1,1,36,0,0.415981," ","integrate(sin(x)^3*(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","\frac{1}{4} \, a \cos\left(x\right)^{4} - \frac{1}{2} \, a \cos\left(x\right)^{2} + \frac{3}{8} \, b x + \frac{1}{8} \, {\left(2 \, b \cos\left(x\right)^{3} - 5 \, b \cos\left(x\right)\right)} \sin\left(x\right)"," ",0,"1/4*a*cos(x)^4 - 1/2*a*cos(x)^2 + 3/8*b*x + 1/8*(2*b*cos(x)^3 - 5*b*cos(x))*sin(x)","A",0
2,1,27,0,0.447351," ","integrate(sin(x)^2*(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","\frac{1}{3} \, b \cos\left(x\right)^{3} - b \cos\left(x\right) - \frac{1}{3} \, {\left(a \cos\left(x\right)^{2} - a\right)} \sin\left(x\right)"," ",0,"1/3*b*cos(x)^3 - b*cos(x) - 1/3*(a*cos(x)^2 - a)*sin(x)","A",0
3,1,19,0,0.402791," ","integrate(sin(x)*(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","-\frac{1}{2} \, a \cos\left(x\right)^{2} - \frac{1}{2} \, b \cos\left(x\right) \sin\left(x\right) + \frac{1}{2} \, b x"," ",0,"-1/2*a*cos(x)^2 - 1/2*b*cos(x)*sin(x) + 1/2*b*x","A",0
4,1,10,0,0.508706," ","integrate(a*cos(x)+b*sin(x),x, algorithm=""fricas"")","-b \cos\left(x\right) + a \sin\left(x\right)"," ",0,"-b*cos(x) + a*sin(x)","A",0
5,1,11,0,0.503978," ","integrate(csc(x)*(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","b x + a \log\left(\frac{1}{2} \, \sin\left(x\right)\right)"," ",0,"b*x + a*log(1/2*sin(x))","A",0
6,1,33,0,0.464782," ","integrate(csc(x)^2*(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","-\frac{b \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) \sin\left(x\right) - b \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) \sin\left(x\right) + 2 \, a}{2 \, \sin\left(x\right)}"," ",0,"-1/2*(b*log(1/2*cos(x) + 1/2)*sin(x) - b*log(-1/2*cos(x) + 1/2)*sin(x) + 2*a)/sin(x)","B",0
7,1,19,0,0.433639," ","integrate(csc(x)^3*(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","\frac{2 \, b \cos\left(x\right) \sin\left(x\right) + a}{2 \, {\left(\cos\left(x\right)^{2} - 1\right)}}"," ",0,"1/2*(2*b*cos(x)*sin(x) + a)/(cos(x)^2 - 1)","A",0
8,1,93,0,0.479318," ","integrate(sin(x)^3/(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","-\frac{a^{3} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right) - {\left(a^{3} + a b^{2}\right)} \cos\left(x\right)^{2} + {\left(a^{2} b + b^{3}\right)} \cos\left(x\right) \sin\left(x\right) - {\left(3 \, a^{2} b + b^{3}\right)} x}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}"," ",0,"-1/2*(a^3*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2) - (a^3 + a*b^2)*cos(x)^2 + (a^2*b + b^3)*cos(x)*sin(x) - (3*a^2*b + b^3)*x)/(a^4 + 2*a^2*b^2 + b^4)","A",0
9,1,144,0,0.479135," ","integrate(sin(x)^2/(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} + b^{2}} a^{2} \log\left(-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right) - 2 \, {\left(a^{2} b + b^{3}\right)} \cos\left(x\right) - 2 \, {\left(a^{3} + a b^{2}\right)} \sin\left(x\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}"," ",0,"1/2*(sqrt(a^2 + b^2)*a^2*log(-(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)) - 2*(a^2*b + b^3)*cos(x) - 2*(a^3 + a*b^2)*sin(x))/(a^4 + 2*a^2*b^2 + b^4)","B",0
10,1,46,0,0.475070," ","integrate(sin(x)/(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","\frac{2 \, b x - a \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right)}{2 \, {\left(a^{2} + b^{2}\right)}}"," ",0,"1/2*(2*b*x - a*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2))/(a^2 + b^2)","A",0
11,1,96,0,0.450656," ","integrate(1/(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","\frac{\log\left(-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right)}{2 \, \sqrt{a^{2} + b^{2}}}"," ",0,"1/2*log(-(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2))/sqrt(a^2 + b^2)","B",0
12,1,44,0,0.453925," ","integrate(csc(x)/(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","-\frac{\log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right) - \log\left(-\frac{1}{4} \, \cos\left(x\right)^{2} + \frac{1}{4}\right)}{2 \, a}"," ",0,"-1/2*(log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2) - log(-1/4*cos(x)^2 + 1/4))/a","A",0
13,1,133,0,0.490591," ","integrate(csc(x)^2/(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","\frac{b \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) \sin\left(x\right) - b \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) \sin\left(x\right) + \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right) \sin\left(x\right) - 2 \, a}{2 \, a^{2} \sin\left(x\right)}"," ",0,"1/2*(b*log(1/2*cos(x) + 1/2)*sin(x) - b*log(-1/2*cos(x) + 1/2)*sin(x) + sqrt(a^2 + b^2)*log(-(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2))*sin(x) - 2*a)/(a^2*sin(x))","B",0
14,1,117,0,0.433404," ","integrate(csc(x)^3/(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) - a^{2} + {\left({\left(a^{2} + b^{2}\right)} \cos\left(x\right)^{2} - a^{2} - b^{2}\right)} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right) - {\left({\left(a^{2} + b^{2}\right)} \cos\left(x\right)^{2} - a^{2} - b^{2}\right)} \log\left(-\frac{1}{4} \, \cos\left(x\right)^{2} + \frac{1}{4}\right)}{2 \, {\left(a^{3} \cos\left(x\right)^{2} - a^{3}\right)}}"," ",0,"-1/2*(2*a*b*cos(x)*sin(x) - a^2 + ((a^2 + b^2)*cos(x)^2 - a^2 - b^2)*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2) - ((a^2 + b^2)*cos(x)^2 - a^2 - b^2)*log(-1/4*cos(x)^2 + 1/4))/(a^3*cos(x)^2 - a^3)","B",0
15,1,240,0,0.448907," ","integrate(sin(x)^3/(a*cos(x)+b*sin(x))^2,x, algorithm=""fricas"")","\frac{2 \, a^{5} - 2 \, a^{3} b^{2} - 4 \, a b^{4} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right)^{2} - 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(x\right) \sin\left(x\right) + 3 \, {\left(a^{3} b \cos\left(x\right) + a^{2} b^{2} \sin\left(x\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right)}{2 \, {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(x\right) + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sin\left(x\right)\right)}}"," ",0,"1/2*(2*a^5 - 2*a^3*b^2 - 4*a*b^4 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*cos(x)^2 - 2*(a^4*b + 2*a^2*b^3 + b^5)*cos(x)*sin(x) + 3*(a^3*b*cos(x) + a^2*b^2*sin(x))*sqrt(a^2 + b^2)*log(-(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)))/((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(x) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sin(x))","B",0
16,1,132,0,0.707082," ","integrate(sin(x)^2/(a*cos(x)+b*sin(x))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} b + {\left(a^{3} - a b^{2}\right)} x\right)} \cos\left(x\right) + {\left(a^{2} b \cos\left(x\right) + a b^{2} \sin\left(x\right)\right)} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right) - {\left(a^{3} - {\left(a^{2} b - b^{3}\right)} x\right)} \sin\left(x\right)}{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(x\right)}"," ",0,"-((a^2*b + (a^3 - a*b^2)*x)*cos(x) + (a^2*b*cos(x) + a*b^2*sin(x))*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2) - (a^3 - (a^2*b - b^3)*x)*sin(x))/((a^5 + 2*a^3*b^2 + a*b^4)*cos(x) + (a^4*b + 2*a^2*b^3 + b^5)*sin(x))","B",0
17,1,164,0,0.454757," ","integrate(sin(x)/(a*cos(x)+b*sin(x))^2,x, algorithm=""fricas"")","\frac{2 \, a^{3} + 2 \, a b^{2} + {\left(a b \cos\left(x\right) + b^{2} \sin\left(x\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right)}{2 \, {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(x\right)\right)}}"," ",0,"1/2*(2*a^3 + 2*a*b^2 + (a*b*cos(x) + b^2*sin(x))*sqrt(a^2 + b^2)*log(-(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)))/((a^5 + 2*a^3*b^2 + a*b^4)*cos(x) + (a^4*b + 2*a^2*b^3 + b^5)*sin(x))","B",0
18,1,39,0,0.437742," ","integrate(1/(a*cos(x)+b*sin(x))^2,x, algorithm=""fricas"")","-\frac{b \cos\left(x\right) - a \sin\left(x\right)}{{\left(a^{3} + a b^{2}\right)} \cos\left(x\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(x\right)}"," ",0,"-(b*cos(x) - a*sin(x))/((a^3 + a*b^2)*cos(x) + (a^2*b + b^3)*sin(x))","B",0
19,1,220,0,0.561999," ","integrate(csc(x)/(a*cos(x)+b*sin(x))^2,x, algorithm=""fricas"")","\frac{2 \, a^{3} + 2 \, a b^{2} + {\left(a b \cos\left(x\right) + b^{2} \sin\left(x\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right) - {\left({\left(a^{3} + a b^{2}\right)} \cos\left(x\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(x\right)\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + {\left({\left(a^{3} + a b^{2}\right)} \cos\left(x\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(x\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{2 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} \cos\left(x\right) + {\left(a^{4} b + a^{2} b^{3}\right)} \sin\left(x\right)\right)}}"," ",0,"1/2*(2*a^3 + 2*a*b^2 + (a*b*cos(x) + b^2*sin(x))*sqrt(a^2 + b^2)*log((2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)) - ((a^3 + a*b^2)*cos(x) + (a^2*b + b^3)*sin(x))*log(1/2*cos(x) + 1/2) + ((a^3 + a*b^2)*cos(x) + (a^2*b + b^3)*sin(x))*log(-1/2*cos(x) + 1/2))/((a^5 + a^3*b^2)*cos(x) + (a^4*b + a^2*b^3)*sin(x))","B",0
20,1,134,0,0.581727," ","integrate(csc(x)^2/(a*cos(x)+b*sin(x))^2,x, algorithm=""fricas"")","\frac{2 \, a^{2} \cos\left(x\right)^{2} + 2 \, a b \cos\left(x\right) \sin\left(x\right) - a^{2} + {\left(b^{2} \cos\left(x\right)^{2} - a b \cos\left(x\right) \sin\left(x\right) - b^{2}\right)} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right) - {\left(b^{2} \cos\left(x\right)^{2} - a b \cos\left(x\right) \sin\left(x\right) - b^{2}\right)} \log\left(-\frac{1}{4} \, \cos\left(x\right)^{2} + \frac{1}{4}\right)}{a^{3} b \cos\left(x\right)^{2} - a^{4} \cos\left(x\right) \sin\left(x\right) - a^{3} b}"," ",0,"(2*a^2*cos(x)^2 + 2*a*b*cos(x)*sin(x) - a^2 + (b^2*cos(x)^2 - a*b*cos(x)*sin(x) - b^2)*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2) - (b^2*cos(x)^2 - a*b*cos(x)*sin(x) - b^2)*log(-1/4*cos(x)^2 + 1/4))/(a^3*b*cos(x)^2 - a^4*cos(x)*sin(x) - a^3*b)","B",0
21,1,345,0,0.596402," ","integrate(csc(x)^3/(a*cos(x)+b*sin(x))^2,x, algorithm=""fricas"")","-\frac{6 \, a^{2} b \cos\left(x\right) \sin\left(x\right) + 4 \, a^{3} + 12 \, a b^{2} - 6 \, {\left(a^{3} + 2 \, a b^{2}\right)} \cos\left(x\right)^{2} - 6 \, {\left(a b \cos\left(x\right)^{3} - a b \cos\left(x\right) + {\left(b^{2} \cos\left(x\right)^{2} - b^{2}\right)} \sin\left(x\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right) + 3 \, {\left({\left(a^{3} + 2 \, a b^{2}\right)} \cos\left(x\right)^{3} - {\left(a^{3} + 2 \, a b^{2}\right)} \cos\left(x\right) - {\left(a^{2} b + 2 \, b^{3} - {\left(a^{2} b + 2 \, b^{3}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - 3 \, {\left({\left(a^{3} + 2 \, a b^{2}\right)} \cos\left(x\right)^{3} - {\left(a^{3} + 2 \, a b^{2}\right)} \cos\left(x\right) - {\left(a^{2} b + 2 \, b^{3} - {\left(a^{2} b + 2 \, b^{3}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{4 \, {\left(a^{5} \cos\left(x\right)^{3} - a^{5} \cos\left(x\right) + {\left(a^{4} b \cos\left(x\right)^{2} - a^{4} b\right)} \sin\left(x\right)\right)}}"," ",0,"-1/4*(6*a^2*b*cos(x)*sin(x) + 4*a^3 + 12*a*b^2 - 6*(a^3 + 2*a*b^2)*cos(x)^2 - 6*(a*b*cos(x)^3 - a*b*cos(x) + (b^2*cos(x)^2 - b^2)*sin(x))*sqrt(a^2 + b^2)*log((2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)) + 3*((a^3 + 2*a*b^2)*cos(x)^3 - (a^3 + 2*a*b^2)*cos(x) - (a^2*b + 2*b^3 - (a^2*b + 2*b^3)*cos(x)^2)*sin(x))*log(1/2*cos(x) + 1/2) - 3*((a^3 + 2*a*b^2)*cos(x)^3 - (a^3 + 2*a*b^2)*cos(x) - (a^2*b + 2*b^3 - (a^2*b + 2*b^3)*cos(x)^2)*sin(x))*log(-1/2*cos(x) + 1/2))/(a^5*cos(x)^3 - a^5*cos(x) + (a^4*b*cos(x)^2 - a^4*b)*sin(x))","B",0
22,1,282,0,0.495046," ","integrate(sin(x)^3/(a*cos(x)+b*sin(x))^3,x, algorithm=""fricas"")","\frac{a^{5} + 7 \, a^{3} b^{2} - 2 \, {\left(6 \, a^{3} b^{2} + {\left(3 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} x\right)} \cos\left(x\right)^{2} + 2 \, {\left(3 \, a^{4} b - 3 \, a^{2} b^{3} - 2 \, {\left(3 \, a^{3} b^{2} - a b^{4}\right)} x\right)} \cos\left(x\right) \sin\left(x\right) - 2 \, {\left(3 \, a^{2} b^{3} - b^{5}\right)} x + {\left(a^{3} b^{2} - 3 \, a b^{4} + {\left(a^{5} - 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{4} b - 3 \, a^{2} b^{3}\right)} \cos\left(x\right) \sin\left(x\right)\right)} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right)}{2 \, {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8} + {\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(x\right) \sin\left(x\right)\right)}}"," ",0,"1/2*(a^5 + 7*a^3*b^2 - 2*(6*a^3*b^2 + (3*a^4*b - 4*a^2*b^3 + b^5)*x)*cos(x)^2 + 2*(3*a^4*b - 3*a^2*b^3 - 2*(3*a^3*b^2 - a*b^4)*x)*cos(x)*sin(x) - 2*(3*a^2*b^3 - b^5)*x + (a^3*b^2 - 3*a*b^4 + (a^5 - 4*a^3*b^2 + 3*a*b^4)*cos(x)^2 + 2*(a^4*b - 3*a^2*b^3)*cos(x)*sin(x))*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2))/(a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8 + (a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*cos(x)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*cos(x)*sin(x))","B",0
23,1,282,0,1.405192," ","integrate(sin(x)^2/(a*cos(x)+b*sin(x))^3,x, algorithm=""fricas"")","-\frac{{\left(a^{2} b^{2} - 2 \, b^{4} + {\left(a^{4} - 3 \, a^{2} b^{2} + 2 \, b^{4}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{3} b - 2 \, a b^{3}\right)} \cos\left(x\right) \sin\left(x\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right) - 6 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cos\left(x\right) - 2 \, {\left(a^{5} + 5 \, a^{3} b^{2} + 4 \, a b^{4}\right)} \sin\left(x\right)}{4 \, {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8} + {\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(x\right) \sin\left(x\right)\right)}}"," ",0,"-1/4*((a^2*b^2 - 2*b^4 + (a^4 - 3*a^2*b^2 + 2*b^4)*cos(x)^2 + 2*(a^3*b - 2*a*b^3)*cos(x)*sin(x))*sqrt(a^2 + b^2)*log(-(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)) - 6*(a^4*b + a^2*b^3)*cos(x) - 2*(a^5 + 5*a^3*b^2 + 4*a*b^4)*sin(x))/(a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8 + (a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*cos(x)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*cos(x)*sin(x))","B",0
24,1,116,0,0.652222," ","integrate(sin(x)/(a*cos(x)+b*sin(x))^3,x, algorithm=""fricas"")","-\frac{4 \, a b^{2} \cos\left(x\right)^{2} - a^{3} - 3 \, a b^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} \cos\left(x\right) \sin\left(x\right)}{2 \, {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6} + {\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(x\right) \sin\left(x\right)\right)}}"," ",0,"-1/2*(4*a*b^2*cos(x)^2 - a^3 - 3*a*b^2 - 2*(a^2*b - b^3)*cos(x)*sin(x))/(a^4*b^2 + 2*a^2*b^4 + b^6 + (a^6 + a^4*b^2 - a^2*b^4 - b^6)*cos(x)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*cos(x)*sin(x))","B",0
25,1,225,0,0.593880," ","integrate(1/(a*cos(x)+b*sin(x))^3,x, algorithm=""fricas"")","\frac{{\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right) - 2 \, {\left(a^{2} b + b^{3}\right)} \cos\left(x\right) + 2 \, {\left(a^{3} + a b^{2}\right)} \sin\left(x\right)}{4 \, {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6} + {\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(x\right) \sin\left(x\right)\right)}}"," ",0,"1/4*((2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)*sqrt(a^2 + b^2)*log(-(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)) - 2*(a^2*b + b^3)*cos(x) + 2*(a^3 + a*b^2)*sin(x))/(a^4*b^2 + 2*a^2*b^4 + b^6 + (a^6 + a^4*b^2 - a^2*b^4 - b^6)*cos(x)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*cos(x)*sin(x))","B",0
26,1,220,0,0.762940," ","integrate(csc(x)/(a*cos(x)+b*sin(x))^3,x, algorithm=""fricas"")","\frac{4 \, a^{2} b^{2} \cos\left(x\right)^{2} + a^{4} - a^{2} b^{2} - 2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} b^{2} + b^{4} + {\left(a^{4} - b^{4}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(x\right) \sin\left(x\right)\right)} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right) + {\left(a^{2} b^{2} + b^{4} + {\left(a^{4} - b^{4}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(x\right) \sin\left(x\right)\right)} \log\left(-\frac{1}{4} \, \cos\left(x\right)^{2} + \frac{1}{4}\right)}{2 \, {\left(a^{5} b^{2} + a^{3} b^{4} + {\left(a^{7} - a^{3} b^{4}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{6} b + a^{4} b^{3}\right)} \cos\left(x\right) \sin\left(x\right)\right)}}"," ",0,"1/2*(4*a^2*b^2*cos(x)^2 + a^4 - a^2*b^2 - 2*(a^3*b - a*b^3)*cos(x)*sin(x) - (a^2*b^2 + b^4 + (a^4 - b^4)*cos(x)^2 + 2*(a^3*b + a*b^3)*cos(x)*sin(x))*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2) + (a^2*b^2 + b^4 + (a^4 - b^4)*cos(x)^2 + 2*(a^3*b + a*b^3)*cos(x)*sin(x))*log(-1/4*cos(x)^2 + 1/4))/(a^5*b^2 + a^3*b^4 + (a^7 - a^3*b^4)*cos(x)^2 + 2*(a^6*b + a^4*b^3)*cos(x)*sin(x))","B",0
27,1,463,0,1.918233," ","integrate(csc(x)^2/(a*cos(x)+b*sin(x))^3,x, algorithm=""fricas"")","-\frac{2 \, a^{5} - 10 \, a^{3} b^{2} - 12 \, a b^{4} - 6 \, {\left(a^{5} - a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(x\right)^{2} - 18 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cos\left(x\right) \sin\left(x\right) - 3 \, {\left(2 \, {\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(x\right)^{3} - 2 \, {\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(x\right) - {\left(a^{2} b^{2} + 2 \, b^{4} + {\left(a^{4} + a^{2} b^{2} - 2 \, b^{4}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right) - 6 \, {\left(2 \, {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right)^{3} - 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right) - {\left(a^{2} b^{3} + b^{5} + {\left(a^{4} b - b^{5}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + 6 \, {\left(2 \, {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right)^{3} - 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right) - {\left(a^{2} b^{3} + b^{5} + {\left(a^{4} b - b^{5}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{4 \, {\left(2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \cos\left(x\right)^{3} - 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \cos\left(x\right) - {\left(a^{6} b^{2} + a^{4} b^{4} + {\left(a^{8} - a^{4} b^{4}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)\right)}}"," ",0,"-1/4*(2*a^5 - 10*a^3*b^2 - 12*a*b^4 - 6*(a^5 - a^3*b^2 - 2*a*b^4)*cos(x)^2 - 18*(a^4*b + a^2*b^3)*cos(x)*sin(x) - 3*(2*(a^3*b + 2*a*b^3)*cos(x)^3 - 2*(a^3*b + 2*a*b^3)*cos(x) - (a^2*b^2 + 2*b^4 + (a^4 + a^2*b^2 - 2*b^4)*cos(x)^2)*sin(x))*sqrt(a^2 + b^2)*log(-(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)) - 6*(2*(a^3*b^2 + a*b^4)*cos(x)^3 - 2*(a^3*b^2 + a*b^4)*cos(x) - (a^2*b^3 + b^5 + (a^4*b - b^5)*cos(x)^2)*sin(x))*log(1/2*cos(x) + 1/2) + 6*(2*(a^3*b^2 + a*b^4)*cos(x)^3 - 2*(a^3*b^2 + a*b^4)*cos(x) - (a^2*b^3 + b^5 + (a^4*b - b^5)*cos(x)^2)*sin(x))*log(-1/2*cos(x) + 1/2))/(2*(a^7*b + a^5*b^3)*cos(x)^3 - 2*(a^7*b + a^5*b^3)*cos(x) - (a^6*b^2 + a^4*b^4 + (a^8 - a^4*b^4)*cos(x)^2)*sin(x))","B",0
28,1,385,0,1.939399," ","integrate(csc(x)^3/(a*cos(x)+b*sin(x))^3,x, algorithm=""fricas"")","-\frac{24 \, a^{2} b^{2} \cos\left(x\right)^{4} - a^{4} + 6 \, a^{2} b^{2} + 2 \, {\left(a^{4} - 15 \, a^{2} b^{2}\right)} \cos\left(x\right)^{2} - 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cos\left(x\right)^{4} - a^{2} b^{2} - 3 \, b^{4} - {\left(a^{4} + a^{2} b^{2} - 6 \, b^{4}\right)} \cos\left(x\right)^{2} + 2 \, {\left({\left(a^{3} b + 3 \, a b^{3}\right)} \cos\left(x\right)^{3} - {\left(a^{3} b + 3 \, a b^{3}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right) + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cos\left(x\right)^{4} - a^{2} b^{2} - 3 \, b^{4} - {\left(a^{4} + a^{2} b^{2} - 6 \, b^{4}\right)} \cos\left(x\right)^{2} + 2 \, {\left({\left(a^{3} b + 3 \, a b^{3}\right)} \cos\left(x\right)^{3} - {\left(a^{3} b + 3 \, a b^{3}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \log\left(-\frac{1}{4} \, \cos\left(x\right)^{2} + \frac{1}{4}\right) - 4 \, {\left(3 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(x\right)^{3} - {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{2 \, {\left(a^{5} b^{2} - {\left(a^{7} - a^{5} b^{2}\right)} \cos\left(x\right)^{4} + {\left(a^{7} - 2 \, a^{5} b^{2}\right)} \cos\left(x\right)^{2} - 2 \, {\left(a^{6} b \cos\left(x\right)^{3} - a^{6} b \cos\left(x\right)\right)} \sin\left(x\right)\right)}}"," ",0,"-1/2*(24*a^2*b^2*cos(x)^4 - a^4 + 6*a^2*b^2 + 2*(a^4 - 15*a^2*b^2)*cos(x)^2 - 2*((a^4 + 2*a^2*b^2 - 3*b^4)*cos(x)^4 - a^2*b^2 - 3*b^4 - (a^4 + a^2*b^2 - 6*b^4)*cos(x)^2 + 2*((a^3*b + 3*a*b^3)*cos(x)^3 - (a^3*b + 3*a*b^3)*cos(x))*sin(x))*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2) + 2*((a^4 + 2*a^2*b^2 - 3*b^4)*cos(x)^4 - a^2*b^2 - 3*b^4 - (a^4 + a^2*b^2 - 6*b^4)*cos(x)^2 + 2*((a^3*b + 3*a*b^3)*cos(x)^3 - (a^3*b + 3*a*b^3)*cos(x))*sin(x))*log(-1/4*cos(x)^2 + 1/4) - 4*(3*(a^3*b - a*b^3)*cos(x)^3 - (2*a^3*b - 3*a*b^3)*cos(x))*sin(x))/(a^5*b^2 - (a^7 - a^5*b^2)*cos(x)^4 + (a^7 - 2*a^5*b^2)*cos(x)^2 - 2*(a^6*b*cos(x)^3 - a^6*b*cos(x))*sin(x))","B",0
29,0,0,0,0.642898," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^n/(sin(d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(i \, d n x + i \, c n + n \log\left(a\right)\right)}}{\left(\frac{1}{2} \, {\left(-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-i \, d x - i \, c\right)}\right)^{n}}, x\right)"," ",0,"integral(e^(I*d*n*x + I*c*n + n*log(a))/(1/2*(-I*e^(2*I*d*x + 2*I*c) + I)*e^(-I*d*x - I*c))^n, x)","F",0
30,1,62,0,0.604863," ","integrate(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, b \cos\left(d x + c\right)^{6} - 15 \, a d x - {\left(8 \, a \cos\left(d x + c\right)^{5} + 10 \, a \cos\left(d x + c\right)^{3} + 15 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, d}"," ",0,"-1/48*(8*b*cos(d*x + c)^6 - 15*a*d*x - (8*a*cos(d*x + c)^5 + 10*a*cos(d*x + c)^3 + 15*a*cos(d*x + c))*sin(d*x + c))/d","A",0
31,1,51,0,0.577192," ","integrate(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, b \cos\left(d x + c\right)^{5} - {\left(3 \, a \cos\left(d x + c\right)^{4} + 4 \, a \cos\left(d x + c\right)^{2} + 8 \, a\right)} \sin\left(d x + c\right)}{15 \, d}"," ",0,"-1/15*(3*b*cos(d*x + c)^5 - (3*a*cos(d*x + c)^4 + 4*a*cos(d*x + c)^2 + 8*a)*sin(d*x + c))/d","A",0
32,1,51,0,0.665226," ","integrate(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b \cos\left(d x + c\right)^{4} - 3 \, a d x - {\left(2 \, a \cos\left(d x + c\right)^{3} + 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/8*(2*b*cos(d*x + c)^4 - 3*a*d*x - (2*a*cos(d*x + c)^3 + 3*a*cos(d*x + c))*sin(d*x + c))/d","A",0
33,1,38,0,0.746052," ","integrate(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{b \cos\left(d x + c\right)^{3} - {\left(a \cos\left(d x + c\right)^{2} + 2 \, a\right)} \sin\left(d x + c\right)}{3 \, d}"," ",0,"-1/3*(b*cos(d*x + c)^3 - (a*cos(d*x + c)^2 + 2*a)*sin(d*x + c))/d","A",0
34,1,35,0,0.589566," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{a d x - b \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(a*d*x - b*cos(d*x + c)^2 + a*cos(d*x + c)*sin(d*x + c))/d","A",0
35,1,23,0,0.524236," ","integrate(a*cos(d*x+c)+b*sin(d*x+c),x, algorithm=""fricas"")","-\frac{b \cos\left(d x + c\right) - a \sin\left(d x + c\right)}{d}"," ",0,"-(b*cos(d*x + c) - a*sin(d*x + c))/d","A",0
36,1,21,0,0.750774," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{a d x - b \log\left(-\cos\left(d x + c\right)\right)}{d}"," ",0,"(a*d*x - b*log(-cos(d*x + c)))/d","A",0
37,1,54,0,0.715510," ","integrate(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{a \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - a \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, b}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(a*cos(d*x + c)*log(sin(d*x + c) + 1) - a*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*b)/(d*cos(d*x + c))","B",0
38,1,30,0,1.258445," ","integrate(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a \cos\left(d x + c\right) \sin\left(d x + c\right) + b}{2 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/2*(2*a*cos(d*x + c)*sin(d*x + c) + b)/(d*cos(d*x + c)^2)","A",0
39,1,74,0,2.159933," ","integrate(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, a \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 6 \, a \cos\left(d x + c\right) \sin\left(d x + c\right) + 4 \, b}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*a*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*a*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 6*a*cos(d*x + c)*sin(d*x + c) + 4*b)/(d*cos(d*x + c)^3)","A",0
40,1,45,0,0.627945," ","integrate(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, {\left(2 \, a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 3 \, b}{12 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/12*(4*(2*a*cos(d*x + c)^3 + a*cos(d*x + c))*sin(d*x + c) + 3*b)/(d*cos(d*x + c)^4)","A",0
41,1,88,0,0.935886," ","integrate(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, a \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, a \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 10 \, {\left(3 \, a \cos\left(d x + c\right)^{3} + 2 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 16 \, b}{80 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/80*(15*a*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*a*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 10*(3*a*cos(d*x + c)^3 + 2*a*cos(d*x + c))*sin(d*x + c) + 16*b)/(d*cos(d*x + c)^5)","A",0
42,1,57,0,0.720640," ","integrate(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, a \cos\left(d x + c\right)^{5} + 4 \, a \cos\left(d x + c\right)^{3} + 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 5 \, b}{30 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/30*(2*(8*a*cos(d*x + c)^5 + 4*a*cos(d*x + c)^3 + 3*a*cos(d*x + c))*sin(d*x + c) + 5*b)/(d*cos(d*x + c)^6)","A",0
43,1,94,0,0.975133," ","integrate(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{30 \, a b \cos\left(d x + c\right)^{7} - {\left(15 \, {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(6 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(6 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} + 48 \, a^{2} + 8 \, b^{2}\right)} \sin\left(d x + c\right)}{105 \, d}"," ",0,"-1/105*(30*a*b*cos(d*x + c)^7 - (15*(a^2 - b^2)*cos(d*x + c)^6 + 3*(6*a^2 + b^2)*cos(d*x + c)^4 + 4*(6*a^2 + b^2)*cos(d*x + c)^2 + 48*a^2 + 8*b^2)*sin(d*x + c))/d","A",0
44,1,95,0,0.498471," ","integrate(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{16 \, a b \cos\left(d x + c\right)^{6} - 3 \, {\left(5 \, a^{2} + b^{2}\right)} d x - {\left(8 \, {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(5 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, d}"," ",0,"-1/48*(16*a*b*cos(d*x + c)^6 - 3*(5*a^2 + b^2)*d*x - (8*(a^2 - b^2)*cos(d*x + c)^5 + 2*(5*a^2 + b^2)*cos(d*x + c)^3 + 3*(5*a^2 + b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
45,1,74,0,0.623453," ","integrate(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, a b \cos\left(d x + c\right)^{5} - {\left(3 \, {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} + {\left(4 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} + 8 \, a^{2} + 2 \, b^{2}\right)} \sin\left(d x + c\right)}{15 \, d}"," ",0,"-1/15*(6*a*b*cos(d*x + c)^5 - (3*(a^2 - b^2)*cos(d*x + c)^4 + (4*a^2 + b^2)*cos(d*x + c)^2 + 8*a^2 + 2*b^2)*sin(d*x + c))/d","A",0
46,1,75,0,0.537261," ","integrate(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, a b \cos\left(d x + c\right)^{4} - {\left(3 \, a^{2} + b^{2}\right)} d x - {\left(2 \, {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/8*(4*a*b*cos(d*x + c)^4 - (3*a^2 + b^2)*d*x - (2*(a^2 - b^2)*cos(d*x + c)^3 + (3*a^2 + b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
47,1,53,0,0.498861," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, a b \cos\left(d x + c\right)^{3} - {\left({\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, a^{2} + b^{2}\right)} \sin\left(d x + c\right)}{3 \, d}"," ",0,"-1/3*(2*a*b*cos(d*x + c)^3 - ((a^2 - b^2)*cos(d*x + c)^2 + 2*a^2 + b^2)*sin(d*x + c))/d","A",0
48,1,52,0,0.607421," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, a b \cos\left(d x + c\right)^{2} - {\left(a^{2} + b^{2}\right)} d x - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(2*a*b*cos(d*x + c)^2 - (a^2 + b^2)*d*x - (a^2 - b^2)*cos(d*x + c)*sin(d*x + c))/d","A",0
