c/2)^2*tan(d*x/2)^2+18*b*pi*tan(c/2)^2+6*b*pi*tan(d*x/2)^6+18*b*pi*tan(d*x/2)^4+18*b*pi*tan(d*x/2)^2+6*b*pi+6*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^6+18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^4+18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^2+6*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6+18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^6+54*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^4+54*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^2+18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4+18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^6+54*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^4+54*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^2+18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2+6*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(d*x/2)^6+18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(d*x/2)^4+18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(d*x/2)^2+6*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))-6*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^6-18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^4-18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^2-6*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6-18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^6-54*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^4-54*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^2-18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4-18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^6-54*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^4-54*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^2-18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2-6*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(d*x/2)^6-18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(d*x/2)^4-18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(d*x/2)^2-6*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))-6*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^6-18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^4-18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^2-6*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6-18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^6-54*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^4-54*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^2-18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4-18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^6-54*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^4-54*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^2-18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2-6*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(d*x/2)^6-18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(d*x/2)^4-18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(d*x/2)^2-6*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))+6*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^6+18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^4+18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^2+6*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6+18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^6+54*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^4+54*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^2+18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4+18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^6+54*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^4+54*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^2+18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2+6*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(d*x/2)^6+18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(d*x/2)^4+18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(d*x/2)^2+6*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))-32*b*tan(c/2)^6*tan(d*x/2)^6+96*b*tan(c/2)^6*tan(d*x/2)^4-96*b*tan(c/2)^6*tan(d*x/2)^2+32*b*tan(c/2)^6+384*b*tan(c/2)^5*tan(d*x/2)^5-768*b*tan(c/2)^5*tan(d*x/2)^3+384*b*tan(c/2)^5*tan(d*x/2)+96*b*tan(c/2)^4*tan(d*x/2)^6-1824*b*tan(c/2)^4*tan(d*x/2)^4+1824*b*tan(c/2)^4*tan(d*x/2)^2-96*b*tan(c/2)^4-768*b*tan(c/2)^3*tan(d*x/2)^5+3584*b*tan(c/2)^3*tan(d*x/2)^3-768*b*tan(c/2)^3*tan(d*x/2)-96*b*tan(c/2)^2*tan(d*x/2)^6+1824*b*tan(c/2)^2*tan(d*x/2)^4-1824*b*tan(c/2)^2*tan(d*x/2)^2+96*b*tan(c/2)^2+384*b*tan(c/2)*tan(d*x/2)^5-768*b*tan(c/2)*tan(d*x/2)^3+384*b*tan(c/2)*tan(d*x/2)+32*b*tan(d*x/2)^6-96*b*tan(d*x/2)^4+96*b*tan(d*x/2)^2-32*b)/(96*d*tan(c/2)^6*tan(d*x/2)^6+288*d*tan(c/2)^6*tan(d*x/2)^4+288*d*tan(c/2)^6*tan(d*x/2)^2+96*d*tan(c/2)^6+288*d*tan(c/2)^4*tan(d*x/2)^6+864*d*tan(c/2)^4*tan(d*x/2)^4+864*d*tan(c/2)^4*tan(d*x/2)^2+288*d*tan(c/2)^4+288*d*tan(c/2)^2*tan(d*x/2)^6+864*d*tan(c/2)^2*tan(d*x/2)^4+864*d*tan(c/2)^2*tan(d*x/2)^2+288*d*tan(c/2)^2+96*d*tan(d*x/2)^6+288*d*tan(d*x/2)^4+288*d*tan(d*x/2)^2+96*d)","F(-2)",0
230,1,99,0,3.260192," ","integrate(cos(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{a \cos\left(3 \, d x + 3 \, c\right)}{12 \, d} - \frac{a \cos\left(d x + c\right)}{4 \, d} - \frac{b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - b \tan\left(d x\right)^{2} - 4 \, b \tan\left(d x\right) \tan\left(c\right) - b \tan\left(c\right)^{2} + b}{4 \, {\left(d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} + d \tan\left(c\right)^{2} + d\right)}}"," ",0,"-1/12*a*cos(3*d*x + 3*c)/d - 1/4*a*cos(d*x + c)/d - 1/4*(b*tan(d*x)^2*tan(c)^2 - b*tan(d*x)^2 - 4*b*tan(d*x)*tan(c) - b*tan(c)^2 + b)/(d*tan(d*x)^2*tan(c)^2 + d*tan(d*x)^2 + d*tan(c)^2 + d)","B",0
231,1,102,0,0.270984," ","integrate(cos(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{a \cos\left(2 \, d x + 2 \, c\right)}{4 \, d} - \frac{b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, c\right)^{2} + b}{d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{2} + d \tan\left(\frac{1}{2} \, c\right)^{2} + d}"," ",0,"-1/4*a*cos(2*d*x + 2*c)/d - (b*tan(1/2*d*x)^2*tan(1/2*c)^2 - b*tan(1/2*d*x)^2 - 4*b*tan(1/2*d*x)*tan(1/2*c) - b*tan(1/2*c)^2 + b)/(d*tan(1/2*d*x)^2*tan(1/2*c)^2 + d*tan(1/2*d*x)^2 + d*tan(1/2*c)^2 + d)","B",0
232,1,27,0,0.156832," ","integrate(a*sin(d*x+c)+b*tan(d*x+c),x, algorithm=""giac"")","-\frac{a \cos\left(d x + c\right)}{d} - \frac{b \log\left({\left| \cos\left(d x + c\right) \right|}\right)}{d}"," ",0,"-a*cos(d*x + c)/d - b*log(abs(cos(d*x + c)))/d","A",0
233,1,107,0,0.286681," ","integrate(sec(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right) - a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right) + \frac{a + 2 \, b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}}{\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1}}{d}"," ",0,"(a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)) - a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)) + (a + 2*b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/d","B",0
234,1,71,0,0.293249," ","integrate(sec(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(a + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{d {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{2}}"," ",0,"2*(a + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/(d*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^2)","B",0
235,1,97,0,0.354791," ","integrate(sec(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(b - \frac{3 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{3 \, a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{3 \, d {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}^{3}}"," ",0,"2/3*(b - 3*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 3*a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 3*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/(d*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)^3)","B",0
236,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
237,1,5161,0,7.762298," ","integrate(cos(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{8} \, a^{2} x - \frac{a^{2} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{3 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + 3 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} + 9 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 9 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + 3 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + 3 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right) + 3 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + 9 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} + 9 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} + 9 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 27 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 9 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 9 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + 9 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} - 3 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} + 9 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 9 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right) - 3 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right) - 32 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 9 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(c\right)^{2} - 32 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + 9 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + 9 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} + 27 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + 9 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} + 9 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} + 9 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(c\right)^{2} + 27 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 9 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 27 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 27 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 3 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + 9 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} - 32 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{3} - 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{4} - 9 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} - 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{5} - 32 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{6} - 9 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} + 9 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) + 27 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 9 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 9 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right) - 9 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right) + 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 9 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 288 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 32 \, a b \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 288 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 27 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 96 \, a b \tan\left(\frac{1}{2} \, d x\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(c\right)^{2} - 96 \, a b \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(c\right)^{2} + 9 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} - 32 \, a b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + 3 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} + 27 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 9 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} + 27 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + 27 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} + 9 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} + 9 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 3 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(c\right)^{2} + 27 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 27 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 9 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 27 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 3 \, b^{2} d x \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{2} - 9 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} + 288 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{3} - 32 \, a b \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{3} + 288 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} - 27 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 96 \, a b \tan\left(\frac{1}{2} \, d x\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{4} + 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{5} - 96 \, a b \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{5} - 9 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} - 32 \, a b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(c\right) + 27 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - 9 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) + 27 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 27 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 3 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right) - 9 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right) + 3 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(c\right)^{2} - 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - 288 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 27 