1,1,25,0,0.312164," ","integrate(sin(x)^3*(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","\frac{1}{4} \, a \sin\left(x\right)^{4} + \frac{1}{32} \, b {\left(12 \, x + \sin\left(4 \, x\right) - 8 \, \sin\left(2 \, x\right)\right)}"," ",0,"1/4*a*sin(x)^4 + 1/32*b*(12*x + sin(4*x) - 8*sin(2*x))","A",0
2,1,20,0,0.321916," ","integrate(sin(x)^2*(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","\frac{1}{3} \, a \sin\left(x\right)^{3} + \frac{1}{3} \, {\left(\cos\left(x\right)^{3} - 3 \, \cos\left(x\right)\right)} b"," ",0,"1/3*a*sin(x)^3 + 1/3*(cos(x)^3 - 3*cos(x))*b","A",0
3,1,21,0,0.319872," ","integrate(sin(x)*(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","-\frac{1}{2} \, a \cos\left(x\right)^{2} + \frac{1}{4} \, b {\left(2 \, x - \sin\left(2 \, x\right)\right)}"," ",0,"-1/2*a*cos(x)^2 + 1/4*b*(2*x - sin(2*x))","A",0
4,1,10,0,0.318716," ","integrate(a*cos(x)+b*sin(x),x, algorithm=""maxima"")","-b \cos\left(x\right) + a \sin\left(x\right)"," ",0,"-b*cos(x) + a*sin(x)","A",0
5,1,9,0,0.311815," ","integrate(csc(x)*(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","b x + a \log\left(\sin\left(x\right)\right)"," ",0,"b*x + a*log(sin(x))","A",0
6,1,24,0,0.321635," ","integrate(csc(x)^2*(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","-\frac{1}{2} \, b {\left(\log\left(\cos\left(x\right) + 1\right) - \log\left(\cos\left(x\right) - 1\right)\right)} - \frac{a}{\sin\left(x\right)}"," ",0,"-1/2*b*(log(cos(x) + 1) - log(cos(x) - 1)) - a/sin(x)","A",0
7,1,15,0,0.322610," ","integrate(csc(x)^3*(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","-\frac{b}{\tan\left(x\right)} - \frac{a}{2 \, \sin\left(x\right)^{2}}"," ",0,"-b/tan(x) - 1/2*a/sin(x)^2","A",0
8,1,209,0,0.427765," ","integrate(sin(x)^3/(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","-\frac{a^{3} \log\left(-a - \frac{2 \, b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{a^{3} \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(3 \, a^{2} b + b^{3}\right)} \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{\frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{2 \, a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{b \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}}{a^{2} + b^{2} + \frac{2 \, {\left(a^{2} + b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{{\left(a^{2} + b^{2}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}}"," ",0,"-a^3*log(-a - 2*b*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2)/(a^4 + 2*a^2*b^2 + b^4) + a^3*log(sin(x)^2/(cos(x) + 1)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (3*a^2*b + b^3)*arctan(sin(x)/(cos(x) + 1))/(a^4 + 2*a^2*b^2 + b^4) - (b*sin(x)/(cos(x) + 1) + 2*a*sin(x)^2/(cos(x) + 1)^2 - b*sin(x)^3/(cos(x) + 1)^3)/(a^2 + b^2 + 2*(a^2 + b^2)*sin(x)^2/(cos(x) + 1)^2 + (a^2 + b^2)*sin(x)^4/(cos(x) + 1)^4)","B",0
9,1,106,0,0.428921," ","integrate(sin(x)^2/(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","-\frac{a^{2} \log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(b + \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1}\right)}}{a^{2} + b^{2} + \frac{{\left(a^{2} + b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}"," ",0,"-a^2*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) - 2*(b + a*sin(x)/(cos(x) + 1))/(a^2 + b^2 + (a^2 + b^2)*sin(x)^2/(cos(x) + 1)^2)","A",0