49,1,62,0,0.657998," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, a b \cos\left(d x + c\right) - b^{2} \log\left(\sin\left(d x + c\right) + 1\right) + b^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(4*a*b*cos(d*x + c) - b^2*log(sin(d*x + c) + 1) + b^2*log(-sin(d*x + c) + 1) - 2*(a^2 - b^2)*sin(d*x + c))/d","A",0
50,1,60,0,0.524544," ","integrate(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} - b^{2}\right)} d x \cos\left(d x + c\right) - 2 \, a b \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right)\right) + b^{2} \sin\left(d x + c\right)}{d \cos\left(d x + c\right)}"," ",0,"((a^2 - b^2)*d*x*cos(d*x + c) - 2*a*b*cos(d*x + c)*log(-cos(d*x + c)) + b^2*sin(d*x + c))/(d*cos(d*x + c))","A",0
51,1,96,0,0.690318," ","integrate(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 8 \, a b \cos\left(d x + c\right) + 2 \, b^{2} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*((2*a^2 - b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*a^2 - b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 8*a*b*cos(d*x + c) + 2*b^2*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
52,1,55,0,0.463685," ","integrate(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, a b \cos\left(d x + c\right) + {\left({\left(3 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right)} \sin\left(d x + c\right)}{3 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/3*(3*a*b*cos(d*x + c) + ((3*a^2 - b^2)*cos(d*x + c)^2 + b^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
53,1,120,0,0.592215," ","integrate(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 32 \, a b \cos\left(d x + c\right) + 6 \, {\left({\left(4 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, b^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(4*a^2 - b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(4*a^2 - b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 32*a*b*cos(d*x + c) + 6*((4*a^2 - b^2)*cos(d*x + c)^2 + 2*b^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
54,1,79,0,0.673334," ","integrate(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{15 \, a b \cos\left(d x + c\right) + 2 \, {\left(2 \, {\left(5 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} + {\left(5 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, b^{2}\right)} \sin\left(d x + c\right)}{30 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/30*(15*a*b*cos(d*x + c) + 2*(2*(5*a^2 - b^2)*cos(d*x + c)^4 + (5*a^2 - b^2)*cos(d*x + c)^2 + 3*b^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
55,1,142,0,0.525377," ","integrate(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{15 \, {\left(6 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(6 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 192 \, a b \cos\left(d x + c\right) + 10 \, {\left(3 \, {\left(6 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(6 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 8 \, b^{2}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(15*(6*a^2 - b^2)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(6*a^2 - b^2)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 192*a*b*cos(d*x + c) + 10*(3*(6*a^2 - b^2)*cos(d*x + c)^4 + 2*(6*a^2 - b^2)*cos(d*x + c)^2 + 8*b^2)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
56,1,100,0,0.666551," ","integrate(sec(d*x+c)^8*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{35 \, a b \cos\left(d x + c\right) + {\left(8 \, {\left(7 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(7 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, b^{2}\right)} \sin\left(d x + c\right)}{105 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/105*(35*a*b*cos(d*x + c) + (8*(7*a^2 - b^2)*cos(d*x + c)^6 + 4*(7*a^2 - b^2)*cos(d*x + c)^4 + 3*(7*a^2 - b^2)*cos(d*x + c)^2 + 15*b^2)*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
57,1,150,0,0.718335," ","integrate(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{64 \, b^{3} \cos\left(d x + c\right)^{6} + 48 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{8} - 15 \, {\left(7 \, a^{3} + 3 \, a b^{2}\right)} d x - {\left(48 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{7} + 8 \, {\left(7 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} + 10 \, {\left(7 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(7 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{384 \, d}"," ",0,"-1/384*(64*b^3*cos(d*x + c)^6 + 48*(3*a^2*b - b^3)*cos(d*x + c)^8 - 15*(7*a^3 + 3*a*b^2)*d*x - (48*(a^3 - 3*a*b^2)*cos(d*x + c)^7 + 8*(7*a^3 + 3*a*b^2)*cos(d*x + c)^5 + 10*(7*a^3 + 3*a*b^2)*cos(d*x + c)^3 + 15*(7*a^3 + 3*a*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
58,1,123,0,0.703907," ","integrate(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{7 \, b^{3} \cos\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{7} - {\left(5 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(2 \, a^{3} + a b^{2}\right)} \cos\left(d x + c\right)^{4} + 16 \, a^{3} + 8 \, a b^{2} + 4 \, {\left(2 \, a^{3} + a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{35 \, d}"," ",0,"-1/35*(7*b^3*cos(d*x + c)^5 + 5*(3*a^2*b - b^3)*cos(d*x + c)^7 - (5*(a^3 - 3*a*b^2)*cos(d*x + c)^6 + 3*(2*a^3 + a*b^2)*cos(d*x + c)^4 + 16*a^3 + 8*a*b^2 + 4*(2*a^3 + a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
59,1,128,0,0.589553," ","integrate(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{12 \, b^{3} \cos\left(d x + c\right)^{4} + 8 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} d x - {\left(8 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, d}"," ",0,"-1/48*(12*b^3*cos(d*x + c)^4 + 8*(3*a^2*b - b^3)*cos(d*x + c)^6 - 3*(5*a^3 + 3*a*b^2)*d*x - (8*(a^3 - 3*a*b^2)*cos(d*x + c)^5 + 2*(5*a^3 + 3*a*b^2)*cos(d*x + c)^3 + 3*(5*a^3 + 3*a*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
60,1,102,0,0.695855," ","integrate(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{5 \, b^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{5} - {\left(3 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} + 8 \, a^{3} + 6 \, a b^{2} + {\left(4 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{15 \, d}"," ",0,"-1/15*(5*b^3*cos(d*x + c)^3 + 3*(3*a^2*b - b^3)*cos(d*x + c)^5 - (3*(a^3 - 3*a*b^2)*cos(d*x + c)^4 + 8*a^3 + 6*a*b^2 + (4*a^3 + 3*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
61,1,100,0,0.693841," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{4 \, b^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(a^{3} + a b^{2}\right)} d x - {\left(2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/8*(4*b^3*cos(d*x + c)^2 + 2*(3*a^2*b - b^3)*cos(d*x + c)^4 - 3*(a^3 + a*b^2)*d*x - (2*(a^3 - 3*a*b^2)*cos(d*x + c)^3 + 3*(a^3 + a*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
62,1,77,0,0.873456," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, b^{3} \cos\left(d x + c\right) + {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(2 \, a^{3} + 3 \, a b^{2} + {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, d}"," ",0,"-1/3*(3*b^3*cos(d*x + c) + (3*a^2*b - b^3)*cos(d*x + c)^3 - (2*a^3 + 3*a*b^2 + (a^3 - 3*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
63,1,79,0,0.714291," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, b^{3} \log\left(-\cos\left(d x + c\right)\right) - {\left(a^{3} + 3 \, a b^{2}\right)} d x + {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(2*b^3*log(-cos(d*x + c)) - (a^3 + 3*a*b^2)*d*x + (3*a^2*b - b^3)*cos(d*x + c)^2 - (a^3 - 3*a*b^2)*cos(d*x + c)*sin(d*x + c))/d","A",0
64,1,109,0,0.647988," ","integrate(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{3 \, a b^{2} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a b^{2} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, b^{3} - 2 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(3*a*b^2*cos(d*x + c)*log(sin(d*x + c) + 1) - 3*a*b^2*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*b^3 - 2*(3*a^2*b - b^3)*cos(d*x + c)^2 + 2*(a^3 - 3*a*b^2)*cos(d*x + c)*sin(d*x + c))/(d*cos(d*x + c))","A",0
65,1,88,0,0.721476," ","integrate(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} d x \cos\left(d x + c\right)^{2} + 6 \, a b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\cos\left(d x + c\right)\right) + b^{3}}{2 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/2*(2*(a^3 - 3*a*b^2)*d*x*cos(d*x + c)^2 + 6*a*b^2*cos(d*x + c)*sin(d*x + c) - 2*(3*a^2*b - b^3)*cos(d*x + c)^2*log(-cos(d*x + c)) + b^3)/(d*cos(d*x + c)^2)","A",0
66,1,123,0,0.718973," ","integrate(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 18 \, a b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) + 4 \, b^{3} + 12 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(2*a^3 - 3*a*b^2)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*a^3 - 3*a*b^2)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 18*a*b^2*cos(d*x + c)*sin(d*x + c) + 4*b^3 + 12*(3*a^2*b - b^3)*cos(d*x + c)^2)/(d*cos(d*x + c)^3)","A",0
67,1,78,0,0.755840," ","integrate(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{b^{3} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(a b^{2} \cos\left(d x + c\right) + {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/4*(b^3 + 2*(3*a^2*b - b^3)*cos(d*x + c)^2 + 4*(a*b^2*cos(d*x + c) + (a^3 - a*b^2)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^4)","B",0
68,1,147,0,0.735248," ","integrate(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 48 \, b^{3} + 80 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left(6 \, a b^{2} \cos\left(d x + c\right) + {\left(4 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(4*a^3 - 3*a*b^2)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(4*a^3 - 3*a*b^2)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 48*b^3 + 80*(3*a^2*b - b^3)*cos(d*x + c)^2 + 30*(6*a*b^2*cos(d*x + c) + (4*a^3 - 3*a*b^2)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
69,1,105,0,0.515000," ","integrate(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{10 \, b^{3} + 15 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(2 \, {\left(5 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} + 9 \, a b^{2} \cos\left(d x + c\right) + {\left(5 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{60 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/60*(10*b^3 + 15*(3*a^2*b - b^3)*cos(d*x + c)^2 + 4*(2*(5*a^3 - 3*a*b^2)*cos(d*x + c)^5 + 9*a*b^2*cos(d*x + c) + (5*a^3 - 3*a*b^2)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
70,1,170,0,0.733013," ","integrate(sec(d*x+c)^8*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{105 \, {\left(2 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{7} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(2 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{7} \log\left(-\sin\left(d x + c\right) + 1\right) + 160 \, b^{3} + 224 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + 70 \, {\left(3 \, {\left(2 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{5} + 8 \, a b^{2} \cos\left(d x + c\right) + 2 \, {\left(2 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{1120 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/1120*(105*(2*a^3 - a*b^2)*cos(d*x + c)^7*log(sin(d*x + c) + 1) - 105*(2*a^3 - a*b^2)*cos(d*x + c)^7*log(-sin(d*x + c) + 1) + 160*b^3 + 224*(3*a^2*b - b^3)*cos(d*x + c)^2 + 70*(3*(2*a^3 - a*b^2)*cos(d*x + c)^5 + 8*a*b^2*cos(d*x + c) + 2*(2*a^3 - a*b^2)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
71,1,128,0,0.807945," ","integrate(sec(d*x+c)^9*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{105 \, b^{3} + 140 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, {\left(7 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{7} + 4 \, {\left(7 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} + 45 \, a b^{2} \cos\left(d x + c\right) + 3 \, {\left(7 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{840 \, d \cos\left(d x + c\right)^{8}}"," ",0,"1/840*(105*b^3 + 140*(3*a^2*b - b^3)*cos(d*x + c)^2 + 8*(8*(7*a^3 - 3*a*b^2)*cos(d*x + c)^7 + 4*(7*a^3 - 3*a*b^2)*cos(d*x + c)^5 + 45*a*b^2*cos(d*x + c) + 3*(7*a^3 - 3*a*b^2)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^8)","A",0
72,1,192,0,0.763080," ","integrate(sec(d*x+c)^10*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{315 \, {\left(8 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{9} \log\left(\sin\left(d x + c\right) + 1\right) - 315 \, {\left(8 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{9} \log\left(-\sin\left(d x + c\right) + 1\right) + 1792 \, b^{3} + 2304 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + 42 \, {\left(15 \, {\left(8 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{7} + 10 \, {\left(8 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} + 144 \, a b^{2} \cos\left(d x + c\right) + 8 \, {\left(8 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{16128 \, d \cos\left(d x + c\right)^{9}}"," ",0,"1/16128*(315*(8*a^3 - 3*a*b^2)*cos(d*x + c)^9*log(sin(d*x + c) + 1) - 315*(8*a^3 - 3*a*b^2)*cos(d*x + c)^9*log(-sin(d*x + c) + 1) + 1792*b^3 + 2304*(3*a^2*b - b^3)*cos(d*x + c)^2 + 42*(15*(8*a^3 - 3*a*b^2)*cos(d*x + c)^7 + 10*(8*a^3 - 3*a*b^2)*cos(d*x + c)^5 + 144*a*b^2*cos(d*x + c) + 8*(8*a^3 - 3*a*b^2)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^9)","A",0
73,1,150,0,0.581775," ","integrate(sec(d*x+c)^11*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{84 \, b^{3} + 105 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, {\left(3 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{9} + 8 \, {\left(3 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{7} + 6 \, {\left(3 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{5} + 35 \, a b^{2} \cos\left(d x + c\right) + 5 \, {\left(3 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{840 \, d \cos\left(d x + c\right)^{10}}"," ",0,"1/840*(84*b^3 + 105*(3*a^2*b - b^3)*cos(d*x + c)^2 + 8*(16*(3*a^3 - a*b^2)*cos(d*x + c)^9 + 8*(3*a^3 - a*b^2)*cos(d*x + c)^7 + 6*(3*a^3 - a*b^2)*cos(d*x + c)^5 + 35*a*b^2*cos(d*x + c) + 5*(3*a^3 - a*b^2)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^10)","A",0
74,1,177,0,0.662075," ","integrate(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{180 \, a b^{3} \cos\left(d x + c\right)^{7} + 140 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{9} - {\left(35 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{8} + 10 \, {\left(4 \, a^{4} + 3 \, a^{2} b^{2} - 5 \, b^{4}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(16 \, a^{4} + 12 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} + 128 \, a^{4} + 96 \, a^{2} b^{2} + 8 \, b^{4} + 4 \, {\left(16 \, a^{4} + 12 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{315 \, d}"," ",0,"-1/315*(180*a*b^3*cos(d*x + c)^7 + 140*(a^3*b - a*b^3)*cos(d*x + c)^9 - (35*(a^4 - 6*a^2*b^2 + b^4)*cos(d*x + c)^8 + 10*(4*a^4 + 3*a^2*b^2 - 5*b^4)*cos(d*x + c)^6 + 3*(16*a^4 + 12*a^2*b^2 + b^4)*cos(d*x + c)^4 + 128*a^4 + 96*a^2*b^2 + 8*b^4 + 4*(16*a^4 + 12*a^2*b^2 + b^4)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
75,1,184,0,0.761528," ","integrate(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{256 \, a b^{3} \cos\left(d x + c\right)^{6} + 192 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{8} - 3 \, {\left(35 \, a^{4} + 30 \, a^{2} b^{2} + 3 \, b^{4}\right)} d x - {\left(48 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{7} + 8 \, {\left(7 \, a^{4} + 6 \, a^{2} b^{2} - 9 \, b^{4}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(35 \, a^{4} + 30 \, a^{2} b^{2} + 3 \, b^{4}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(35 \, a^{4} + 30 \, a^{2} b^{2} + 3 \, b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{384 \, d}"," ",0,"-1/384*(256*a*b^3*cos(d*x + c)^6 + 192*(a^3*b - a*b^3)*cos(d*x + c)^8 - 3*(35*a^4 + 30*a^2*b^2 + 3*b^4)*d*x - (48*(a^4 - 6*a^2*b^2 + b^4)*cos(d*x + c)^7 + 8*(7*a^4 + 6*a^2*b^2 - 9*b^4)*cos(d*x + c)^5 + 2*(35*a^4 + 30*a^2*b^2 + 3*b^4)*cos(d*x + c)^3 + 3*(35*a^4 + 30*a^2*b^2 + 3*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
76,1,149,0,0.620567," ","integrate(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{28 \, a b^{3} \cos\left(d x + c\right)^{5} + 20 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{7} - {\left(5 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{4} + 3 \, a^{2} b^{2} - 4 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 16 \, a^{4} + 16 \, a^{2} b^{2} + 2 \, b^{4} + {\left(8 \, a^{4} + 8 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{35 \, d}"," ",0,"-1/35*(28*a*b^3*cos(d*x + c)^5 + 20*(a^3*b - a*b^3)*cos(d*x + c)^7 - (5*(a^4 - 6*a^2*b^2 + b^4)*cos(d*x + c)^6 + 2*(3*a^4 + 3*a^2*b^2 - 4*b^4)*cos(d*x + c)^4 + 16*a^4 + 16*a^2*b^2 + 2*b^4 + (8*a^4 + 8*a^2*b^2 + b^4)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
77,1,151,0,0.685450," ","integrate(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{48 \, a b^{3} \cos\left(d x + c\right)^{4} + 32 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(5 \, a^{4} + 6 \, a^{2} b^{2} + b^{4}\right)} d x - {\left(8 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(5 \, a^{4} + 6 \, a^{2} b^{2} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{4} + 6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, d}"," ",0,"-1/48*(48*a*b^3*cos(d*x + c)^4 + 32*(a^3*b - a*b^3)*cos(d*x + c)^6 - 3*(5*a^4 + 6*a^2*b^2 + b^4)*d*x - (8*(a^4 - 6*a^2*b^2 + b^4)*cos(d*x + c)^5 + 2*(5*a^4 + 6*a^2*b^2 - 7*b^4)*cos(d*x + c)^3 + 3*(5*a^4 + 6*a^2*b^2 + b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
78,1,123,0,0.775897," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{20 \, a b^{3} \cos\left(d x + c\right)^{3} + 12 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{5} - {\left(3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} + 8 \, a^{4} + 12 \, a^{2} b^{2} + 3 \, b^{4} + 2 \, {\left(2 \, a^{4} + 3 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{15 \, d}"," ",0,"-1/15*(20*a*b^3*cos(d*x + c)^3 + 12*(a^3*b - a*b^3)*cos(d*x + c)^5 - (3*(a^4 - 6*a^2*b^2 + b^4)*cos(d*x + c)^4 + 8*a^4 + 12*a^2*b^2 + 3*b^4 + 2*(2*a^4 + 3*a^2*b^2 - 3*b^4)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
79,1,121,0,0.927234," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{16 \, a b^{3} \cos\left(d x + c\right)^{2} + 8 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d x - {\left(2 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 6 \, a^{2} b^{2} - 5 \, b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/8*(16*a*b^3*cos(d*x + c)^2 + 8*(a^3*b - a*b^3)*cos(d*x + c)^4 - 3*(a^4 + 2*a^2*b^2 + b^4)*d*x - (2*(a^4 - 6*a^2*b^2 + b^4)*cos(d*x + c)^3 + (3*a^4 + 6*a^2*b^2 - 5*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
80,1,121,0,0.827177," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{24 \, a b^{3} \cos\left(d x + c\right) - 3 \, b^{4} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, b^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 8 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(2 \, a^{4} + 6 \, a^{2} b^{2} - 4 \, b^{4} + {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(24*a*b^3*cos(d*x + c) - 3*b^4*log(sin(d*x + c) + 1) + 3*b^4*log(-sin(d*x + c) + 1) + 8*(a^3*b - a*b^3)*cos(d*x + c)^3 - 2*(2*a^4 + 6*a^2*b^2 - 4*b^4 + (a^4 - 6*a^2*b^2 + b^4)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
81,1,136,0,0.827020," ","integrate(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{8 \, a b^{3} \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right)\right) + 4 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(2 \, a^{3} b - 2 \, a b^{3} + {\left(a^{4} + 6 \, a^{2} b^{2} - 3 \, b^{4}\right)} d x\right)} \cos\left(d x + c\right) - {\left(2 \, b^{4} + {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"-1/2*(8*a*b^3*cos(d*x + c)*log(-cos(d*x + c)) + 4*(a^3*b - a*b^3)*cos(d*x + c)^3 - (2*a^3*b - 2*a*b^3 + (a^4 + 6*a^2*b^2 - 3*b^4)*d*x)*cos(d*x + c) - (2*b^4 + (a^4 - 6*a^2*b^2 + b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
82,1,153,0,1.051575," ","integrate(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{16 \, a b^{3} \cos\left(d x + c\right) - 16 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(b^{4} + 2 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(16*a*b^3*cos(d*x + c) - 16*(a^3*b - a*b^3)*cos(d*x + c)^3 + 3*(4*a^2*b^2 - b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - 3*(4*a^2*b^2 - b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(b^4 + 2*(a^4 - 6*a^2*b^2 + b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
83,1,119,0,0.578876," ","integrate(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} d x \cos\left(d x + c\right)^{3} + 6 \, a b^{3} \cos\left(d x + c\right) - 12 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\cos\left(d x + c\right)\right) + {\left(b^{4} + 2 \, {\left(9 \, a^{2} b^{2} - 2 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/3*(3*(a^4 - 6*a^2*b^2 + b^4)*d*x*cos(d*x + c)^3 + 6*a*b^3*cos(d*x + c) - 12*(a^3*b - a*b^3)*cos(d*x + c)^3*log(-cos(d*x + c)) + (b^4 + 2*(9*a^2*b^2 - 2*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
84,1,163,0,0.758529," ","integrate(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, a^{4} - 24 \, a^{2} b^{2} + 3 \, b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(8 \, a^{4} - 24 \, a^{2} b^{2} + 3 \, b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 64 \, a b^{3} \cos\left(d x + c\right) + 192 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(2 \, b^{4} + {\left(24 \, a^{2} b^{2} - 5 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(8*a^4 - 24*a^2*b^2 + 3*b^4)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(8*a^4 - 24*a^2*b^2 + 3*b^4)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 64*a*b^3*cos(d*x + c) + 192*(a^3*b - a*b^3)*cos(d*x + c)^3 + 6*(2*b^4 + (24*a^2*b^2 - 5*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
85,1,109,0,0.529047," ","integrate(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{5 \, a b^{3} \cos\left(d x + c\right) + 10 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(5 \, a^{4} - 10 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} + b^{4} + 2 \, {\left(5 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{5 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/5*(5*a*b^3*cos(d*x + c) + 10*(a^3*b - a*b^3)*cos(d*x + c)^3 + ((5*a^4 - 10*a^2*b^2 + b^4)*cos(d*x + c)^4 + b^4 + 2*(5*a^2*b^2 - b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","B",0
86,1,187,0,0.810705," ","integrate(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, a^{4} - 12 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(8 \, a^{4} - 12 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 384 \, a b^{3} \cos\left(d x + c\right) + 640 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3} + 10 \, {\left(3 \, {\left(8 \, a^{4} - 12 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} + 8 \, b^{4} + 2 \, {\left(36 \, a^{2} b^{2} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(15*(8*a^4 - 12*a^2*b^2 + b^4)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(8*a^4 - 12*a^2*b^2 + b^4)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 384*a*b^3*cos(d*x + c) + 640*(a^3*b - a*b^3)*cos(d*x + c)^3 + 10*(3*(8*a^4 - 12*a^2*b^2 + b^4)*cos(d*x + c)^4 + 8*b^4 + 2*(36*a^2*b^2 - 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
87,1,142,0,0.493360," ","integrate(sec(d*x+c)^8*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{70 \, a b^{3} \cos\left(d x + c\right) + 105 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, {\left(35 \, a^{4} - 42 \, a^{2} b^{2} + 3 \, b^{4}\right)} \cos\left(d x + c\right)^{6} + {\left(35 \, a^{4} - 42 \, a^{2} b^{2} + 3 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 15 \, b^{4} + 6 \, {\left(21 \, a^{2} b^{2} - 4 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{105 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/105*(70*a*b^3*cos(d*x + c) + 105*(a^3*b - a*b^3)*cos(d*x + c)^3 + (2*(35*a^4 - 42*a^2*b^2 + 3*b^4)*cos(d*x + c)^6 + (35*a^4 - 42*a^2*b^2 + 3*b^4)*cos(d*x + c)^4 + 15*b^4 + 6*(21*a^2*b^2 - 4*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
88,1,214,0,0.555063," ","integrate(sec(d*x+c)^9*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left(16 \, a^{4} - 16 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{8} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(16 \, a^{4} - 16 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{8} \log\left(-\sin\left(d x + c\right) + 1\right) + 5120 \, a b^{3} \cos\left(d x + c\right) + 7168 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3} + 70 \, {\left(3 \, {\left(16 \, a^{4} - 16 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{6} + 2 \, {\left(16 \, a^{4} - 16 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} + 16 \, b^{4} + 8 \, {\left(16 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{8960 \, d \cos\left(d x + c\right)^{8}}"," ",0,"1/8960*(105*(16*a^4 - 16*a^2*b^2 + b^4)*cos(d*x + c)^8*log(sin(d*x + c) + 1) - 105*(16*a^4 - 16*a^2*b^2 + b^4)*cos(d*x + c)^8*log(-sin(d*x + c) + 1) + 5120*a*b^3*cos(d*x + c) + 7168*(a^3*b - a*b^3)*cos(d*x + c)^3 + 70*(3*(16*a^4 - 16*a^2*b^2 + b^4)*cos(d*x + c)^6 + 2*(16*a^4 - 16*a^2*b^2 + b^4)*cos(d*x + c)^4 + 16*b^4 + 8*(16*a^2*b^2 - 3*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^8)","A",0
89,1,167,0,0.761279," ","integrate(sec(d*x+c)^10*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{315 \, a b^{3} \cos\left(d x + c\right) + 420 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(8 \, {\left(21 \, a^{4} - 18 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{8} + 4 \, {\left(21 \, a^{4} - 18 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(21 \, a^{4} - 18 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} + 35 \, b^{4} + 10 \, {\left(27 \, a^{2} b^{2} - 5 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{630 \, d \cos\left(d x + c\right)^{9}}"," ",0,"1/630*(315*a*b^3*cos(d*x + c) + 420*(a^3*b - a*b^3)*cos(d*x + c)^3 + 2*(8*(21*a^4 - 18*a^2*b^2 + b^4)*cos(d*x + c)^8 + 4*(21*a^4 - 18*a^2*b^2 + b^4)*cos(d*x + c)^6 + 3*(21*a^4 - 18*a^2*b^2 + b^4)*cos(d*x + c)^4 + 35*b^4 + 10*(27*a^2*b^2 - 5*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^9)","A",0
90,1,251,0,0.899364," ","integrate(sec(d*x+c)^11*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{315 \, {\left(80 \, a^{4} - 60 \, a^{2} b^{2} + 3 \, b^{4}\right)} \cos\left(d x + c\right)^{10} \log\left(\sin\left(d x + c\right) + 1\right) - 315 \, {\left(80 \, a^{4} - 60 \, a^{2} b^{2} + 3 \, b^{4}\right)} \cos\left(d x + c\right)^{10} \log\left(-\sin\left(d x + c\right) + 1\right) + 71680 \, a b^{3} \cos\left(d x + c\right) + 92160 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3} + 42 \, {\left(15 \, {\left(80 \, a^{4} - 60 \, a^{2} b^{2} + 3 \, b^{4}\right)} \cos\left(d x + c\right)^{8} + 10 \, {\left(80 \, a^{4} - 60 \, a^{2} b^{2} + 3 \, b^{4}\right)} \cos\left(d x + c\right)^{6} + 8 \, {\left(80 \, a^{4} - 60 \, a^{2} b^{2} + 3 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 384 \, b^{4} + 48 \, {\left(60 \, a^{2} b^{2} - 11 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{161280 \, d \cos\left(d x + c\right)^{10}}"," ",0,"1/161280*(315*(80*a^4 - 60*a^2*b^2 + 3*b^4)*cos(d*x + c)^10*log(sin(d*x + c) + 1) - 315*(80*a^4 - 60*a^2*b^2 + 3*b^4)*cos(d*x + c)^10*log(-sin(d*x + c) + 1) + 71680*a*b^3*cos(d*x + c) + 92160*(a^3*b - a*b^3)*cos(d*x + c)^3 + 42*(15*(80*a^4 - 60*a^2*b^2 + 3*b^4)*cos(d*x + c)^8 + 10*(80*a^4 - 60*a^2*b^2 + 3*b^4)*cos(d*x + c)^6 + 8*(80*a^4 - 60*a^2*b^2 + 3*b^4)*cos(d*x + c)^4 + 384*b^4 + 48*(60*a^2*b^2 - 11*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^10)","A",0