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 96 \, a b \tan\left(\frac{1}{2} \, d x\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} - 288 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 288 \, a b \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 27 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 288 \, a b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 96 \, a b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(c\right)^{2} + 3 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + 9 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} + 3 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{6} + 27 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 27 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 9 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + 27 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, b^{2} d x \tan\left(\frac{1}{2} \, c\right)^{6} + 9 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + 9 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 9 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 27 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 9 \, b^{2} d x \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 3 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{6} - 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 288 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} - 27 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 96 \, a b \tan\left(\frac{1}{2} \, d x\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{2} - 288 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{3} + 288 \, a b \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{3} - 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} - 27 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + 288 \, a b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} + 96 \, a b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{5} - 3 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{6} + 9 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) - 3 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(c\right) + 27 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - 27 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) + 9 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 27 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) - 3 \, b^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right) + 32 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(c\right)^{2} + 9 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - 96 \, a b \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 27 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} - 288 \, a b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 32 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} - 288 \, a b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 9 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} - 96 \, a b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 9 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + 9 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{4} + 9 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 27 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 9 \, b^{2} d x \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 9 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + 9 \, b^{2} d x \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 32 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{3} - 9 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{4} + 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 96 \, a b \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 96 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 27 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 288 \, a b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 32 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{3} - 288 \, a b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{3} - 9 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} - 96 \, a b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{4} + 9 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right) - 9 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right) + 9 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - 27 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - 9 \, b^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right) + 9 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + 32 \, a b \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(c\right)^{2} + 96 \, a b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 9 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 96 \, a b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 32 \, a b \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(c\right)^{2} + 3 \, b^{2} d x \tan\left(d x\right)^{2} + 9 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} + 9 \, b^{2} d x \tan\left(\frac{1}{2} \, c\right)^{2} + 3 \, b^{2} d x \tan\left(c\right)^{2} - 9 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 32 \, a b \tan\left(\frac{1}{2} \, d x\right)^{3} + 96 \, a b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 9 \, b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 96 \, a b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 32 \, a b \tan\left(\frac{1}{2} \, c\right)^{3} + 3 \, b^{2} \tan\left(d x\right)^{2} \tan\left(c\right) - 9 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right) - 9 \, b^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) + 3 \, b^{2} \tan\left(d x\right) \tan\left(c\right)^{2} + 3 \, b^{2} d x - 3 \, b^{2} \tan\left(d x\right) - 3 \, b^{2} \tan\left(c\right)}{6 \, {\left(d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 3 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + 3 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} + d \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 9 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 3 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + 3 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} + 9 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(c\right)^{2} + 9 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 9 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 9 \, d \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{6} + 9 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} + 9 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + 9 \, d \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{6} \tan\left(c\right)^{2} + 9 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 9 \, d \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 3 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 9 \, d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + d \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(c\right)^{2} + 3 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{4} + d \tan\left(\frac{1}{2} \, d x\right)^{6} + 9 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 9 \, d \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 3 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + 9 \, d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + d \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(c\right)^{2} + 3 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 9 \, d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 3 \, d \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(c\right)^{2} + 3 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{4} + 3 \, d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 9 \, d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 3 \, d \tan\left(\frac{1}{2} \, c\right)^{4} + d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + 3 \, d \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} + 3 \, d \tan\left(\frac{1}{2} \, d x\right)^{2} + 3 \, d \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(c\right)^{2} + d\right)}}"," ",0,"1/8*a^2*x - 1/32*a^2*sin(4*d*x + 4*c)/d + 1/6*(3*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + 3*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6 + 9*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 + 9*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^2 + 3*b^2*d*x*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + 3*b^2*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c) + 3*b^2*tan(d*x)*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + 9*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4 + 9*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6 + 3*b^2*d*x*tan(1/2*d*x)^6*tan(1/2*c)^6 + 9*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 + 27*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 9*b^2*d*x*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 + 9*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 + 9*b^2*d*x*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^2 - 3*b^2*tan(d*x)*tan(1/2*d*x)^6*tan(1/2*c)^6 + 9*b^2*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c) + 9*b^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c) - 3*b^2*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c) - 32*a*b*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^3*tan(c)^2 - 96*a*b*tan(d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)^4*tan(c)^2 + 9*b^2*tan(d*x)*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 - 96*a*b*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^5*tan(c)^2 - 32*a*b*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^6*tan(c)^2 + 9*b^2*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^2 + 9*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2 + 27*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4 + 9*b^2*d*x*tan(1/2*d*x)^6*tan(1/2*c)^4 + 9*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^6 + 9*b^2*d*x*tan(1/2*d*x)^4*tan(1/2*c)^6 + 3*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^6*tan(c)^2 + 27*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^2 + 9*b^2*d*x*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 + 27*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 + 27*b^2*d*x*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 3*b^2*d*x*tan(d*x)^2*tan(1/2*c)^6*tan(c)^2 + 9*b^2*d*x*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 - 32*a*b*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^3 - 96*a*b*tan(d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)^4 - 9*b^2*tan(d*x)*tan(1/2*d*x)^6*tan(1/2*c)^4 - 96*a*b*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^5 - 32*a*b*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^6 - 9*b^2*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^6 + 9*b^2*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c) + 27*b^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) - 9*b^2*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c) + 9*b^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c) - 9*b^2*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c) + 96*a*b*tan(d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)^2*tan(c)^2 + 9*b^2*tan(d*x)*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 + 288*a*b*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^3*tan(c)^2 - 32*a*b*tan(1/2*d*x)^6*tan(1/2*c)^3*tan(c)^2 + 288*a*b*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^4*tan(c)^2 + 27*b^2*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 - 96*a*b*tan(1/2*d*x)^5*tan(1/2*c)^4*tan(c)^2 + 96*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^5*tan(c)^2 - 96*a*b*tan(1/2*d*x)^4*tan(1/2*c)^5*tan(c)^2 + 9*b^2*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 - 32*a*b*tan(1/2*d*x)^3*tan(1/2*c)^6*tan(c)^2 + 3*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^6 + 27*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2 + 9*b^2*d*x*tan(1/2*d*x)^6*tan(1/2*c)^2 + 27*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^4 + 27*b^2*d*x*tan(1/2*d*x)^4*tan(1/2*c)^4 + 3*b^2*d*x*tan(d*x)^2*tan(1/2*c)^6 + 9*b^2*d*x*tan(1/2*d*x)^2*tan(1/2*c)^6 + 9*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^2 + 3*b^2*d*x*tan(1/2*d*x)^6*tan(c)^2 + 27*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 27*b^2*d*x*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^2 + 9*b^2*d*x*tan(d*x)^2*tan(1/2*c)^4*tan(c)^2 + 27*b^2*d*x*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 + 3*b^2*d*x*tan(1/2*c)^6*tan(c)^2 + 96*a*b*tan(d*x)^2*tan(1/2*d*x)^5*tan(1/2*c)^2 - 9*b^2*tan(d*x)*tan(1/2*d*x)^6*tan(1/2*c)^2 + 288*a*b*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^3 - 32*a*b*tan(1/2*d*x)^6*tan(1/2*c)^3 + 288*a*b*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^4 - 27*b^2*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^4 - 96*a*b*tan(1/2*d*x)^5*tan(1/2*c)^4 + 96*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^5 - 96*a*b*tan(1/2*d*x)^4*tan(1/2*c)^5 - 9*b^2*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^6 - 32*a*b*tan(1/2*d*x)^3*tan(1/2*c)^6 + 3*b^2*tan(d*x)^2*tan(1/2*d*x)^6*tan(c) + 27*b^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c) - 9*b^2*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c) + 27*b^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c) - 27*b^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c) + 3*b^2*tan(d*x)^2*tan(1/2*c)^6*tan(c) - 9*b^2*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c) + 3*b^2*tan(d*x)*tan(1/2*d*x)^6*tan(c)^2 - 96*a*b*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)*tan(c)^2 - 288*a*b*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^2*tan(c)^2 + 27*b^2*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^2 + 96*a*b*tan(1/2*d*x)^5*tan(1/2*c)^2*tan(c)^2 - 288*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^3*tan(c)^2 + 288*a*b*tan(1/2*d*x)^4*tan(1/2*c)^3*tan(c)^2 - 96*a*b*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^4*tan(c)^2 + 27*b^2*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 + 288*a*b*tan(1/2*d*x)^3*tan(1/2*c)^4*tan(c)^2 + 96*a*b*tan(1/2*d*x)^2*tan(1/2*c)^5*tan(c)^2 + 3*b^2*tan(d*x)*tan(1/2*c)^6*tan(c)^2 + 9*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^4 + 3*b^2*d*x*tan(1/2*d*x)^6 + 27*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 27*b^2*d*x*tan(1/2*d*x)^4*tan(1/2*c)^2 + 9*b^2*d*x*tan(d*x)^2*tan(1/2*c)^4 + 27*b^2*d*x*tan(1/2*d*x)^2*tan(1/2*c)^4 + 3*b^2*d*x*tan(1/2*c)^6 + 9*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 + 9*b^2*d*x*tan(1/2*d*x)^4*tan(c)^2 + 9*b^2*d*x*tan(d*x)^2*tan(1/2*c)^2*tan(c)^2 + 27*b^2*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 9*b^2*d*x*tan(1/2*c)^4*tan(c)^2 - 3*b^2*tan(d*x)*tan(1/2*d*x)^6 - 96*a*b*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c) - 288*a*b*tan(d*x)^2*tan(1/2*d*x)^3*tan(1/2*c)^2 - 27*b^2*tan(d*x)*tan(1/2*d*x)^4*tan(1/2*c)^2 + 96*a*b*tan(1/2*d*x)^5*tan(1/2*c)^2 - 288*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^3 + 288*a*b*tan(1/2*d*x)^4*tan(1/2*c)^3 - 96*a*b*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^4 - 27*b^2*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^4 + 288*a*b*tan(1/2*d*x)^3*tan(1/2*c)^4 + 96*a*b*tan(1/2*d*x)^2*tan(1/2*c)^5 - 3*b^2*tan(d*x)*tan(1/2*c)^6 + 9*b^2*tan(d*x)^2*tan(1/2*d*x)^4*tan(c) - 3*b^2*tan(1/2*d*x)^6*tan(c) + 27*b^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - 27*b^2*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c) + 9*b^2*tan(d*x)^2*tan(1/2*c)^4*tan(c) - 27*b^2*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c) - 3*b^2*tan(1/2*c)^6*tan(c) + 32*a*b*tan(d*x)^2*tan(1/2*d*x)^3*tan(c)^2 + 9*b^2*tan(d*x)*tan(1/2*d*x)^4*tan(c)^2 + 96*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)*tan(c)^2 - 96*a*b*tan(1/2*d*x)^4*tan(1/2*c)*tan(c)^2 + 96*a*b*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^2*tan(c)^2 + 27*b^2*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 - 288*a*b*tan(1/2*d*x)^3*tan(1/2*c)^2*tan(c)^2 + 32*a*b*tan(d*x)^2*tan(1/2*c)^3*tan(c)^2 - 288*a*b*tan(1/2*d*x)^2*tan(1/2*c)^3*tan(c)^2 + 9*b^2*tan(d*x)*tan(1/2*c)^4*tan(c)^2 - 96*a*b*tan(1/2*d*x)*tan(1/2*c)^4*tan(c)^2 + 9*b^2*d*x*tan(d*x)^2*tan(1/2*d*x)^2 + 9*b^2*d*x*tan(1/2*d*x)^4 + 9*b^2*d*x*tan(d*x)^2*tan(1/2*c)^2 + 27*b^2*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + 9*b^2*d*x*tan(1/2*c)^4 + 3*b^2*d*x*tan(d*x)^2*tan(c)^2 + 9*b^2*d*x*tan(1/2*d*x)^2*tan(c)^2 + 9*b^2*d*x*tan(1/2*c)^2*tan(c)^2 + 32*a*b*tan(d*x)^2*tan(1/2*d*x)^3 - 9*b^2*tan(d*x)*tan(1/2*d*x)^4 + 96*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c) - 96*a*b*tan(1/2*d*x)^4*tan(1/2*c) + 96*a*b*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^2 - 27*b^2*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 288*a*b*tan(1/2*d*x)^3*tan(1/2*c)^2 + 32*a*b*tan(d*x)^2*tan(1/2*c)^3 - 288*a*b*tan(1/2*d*x)^2*tan(1/2*c)^3 - 9*b^2*tan(d*x)*tan(1/2*c)^4 - 96*a*b*tan(1/2*d*x)*tan(1/2*c)^4 + 9*b^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(c) - 9*b^2*tan(1/2*d*x)^4*tan(c) + 9*b^2*tan(d*x)^2*tan(1/2*c)^2*tan(c) - 27*b^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - 9*b^2*tan(1/2*c)^4*tan(c) + 9*b^2*tan(d*x)*tan(1/2*d*x)^2*tan(c)^2 + 32*a*b*tan(1/2*d*x)^3*tan(c)^2 + 96*a*b*tan(1/2*d*x)^2*tan(1/2*c)*tan(c)^2 + 9*b^2*tan(d*x)*tan(1/2*c)^2*tan(c)^2 + 96*a*b*tan(1/2*d*x)*tan(1/2*c)^2*tan(c)^2 + 32*a*b*tan(1/2*c)^3*tan(c)^2 + 3*b^2*d*x*tan(d*x)^2 + 9*b^2*d*x*tan(1/2*d*x)^2 + 9*b^2*d*x*tan(1/2*c)^2 + 3*b^2*d*x*tan(c)^2 - 9*b^2*tan(d*x)*tan(1/2*d*x)^2 + 32*a*b*tan(1/2*d*x)^3 + 96*a*b*tan(1/2*d*x)^2*tan(1/2*c) - 9*b^2*tan(d*x)*tan(1/2*c)^2 + 96*a*b*tan(1/2*d*x)*tan(1/2*c)^2 + 32*a*b*tan(1/2*c)^3 + 3*b^2*tan(d*x)^2*tan(c) - 9*b^2*tan(1/2*d*x)^2*tan(c) - 9*b^2*tan(1/2*c)^2*tan(c) + 3*b^2*tan(d*x)*tan(c)^2 + 3*b^2*d*x - 3*b^2*tan(d*x) - 3*b^2*tan(c))/(d*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + d*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^6 + 3*d*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 + 3*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^2 + d*tan(1/2*d*x)^6*tan(1/2*c)^6*tan(c)^2 + 3*d*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^4 + 3*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^6 + d*tan(1/2*d*x)^6*tan(1/2*c)^6 + 3*d*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 + 9*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + 3*d*tan(1/2*d*x)^6*tan(1/2*c)^4*tan(c)^2 + 3*d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 + 3*d*tan(1/2*d*x)^4*tan(1/2*c)^6*tan(c)^2 + 3*d*tan(d*x)^2*tan(1/2*d*x)^6*tan(1/2*c)^2 + 9*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^4 + 3*d*tan(1/2*d*x)^6*tan(1/2*c)^4 + 3*d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^6 + 3*d*tan(1/2*d*x)^4*tan(1/2*c)^6 + d*tan(d*x)^2*tan(1/2*d*x)^6*tan(c)^2 + 9*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^2 + 3*d*tan(1/2*d*x)^6*tan(1/2*c)^2*tan(c)^2 + 9*d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 + 9*d*tan(1/2*d*x)^4*tan(1/2*c)^4*tan(c)^2 + d*tan(d*x)^2*tan(1/2*c)^6*tan(c)^2 + 3*d*tan(1/2*d*x)^2*tan(1/2*c)^6*tan(c)^2 + d*tan(d*x)^2*tan(1/2*d*x)^6 + 9*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(1/2*c)^2 + 3*d*tan(1/2*d*x)^6*tan(1/2*c)^2 + 9*d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^4 + 9*d*tan(1/2*d*x)^4*tan(1/2*c)^4 + d*tan(d*x)^2*tan(1/2*c)^6 + 3*d*tan(1/2*d*x)^2*tan(1/2*c)^6 + 3*d*tan(d*x)^2*tan(1/2*d*x)^4*tan(c)^2 + d*tan(1/2*d*x)^6*tan(c)^2 + 9*d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 9*d*tan(1/2*d*x)^4*tan(1/2*c)^2*tan(c)^2 + 3*d*tan(d*x)^2*tan(1/2*c)^4*tan(c)^2 + 9*d*tan(1/2*d*x)^2*tan(1/2*c)^4*tan(c)^2 + d*tan(1/2*c)^6*tan(c)^2 + 3*d*tan(d*x)^2*tan(1/2*d*x)^4 + d*tan(1/2*d*x)^6 + 9*d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 9*d*tan(1/2*d*x)^4*tan(1/2*c)^2 + 3*d*tan(d*x)^2*tan(1/2*c)^4 + 9*d*tan(1/2*d*x)^2*tan(1/2*c)^4 + d*tan(1/2*c)^6 + 3*d*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 + 3*d*tan(1/2*d*x)^4*tan(c)^2 + 3*d*tan(d*x)^2*tan(1/2*c)^2*tan(c)^2 + 9*d*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 3*d*tan(1/2*c)^4*tan(c)^2 + 3*d*tan(d*x)^2*tan(1/2*d*x)^2 + 3*d*tan(1/2*d*x)^4 + 3*d*tan(d*x)^2*tan(1/2*c)^2 + 9*d*tan(1/2*d*x)^2*tan(1/2*c)^2 + 3*d*tan(1/2*c)^4 + d*tan(d*x)^2*tan(c)^2 + 3*d*tan(1/2*d*x)^2*tan(c)^2 + 3*d*tan(1/2*c)^2*tan(c)^2 + d*tan(d*x)^2 + 3*d*tan(1/2*d*x)^2 + 3*d*tan(1/2*c)^2 + d*tan(c)^2 + d)","B",0
238,1,5713,0,4.221345," ","integrate(cos(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{a^{2} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{a^{2} \sin\left(d x + c\right)}{4 \, d} + \frac{2 \, a b d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 2 \, a b d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a b d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + 2 \, a b d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 2 \, a b d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + 4 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 4 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 2 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 2 \, a b d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, a b d x \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a b d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a b d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 2 \, a b d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + 2 \, a b d x \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right) + 2 \, a b \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - 2 \, a b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 4 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(c\right)^{2} - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + 2 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} - 4 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 4 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 2 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 4 \, b^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + 2 \, a b d x \tan\left(d x\right)^{2} + 2 \, a b d x \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, a b d x \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a b d x \tan\left(c\right)^{2} - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} - 4 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right) - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, b^{2} \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{2} + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a b \tan\left(d x\right)^{2} \tan\left(c\right) - 2 \, a b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right) - 2 \, a b \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(c\right)^{2} + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(c\right)^{2} + 2 \, a b \tan\left(d x\right) \tan\left(c\right)^{2} - 4 \, b^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(c\right)^{2} - 4 \, b^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right)^{2} + 2 \, a b d x - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) - 2 \, a b \tan\left(d x\right) - 4 \, b^{2} \tan\left(\frac{1}{2} \, d x\right) - 4 \, b^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a b \tan\left(c\right)}{2 \, {\left(d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right)^{2} + d \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{2} + d \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(c\right)^{2} + d\right)}}"," ",0,"-1/12*a^2*sin(3*d*x + 3*c)/d + 1/4*a^2*sin(d*x + c)/d + 1/2*(2*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 2*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 + 2*a*b*d*x*tan(d*x)^2*tan(1/2*c)^2*tan(c)^2 + 2*a*b*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 + 4*b^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)*tan(c)^2 - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)^2*tan(1/2*c)^2*tan(c)^2 + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)^2*tan(1/2*c)^2*tan(c)^2 + 4*b^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^2*tan(c)^2 - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 2*a*b*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + 2*a*b*d*x*tan(d*x)^2*tan(1/2*d*x)^2 + 2*a*b*d*x*tan(d*x)^2*tan(1/2*c)^2 + 2*a*b*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*b*d*x*tan(d*x)^2*tan(c)^2 + 2*a*b*d*x*tan(1/2*d*x)^2*tan(c)^2 + 2*a*b*d*x*tan(1/2*c)^2*tan(c)^2 - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)^2*tan(1/2*d*x)^2 + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)^2*tan(1/2*d*x)^2 + 4*b^2*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c) - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)^2*tan(1/2*c)^2 + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)^2*tan(1/2*c)^2 + 4*b^2*tan(d*x)^2*tan(1/2*d*x)*tan(1/2*c)^2 - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(1/2*c)^2 + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a*b*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*b*tan(d*x)^2*tan(1/2*d*x)^2*tan(c) + 2*a*b*tan(d*x)^2*tan(1/2*c)^2*tan(c) - 2*a*b*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)^2*tan(c)^2 + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)^2*tan(c)^2 - 4*b^2*tan(d*x)^2*tan(1/2*d*x)*tan(c)^2 - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(c)^2 + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(c)^2 + 2*a*b*tan(d*x)*tan(1/2*d*x)^2*tan(c)^2 - 4*b^2*tan(d*x)^2*tan(1/2*c)*tan(c)^2 + 4*b^2*tan(1/2*d*x)^2*tan(1/2*c)*tan(c)^2 - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^2*tan(c)^2 + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^2*tan(c)^2 + 2*a*b*tan(d*x)*tan(1/2*c)^2*tan(c)^2 + 4*b^2*tan(1/2*d*x)*tan(1/2*c)^2*tan(c)^2 + 2*a*b*d*x*tan(d*x)^2 + 2*a*b*d*x*tan(1/2*d*x)^2 + 2*a*b*d*x*tan(1/2*c)^2 + 2*a*b*d*x*tan(c)^2 - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)^2 + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)^2 - 4*b^2*tan(d*x)^2*tan(1/2*d*x) - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2 + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2 - 2*a*b*tan(d*x)*tan(1/2*d*x)^2 - 4*b^2*tan(d*x)^2*tan(1/2*c) + 4*b^2*tan(1/2*d*x)^2*tan(1/2*c) - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^2 + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^2 - 2*a*b*tan(d*x)*tan(1/2*c)^2 + 4*b^2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*a*b*tan(d*x)^2*tan(c) - 2*a*b*tan(1/2*d*x)^2*tan(c) - 2*a*b*tan(1/2*c)^2*tan(c) - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(c)^2 + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(c)^2 + 2*a*b*tan(d*x)*tan(c)^2 - 4*b^2*tan(1/2*d*x)*tan(c)^2 - 4*b^2*tan(1/2*c)*tan(c)^2 + 2*a*b*d*x - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1)) + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1)) - 2*a*b*tan(d*x) - 4*b^2*tan(1/2*d*x) - 4*b^2*tan(1/2*c) - 2*a*b*tan(c))/(d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + d*tan(d*x)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + d*tan(d*x)^2*tan(1/2*d*x)^2*tan(c)^2 + d*tan(d*x)^2*tan(1/2*c)^2*tan(c)^2 + d*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c)^2 + d*tan(d*x)^2*tan(1/2*d*x)^2 + d*tan(d*x)^2*tan(1/2*c)^2 + d*tan(1/2*d*x)^2*tan(1/2*c)^2 + d*tan(d*x)^2*tan(c)^2 + d*tan(1/2*d*x)^2*tan(c)^2 + d*tan(1/2*c)^2*tan(c)^2 + d*tan(d*x)^2 + d*tan(1/2*d*x)^2 + d*tan(1/2*c)^2 + d*tan(c)^2 + d)","B",0