10,1,88,0,0.425256," ","integrate(sin(x)/(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","\frac{2 \, b \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{2} + b^{2}} - \frac{a \log\left(-a - \frac{2 \, b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{a^{2} + b^{2}} + \frac{a \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{a^{2} + b^{2}}"," ",0,"2*b*arctan(sin(x)/(cos(x) + 1))/(a^2 + b^2) - a*log(-a - 2*b*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2)/(a^2 + b^2) + a*log(sin(x)^2/(cos(x) + 1)^2 + 1)/(a^2 + b^2)","B",0
11,1,61,0,0.426897," ","integrate(1/(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","-\frac{\log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}}}"," ",0,"-log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/sqrt(a^2 + b^2)","A",0
12,1,48,0,0.323943," ","integrate(csc(x)/(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","-\frac{\log\left(-a - \frac{2 \, b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{a} + \frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a}"," ",0,"-log(-a - 2*b*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2)/a + log(sin(x)/(cos(x) + 1))/a","B",0
13,1,107,0,0.430247," ","integrate(csc(x)^2/(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","-\frac{b \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{2}} - \frac{\sqrt{a^{2} + b^{2}} \log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{a^{2}} - \frac{\cos\left(x\right) + 1}{2 \, a \sin\left(x\right)} - \frac{\sin\left(x\right)}{2 \, a {\left(\cos\left(x\right) + 1\right)}}"," ",0,"-b*log(sin(x)/(cos(x) + 1))/a^2 - sqrt(a^2 + b^2)*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/a^2 - 1/2*(cos(x) + 1)/(a*sin(x)) - 1/2*sin(x)/(a*(cos(x) + 1))","B",0
14,1,119,0,0.323698," ","integrate(csc(x)^3/(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","-\frac{\frac{4 \, b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}{8 \, a^{2}} - \frac{{\left(a^{2} + b^{2}\right)} \log\left(-a - \frac{2 \, b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{a^{3}} + \frac{{\left(a^{2} + b^{2}\right)} \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{3}} - \frac{{\left(a - \frac{4 \, b \sin\left(x\right)}{\cos\left(x\right) + 1}\right)} {\left(\cos\left(x\right) + 1\right)}^{2}}{8 \, a^{2} \sin\left(x\right)^{2}}"," ",0,"-1/8*(4*b*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2)/a^2 - (a^2 + b^2)*log(-a - 2*b*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2)/a^3 + (a^2 + b^2)*log(sin(x)/(cos(x) + 1))/a^3 - 1/8*(a - 4*b*sin(x)/(cos(x) + 1))*(cos(x) + 1)^2/(a^2*sin(x)^2)","B",0
15,1,253,0,0.423934," ","integrate(sin(x)^3/(a*cos(x)+b*sin(x))^2,x, algorithm=""maxima"")","-\frac{3 \, a^{2} b \log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} + \frac{2 \, {\left(2 \, a^{3} - a b^{2} - \frac{3 \, a b^{2} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{3 \, a^{2} b \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{{\left(a^{2} b - 2 \, b^{3}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1}\right)}}{a^{5} + 2 \, a^{3} b^{2} + a b^{4} + \frac{2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}}"," ",0,"-3*a^2*b*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) + 2*(2*a^3 - a*b^2 - 3*a*b^2*sin(x)^2/(cos(x) + 1)^2 + 3*a^2*b*sin(x)^3/(cos(x) + 1)^3 + (a^2*b - 2*b^3)*sin(x)/(cos(x) + 1))/(a^5 + 2*a^3*b^2 + a*b^4 + 2*(a^4*b + 2*a^2*b^3 + b^5)*sin(x)/(cos(x) + 1) + 2*(a^4*b + 2*a^2*b^3 + b^5)*sin(x)^3/(cos(x) + 1)^3 - (a^5 + 2*a^3*b^2 + a*b^4)*sin(x)^4/(cos(x) + 1)^4)","B",0