91,1,194,0,0.482592," ","integrate(sec(d*x+c)^12*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{924 \, a b^{3} \cos\left(d x + c\right) + 1155 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(16 \, {\left(33 \, a^{4} - 22 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{10} + 8 \, {\left(33 \, a^{4} - 22 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{8} + 6 \, {\left(33 \, a^{4} - 22 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{6} + 5 \, {\left(33 \, a^{4} - 22 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} + 105 \, b^{4} + 70 \, {\left(11 \, a^{2} b^{2} - 2 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{2310 \, d \cos\left(d x + c\right)^{11}}"," ",0,"1/2310*(924*a*b^3*cos(d*x + c) + 1155*(a^3*b - a*b^3)*cos(d*x + c)^3 + 2*(16*(33*a^4 - 22*a^2*b^2 + b^4)*cos(d*x + c)^10 + 8*(33*a^4 - 22*a^2*b^2 + b^4)*cos(d*x + c)^8 + 6*(33*a^4 - 22*a^2*b^2 + b^4)*cos(d*x + c)^6 + 5*(33*a^4 - 22*a^2*b^2 + b^4)*cos(d*x + c)^4 + 105*b^4 + 70*(11*a^2*b^2 - 2*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^11)","A",0
92,1,250,0,0.808497," ","integrate(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","-\frac{640 \, b^{5} \cos\left(d x + c\right)^{6} + 384 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{10} + 960 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{8} - 15 \, {\left(63 \, a^{5} + 70 \, a^{3} b^{2} + 15 \, a b^{4}\right)} d x - {\left(384 \, {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{9} + 48 \, {\left(9 \, a^{5} + 10 \, a^{3} b^{2} - 55 \, a b^{4}\right)} \cos\left(d x + c\right)^{7} + 8 \, {\left(63 \, a^{5} + 70 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 10 \, {\left(63 \, a^{5} + 70 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(63 \, a^{5} + 70 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3840 \, d}"," ",0,"-1/3840*(640*b^5*cos(d*x + c)^6 + 384*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^10 + 960*(5*a^2*b^3 - b^5)*cos(d*x + c)^8 - 15*(63*a^5 + 70*a^3*b^2 + 15*a*b^4)*d*x - (384*(a^5 - 10*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^9 + 48*(9*a^5 + 10*a^3*b^2 - 55*a*b^4)*cos(d*x + c)^7 + 8*(63*a^5 + 70*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^5 + 10*(63*a^5 + 70*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^3 + 15*(63*a^5 + 70*a^3*b^2 + 15*a*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
93,1,217,0,0.677356," ","integrate(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","-\frac{63 \, b^{5} \cos\left(d x + c\right)^{5} + 35 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{9} + 90 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{7} - {\left(35 \, {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{8} + 10 \, {\left(4 \, a^{5} + 5 \, a^{3} b^{2} - 25 \, a b^{4}\right)} \cos\left(d x + c\right)^{6} + 128 \, a^{5} + 160 \, a^{3} b^{2} + 40 \, a b^{4} + 3 \, {\left(16 \, a^{5} + 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(16 \, a^{5} + 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{315 \, d}"," ",0,"-1/315*(63*b^5*cos(d*x + c)^5 + 35*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^9 + 90*(5*a^2*b^3 - b^5)*cos(d*x + c)^7 - (35*(a^5 - 10*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^8 + 10*(4*a^5 + 5*a^3*b^2 - 25*a*b^4)*cos(d*x + c)^6 + 128*a^5 + 160*a^3*b^2 + 40*a*b^4 + 3*(16*a^5 + 20*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^4 + 4*(16*a^5 + 20*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
94,1,220,0,0.703886," ","integrate(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","-\frac{96 \, b^{5} \cos\left(d x + c\right)^{4} + 48 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{8} + 128 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{6} - 15 \, {\left(7 \, a^{5} + 10 \, a^{3} b^{2} + 3 \, a b^{4}\right)} d x - {\left(48 \, {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{7} + 8 \, {\left(7 \, a^{5} + 10 \, a^{3} b^{2} - 45 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 10 \, {\left(7 \, a^{5} + 10 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(7 \, a^{5} + 10 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{384 \, d}"," ",0,"-1/384*(96*b^5*cos(d*x + c)^4 + 48*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^8 + 128*(5*a^2*b^3 - b^5)*cos(d*x + c)^6 - 15*(7*a^5 + 10*a^3*b^2 + 3*a*b^4)*d*x - (48*(a^5 - 10*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^7 + 8*(7*a^5 + 10*a^3*b^2 - 45*a*b^4)*cos(d*x + c)^5 + 10*(7*a^5 + 10*a^3*b^2 + 3*a*b^4)*cos(d*x + c)^3 + 15*(7*a^5 + 10*a^3*b^2 + 3*a*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
95,1,186,0,0.629656," ","integrate(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","-\frac{35 \, b^{5} \cos\left(d x + c\right)^{3} + 15 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{7} + 42 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{5} - {\left(15 \, {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{6} + 48 \, a^{5} + 80 \, a^{3} b^{2} + 30 \, a b^{4} + 6 \, {\left(3 \, a^{5} + 5 \, a^{3} b^{2} - 20 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} + {\left(24 \, a^{5} + 40 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{105 \, d}"," ",0,"-1/105*(35*b^5*cos(d*x + c)^3 + 15*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^7 + 42*(5*a^2*b^3 - b^5)*cos(d*x + c)^5 - (15*(a^5 - 10*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^6 + 48*a^5 + 80*a^3*b^2 + 30*a*b^4 + 6*(3*a^5 + 5*a^3*b^2 - 20*a*b^4)*cos(d*x + c)^4 + (24*a^5 + 40*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
96,1,182,0,0.618726," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","-\frac{24 \, b^{5} \cos\left(d x + c\right)^{2} + 8 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{6} + 24 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{4} - 15 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d x - {\left(8 \, {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 10 \, {\left(a^{5} + 2 \, a^{3} b^{2} - 7 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, d}"," ",0,"-1/48*(24*b^5*cos(d*x + c)^2 + 8*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^6 + 24*(5*a^2*b^3 - b^5)*cos(d*x + c)^4 - 15*(a^5 + 2*a^3*b^2 + a*b^4)*d*x - (8*(a^5 - 10*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^5 + 10*(a^5 + 2*a^3*b^2 - 7*a*b^4)*cos(d*x + c)^3 + 15*(a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
97,1,155,0,0.679308," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","-\frac{15 \, b^{5} \cos\left(d x + c\right) + 3 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{5} + 10 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{3} - {\left(8 \, a^{5} + 20 \, a^{3} b^{2} + 15 \, a b^{4} + 3 \, {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{5} + 5 \, a^{3} b^{2} - 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{15 \, d}"," ",0,"-1/15*(15*b^5*cos(d*x + c) + 3*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^5 + 10*(5*a^2*b^3 - b^5)*cos(d*x + c)^3 - (8*a^5 + 20*a^3*b^2 + 15*a*b^4 + 3*(a^5 - 10*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^4 + 2*(2*a^5 + 5*a^3*b^2 - 15*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
98,1,160,0,0.534359," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","-\frac{8 \, b^{5} \log\left(-\cos\left(d x + c\right)\right) + 2 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} - {\left(3 \, a^{5} + 10 \, a^{3} b^{2} + 15 \, a b^{4}\right)} d x + 8 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} - {\left(2 \, {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, a^{5} + 10 \, a^{3} b^{2} - 25 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/8*(8*b^5*log(-cos(d*x + c)) + 2*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^4 - (3*a^5 + 10*a^3*b^2 + 15*a*b^4)*d*x + 8*(5*a^2*b^3 - b^5)*cos(d*x + c)^2 - (2*(a^5 - 10*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^3 + (3*a^5 + 10*a^3*b^2 - 25*a*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
99,1,177,0,0.608785," ","integrate(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","\frac{15 \, a b^{4} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, a b^{4} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 6 \, b^{5} - 2 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} - 12 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{5} + 5 \, a^{3} b^{2} - 10 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)}"," ",0,"1/6*(15*a*b^4*cos(d*x + c)*log(sin(d*x + c) + 1) - 15*a*b^4*cos(d*x + c)*log(-sin(d*x + c) + 1) + 6*b^5 - 2*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^4 - 12*(5*a^2*b^3 - b^5)*cos(d*x + c)^2 + 2*((a^5 - 10*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^3 + 2*(a^5 + 5*a^3*b^2 - 10*a*b^4)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
100,1,177,0,0.456105," ","integrate(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","\frac{2 \, b^{5} - 2 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} - 8 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} \log\left(-\cos\left(d x + c\right)\right) + {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5} + 2 \, {\left(a^{5} + 10 \, a^{3} b^{2} - 15 \, a b^{4}\right)} d x\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(10 \, a b^{4} \cos\left(d x + c\right) + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(2*b^5 - 2*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^4 - 8*(5*a^2*b^3 - b^5)*cos(d*x + c)^2*log(-cos(d*x + c)) + (5*a^4*b - 10*a^2*b^3 + b^5 + 2*(a^5 + 10*a^3*b^2 - 15*a*b^4)*d*x)*cos(d*x + c)^2 + 2*(10*a*b^4*cos(d*x + c) + (a^5 - 10*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
101,1,190,0,0.496743," ","integrate(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","\frac{4 \, b^{5} - 12 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 24 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(5 \, a b^{4} \cos\left(d x + c\right) + 2 \, {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(4*b^5 - 12*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^4 + 15*(4*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 15*(4*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 24*(5*a^2*b^3 - b^5)*cos(d*x + c)^2 + 6*(5*a*b^4*cos(d*x + c) + 2*(a^5 - 10*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
102,1,155,0,0.639939," ","integrate(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","\frac{12 \, {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d x \cos\left(d x + c\right)^{4} - 12 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(-\cos\left(d x + c\right)\right) + 3 \, b^{5} + 12 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 20 \, {\left(a b^{4} \cos\left(d x + c\right) + 2 \, {\left(3 \, a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/12*(12*(a^5 - 10*a^3*b^2 + 5*a*b^4)*d*x*cos(d*x + c)^4 - 12*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^4*log(-cos(d*x + c)) + 3*b^5 + 12*(5*a^2*b^3 - b^5)*cos(d*x + c)^2 + 20*(a*b^4*cos(d*x + c) + 2*(3*a^3*b^2 - 2*a*b^4)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
103,1,196,0,0.643155," ","integrate(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, a^{5} - 40 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(8 \, a^{5} - 40 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 48 \, b^{5} + 240 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} + 160 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 150 \, {\left(2 \, a b^{4} \cos\left(d x + c\right) + {\left(8 \, a^{3} b^{2} - 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(8*a^5 - 40*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(8*a^5 - 40*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 48*b^5 + 240*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^4 + 160*(5*a^2*b^3 - b^5)*cos(d*x + c)^2 + 150*(2*a*b^4*cos(d*x + c) + (8*a^3*b^2 - 5*a*b^4)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
104,1,144,0,0.522107," ","integrate(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","\frac{b^{5} + 3 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a b^{4} \cos\left(d x + c\right) + {\left(3 \, a^{5} - 10 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(5 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/6*(b^5 + 3*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^4 + 3*(5*a^2*b^3 - b^5)*cos(d*x + c)^2 + 2*(3*a*b^4*cos(d*x + c) + (3*a^5 - 10*a^3*b^2 + 3*a*b^4)*cos(d*x + c)^5 + 2*(5*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^6)","B",0
105,1,227,0,0.593732," ","integrate(sec(d*x+c)^8*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","\frac{105 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{7} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{7} \log\left(-\sin\left(d x + c\right) + 1\right) + 480 \, b^{5} + 1120 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} + 1344 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 70 \, {\left(40 \, a b^{4} \cos\left(d x + c\right) + 3 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 10 \, {\left(12 \, a^{3} b^{2} - 7 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{3360 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/3360*(105*(8*a^5 - 20*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^7*log(sin(d*x + c) + 1) - 105*(8*a^5 - 20*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^7*log(-sin(d*x + c) + 1) + 480*b^5 + 1120*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^4 + 1344*(5*a^2*b^3 - b^5)*cos(d*x + c)^2 + 70*(40*a*b^4*cos(d*x + c) + 3*(8*a^5 - 20*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^5 + 10*(12*a^3*b^2 - 7*a*b^4)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
106,1,176,0,0.447135," ","integrate(sec(d*x+c)^9*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","\frac{21 \, b^{5} + 42 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} + 56 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(2 \, {\left(7 \, a^{5} - 14 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{7} + 15 \, a b^{4} \cos\left(d x + c\right) + {\left(7 \, a^{5} - 14 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 6 \, {\left(7 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{168 \, d \cos\left(d x + c\right)^{8}}"," ",0,"1/168*(21*b^5 + 42*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^4 + 56*(5*a^2*b^3 - b^5)*cos(d*x + c)^2 + 8*(2*(7*a^5 - 14*a^3*b^2 + 3*a*b^4)*cos(d*x + c)^7 + 15*a*b^4*cos(d*x + c) + (7*a^5 - 14*a^3*b^2 + 3*a*b^4)*cos(d*x + c)^5 + 6*(7*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^8)","A",0
107,1,257,0,0.623803," ","integrate(sec(d*x+c)^10*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","\frac{315 \, {\left(48 \, a^{5} - 80 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{9} \log\left(\sin\left(d x + c\right) + 1\right) - 315 \, {\left(48 \, a^{5} - 80 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{9} \log\left(-\sin\left(d x + c\right) + 1\right) + 8960 \, b^{5} + 16128 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} + 23040 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 210 \, {\left(3 \, {\left(48 \, a^{5} - 80 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{7} + 240 \, a b^{4} \cos\left(d x + c\right) + 2 \, {\left(48 \, a^{5} - 80 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 40 \, {\left(16 \, a^{3} b^{2} - 9 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{80640 \, d \cos\left(d x + c\right)^{9}}"," ",0,"1/80640*(315*(48*a^5 - 80*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^9*log(sin(d*x + c) + 1) - 315*(48*a^5 - 80*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^9*log(-sin(d*x + c) + 1) + 8960*b^5 + 16128*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^4 + 23040*(5*a^2*b^3 - b^5)*cos(d*x + c)^2 + 210*(3*(48*a^5 - 80*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^7 + 240*a*b^4*cos(d*x + c) + 2*(48*a^5 - 80*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^5 + 40*(16*a^3*b^2 - 9*a*b^4)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^9)","A",0
108,1,207,0,0.527593," ","integrate(sec(d*x+c)^11*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","\frac{126 \, b^{5} + 210 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} + 315 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(8 \, {\left(21 \, a^{5} - 30 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{9} + 4 \, {\left(21 \, a^{5} - 30 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{7} + 175 \, a b^{4} \cos\left(d x + c\right) + 3 \, {\left(21 \, a^{5} - 30 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 50 \, {\left(9 \, a^{3} b^{2} - 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{1260 \, d \cos\left(d x + c\right)^{10}}"," ",0,"1/1260*(126*b^5 + 210*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^4 + 315*(5*a^2*b^3 - b^5)*cos(d*x + c)^2 + 4*(8*(21*a^5 - 30*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^9 + 4*(21*a^5 - 30*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^7 + 175*a*b^4*cos(d*x + c) + 3*(21*a^5 - 30*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^5 + 50*(9*a^3*b^2 - 5*a*b^4)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^10)","A",0
109,1,287,0,0.673904," ","integrate(sec(d*x+c)^12*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""fricas"")","\frac{3465 \, {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{11} \log\left(\sin\left(d x + c\right) + 1\right) - 3465 \, {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{11} \log\left(-\sin\left(d x + c\right) + 1\right) + 32256 \, b^{5} + 50688 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} + 78848 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 462 \, {\left(15 \, {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{9} + 10 \, {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{7} + 384 \, a b^{4} \cos\left(d x + c\right) + 8 \, {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 48 \, {\left(20 \, a^{3} b^{2} - 11 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{354816 \, d \cos\left(d x + c\right)^{11}}"," ",0,"1/354816*(3465*(16*a^5 - 20*a^3*b^2 + 3*a*b^4)*cos(d*x + c)^11*log(sin(d*x + c) + 1) - 3465*(16*a^5 - 20*a^3*b^2 + 3*a*b^4)*cos(d*x + c)^11*log(-sin(d*x + c) + 1) + 32256*b^5 + 50688*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(d*x + c)^4 + 78848*(5*a^2*b^3 - b^5)*cos(d*x + c)^2 + 462*(15*(16*a^5 - 20*a^3*b^2 + 3*a*b^4)*cos(d*x + c)^9 + 10*(16*a^5 - 20*a^3*b^2 + 3*a*b^4)*cos(d*x + c)^7 + 384*a*b^4*cos(d*x + c) + 8*(16*a^5 - 20*a^3*b^2 + 3*a*b^4)*cos(d*x + c)^5 + 48*(20*a^3*b^2 - 11*a*b^4)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^11)","A",0
110,1,208,0,0.598435," ","integrate(cos(d*x+c)^5/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, b^{5} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{5} + 10 \, a^{3} b^{2} + 15 \, a b^{4}\right)} d x + 4 \, {\left(a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, a^{5} + 10 \, a^{3} b^{2} + 7 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d}"," ",0,"1/8*(4*b^5*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) + 2*(a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^4 + (3*a^5 + 10*a^3*b^2 + 15*a*b^4)*d*x + 4*(a^2*b^3 + b^5)*cos(d*x + c)^2 + (2*(a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c)^3 + (3*a^5 + 10*a^3*b^2 + 7*a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d)","A",0
111,1,262,0,0.573380," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, \sqrt{a^{2} + b^{2}} b^{4} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right) + 2 \, {\left(2 \, a^{5} + 7 \, a^{3} b^{2} + 5 \, a b^{4} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d}"," ",0,"1/6*(3*sqrt(a^2 + b^2)*b^4*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) + 2*(a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^3 + 6*(a^2*b^3 + b^5)*cos(d*x + c) + 2*(2*a^5 + 7*a^3*b^2 + 5*a*b^4 + (a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d)","A",0
112,1,119,0,0.586694," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{b^{3} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) + {\left(a^{3} + 3 \, a b^{2}\right)} d x + {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d}"," ",0,"1/2*(b^3*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) + (a^3 + 3*a*b^2)*d*x + (a^2*b + b^3)*cos(d*x + c)^2 + (a^3 + a*b^2)*cos(d*x + c)*sin(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d)","A",0
113,1,187,0,0.644208," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} + b^{2}} b^{2} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) + 2 \, {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right) + 2 \, {\left(a^{3} + a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d}"," ",0,"1/2*(sqrt(a^2 + b^2)*b^2*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) + 2*(a^2*b + b^3)*cos(d*x + c) + 2*(a^3 + a*b^2)*sin(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d)","B",0
114,1,61,0,0.694793," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a d x + b \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right)}{2 \, {\left(a^{2} + b^{2}\right)} d}"," ",0,"1/2*(2*a*d*x + b*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2))/((a^2 + b^2)*d)","A",0
115,1,131,0,0.763501," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right)}{2 \, \sqrt{a^{2} + b^{2}} d}"," ",0,"1/2*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2))/(sqrt(a^2 + b^2)*d)","B",0
116,1,59,0,0.754553," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - \log\left(\cos\left(d x + c\right)^{2}\right)}{2 \, b d}"," ",0,"1/2*(log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - log(cos(d*x + c)^2))/(b*d)","A",0
117,1,191,0,0.717615," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{a \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - a \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) - \sqrt{a^{2} + b^{2}} \cos\left(d x + c\right) \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 2 \, b}{2 \, b^{2} d \cos\left(d x + c\right)}"," ",0,"-1/2*(a*cos(d*x + c)*log(sin(d*x + c) + 1) - a*cos(d*x + c)*log(-sin(d*x + c) + 1) - sqrt(a^2 + b^2)*cos(d*x + c)*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 2*b)/(b^2*d*cos(d*x + c))","B",0
118,1,117,0,0.659001," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\cos\left(d x + c\right)^{2}\right) - 2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + b^{2}}{2 \, b^{3} d \cos\left(d x + c\right)^{2}}"," ",0,"1/2*((a^2 + b^2)*cos(d*x + c)^2*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - (a^2 + b^2)*cos(d*x + c)^2*log(cos(d*x + c)^2) - 2*a*b*cos(d*x + c)*sin(d*x + c) + b^2)/(b^3*d*cos(d*x + c)^2)","A",0
119,1,259,0,0.715277," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, {\left(a^{2} + b^{2}\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{3} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) - 6 \, a b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) + 4 \, b^{3} + 12 \, {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}}{12 \, b^{4} d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(6*(a^2 + b^2)^(3/2)*cos(d*x + c)^3*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 3*(2*a^3 + 3*a*b^2)*cos(d*x + c)^3*log(sin(d*x + c) + 1) + 3*(2*a^3 + 3*a*b^2)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) - 6*a*b^2*cos(d*x + c)*sin(d*x + c) + 4*b^3 + 12*(a^2*b + b^3)*cos(d*x + c)^2)/(b^4*d*cos(d*x + c)^3)","A",0
120,1,183,0,0.451924," ","integrate(sec(d*x+c)^5/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - 6 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(\cos\left(d x + c\right)^{2}\right) + 3 \, b^{4} + 6 \, {\left(a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(a b^{3} \cos\left(d x + c\right) + {\left(3 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{12 \, b^{5} d \cos\left(d x + c\right)^{4}}"," ",0,"1/12*(6*(a^4 + 2*a^2*b^2 + b^4)*cos(d*x + c)^4*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 6*(a^4 + 2*a^2*b^2 + b^4)*cos(d*x + c)^4*log(cos(d*x + c)^2) + 3*b^4 + 6*(a^2*b^2 + b^4)*cos(d*x + c)^2 - 4*(a*b^3*cos(d*x + c) + (3*a^3*b + 5*a*b^3)*cos(d*x + c)^3)*sin(d*x + c))/(b^5*d*cos(d*x + c)^4)","A",0
121,1,346,0,0.895081," ","integrate(sec(d*x+c)^6/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{120 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}} \cos\left(d x + c\right)^{5} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 15 \, {\left(8 \, a^{5} + 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, {\left(8 \, a^{5} + 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 48 \, b^{5} + 240 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} + 80 \, {\left(a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} - 30 \, {\left(2 \, a b^{4} \cos\left(d x + c\right) + {\left(4 \, a^{3} b^{2} + 7 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{240 \, b^{6} d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(120*(a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)*cos(d*x + c)^5*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 15*(8*a^5 + 20*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^5*log(sin(d*x + c) + 1) + 15*(8*a^5 + 20*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 48*b^5 + 240*(a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^4 + 80*(a^2*b^3 + b^5)*cos(d*x + c)^2 - 30*(2*a*b^4*cos(d*x + c) + (4*a^3*b^2 + 7*a*b^4)*cos(d*x + c)^3)*sin(d*x + c))/(b^6*d*cos(d*x + c)^5)","A",0
122,1,279,0,0.618651," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{2} b^{3} + 3 \, b^{5} - {\left(a^{5} + 6 \, a^{3} b^{2} - 3 \, a b^{4}\right)} d x\right)} \cos\left(d x + c\right) + 4 \, {\left(a^{2} b^{3} \cos\left(d x + c\right) + a b^{4} \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - {\left(a^{3} b^{2} - a b^{4} - {\left(a^{4} b + 6 \, a^{2} b^{3} - 3 \, b^{5}\right)} d x - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d \sin\left(d x + c\right)\right)}}"," ",0,"1/2*((a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^3 - (a^2*b^3 + 3*b^5 - (a^5 + 6*a^3*b^2 - 3*a*b^4)*d*x)*cos(d*x + c) + 4*(a^2*b^3*cos(d*x + c) + a*b^4*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - (a^3*b^2 - a*b^4 - (a^4*b + 6*a^2*b^3 - 3*b^5)*d*x - (a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d*cos(d*x + c) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d*sin(d*x + c))","A",0
123,1,302,0,0.565505," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, a^{4} b - 2 \, a^{2} b^{3} - 4 \, b^{5} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, {\left(a^{2} b^{2} \cos\left(d x + c\right) + a b^{3} \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right)}{2 \, {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d \sin\left(d x + c\right)\right)}}"," ",0,"1/2*(2*a^4*b - 2*a^2*b^3 - 4*b^5 + 2*(a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c)*sin(d*x + c) + 3*(a^2*b^2*cos(d*x + c) + a*b^3*sin(d*x + c))*sqrt(a^2 + b^2)*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)))/((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d*cos(d*x + c) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d*sin(d*x + c))","B",0
124,1,173,0,0.538281," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(b^{3} - {\left(a^{3} - a b^{2}\right)} d x\right)} \cos\left(d x + c\right) - {\left(a^{2} b \cos\left(d x + c\right) + a b^{2} \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - {\left(a b^{2} + {\left(a^{2} b - b^{3}\right)} d x\right)} \sin\left(d x + c\right)}{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \sin\left(d x + c\right)}"," ",0,"-((b^3 - (a^3 - a*b^2)*d*x)*cos(d*x + c) - (a^2*b*cos(d*x + c) + a*b^2*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - (a*b^2 + (a^2*b - b^3)*d*x)*sin(d*x + c))/((a^5 + 2*a^3*b^2 + a*b^4)*d*cos(d*x + c) + (a^4*b + 2*a^2*b^3 + b^5)*d*sin(d*x + c))","B",0
125,1,215,0,0.552828," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} b + 2 \, b^{3} - {\left(a^{2} \cos\left(d x + c\right) + a b \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right)}{2 \, {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \sin\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*a^2*b + 2*b^3 - (a^2*cos(d*x + c) + a*b*sin(d*x + c))*sqrt(a^2 + b^2)*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)))/((a^5 + 2*a^3*b^2 + a*b^4)*d*cos(d*x + c) + (a^4*b + 2*a^2*b^3 + b^5)*d*sin(d*x + c))","B",0