239,1,2752,0,1.275513," ","integrate((a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{2} \, a^{2} x - \frac{a^{2} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} - \frac{b^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) + a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + b^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right) + b^{2} d x \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right) - a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right) - 4 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) + a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - 4 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) + b^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} - b^{2} d x \tan\left(\frac{1}{2} \, c\right)^{2} + b^{2} d x \tan\left(d x\right) \tan\left(c\right) - a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, a b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{2} + a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{2} + b^{2} \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right) - a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(d x\right) \tan\left(c\right) + 4 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right) \tan\left(c\right) + b^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right) + 4 \, a b \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(c\right) + b^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - b^{2} d x - a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) + a b \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) + b^{2} \tan\left(d x\right) - 4 \, a b \tan\left(\frac{1}{2} \, d x\right) - 4 \, a b \tan\left(\frac{1}{2} \, c\right) + b^{2} \tan\left(c\right)}{d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(c\right) + d \tan\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(c\right) - d \tan\left(\frac{1}{2} \, d x\right)^{2} - d \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(d x\right) \tan\left(c\right) - d}"," ",0,"1/2*a^2*x - 1/4*a^2*sin(2*d*x + 2*c)/d - (b^2*d*x*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) + a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - b^2*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + b^2*d*x*tan(d*x)*tan(1/2*d*x)^2*tan(c) + b^2*d*x*tan(d*x)*tan(1/2*c)^2*tan(c) - a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(1/2*c)^2 + a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(1/2*c)^2 + b^2*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 + a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)*tan(1/2*d*x)^2*tan(c) - a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)*tan(1/2*d*x)^2*tan(c) - 4*a*b*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)*tan(c) + a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)*tan(1/2*c)^2*tan(c) - a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)*tan(1/2*c)^2*tan(c) - 4*a*b*tan(d*x)*tan(1/2*d*x)*tan(1/2*c)^2*tan(c) + b^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - b^2*d*x*tan(1/2*d*x)^2 - b^2*d*x*tan(1/2*c)^2 + b^2*d*x*tan(d*x)*tan(c) - a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2 + a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2 + b^2*tan(d*x)*tan(1/2*d*x)^2 + 4*a*b*tan(1/2*d*x)^2*tan(1/2*c) - a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^2 + a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^2 + b^2*tan(d*x)*tan(1/2*c)^2 + 4*a*b*tan(1/2*d*x)*tan(1/2*c)^2 + a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)*tan(c) - a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(d*x)*tan(c) + 4*a*b*tan(d*x)*tan(1/2*d*x)*tan(c) + b^2*tan(1/2*d*x)^2*tan(c) + 4*a*b*tan(d*x)*tan(1/2*c)*tan(c) + b^2*tan(1/2*c)^2*tan(c) - b^2*d*x - a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1)) + a*b*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1)) + b^2*tan(d*x) - 4*a*b*tan(1/2*d*x) - 4*a*b*tan(1/2*c) + b^2*tan(c))/(d*tan(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(c) - d*tan(1/2*d*x)^2*tan(1/2*c)^2 + d*tan(d*x)*tan(1/2*d*x)^2*tan(c) + d*tan(d*x)*tan(1/2*c)^2*tan(c) - d*tan(1/2*d*x)^2 - d*tan(1/2*c)^2 + d*tan(d*x)*tan(c) - d)","B",0
240,1,171,0,1.584654," ","integrate(sec(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{4 \, {\left(d x + c\right)} a b - {\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{4 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + \frac{2 \, {\left(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*(4*(d*x + c)*a*b - (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)) + 4*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 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
241,1,158,0,2.093064," ","integrate(sec(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{3 \, {\left(d x + c\right)} a^{2} + 3 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(d*x + c)*a^2 + 3*a*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*a*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(3*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*a*b*tan(1/2*d*x + 1/2*c)^5 - 6*a^2*tan(1/2*d*x + 1/2*c)^3 + 4*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*a^2*tan(1/2*d*x + 1/2*c) + 3*a*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
242,1,226,0,1.889380," ","integrate(sec(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{3 \, {\left(4 \, a^{2} + 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} + 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} + 3 \, 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} - 64 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, 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} + 64 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, 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) + 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)}^{4}}}{24 \, d}"," ",0,"-1/24*(3*(4*a^2 + b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*a^2 + 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 + 3*b^2*tan(1/2*d*x + 1/2*c)^7 - 12*a^2*tan(1/2*d*x + 1/2*c)^5 - 64*a*b*tan(1/2*d*x + 1/2*c)^5 + 21*b^2*tan(1/2*d*x + 1/2*c)^5 - 12*a^2*tan(1/2*d*x + 1/2*c)^3 + 64*a*b*tan(1/2*d*x + 1/2*c)^3 + 21*b^2*tan(1/2*d*x + 1/2*c)^3 + 12*a^2*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)^4)/d","A",0
243,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
245,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
246,-2,0,0,0.000000," ","integrate((a*sin(d*x+c)+b*tan(d*x+c))^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:Modgcd: no suitable evaluation pointindex.cc index_m operator + Error: Bad Argument ValueUnable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Evaluation time: 62.4Done","F(-2)",0
247,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))^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:Modgcd: no suitable evaluation pointindex.cc index_m operator + Error: Bad Argument ValueUnable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (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: 61.28Done","F(-2)",0
248,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c))^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:Modgcd: no suitable evaluation pointindex.cc index_m operator + Error: Bad Argument ValueUnable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (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: 76.28Done","F(-2)",0
249,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^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:Modgcd: no suitable evaluation pointindex.cc index_m operator + Error: Bad Argument ValueUnable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (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: 78.52Done","F(-2)",0
250,1,303,0,0.397359," ","integrate(cos(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, b^{4} \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{5} - a^{3} b^{2}} - \frac{\log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a + b} + \frac{2 \, {\left(a^{2} + b^{2}\right)} \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{3}} - \frac{3 \, a^{2} - 4 \, a b + 3 \, b^{2} - \frac{2 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{4 \, a b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{6 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a^{3} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(2*b^4*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^5 - a^3*b^2) - log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a + b) + 2*(a^2 + b^2)*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^3 - (3*a^2 - 4*a*b + 3*b^2 - 2*a^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 4*a*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 6*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 3*a^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 3*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/(a^3*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)^2))/d","B",0
251,1,190,0,0.354546," ","integrate(cos(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, b^{3} \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{4} - a^{2} b^{2}} + \frac{\log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a + b} + \frac{2 \, b \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{2}} - \frac{2 \, {\left(2 \, a - b + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{a^{2} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1\right)}}}{2 \, d}"," ",0,"1/2*(2*b^3*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^4 - a^2*b^2) + log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a + b) + 2*b*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^2 - 2*(2*a - b + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/(a^2*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1)))/d","B",0
252,1,257,0,0.386709," ","integrate(cos(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{a \log\left({\left| -a - b + \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} \right|}\right)}{a^{2} - b^{2}} - \frac{{\left(a^{2} - 2 \, b^{2}\right)} \log\left(\frac{{\left| -2 \, b - \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - 2 \, {\left| a \right|} \right|}}{{\left| -2 \, b - \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + 2 \, {\left| a \right|} \right|}}\right)}{{\left(a^{2} - b^{2}\right)} {\left| a \right|}} - \frac{\log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a + b}}{2 \, d}"," ",0,"-1/2*(a*log(abs(-a - b + 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2))/(a^2 - b^2) - (a^2 - 2*b^2)*log(abs(-2*b - 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*abs(a))/abs(-2*b - 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*abs(a)))/((a^2 - b^2)*abs(a)) - log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a + b))/d","B",0
253,1,100,0,0.206112," ","integrate(1/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, b \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{2} - b^{2}} + \frac{\log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a + b}}{2 \, d}"," ",0,"1/2*(2*b*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^2 - b^2) + log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a + b))/d","A",0
254,1,101,0,0.321459," ","integrate(sec(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, a \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{2} - b^{2}} - \frac{\log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a + b}}{2 \, d}"," ",0,"-1/2*(2*a*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^2 - b^2) - log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a + b))/d","A",0
255,1,253,0,0.387170," ","integrate(sec(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{b \log\left({\left| a + b + \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} \right|}\right)}{a^{2} - b^{2}} + \frac{{\left(2 \, a^{2} - b^{2}\right)} \log\left(\frac{{\left| -2 \, a - \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - 2 \, {\left| b \right|} \right|}}{{\left| -2 \, a - \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + 2 \, {\left| b \right|} \right|}}\right)}{{\left(a^{2} - b^{2}\right)} {\left| b \right|}} + \frac{\log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a + b}}{2 \, d}"," ",0,"1/2*(b*log(abs(a + b + 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + a*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2))/(a^2 - b^2) + (2*a^2 - b^2)*log(abs(-2*a - 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*abs(b))/abs(-2*a - 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*abs(b)))/((a^2 - b^2)*abs(b)) + log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a + b))/d","B",0