16,1,117,0,0.421322," ","integrate(sin(x)^2/(a*cos(x)+b*sin(x))^2,x, algorithm=""maxima"")","-\frac{2 \, a b \log\left(b \tan\left(x\right) + a\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{a b \log\left(\tan\left(x\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{a^{2}}{a^{3} b + a b^{3} + {\left(a^{2} b^{2} + b^{4}\right)} \tan\left(x\right)} - \frac{{\left(a^{2} - b^{2}\right)} x}{a^{4} + 2 \, a^{2} b^{2} + b^{4}}"," ",0,"-2*a*b*log(b*tan(x) + a)/(a^4 + 2*a^2*b^2 + b^4) + a*b*log(tan(x)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - a^2/(a^3*b + a*b^3 + (a^2*b^2 + b^4)*tan(x)) - (a^2 - b^2)*x/(a^4 + 2*a^2*b^2 + b^4)","A",0
17,1,128,0,0.420157," ","integrate(sin(x)/(a*cos(x)+b*sin(x))^2,x, algorithm=""maxima"")","-\frac{b \log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(a + \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1}\right)}}{a^{3} + a b^{2} + \frac{2 \, {\left(a^{2} b + b^{3}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{{\left(a^{3} + a b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}"," ",0,"-b*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) + 2*(a + b*sin(x)/(cos(x) + 1))/(a^3 + a*b^2 + 2*(a^2*b + b^3)*sin(x)/(cos(x) + 1) - (a^3 + a*b^2)*sin(x)^2/(cos(x) + 1)^2)","B",0
18,1,14,0,0.313247," ","integrate(1/(a*cos(x)+b*sin(x))^2,x, algorithm=""maxima"")","-\frac{1}{b^{2} \tan\left(x\right) + a b}"," ",0,"-1/(b^2*tan(x) + a*b)","A",0
19,1,128,0,0.435951," ","integrate(csc(x)/(a*cos(x)+b*sin(x))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(a + \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1}\right)}}{a^{3} + \frac{2 \, a^{2} b \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{a^{3} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}} + \frac{b \log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} a^{2}} + \frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{2}}"," ",0,"2*(a + b*sin(x)/(cos(x) + 1))/(a^3 + 2*a^2*b*sin(x)/(cos(x) + 1) - a^3*sin(x)^2/(cos(x) + 1)^2) + b*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*a^2) + log(sin(x)/(cos(x) + 1))/a^2","B",0
20,1,62,0,0.341810," ","integrate(csc(x)^2/(a*cos(x)+b*sin(x))^2,x, algorithm=""maxima"")","-\frac{a b + {\left(a^{2} + 2 \, b^{2}\right)} \tan\left(x\right)}{a^{2} b^{2} \tan\left(x\right)^{2} + a^{3} b \tan\left(x\right)} + \frac{2 \, b \log\left(b \tan\left(x\right) + a\right)}{a^{3}} - \frac{2 \, b \log\left(\tan\left(x\right)\right)}{a^{3}}"," ",0,"-(a*b + (a^2 + 2*b^2)*tan(x))/(a^2*b^2*tan(x)^2 + a^3*b*tan(x)) + 2*b*log(b*tan(x) + a)/a^3 - 2*b*log(tan(x))/a^3","A",0
21,1,242,0,0.434846," ","integrate(csc(x)^3/(a*cos(x)+b*sin(x))^2,x, algorithm=""maxima"")","-\frac{a^{3} - \frac{6 \, a^{2} b \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{{\left(17 \, a^{3} + 32 \, a b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{8 \, {\left(a^{2} b + 2 \, b^{3}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}}{8 \, {\left(\frac{a^{5} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{2 \, a^{4} b \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{a^{5} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}\right)}} + \frac{\frac{8 \, b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}{8 \, a^{3}} + \frac{3 \, {\left(a^{2} + 2 \, b^{2}\right)} \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{2 \, a^{4}} + \frac{3 \, {\left(a^{2} b + b^{3}\right)} \log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} a^{4}}"," ",0,"-1/8*(a^3 - 6*a^2*b*sin(x)/(cos(x) + 1) - (17*a^3 + 32*a*b^2)*sin(x)^2/(cos(x) + 1)^2 - 8*(a^2*b + 2*b^3)*sin(x)^3/(cos(x) + 1)^3)/(a^5*sin(x)^2/(cos(x) + 1)^2 + 2*a^4*b*sin(x)^3/(cos(x) + 1)^3 - a^5*sin(x)^4/(cos(x) + 1)^4) + 1/8*(8*b*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2)/a^3 + 3/2*(a^2 + 2*b^2)*log(sin(x)/(cos(x) + 1))/a^4 + 3*(a^2*b + b^3)*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*a^4)","B",0