126,1,57,0,0.552557," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{b \cos\left(d x + c\right) - a \sin\left(d x + c\right)}{{\left(a^{3} + a b^{2}\right)} d \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} d \sin\left(d x + c\right)}"," ",0,"-(b*cos(d*x + c) - a*sin(d*x + c))/((a^3 + a*b^2)*d*cos(d*x + c) + (a^2*b + b^3)*d*sin(d*x + c))","A",0
127,1,293,0,0.588801," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} b + 2 \, b^{3} - {\left(a^{2} \cos\left(d x + c\right) + a b \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - {\left({\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} d \sin\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*a^2*b + 2*b^3 - (a^2*cos(d*x + c) + a*b*sin(d*x + c))*sqrt(a^2 + b^2)*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - ((a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))*log(sin(d*x + c) + 1) + ((a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))*log(-sin(d*x + c) + 1))/((a^3*b^2 + a*b^4)*d*cos(d*x + c) + (a^2*b^3 + b^5)*d*sin(d*x + c))","B",0
128,1,178,0,0.482307," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - b^{2} + {\left(a^{2} \cos\left(d x + c\right)^{2} + a b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - {\left(a^{2} \cos\left(d x + c\right)^{2} + a b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2}\right)}{a b^{3} d \cos\left(d x + c\right)^{2} + b^{4} d \cos\left(d x + c\right) \sin\left(d x + c\right)}"," ",0,"-(2*b^2*cos(d*x + c)^2 - 2*a*b*cos(d*x + c)*sin(d*x + c) - b^2 + (a^2*cos(d*x + c)^2 + a*b*cos(d*x + c)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - (a^2*cos(d*x + c)^2 + a*b*cos(d*x + c)*sin(d*x + c))*log(cos(d*x + c)^2))/(a*b^3*d*cos(d*x + c)^2 + b^4*d*cos(d*x + c)*sin(d*x + c))","B",0
129,1,355,0,0.614711," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, a b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, b^{3} + 6 \, {\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2} - 6 \, {\left(a^{2} \cos\left(d x + c\right)^{3} + a b \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 3 \, {\left({\left(2 \, a^{3} + a b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(2 \, a^{3} + a b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{4 \, {\left(a b^{4} d \cos\left(d x + c\right)^{3} + b^{5} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)\right)}}"," ",0,"-1/4*(6*a*b^2*cos(d*x + c)*sin(d*x + c) - 2*b^3 + 6*(2*a^2*b + b^3)*cos(d*x + c)^2 - 6*(a^2*cos(d*x + c)^3 + a*b*cos(d*x + c)^2*sin(d*x + c))*sqrt(a^2 + b^2)*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 3*((2*a^3 + a*b^2)*cos(d*x + c)^3 + (2*a^2*b + b^3)*cos(d*x + c)^2*sin(d*x + c))*log(sin(d*x + c) + 1) + 3*((2*a^3 + a*b^2)*cos(d*x + c)^3 + (2*a^2*b + b^3)*cos(d*x + c)^2*sin(d*x + c))*log(-sin(d*x + c) + 1))/(a*b^4*d*cos(d*x + c)^3 + b^5*d*cos(d*x + c)^2*sin(d*x + c))","B",0
130,1,281,0,0.457803," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(3 \, a^{2} b^{2} + 2 \, b^{4}\right)} \cos\left(d x + c\right)^{4} - b^{4} - 2 \, {\left(3 \, a^{2} b^{2} + 2 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} \cos\left(d x + c\right)^{4} + {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} \cos\left(d x + c\right)^{4} + {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2}\right) + 2 \, {\left(a b^{3} \cos\left(d x + c\right) - 2 \, {\left(3 \, a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{3 \, {\left(a b^{5} d \cos\left(d x + c\right)^{4} + b^{6} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right)\right)}}"," ",0,"-1/3*(4*(3*a^2*b^2 + 2*b^4)*cos(d*x + c)^4 - b^4 - 2*(3*a^2*b^2 + 2*b^4)*cos(d*x + c)^2 + 6*((a^4 + a^2*b^2)*cos(d*x + c)^4 + (a^3*b + a*b^3)*cos(d*x + c)^3*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 6*((a^4 + a^2*b^2)*cos(d*x + c)^4 + (a^3*b + a*b^3)*cos(d*x + c)^3*sin(d*x + c))*log(cos(d*x + c)^2) + 2*(a*b^3*cos(d*x + c) - 2*(3*a^3*b + 2*a*b^3)*cos(d*x + c)^3)*sin(d*x + c))/(a*b^5*d*cos(d*x + c)^4 + b^6*d*cos(d*x + c)^3*sin(d*x + c))","B",0
131,1,480,0,0.565245," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{2} b^{4} - b^{6} + {\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(4 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) + 2 \, {\left(4 \, a^{6} b - 10 \, a^{4} b^{3} - 17 \, a^{2} b^{5} - 3 \, b^{7}\right)} \cos\left(d x + c\right) + 2 \, {\left(2 \, a^{5} b^{2} - 11 \, a^{3} b^{4} - 13 \, a b^{6} + 2 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}\right)} d\right)}}"," ",0,"1/4*(4*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*cos(d*x + c)^3 - 3*(4*a^2*b^4 - b^6 + (4*a^4*b^2 - 5*a^2*b^4 + b^6)*cos(d*x + c)^2 + 2*(4*a^3*b^3 - a*b^5)*cos(d*x + c)*sin(d*x + c))*sqrt(a^2 + b^2)*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) + 2*(4*a^6*b - 10*a^4*b^3 - 17*a^2*b^5 - 3*b^7)*cos(d*x + c) + 2*(2*a^5*b^2 - 11*a^3*b^4 - 13*a*b^6 + 2*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*d*cos(d*x + c)^2 + 2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)*sin(d*x + c) + (a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)*d)","B",0
132,1,341,0,0.565087," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{5 \, a^{2} b^{3} - b^{5} + 2 \, {\left(a^{3} b^{2} - 3 \, a b^{4}\right)} d x - 2 \, {\left(6 \, a^{2} b^{3} - {\left(a^{5} - 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} d x\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} - 3 \, a b^{4} + 2 \, {\left(a^{4} b - 3 \, a^{2} b^{3}\right)} d x\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(3 \, a^{2} b^{3} - b^{5} + {\left(3 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right)}{2 \, {\left({\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d\right)}}"," ",0,"1/2*(5*a^2*b^3 - b^5 + 2*(a^3*b^2 - 3*a*b^4)*d*x - 2*(6*a^2*b^3 - (a^5 - 4*a^3*b^2 + 3*a*b^4)*d*x)*cos(d*x + c)^2 + 2*(3*a^3*b^2 - 3*a*b^4 + 2*(a^4*b - 3*a^2*b^3)*d*x)*cos(d*x + c)*sin(d*x + c) + (3*a^2*b^3 - b^5 + (3*a^4*b - 4*a^2*b^3 + b^5)*cos(d*x + c)^2 + 2*(3*a^3*b^2 - a*b^4)*cos(d*x + c)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2))/((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d*cos(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d)","B",0
133,1,352,0,0.673125," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{2} b^{2} - b^{4} + {\left(2 \, a^{4} - 3 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) + 2 \, {\left(4 \, a^{4} b + 5 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right) + 6 \, {\left(a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d\right)}}"," ",0,"-1/4*((2*a^2*b^2 - b^4 + (2*a^4 - 3*a^2*b^2 + b^4)*cos(d*x + c)^2 + 2*(2*a^3*b - a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(a^2 + b^2)*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) + 2*(4*a^4*b + 5*a^2*b^3 + b^5)*cos(d*x + c) + 6*(a^3*b^2 + a*b^4)*sin(d*x + c))/((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d*cos(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d)","B",0
134,1,142,0,0.528247," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{4 \, a^{2} b \cos\left(d x + c\right)^{2} - a^{2} b + b^{3} - 2 \, {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d\right)}}"," ",0,"-1/2*(4*a^2*b*cos(d*x + c)^2 - a^2*b + b^3 - 2*(a^3 - a*b^2)*cos(d*x + c)*sin(d*x + c))/((a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*d)","B",0
135,1,294,0,0.611908," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 2 \, {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right) + 2 \, {\left(a^{3} + a b^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d\right)}}"," ",0,"1/4*((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)*sqrt(a^2 + b^2)*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 2*(a^2*b + b^3)*cos(d*x + c) + 2*(a^3 + a*b^2)*sin(d*x + c))/((a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*d)","B",0
136,1,284,0,0.596014," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, a^{2} b^{2} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b^{2} - b^{4} - 2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4} + {\left(a^{4} - b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - {\left(a^{2} b^{2} + b^{4} + {\left(a^{4} - b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2}\right)}{2 \, {\left({\left(a^{4} b^{3} - b^{7}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} b^{5} + b^{7}\right)} d\right)}}"," ",0,"1/2*(4*a^2*b^2*cos(d*x + c)^2 - 3*a^2*b^2 - b^4 - 2*(a^3*b - a*b^3)*cos(d*x + c)*sin(d*x + c) + (a^2*b^2 + b^4 + (a^4 - b^4)*cos(d*x + c)^2 + 2*(a^3*b + a*b^3)*cos(d*x + c)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - (a^2*b^2 + b^4 + (a^4 - b^4)*cos(d*x + c)^2 + 2*(a^3*b + a*b^3)*cos(d*x + c)*sin(d*x + c))*log(cos(d*x + c)^2))/((a^4*b^3 - b^7)*d*cos(d*x + c)^2 + 2*(a^3*b^4 + a*b^6)*d*cos(d*x + c)*sin(d*x + c) + (a^2*b^5 + b^7)*d)","B",0
137,1,513,0,0.616158," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, a^{2} b^{3} + 4 \, b^{5} + 6 \, {\left(2 \, a^{4} b + a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 18 \, {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, {\left({\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 6 \, {\left({\left(a^{5} - a b^{4}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 6 \, {\left({\left(a^{5} - a b^{4}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{4 \, {\left({\left(a^{4} b^{4} - b^{8}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)\right)}}"," ",0,"1/4*(4*a^2*b^3 + 4*b^5 + 6*(2*a^4*b + a^2*b^3 - b^5)*cos(d*x + c)^2 + 18*(a^3*b^2 + a*b^4)*cos(d*x + c)*sin(d*x + c) + 3*((2*a^4 - a^2*b^2 - b^4)*cos(d*x + c)^3 + 2*(2*a^3*b + a*b^3)*cos(d*x + c)^2*sin(d*x + c) + (2*a^2*b^2 + b^4)*cos(d*x + c))*sqrt(a^2 + b^2)*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 6*((a^5 - a*b^4)*cos(d*x + c)^3 + 2*(a^4*b + a^2*b^3)*cos(d*x + c)^2*sin(d*x + c) + (a^3*b^2 + a*b^4)*cos(d*x + c))*log(sin(d*x + c) + 1) + 6*((a^5 - a*b^4)*cos(d*x + c)^3 + 2*(a^4*b + a^2*b^3)*cos(d*x + c)^2*sin(d*x + c) + (a^3*b^2 + a*b^4)*cos(d*x + c))*log(-sin(d*x + c) + 1))/((a^4*b^4 - b^8)*d*cos(d*x + c)^3 + 2*(a^3*b^5 + a*b^7)*d*cos(d*x + c)^2*sin(d*x + c) + (a^2*b^6 + b^8)*d*cos(d*x + c))","B",0
138,1,354,0,0.692396," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{24 \, a^{2} b^{2} \cos\left(d x + c\right)^{4} + b^{4} - 2 \, {\left(9 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(3 \, a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + {\left(3 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - 2 \, {\left({\left(3 \, a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + {\left(3 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\cos\left(d x + c\right)^{2}\right) - 4 \, {\left(a b^{3} \cos\left(d x + c\right) + 3 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(2 \, a b^{6} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + b^{7} d \cos\left(d x + c\right)^{2} + {\left(a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/2*(24*a^2*b^2*cos(d*x + c)^4 + b^4 - 2*(9*a^2*b^2 + b^4)*cos(d*x + c)^2 + 2*((3*a^4 - 2*a^2*b^2 - b^4)*cos(d*x + c)^4 + 2*(3*a^3*b + a*b^3)*cos(d*x + c)^3*sin(d*x + c) + (3*a^2*b^2 + b^4)*cos(d*x + c)^2)*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 2*((3*a^4 - 2*a^2*b^2 - b^4)*cos(d*x + c)^4 + 2*(3*a^3*b + a*b^3)*cos(d*x + c)^3*sin(d*x + c) + (3*a^2*b^2 + b^4)*cos(d*x + c)^2)*log(cos(d*x + c)^2) - 4*(a*b^3*cos(d*x + c) + 3*(a^3*b - a*b^3)*cos(d*x + c)^3)*sin(d*x + c))/(2*a*b^6*d*cos(d*x + c)^3*sin(d*x + c) + b^7*d*cos(d*x + c)^2 + (a^2*b^5 - b^7)*d*cos(d*x + c)^4)","B",0
139,1,564,0,0.888736," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, b^{5} + 30 \, {\left(4 \, a^{4} b + a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{4} + 20 \, {\left(2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left({\left(4 \, a^{4} - 3 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + {\left(4 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 15 \, {\left({\left(4 \, a^{5} - a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{4} b + 3 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + {\left(4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, {\left({\left(4 \, a^{5} - a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{4} b + 3 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + {\left(4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 10 \, {\left(a b^{4} \cos\left(d x + c\right) - 6 \, {\left(3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{12 \, {\left(2 \, a b^{7} d \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + b^{8} d \cos\left(d x + c\right)^{3} + {\left(a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{5}\right)}}"," ",0,"1/12*(4*b^5 + 30*(4*a^4*b + a^2*b^3 - b^5)*cos(d*x + c)^4 + 20*(2*a^2*b^3 + b^5)*cos(d*x + c)^2 + 15*((4*a^4 - 3*a^2*b^2 - b^4)*cos(d*x + c)^5 + 2*(4*a^3*b + a*b^3)*cos(d*x + c)^4*sin(d*x + c) + (4*a^2*b^2 + b^4)*cos(d*x + c)^3)*sqrt(a^2 + b^2)*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 15*((4*a^5 - a^3*b^2 - 3*a*b^4)*cos(d*x + c)^5 + 2*(4*a^4*b + 3*a^2*b^3)*cos(d*x + c)^4*sin(d*x + c) + (4*a^3*b^2 + 3*a*b^4)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) + 15*((4*a^5 - a^3*b^2 - 3*a*b^4)*cos(d*x + c)^5 + 2*(4*a^4*b + 3*a^2*b^3)*cos(d*x + c)^4*sin(d*x + c) + (4*a^3*b^2 + 3*a*b^4)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 10*(a*b^4*cos(d*x + c) - 6*(3*a^3*b^2 + 2*a*b^4)*cos(d*x + c)^3)*sin(d*x + c))/(2*a*b^7*d*cos(d*x + c)^4*sin(d*x + c) + b^8*d*cos(d*x + c)^3 + (a^2*b^6 - b^8)*d*cos(d*x + c)^5)","A",0
140,1,476,0,0.776813," ","integrate(sec(d*x+c)^5/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{8 \, {\left(15 \, a^{4} b^{2} + 13 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{6} + b^{6} - 2 \, {\left(45 \, a^{4} b^{2} + 44 \, a^{2} b^{4} + 3 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(5 \, a^{2} b^{4} + 3 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left({\left(5 \, a^{6} + a^{4} b^{2} - 5 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{6} + 2 \, {\left(5 \, a^{5} b + 6 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{5} \sin\left(d x + c\right) + {\left(5 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - 6 \, {\left({\left(5 \, a^{6} + a^{4} b^{2} - 5 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{6} + 2 \, {\left(5 \, a^{5} b + 6 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{5} \sin\left(d x + c\right) + {\left(5 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(\cos\left(d x + c\right)^{2}\right) - 2 \, {\left(a b^{5} \cos\left(d x + c\right) + 2 \, {\left(15 \, a^{5} b - 2 \, a^{3} b^{3} - 13 \, a b^{5}\right)} \cos\left(d x + c\right)^{5} + 10 \, {\left(a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{4 \, {\left(2 \, a b^{8} d \cos\left(d x + c\right)^{5} \sin\left(d x + c\right) + b^{9} d \cos\left(d x + c\right)^{4} + {\left(a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"1/4*(8*(15*a^4*b^2 + 13*a^2*b^4)*cos(d*x + c)^6 + b^6 - 2*(45*a^4*b^2 + 44*a^2*b^4 + 3*b^6)*cos(d*x + c)^4 + (5*a^2*b^4 + 3*b^6)*cos(d*x + c)^2 + 6*((5*a^6 + a^4*b^2 - 5*a^2*b^4 - b^6)*cos(d*x + c)^6 + 2*(5*a^5*b + 6*a^3*b^3 + a*b^5)*cos(d*x + c)^5*sin(d*x + c) + (5*a^4*b^2 + 6*a^2*b^4 + b^6)*cos(d*x + c)^4)*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 6*((5*a^6 + a^4*b^2 - 5*a^2*b^4 - b^6)*cos(d*x + c)^6 + 2*(5*a^5*b + 6*a^3*b^3 + a*b^5)*cos(d*x + c)^5*sin(d*x + c) + (5*a^4*b^2 + 6*a^2*b^4 + b^6)*cos(d*x + c)^4)*log(cos(d*x + c)^2) - 2*(a*b^5*cos(d*x + c) + 2*(15*a^5*b - 2*a^3*b^3 - 13*a*b^5)*cos(d*x + c)^5 + 10*(a^3*b^3 + a*b^5)*cos(d*x + c)^3)*sin(d*x + c))/(2*a*b^8*d*cos(d*x + c)^5*sin(d*x + c) + b^9*d*cos(d*x + c)^4 + (a^2*b^7 - b^9)*d*cos(d*x + c)^6)","B",0
141,1,575,0,0.581844," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{{\left(54 \, a^{4} b^{3} - 30 \, a^{2} b^{5} + 4 \, b^{7} - 3 \, {\left(a^{7} - 9 \, a^{5} b^{2} + 19 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d x\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(10 \, a^{4} b^{3} - 11 \, a^{2} b^{5} + b^{7} + 3 \, {\left(a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} d x\right)} \cos\left(d x + c\right) - 6 \, {\left({\left(a^{6} b - 4 \, a^{4} b^{3} + 3 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} \cos\left(d x + c\right) + {\left(a^{3} b^{4} - a b^{6} + {\left(3 \, a^{5} b^{2} - 4 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - {\left(13 \, a^{3} b^{4} - 9 \, a b^{6} + 3 \, {\left(a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} d x + {\left(18 \, a^{5} b^{2} - 58 \, a^{3} b^{4} + 12 \, a b^{6} + 3 \, {\left(3 \, a^{6} b - 19 \, a^{4} b^{3} + 9 \, a^{2} b^{5} - b^{7}\right)} d x\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left({\left(a^{11} + a^{9} b^{2} - 6 \, a^{7} b^{4} - 14 \, a^{5} b^{6} - 11 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right) + {\left({\left(3 \, a^{10} b + 11 \, a^{8} b^{3} + 14 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - a^{2} b^{9} - b^{11}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{8} b^{3} + 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + 4 \, a^{2} b^{9} + b^{11}\right)} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/3*((54*a^4*b^3 - 30*a^2*b^5 + 4*b^7 - 3*(a^7 - 9*a^5*b^2 + 19*a^3*b^4 - 3*a*b^6)*d*x)*cos(d*x + c)^3 - 3*(10*a^4*b^3 - 11*a^2*b^5 + b^7 + 3*(a^5*b^2 - 6*a^3*b^4 + a*b^6)*d*x)*cos(d*x + c) - 6*((a^6*b - 4*a^4*b^3 + 3*a^2*b^5)*cos(d*x + c)^3 + 3*(a^4*b^3 - a^2*b^5)*cos(d*x + c) + (a^3*b^4 - a*b^6 + (3*a^5*b^2 - 4*a^3*b^4 + a*b^6)*cos(d*x + c)^2)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - (13*a^3*b^4 - 9*a*b^6 + 3*(a^4*b^3 - 6*a^2*b^5 + b^7)*d*x + (18*a^5*b^2 - 58*a^3*b^4 + 12*a*b^6 + 3*(3*a^6*b - 19*a^4*b^3 + 9*a^2*b^5 - b^7)*d*x)*cos(d*x + c)^2)*sin(d*x + c))/((a^11 + a^9*b^2 - 6*a^7*b^4 - 14*a^5*b^6 - 11*a^3*b^8 - 3*a*b^10)*d*cos(d*x + c)^3 + 3*(a^9*b^2 + 4*a^7*b^4 + 6*a^5*b^6 + 4*a^3*b^8 + a*b^10)*d*cos(d*x + c) + ((3*a^10*b + 11*a^8*b^3 + 14*a^6*b^5 + 6*a^4*b^7 - a^2*b^9 - b^11)*d*cos(d*x + c)^2 + (a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*d)*sin(d*x + c))","B",0
142,1,524,0,0.758007," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{22 \, a^{4} b^{3} + 14 \, a^{2} b^{5} - 8 \, b^{7} + 12 \, {\left(3 \, a^{6} b + 2 \, a^{4} b^{3} + b^{7}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(9 \, a^{5} b^{2} + 8 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, {\left({\left(2 \, a^{6} - 9 \, a^{4} b^{2} + 9 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{4} b^{2} - 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) + {\left(2 \, a^{3} b^{3} - 3 \, a b^{5} + {\left(6 \, a^{5} b - 11 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right)}{12 \, {\left({\left(a^{11} + a^{9} b^{2} - 6 \, a^{7} b^{4} - 14 \, a^{5} b^{6} - 11 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right) + {\left({\left(3 \, a^{10} b + 11 \, a^{8} b^{3} + 14 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - a^{2} b^{9} - b^{11}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{8} b^{3} + 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + 4 \, a^{2} b^{9} + b^{11}\right)} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/12*(22*a^4*b^3 + 14*a^2*b^5 - 8*b^7 + 12*(3*a^6*b + 2*a^4*b^3 + b^7)*cos(d*x + c)^2 + 6*(9*a^5*b^2 + 8*a^3*b^4 - a*b^6)*cos(d*x + c)*sin(d*x + c) + 3*((2*a^6 - 9*a^4*b^2 + 9*a^2*b^4)*cos(d*x + c)^3 + 3*(2*a^4*b^2 - 3*a^2*b^4)*cos(d*x + c) + (2*a^3*b^3 - 3*a*b^5 + (6*a^5*b - 11*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 + b^2)*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)))/((a^11 + a^9*b^2 - 6*a^7*b^4 - 14*a^5*b^6 - 11*a^3*b^8 - 3*a*b^10)*d*cos(d*x + c)^3 + 3*(a^9*b^2 + 4*a^7*b^4 + 6*a^5*b^6 + 4*a^3*b^8 + a*b^10)*d*cos(d*x + c) + ((3*a^10*b + 11*a^8*b^3 + 14*a^6*b^5 + 6*a^4*b^7 - a^2*b^9 - b^11)*d*cos(d*x + c)^2 + (a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*d)*sin(d*x + c))","B",0
143,1,255,0,0.568911," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{{\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(a^{4} b - 3 \, a^{2} b^{3}\right)} \cos\left(d x + c\right) - {\left(a^{3} b^{2} - 3 \, a b^{4} + {\left(3 \, a^{5} - 10 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left({\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b^{2} + 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right) + {\left({\left(3 \, a^{8} b + 8 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - b^{9}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/3*((9*a^4*b - 6*a^2*b^3 + b^5)*cos(d*x + c)^3 - 3*(a^4*b - 3*a^2*b^3)*cos(d*x + c) - (a^3*b^2 - 3*a*b^4 + (3*a^5 - 10*a^3*b^2 + 3*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/((a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d*cos(d*x + c)^3 + 3*(a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*d*cos(d*x + c) + ((3*a^8*b + 8*a^6*b^3 + 6*a^4*b^5 - b^9)*d*cos(d*x + c)^2 + (a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*d)*sin(d*x + c))","B",0
144,1,420,0,0.741379," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{2 \, a^{4} b - 2 \, a^{2} b^{3} - 4 \, b^{5} - 12 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(a^{5} - a b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, {\left(3 \, a^{2} b^{2} \cos\left(d x + c\right) + {\left(a^{4} - 3 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(a b^{3} + {\left(3 \, a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right)}{12 \, {\left({\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b^{2} + 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right) + {\left({\left(3 \, a^{8} b + 8 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - b^{9}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/12*(2*a^4*b - 2*a^2*b^3 - 4*b^5 - 12*(a^4*b + a^2*b^3)*cos(d*x + c)^2 + 6*(a^5 - a*b^4)*cos(d*x + c)*sin(d*x + c) + 3*(3*a^2*b^2*cos(d*x + c) + (a^4 - 3*a^2*b^2)*cos(d*x + c)^3 + (a*b^3 + (3*a^3*b - a*b^3)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 + b^2)*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)))/((a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d*cos(d*x + c)^3 + 3*(a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*d*cos(d*x + c) + ((3*a^8*b + 8*a^6*b^3 + 6*a^4*b^5 - b^9)*d*cos(d*x + c)^2 + (a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*d)*sin(d*x + c))","B",0
145,1,217,0,0.558290," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right) - {\left(a^{3} + 3 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left({\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) + {\left({\left(3 \, a^{6} b + 5 \, a^{4} b^{3} + a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/3*(2*(3*a^2*b - b^3)*cos(d*x + c)^3 - 3*(a^2*b - b^3)*cos(d*x + c) - (a^3 + 3*a*b^2 + 2*(a^3 - 3*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/((a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*d*cos(d*x + c)^3 + 3*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d*cos(d*x + c) + ((3*a^6*b + 5*a^4*b^3 + a^2*b^5 - b^7)*d*cos(d*x + c)^2 + (a^4*b^3 + 2*a^2*b^5 + b^7)*d)*sin(d*x + c))","B",0
146,1,745,0,0.781101," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{22 \, a^{4} b^{3} + 38 \, a^{2} b^{5} + 16 \, b^{7} + 12 \, {\left(a^{6} b - 2 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(5 \, a^{5} b^{2} + 8 \, a^{3} b^{4} + 3 \, a b^{6}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, {\left({\left(2 \, a^{6} - 3 \, a^{4} b^{2} - 9 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) + {\left(2 \, a^{3} b^{3} + 3 \, a b^{5} + {\left(6 \, a^{5} b + 7 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 6 \, {\left({\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7} + {\left(3 \, a^{6} b + 5 \, a^{4} b^{3} + a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 6 \, {\left({\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7} + {\left(3 \, a^{6} b + 5 \, a^{4} b^{3} + a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{12 \, {\left({\left(a^{7} b^{4} - a^{5} b^{6} - 5 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{6} + 2 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right) + {\left({\left(3 \, a^{6} b^{5} + 5 \, a^{4} b^{7} + a^{2} b^{9} - b^{11}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{7} + 2 \, a^{2} b^{9} + b^{11}\right)} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/12*(22*a^4*b^3 + 38*a^2*b^5 + 16*b^7 + 12*(a^6*b - 2*a^2*b^5 - b^7)*cos(d*x + c)^2 + 6*(5*a^5*b^2 + 8*a^3*b^4 + 3*a*b^6)*cos(d*x + c)*sin(d*x + c) - 3*((2*a^6 - 3*a^4*b^2 - 9*a^2*b^4)*cos(d*x + c)^3 + 3*(2*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c) + (2*a^3*b^3 + 3*a*b^5 + (6*a^5*b + 7*a^3*b^3 - 3*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 + b^2)*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 6*((a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*cos(d*x + c)^3 + 3*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*cos(d*x + c) + (a^4*b^3 + 2*a^2*b^5 + b^7 + (3*a^6*b + 5*a^4*b^3 + a^2*b^5 - b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(sin(d*x + c) + 1) + 6*((a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*cos(d*x + c)^3 + 3*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*cos(d*x + c) + (a^4*b^3 + 2*a^2*b^5 + b^7 + (3*a^6*b + 5*a^4*b^3 + a^2*b^5 - b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(-sin(d*x + c) + 1))/((a^7*b^4 - a^5*b^6 - 5*a^3*b^8 - 3*a*b^10)*d*cos(d*x + c)^3 + 3*(a^5*b^6 + 2*a^3*b^8 + a*b^10)*d*cos(d*x + c) + ((3*a^6*b^5 + 5*a^4*b^7 + a^2*b^9 - b^11)*d*cos(d*x + c)^2 + (a^4*b^7 + 2*a^2*b^9 + b^11)*d)*sin(d*x + c))","B",0
147,1,537,0,0.719114," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, a^{2} b^{4} + 3 \, b^{6} - 4 \, {\left(9 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - 2 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 6 \, {\left(5 \, a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - 6 \, {\left({\left(a^{6} - 2 \, a^{4} b^{2} - 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(3 \, a^{5} b + 2 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) + 6 \, {\left({\left(a^{6} - 2 \, a^{4} b^{2} - 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(3 \, a^{5} b + 2 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2}\right) + 2 \, {\left(2 \, {\left(3 \, a^{5} b - 7 \, a^{3} b^{3} - 6 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(11 \, a^{3} b^{3} + 9 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3 \, {\left({\left(a^{5} b^{5} - 2 \, a^{3} b^{7} - 3 \, a b^{9}\right)} d \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)^{2} + {\left({\left(3 \, a^{4} b^{6} + 2 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/3*(3*a^2*b^4 + 3*b^6 - 4*(9*a^4*b^2 + 3*a^2*b^4 - 2*b^6)*cos(d*x + c)^4 + 6*(5*a^4*b^2 + a^2*b^4 - 2*b^6)*cos(d*x + c)^2 - 6*((a^6 - 2*a^4*b^2 - 3*a^2*b^4)*cos(d*x + c)^4 + 3*(a^4*b^2 + a^2*b^4)*cos(d*x + c)^2 + ((3*a^5*b + 2*a^3*b^3 - a*b^5)*cos(d*x + c)^3 + (a^3*b^3 + a*b^5)*cos(d*x + c))*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) + 6*((a^6 - 2*a^4*b^2 - 3*a^2*b^4)*cos(d*x + c)^4 + 3*(a^4*b^2 + a^2*b^4)*cos(d*x + c)^2 + ((3*a^5*b + 2*a^3*b^3 - a*b^5)*cos(d*x + c)^3 + (a^3*b^3 + a*b^5)*cos(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2) + 2*(2*(3*a^5*b - 7*a^3*b^3 - 6*a*b^5)*cos(d*x + c)^3 + (11*a^3*b^3 + 9*a*b^5)*cos(d*x + c))*sin(d*x + c))/((a^5*b^5 - 2*a^3*b^7 - 3*a*b^9)*d*cos(d*x + c)^4 + 3*(a^3*b^7 + a*b^9)*d*cos(d*x + c)^2 + ((3*a^4*b^6 + 2*a^2*b^8 - b^10)*d*cos(d*x + c)^3 + (a^2*b^8 + b^10)*d*cos(d*x + c))*sin(d*x + c))","B",0