256,1,190,0,0.387985," ","integrate(sec(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, a^{3} \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{2} b^{2} - b^{4}} - \frac{\log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a + b} - \frac{2 \, a \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} - 1 \right|}\right)}{b^{2}} + \frac{2 \, {\left(a - 2 \, b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}}{b^{2} {\left(\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1\right)}}}{2 \, d}"," ",0,"-1/2*(2*a^3*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^2*b^2 - b^4) - log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a + b) - 2*a*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 1))/b^2 + 2*(a - 2*b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))/(b^2*((cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1)))/d","A",0
257,1,1362,0,1.128188," ","integrate(cos(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left({\left(2 \, a^{4} b - 2 \, a^{3} b^{2} - 4 \, a^{2} b^{3} - a b^{4} + 2 \, b^{5}\right)} \sqrt{-a^{2} + b^{2}} {\left| a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4} \right|} {\left| a - b \right|} - {\left(2 \, a^{11} b - 2 \, a^{10} b^{2} - 8 \, a^{9} b^{3} + 13 \, a^{8} b^{4} + 12 \, a^{7} b^{5} - 24 \, a^{6} b^{6} - 8 \, a^{5} b^{7} + 17 \, a^{4} b^{8} + 2 \, a^{3} b^{9} - 4 \, a^{2} b^{10}\right)} \sqrt{-a^{2} + b^{2}} {\left| a - b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5} + \sqrt{{\left(a^{7} + a^{6} b - 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4} + a^{2} b^{5}\right)} {\left(a^{7} - a^{6} b - 2 \, a^{5} b^{2} + 2 \, a^{4} b^{3} + a^{3} b^{4} - a^{2} b^{5}\right)} + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)}^{2}}}{a^{7} - a^{6} b - 2 \, a^{5} b^{2} + 2 \, a^{4} b^{3} + a^{3} b^{4} - a^{2} b^{5}}}}\right)\right)}}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} + {\left(a^{8} b - 2 \, a^{7} b^{2} - a^{6} b^{3} + 4 \, a^{5} b^{4} - a^{4} b^{5} - 2 \, a^{3} b^{6} + a^{2} b^{7}\right)} {\left| a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4} \right|}} + \frac{2 \, {\left(2 \, a^{11} b - 2 \, a^{10} b^{2} - 8 \, a^{9} b^{3} + 13 \, a^{8} b^{4} + 12 \, a^{7} b^{5} - 24 \, a^{6} b^{6} - 8 \, a^{5} b^{7} + 17 \, a^{4} b^{8} + 2 \, a^{3} b^{9} - 4 \, a^{2} b^{10} + 2 \, a^{4} b {\left| a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4} \right|} - 2 \, a^{3} b^{2} {\left| a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4} \right|} - 4 \, a^{2} b^{3} {\left| a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4} \right|} - a b^{4} {\left| a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4} \right|} + 2 \, b^{5} {\left| a^{7} - 2 \, a^{5} b^{2} + a^{3} 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^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5} - \sqrt{{\left(a^{7} + a^{6} b - 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4} + a^{2} b^{5}\right)} {\left(a^{7} - a^{6} b - 2 \, a^{5} b^{2} + 2 \, a^{4} b^{3} + a^{3} b^{4} - a^{2} b^{5}\right)} + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)}^{2}}}{a^{7} - a^{6} b - 2 \, a^{5} b^{2} + 2 \, a^{4} b^{3} + a^{3} b^{4} - a^{2} b^{5}}}}\right)\right)}}{a^{6} b {\left| a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4} \right|} - 2 \, a^{4} b^{3} {\left| a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4} \right|} + a^{2} b^{5} {\left| a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4} \right|} - {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)}^{2}} + \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{5 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 7 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 5 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 7 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 4 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{5} + a^{4} b + a^{3} b^{2} - a^{2} b^{3}}{{\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)^{5} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 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) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}}{2 \, d}"," ",0,"-1/2*(2*((2*a^4*b - 2*a^3*b^2 - 4*a^2*b^3 - a*b^4 + 2*b^5)*sqrt(-a^2 + b^2)*abs(a^7 - 2*a^5*b^2 + a^3*b^4)*abs(a - b) - (2*a^11*b - 2*a^10*b^2 - 8*a^9*b^3 + 13*a^8*b^4 + 12*a^7*b^5 - 24*a^6*b^6 - 8*a^5*b^7 + 17*a^4*b^8 + 2*a^3*b^9 - 4*a^2*b^10)*sqrt(-a^2 + b^2)*abs(a - b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^6*b - 2*a^4*b^3 + a^2*b^5 + sqrt((a^7 + a^6*b - 2*a^5*b^2 - 2*a^4*b^3 + a^3*b^4 + a^2*b^5)*(a^7 - a^6*b - 2*a^5*b^2 + 2*a^4*b^3 + a^3*b^4 - a^2*b^5) + (a^6*b - 2*a^4*b^3 + a^2*b^5)^2))/(a^7 - a^6*b - 2*a^5*b^2 + 2*a^4*b^3 + a^3*b^4 - a^2*b^5))))/((a^7 - 2*a^5*b^2 + a^3*b^4)^2*(a^2 - 2*a*b + b^2) + (a^8*b - 2*a^7*b^2 - a^6*b^3 + 4*a^5*b^4 - a^4*b^5 - 2*a^3*b^6 + a^2*b^7)*abs(a^7 - 2*a^5*b^2 + a^3*b^4)) + 2*(2*a^11*b - 2*a^10*b^2 - 8*a^9*b^3 + 13*a^8*b^4 + 12*a^7*b^5 - 24*a^6*b^6 - 8*a^5*b^7 + 17*a^4*b^8 + 2*a^3*b^9 - 4*a^2*b^10 + 2*a^4*b*abs(a^7 - 2*a^5*b^2 + a^3*b^4) - 2*a^3*b^2*abs(a^7 - 2*a^5*b^2 + a^3*b^4) - 4*a^2*b^3*abs(a^7 - 2*a^5*b^2 + a^3*b^4) - a*b^4*abs(a^7 - 2*a^5*b^2 + a^3*b^4) + 2*b^5*abs(a^7 - 2*a^5*b^2 + a^3*b^4))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^6*b - 2*a^4*b^3 + a^2*b^5 - sqrt((a^7 + a^6*b - 2*a^5*b^2 - 2*a^4*b^3 + a^3*b^4 + a^2*b^5)*(a^7 - a^6*b - 2*a^5*b^2 + 2*a^4*b^3 + a^3*b^4 - a^2*b^5) + (a^6*b - 2*a^4*b^3 + a^2*b^5)^2))/(a^7 - a^6*b - 2*a^5*b^2 + 2*a^4*b^3 + a^3*b^4 - a^2*b^5))))/(a^6*b*abs(a^7 - 2*a^5*b^2 + a^3*b^4) - 2*a^4*b^3*abs(a^7 - 2*a^5*b^2 + a^3*b^4) + a^2*b^5*abs(a^7 - 2*a^5*b^2 + a^3*b^4) - (a^7 - 2*a^5*b^2 + a^3*b^4)^2) + tan(1/2*d*x + 1/2*c)/(a^2 - 2*a*b + b^2) + (5*a^5*tan(1/2*d*x + 1/2*c)^4 - 7*a^4*b*tan(1/2*d*x + 1/2*c)^4 - 5*a^3*b^2*tan(1/2*d*x + 1/2*c)^4 + 7*a^2*b^3*tan(1/2*d*x + 1/2*c)^4 + 4*a*b^4*tan(1/2*d*x + 1/2*c)^4 - 8*b^5*tan(1/2*d*x + 1/2*c)^4 - 4*a^5*tan(1/2*d*x + 1/2*c)^2 - 6*a^4*b*tan(1/2*d*x + 1/2*c)^2 + 12*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 + 6*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 - 4*a*b^4*tan(1/2*d*x + 1/2*c)^2 - 8*b^5*tan(1/2*d*x + 1/2*c)^2 - a^5 + a^4*b + a^3*b^2 - a^2*b^3)/((a^6 - 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*d*x + 1/2*c)^5 - b*tan(1/2*d*x + 1/2*c)^5 - 2*b*tan(1/2*d*x + 1/2*c)^3 - a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))))/d","B",0
258,1,331,0,0.737766," ","integrate(cos(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{4} + a^{3} b + a^{2} b^{2} - a b^{3}}{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}} - \frac{2 \, {\left(d x + c\right)}}{a^{2}}}{2 \, d}"," ",0,"1/2*(4*(4*a^2*b^3 - b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6 - 2*a^4*b^2 + a^2*b^4)*sqrt(-a^2 + b^2)) + tan(1/2*d*x + 1/2*c)/(a^2 - 2*a*b + b^2) - (a^4*tan(1/2*d*x + 1/2*c)^2 - 3*a^3*b*tan(1/2*d*x + 1/2*c)^2 + 3*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - a*b^3*tan(1/2*d*x + 1/2*c)^2 + 4*b^4*tan(1/2*d*x + 1/2*c)^2 - a^4 + a^3*b + a^2*b^2 - a*b^3)/((a^5 - 2*a^3*b^2 + a*b^4)*(a*tan(1/2*d*x + 1/2*c)^3 - b*tan(1/2*d*x + 1/2*c)^3 - a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))) - 2*(d*x + c)/a^2)/d","A",0
259,1,282,0,0.666324," ","integrate(cos(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))^2,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 b^{2}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 5 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{3} + a^{2} b + a b^{2} - b^{3}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}}{2 \, d}"," ",0,"-1/2*(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*b^2/((a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)) + tan(1/2*d*x + 1/2*c)/(a^2 - 2*a*b + b^2) + (a^3*tan(1/2*d*x + 1/2*c)^2 - 3*a^2*b*tan(1/2*d*x + 1/2*c)^2 + 3*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 5*b^3*tan(1/2*d*x + 1/2*c)^2 - a^3 + a^2*b + a*b^2 - b^3)/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^3 - b*tan(1/2*d*x + 1/2*c)^3 - a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))))/d","A",0
260,1,289,0,0.238964," ","integrate(1/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(2 \, a^{2} b + b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{3} + a^{2} b + a b^{2} - b^{3}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}}{2 \, d}"," ",0,"1/2*(4*(2*a^2*b + b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)) + tan(1/2*d*x + 1/2*c)/(a^2 - 2*a*b + b^2) - (a^3*tan(1/2*d*x + 1/2*c)^2 - 3*a^2*b*tan(1/2*d*x + 1/2*c)^2 + 7*a*b^2*tan(1/2*d*x + 1/2*c)^2 - b^3*tan(1/2*d*x + 1/2*c)^2 - a^3 + a^2*b + a*b^2 - b^3)/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^3 - b*tan(1/2*d*x + 1/2*c)^3 - a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))))/d","A",0
261,1,288,0,0.497916," ","integrate(sec(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\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^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{3} + a^{2} b + a b^{2} - b^{3}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}}{2 \, d}"," ",0,"-1/2*(4*(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^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)) + tan(1/2*d*x + 1/2*c)/(a^2 - 2*a*b + b^2) + (a^3*tan(1/2*d*x + 1/2*c)^2 - 7*a^2*b*tan(1/2*d*x + 1/2*c)^2 + 3*a*b^2*tan(1/2*d*x + 1/2*c)^2 - b^3*tan(1/2*d*x + 1/2*c)^2 - a^3 + a^2*b + a*b^2 - b^3)/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^3 - b*tan(1/2*d*x + 1/2*c)^3 - a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))))/d","B",0
262,1,284,0,0.558819," ","integrate(sec(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c))^2,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^{2} b}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{3} + a^{2} b + a b^{2} - b^{3}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}}{2 \, d}"," ",0,"1/2*(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^2*b/((a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)) + tan(1/2*d*x + 1/2*c)/(a^2 - 2*a*b + b^2) - (5*a^3*tan(1/2*d*x + 1/2*c)^2 - 3*a^2*b*tan(1/2*d*x + 1/2*c)^2 + 3*a*b^2*tan(1/2*d*x + 1/2*c)^2 - b^3*tan(1/2*d*x + 1/2*c)^2 - a^3 + a^2*b + a*b^2 - b^3)/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^3 - b*tan(1/2*d*x + 1/2*c)^3 - a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))))/d","B",0
263,1,354,0,0.677584," ","integrate(sec(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(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^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{4 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{3} b - a^{2} b^{2} - a b^{3} + b^{4}}{{\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}} + \frac{2 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{2}} - \frac{2 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{2}}}{2 \, d}"," ",0,"1/2*(4*(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^4*b^2 - 2*a^2*b^4 + b^6)*sqrt(-a^2 + b^2)) - tan(1/2*d*x + 1/2*c)/(a^2 - 2*a*b + b^2) + (4*a^4*tan(1/2*d*x + 1/2*c)^2 - a^3*b*tan(1/2*d*x + 1/2*c)^2 + 3*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*a*b^3*tan(1/2*d*x + 1/2*c)^2 + b^4*tan(1/2*d*x + 1/2*c)^2 + a^3*b - a^2*b^2 - a*b^3 + b^4)/((a^4*b - 2*a^2*b^3 + b^5)*(a*tan(1/2*d*x + 1/2*c)^3 - b*tan(1/2*d*x + 1/2*c)^3 - a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))) + 2*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^2 - 2*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^2)/d","A",0
264,1,848,0,1.635615," ","integrate(cos(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(2 \, a + 5 \, b\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{8 \, {\left(15 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}} - \frac{{\left(a + b + \frac{4 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{10 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} {\left(\cos\left(d x + c\right) - 1\right)}} - \frac{\cos\left(d x + c\right) - 1}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{4 \, {\left(45 \, a^{6} b^{4} + 66 \, a^{5} b^{5} - 15 \, a^{4} b^{6} - 44 \, a^{3} b^{7} - a^{2} b^{8} + 10 \, a b^{9} + 3 \, b^{10} + \frac{90 \, a^{6} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{24 \, a^{5} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{118 \, a^{4} b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{28 \, a^{3} b^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{34 \, a^{2} b^{8} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{4 \, a b^{9} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{6 \, b^{10} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{45 \, a^{6} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{90 \, a^{5} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{33 \, a^{4} b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{24 \, a^{3} b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{9 \, a^{2} b^{8} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, a b^{9} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, b^{10} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{{\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} {\left(a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}^{2}} - \frac{8 \, \log\left({\left| -\frac{\cos\left(d x + c\right) - 1}{\cos\left(d x + c\right) + 1} + 1 \right|}\right)}{a^{3}}}{8 \, d}"," ",0,"-1/8*(2*(2*a + 5*b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + 8*(15*a^4*b^4 - 4*a^2*b^6 + b^8)*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8) - (a + b + 4*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 10*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*(cos(d*x + c) + 1)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*(cos(d*x + c) - 1)) - (cos(d*x + c) - 1)/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(cos(d*x + c) + 1)) - 4*(45*a^6*b^4 + 66*a^5*b^5 - 15*a^4*b^6 - 44*a^3*b^7 - a^2*b^8 + 10*a*b^9 + 3*b^10 + 90*a^6*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 24*a^5*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 118*a^4*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 28*a^3*b^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 34*a^2*b^8*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 4*a*b^9*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 6*b^10*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 45*a^6*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 90*a^5*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 33*a^4*b^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 24*a^3*b^7*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 9*a^2*b^8*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 6*a*b^9*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 3*b^10*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))^2) - 8*log(abs(-(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 1))/a^3)/d","B",0