22,1,359,0,0.445370," ","integrate(sin(x)^3/(a*cos(x)+b*sin(x))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, a^{2} b - b^{3}\right)} \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(a^{3} - 3 \, a b^{2}\right)} \log\left(-a - \frac{2 \, b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(a^{3} - 3 \, a b^{2}\right)} \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(\frac{2 \, a^{2} b \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{2 \, a^{2} b \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{{\left(a^{3} + 5 \, a b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}}{a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4} + \frac{4 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{2 \, {\left(a^{6} - 3 \, a^{2} b^{4} - 2 \, b^{6}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{4 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{{\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}}"," ",0,"-2*(3*a^2*b - b^3)*arctan(sin(x)/(cos(x) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (a^3 - 3*a*b^2)*log(-a - 2*b*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (a^3 - 3*a*b^2)*log(sin(x)^2/(cos(x) + 1)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(2*a^2*b*sin(x)/(cos(x) + 1) - 2*a^2*b*sin(x)^3/(cos(x) + 1)^3 + (a^3 + 5*a*b^2)*sin(x)^2/(cos(x) + 1)^2)/(a^6 + 2*a^4*b^2 + a^2*b^4 + 4*(a^5*b + 2*a^3*b^3 + a*b^5)*sin(x)/(cos(x) + 1) - 2*(a^6 - 3*a^2*b^4 - 2*b^6)*sin(x)^2/(cos(x) + 1)^2 - 4*(a^5*b + 2*a^3*b^3 + a*b^5)*sin(x)^3/(cos(x) + 1)^3 + (a^6 + 2*a^4*b^2 + a^2*b^4)*sin(x)^4/(cos(x) + 1)^4)","B",0
23,1,299,0,0.434594," ","integrate(sin(x)^2/(a*cos(x)+b*sin(x))^3,x, algorithm=""maxima"")","\frac{{\left(a^{2} - 2 \, b^{2}\right)} \log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} + \frac{3 \, a^{2} b + \frac{{\left(a^{3} + 10 \, a b^{2}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{3 \, {\left(a^{2} b - 2 \, b^{3}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{{\left(a^{3} - 2 \, a b^{2}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}}{a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4} + \frac{4 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{2 \, {\left(a^{6} - 3 \, a^{2} b^{4} - 2 \, b^{6}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{4 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{{\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}}"," ",0,"1/2*(a^2 - 2*b^2)*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) + (3*a^2*b + (a^3 + 10*a*b^2)*sin(x)/(cos(x) + 1) - 3*(a^2*b - 2*b^3)*sin(x)^2/(cos(x) + 1)^2 + (a^3 - 2*a*b^2)*sin(x)^3/(cos(x) + 1)^3)/(a^6 + 2*a^4*b^2 + a^2*b^4 + 4*(a^5*b + 2*a^3*b^3 + a*b^5)*sin(x)/(cos(x) + 1) - 2*(a^6 - 3*a^2*b^4 - 2*b^6)*sin(x)^2/(cos(x) + 1)^2 - 4*(a^5*b + 2*a^3*b^3 + a*b^5)*sin(x)^3/(cos(x) + 1)^3 + (a^6 + 2*a^4*b^2 + a^2*b^4)*sin(x)^4/(cos(x) + 1)^4)","B",0