148,1,820,0,0.813225," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{6 \, a^{2} b^{5} + 6 \, b^{7} - 30 \, {\left(4 \, a^{6} b - 3 \, a^{4} b^{3} - 8 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{4} - 20 \, {\left(11 \, a^{4} b^{3} + 13 \, a^{2} b^{5} + 2 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left({\left(4 \, a^{6} - 9 \, a^{4} b^{2} - 9 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(4 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(12 \, a^{5} b + 5 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} + {\left(4 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) + 15 \, {\left({\left(4 \, a^{7} - 7 \, a^{5} b^{2} - 14 \, a^{3} b^{4} - 3 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(4 \, a^{5} b^{2} + 5 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(12 \, a^{6} b + 11 \, a^{4} b^{3} - 2 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(4 \, a^{4} b^{3} + 5 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(4 \, a^{7} - 7 \, a^{5} b^{2} - 14 \, a^{3} b^{4} - 3 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(4 \, a^{5} b^{2} + 5 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(12 \, a^{6} b + 11 \, a^{4} b^{3} - 2 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(4 \, a^{4} b^{3} + 5 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 30 \, {\left(10 \, {\left(a^{5} b^{2} + a^{3} b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{5} b^{6} - 2 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d \cos\left(d x + c\right)^{5} + 3 \, {\left(a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)^{3} + {\left({\left(3 \, a^{4} b^{7} + 2 \, a^{2} b^{9} - b^{11}\right)} d \cos\left(d x + c\right)^{4} + {\left(a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/12*(6*a^2*b^5 + 6*b^7 - 30*(4*a^6*b - 3*a^4*b^3 - 8*a^2*b^5 - b^7)*cos(d*x + c)^4 - 20*(11*a^4*b^3 + 13*a^2*b^5 + 2*b^7)*cos(d*x + c)^2 + 15*((4*a^6 - 9*a^4*b^2 - 9*a^2*b^4)*cos(d*x + c)^5 + 3*(4*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c)^3 + ((12*a^5*b + 5*a^3*b^3 - 3*a*b^5)*cos(d*x + c)^4 + (4*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 + b^2)*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) + 15*((4*a^7 - 7*a^5*b^2 - 14*a^3*b^4 - 3*a*b^6)*cos(d*x + c)^5 + 3*(4*a^5*b^2 + 5*a^3*b^4 + a*b^6)*cos(d*x + c)^3 + ((12*a^6*b + 11*a^4*b^3 - 2*a^2*b^5 - b^7)*cos(d*x + c)^4 + (4*a^4*b^3 + 5*a^2*b^5 + b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(sin(d*x + c) + 1) - 15*((4*a^7 - 7*a^5*b^2 - 14*a^3*b^4 - 3*a*b^6)*cos(d*x + c)^5 + 3*(4*a^5*b^2 + 5*a^3*b^4 + a*b^6)*cos(d*x + c)^3 + ((12*a^6*b + 11*a^4*b^3 - 2*a^2*b^5 - b^7)*cos(d*x + c)^4 + (4*a^4*b^3 + 5*a^2*b^5 + b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(-sin(d*x + c) + 1) - 30*(10*(a^5*b^2 + a^3*b^4)*cos(d*x + c)^3 + (a^3*b^4 + a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^5*b^6 - 2*a^3*b^8 - 3*a*b^10)*d*cos(d*x + c)^5 + 3*(a^3*b^8 + a*b^10)*d*cos(d*x + c)^3 + ((3*a^4*b^7 + 2*a^2*b^9 - b^11)*d*cos(d*x + c)^4 + (a^2*b^9 + b^11)*d*cos(d*x + c)^2)*sin(d*x + c))","B",0
149,1,553,0,0.775963," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{4 \, {\left(45 \, a^{4} b^{2} - 3 \, a^{2} b^{4} - 4 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - b^{6} - 6 \, {\left(25 \, a^{4} b^{2} - 5 \, a^{2} b^{4} - 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(5 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left({\left(5 \, a^{6} - 12 \, a^{4} b^{2} - 9 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{4} + {\left({\left(15 \, a^{5} b + 4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{5} + {\left(5 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - 6 \, {\left({\left(5 \, a^{6} - 12 \, a^{4} b^{2} - 9 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{4} + {\left({\left(15 \, a^{5} b + 4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{5} + {\left(5 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2}\right) + {\left(3 \, a b^{5} \cos\left(d x + c\right) - 4 \, {\left(15 \, a^{5} b - 41 \, a^{3} b^{3} - 12 \, a b^{5}\right)} \cos\left(d x + c\right)^{5} - 2 \, {\left(55 \, a^{3} b^{3} + 21 \, a b^{5}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{3 \, {\left(3 \, a b^{9} d \cos\left(d x + c\right)^{4} + {\left(a^{3} b^{7} - 3 \, a b^{9}\right)} d \cos\left(d x + c\right)^{6} + {\left(b^{10} d \cos\left(d x + c\right)^{3} + {\left(3 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)^{5}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/3*(4*(45*a^4*b^2 - 3*a^2*b^4 - 4*b^6)*cos(d*x + c)^6 - b^6 - 6*(25*a^4*b^2 - 5*a^2*b^4 - 4*b^6)*cos(d*x + c)^4 - 3*(5*a^2*b^4 + 2*b^6)*cos(d*x + c)^2 + 6*((5*a^6 - 12*a^4*b^2 - 9*a^2*b^4)*cos(d*x + c)^6 + 3*(5*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c)^4 + ((15*a^5*b + 4*a^3*b^3 - 3*a*b^5)*cos(d*x + c)^5 + (5*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^3)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 6*((5*a^6 - 12*a^4*b^2 - 9*a^2*b^4)*cos(d*x + c)^6 + 3*(5*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c)^4 + ((15*a^5*b + 4*a^3*b^3 - 3*a*b^5)*cos(d*x + c)^5 + (5*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^3)*sin(d*x + c))*log(cos(d*x + c)^2) + (3*a*b^5*cos(d*x + c) - 4*(15*a^5*b - 41*a^3*b^3 - 12*a*b^5)*cos(d*x + c)^5 - 2*(55*a^3*b^3 + 21*a*b^5)*cos(d*x + c)^3)*sin(d*x + c))/(3*a*b^9*d*cos(d*x + c)^4 + (a^3*b^7 - 3*a*b^9)*d*cos(d*x + c)^6 + (b^10*d*cos(d*x + c)^3 + (3*a^2*b^8 - b^10)*d*cos(d*x + c)^5)*sin(d*x + c))","B",0
150,1,76,0,0.591313," ","integrate(cos(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(120 \, d x e^{\left(6 i \, d x + 6 i \, c\right)} - 3 i \, e^{\left(10 i \, d x + 10 i \, c\right)} - 30 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 60 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 15 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{384 \, a d}"," ",0,"1/384*(120*d*x*e^(6*I*d*x + 6*I*c) - 3*I*e^(10*I*d*x + 10*I*c) - 30*I*e^(8*I*d*x + 8*I*c) + 60*I*e^(4*I*d*x + 4*I*c) + 15*I*e^(2*I*d*x + 2*I*c) + 2*I)*e^(-6*I*d*x - 6*I*c)/(a*d)","A",0
151,1,63,0,0.538377," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-5 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 60 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 90 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 20 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{240 \, a d}"," ",0,"1/240*(-5*I*e^(8*I*d*x + 8*I*c) - 60*I*e^(6*I*d*x + 6*I*c) + 90*I*e^(4*I*d*x + 4*I*c) + 20*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(-5*I*d*x - 5*I*c)/(a*d)","A",0
152,1,54,0,0.556125," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(12 \, d x e^{\left(4 i \, d x + 4 i \, c\right)} - 2 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{32 \, a d}"," ",0,"1/32*(12*d*x*e^(4*I*d*x + 4*I*c) - 2*I*e^(6*I*d*x + 6*I*c) + 6*I*e^(2*I*d*x + 2*I*c) + I)*e^(-4*I*d*x - 4*I*c)/(a*d)","A",0
153,1,41,0,0.492793," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-3 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{12 \, a d}"," ",0,"1/12*(-3*I*e^(4*I*d*x + 4*I*c) + 6*I*e^(2*I*d*x + 2*I*c) + I)*e^(-3*I*d*x - 3*I*c)/(a*d)","A",0
154,1,32,0,0.599511," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, d x e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"1/4*(2*d*x*e^(2*I*d*x + 2*I*c) + I)*e^(-2*I*d*x - 2*I*c)/(a*d)","A",0
155,1,17,0,0.565336," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{i \, e^{\left(-i \, d x - i \, c\right)}}{a d}"," ",0,"I*e^(-I*d*x - I*c)/(a*d)","A",0
156,1,26,0,0.549505," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d x + i \, \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{a d}"," ",0,"(2*d*x + I*log(e^(2*I*d*x + 2*I*c) + 1))/(a*d)","A",0
157,1,80,0,0.607664," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 2 i \, e^{\left(i \, d x + i \, c\right)}}{a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d}"," ",0,"((e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) + I) - (e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) - I) - 2*I*e^(I*d*x + I*c))/(a*d*e^(2*I*d*x + 2*I*c) + a*d)","B",0
158,1,33,0,0.547750," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 i}{a d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d}"," ",0,"2*I/(a*d*e^(4*I*d*x + 4*I*c) + 2*a*d*e^(2*I*d*x + 2*I*c) + a*d)","A",0
159,1,174,0,0.518029," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 3 \, {\left(e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 6 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 16 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 6 i \, e^{\left(i \, d x + i \, c\right)}}{6 \, {\left(a d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/6*(3*(e^(6*I*d*x + 6*I*c) + 3*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) + I) - 3*(e^(6*I*d*x + 6*I*c) + 3*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) - I) - 6*I*e^(5*I*d*x + 5*I*c) - 16*I*e^(3*I*d*x + 3*I*c) + 6*I*e^(I*d*x + I*c))/(a*d*e^(6*I*d*x + 6*I*c) + 3*a*d*e^(4*I*d*x + 4*I*c) + 3*a*d*e^(2*I*d*x + 2*I*c) + a*d)","B",0
160,1,72,0,0.474805," ","integrate(sec(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{16 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i}{3 \, {\left(a d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/3*(16*I*e^(2*I*d*x + 2*I*c) + 4*I)/(a*d*e^(8*I*d*x + 8*I*c) + 4*a*d*e^(6*I*d*x + 6*I*c) + 6*a*d*e^(4*I*d*x + 4*I*c) + 4*a*d*e^(2*I*d*x + 2*I*c) + a*d)","A",0
161,1,266,0,0.599034," ","integrate(sec(d*x+c)^6/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 15 \, {\left(e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 30 i \, e^{\left(9 i \, d x + 9 i \, c\right)} - 140 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 256 i \, e^{\left(5 i \, d x + 5 i \, c\right)} + 140 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 30 i \, e^{\left(i \, d x + i \, c\right)}}{40 \, {\left(a d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/40*(15*(e^(10*I*d*x + 10*I*c) + 5*e^(8*I*d*x + 8*I*c) + 10*e^(6*I*d*x + 6*I*c) + 10*e^(4*I*d*x + 4*I*c) + 5*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) + I) - 15*(e^(10*I*d*x + 10*I*c) + 5*e^(8*I*d*x + 8*I*c) + 10*e^(6*I*d*x + 6*I*c) + 10*e^(4*I*d*x + 4*I*c) + 5*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) - I) - 30*I*e^(9*I*d*x + 9*I*c) - 140*I*e^(7*I*d*x + 7*I*c) - 256*I*e^(5*I*d*x + 5*I*c) + 140*I*e^(3*I*d*x + 3*I*c) + 30*I*e^(I*d*x + I*c))/(a*d*e^(10*I*d*x + 10*I*c) + 5*a*d*e^(8*I*d*x + 8*I*c) + 10*a*d*e^(6*I*d*x + 6*I*c) + 10*a*d*e^(4*I*d*x + 4*I*c) + 5*a*d*e^(2*I*d*x + 2*I*c) + a*d)","B",0
162,1,109,0,0.468754," ","integrate(sec(d*x+c)^7/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{240 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 96 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 16 i}{15 \, {\left(a d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, a d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, a d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, a d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/15*(240*I*e^(4*I*d*x + 4*I*c) + 96*I*e^(2*I*d*x + 2*I*c) + 16*I)/(a*d*e^(12*I*d*x + 12*I*c) + 6*a*d*e^(10*I*d*x + 10*I*c) + 15*a*d*e^(8*I*d*x + 8*I*c) + 20*a*d*e^(6*I*d*x + 6*I*c) + 15*a*d*e^(4*I*d*x + 4*I*c) + 6*a*d*e^(2*I*d*x + 2*I*c) + a*d)","A",0
163,1,74,0,0.580652," ","integrate(cos(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(-7 i \, e^{\left(10 i \, d x + 10 i \, c\right)} - 105 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 210 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 70 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 21 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(-7 i \, d x - 7 i \, c\right)}}{672 \, a^{2} d}"," ",0,"1/672*(-7*I*e^(10*I*d*x + 10*I*c) - 105*I*e^(8*I*d*x + 8*I*c) + 210*I*e^(6*I*d*x + 6*I*c) + 70*I*e^(4*I*d*x + 4*I*c) + 21*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(-7*I*d*x - 7*I*c)/(a^2*d)","A",0
164,1,65,0,0.577201," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(24 \, d x e^{\left(6 i \, d x + 6 i \, c\right)} - 3 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 18 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{2} d}"," ",0,"1/96*(24*d*x*e^(6*I*d*x + 6*I*c) - 3*I*e^(8*I*d*x + 8*I*c) + 18*I*e^(4*I*d*x + 4*I*c) + 6*I*e^(2*I*d*x + 2*I*c) + I)*e^(-6*I*d*x - 6*I*c)/(a^2*d)","A",0
165,1,52,0,0.421753," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(-5 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 15 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{40 \, a^{2} d}"," ",0,"1/40*(-5*I*e^(6*I*d*x + 6*I*c) + 15*I*e^(4*I*d*x + 4*I*c) + 5*I*e^(2*I*d*x + 2*I*c) + I)*e^(-5*I*d*x - 5*I*c)/(a^2*d)","A",0
166,1,43,0,0.474066," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(4 \, d x e^{\left(4 i \, d x + 4 i \, c\right)} + 4 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{16 \, a^{2} d}"," ",0,"1/16*(4*d*x*e^(4*I*d*x + 4*I*c) + 4*I*e^(2*I*d*x + 2*I*c) + I)*e^(-4*I*d*x - 4*I*c)/(a^2*d)","A",0
167,1,30,0,0.585035," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(3 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{6 \, a^{2} d}"," ",0,"1/6*(3*I*e^(2*I*d*x + 2*I*c) + I)*e^(-3*I*d*x - 3*I*c)/(a^2*d)","A",0
168,1,17,0,0.428930," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{i \, e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a^{2} d}"," ",0,"1/2*I*e^(-2*I*d*x - 2*I*c)/(a^2*d)","A",0
169,1,64,0,0.487301," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(e^{\left(i \, d x + i \, c\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - e^{\left(i \, d x + i \, c\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 2 i\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2} d}"," ",0,"-(e^(I*d*x + I*c)*log(e^(I*d*x + I*c) + I) - e^(I*d*x + I*c)*log(e^(I*d*x + I*c) - I) - 2*I)*e^(-I*d*x - I*c)/(a^2*d)","A",0
170,1,68,0,0.592846," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, d x e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, d x + {\left(2 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 2 i}{a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d}"," ",0,"(4*d*x*e^(2*I*d*x + 2*I*c) + 4*d*x + (2*I*e^(2*I*d*x + 2*I*c) + 2*I)*log(e^(2*I*d*x + 2*I*c) + 1) - 2*I)/(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","A",0
171,1,134,0,0.888544," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 3 \, {\left(e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 6 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 10 i \, e^{\left(i \, d x + i \, c\right)}}{2 \, {\left(a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/2*(3*(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) + I) - 3*(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) - I) - 6*I*e^(3*I*d*x + 3*I*c) - 10*I*e^(I*d*x + I*c))/(a^2*d*e^(4*I*d*x + 4*I*c) + 2*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","B",0
172,1,54,0,0.635123," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{8 i}{3 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"8/3*I/(a^2*d*e^(6*I*d*x + 6*I*c) + 3*a^2*d*e^(4*I*d*x + 4*I*c) + 3*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","B",0
173,1,230,0,0.507779," ","integrate(sec(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{15 \, {\left(e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 15 \, {\left(e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 30 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 110 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 146 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 30 i \, e^{\left(i \, d x + i \, c\right)}}{24 \, {\left(a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/24*(15*(e^(8*I*d*x + 8*I*c) + 4*e^(6*I*d*x + 6*I*c) + 6*e^(4*I*d*x + 4*I*c) + 4*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) + I) - 15*(e^(8*I*d*x + 8*I*c) + 4*e^(6*I*d*x + 6*I*c) + 6*e^(4*I*d*x + 4*I*c) + 4*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) - I) - 30*I*e^(7*I*d*x + 7*I*c) - 110*I*e^(5*I*d*x + 5*I*c) - 146*I*e^(3*I*d*x + 3*I*c) + 30*I*e^(I*d*x + I*c))/(a^2*d*e^(8*I*d*x + 8*I*c) + 4*a^2*d*e^(6*I*d*x + 6*I*c) + 6*a^2*d*e^(4*I*d*x + 4*I*c) + 4*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","B",0
174,1,97,0,0.806829," ","integrate(sec(d*x+c)^6/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{40 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i}{5 \, {\left(a^{2} d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/5*(40*I*e^(2*I*d*x + 2*I*c) + 8*I)/(a^2*d*e^(10*I*d*x + 10*I*c) + 5*a^2*d*e^(8*I*d*x + 8*I*c) + 10*a^2*d*e^(6*I*d*x + 6*I*c) + 10*a^2*d*e^(4*I*d*x + 4*I*c) + 5*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","A",0
175,1,76,0,1.259435," ","integrate(cos(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(120 \, d x e^{\left(8 i \, d x + 8 i \, c\right)} - 12 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 120 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 60 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 20 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{768 \, a^{3} d}"," ",0,"1/768*(120*d*x*e^(8*I*d*x + 8*I*c) - 12*I*e^(10*I*d*x + 10*I*c) + 120*I*e^(6*I*d*x + 6*I*c) + 60*I*e^(4*I*d*x + 4*I*c) + 20*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(-8*I*d*x - 8*I*c)/(a^3*d)","A",0
176,1,63,0,2.121435," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(-35 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 140 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 70 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 28 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i\right)} e^{\left(-7 i \, d x - 7 i \, c\right)}}{560 \, a^{3} d}"," ",0,"1/560*(-35*I*e^(8*I*d*x + 8*I*c) + 140*I*e^(6*I*d*x + 6*I*c) + 70*I*e^(4*I*d*x + 4*I*c) + 28*I*e^(2*I*d*x + 2*I*c) + 5*I)*e^(-7*I*d*x - 7*I*c)/(a^3*d)","A",0
177,1,54,0,0.620228," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(12 \, d x e^{\left(6 i \, d x + 6 i \, c\right)} + 18 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 9 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"1/96*(12*d*x*e^(6*I*d*x + 6*I*c) + 18*I*e^(4*I*d*x + 4*I*c) + 9*I*e^(2*I*d*x + 2*I*c) + 2*I)*e^(-6*I*d*x - 6*I*c)/(a^3*d)","A",0
178,1,41,0,0.909132," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(15 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 10 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{60 \, a^{3} d}"," ",0,"1/60*(15*I*e^(4*I*d*x + 4*I*c) + 10*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(-5*I*d*x - 5*I*c)/(a^3*d)","A",0
179,1,30,0,0.670033," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(2 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{8 \, a^{3} d}"," ",0,"1/8*(2*I*e^(2*I*d*x + 2*I*c) + I)*e^(-4*I*d*x - 4*I*c)/(a^3*d)","A",0
180,1,17,0,0.997841," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{i \, e^{\left(-3 i \, d x - 3 i \, c\right)}}{3 \, a^{3} d}"," ",0,"1/3*I*e^(-3*I*d*x - 3*I*c)/(a^3*d)","A",0
181,1,55,0,0.561420," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(2 \, d x e^{\left(2 i \, d x + 2 i \, c\right)} + i \, e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a^{3} d}"," ",0,"-(2*d*x*e^(2*I*d*x + 2*I*c) + I*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - I)*e^(-2*I*d*x - 2*I*c)/(a^3*d)","A",0
182,1,112,0,0.611248," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 3 \, {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i}{a^{3} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{3} d e^{\left(i \, d x + i \, c\right)}}"," ",0,"-(3*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c))*log(e^(I*d*x + I*c) + I) - 3*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c))*log(e^(I*d*x + I*c) - I) - 6*I*e^(2*I*d*x + 2*I*c) - 4*I)/(a^3*d*e^(3*I*d*x + 3*I*c) + a^3*d*e^(I*d*x + I*c))","A",0
183,1,110,0,1.079744," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{8 \, d x e^{\left(4 i \, d x + 4 i \, c\right)} + 8 \, d x + {\left(16 \, d x - 4 i\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 8 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 6 i}{a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d}"," ",0,"(8*d*x*e^(4*I*d*x + 4*I*c) + 8*d*x + (16*d*x - 4*I)*e^(2*I*d*x + 2*I*c) + (4*I*e^(4*I*d*x + 4*I*c) + 8*I*e^(2*I*d*x + 2*I*c) + 4*I)*log(e^(2*I*d*x + 2*I*c) + 1) - 6*I)/(a^3*d*e^(4*I*d*x + 4*I*c) + 2*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","A",0
184,1,182,0,0.459362," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 15 \, {\left(e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 30 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 80 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 66 i \, e^{\left(i \, d x + i \, c\right)}}{6 \, {\left(a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)}}"," ",0,"1/6*(15*(e^(6*I*d*x + 6*I*c) + 3*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) + I) - 15*(e^(6*I*d*x + 6*I*c) + 3*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) - I) - 30*I*e^(5*I*d*x + 5*I*c) - 80*I*e^(3*I*d*x + 3*I*c) - 66*I*e^(I*d*x + I*c))/(a^3*d*e^(6*I*d*x + 6*I*c) + 3*a^3*d*e^(4*I*d*x + 4*I*c) + 3*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","B",0
185,1,69,0,1.423581," ","integrate(sec(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 i}{a^{3} d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d}"," ",0,"4*I/(a^3*d*e^(8*I*d*x + 8*I*c) + 4*a^3*d*e^(6*I*d*x + 6*I*c) + 6*a^3*d*e^(4*I*d*x + 4*I*c) + 4*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","B",0
186,1,278,0,1.082057," ","integrate(sec(d*x+c)^6/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{105 \, {\left(e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 105 \, {\left(e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 210 i \, e^{\left(9 i \, d x + 9 i \, c\right)} - 980 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 1792 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 1580 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 210 i \, e^{\left(i \, d x + i \, c\right)}}{120 \, {\left(a^{3} d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a^{3} d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)}}"," ",0,"1/120*(105*(e^(10*I*d*x + 10*I*c) + 5*e^(8*I*d*x + 8*I*c) + 10*e^(6*I*d*x + 6*I*c) + 10*e^(4*I*d*x + 4*I*c) + 5*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) + I) - 105*(e^(10*I*d*x + 10*I*c) + 5*e^(8*I*d*x + 8*I*c) + 10*e^(6*I*d*x + 6*I*c) + 10*e^(4*I*d*x + 4*I*c) + 5*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) - I) - 210*I*e^(9*I*d*x + 9*I*c) - 980*I*e^(7*I*d*x + 7*I*c) - 1792*I*e^(5*I*d*x + 5*I*c) - 1580*I*e^(3*I*d*x + 3*I*c) + 210*I*e^(I*d*x + I*c))/(a^3*d*e^(10*I*d*x + 10*I*c) + 5*a^3*d*e^(8*I*d*x + 8*I*c) + 10*a^3*d*e^(6*I*d*x + 6*I*c) + 10*a^3*d*e^(4*I*d*x + 4*I*c) + 5*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","B",0
187,0,0,0,0.677755," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^n/(cos(d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(i \, d n x + i \, c n + n \log\left(a\right)\right)}}{\left(\frac{1}{2} \, {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-i \, d x - i \, c\right)}\right)^{n}}, x\right)"," ",0,"integral(e^(I*d*n*x + I*c*n + n*log(a))/(1/2*(e^(2*I*d*x + 2*I*c) + 1)*e^(-I*d*x - I*c))^n, x)","F",0
188,1,5,0,1.046242," ","integrate(1/(sec(x)+tan(x)),x, algorithm=""fricas"")","\log\left(\sin\left(x\right) + 1\right)"," ",0,"log(sin(x) + 1)","A",0
189,1,10,0,0.763010," ","integrate(sin(x)/(sec(x)+tan(x)),x, algorithm=""fricas"")","-\log\left(\sin\left(x\right) + 1\right) + \sin\left(x\right)"," ",0,"-log(sin(x) + 1) + sin(x)","A",0
190,1,4,0,1.370966," ","integrate(cos(x)/(sec(x)+tan(x)),x, algorithm=""fricas"")","x + \cos\left(x\right)"," ",0,"x + cos(x)","A",0
191,1,24,0,0.701128," ","integrate(tan(x)/(sec(x)+tan(x)),x, algorithm=""fricas"")","\frac{{\left(x + 1\right)} \cos\left(x\right) + {\left(x - 1\right)} \sin\left(x\right) + x + 1}{\cos\left(x\right) + \sin\left(x\right) + 1}"," ",0,"((x + 1)*cos(x) + (x - 1)*sin(x) + x + 1)/(cos(x) + sin(x) + 1)","B",0
192,1,22,0,0.679579," ","integrate(cot(x)/(sec(x)+tan(x)),x, algorithm=""fricas"")","-x - \frac{1}{2} \, \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{2} \, \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"-x - 1/2*log(1/2*cos(x) + 1/2) + 1/2*log(-1/2*cos(x) + 1/2)","B",0
193,1,18,0,1.951765," ","integrate(sec(x)/(sec(x)+tan(x)),x, algorithm=""fricas"")","-\frac{\cos\left(x\right) - \sin\left(x\right) + 1}{\cos\left(x\right) + \sin\left(x\right) + 1}"," ",0,"-(cos(x) - sin(x) + 1)/(cos(x) + sin(x) + 1)","A",0
194,1,13,0,0.499007," ","integrate(csc(x)/(sec(x)+tan(x)),x, algorithm=""fricas"")","\log\left(\frac{1}{2} \, \sin\left(x\right)\right) - \log\left(\sin\left(x\right) + 1\right)"," ",0,"log(1/2*sin(x)) - log(sin(x) + 1)","A",0
195,1,9,0,0.495781," ","integrate(1/(sec(x)-tan(x)),x, algorithm=""fricas"")","-\log\left(-\sin\left(x\right) + 1\right)"," ",0,"-log(-sin(x) + 1)","A",0
196,1,14,0,1.462673," ","integrate(sin(x)/(sec(x)-tan(x)),x, algorithm=""fricas"")","-\log\left(-\sin\left(x\right) + 1\right) - \sin\left(x\right)"," ",0,"-log(-sin(x) + 1) - sin(x)","A",0
197,1,6,0,0.583488," ","integrate(cos(x)/(sec(x)-tan(x)),x, algorithm=""fricas"")","x - \cos\left(x\right)"," ",0,"x - cos(x)","A",0
198,1,28,0,0.534301," ","integrate(tan(x)/(sec(x)-tan(x)),x, algorithm=""fricas"")","-\frac{{\left(x - 1\right)} \cos\left(x\right) - {\left(x + 1\right)} \sin\left(x\right) + x - 1}{\cos\left(x\right) - \sin\left(x\right) + 1}"," ",0,"-((x - 1)*cos(x) - (x + 1)*sin(x) + x - 1)/(cos(x) - sin(x) + 1)","A",0
199,1,20,0,0.463092," ","integrate(cot(x)/(sec(x)-tan(x)),x, algorithm=""fricas"")","x - \frac{1}{2} \, \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{2} \, \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"x - 1/2*log(1/2*cos(x) + 1/2) + 1/2*log(-1/2*cos(x) + 1/2)","B",0
200,1,17,0,0.485319," ","integrate(sec(x)/(sec(x)-tan(x)),x, algorithm=""fricas"")","\frac{\cos\left(x\right) + \sin\left(x\right) + 1}{\cos\left(x\right) - \sin\left(x\right) + 1}"," ",0,"(cos(x) + sin(x) + 1)/(cos(x) - sin(x) + 1)","A",0
201,1,15,0,0.688419," ","integrate(csc(x)/(sec(x)-tan(x)),x, algorithm=""fricas"")","\log\left(\frac{1}{2} \, \sin\left(x\right)\right) - \log\left(-\sin\left(x\right) + 1\right)"," ",0,"log(1/2*sin(x)) - log(-sin(x) + 1)","A",0
202,1,21,0,0.502299," ","integrate(csc(d*x+c)*(cot(d*x+c)+csc(d*x+c)),x, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right) + 1}{d \sin\left(d x + c\right)}"," ",0,"-(cos(d*x + c) + 1)/(d*sin(d*x + c))","A",0
203,1,6,0,1.474509," ","integrate(sin(x)/(cot(x)+csc(x)),x, algorithm=""fricas"")","x - \sin\left(x\right)"," ",0,"x - sin(x)","A",0
204,1,12,0,2.001461," ","integrate(cos(x)/(cot(x)+csc(x)),x, algorithm=""fricas"")","-\cos\left(x\right) + \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"-cos(x) + log(1/2*cos(x) + 1/2)","A",0
205,1,20,0,0.712340," ","integrate(tan(x)/(cot(x)+csc(x)),x, algorithm=""fricas"")","-x + \frac{1}{2} \, \log\left(\sin\left(x\right) + 1\right) - \frac{1}{2} \, \log\left(-\sin\left(x\right) + 1\right)"," ",0,"-x + 1/2*log(sin(x) + 1) - 1/2*log(-sin(x) + 1)","B",0
206,1,17,0,0.592658," ","integrate(cot(x)/(cot(x)+csc(x)),x, algorithm=""fricas"")","\frac{x \cos\left(x\right) + x - \sin\left(x\right)}{\cos\left(x\right) + 1}"," ",0,"(x*cos(x) + x - sin(x))/(cos(x) + 1)","A",0
207,1,15,0,1.045611," ","integrate(sec(x)/(cot(x)+csc(x)),x, algorithm=""fricas"")","-\log\left(-\cos\left(x\right)\right) + \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"-log(-cos(x)) + log(1/2*cos(x) + 1/2)","A",0
208,1,9,0,0.576937," ","integrate(csc(x)/(cot(x)+csc(x)),x, algorithm=""fricas"")","\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}"," ",0,"sin(x)/(cos(x) + 1)","A",0
209,1,4,0,0.623991," ","integrate(sin(x)/(-cot(x)+csc(x)),x, algorithm=""fricas"")","x + \sin\left(x\right)"," ",0,"x + sin(x)","A",0
210,1,10,0,0.803253," ","integrate(cos(x)/(-cot(x)+csc(x)),x, algorithm=""fricas"")","\cos\left(x\right) + \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"cos(x) + log(-1/2*cos(x) + 1/2)","A",0
211,1,18,0,0.780819," ","integrate(tan(x)/(-cot(x)+csc(x)),x, algorithm=""fricas"")","x + \frac{1}{2} \, \log\left(\sin\left(x\right) + 1\right) - \frac{1}{2} \, \log\left(-\sin\left(x\right) + 1\right)"," ",0,"x + 1/2*log(sin(x) + 1) - 1/2*log(-sin(x) + 1)","B",0
212,1,14,0,0.688844," ","integrate(cot(x)/(-cot(x)+csc(x)),x, algorithm=""fricas"")","-\frac{x \sin\left(x\right) + \cos\left(x\right) + 1}{\sin\left(x\right)}"," ",0,"-(x*sin(x) + cos(x) + 1)/sin(x)","A",0
213,1,15,0,0.535691," ","integrate(sec(x)/(-cot(x)+csc(x)),x, algorithm=""fricas"")","-\log\left(-\cos\left(x\right)\right) + \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"-log(-cos(x)) + log(-1/2*cos(x) + 1/2)","A",0