265,1,676,0,1.393951," ","integrate(cos(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(a + 4 \, b\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{16 \, {\left(5 \, a^{2} b^{3} + b^{5}\right)} \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} - \frac{{\left(a + b + \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{8 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} {\left(\cos\left(d x + c\right) - 1\right)}} + \frac{\cos\left(d x + c\right) - 1}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{8 \, {\left(15 \, a^{4} b^{3} + 20 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 4 \, a b^{6} + 3 \, b^{7} + \frac{30 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{10 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{26 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{10 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{4 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{15 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{30 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{18 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}^{2}}}{8 \, d}"," ",0,"-1/8*(2*(a + 4*b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - 16*(5*a^2*b^3 + b^5)*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) - (a + b + 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 8*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*(cos(d*x + c) + 1)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*(cos(d*x + c) - 1)) + (cos(d*x + c) - 1)/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(cos(d*x + c) + 1)) + 8*(15*a^4*b^3 + 20*a^3*b^4 - 2*a^2*b^5 - 4*a*b^6 + 3*b^7 + 30*a^4*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 10*a^3*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 26*a^2*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 10*a*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 4*b^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 15*a^4*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 30*a^3*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 18*a^2*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 6*a*b^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 3*b^7*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))^2))/d","B",0
266,1,690,0,1.437434," ","integrate(cos(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{6 \, b \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{48 \, {\left(a^{3} b^{2} + a b^{4}\right)} \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} - \frac{{\left(a + b + \frac{6 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} {\left(\cos\left(d x + c\right) - 1\right)}} - \frac{\cos\left(d x + c\right) - 1}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{8 \, {\left(9 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 2 \, a^{3} b^{4} + 8 \, a^{2} b^{5} + 5 \, a b^{6} - 2 \, b^{7} + \frac{18 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{8 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{6 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{16 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{9 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{18 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{18 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{18 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{9 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}^{2}}}{8 \, d}"," ",0,"-1/8*(6*b*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + 48*(a^3*b^2 + a*b^4)*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) - (a + b + 6*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*(cos(d*x + c) + 1)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*(cos(d*x + c) - 1)) - (cos(d*x + c) - 1)/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(cos(d*x + c) + 1)) - 8*(9*a^5*b^2 + 10*a^4*b^3 + 2*a^3*b^4 + 8*a^2*b^5 + 5*a*b^6 - 2*b^7 + 18*a^5*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 8*a^4*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*a^3*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 6*a^2*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 16*a*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*b^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 9*a^5*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 18*a^4*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 18*a^3*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 18*a^2*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 9*a*b^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))^2))/d","B",0
267,1,800,0,0.415430," ","integrate(1/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a - 2 \, b\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{8 \, {\left(3 \, a^{4} b + 8 \, a^{2} b^{3} + b^{5}\right)} \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} + \frac{{\left(a + b - \frac{2 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{4 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} {\left(\cos\left(d x + c\right) - 1\right)}} - \frac{\cos\left(d x + c\right) - 1}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{4 \, {\left(9 \, a^{6} b + 6 \, a^{5} b^{2} + 9 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 11 \, a^{2} b^{5} - 2 \, a b^{6} + 3 \, b^{7} + \frac{18 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{12 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{26 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{4 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{38 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{8 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{6 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{9 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{18 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{33 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{48 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{27 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, b^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}^{2}}}{8 \, d}"," ",0,"1/8*(2*(a - 2*b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + 8*(3*a^4*b + 8*a^2*b^3 + b^5)*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) + (a + b - 2*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 4*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*(cos(d*x + c) + 1)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*(cos(d*x + c) - 1)) - (cos(d*x + c) - 1)/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(cos(d*x + c) + 1)) - 4*(9*a^6*b + 6*a^5*b^2 + 9*a^4*b^3 + 28*a^3*b^4 + 11*a^2*b^5 - 2*a*b^6 + 3*b^7 + 18*a^6*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 12*a^5*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 26*a^4*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 4*a^3*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 38*a^2*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 8*a*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 6*b^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 9*a^6*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 18*a^5*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 33*a^4*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 48*a^3*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 27*a^2*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 6*a*b^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 3*b^7*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))^2))/d","B",0
268,1,801,0,0.942252," ","integrate(sec(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(2 \, a - b\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{8 \, {\left(a^{5} + 8 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} + \frac{{\left(a + b - \frac{4 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} {\left(\cos\left(d x + c\right) - 1\right)}} + \frac{\cos\left(d x + c\right) - 1}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{4 \, {\left(3 \, a^{7} - 2 \, a^{6} b + 11 \, a^{5} b^{2} + 28 \, a^{4} b^{3} + 9 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 9 \, a b^{6} + \frac{6 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{8 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{38 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{4 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{26 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{12 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{18 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{27 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{48 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{33 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{18 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{9 \, a b^{6} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}^{2}}}{8 \, d}"," ",0,"1/8*(2*(2*a - b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - 8*(a^5 + 8*a^3*b^2 + 3*a*b^4)*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) + (a + b - 4*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*(cos(d*x + c) + 1)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*(cos(d*x + c) - 1)) + (cos(d*x + c) - 1)/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(cos(d*x + c) + 1)) + 4*(3*a^7 - 2*a^6*b + 11*a^5*b^2 + 28*a^4*b^3 + 9*a^3*b^4 + 6*a^2*b^5 + 9*a*b^6 + 6*a^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 8*a^6*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 38*a^5*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 4*a^4*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 26*a^3*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 12*a^2*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 18*a*b^6*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 3*a^7*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 6*a^6*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 27*a^5*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 48*a^4*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 33*a^3*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 18*a^2*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 9*a*b^6*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))^2))/d","B",0
269,1,689,0,1.109134," ","integrate(sec(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{6 \, a \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{48 \, {\left(a^{4} b + a^{2} b^{3}\right)} \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} + \frac{{\left(a + b - \frac{6 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} {\left(\cos\left(d x + c\right) - 1\right)}} - \frac{\cos\left(d x + c\right) - 1}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{8 \, {\left(2 \, a^{7} - 5 \, a^{6} b - 8 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 10 \, a^{3} b^{4} - 9 \, a^{2} b^{5} + \frac{2 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{16 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{6 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{8 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{18 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{9 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{18 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{18 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{18 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{9 \, a^{2} b^{5} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}^{2}}}{8 \, d}"," ",0,"1/8*(6*a*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + 48*(a^4*b + a^2*b^3)*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) + (a + b - 6*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*(cos(d*x + c) + 1)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*(cos(d*x + c) - 1)) - (cos(d*x + c) - 1)/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(cos(d*x + c) + 1)) + 8*(2*a^7 - 5*a^6*b - 8*a^5*b^2 - 2*a^4*b^3 - 10*a^3*b^4 - 9*a^2*b^5 + 2*a^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 16*a^6*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 6*a^5*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*a^4*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 8*a^3*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 18*a^2*b^5*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 9*a^6*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 18*a^5*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 18*a^4*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 18*a^3*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 9*a^2*b^5*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))^2))/d","B",0