24,1,84,0,0.337286," ","integrate(sin(x)/(a*cos(x)+b*sin(x))^3,x, algorithm=""maxima"")","\frac{2 \, \sin\left(x\right)^{2}}{{\left(a^{3} + \frac{4 \, a^{2} b \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{4 \, a^{2} b \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{a^{3} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{2 \, {\left(a^{3} - 2 \, a b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)} {\left(\cos\left(x\right) + 1\right)}^{2}}"," ",0,"2*sin(x)^2/((a^3 + 4*a^2*b*sin(x)/(cos(x) + 1) - 4*a^2*b*sin(x)^3/(cos(x) + 1)^3 + a^3*sin(x)^4/(cos(x) + 1)^4 - 2*(a^3 - 2*a*b^2)*sin(x)^2/(cos(x) + 1)^2)*(cos(x) + 1)^2)","B",0
25,1,250,0,0.443052," ","integrate(1/(a*cos(x)+b*sin(x))^3,x, algorithm=""maxima"")","-\frac{a^{2} b - \frac{{\left(a^{3} - 2 \, a b^{2}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{{\left(a^{2} b - 2 \, b^{3}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{{\left(a^{3} + 2 \, a b^{2}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}}{a^{6} + a^{4} b^{2} + \frac{4 \, {\left(a^{5} b + a^{3} b^{3}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{2 \, {\left(a^{6} - a^{4} b^{2} - 2 \, a^{2} b^{4}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{4 \, {\left(a^{5} b + a^{3} b^{3}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{{\left(a^{6} + a^{4} b^{2}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}} - \frac{\log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{2 \, {\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}}"," ",0,"-(a^2*b - (a^3 - 2*a*b^2)*sin(x)/(cos(x) + 1) - (a^2*b - 2*b^3)*sin(x)^2/(cos(x) + 1)^2 - (a^3 + 2*a*b^2)*sin(x)^3/(cos(x) + 1)^3)/(a^6 + a^4*b^2 + 4*(a^5*b + a^3*b^3)*sin(x)/(cos(x) + 1) - 2*(a^6 - a^4*b^2 - 2*a^2*b^4)*sin(x)^2/(cos(x) + 1)^2 - 4*(a^5*b + a^3*b^3)*sin(x)^3/(cos(x) + 1)^3 + (a^6 + a^4*b^2)*sin(x)^4/(cos(x) + 1)^4) - 1/2*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2)","B",0
26,1,172,0,0.337005," ","integrate(csc(x)/(a*cos(x)+b*sin(x))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{2 \, a b \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{2 \, a b \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{{\left(a^{2} - 3 \, b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}}{a^{5} + \frac{4 \, a^{4} b \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{4 \, a^{4} b \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{a^{5} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{2 \, {\left(a^{5} - 2 \, a^{3} b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}} - \frac{\log\left(-a - \frac{2 \, b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{a^{3}} + \frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{3}}"," ",0,"-2*(2*a*b*sin(x)/(cos(x) + 1) - 2*a*b*sin(x)^3/(cos(x) + 1)^3 - (a^2 - 3*b^2)*sin(x)^2/(cos(x) + 1)^2)/(a^5 + 4*a^4*b*sin(x)/(cos(x) + 1) - 4*a^4*b*sin(x)^3/(cos(x) + 1)^3 + a^5*sin(x)^4/(cos(x) + 1)^4 - 2*(a^5 - 2*a^3*b^2)*sin(x)^2/(cos(x) + 1)^2) - log(-a - 2*b*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2)/a^3 + log(sin(x)/(cos(x) + 1))/a^3","B",0
27,1,276,0,0.435059," ","integrate(csc(x)^2/(a*cos(x)+b*sin(x))^3,x, algorithm=""maxima"")","-\frac{a^{3} + \frac{14 \, a^{2} b \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{4 \, {\left(a^{3} - 8 \, a b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{2 \, {\left(7 \, a^{2} b - 10 \, b^{3}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{{\left(a^{3} + 12 \, a b^{2}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}}{2 \, {\left(\frac{a^{6} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{4 \, a^{5} b \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{4 \, a^{5} b \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{a^{6} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{2 