214,1,10,0,0.907215," ","integrate(csc(x)/(-cot(x)+csc(x)),x, algorithm=""fricas"")","-\frac{\cos\left(x\right) + 1}{\sin\left(x\right)}"," ",0,"-(cos(x) + 1)/sin(x)","A",0
215,1,44,0,0.645468," ","integrate(1/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{2} \log\left(-\frac{\cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - 2}\right)}{4 \, d}"," ",0,"1/4*sqrt(2)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*cos(d*x + c) + 2)/(cos(d*x + c)^2 - 2))/d","B",0
216,1,52,0,0.611859," ","integrate(sin(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, d x + \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2}}{4 \, \cos\left(d x + c\right) \sin\left(d x + c\right)}\right)}{4 \, d}"," ",0,"1/4*(4*d*x + sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(d*x + c)^2 - 2*sqrt(2))/(cos(d*x + c)*sin(d*x + c))))/d","A",0
217,1,18,0,0.501222," ","integrate(cos(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""fricas"")","\frac{\log\left(-\cos\left(d x + c\right)^{2} + 2\right)}{2 \, d}"," ",0,"1/2*log(-cos(d*x + c)^2 + 2)/d","A",0
218,1,37,0,0.435849," ","integrate(tan(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, \arctan\left(\sin\left(d x + c\right)\right) - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(-\sin\left(d x + c\right) + 1\right)}{4 \, d}"," ",0,"-1/4*(2*arctan(sin(d*x + c)) - log(sin(d*x + c) + 1) + log(-sin(d*x + c) + 1))/d","A",0
219,1,11,0,0.489843," ","integrate(cot(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""fricas"")","\frac{\arctan\left(\sin\left(d x + c\right)\right)}{d}"," ",0,"arctan(sin(d*x + c))/d","A",0
220,1,30,0,0.500238," ","integrate(sec(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""fricas"")","\frac{\log\left(-\cos\left(d x + c\right)^{2} + 2\right) - 2 \, \log\left(-\cos\left(d x + c\right)\right)}{4 \, d}"," ",0,"1/4*(log(-cos(d*x + c)^2 + 2) - 2*log(-cos(d*x + c)))/d","B",0
221,1,46,0,0.510093," ","integrate(csc(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""fricas"")","-\frac{\sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2}}{4 \, \cos\left(d x + c\right) \sin\left(d x + c\right)}\right)}{4 \, d}"," ",0,"-1/4*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(d*x + c)^2 - 2*sqrt(2))/(cos(d*x + c)*sin(d*x + c)))/d","A",0
222,1,12,0,0.459096," ","integrate(1/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""fricas"")","\frac{1}{d \cos\left(d x + c\right)}"," ",0,"1/(d*cos(d*x + c))","A",0
223,1,31,0,0.416678," ","integrate(sin(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""fricas"")","-\frac{d x \cos\left(d x + c\right) - \sin\left(d x + c\right)}{d \cos\left(d x + c\right)}"," ",0,"-(d*x*cos(d*x + c) - sin(d*x + c))/(d*cos(d*x + c))","B",0
224,1,14,0,0.455981," ","integrate(cos(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""fricas"")","-\frac{\log\left(-\cos\left(d x + c\right)\right)}{d}"," ",0,"-log(-cos(d*x + c))/d","A",0
225,1,61,0,0.427250," ","integrate(tan(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"-1/4*(cos(d*x + c)^2*log(sin(d*x + c) + 1) - cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*sin(d*x + c))/(d*cos(d*x + c)^2)","B",0
226,1,28,0,0.448195," ","integrate(cot(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""fricas"")","\frac{\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, d}"," ",0,"1/2*(log(sin(d*x + c) + 1) - log(-sin(d*x + c) + 1))/d","B",0
227,1,13,0,0.389678," ","integrate(sec(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""fricas"")","\frac{1}{2 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/2/(d*cos(d*x + c)^2)","A",0
228,1,18,0,0.415381," ","integrate(csc(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""fricas"")","\frac{\sin\left(d x + c\right)}{d \cos\left(d x + c\right)}"," ",0,"sin(d*x + c)/(d*cos(d*x + c))","A",0
229,1,28,0,0.409044," ","integrate(cos(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, a \cos\left(d x + c\right)^{4} + 4 \, b \cos\left(d x + c\right)^{3}}{12 \, d}"," ",0,"-1/12*(3*a*cos(d*x + c)^4 + 4*b*cos(d*x + c)^3)/d","A",0
230,1,28,0,0.490878," ","integrate(cos(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a \cos\left(d x + c\right)^{3} + 3 \, b \cos\left(d x + c\right)^{2}}{6 \, d}"," ",0,"-1/6*(2*a*cos(d*x + c)^3 + 3*b*cos(d*x + c)^2)/d","A",0
231,1,25,0,0.405889," ","integrate(cos(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{a \cos\left(d x + c\right)^{2} + 2 \, b \cos\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(a*cos(d*x + c)^2 + 2*b*cos(d*x + c))/d","A",0
232,1,25,0,0.424250," ","integrate(a*sin(d*x+c)+b*tan(d*x+c),x, algorithm=""fricas"")","-\frac{a \cos\left(d x + c\right) + b \log\left(-\cos\left(d x + c\right)\right)}{d}"," ",0,"-(a*cos(d*x + c) + b*log(-cos(d*x + c)))/d","A",0
233,1,34,0,0.508985," ","integrate(sec(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{a \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right)\right) - b}{d \cos\left(d x + c\right)}"," ",0,"-(a*cos(d*x + c)*log(-cos(d*x + c)) - b)/(d*cos(d*x + c))","A",0
234,1,24,0,0.619700," ","integrate(sec(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a \cos\left(d x + c\right) + b}{2 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/2*(2*a*cos(d*x + c) + b)/(d*cos(d*x + c)^2)","A",0
235,1,26,0,0.577262," ","integrate(sec(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, a \cos\left(d x + c\right) + 2 \, b}{6 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/6*(3*a*cos(d*x + c) + 2*b)/(d*cos(d*x + c)^3)","A",0
236,1,85,0,0.591857," ","integrate(cos(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{15 \, a b d x - {\left(12 \, a^{2} \cos\left(d x + c\right)^{4} + 30 \, a b \cos\left(d x + c\right)^{3} - 15 \, a b \cos\left(d x + c\right) - 4 \, {\left(a^{2} - 5 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 8 \, a^{2} - 20 \, b^{2}\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(15*a*b*d*x - (12*a^2*cos(d*x + c)^4 + 30*a*b*cos(d*x + c)^3 - 15*a*b*cos(d*x + c) - 4*(a^2 - 5*b^2)*cos(d*x + c)^2 - 8*a^2 - 20*b^2)*sin(d*x + c))/d","A",0
237,1,74,0,0.681288," ","integrate(cos(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{2} + 4 \, b^{2}\right)} d x - {\left(6 \, a^{2} \cos\left(d x + c\right)^{3} + 16 \, a b \cos\left(d x + c\right)^{2} - 16 \, a b - 3 \, {\left(a^{2} - 4 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(a^2 + 4*b^2)*d*x - (6*a^2*cos(d*x + c)^3 + 16*a*b*cos(d*x + c)^2 - 16*a*b - 3*(a^2 - 4*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
238,1,83,0,0.546961," ","integrate(cos(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{6 \, a b d x + 3 \, b^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, b^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{2} \cos\left(d x + c\right)^{2} + 3 \, a b \cos\left(d x + c\right) - a^{2} + 3 \, b^{2}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(6*a*b*d*x + 3*b^2*log(sin(d*x + c) + 1) - 3*b^2*log(-sin(d*x + c) + 1) - 2*(a^2*cos(d*x + c)^2 + 3*a*b*cos(d*x + c) - a^2 + 3*b^2)*sin(d*x + c))/d","A",0
239,1,108,0,0.649532," ","integrate((a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} - 2 \, b^{2}\right)} d x \cos\left(d x + c\right) + 2 \, a b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, a b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(a^{2} \cos\left(d x + c\right)^{2} + 4 \, a b \cos\left(d x + c\right) - 2 \, b^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*((a^2 - 2*b^2)*d*x*cos(d*x + c) + 2*a*b*cos(d*x + c)*log(sin(d*x + c) + 1) - 2*a*b*cos(d*x + c)*log(-sin(d*x + c) + 1) - (a^2*cos(d*x + c)^2 + 4*a*b*cos(d*x + c) - 2*b^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
240,1,126,0,0.706316," ","integrate(sec(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{8 \, a b d x \cos\left(d x + c\right)^{2} - {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, a^{2} \cos\left(d x + c\right)^{2} - 4 \, a b \cos\left(d x + c\right) - b^{2}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"-1/4*(8*a*b*d*x*cos(d*x + c)^2 - (2*a^2 - b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (2*a^2 - b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*a^2*cos(d*x + c)^2 - 4*a*b*cos(d*x + c) - b^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
241,1,115,0,0.654325," ","integrate(sec(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, a^{2} d x \cos\left(d x + c\right)^{3} + 3 \, a b \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a b \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(3 \, a b \cos\left(d x + c\right) + {\left(3 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)^{3}}"," ",0,"-1/6*(6*a^2*d*x*cos(d*x + c)^3 + 3*a*b*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*a*b*cos(d*x + c)^3*log(-sin(d*x + c) + 1) - 2*(3*a*b*cos(d*x + c) + (3*a^2 - b^2)*cos(d*x + c)^2 + b^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
242,1,129,0,0.576801," ","integrate(sec(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(4 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, a b \cos\left(d x + c\right)^{3} - 16 \, a b \cos\left(d x + c\right) - 3 \, {\left(4 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 6 \, b^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"-1/48*(3*(4*a^2 + b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(4*a^2 + b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*a*b*cos(d*x + c)^3 - 16*a*b*cos(d*x + c) - 3*(4*a^2 - b^2)*cos(d*x + c)^2 - 6*b^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
243,1,100,0,1.267930," ","integrate(cos(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{10 \, a^{3} \cos\left(d x + c\right)^{6} + 36 \, a^{2} b \cos\left(d x + c\right)^{5} - 90 \, a b^{2} \cos\left(d x + c\right)^{2} - 15 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} - 60 \, b^{3} \cos\left(d x + c\right) - 20 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{3}}{60 \, d}"," ",0,"1/60*(10*a^3*cos(d*x + c)^6 + 36*a^2*b*cos(d*x + c)^5 - 90*a*b^2*cos(d*x + c)^2 - 15*(a^3 - 3*a*b^2)*cos(d*x + c)^4 - 60*b^3*cos(d*x + c) - 20*(3*a^2*b - b^3)*cos(d*x + c)^3)/d","A",0
244,1,101,0,0.693553," ","integrate(cos(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{12 \, a^{3} \cos\left(d x + c\right)^{5} + 45 \, a^{2} b \cos\left(d x + c\right)^{4} - 180 \, a b^{2} \cos\left(d x + c\right) - 20 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - 60 \, b^{3} \log\left(-\cos\left(d x + c\right)\right) - 30 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}}{60 \, d}"," ",0,"1/60*(12*a^3*cos(d*x + c)^5 + 45*a^2*b*cos(d*x + c)^4 - 180*a*b^2*cos(d*x + c) - 20*(a^3 - 3*a*b^2)*cos(d*x + c)^3 - 60*b^3*log(-cos(d*x + c)) - 30*(3*a^2*b - b^3)*cos(d*x + c)^2)/d","A",0
245,1,128,0,0.611077," ","integrate(cos(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{8 \, a^{3} \cos\left(d x + c\right)^{5} + 32 \, a^{2} b \cos\left(d x + c\right)^{4} - 96 \, a b^{2} \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right)\right) - 16 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 32 \, b^{3} - 32 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{3} - 24 \, a b^{2}\right)} \cos\left(d x + c\right)}{32 \, d \cos\left(d x + c\right)}"," ",0,"1/32*(8*a^3*cos(d*x + c)^5 + 32*a^2*b*cos(d*x + c)^4 - 96*a*b^2*cos(d*x + c)*log(-cos(d*x + c)) - 16*(a^3 - 3*a*b^2)*cos(d*x + c)^3 + 32*b^3 - 32*(3*a^2*b - b^3)*cos(d*x + c)^2 + (5*a^3 - 24*a*b^2)*cos(d*x + c))/(d*cos(d*x + c))","A",0
246,1,123,0,0.614816," ","integrate((a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, a^{3} \cos\left(d x + c\right)^{5} + 18 \, a^{2} b \cos\left(d x + c\right)^{4} - 9 \, a^{2} b \cos\left(d x + c\right)^{2} + 36 \, a b^{2} \cos\left(d x + c\right) - 12 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - 12 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\cos\left(d x + c\right)\right) + 6 \, b^{3}}{12 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/12*(4*a^3*cos(d*x + c)^5 + 18*a^2*b*cos(d*x + c)^4 - 9*a^2*b*cos(d*x + c)^2 + 36*a*b^2*cos(d*x + c) - 12*(a^3 - 3*a*b^2)*cos(d*x + c)^3 - 12*(3*a^2*b - b^3)*cos(d*x + c)^2*log(-cos(d*x + c)) + 6*b^3)/(d*cos(d*x + c)^2)","A",0
247,1,122,0,0.491773," ","integrate(sec(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{6 \, a^{3} \cos\left(d x + c\right)^{5} + 36 \, a^{2} b \cos\left(d x + c\right)^{4} - 3 \, a^{3} \cos\left(d x + c\right)^{3} - 12 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(-\cos\left(d x + c\right)\right) + 18 \, a b^{2} \cos\left(d x + c\right) + 4 \, b^{3} + 12 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(6*a^3*cos(d*x + c)^5 + 36*a^2*b*cos(d*x + c)^4 - 3*a^3*cos(d*x + c)^3 - 12*(a^3 - 3*a*b^2)*cos(d*x + c)^3*log(-cos(d*x + c)) + 18*a*b^2*cos(d*x + c) + 4*b^3 + 12*(3*a^2*b - b^3)*cos(d*x + c)^2)/(d*cos(d*x + c)^3)","A",0
248,1,107,0,0.608218," ","integrate(sec(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, a^{3} \cos\left(d x + c\right)^{5} + 12 \, a^{2} b \cos\left(d x + c\right)^{4} \log\left(-\cos\left(d x + c\right)\right) + 4 \, a b^{2} \cos\left(d x + c\right) + 4 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + b^{3} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}}{4 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/4*(4*a^3*cos(d*x + c)^5 + 12*a^2*b*cos(d*x + c)^4*log(-cos(d*x + c)) + 4*a*b^2*cos(d*x + c) + 4*(a^3 - 3*a*b^2)*cos(d*x + c)^3 + b^3 + 2*(3*a^2*b - b^3)*cos(d*x + c)^2)/(d*cos(d*x + c)^4)","A",0
249,1,109,0,0.649412," ","integrate(sec(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{60 \, a^{3} \cos\left(d x + c\right)^{5} \log\left(-\cos\left(d x + c\right)\right) - 180 \, a^{2} b \cos\left(d x + c\right)^{4} + 45 \, a b^{2} \cos\left(d x + c\right) + 30 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 12 \, b^{3} + 20 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}}{60 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/60*(60*a^3*cos(d*x + c)^5*log(-cos(d*x + c)) - 180*a^2*b*cos(d*x + c)^4 + 45*a*b^2*cos(d*x + c) + 30*(a^3 - 3*a*b^2)*cos(d*x + c)^3 + 12*b^3 + 20*(3*a^2*b - b^3)*cos(d*x + c)^2)/(d*cos(d*x + c)^5)","A",0
250,1,123,0,0.636386," ","integrate(cos(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b^{4} \log\left(a \cos\left(d x + c\right) + b\right) - {\left(a^{4} - a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right) - {\left(a^{4} + a^{3} b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a^{4} - a^{3} b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left(a^{5} - a^{3} b^{2}\right)} d}"," ",0,"-1/2*(2*b^4*log(a*cos(d*x + c) + b) - (a^4 - a^2*b^2)*cos(d*x + c)^2 + 2*(a^3*b - a*b^3)*cos(d*x + c) - (a^4 + a^3*b)*log(1/2*cos(d*x + c) + 1/2) - (a^4 - a^3*b)*log(-1/2*cos(d*x + c) + 1/2))/((a^5 - a^3*b^2)*d)","A",0
251,1,98,0,0.778793," ","integrate(cos(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, b^{3} \log\left(a \cos\left(d x + c\right) + b\right) + 2 \, {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right) - {\left(a^{3} + a^{2} b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{3} - a^{2} b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left(a^{4} - a^{2} b^{2}\right)} d}"," ",0,"1/2*(2*b^3*log(a*cos(d*x + c) + b) + 2*(a^3 - a*b^2)*cos(d*x + c) - (a^3 + a^2*b)*log(1/2*cos(d*x + c) + 1/2) + (a^3 - a^2*b)*log(-1/2*cos(d*x + c) + 1/2))/((a^4 - a^2*b^2)*d)","A",0
252,1,75,0,0.555972," ","integrate(cos(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b^{2} \log\left(a \cos\left(d x + c\right) + b\right) - {\left(a^{2} + a b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a^{2} - a b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left(a^{3} - a b^{2}\right)} d}"," ",0,"-1/2*(2*b^2*log(a*cos(d*x + c) + b) - (a^2 + a*b)*log(1/2*cos(d*x + c) + 1/2) - (a^2 - a*b)*log(-1/2*cos(d*x + c) + 1/2))/((a^3 - a*b^2)*d)","A",0
253,1,64,0,0.540980," ","integrate(1/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, b \log\left(a \cos\left(d x + c\right) + b\right) - {\left(a + b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a - b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left(a^{2} - b^{2}\right)} d}"," ",0,"1/2*(2*b*log(a*cos(d*x + c) + b) - (a + b)*log(1/2*cos(d*x + c) + 1/2) + (a - b)*log(-1/2*cos(d*x + c) + 1/2))/((a^2 - b^2)*d)","A",0
254,1,65,0,0.774673," ","integrate(sec(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a \log\left(a \cos\left(d x + c\right) + b\right) - {\left(a + b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a - b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left(a^{2} - b^{2}\right)} d}"," ",0,"-1/2*(2*a*log(a*cos(d*x + c) + b) - (a + b)*log(1/2*cos(d*x + c) + 1/2) - (a - b)*log(-1/2*cos(d*x + c) + 1/2))/((a^2 - b^2)*d)","A",0
255,1,96,0,0.896302," ","integrate(sec(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a^{2} \log\left(a \cos\left(d x + c\right) + b\right) - 2 \, {\left(a^{2} - b^{2}\right)} \log\left(-\cos\left(d x + c\right)\right) - {\left(a b + b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a b - b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left(a^{2} b - b^{3}\right)} d}"," ",0,"1/2*(2*a^2*log(a*cos(d*x + c) + b) - 2*(a^2 - b^2)*log(-cos(d*x + c)) - (a*b + b^2)*log(1/2*cos(d*x + c) + 1/2) + (a*b - b^2)*log(-1/2*cos(d*x + c) + 1/2))/((a^2*b - b^3)*d)","A",0
256,1,147,0,0.672283," ","integrate(sec(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a^{3} \cos\left(d x + c\right) \log\left(a \cos\left(d x + c\right) + b\right) - 2 \, a^{2} b + 2 \, b^{3} - 2 \, {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right)\right) - {\left(a b^{2} + b^{3}\right)} \cos\left(d x + c\right) \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a b^{2} - b^{3}\right)} \cos\left(d x + c\right) \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left(a^{2} b^{2} - b^{4}\right)} d \cos\left(d x + c\right)}"," ",0,"-1/2*(2*a^3*cos(d*x + c)*log(a*cos(d*x + c) + b) - 2*a^2*b + 2*b^3 - 2*(a^3 - a*b^2)*cos(d*x + c)*log(-cos(d*x + c)) - (a*b^2 + b^3)*cos(d*x + c)*log(1/2*cos(d*x + c) + 1/2) - (a*b^2 - b^3)*cos(d*x + c)*log(-1/2*cos(d*x + c) + 1/2))/((a^2*b^2 - b^4)*d*cos(d*x + c))","A",0
257,1,857,0,0.591076," ","integrate(cos(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{7} b - 6 \, a^{5} b^{3} + 6 \, a^{3} b^{5} - 4 \, a b^{7} - 2 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(5 \, a^{2} b^{5} - 2 \, b^{7} + {\left(5 \, a^{3} b^{4} - 2 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) \sin\left(d x + c\right) - 2 \, {\left(3 \, a^{7} b - 5 \, a^{5} b^{3} + 4 \, a^{3} b^{5} - 2 \, a b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{8} - 5 \, a^{6} b^{2} + 4 \, a^{4} b^{4} - a^{2} b^{6}\right)} \cos\left(d x + c\right) - 4 \, {\left({\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d x \cos\left(d x + c\right) + {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d x\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{9} b - 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - a^{3} b^{7}\right)} d\right)} \sin\left(d x + c\right)}, -\frac{2 \, a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - 2 \, a b^{7} - {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} - {\left(5 \, a^{2} b^{5} - 2 \, b^{7} + {\left(5 \, a^{3} b^{4} - 2 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - {\left(3 \, a^{7} b - 5 \, a^{5} b^{3} + 4 \, a^{3} b^{5} - 2 \, a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{8} - 5 \, a^{6} b^{2} + 4 \, a^{4} b^{4} - a^{2} b^{6}\right)} \cos\left(d x + c\right) - 2 \, {\left({\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d x \cos\left(d x + c\right) + {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d x\right)} \sin\left(d x + c\right)}{{\left({\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{9} b - 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - a^{3} b^{7}\right)} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/2*(4*a^7*b - 6*a^5*b^3 + 6*a^3*b^5 - 4*a*b^7 - 2*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*cos(d*x + c)^3 + (5*a^2*b^5 - 2*b^7 + (5*a^3*b^4 - 2*a*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2))*sin(d*x + c) - 2*(3*a^7*b - 5*a^5*b^3 + 4*a^3*b^5 - 2*a*b^7)*cos(d*x + c)^2 + 2*(2*a^8 - 5*a^6*b^2 + 4*a^4*b^4 - a^2*b^6)*cos(d*x + c) - 4*((a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x*cos(d*x + c) + (a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*x)*sin(d*x + c))/(((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*d*cos(d*x + c) + (a^9*b - 3*a^7*b^3 + 3*a^5*b^5 - a^3*b^7)*d)*sin(d*x + c)), -(2*a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - 2*a*b^7 - (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*cos(d*x + c)^3 - (5*a^2*b^5 - 2*b^7 + (5*a^3*b^4 - 2*a*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*sin(d*x + c) - (3*a^7*b - 5*a^5*b^3 + 4*a^3*b^5 - 2*a*b^7)*cos(d*x + c)^2 + (2*a^8 - 5*a^6*b^2 + 4*a^4*b^4 - a^2*b^6)*cos(d*x + c) - 2*((a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x*cos(d*x + c) + (a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*x)*sin(d*x + c))/(((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*d*cos(d*x + c) + (a^9*b - 3*a^7*b^3 + 3*a^5*b^5 - a^3*b^7)*d)*sin(d*x + c))]","A",0
258,1,705,0,0.739535," ","integrate(cos(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{4 \, a^{5} b^{2} - 2 \, a^{3} b^{4} - 2 \, a b^{6} - {\left(4 \, a^{2} b^{4} - b^{6} + {\left(4 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) \sin\left(d x + c\right) - 2 \, {\left(a^{7} - a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right) - 2 \, {\left({\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d x \cos\left(d x + c\right) + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d x\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b - 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - a^{2} b^{7}\right)} d\right)} \sin\left(d x + c\right)}, \frac{2 \, a^{5} b^{2} - a^{3} b^{4} - a b^{6} - {\left(4 \, a^{2} b^{4} - b^{6} + {\left(4 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - {\left(a^{7} - a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right) - {\left({\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d x \cos\left(d x + c\right) + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d x\right)} \sin\left(d x + c\right)}{{\left({\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b - 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - a^{2} b^{7}\right)} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[1/2*(4*a^5*b^2 - 2*a^3*b^4 - 2*a*b^6 - (4*a^2*b^4 - b^6 + (4*a^3*b^3 - a*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2))*sin(d*x + c) - 2*(a^7 - a*b^6)*cos(d*x + c)^2 + 2*(a^6*b - 2*a^4*b^3 + a^2*b^5)*cos(d*x + c) - 2*((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*x*cos(d*x + c) + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d*x)*sin(d*x + c))/(((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*d*cos(d*x + c) + (a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*d)*sin(d*x + c)), (2*a^5*b^2 - a^3*b^4 - a*b^6 - (4*a^2*b^4 - b^6 + (4*a^3*b^3 - a*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*sin(d*x + c) - (a^7 - a*b^6)*cos(d*x + c)^2 + (a^6*b - 2*a^4*b^3 + a^2*b^5)*cos(d*x + c) - ((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*x*cos(d*x + c) + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d*x)*sin(d*x + c))/(((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*d*cos(d*x + c) + (a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*d)*sin(d*x + c))]","A",0
259,1,518,0,0.541386," ","integrate(cos(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a^{4} b + 2 \, a^{2} b^{3} - 4 \, b^{5} - 3 \, {\left(a^{2} b^{2} \cos\left(d x + c\right) + a b^{3}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) \sin\left(d x + c\right) - 2 \, {\left(2 \, a^{4} b - a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)}{2 \, {\left({\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d\right)} \sin\left(d x + c\right)}, -\frac{a^{4} b + a^{2} b^{3} - 2 \, b^{5} - 3 \, {\left(a^{2} b^{2} \cos\left(d x + c\right) + a b^{3}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - {\left(2 \, a^{4} b - a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)}{{\left({\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/2*(2*a^4*b + 2*a^2*b^3 - 4*b^5 - 3*(a^2*b^2*cos(d*x + c) + a*b^3)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2))*sin(d*x + c) - 2*(2*a^4*b - a^2*b^3 - b^5)*cos(d*x + c)^2 + 2*(a^5 - 2*a^3*b^2 + a*b^4)*cos(d*x + c))/(((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c) + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d)*sin(d*x + c)), -(a^4*b + a^2*b^3 - 2*b^5 - 3*(a^2*b^2*cos(d*x + c) + a*b^3)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*sin(d*x + c) - (2*a^4*b - a^2*b^3 - b^5)*cos(d*x + c)^2 + (a^5 - 2*a^3*b^2 + a*b^4)*cos(d*x + c))/(((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c) + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d)*sin(d*x + c))]","A",0
260,1,526,0,0.696587," ","integrate(1/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{6 \, a^{3} b^{2} - 6 \, a b^{4} + {\left(2 \, a^{2} b^{2} + b^{4} + {\left(2 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) \sin\left(d x + c\right) - 2 \, {\left(a^{5} + a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)}{2 \, {\left({\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d\right)} \sin\left(d x + c\right)}, \frac{3 \, a^{3} b^{2} - 3 \, a b^{4} - {\left(2 \, a^{2} b^{2} + b^{4} + {\left(2 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - {\left(a^{5} + a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)}{{\left({\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[1/2*(6*a^3*b^2 - 6*a*b^4 + (2*a^2*b^2 + b^4 + (2*a^3*b + a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2))*sin(d*x + c) - 2*(a^5 + a^3*b^2 - 2*a*b^4)*cos(d*x + c)^2 + 2*(a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c))/(((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c) + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d)*sin(d*x + c)), (3*a^3*b^2 - 3*a*b^4 - (2*a^2*b^2 + b^4 + (2*a^3*b + a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*sin(d*x + c) - (a^5 + a^3*b^2 - 2*a*b^4)*cos(d*x + c)^2 + (a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c))/(((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c) + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d)*sin(d*x + c))]","A",0
261,1,532,0,0.880075," ","integrate(sec(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{4} b - 2 \, a^{2} b^{3} - 2 \, b^{5} - {\left(a^{3} b + 2 \, a b^{3} + {\left(a^{4} + 2 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) \sin\left(d x + c\right) - 6 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)}{2 \, {\left({\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d\right)} \sin\left(d x + c\right)}, -\frac{2 \, a^{4} b - a^{2} b^{3} - b^{5} - {\left(a^{3} b + 2 \, a b^{3} + {\left(a^{4} + 2 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)}{{\left({\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/2*(4*a^4*b - 2*a^2*b^3 - 2*b^5 - (a^3*b + 2*a*b^3 + (a^4 + 2*a^2*b^2)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2))*sin(d*x + c) - 6*(a^4*b - a^2*b^3)*cos(d*x + c)^2 + 2*(a^5 - 2*a^3*b^2 + a*b^4)*cos(d*x + c))/(((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c) + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d)*sin(d*x + c)), -(2*a^4*b - a^2*b^3 - b^5 - (a^3*b + 2*a*b^3 + (a^4 + 2*a^2*b^2)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*sin(d*x + c) - 3*(a^4*b - a^2*b^3)*cos(d*x + c)^2 + (a^5 - 2*a^3*b^2 + a*b^4)*cos(d*x + c))/(((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c) + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d)*sin(d*x + c))]","A",0