270,1,675,0,1.252105," ","integrate(sec(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(4 \, a + b\right)} \log\left(\frac{{\left| -\cos\left(d x + c\right) + 1 \right|}}{{\left| \cos\left(d x + c\right) + 1 \right|}}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{16 \, {\left(a^{5} + 5 \, a^{3} b^{2}\right)} \log\left({\left| -a - b - \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} \right|}\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} + \frac{{\left(a + b - \frac{8 \, a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{2 \, b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} {\left(\cos\left(d x + c\right) - 1\right)}} + \frac{\cos\left(d x + c\right) - 1}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{8 \, {\left(3 \, a^{7} - 4 \, a^{6} b - 2 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + \frac{4 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{10 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{26 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{10 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{30 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{7} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, a^{6} b {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{18 \, a^{5} b^{2} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{30 \, a^{4} b^{3} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a^{3} b^{4} {\left(\cos\left(d x + c\right) - 1\right)}^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(a + b + \frac{a {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1} - \frac{b {\left(\cos\left(d x + c\right) - 1\right)}}{\cos\left(d x + c\right) + 1}\right)}^{2}}}{8 \, d}"," ",0,"1/8*(2*(4*a + b)*log(abs(-cos(d*x + c) + 1)/abs(cos(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - 16*(a^5 + 5*a^3*b^2)*log(abs(-a - b - a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1)))/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) + (a + b - 8*a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 2*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))*(cos(d*x + c) + 1)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*(cos(d*x + c) - 1)) + (cos(d*x + c) - 1)/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(cos(d*x + c) + 1)) + 8*(3*a^7 - 4*a^6*b - 2*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 4*a^7*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 10*a^6*b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 26*a^5*b^2*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 10*a^4*b^3*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - 30*a^3*b^4*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) + 3*a^7*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 6*a^6*b*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 18*a^5*b^2*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 - 30*a^4*b^3*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2 + 15*a^3*b^4*(cos(d*x + c) - 1)^2/(cos(d*x + c) + 1)^2)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(a + b + a*(cos(d*x + c) - 1)/(cos(d*x + c) + 1) - b*(cos(d*x + c) - 1)/(cos(d*x + c) + 1))^2))/d","B",0
271,-2,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a*sin(d*x+c)+b*tan(d*x+c))^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:Modgcd: no suitable evaluation pointindex.cc index_m operator + Error: Bad Argument ValueUnable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (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: 61.5Done","F(-2)",0
272,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + b \tan\left(d x + c\right)\right)}^{2} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + b*tan(d*x + c))^2*cos(d*x + c)^m, x)","F",0
273,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + b \tan\left(d x + c\right)\right)} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + b*tan(d*x + c))*cos(d*x + c)^m, x)","F",0
274,0,0,0,0.000000," ","integrate(cos(d*x+c)^m/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{m}}{a \sin\left(d x + c\right) + b \tan\left(d x + c\right)}\,{d x}"," ",0,"integrate(cos(d*x + c)^m/(a*sin(d*x + c) + b*tan(d*x + c)), x)","F",0
275,1,94,0,5.984643," ","integrate(cos(x)*sin(x)/(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","\frac{a b \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, x\right) - a\right)}}{{\left(a^{2} + b^{2}\right)} {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}}"," ",0,"a*b*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) + 2*(b*tan(1/2*x) - a)/((a^2 + b^2)*(tan(1/2*x)^2 + 1))","A",0
276,1,152,0,2.008322," ","integrate(cos(x)*sin(x)^2/(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","\frac{a^{2} b^{2} \log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a^{4} b + 2 \, a^{2} b^{3} + b^{5}} - \frac{a^{2} b \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}} + \frac{{\left(a^{3} - a b^{2}\right)} x}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}} + \frac{a^{2} b \tan\left(x\right)^{2} - a^{3} \tan\left(x\right) - a b^{2} \tan\left(x\right) - b^{3}}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(x\right)^{2} + 1\right)}}"," ",0,"a^2*b^2*log(abs(b*tan(x) + a))/(a^4*b + 2*a^2*b^3 + b^5) - 1/2*a^2*b*log(tan(x)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 1/2*(a^3 - a*b^2)*x/(a^4 + 2*a^2*b^2 + b^4) + 1/2*(a^2*b*tan(x)^2 - a^3*tan(x) - a*b^2*tan(x) - b^3)/((a^4 + 2*a^2*b^2 + b^4)*(tan(x)^2 + 1))","A",0
277,1,190,0,4.002898," ","integrate(cos(x)*sin(x)^3/(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","\frac{a^{3} b \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} + \frac{2 \, {\left(3 \, a^{2} b \tan\left(\frac{1}{2} \, x\right)^{5} + 3 \, a b^{2} \tan\left(\frac{1}{2} \, x\right)^{4} + 10 \, a^{2} b \tan\left(\frac{1}{2} \, x\right)^{3} + 4 \, b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} - 6 \, a^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + 3 \, a^{2} b \tan\left(\frac{1}{2} \, x\right) - 2 \, a^{3} + a b^{2}\right)}}{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{3}}"," ",0,"a^3*b*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) + 2/3*(3*a^2*b*tan(1/2*x)^5 + 3*a*b^2*tan(1/2*x)^4 + 10*a^2*b*tan(1/2*x)^3 + 4*b^3*tan(1/2*x)^3 - 6*a^3*tan(1/2*x)^2 + 3*a^2*b*tan(1/2*x) - 2*a^3 + a*b^2)/((a^4 + 2*a^2*b^2 + b^4)*(tan(1/2*x)^2 + 1)^3)","A",0
278,1,156,0,1.922261," ","integrate(cos(x)^2*sin(x)/(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","-\frac{a b^{3} \log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a^{4} b + 2 \, a^{2} b^{3} + b^{5}} + \frac{a b^{2} \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}} - \frac{{\left(a^{2} b - b^{3}\right)} x}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}} - \frac{a b^{2} \tan\left(x\right)^{2} - a^{2} b \tan\left(x\right) - b^{3} \tan\left(x\right) + a^{3} + 2 \, a b^{2}}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(x\right)^{2} + 1\right)}}"," ",0,"-a*b^3*log(abs(b*tan(x) + a))/(a^4*b + 2*a^2*b^3 + b^5) + 1/2*a*b^2*log(tan(x)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 1/2*(a^2*b - b^3)*x/(a^4 + 2*a^2*b^2 + b^4) - 1/2*(a*b^2*tan(x)^2 - a^2*b*tan(x) - b^3*tan(x) + a^3 + 2*a*b^2)/((a^4 + 2*a^2*b^2 + b^4)*(tan(x)^2 + 1))","A",0
279,1,192,0,8.001972," ","integrate(cos(x)^2*sin(x)^2/(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","-\frac{a^{2} b^{2} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(3 \, a b^{2} \tan\left(\frac{1}{2} \, x\right)^{5} + 3 \, b^{3} \tan\left(\frac{1}{2} \, x\right)^{4} - 4 \, a^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, a b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 6 \, a^{2} b \tan\left(\frac{1}{2} \, x\right)^{2} + 3 \, a b^{2} \tan\left(\frac{1}{2} \, x\right) - 2 \, a^{2} b + b^{3}\right)}}{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{3}}"," ",0,"-a^2*b^2*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2/3*(3*a*b^2*tan(1/2*x)^5 + 3*b^3*tan(1/2*x)^4 - 4*a^3*tan(1/2*x)^3 + 2*a*b^2*tan(1/2*x)^3 - 6*a^2*b*tan(1/2*x)^2 + 3*a*b^2*tan(1/2*x) - 2*a^2*b + b^3)/((a^4 + 2*a^2*b^2 + b^4)*(tan(1/2*x)^2 + 1)^3)","A",0
280,1,275,0,1.916262," ","integrate(cos(x)^2*sin(x)^3/(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","-\frac{a^{3} b^{3} \log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} + \frac{a^{3} b^{2} \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}} - \frac{{\left(3 \, a^{4} b - 6 \, a^{2} b^{3} - b^{5}\right)} x}{8 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}} - \frac{6 \, a^{3} b^{2} \tan\left(x\right)^{4} - 5 \, a^{4} b \tan\left(x\right)^{3} - 6 \, a^{2} b^{3} \tan\left(x\right)^{3} - b^{5} \tan\left(x\right)^{3} + 4 \, a^{5} \tan\left(x\right)^{2} + 16 \, a^{3} b^{2} \tan\left(x\right)^{2} - 3 \, a^{4} b \tan\left(x\right) - 2 \, a^{2} b^{3} \tan\left(x\right) + b^{5} \tan\left(x\right) + 2 \, a^{5} + 6 \, a^{3} b^{2} - 2 \, a b^{4}}{8 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(\tan\left(x\right)^{2} + 1\right)}^{2}}"," ",0,"-a^3*b^3*log(abs(b*tan(x) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) + 1/2*a^3*b^2*log(tan(x)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 1/8*(3*a^4*b - 6*a^2*b^3 - b^5)*x/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 1/8*(6*a^3*b^2*tan(x)^4 - 5*a^4*b*tan(x)^3 - 6*a^2*b^3*tan(x)^3 - b^5*tan(x)^3 + 4*a^5*tan(x)^2 + 16*a^3*b^2*tan(x)^2 - 3*a^4*b*tan(x) - 2*a^2*b^3*tan(x) + b^5*tan(x) + 2*a^5 + 6*a^3*b^2 - 2*a*b^4)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(tan(x)^2 + 1)^2)","A",0
281,1,201,0,8.014280," ","integrate(cos(x)^3*sin(x)/(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","\frac{a b^{3} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} + \frac{2 \, {\left(3 \, b^{3} \tan\left(\frac{1}{2} \, x\right)^{5} - 3 \, a^{3} \tan\left(\frac{1}{2} \, x\right)^{4} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 4 \, a^{2} b \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 3 \, b^{3} \tan\left(\frac{1}{2} \, x\right) - a^{3} - 4 \, a b^{2}\right)}}{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{3}}"," ",0,"a*b^3*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) + 2/3*(3*b^3*tan(1/2*x)^5 - 3*a^3*tan(1/2*x)^4 - 6*a*b^2*tan(1/2*x)^4 - 4*a^2*b*tan(1/2*x)^3 + 2*b^3*tan(1/2*x)^3 - 6*a*b^2*tan(1/2*x)^2 + 3*b^3*tan(1/2*x) - a^3 - 4*a*b^2)/((a^4 + 2*a^2*b^2 + b^4)*(tan(1/2*x)^2 + 1)^3)","A",0
282,1,273,0,0.205581," ","integrate(cos(x)^3*sin(x)^2/(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","\frac{a^{2} b^{4} \log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} - \frac{a^{2} b^{3} \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}} + \frac{{\left(a^{5} + 6 \, a^{3} b^{2} - 3 \, a b^{4}\right)} x}{8 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}} + \frac{6 \, a^{2} b^{3} \tan\left(x\right)^{4} + a^{5} \tan\left(x\right)^{3} - 2 \, a^{3} b^{2} \tan\left(x\right)^{3} - 3 \, a b^{4} \tan\left(x\right)^{3} + 4 \, a^{4} b \tan\left(x\right)^{2} + 16 \, a^{2} b^{3} \tan\left(x\right)^{2} - a^{5} \tan\left(x\right) - 6 \, a^{3} b^{2} \tan\left(x\right) - 5 \, a b^{4} \tan\left(x\right) + 2 \, a^{4} b + 6 \, a^{2} b^{3} - 2 \, b^{5}}{8 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(\tan\left(x\right)^{2} + 1\right)}^{2}}"," ",0,"a^2*b^4*log(abs(b*tan(x) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) - 1/2*a^2*b^3*log(tan(x)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 1/8*(a^5 + 6*a^3*b^2 - 3*a*b^4)*x/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 1/8*(6*a^2*b^3*tan(x)^4 + a^5*tan(x)^3 - 2*a^3*b^2*tan(x)^3 - 3*a*b^4*tan(x)^3 + 4*a^4*b*tan(x)^2 + 16*a^2*b^3*tan(x)^2 - a^5*tan(x) - 6*a^3*b^2*tan(x) - 5*a*b^4*tan(x) + 2*a^4*b + 6*a^2*b^3 - 2*b^5)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(tan(x)^2 + 1)^2)","A",0
283,1,361,0,1.688488," ","integrate(cos(x)^3*sin(x)^3/(a*cos(x)+b*sin(x)),x, algorithm=""giac"")","\frac{a^{3} b^{3} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} + b^{2}}} + \frac{2 \, {\left(15 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right)^{9} + 15 \, a b^{4} \tan\left(\frac{1}{2} \, x\right)^{8} + 80 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right)^{7} + 20 \, b^{5} \tan\left(\frac{1}{2} \, x\right)^{7} - 30 \, a^{5} \tan\left(\frac{1}{2} \, x\right)^{6} - 90 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right)^{6} - 48 \, a^{4} b \tan\left(\frac{1}{2} \, x\right)^{5} + 34 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right)^{5} - 8 \, b^{5} \tan\left(\frac{1}{2} \, x\right)^{5} + 10 \, a^{5} \tan\left(\frac{1}{2} \, x\right)^{4} - 50 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right)^{4} + 30 \, a b^{4} \tan\left(\frac{1}{2} \, x\right)^{4} + 80 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + 20 \, b^{5} \tan\left(\frac{1}{2} \, x\right)^{3} - 10 \, a^{5} \tan\left(\frac{1}{2} \, x\right)^{2} - 70 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 15 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right) - 2 \, a^{5} - 14 \, a^{3} b^{2} + 3 \, a b^{4}\right)}}{15 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{5}}"," ",0,"a^3*b^3*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a^2 + b^2)) + 2/15*(15*a^2*b^3*tan(1/2*x)^9 + 15*a*b^4*tan(1/2*x)^8 + 80*a^2*b^3*tan(1/2*x)^7 + 20*b^5*tan(1/2*x)^7 - 30*a^5*tan(1/2*x)^6 - 90*a^3*b^2*tan(1/2*x)^6 - 48*a^4*b*tan(1/2*x)^5 + 34*a^2*b^3*tan(1/2*x)^5 - 8*b^5*tan(1/2*x)^5 + 10*a^5*tan(1/2*x)^4 - 50*a^3*b^2*tan(1/2*x)^4 + 30*a*b^4*tan(1/2*x)^4 + 80*a^2*b^3*tan(1/2*x)^3 + 20*b^5*tan(1/2*x)^3 - 10*a^5*tan(1/2*x)^2 - 70*a^3*b^2*tan(1/2*x)^2 + 15*a^2*b^3*tan(1/2*x) - 2*a^5 - 14*a^3*b^2 + 3*a*b^4)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(tan(1/2*x)^2 + 1)^5)","B",0