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}} - \frac{3 \, b \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{4}} - \frac{3 \, {\left(a^{2} + 2 \, b^{2}\right)} \log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{2 \, \sqrt{a^{2} + b^{2}} a^{4}} - \frac{\sin\left(x\right)}{2 \, a^{3} {\left(\cos\left(x\right) + 1\right)}}"," ",0,"-1/2*(a^3 + 14*a^2*b*sin(x)/(cos(x) + 1) - 4*(a^3 - 8*a*b^2)*sin(x)^2/(cos(x) + 1)^2 - 2*(7*a^2*b - 10*b^3)*sin(x)^3/(cos(x) + 1)^3 - (a^3 + 12*a*b^2)*sin(x)^4/(cos(x) + 1)^4)/(a^6*sin(x)/(cos(x) + 1) + 4*a^5*b*sin(x)^2/(cos(x) + 1)^2 - 4*a^5*b*sin(x)^4/(cos(x) + 1)^4 + a^6*sin(x)^5/(cos(x) + 1)^5 - 2*(a^6 - 2*a^4*b^2)*sin(x)^3/(cos(x) + 1)^3) - 3*b*log(sin(x)/(cos(x) + 1))/a^4 - 3/2*(a^2 + 2*b^2)*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*a^4) - 1/2*sin(x)/(a^3*(cos(x) + 1))","A",0
28,1,308,0,0.360747," ","integrate(csc(x)^3/(a*cos(x)+b*sin(x))^3,x, algorithm=""maxima"")","-\frac{a^{4} - \frac{8 \, a^{3} b \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{2 \, {\left(a^{4} + 22 \, a^{2} b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{4 \, {\left(21 \, a^{3} b + 4 \, a b^{3}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{{\left(15 \, a^{4} - 144 \, a^{2} b^{2} - 112 \, b^{4}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{4 \, {\left(19 \, a^{3} b + 16 \, a b^{3}\right)} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}}}{8 \, {\left(\frac{a^{7} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{4 \, a^{6} b \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{4 \, a^{6} b \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{a^{7} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - \frac{2 \, {\left(a^{7} - 2 \, a^{5} b^{2}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}\right)}} - \frac{\frac{12 \, b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}{8 \, a^{4}} - \frac{2 \, {\left(a^{2} + 3 \, b^{2}\right)} \log\left(-a - \frac{2 \, b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{a^{5}} + \frac{2 \, {\left(a^{2} + 3 \, b^{2}\right)} \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{5}}"," ",0,"-1/8*(a^4 - 8*a^3*b*sin(x)/(cos(x) + 1) - 2*(a^4 + 22*a^2*b^2)*sin(x)^2/(cos(x) + 1)^2 + 4*(21*a^3*b + 4*a*b^3)*sin(x)^3/(cos(x) + 1)^3 - (15*a^4 - 144*a^2*b^2 - 112*b^4)*sin(x)^4/(cos(x) + 1)^4 - 4*(19*a^3*b + 16*a*b^3)*sin(x)^5/(cos(x) + 1)^5)/(a^7*sin(x)^2/(cos(x) + 1)^2 + 4*a^6*b*sin(x)^3/(cos(x) + 1)^3 - 4*a^6*b*sin(x)^5/(cos(x) + 1)^5 + a^7*sin(x)^6/(cos(x) + 1)^6 - 2*(a^7 - 2*a^5*b^2)*sin(x)^4/(cos(x) + 1)^4) - 1/8*(12*b*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2)/a^4 - 2*(a^2 + 3*b^2)*log(-a - 2*b*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2)/a^5 + 2*(a^2 + 3*b^2)*log(sin(x)/(cos(x) + 1))/a^5","B",0
29,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^n/(sin(d*x+c)^n),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right)\right)}^{n} \sin\left(d x + c\right)^{-n}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + I*a*sin(d*x + c))^n*sin(d*x + c)^(-n), x)","F",0
30,1,62,0,0.326328," ","integrate(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{32 \, b \cos\left(d x + c\right)^{6} + {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a}{192 \, d}"," ",0,"-1/192*(32*b*cos(d*x + c)^6 + (4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a)/d","A",0