262,1,516,0,0.706779," ","integrate(sec(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, a^{5} + 2 \, a^{3} b^{2} - 4 \, a b^{4} + 3 \, {\left(a^{3} b \cos\left(d x + c\right) + a^{2} b^{2}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) \sin\left(d x + c\right) - 2 \, {\left(2 \, a^{5} - a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)}{2 \, {\left({\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d\right)} \sin\left(d x + c\right)}, \frac{a^{5} + a^{3} b^{2} - 2 \, a b^{4} - 3 \, {\left(a^{3} b \cos\left(d x + c\right) + a^{2} b^{2}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - {\left(2 \, a^{5} - a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)}{{\left({\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[1/2*(2*a^5 + 2*a^3*b^2 - 4*a*b^4 + 3*(a^3*b*cos(d*x + c) + a^2*b^2)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2))*sin(d*x + c) - 2*(2*a^5 - a^3*b^2 - a*b^4)*cos(d*x + c)^2 + 2*(a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c))/(((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c) + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d)*sin(d*x + c)), (a^5 + a^3*b^2 - 2*a*b^4 - 3*(a^3*b*cos(d*x + c) + a^2*b^2)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*sin(d*x + c) - (2*a^5 - a^3*b^2 - a*b^4)*cos(d*x + c)^2 + (a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c))/(((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c) + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d)*sin(d*x + c))]","A",0
263,1,864,0,1.658651," ","integrate(sec(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a^{6} b - 2 \, b^{7} + {\left(a^{5} b - 4 \, a^{3} b^{3} + {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) \sin\left(d x + c\right) - 2 \, {\left(a^{6} b + a^{4} b^{3} - 2 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} - {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7} + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7} + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)}{2 \, {\left({\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} d\right)} \sin\left(d x + c\right)}, -\frac{2 \, a^{6} b - 2 \, b^{7} + 2 \, {\left(a^{5} b - 4 \, a^{3} b^{3} + {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 2 \, {\left(a^{6} b + a^{4} b^{3} - 2 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} - {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7} + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7} + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)}{2 \, {\left({\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/2*(2*a^6*b - 2*b^7 + (a^5*b - 4*a^3*b^3 + (a^6 - 4*a^4*b^2)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2))*sin(d*x + c) - 2*(a^6*b + a^4*b^3 - 2*a^2*b^5)*cos(d*x + c)^2 - (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7 + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cos(d*x + c))*log(sin(d*x + c) + 1)*sin(d*x + c) + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7 + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cos(d*x + c))*log(-sin(d*x + c) + 1)*sin(d*x + c) + 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*cos(d*x + c))/(((a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*d*cos(d*x + c) + (a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*d)*sin(d*x + c)), -1/2*(2*a^6*b - 2*b^7 + 2*(a^5*b - 4*a^3*b^3 + (a^6 - 4*a^4*b^2)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*sin(d*x + c) - 2*(a^6*b + a^4*b^3 - 2*a^2*b^5)*cos(d*x + c)^2 - (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7 + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cos(d*x + c))*log(sin(d*x + c) + 1)*sin(d*x + c) + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7 + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cos(d*x + c))*log(-sin(d*x + c) + 1)*sin(d*x + c) + 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*cos(d*x + c))/(((a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*d*cos(d*x + c) + (a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*d)*sin(d*x + c))]","A",0
264,1,1180,0,1.080116," ","integrate(cos(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, a^{8} b^{2} + 4 \, a^{6} b^{4} + 16 \, a^{4} b^{6} - 28 \, a^{2} b^{8} + 6 \, b^{10} - 2 \, {\left(3 \, a^{9} b - 2 \, a^{7} b^{3} + 11 \, a^{5} b^{5} - 16 \, a^{3} b^{7} + 4 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{10} - 4 \, a^{8} b^{2} + a^{6} b^{4} - 9 \, a^{4} b^{6} + 14 \, a^{2} b^{8} - 3 \, b^{10}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{9} b + a^{7} b^{3} + 8 \, a^{5} b^{5} - 15 \, a^{3} b^{7} + 4 \, a b^{9}\right)} \cos\left(d x + c\right) + 4 \, {\left(15 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10} - {\left(15 \, a^{6} b^{4} - 4 \, a^{4} b^{6} + a^{2} b^{8}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(15 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(15 \, a^{6} b^{4} - 19 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right) + {\left(2 \, a^{8} b^{2} + 3 \, a^{7} b^{3} - 8 \, a^{6} b^{4} - 22 \, a^{5} b^{5} - 18 \, a^{4} b^{6} - 5 \, a^{3} b^{7} - {\left(2 \, a^{10} + 3 \, a^{9} b - 8 \, a^{8} b^{2} - 22 \, a^{7} b^{3} - 18 \, a^{6} b^{4} - 5 \, a^{5} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(2 \, a^{9} b + 3 \, a^{8} b^{2} - 8 \, a^{7} b^{3} - 22 \, a^{6} b^{4} - 18 \, a^{5} b^{5} - 5 \, a^{4} b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, a^{10} + 3 \, a^{9} b - 10 \, a^{8} b^{2} - 25 \, a^{7} b^{3} - 10 \, a^{6} b^{4} + 17 \, a^{5} b^{5} + 18 \, a^{4} b^{6} + 5 \, a^{3} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{9} b + 3 \, a^{8} b^{2} - 8 \, a^{7} b^{3} - 22 \, a^{6} b^{4} - 18 \, a^{5} b^{5} - 5 \, a^{4} b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(2 \, a^{8} b^{2} - 3 \, a^{7} b^{3} - 8 \, a^{6} b^{4} + 22 \, a^{5} b^{5} - 18 \, a^{4} b^{6} + 5 \, a^{3} b^{7} - {\left(2 \, a^{10} - 3 \, a^{9} b - 8 \, a^{8} b^{2} + 22 \, a^{7} b^{3} - 18 \, a^{6} b^{4} + 5 \, a^{5} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(2 \, a^{9} b - 3 \, a^{8} b^{2} - 8 \, a^{7} b^{3} + 22 \, a^{6} b^{4} - 18 \, a^{5} b^{5} + 5 \, a^{4} b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, a^{10} - 3 \, a^{9} b - 10 \, a^{8} b^{2} + 25 \, a^{7} b^{3} - 10 \, a^{6} b^{4} - 17 \, a^{5} b^{5} + 18 \, a^{4} b^{6} - 5 \, a^{3} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{9} b - 3 \, a^{8} b^{2} - 8 \, a^{7} b^{3} + 22 \, a^{6} b^{4} - 18 \, a^{5} b^{5} + 5 \, a^{4} b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left({\left(a^{13} - 4 \, a^{11} b^{2} + 6 \, a^{9} b^{4} - 4 \, a^{7} b^{6} + a^{5} b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{12} b - 4 \, a^{10} b^{3} + 6 \, a^{8} b^{5} - 4 \, a^{6} b^{7} + a^{4} b^{9}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{13} - 5 \, a^{11} b^{2} + 10 \, a^{9} b^{4} - 10 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - a^{3} b^{10}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{12} b - 4 \, a^{10} b^{3} + 6 \, a^{8} b^{5} - 4 \, a^{6} b^{7} + a^{4} b^{9}\right)} d \cos\left(d x + c\right) - {\left(a^{11} b^{2} - 4 \, a^{9} b^{4} + 6 \, a^{7} b^{6} - 4 \, a^{5} b^{8} + a^{3} b^{10}\right)} d\right)}}"," ",0,"1/4*(2*a^8*b^2 + 4*a^6*b^4 + 16*a^4*b^6 - 28*a^2*b^8 + 6*b^10 - 2*(3*a^9*b - 2*a^7*b^3 + 11*a^5*b^5 - 16*a^3*b^7 + 4*a*b^9)*cos(d*x + c)^3 + 2*(a^10 - 4*a^8*b^2 + a^6*b^4 - 9*a^4*b^6 + 14*a^2*b^8 - 3*b^10)*cos(d*x + c)^2 + 2*(2*a^9*b + a^7*b^3 + 8*a^5*b^5 - 15*a^3*b^7 + 4*a*b^9)*cos(d*x + c) + 4*(15*a^4*b^6 - 4*a^2*b^8 + b^10 - (15*a^6*b^4 - 4*a^4*b^6 + a^2*b^8)*cos(d*x + c)^4 - 2*(15*a^5*b^5 - 4*a^3*b^7 + a*b^9)*cos(d*x + c)^3 + (15*a^6*b^4 - 19*a^4*b^6 + 5*a^2*b^8 - b^10)*cos(d*x + c)^2 + 2*(15*a^5*b^5 - 4*a^3*b^7 + a*b^9)*cos(d*x + c))*log(a*cos(d*x + c) + b) + (2*a^8*b^2 + 3*a^7*b^3 - 8*a^6*b^4 - 22*a^5*b^5 - 18*a^4*b^6 - 5*a^3*b^7 - (2*a^10 + 3*a^9*b - 8*a^8*b^2 - 22*a^7*b^3 - 18*a^6*b^4 - 5*a^5*b^5)*cos(d*x + c)^4 - 2*(2*a^9*b + 3*a^8*b^2 - 8*a^7*b^3 - 22*a^6*b^4 - 18*a^5*b^5 - 5*a^4*b^6)*cos(d*x + c)^3 + (2*a^10 + 3*a^9*b - 10*a^8*b^2 - 25*a^7*b^3 - 10*a^6*b^4 + 17*a^5*b^5 + 18*a^4*b^6 + 5*a^3*b^7)*cos(d*x + c)^2 + 2*(2*a^9*b + 3*a^8*b^2 - 8*a^7*b^3 - 22*a^6*b^4 - 18*a^5*b^5 - 5*a^4*b^6)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (2*a^8*b^2 - 3*a^7*b^3 - 8*a^6*b^4 + 22*a^5*b^5 - 18*a^4*b^6 + 5*a^3*b^7 - (2*a^10 - 3*a^9*b - 8*a^8*b^2 + 22*a^7*b^3 - 18*a^6*b^4 + 5*a^5*b^5)*cos(d*x + c)^4 - 2*(2*a^9*b - 3*a^8*b^2 - 8*a^7*b^3 + 22*a^6*b^4 - 18*a^5*b^5 + 5*a^4*b^6)*cos(d*x + c)^3 + (2*a^10 - 3*a^9*b - 10*a^8*b^2 + 25*a^7*b^3 - 10*a^6*b^4 - 17*a^5*b^5 + 18*a^4*b^6 - 5*a^3*b^7)*cos(d*x + c)^2 + 2*(2*a^9*b - 3*a^8*b^2 - 8*a^7*b^3 + 22*a^6*b^4 - 18*a^5*b^5 + 5*a^4*b^6)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^13 - 4*a^11*b^2 + 6*a^9*b^4 - 4*a^7*b^6 + a^5*b^8)*d*cos(d*x + c)^4 + 2*(a^12*b - 4*a^10*b^3 + 6*a^8*b^5 - 4*a^6*b^7 + a^4*b^9)*d*cos(d*x + c)^3 - (a^13 - 5*a^11*b^2 + 10*a^9*b^4 - 10*a^7*b^6 + 5*a^5*b^8 - a^3*b^10)*d*cos(d*x + c)^2 - 2*(a^12*b - 4*a^10*b^3 + 6*a^8*b^5 - 4*a^6*b^7 + a^4*b^9)*d*cos(d*x + c) - (a^11*b^2 - 4*a^9*b^4 + 6*a^7*b^6 - 4*a^5*b^8 + a^3*b^10)*d)","B",0
265,1,1045,0,1.867319," ","integrate(cos(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{6 \, a^{6} b^{3} + 14 \, a^{4} b^{5} - 22 \, a^{2} b^{7} + 2 \, b^{9} - 2 \, {\left(a^{9} + 2 \, a^{7} b^{2} + 7 \, a^{5} b^{4} - 12 \, a^{3} b^{6} + 2 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{8} b - 6 \, a^{6} b^{3} - 4 \, a^{4} b^{5} + 10 \, a^{2} b^{7} - b^{9}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, a^{7} b^{2} + 4 \, a^{5} b^{4} - 11 \, a^{3} b^{6} + 2 \, a b^{8}\right)} \cos\left(d x + c\right) + 8 \, {\left(5 \, a^{4} b^{5} + a^{2} b^{7} - {\left(5 \, a^{6} b^{3} + a^{4} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(5 \, a^{5} b^{4} + a^{3} b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(5 \, a^{6} b^{3} - 4 \, a^{4} b^{5} - a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, a^{5} b^{4} + a^{3} b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right) + {\left(a^{7} b^{2} - 10 \, a^{5} b^{4} - 20 \, a^{4} b^{5} - 15 \, a^{3} b^{6} - 4 \, a^{2} b^{7} - {\left(a^{9} - 10 \, a^{7} b^{2} - 20 \, a^{6} b^{3} - 15 \, a^{5} b^{4} - 4 \, a^{4} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{8} b - 10 \, a^{6} b^{3} - 20 \, a^{5} b^{4} - 15 \, a^{4} b^{5} - 4 \, a^{3} b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{9} - 11 \, a^{7} b^{2} - 20 \, a^{6} b^{3} - 5 \, a^{5} b^{4} + 16 \, a^{4} b^{5} + 15 \, a^{3} b^{6} + 4 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b - 10 \, a^{6} b^{3} - 20 \, a^{5} b^{4} - 15 \, a^{4} b^{5} - 4 \, a^{3} b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a^{7} b^{2} - 10 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 15 \, a^{3} b^{6} + 4 \, a^{2} b^{7} - {\left(a^{9} - 10 \, a^{7} b^{2} + 20 \, a^{6} b^{3} - 15 \, a^{5} b^{4} + 4 \, a^{4} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{8} b - 10 \, a^{6} b^{3} + 20 \, a^{5} b^{4} - 15 \, a^{4} b^{5} + 4 \, a^{3} b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{9} - 11 \, a^{7} b^{2} + 20 \, a^{6} b^{3} - 5 \, a^{5} b^{4} - 16 \, a^{4} b^{5} + 15 \, a^{3} b^{6} - 4 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b - 10 \, a^{6} b^{3} + 20 \, a^{5} b^{4} - 15 \, a^{4} b^{5} + 4 \, a^{3} b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left({\left(a^{12} - 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} - 4 \, a^{6} b^{6} + a^{4} b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{11} b - 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} - 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{12} - 5 \, a^{10} b^{2} + 10 \, a^{8} b^{4} - 10 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - a^{2} b^{10}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{11} b - 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} - 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} d \cos\left(d x + c\right) - {\left(a^{10} b^{2} - 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} - 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} d\right)}}"," ",0,"-1/4*(6*a^6*b^3 + 14*a^4*b^5 - 22*a^2*b^7 + 2*b^9 - 2*(a^9 + 2*a^7*b^2 + 7*a^5*b^4 - 12*a^3*b^6 + 2*a*b^8)*cos(d*x + c)^3 + 2*(a^8*b - 6*a^6*b^3 - 4*a^4*b^5 + 10*a^2*b^7 - b^9)*cos(d*x + c)^2 + 2*(5*a^7*b^2 + 4*a^5*b^4 - 11*a^3*b^6 + 2*a*b^8)*cos(d*x + c) + 8*(5*a^4*b^5 + a^2*b^7 - (5*a^6*b^3 + a^4*b^5)*cos(d*x + c)^4 - 2*(5*a^5*b^4 + a^3*b^6)*cos(d*x + c)^3 + (5*a^6*b^3 - 4*a^4*b^5 - a^2*b^7)*cos(d*x + c)^2 + 2*(5*a^5*b^4 + a^3*b^6)*cos(d*x + c))*log(a*cos(d*x + c) + b) + (a^7*b^2 - 10*a^5*b^4 - 20*a^4*b^5 - 15*a^3*b^6 - 4*a^2*b^7 - (a^9 - 10*a^7*b^2 - 20*a^6*b^3 - 15*a^5*b^4 - 4*a^4*b^5)*cos(d*x + c)^4 - 2*(a^8*b - 10*a^6*b^3 - 20*a^5*b^4 - 15*a^4*b^5 - 4*a^3*b^6)*cos(d*x + c)^3 + (a^9 - 11*a^7*b^2 - 20*a^6*b^3 - 5*a^5*b^4 + 16*a^4*b^5 + 15*a^3*b^6 + 4*a^2*b^7)*cos(d*x + c)^2 + 2*(a^8*b - 10*a^6*b^3 - 20*a^5*b^4 - 15*a^4*b^5 - 4*a^3*b^6)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - (a^7*b^2 - 10*a^5*b^4 + 20*a^4*b^5 - 15*a^3*b^6 + 4*a^2*b^7 - (a^9 - 10*a^7*b^2 + 20*a^6*b^3 - 15*a^5*b^4 + 4*a^4*b^5)*cos(d*x + c)^4 - 2*(a^8*b - 10*a^6*b^3 + 20*a^5*b^4 - 15*a^4*b^5 + 4*a^3*b^6)*cos(d*x + c)^3 + (a^9 - 11*a^7*b^2 + 20*a^6*b^3 - 5*a^5*b^4 - 16*a^4*b^5 + 15*a^3*b^6 - 4*a^2*b^7)*cos(d*x + c)^2 + 2*(a^8*b - 10*a^6*b^3 + 20*a^5*b^4 - 15*a^4*b^5 + 4*a^3*b^6)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^12 - 4*a^10*b^2 + 6*a^8*b^4 - 4*a^6*b^6 + a^4*b^8)*d*cos(d*x + c)^4 + 2*(a^11*b - 4*a^9*b^3 + 6*a^7*b^5 - 4*a^5*b^7 + a^3*b^9)*d*cos(d*x + c)^3 - (a^12 - 5*a^10*b^2 + 10*a^8*b^4 - 10*a^6*b^6 + 5*a^4*b^8 - a^2*b^10)*d*cos(d*x + c)^2 - 2*(a^11*b - 4*a^9*b^3 + 6*a^7*b^5 - 4*a^5*b^7 + a^3*b^9)*d*cos(d*x + c) - (a^10*b^2 - 4*a^8*b^4 + 6*a^6*b^6 - 4*a^4*b^8 + a^2*b^10)*d)","B",0
266,1,994,0,0.736067," ","integrate(cos(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, a^{6} b^{2} + 18 \, a^{4} b^{4} - 18 \, a^{2} b^{6} - 2 \, b^{8} - 6 \, {\left(a^{7} b + 2 \, a^{5} b^{3} - 3 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{8} - 4 \, a^{6} b^{2} - 6 \, a^{4} b^{4} + 8 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{7} b + 9 \, a^{5} b^{3} - 12 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right) + 24 \, {\left(a^{4} b^{4} + a^{2} b^{6} - {\left(a^{6} b^{2} + a^{4} b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} b^{3} + a^{3} b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{6} b^{2} - a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{3} + a^{3} b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right) - 3 \, {\left(a^{5} b^{3} + 4 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + 4 \, a^{2} b^{6} + a b^{7} - {\left(a^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b^{2} + 4 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 4 \, a^{3} b^{5} + a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} - 5 \, a^{3} b^{5} - 4 \, a^{2} b^{6} - a b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b^{2} + 4 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 4 \, a^{3} b^{5} + a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(a^{5} b^{3} - 4 \, a^{4} b^{4} + 6 \, a^{3} b^{5} - 4 \, a^{2} b^{6} + a b^{7} - {\left(a^{7} b - 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} - 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b^{2} - 4 \, a^{5} b^{3} + 6 \, a^{4} b^{4} - 4 \, a^{3} b^{5} + a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{7} b - 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} - 5 \, a^{3} b^{5} + 4 \, a^{2} b^{6} - a b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b^{2} - 4 \, a^{5} b^{3} + 6 \, a^{4} b^{4} - 4 \, a^{3} b^{5} + a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left({\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{11} - 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} - a b^{10}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right) - {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d\right)}}"," ",0,"1/4*(2*a^6*b^2 + 18*a^4*b^4 - 18*a^2*b^6 - 2*b^8 - 6*(a^7*b + 2*a^5*b^3 - 3*a^3*b^5)*cos(d*x + c)^3 + 2*(a^8 - 4*a^6*b^2 - 6*a^4*b^4 + 8*a^2*b^6 + b^8)*cos(d*x + c)^2 + 2*(2*a^7*b + 9*a^5*b^3 - 12*a^3*b^5 + a*b^7)*cos(d*x + c) + 24*(a^4*b^4 + a^2*b^6 - (a^6*b^2 + a^4*b^4)*cos(d*x + c)^4 - 2*(a^5*b^3 + a^3*b^5)*cos(d*x + c)^3 + (a^6*b^2 - a^2*b^6)*cos(d*x + c)^2 + 2*(a^5*b^3 + a^3*b^5)*cos(d*x + c))*log(a*cos(d*x + c) + b) - 3*(a^5*b^3 + 4*a^4*b^4 + 6*a^3*b^5 + 4*a^2*b^6 + a*b^7 - (a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*cos(d*x + c)^4 - 2*(a^6*b^2 + 4*a^5*b^3 + 6*a^4*b^4 + 4*a^3*b^5 + a^2*b^6)*cos(d*x + c)^3 + (a^7*b + 4*a^6*b^2 + 5*a^5*b^3 - 5*a^3*b^5 - 4*a^2*b^6 - a*b^7)*cos(d*x + c)^2 + 2*(a^6*b^2 + 4*a^5*b^3 + 6*a^4*b^4 + 4*a^3*b^5 + a^2*b^6)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 3*(a^5*b^3 - 4*a^4*b^4 + 6*a^3*b^5 - 4*a^2*b^6 + a*b^7 - (a^7*b - 4*a^6*b^2 + 6*a^5*b^3 - 4*a^4*b^4 + a^3*b^5)*cos(d*x + c)^4 - 2*(a^6*b^2 - 4*a^5*b^3 + 6*a^4*b^4 - 4*a^3*b^5 + a^2*b^6)*cos(d*x + c)^3 + (a^7*b - 4*a^6*b^2 + 5*a^5*b^3 - 5*a^3*b^5 + 4*a^2*b^6 - a*b^7)*cos(d*x + c)^2 + 2*(a^6*b^2 - 4*a^5*b^3 + 6*a^4*b^4 - 4*a^3*b^5 + a^2*b^6)*cos(d*x + c))*log(-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)*d*cos(d*x + c)^4 + 2*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c)^3 - (a^11 - 5*a^9*b^2 + 10*a^7*b^4 - 10*a^5*b^6 + 5*a^3*b^8 - a*b^10)*d*cos(d*x + c)^2 - 2*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c) - (a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d)","B",0
267,1,1071,0,0.972063," ","integrate(1/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{16 \, a^{4} b^{3} - 8 \, a^{2} b^{5} - 8 \, b^{7} - 2 \, {\left(a^{7} + 8 \, a^{5} b^{2} - 7 \, a^{3} b^{4} - 2 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{6} b - 11 \, a^{4} b^{3} + 7 \, a^{2} b^{5} + 3 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, a^{5} b^{2} - 10 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right) + 4 \, {\left(3 \, a^{4} b^{3} + 8 \, a^{2} b^{5} + b^{7} - {\left(3 \, a^{6} b + 8 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} b^{2} + 8 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, a^{6} b + 5 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{5} b^{2} + 8 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right) - {\left(a^{5} b^{2} + 6 \, a^{4} b^{3} + 14 \, a^{3} b^{4} + 16 \, a^{2} b^{5} + 9 \, a b^{6} + 2 \, b^{7} - {\left(a^{7} + 6 \, a^{6} b + 14 \, a^{5} b^{2} + 16 \, a^{4} b^{3} + 9 \, a^{3} b^{4} + 2 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b + 6 \, a^{5} b^{2} + 14 \, a^{4} b^{3} + 16 \, a^{3} b^{4} + 9 \, a^{2} b^{5} + 2 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{7} + 6 \, a^{6} b + 13 \, a^{5} b^{2} + 10 \, a^{4} b^{3} - 5 \, a^{3} b^{4} - 14 \, a^{2} b^{5} - 9 \, a b^{6} - 2 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b + 6 \, a^{5} b^{2} + 14 \, a^{4} b^{3} + 16 \, a^{3} b^{4} + 9 \, a^{2} b^{5} + 2 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{5} b^{2} - 6 \, a^{4} b^{3} + 14 \, a^{3} b^{4} - 16 \, a^{2} b^{5} + 9 \, a b^{6} - 2 \, b^{7} - {\left(a^{7} - 6 \, a^{6} b + 14 \, a^{5} b^{2} - 16 \, a^{4} b^{3} + 9 \, a^{3} b^{4} - 2 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b - 6 \, a^{5} b^{2} + 14 \, a^{4} b^{3} - 16 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 2 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{7} - 6 \, a^{6} b + 13 \, a^{5} b^{2} - 10 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + 14 \, a^{2} b^{5} - 9 \, a b^{6} + 2 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b - 6 \, a^{5} b^{2} + 14 \, a^{4} b^{3} - 16 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 2 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left({\left(a^{10} - 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} - 4 \, a^{4} b^{6} + a^{2} b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{10} - 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} - 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) - {\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d\right)}}"," ",0,"-1/4*(16*a^4*b^3 - 8*a^2*b^5 - 8*b^7 - 2*(a^7 + 8*a^5*b^2 - 7*a^3*b^4 - 2*a*b^6)*cos(d*x + c)^3 + 2*(a^6*b - 11*a^4*b^3 + 7*a^2*b^5 + 3*b^7)*cos(d*x + c)^2 + 2*(11*a^5*b^2 - 10*a^3*b^4 - a*b^6)*cos(d*x + c) + 4*(3*a^4*b^3 + 8*a^2*b^5 + b^7 - (3*a^6*b + 8*a^4*b^3 + a^2*b^5)*cos(d*x + c)^4 - 2*(3*a^5*b^2 + 8*a^3*b^4 + a*b^6)*cos(d*x + c)^3 + (3*a^6*b + 5*a^4*b^3 - 7*a^2*b^5 - b^7)*cos(d*x + c)^2 + 2*(3*a^5*b^2 + 8*a^3*b^4 + a*b^6)*cos(d*x + c))*log(a*cos(d*x + c) + b) - (a^5*b^2 + 6*a^4*b^3 + 14*a^3*b^4 + 16*a^2*b^5 + 9*a*b^6 + 2*b^7 - (a^7 + 6*a^6*b + 14*a^5*b^2 + 16*a^4*b^3 + 9*a^3*b^4 + 2*a^2*b^5)*cos(d*x + c)^4 - 2*(a^6*b + 6*a^5*b^2 + 14*a^4*b^3 + 16*a^3*b^4 + 9*a^2*b^5 + 2*a*b^6)*cos(d*x + c)^3 + (a^7 + 6*a^6*b + 13*a^5*b^2 + 10*a^4*b^3 - 5*a^3*b^4 - 14*a^2*b^5 - 9*a*b^6 - 2*b^7)*cos(d*x + c)^2 + 2*(a^6*b + 6*a^5*b^2 + 14*a^4*b^3 + 16*a^3*b^4 + 9*a^2*b^5 + 2*a*b^6)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (a^5*b^2 - 6*a^4*b^3 + 14*a^3*b^4 - 16*a^2*b^5 + 9*a*b^6 - 2*b^7 - (a^7 - 6*a^6*b + 14*a^5*b^2 - 16*a^4*b^3 + 9*a^3*b^4 - 2*a^2*b^5)*cos(d*x + c)^4 - 2*(a^6*b - 6*a^5*b^2 + 14*a^4*b^3 - 16*a^3*b^4 + 9*a^2*b^5 - 2*a*b^6)*cos(d*x + c)^3 + (a^7 - 6*a^6*b + 13*a^5*b^2 - 10*a^4*b^3 - 5*a^3*b^4 + 14*a^2*b^5 - 9*a*b^6 + 2*b^7)*cos(d*x + c)^2 + 2*(a^6*b - 6*a^5*b^2 + 14*a^4*b^3 - 16*a^3*b^4 + 9*a^2*b^5 - 2*a*b^6)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8)*d*cos(d*x + c)^4 + 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)^3 - (a^10 - 5*a^8*b^2 + 10*a^6*b^4 - 10*a^4*b^6 + 5*a^2*b^8 - b^10)*d*cos(d*x + c)^2 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c) - (a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d)","B",0
268,1,1076,0,0.840425," ","integrate(sec(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{8 \, a^{5} b^{2} + 8 \, a^{3} b^{4} - 16 \, a b^{6} - 2 \, {\left(7 \, a^{6} b - 2 \, a^{4} b^{3} - 5 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{7} - 7 \, a^{5} b^{2} - a^{3} b^{4} + 7 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{6} b + a^{4} b^{3} - 8 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right) + 4 \, {\left(a^{5} b^{2} + 8 \, a^{3} b^{4} + 3 \, a b^{6} - {\left(a^{7} + 8 \, a^{5} b^{2} + 3 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b + 8 \, a^{4} b^{3} + 3 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{7} + 7 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b + 8 \, a^{4} b^{3} + 3 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right) - {\left(2 \, a^{5} b^{2} + 9 \, a^{4} b^{3} + 16 \, a^{3} b^{4} + 14 \, a^{2} b^{5} + 6 \, a b^{6} + b^{7} - {\left(2 \, a^{7} + 9 \, a^{6} b + 16 \, a^{5} b^{2} + 14 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(2 \, a^{6} b + 9 \, a^{5} b^{2} + 16 \, a^{4} b^{3} + 14 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, a^{7} + 9 \, a^{6} b + 14 \, a^{5} b^{2} + 5 \, a^{4} b^{3} - 10 \, a^{3} b^{4} - 13 \, a^{2} b^{5} - 6 \, a b^{6} - b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{6} b + 9 \, a^{5} b^{2} + 16 \, a^{4} b^{3} + 14 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(2 \, a^{5} b^{2} - 9 \, a^{4} b^{3} + 16 \, a^{3} b^{4} - 14 \, a^{2} b^{5} + 6 \, a b^{6} - b^{7} - {\left(2 \, a^{7} - 9 \, a^{6} b + 16 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 6 \, a^{3} b^{4} - a^{2} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(2 \, a^{6} b - 9 \, a^{5} b^{2} + 16 \, a^{4} b^{3} - 14 \, a^{3} b^{4} + 6 \, a^{2} b^{5} - a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, a^{7} - 9 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3} - 10 \, a^{3} b^{4} + 13 \, a^{2} b^{5} - 6 \, a b^{6} + b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{6} b - 9 \, a^{5} b^{2} + 16 \, a^{4} b^{3} - 14 \, a^{3} b^{4} + 6 \, a^{2} b^{5} - a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left({\left(a^{10} - 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} - 4 \, a^{4} b^{6} + a^{2} b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{10} - 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} - 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) - {\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d\right)}}"," ",0,"1/4*(8*a^5*b^2 + 8*a^3*b^4 - 16*a*b^6 - 2*(7*a^6*b - 2*a^4*b^3 - 5*a^2*b^5)*cos(d*x + c)^3 + 2*(a^7 - 7*a^5*b^2 - a^3*b^4 + 7*a*b^6)*cos(d*x + c)^2 + 2*(6*a^6*b + a^4*b^3 - 8*a^2*b^5 + b^7)*cos(d*x + c) + 4*(a^5*b^2 + 8*a^3*b^4 + 3*a*b^6 - (a^7 + 8*a^5*b^2 + 3*a^3*b^4)*cos(d*x + c)^4 - 2*(a^6*b + 8*a^4*b^3 + 3*a^2*b^5)*cos(d*x + c)^3 + (a^7 + 7*a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*cos(d*x + c)^2 + 2*(a^6*b + 8*a^4*b^3 + 3*a^2*b^5)*cos(d*x + c))*log(a*cos(d*x + c) + b) - (2*a^5*b^2 + 9*a^4*b^3 + 16*a^3*b^4 + 14*a^2*b^5 + 6*a*b^6 + b^7 - (2*a^7 + 9*a^6*b + 16*a^5*b^2 + 14*a^4*b^3 + 6*a^3*b^4 + a^2*b^5)*cos(d*x + c)^4 - 2*(2*a^6*b + 9*a^5*b^2 + 16*a^4*b^3 + 14*a^3*b^4 + 6*a^2*b^5 + a*b^6)*cos(d*x + c)^3 + (2*a^7 + 9*a^6*b + 14*a^5*b^2 + 5*a^4*b^3 - 10*a^3*b^4 - 13*a^2*b^5 - 6*a*b^6 - b^7)*cos(d*x + c)^2 + 2*(2*a^6*b + 9*a^5*b^2 + 16*a^4*b^3 + 14*a^3*b^4 + 6*a^2*b^5 + a*b^6)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - (2*a^5*b^2 - 9*a^4*b^3 + 16*a^3*b^4 - 14*a^2*b^5 + 6*a*b^6 - b^7 - (2*a^7 - 9*a^6*b + 16*a^5*b^2 - 14*a^4*b^3 + 6*a^3*b^4 - a^2*b^5)*cos(d*x + c)^4 - 2*(2*a^6*b - 9*a^5*b^2 + 16*a^4*b^3 - 14*a^3*b^4 + 6*a^2*b^5 - a*b^6)*cos(d*x + c)^3 + (2*a^7 - 9*a^6*b + 14*a^5*b^2 - 5*a^4*b^3 - 10*a^3*b^4 + 13*a^2*b^5 - 6*a*b^6 + b^7)*cos(d*x + c)^2 + 2*(2*a^6*b - 9*a^5*b^2 + 16*a^4*b^3 - 14*a^3*b^4 + 6*a^2*b^5 - a*b^6)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8)*d*cos(d*x + c)^4 + 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)^3 - (a^10 - 5*a^8*b^2 + 10*a^6*b^4 - 10*a^4*b^6 + 5*a^2*b^8 - b^10)*d*cos(d*x + c)^2 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c) - (a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d)","B",0
269,1,939,0,1.008363," ","integrate(sec(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, a^{6} b + 18 \, a^{4} b^{3} - 18 \, a^{2} b^{5} - 2 \, b^{7} - 6 \, {\left(a^{7} + 2 \, a^{5} b^{2} - 3 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)^{3} - 24 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{7} + 9 \, a^{5} b^{2} - 12 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + 24 \, {\left(a^{4} b^{3} + a^{2} b^{5} - {\left(a^{6} b + a^{4} b^{3}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} b^{2} + a^{3} b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{6} b - a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{2} + a^{3} b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right) - 3 \, {\left(a^{5} b^{2} + 4 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 4 \, a^{2} b^{5} + a b^{6} - {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b + 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b + 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(a^{5} b^{2} - 4 \, a^{4} b^{3} + 6 \, a^{3} b^{4} - 4 \, a^{2} b^{5} + a b^{6} - {\left(a^{7} - 4 \, a^{6} b + 6 \, a^{5} b^{2} - 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 4 \, a^{2} b^{5} - a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left({\left(a^{10} - 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} - 4 \, a^{4} b^{6} + a^{2} b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{10} - 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} - 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) - {\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d\right)}}"," ",0,"-1/4*(2*a^6*b + 18*a^4*b^3 - 18*a^2*b^5 - 2*b^7 - 6*(a^7 + 2*a^5*b^2 - 3*a^3*b^4)*cos(d*x + c)^3 - 24*(a^4*b^3 - a^2*b^5)*cos(d*x + c)^2 + 2*(2*a^7 + 9*a^5*b^2 - 12*a^3*b^4 + a*b^6)*cos(d*x + c) + 24*(a^4*b^3 + a^2*b^5 - (a^6*b + a^4*b^3)*cos(d*x + c)^4 - 2*(a^5*b^2 + a^3*b^4)*cos(d*x + c)^3 + (a^6*b - a^2*b^5)*cos(d*x + c)^2 + 2*(a^5*b^2 + a^3*b^4)*cos(d*x + c))*log(a*cos(d*x + c) + b) - 3*(a^5*b^2 + 4*a^4*b^3 + 6*a^3*b^4 + 4*a^2*b^5 + a*b^6 - (a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*cos(d*x + c)^4 - 2*(a^6*b + 4*a^5*b^2 + 6*a^4*b^3 + 4*a^3*b^4 + a^2*b^5)*cos(d*x + c)^3 + (a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*cos(d*x + c)^2 + 2*(a^6*b + 4*a^5*b^2 + 6*a^4*b^3 + 4*a^3*b^4 + a^2*b^5)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 3*(a^5*b^2 - 4*a^4*b^3 + 6*a^3*b^4 - 4*a^2*b^5 + a*b^6 - (a^7 - 4*a^6*b + 6*a^5*b^2 - 4*a^4*b^3 + a^3*b^4)*cos(d*x + c)^4 - 2*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*cos(d*x + c)^3 + (a^7 - 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 + 4*a^2*b^5 - a*b^6)*cos(d*x + c)^2 + 2*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8)*d*cos(d*x + c)^4 + 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)^3 - (a^10 - 5*a^8*b^2 + 10*a^6*b^4 - 10*a^4*b^6 + 5*a^2*b^8 - b^10)*d*cos(d*x + c)^2 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c) - (a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d)","B",0