284,1,144,0,0.189242," ","integrate(cos(x)*sin(x)/(a*cos(x)+b*sin(x))^2,x, algorithm=""giac"")","\frac{2 \, a b x}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{2} - b^{2}\right)} \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}} - \frac{{\left(a^{2} b - b^{3}\right)} \log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a^{4} b + 2 \, a^{2} b^{3} + b^{5}} + \frac{a^{2} b \tan\left(x\right) - b^{3} \tan\left(x\right) + 2 \, a^{3}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \tan\left(x\right) + a\right)}}"," ",0,"2*a*b*x/(a^4 + 2*a^2*b^2 + b^4) + 1/2*(a^2 - b^2)*log(tan(x)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - (a^2*b - b^3)*log(abs(b*tan(x) + a))/(a^4*b + 2*a^2*b^3 + b^5) + (a^2*b*tan(x) - b^3*tan(x) + 2*a^3)/((a^4 + 2*a^2*b^2 + b^4)*(b*tan(x) + a))","B",0
285,1,209,0,0.202881," ","integrate(cos(x)*sin(x)^2/(a*cos(x)+b*sin(x))^2,x, algorithm=""giac"")","-\frac{{\left(a^{3} - 2 \, a b^{2}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(a^{3} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, a b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - a^{2} b \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - a^{3} \tan\left(\frac{1}{2} \, x\right) - 4 \, a b^{2} \tan\left(\frac{1}{2} \, x\right) - 3 \, a^{2} b\right)}}{{\left(a \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, b \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, b \tan\left(\frac{1}{2} \, x\right) - a\right)} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}"," ",0,"-(a^3 - 2*a*b^2)*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2*(a^3*tan(1/2*x)^3 - 2*a*b^2*tan(1/2*x)^3 - a^2*b*tan(1/2*x)^2 + 2*b^3*tan(1/2*x)^2 - a^3*tan(1/2*x) - 4*a*b^2*tan(1/2*x) - 3*a^2*b)/((a*tan(1/2*x)^4 - 2*b*tan(1/2*x)^3 - 2*b*tan(1/2*x) - a)*(a^4 + 2*a^2*b^2 + b^4))","A",0
286,1,223,0,0.445440," ","integrate(cos(x)*sin(x)^3/(a*cos(x)+b*sin(x))^2,x, algorithm=""giac"")","\frac{{\left(3 \, a^{3} b - a b^{3}\right)} x}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(a^{4} - 3 \, a^{2} b^{2}\right)} \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}} - \frac{{\left(a^{4} b - 3 \, a^{2} b^{3}\right)} \log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} + \frac{2 \, a^{3} \tan\left(x\right)^{2} - 2 \, a b^{2} \tan\left(x\right)^{2} - a^{2} b \tan\left(x\right) - b^{3} \tan\left(x\right) + 3 \, a^{3} - a b^{2}}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \tan\left(x\right)^{3} + a \tan\left(x\right)^{2} + b \tan\left(x\right) + a\right)}}"," ",0,"(3*a^3*b - a*b^3)*x/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 1/2*(a^4 - 3*a^2*b^2)*log(tan(x)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (a^4*b - 3*a^2*b^3)*log(abs(b*tan(x) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) + 1/2*(2*a^3*tan(x)^2 - 2*a*b^2*tan(x)^2 - a^2*b*tan(x) - b^3*tan(x) + 3*a^3 - a*b^2)/((a^4 + 2*a^2*b^2 + b^4)*(b*tan(x)^3 + a*tan(x)^2 + b*tan(x) + a))","A",0
287,1,204,0,0.989231," ","integrate(cos(x)^2*sin(x)/(a*cos(x)+b*sin(x))^2,x, algorithm=""giac"")","\frac{{\left(2 \, a^{2} b - b^{3}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} + \frac{2 \, {\left(2 \, a^{2} b \tan\left(\frac{1}{2} \, x\right)^{3} - b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} - a^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, a b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 3 \, b^{3} \tan\left(\frac{1}{2} \, x\right) + a^{3} - 2 \, a b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, b \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, b \tan\left(\frac{1}{2} \, x\right) - a\right)} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}"," ",0,"(2*a^2*b - b^3)*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) + 2*(2*a^2*b*tan(1/2*x)^3 - b^3*tan(1/2*x)^3 - a^3*tan(1/2*x)^2 - 4*a*b^2*tan(1/2*x)^2 - 3*b^3*tan(1/2*x) + a^3 - 2*a*b^2)/((a*tan(1/2*x)^4 - 2*b*tan(1/2*x)^3 - 2*b*tan(1/2*x) - a)*(a^4 + 2*a^2*b^2 + b^4))","A",0
288,1,219,0,0.147090," ","integrate(cos(x)^2*sin(x)^2/(a*cos(x)+b*sin(x))^2,x, algorithm=""giac"")","\frac{{\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} x}{2 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}} - \frac{{\left(a^{3} b - a b^{3}\right)} \log\left(\tan\left(x\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(a^{3} b^{2} - a b^{4}\right)} \log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} - \frac{3 \, a^{2} b \tan\left(x\right)^{2} - b^{3} \tan\left(x\right)^{2} + a^{3} \tan\left(x\right) + a b^{2} \tan\left(x\right) + 4 \, a^{2} b}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \tan\left(x\right)^{3} + a \tan\left(x\right)^{2} + b \tan\left(x\right) + a\right)}}"," ",0,"1/2*(a^4 - 6*a^2*b^2 + b^4)*x/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (a^3*b - a*b^3)*log(tan(x)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(a^3*b^2 - a*b^4)*log(abs(b*tan(x) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) - 1/2*(3*a^2*b*tan(x)^2 - b^3*tan(x)^2 + a^3*tan(x) + a*b^2*tan(x) + 4*a^2*b)/((a^4 + 2*a^2*b^2 + b^4)*(b*tan(x)^3 + a*tan(x)^2 + b*tan(x) + a))","A",0
289,1,342,0,0.247960," ","integrate(cos(x)^2*sin(x)^3/(a*cos(x)+b*sin(x))^2,x, algorithm=""giac"")","\frac{{\left(2 \, a^{4} b - 3 \, a^{2} b^{3}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right) + a^{3} b^{2}\right)}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, x\right) - a\right)}} + \frac{2 \, {\left(6 \, a^{3} b \tan\left(\frac{1}{2} \, x\right)^{5} - 6 \, a b^{3} \tan\left(\frac{1}{2} \, x\right)^{5} + 9 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 3 \, b^{4} \tan\left(\frac{1}{2} \, x\right)^{4} + 20 \, a^{3} b \tan\left(\frac{1}{2} \, x\right)^{3} - 4 \, a b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} - 6 \, a^{4} \tan\left(\frac{1}{2} \, x\right)^{2} + 18 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 6 \, a^{3} b \tan\left(\frac{1}{2} \, x\right) - 6 \, a b^{3} \tan\left(\frac{1}{2} \, x\right) - 2 \, a^{4} + 9 \, a^{2} b^{2} - b^{4}\right)}}{3 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{3}}"," ",0,"(2*a^4*b - 3*a^2*b^3)*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a^2 + b^2)) - 2*(a^2*b^3*tan(1/2*x) + a^3*b^2)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(a*tan(1/2*x)^2 - 2*b*tan(1/2*x) - a)) + 2/3*(6*a^3*b*tan(1/2*x)^5 - 6*a*b^3*tan(1/2*x)^5 + 9*a^2*b^2*tan(1/2*x)^4 - 3*b^4*tan(1/2*x)^4 + 20*a^3*b*tan(1/2*x)^3 - 4*a*b^3*tan(1/2*x)^3 - 6*a^4*tan(1/2*x)^2 + 18*a^2*b^2*tan(1/2*x)^2 + 6*a^3*b*tan(1/2*x) - 6*a*b^3*tan(1/2*x) - 2*a^4 + 9*a^2*b^2 - b^4)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(tan(1/2*x)^2 + 1)^3)","B",0
290,1,214,0,0.189157," ","integrate(cos(x)^3*sin(x)/(a*cos(x)+b*sin(x))^2,x, algorithm=""giac"")","-\frac{{\left(a^{3} b - 3 \, a b^{3}\right)} x}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(3 \, a^{2} b^{2} - b^{4}\right)} \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}} - \frac{{\left(3 \, a^{2} b^{3} - b^{5}\right)} \log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} + \frac{4 \, a b^{2} \tan\left(x\right)^{2} + a^{2} b \tan\left(x\right) + b^{3} \tan\left(x\right) - a^{3} + 3 \, a b^{2}}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \tan\left(x\right)^{3} + a \tan\left(x\right)^{2} + b \tan\left(x\right) + a\right)}}"," ",0,"-(a^3*b - 3*a*b^3)*x/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 1/2*(3*a^2*b^2 - b^4)*log(tan(x)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (3*a^2*b^3 - b^5)*log(abs(b*tan(x) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) + 1/2*(4*a*b^2*tan(x)^2 + a^2*b*tan(x) + b^3*tan(x) - a^3 + 3*a*b^2)/((a^4 + 2*a^2*b^2 + b^4)*(b*tan(x)^3 + a*tan(x)^2 + b*tan(x) + a))","A",0
291,1,335,0,0.255192," ","integrate(cos(x)^3*sin(x)^2/(a*cos(x)+b*sin(x))^2,x, algorithm=""giac"")","-\frac{{\left(3 \, a^{3} b^{2} - 2 \, a b^{4}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, x\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} + b^{2}}} + \frac{2 \, {\left(a b^{4} \tan\left(\frac{1}{2} \, x\right) + a^{2} b^{3}\right)}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, x\right) - a\right)}} - \frac{2 \, {\left(9 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x\right)^{5} - 3 \, b^{4} \tan\left(\frac{1}{2} \, x\right)^{5} + 12 \, a b^{3} \tan\left(\frac{1}{2} \, x\right)^{4} - 4 \, a^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 18 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, b^{4} \tan\left(\frac{1}{2} \, x\right)^{3} - 12 \, a^{3} b \tan\left(\frac{1}{2} \, x\right)^{2} + 12 \, a b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + 9 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x\right) - 3 \, b^{4} \tan\left(\frac{1}{2} \, x\right) - 4 \, a^{3} b + 8 \, a b^{3}\right)}}{3 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{3}}"," ",0,"-(3*a^3*b^2 - 2*a*b^4)*log(abs(2*a*tan(1/2*x) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*x) - 2*b + 2*sqrt(a^2 + b^2)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a^2 + b^2)) + 2*(a*b^4*tan(1/2*x) + a^2*b^3)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(a*tan(1/2*x)^2 - 2*b*tan(1/2*x) - a)) - 2/3*(9*a^2*b^2*tan(1/2*x)^5 - 3*b^4*tan(1/2*x)^5 + 12*a*b^3*tan(1/2*x)^4 - 4*a^4*tan(1/2*x)^3 + 18*a^2*b^2*tan(1/2*x)^3 - 2*b^4*tan(1/2*x)^3 - 12*a^3*b*tan(1/2*x)^2 + 12*a*b^3*tan(1/2*x)^2 + 9*a^2*b^2*tan(1/2*x) - 3*b^4*tan(1/2*x) - 4*a^3*b + 8*a*b^3)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(tan(1/2*x)^2 + 1)^3)","A",0
292,1,435,0,0.155920," ","integrate(cos(x)^3*sin(x)^3/(a*cos(x)+b*sin(x))^2,x, algorithm=""giac"")","-\frac{3 \, {\left(a^{5} b - 6 \, a^{3} b^{3} + a b^{5}\right)} x}{4 \, {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)}} + \frac{3 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)}} - \frac{3 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} \log\left({\left| b \tan\left(x\right) + a \right|}\right)}{a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}} + \frac{3 \, a^{4} b^{3} \tan\left(x\right) - 3 \, a^{2} b^{5} \tan\left(x\right) + 4 \, a^{5} b^{2} - 2 \, a^{3} b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(x\right) + a\right)}} - \frac{9 \, a^{4} b^{2} \tan\left(x\right)^{4} - 9 \, a^{2} b^{4} \tan\left(x\right)^{4} - 5 \, a^{5} b \tan\left(x\right)^{3} - 2 \, a^{3} b^{3} \tan\left(x\right)^{3} + 3 \, a b^{5} \tan\left(x\right)^{3} + 2 \, a^{6} \tan\left(x\right)^{2} + 14 \, a^{4} b^{2} \tan\left(x\right)^{2} - 24 \, a^{2} b^{4} \tan\left(x\right)^{2} - 3 \, a^{5} b \tan\left(x\right) + 2 \, a^{3} b^{3} \tan\left(x\right) + 5 \, a b^{5} \tan\left(x\right) + a^{6} + 4 \, a^{4} b^{2} - 14 \, a^{2} b^{4} + b^{6}}{4 \, {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\tan\left(x\right)^{2} + 1\right)}^{2}}"," ",0,"-3/4*(a^5*b - 6*a^3*b^3 + a*b^5)*x/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 3/2*(a^4*b^2 - a^2*b^4)*log(tan(x)^2 + 1)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 3*(a^4*b^3 - a^2*b^5)*log(abs(b*tan(x) + a))/(a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9) + (3*a^4*b^3*tan(x) - 3*a^2*b^5*tan(x) + 4*a^5*b^2 - 2*a^3*b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*(b*tan(x) + a)) - 1/4*(9*a^4*b^2*tan(x)^4 - 9*a^2*b^4*tan(x)^4 - 5*a^5*b*tan(x)^3 - 2*a^3*b^3*tan(x)^3 + 3*a*b^5*tan(x)^3 + 2*a^6*tan(x)^2 + 14*a^4*b^2*tan(x)^2 - 24*a^2*b^4*tan(x)^2 - 3*a^5*b*tan(x) + 2*a^3*b^3*tan(x) + 5*a*b^5*tan(x) + a^6 + 4*a^4*b^2 - 14*a^2*b^4 + b^6)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*(tan(x)^2 + 1)^2)","B",0
293,1,90,0,1.781038," ","integrate(tan(x)/(b*cos(x)+a*sin(x)),x, algorithm=""giac"")","\frac{b \log\left(\frac{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, a - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, a + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} a} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right)}{a} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right)}{a}"," ",0,"b*log(abs(2*b*tan(1/2*x) - 2*a - 2*sqrt(a^2 + b^2))/abs(2*b*tan(1/2*x) - 2*a + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*a) + log(abs(tan(1/2*x) + 1))/a - log(abs(tan(1/2*x) - 1))/a","B",0
294,1,75,0,0.210779," ","integrate(cot(x)/(b*cos(x)+a*sin(x)),x, algorithm=""giac"")","\frac{a \log\left(\frac{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, a - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, a + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} b} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{b}"," ",0,"a*log(abs(2*b*tan(1/2*x) - 2*a - 2*sqrt(a^2 + b^2))/abs(2*b*tan(1/2*x) - 2*a + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b) + log(abs(tan(1/2*x)))/b","A",0