31,1,49,0,0.320098," ","integrate(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, b \cos\left(d x + c\right)^{5} - {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a}{15 \, d}"," ",0,"-1/15*(3*b*cos(d*x + c)^5 - (3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a)/d","A",0
32,1,48,0,0.330343," ","integrate(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{8 \, b \cos\left(d x + c\right)^{4} - {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a}{32 \, d}"," ",0,"-1/32*(8*b*cos(d*x + c)^4 - (12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a)/d","A",0
33,1,35,0,0.319437," ","integrate(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{b \cos\left(d x + c\right)^{3} + {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a}{3 \, d}"," ",0,"-1/3*(b*cos(d*x + c)^3 + (sin(d*x + c)^3 - 3*sin(d*x + c))*a)/d","A",0
34,1,37,0,0.317385," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, b \cos\left(d x + c\right)^{2} - {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a}{4 \, d}"," ",0,"-1/4*(2*b*cos(d*x + c)^2 - (2*d*x + 2*c + sin(2*d*x + 2*c))*a)/d","A",0
35,1,24,0,0.317938," ","integrate(a*cos(d*x+c)+b*sin(d*x+c),x, algorithm=""maxima"")","-\frac{b \cos\left(d x + c\right)}{d} + \frac{a \sin\left(d x + c\right)}{d}"," ",0,"-b*cos(d*x + c)/d + a*sin(d*x + c)/d","A",0
36,1,30,0,0.333883," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} a - b \log\left(-\sin\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*a - b*log(-sin(d*x + c)^2 + 1))/d","A",0
37,1,40,0,0.324569," ","integrate(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{2 \, b}{\cos\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*b/cos(d*x + c))/d","A",0
38,1,30,0,0.322294," ","integrate(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, a \tan\left(d x + c\right) - \frac{b}{\sin\left(d x + c\right)^{2} - 1}}{2 \, d}"," ",0,"1/2*(2*a*tan(d*x + c) - b/(sin(d*x + c)^2 - 1))/d","A",0
39,1,61,0,0.323568," ","integrate(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - \frac{4 \, b}{\cos\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"-1/12*(3*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 4*b/cos(d*x + c)^3)/d","A",0
40,1,41,0,0.325976," ","integrate(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a + \frac{3 \, b}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*a + 3*b/(sin(d*x + c)^2 - 1)^2)/d","A",0
41,1,86,0,0.327085," ","integrate(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{5 \, a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - \frac{16 \, b}{\cos\left(d x + c\right)^{5}}}{80 \, d}"," ",0,"-1/80*(5*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 16*b/cos(d*x + c)^5)/d","A",0
42,1,53,0,0.328551," ","integrate(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} a - \frac{5 \, b}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{3}}}{30 \, d}"," ",0,"1/30*(2*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a - 5*b/(sin(d*x + c)^2 - 1)^3)/d","A",0
43,1,98,0,0.327468," ","integrate(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{30 \, a b \cos\left(d x + c\right)^{7} + 3 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} a^{2} - {\left(15 \, \sin\left(d x + c\right)^{7} - 42 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3}\right)} b^{2}}{105 \, d}"," ",0,"-1/105*(30*a*b*cos(d*x + c)^7 + 3*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*a^2 - (15*sin(d*x + c)^7 - 42*sin(d*x + c)^5 + 35*sin(d*x + c)^3)*b^2)/d","A",0