270,1,971,0,0.781687," ","integrate(sec(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, a^{7} - 22 \, a^{5} b^{2} + 14 \, a^{3} b^{4} + 6 \, a b^{6} + 2 \, {\left(11 \, a^{6} b - 10 \, a^{4} b^{3} - a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} - 4 \, {\left(a^{7} - 7 \, a^{5} b^{2} + 5 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(10 \, a^{6} b - 7 \, a^{4} b^{3} - 4 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right) - 8 \, {\left(a^{5} b^{2} + 5 \, a^{3} b^{4} - {\left(a^{7} + 5 \, a^{5} b^{2}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b + 5 \, a^{4} b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{7} + 4 \, a^{5} b^{2} - 5 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b + 5 \, a^{4} b^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(a \cos\left(d x + c\right) + b\right) + {\left(4 \, a^{5} b^{2} + 15 \, a^{4} b^{3} + 20 \, a^{3} b^{4} + 10 \, a^{2} b^{5} - b^{7} - {\left(4 \, a^{7} + 15 \, a^{6} b + 20 \, a^{5} b^{2} + 10 \, a^{4} b^{3} - a^{2} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(4 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(4 \, a^{7} + 15 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3} - 20 \, a^{3} b^{4} - 11 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(4 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(4 \, a^{5} b^{2} - 15 \, a^{4} b^{3} + 20 \, a^{3} b^{4} - 10 \, a^{2} b^{5} + b^{7} - {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(4 \, a^{6} b - 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} - 10 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(4 \, a^{7} - 15 \, a^{6} b + 16 \, a^{5} b^{2} + 5 \, a^{4} b^{3} - 20 \, a^{3} b^{4} + 11 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(4 \, a^{6} b - 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} - 10 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left({\left(a^{10} - 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} - 4 \, a^{4} b^{6} + a^{2} b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{10} - 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} - 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) - {\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d\right)}}"," ",0,"-1/4*(2*a^7 - 22*a^5*b^2 + 14*a^3*b^4 + 6*a*b^6 + 2*(11*a^6*b - 10*a^4*b^3 - a^2*b^5)*cos(d*x + c)^3 - 4*(a^7 - 7*a^5*b^2 + 5*a^3*b^4 + a*b^6)*cos(d*x + c)^2 - 2*(10*a^6*b - 7*a^4*b^3 - 4*a^2*b^5 + b^7)*cos(d*x + c) - 8*(a^5*b^2 + 5*a^3*b^4 - (a^7 + 5*a^5*b^2)*cos(d*x + c)^4 - 2*(a^6*b + 5*a^4*b^3)*cos(d*x + c)^3 + (a^7 + 4*a^5*b^2 - 5*a^3*b^4)*cos(d*x + c)^2 + 2*(a^6*b + 5*a^4*b^3)*cos(d*x + c))*log(a*cos(d*x + c) + b) + (4*a^5*b^2 + 15*a^4*b^3 + 20*a^3*b^4 + 10*a^2*b^5 - b^7 - (4*a^7 + 15*a^6*b + 20*a^5*b^2 + 10*a^4*b^3 - a^2*b^5)*cos(d*x + c)^4 - 2*(4*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 10*a^3*b^4 - a*b^6)*cos(d*x + c)^3 + (4*a^7 + 15*a^6*b + 16*a^5*b^2 - 5*a^4*b^3 - 20*a^3*b^4 - 11*a^2*b^5 + b^7)*cos(d*x + c)^2 + 2*(4*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 10*a^3*b^4 - a*b^6)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (4*a^5*b^2 - 15*a^4*b^3 + 20*a^3*b^4 - 10*a^2*b^5 + b^7 - (4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*cos(d*x + c)^4 - 2*(4*a^6*b - 15*a^5*b^2 + 20*a^4*b^3 - 10*a^3*b^4 + a*b^6)*cos(d*x + c)^3 + (4*a^7 - 15*a^6*b + 16*a^5*b^2 + 5*a^4*b^3 - 20*a^3*b^4 + 11*a^2*b^5 - b^7)*cos(d*x + c)^2 + 2*(4*a^6*b - 15*a^5*b^2 + 20*a^4*b^3 - 10*a^3*b^4 + a*b^6)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8)*d*cos(d*x + c)^4 + 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)^3 - (a^10 - 5*a^8*b^2 + 10*a^6*b^4 - 10*a^4*b^6 + 5*a^2*b^8 - b^10)*d*cos(d*x + c)^2 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c) - (a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d)","B",0
271,1,412,0,0.531541," ","integrate(cos(d*x+c)^m*(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(b^{3} m^{5} + 5 \, b^{3} m^{4} + 5 \, b^{3} m^{3} - {\left(a^{3} m^{5} - 5 \, a^{3} m^{3} + 4 \, a^{3} m\right)} \cos\left(d x + c\right)^{5} - 5 \, b^{3} m^{2} - 3 \, {\left(a^{2} b m^{5} + a^{2} b m^{4} - 7 \, a^{2} b m^{3} - a^{2} b m^{2} + 6 \, a^{2} b m\right)} \cos\left(d x + c\right)^{4} - 6 \, b^{3} m + {\left({\left(a^{3} - 3 \, a b^{2}\right)} m^{5} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} m^{4} - 7 \, {\left(a^{3} - 3 \, a b^{2}\right)} m^{3} - 8 \, {\left(a^{3} - 3 \, a b^{2}\right)} m^{2} + 12 \, {\left(a^{3} - 3 \, a b^{2}\right)} m\right)} \cos\left(d x + c\right)^{3} + {\left({\left(3 \, a^{2} b - b^{3}\right)} m^{5} + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} m^{4} - 5 \, {\left(3 \, a^{2} b - b^{3}\right)} m^{3} + 36 \, a^{2} b - 12 \, b^{3} - 15 \, {\left(3 \, a^{2} b - b^{3}\right)} m^{2} + 4 \, {\left(3 \, a^{2} b - b^{3}\right)} m\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a b^{2} m^{5} + 4 \, a b^{2} m^{4} - a b^{2} m^{3} - 16 \, a b^{2} m^{2} - 12 \, a b^{2} m\right)} \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{m}}{{\left(d m^{6} + 3 \, d m^{5} - 5 \, d m^{4} - 15 \, d m^{3} + 4 \, d m^{2} + 12 \, d m\right)} \cos\left(d x + c\right)^{2}}"," ",0,"-(b^3*m^5 + 5*b^3*m^4 + 5*b^3*m^3 - (a^3*m^5 - 5*a^3*m^3 + 4*a^3*m)*cos(d*x + c)^5 - 5*b^3*m^2 - 3*(a^2*b*m^5 + a^2*b*m^4 - 7*a^2*b*m^3 - a^2*b*m^2 + 6*a^2*b*m)*cos(d*x + c)^4 - 6*b^3*m + ((a^3 - 3*a*b^2)*m^5 + 2*(a^3 - 3*a*b^2)*m^4 - 7*(a^3 - 3*a*b^2)*m^3 - 8*(a^3 - 3*a*b^2)*m^2 + 12*(a^3 - 3*a*b^2)*m)*cos(d*x + c)^3 + ((3*a^2*b - b^3)*m^5 + 3*(3*a^2*b - b^3)*m^4 - 5*(3*a^2*b - b^3)*m^3 + 36*a^2*b - 12*b^3 - 15*(3*a^2*b - b^3)*m^2 + 4*(3*a^2*b - b^3)*m)*cos(d*x + c)^2 + 3*(a*b^2*m^5 + 4*a*b^2*m^4 - a*b^2*m^3 - 16*a*b^2*m^2 - 12*a*b^2*m)*cos(d*x + c))*cos(d*x + c)^m/((d*m^6 + 3*d*m^5 - 5*d*m^4 - 15*d*m^3 + 4*d*m^2 + 12*d*m)*cos(d*x + c)^2)","B",0
272,0,0,0,1.470566," ","integrate(cos(d*x+c)^m*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) \tan\left(d x + c\right) - b^{2} \tan\left(d x + c\right)^{2} - a^{2}\right)} \cos\left(d x + c\right)^{m}, x\right)"," ",0,"integral(-(a^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c)*tan(d*x + c) - b^2*tan(d*x + c)^2 - a^2)*cos(d*x + c)^m, x)","F",0
273,1,35,0,0.520623," ","integrate(cos(d*x+c)^m*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a m \cos\left(d x + c\right) + b m + b\right)} \cos\left(d x + c\right)^{m}}{d m^{2} + d m}"," ",0,"-(a*m*cos(d*x + c) + b*m + b)*cos(d*x + c)^m/(d*m^2 + d*m)","A",0
274,0,0,0,0.470279," ","integrate(cos(d*x+c)^m/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{m}}{a \sin\left(d x + c\right) + b \tan\left(d x + c\right)}, x\right)"," ",0,"integral(cos(d*x + c)^m/(a*sin(d*x + c) + b*tan(d*x + c)), x)","F",0
275,1,142,0,0.648940," ","integrate(cos(x)*sin(x)/(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} + b^{2}} a b \log\left(\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right) - 2 \, {\left(a^{3} + a b^{2}\right)} \cos\left(x\right) + 2 \, {\left(a^{2} b + b^{3}\right)} \sin\left(x\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}"," ",0,"1/2*(sqrt(a^2 + b^2)*a*b*log((2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)) - 2*(a^3 + a*b^2)*cos(x) + 2*(a^2*b + b^3)*sin(x))/(a^4 + 2*a^2*b^2 + b^4)","B",0
276,1,94,0,0.467294," ","integrate(cos(x)*sin(x)^2/(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","\frac{a^{2} b \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right) - {\left(a^{2} b + b^{3}\right)} \cos\left(x\right)^{2} - {\left(a^{3} + a b^{2}\right)} \cos\left(x\right) \sin\left(x\right) + {\left(a^{3} - a b^{2}\right)} x}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}"," ",0,"1/2*(a^2*b*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2) - (a^2*b + b^3)*cos(x)^2 - (a^3 + a*b^2)*cos(x)*sin(x) + (a^3 - a*b^2)*x)/(a^4 + 2*a^2*b^2 + b^4)","A",0
277,1,210,0,0.439943," ","integrate(cos(x)*sin(x)^3/(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","\frac{3 \, \sqrt{a^{2} + b^{2}} a^{3} b \log\left(\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right) + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right)^{3} - 6 \, {\left(a^{5} + a^{3} b^{2}\right)} \cos\left(x\right) + 2 \, {\left(4 \, a^{4} b + 5 \, a^{2} b^{3} + b^{5} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{6 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}}"," ",0,"1/6*(3*sqrt(a^2 + b^2)*a^3*b*log((2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)) + 2*(a^5 + 2*a^3*b^2 + a*b^4)*cos(x)^3 - 6*(a^5 + a^3*b^2)*cos(x) + 2*(4*a^4*b + 5*a^2*b^3 + b^5 - (a^4*b + 2*a^2*b^3 + b^5)*cos(x)^2)*sin(x))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)","A",0
278,1,94,0,0.476573," ","integrate(cos(x)^2*sin(x)/(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","-\frac{a b^{2} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right) + {\left(a^{3} + a b^{2}\right)} \cos\left(x\right)^{2} - {\left(a^{2} b + b^{3}\right)} \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} b - b^{3}\right)} x}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}"," ",0,"-1/2*(a*b^2*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2) + (a^3 + a*b^2)*cos(x)^2 - (a^2*b + b^3)*cos(x)*sin(x) + (a^2*b - b^3)*x)/(a^4 + 2*a^2*b^2 + b^4)","A",0
279,1,215,0,0.771226," ","integrate(cos(x)^2*sin(x)^2/(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","\frac{3 \, \sqrt{a^{2} + b^{2}} a^{2} b^{2} \log\left(-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right) - 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(x\right)^{3} + 6 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cos\left(x\right) + 2 \, {\left(a^{5} - a^{3} b^{2} - 2 \, a b^{4} - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{6 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}}"," ",0,"1/6*(3*sqrt(a^2 + b^2)*a^2*b^2*log(-(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)) - 2*(a^4*b + 2*a^2*b^3 + b^5)*cos(x)^3 + 6*(a^4*b + a^2*b^3)*cos(x) + 2*(a^5 - a^3*b^2 - 2*a*b^4 - (a^5 + 2*a^3*b^2 + a*b^4)*cos(x)^2)*sin(x))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)","B",0
280,1,174,0,0.726458," ","integrate(cos(x)^2*sin(x)^3/(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","-\frac{4 \, a^{3} b^{2} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right) - 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right)^{4} + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} \cos\left(x\right)^{2} + {\left(3 \, a^{4} b - 6 \, a^{2} b^{3} - b^{5}\right)} x + {\left(2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(x\right)^{3} - {\left(5 \, a^{4} b + 6 \, a^{2} b^{3} + b^{5}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{8 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}}"," ",0,"-1/8*(4*a^3*b^2*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2) - 2*(a^5 + 2*a^3*b^2 + a*b^4)*cos(x)^4 + 4*(a^5 + a^3*b^2)*cos(x)^2 + (3*a^4*b - 6*a^2*b^3 - b^5)*x + (2*(a^4*b + 2*a^2*b^3 + b^5)*cos(x)^3 - (5*a^4*b + 6*a^2*b^3 + b^5)*cos(x))*sin(x))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)","A",0
281,1,213,0,0.521468," ","integrate(cos(x)^3*sin(x)/(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","\frac{3 \, \sqrt{a^{2} + b^{2}} a b^{3} \log\left(\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right) - 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right)^{3} - 6 \, {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right) - 2 \, {\left(a^{4} b - a^{2} b^{3} - 2 \, b^{5} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{6 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}}"," ",0,"1/6*(3*sqrt(a^2 + b^2)*a*b^3*log((2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)) - 2*(a^5 + 2*a^3*b^2 + a*b^4)*cos(x)^3 - 6*(a^3*b^2 + a*b^4)*cos(x) - 2*(a^4*b - a^2*b^3 - 2*b^5 - (a^4*b + 2*a^2*b^3 + b^5)*cos(x)^2)*sin(x))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)","A",0
282,1,175,0,0.644074," ","integrate(cos(x)^3*sin(x)^2/(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","\frac{4 \, a^{2} b^{3} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right) - 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(x\right)^{4} + 4 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cos\left(x\right)^{2} + {\left(a^{5} + 6 \, a^{3} b^{2} - 3 \, a b^{4}\right)} x - {\left(2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right)^{3} - {\left(a^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{8 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}}"," ",0,"1/8*(4*a^2*b^3*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2) - 2*(a^4*b + 2*a^2*b^3 + b^5)*cos(x)^4 + 4*(a^4*b + a^2*b^3)*cos(x)^2 + (a^5 + 6*a^3*b^2 - 3*a*b^4)*x - (2*(a^5 + 2*a^3*b^2 + a*b^4)*cos(x)^3 - (a^5 - 2*a^3*b^2 - 3*a*b^4)*cos(x))*sin(x))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)","A",0
283,1,307,0,0.600872," ","integrate(cos(x)^3*sin(x)^3/(a*cos(x)+b*sin(x)),x, algorithm=""fricas"")","\frac{15 \, \sqrt{a^{2} + b^{2}} a^{3} b^{3} \log\left(\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right) + 6 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(x\right)^{5} - 10 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \cos\left(x\right)^{3} - 30 \, {\left(a^{5} b^{2} + a^{3} b^{4}\right)} \cos\left(x\right) - 2 \, {\left(3 \, a^{6} b - 11 \, a^{4} b^{3} - 16 \, a^{2} b^{5} - 2 \, b^{7} + 3 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \cos\left(x\right)^{4} - {\left(6 \, a^{6} b + 13 \, a^{4} b^{3} + 8 \, a^{2} b^{5} + b^{7}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{30 \, {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)}}"," ",0,"1/30*(15*sqrt(a^2 + b^2)*a^3*b^3*log((2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)) + 6*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(x)^5 - 10*(a^7 + 2*a^5*b^2 + a^3*b^4)*cos(x)^3 - 30*(a^5*b^2 + a^3*b^4)*cos(x) - 2*(3*a^6*b - 11*a^4*b^3 - 16*a^2*b^5 - 2*b^7 + 3*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*cos(x)^4 - (6*a^6*b + 13*a^4*b^3 + 8*a^2*b^5 + b^7)*cos(x)^2)*sin(x))/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)","A",0
284,1,138,0,0.510052," ","integrate(cos(x)*sin(x)/(a*cos(x)+b*sin(x))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} b x + a b^{2}\right)} \cos\left(x\right) - {\left({\left(a^{3} - a b^{2}\right)} \cos\left(x\right) + {\left(a^{2} b - b^{3}\right)} \sin\left(x\right)\right)} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right) + 2 \, {\left(2 \, a b^{2} x - a^{2} b\right)} \sin\left(x\right)}{2 \, {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(x\right)\right)}}"," ",0,"1/2*(2*(2*a^2*b*x + a*b^2)*cos(x) - ((a^3 - a*b^2)*cos(x) + (a^2*b - b^3)*sin(x))*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2) + 2*(2*a*b^2*x - a^2*b)*sin(x))/((a^5 + 2*a^3*b^2 + a*b^4)*cos(x) + (a^4*b + 2*a^2*b^3 + b^5)*sin(x))","A",0
285,1,252,0,0.513330," ","integrate(cos(x)*sin(x)^2/(a*cos(x)+b*sin(x))^2,x, algorithm=""fricas"")","-\frac{4 \, a^{4} b + 2 \, a^{2} b^{3} - 2 \, b^{5} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right) \sin\left(x\right) + \sqrt{a^{2} + b^{2}} {\left({\left(a^{4} - 2 \, a^{2} b^{2}\right)} \cos\left(x\right) + {\left(a^{3} b - 2 \, a b^{3}\right)} \sin\left(x\right)\right)} \log\left(\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right)}{2 \, {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(x\right) + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sin\left(x\right)\right)}}"," ",0,"-1/2*(4*a^4*b + 2*a^2*b^3 - 2*b^5 + 2*(a^4*b + 2*a^2*b^3 + b^5)*cos(x)^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*cos(x)*sin(x) + sqrt(a^2 + b^2)*((a^4 - 2*a^2*b^2)*cos(x) + (a^3*b - 2*a*b^3)*sin(x))*log((2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)))/((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(x) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sin(x))","B",0
286,1,236,0,0.740608," ","integrate(cos(x)*sin(x)^3/(a*cos(x)+b*sin(x))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right)^{3} - {\left(a^{5} + 3 \, a b^{4} - 4 \, {\left(3 \, a^{4} b - a^{2} b^{3}\right)} x\right)} \cos\left(x\right) - 2 \, {\left({\left(a^{5} - 3 \, a^{3} b^{2}\right)} \cos\left(x\right) + {\left(a^{4} b - 3 \, a^{2} b^{3}\right)} \sin\left(x\right)\right)} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right) - {\left(5 \, a^{4} b - b^{5} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(x\right)^{2} - 4 \, {\left(3 \, a^{3} b^{2} - a b^{4}\right)} x\right)} \sin\left(x\right)}{4 \, {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(x\right) + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sin\left(x\right)\right)}}"," ",0,"1/4*(2*(a^5 + 2*a^3*b^2 + a*b^4)*cos(x)^3 - (a^5 + 3*a*b^4 - 4*(3*a^4*b - a^2*b^3)*x)*cos(x) - 2*((a^5 - 3*a^3*b^2)*cos(x) + (a^4*b - 3*a^2*b^3)*sin(x))*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2) - (5*a^4*b - b^5 + 2*(a^4*b + 2*a^2*b^3 + b^5)*cos(x)^2 - 4*(3*a^3*b^2 - a*b^4)*x)*sin(x))/((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(x) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sin(x))","A",0
287,1,252,0,0.661726," ","integrate(cos(x)^2*sin(x)/(a*cos(x)+b*sin(x))^2,x, algorithm=""fricas"")","\frac{6 \, a^{3} b^{2} + 6 \, a b^{4} - 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right)^{2} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(x\right) \sin\left(x\right) - \sqrt{a^{2} + b^{2}} {\left({\left(2 \, a^{3} b - a b^{3}\right)} \cos\left(x\right) + {\left(2 \, a^{2} b^{2} - b^{4}\right)} \sin\left(x\right)\right)} \log\left(-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right)}{2 \, {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(x\right) + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sin\left(x\right)\right)}}"," ",0,"1/2*(6*a^3*b^2 + 6*a*b^4 - 2*(a^5 + 2*a^3*b^2 + a*b^4)*cos(x)^2 + 2*(a^4*b + 2*a^2*b^3 + b^5)*cos(x)*sin(x) - sqrt(a^2 + b^2)*((2*a^3*b - a*b^3)*cos(x) + (2*a^2*b^2 - b^4)*sin(x))*log(-(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)))/((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(x) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sin(x))","B",0
288,1,244,0,0.649570," ","integrate(cos(x)^2*sin(x)^2/(a*cos(x)+b*sin(x))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(x\right)^{3} + {\left(a^{2} b^{3} - b^{5} - {\left(a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} x\right)} \cos\left(x\right) - 2 \, {\left({\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(x\right) + {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(x\right)\right)} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right) - {\left(3 \, a^{3} b^{2} + a b^{4} - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right)^{2} + {\left(a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} x\right)} \sin\left(x\right)}{2 \, {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(x\right) + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sin\left(x\right)\right)}}"," ",0,"-1/2*((a^4*b + 2*a^2*b^3 + b^5)*cos(x)^3 + (a^2*b^3 - b^5 - (a^5 - 6*a^3*b^2 + a*b^4)*x)*cos(x) - 2*((a^4*b - a^2*b^3)*cos(x) + (a^3*b^2 - a*b^4)*sin(x))*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2) - (3*a^3*b^2 + a*b^4 - (a^5 + 2*a^3*b^2 + a*b^4)*cos(x)^2 + (a^4*b - 6*a^2*b^3 + b^5)*x)*sin(x))/((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(x) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sin(x))","A",0
289,1,360,0,0.604290," ","integrate(cos(x)^2*sin(x)^3/(a*cos(x)+b*sin(x))^2,x, algorithm=""fricas"")","\frac{22 \, a^{5} b^{2} + 14 \, a^{3} b^{4} - 8 \, a b^{6} + 2 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(x\right)^{4} - 2 \, {\left(3 \, a^{7} + 4 \, a^{5} b^{2} - a^{3} b^{4} - 2 \, a b^{6}\right)} \cos\left(x\right)^{2} - 3 \, \sqrt{a^{2} + b^{2}} {\left({\left(2 \, a^{5} b - 3 \, a^{3} b^{3}\right)} \cos\left(x\right) + {\left(2 \, a^{4} b^{2} - 3 \, a^{2} b^{4}\right)} \sin\left(x\right)\right)} \log\left(-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right) - 2 \, {\left({\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \cos\left(x\right)^{3} - 5 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{6 \, {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(x\right) + {\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} \sin\left(x\right)\right)}}"," ",0,"1/6*(22*a^5*b^2 + 14*a^3*b^4 - 8*a*b^6 + 2*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(x)^4 - 2*(3*a^7 + 4*a^5*b^2 - a^3*b^4 - 2*a*b^6)*cos(x)^2 - 3*sqrt(a^2 + b^2)*((2*a^5*b - 3*a^3*b^3)*cos(x) + (2*a^4*b^2 - 3*a^2*b^4)*sin(x))*log(-(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)) - 2*((a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*cos(x)^3 - 5*(a^6*b + 2*a^4*b^3 + a^2*b^5)*cos(x))*sin(x))/((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*cos(x) + (a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*sin(x))","B",0
290,1,252,0,0.649942," ","integrate(cos(x)^3*sin(x)/(a*cos(x)+b*sin(x))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right)^{3} - {\left(a^{5} + 4 \, a^{3} b^{2} + 7 \, a b^{4} - 4 \, {\left(a^{4} b - 3 \, a^{2} b^{3}\right)} x\right)} \cos\left(x\right) + 2 \, {\left({\left(3 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(x\right) + {\left(3 \, a^{2} b^{3} - b^{5}\right)} \sin\left(x\right)\right)} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right) - {\left(a^{4} b - 4 \, a^{2} b^{3} - b^{5} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(x\right)^{2} - 4 \, {\left(a^{3} b^{2} - 3 \, a b^{4}\right)} x\right)} \sin\left(x\right)}{4 \, {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(x\right) + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sin\left(x\right)\right)}}"," ",0,"-1/4*(2*(a^5 + 2*a^3*b^2 + a*b^4)*cos(x)^3 - (a^5 + 4*a^3*b^2 + 7*a*b^4 - 4*(a^4*b - 3*a^2*b^3)*x)*cos(x) + 2*((3*a^3*b^2 - a*b^4)*cos(x) + (3*a^2*b^3 - b^5)*sin(x))*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2) - (a^4*b - 4*a^2*b^3 - b^5 + 2*(a^4*b + 2*a^2*b^3 + b^5)*cos(x)^2 - 4*(a^3*b^2 - 3*a*b^4)*x)*sin(x))/((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(x) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sin(x))","A",0
291,1,369,0,0.560097," ","integrate(cos(x)^3*sin(x)^2/(a*cos(x)+b*sin(x))^2,x, algorithm=""fricas"")","\frac{2 \, a^{6} b - 22 \, a^{4} b^{3} - 20 \, a^{2} b^{5} + 4 \, b^{7} - 2 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \cos\left(x\right)^{4} + 2 \, {\left(4 \, a^{6} b + 7 \, a^{4} b^{3} + 2 \, a^{2} b^{5} - b^{7}\right)} \cos\left(x\right)^{2} - 3 \, \sqrt{a^{2} + b^{2}} {\left({\left(3 \, a^{4} b^{2} - 2 \, a^{2} b^{4}\right)} \cos\left(x\right) + {\left(3 \, a^{3} b^{3} - 2 \, a b^{5}\right)} \sin\left(x\right)\right)} \log\left(\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(x\right) - a \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}}\right) - 2 \, {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(x\right)^{3} - {\left(a^{7} - 2 \, a^{5} b^{2} - 7 \, a^{3} b^{4} - 4 \, a b^{6}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{6 \, {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(x\right) + {\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} \sin\left(x\right)\right)}}"," ",0,"1/6*(2*a^6*b - 22*a^4*b^3 - 20*a^2*b^5 + 4*b^7 - 2*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*cos(x)^4 + 2*(4*a^6*b + 7*a^4*b^3 + 2*a^2*b^5 - b^7)*cos(x)^2 - 3*sqrt(a^2 + b^2)*((3*a^4*b^2 - 2*a^2*b^4)*cos(x) + (3*a^3*b^3 - 2*a*b^5)*sin(x))*log((2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(x) - a*sin(x)))/(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2)) - 2*((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(x)^3 - (a^7 - 2*a^5*b^2 - 7*a^3*b^4 - 4*a*b^6)*cos(x))*sin(x))/((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*cos(x) + (a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*sin(x))","B",0
292,1,371,0,0.498983," ","integrate(cos(x)^3*sin(x)^3/(a*cos(x)+b*sin(x))^2,x, algorithm=""fricas"")","\frac{8 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(x\right)^{5} - 8 \, {\left(2 \, a^{7} + 3 \, a^{5} b^{2} - a b^{6}\right)} \cos\left(x\right)^{3} + {\left(5 \, a^{7} + 21 \, a^{5} b^{2} + 27 \, a^{3} b^{4} - 21 \, a b^{6} - 24 \, {\left(a^{6} b - 6 \, a^{4} b^{3} + a^{2} b^{5}\right)} x\right)} \cos\left(x\right) - 48 \, {\left({\left(a^{5} b^{2} - a^{3} b^{4}\right)} \cos\left(x\right) + {\left(a^{4} b^{3} - a^{2} b^{5}\right)} \sin\left(x\right)\right)} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + b^{2}\right) + {\left(5 \, a^{6} b - 51 \, a^{4} b^{3} - 21 \, a^{2} b^{5} + 3 \, b^{7} - 8 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \cos\left(x\right)^{4} + 24 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(x\right)^{2} - 24 \, {\left(a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} x\right)} \sin\left(x\right)}{32 \, {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(x\right) + {\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} \sin\left(x\right)\right)}}"," ",0,"1/32*(8*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(x)^5 - 8*(2*a^7 + 3*a^5*b^2 - a*b^6)*cos(x)^3 + (5*a^7 + 21*a^5*b^2 + 27*a^3*b^4 - 21*a*b^6 - 24*(a^6*b - 6*a^4*b^3 + a^2*b^5)*x)*cos(x) - 48*((a^5*b^2 - a^3*b^4)*cos(x) + (a^4*b^3 - a^2*b^5)*sin(x))*log(2*a*b*cos(x)*sin(x) + (a^2 - b^2)*cos(x)^2 + b^2) + (5*a^6*b - 51*a^4*b^3 - 21*a^2*b^5 + 3*b^7 - 8*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*cos(x)^4 + 24*(a^6*b + 2*a^4*b^3 + a^2*b^5)*cos(x)^2 - 24*(a^5*b^2 - 6*a^3*b^4 + a*b^6)*x)*sin(x))/((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*cos(x) + (a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*sin(x))","A",0
293,1,140,0,0.698101," ","integrate(tan(x)/(b*cos(x)+a*sin(x)),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} + b^{2}} b \log\left(\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - a^{2} - 2 \, b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(a \cos\left(x\right) - b \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2}}\right) + {\left(a^{2} + b^{2}\right)} \log\left(\sin\left(x\right) + 1\right) - {\left(a^{2} + b^{2}\right)} \log\left(-\sin\left(x\right) + 1\right)}{2 \, {\left(a^{3} + a b^{2}\right)}}"," ",0,"1/2*(sqrt(a^2 + b^2)*b*log((2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 - a^2 - 2*b^2 - 2*sqrt(a^2 + b^2)*(a*cos(x) - b*sin(x)))/(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 + a^2)) + (a^2 + b^2)*log(sin(x) + 1) - (a^2 + b^2)*log(-sin(x) + 1))/(a^3 + a*b^2)","B",0
294,1,142,0,0.467993," ","integrate(cot(x)/(b*cos(x)+a*sin(x)),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} + b^{2}} a \log\left(\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - a^{2} - 2 \, b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(a \cos\left(x\right) - b \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2}}\right) - {\left(a^{2} + b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + {\left(a^{2} + b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{2 \, {\left(a^{2} b + b^{3}\right)}}"," ",0,"1/2*(sqrt(a^2 + b^2)*a*log((2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 - a^2 - 2*b^2 - 2*sqrt(a^2 + b^2)*(a*cos(x) - b*sin(x)))/(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 + a^2)) - (a^2 + b^2)*log(1/2*cos(x) + 1/2) + (a^2 + b^2)*log(-1/2*cos(x) + 1/2))/(a^2*b + b^3)","B",0