44,1,102,0,0.339443," ","integrate(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{64 \, a b \cos\left(d x + c\right)^{6} + {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} - {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} b^{2}}{192 \, d}"," ",0,"-1/192*(64*a*b*cos(d*x + c)^6 + (4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^2 - (4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*b^2)/d","A",0
45,1,77,0,0.322625," ","integrate(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{6 \, a b \cos\left(d x + c\right)^{5} - {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{2} + {\left(3 \, \sin\left(d x + c\right)^{5} - 5 \, \sin\left(d x + c\right)^{3}\right)} b^{2}}{15 \, d}"," ",0,"-1/15*(6*a*b*cos(d*x + c)^5 - (3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^2 + (3*sin(d*x + c)^5 - 5*sin(d*x + c)^3)*b^2)/d","A",0
46,1,75,0,0.318488," ","integrate(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{16 \, a b \cos\left(d x + c\right)^{4} - {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} - {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} b^{2}}{32 \, d}"," ",0,"-1/32*(16*a*b*cos(d*x + c)^4 - (12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^2 - (4*d*x + 4*c - sin(4*d*x + 4*c))*b^2)/d","A",0
47,1,52,0,0.329777," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, a b \cos\left(d x + c\right)^{3} - b^{2} \sin\left(d x + c\right)^{3} + {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{2}}{3 \, d}"," ",0,"-1/3*(2*a*b*cos(d*x + c)^3 - b^2*sin(d*x + c)^3 + (sin(d*x + c)^3 - 3*sin(d*x + c))*a^2)/d","A",0
48,1,68,0,0.319045," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a b \cos\left(d x + c\right)^{2}}{d} + \frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2}}{4 \, d} + \frac{{\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} b^{2}}{4 \, d}"," ",0,"-a*b*cos(d*x + c)^2/d + 1/4*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^2/d + 1/4*(2*d*x + 2*c - sin(2*d*x + 2*c))*b^2/d","A",0
49,1,60,0,0.331640," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)} - 4 \, a b \cos\left(d x + c\right) + 2 \, a^{2} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)) - 4*a*b*cos(d*x + c) + 2*a^2*sin(d*x + c))/d","A",0
50,1,49,0,0.430838," ","integrate(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} a^{2} - {\left(d x + c - \tan\left(d x + c\right)\right)} b^{2} - a b \log\left(-\sin\left(d x + c\right)^{2} + 1\right)}{d}"," ",0,"((d*x + c)*a^2 - (d*x + c - tan(d*x + c))*b^2 - a*b*log(-sin(d*x + c)^2 + 1))/d","A",0
51,1,89,0,0.327668," ","integrate(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 2 \, a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - \frac{8 \, a b}{\cos\left(d x + c\right)}}{4 \, d}"," ",0,"-1/4*(b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 2*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 8*a*b/cos(d*x + c))/d","A",0
52,1,45,0,0.328480," ","integrate(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{b^{2} \tan\left(d x + c\right)^{3} + 3 \, a^{2} \tan\left(d x + c\right) - \frac{3 \, a b}{\sin\left(d x + c\right)^{2} - 1}}{3 \, d}"," ",0,"1/3*(b^2*tan(d*x + c)^3 + 3*a^2*tan(d*x + c) - 3*a*b/(sin(d*x + c)^2 - 1))/d","A",0
53,1,129,0,0.333940," ","integrate(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, b^{2} {\left(\frac{2 \, {\left(\sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{32 \, a b}{\cos\left(d x + c\right)^{3}}}{48 \, d}"," ",0,"1/48*(3*b^2*(2*(sin(d*x + c)^3 + sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 32*a*b/cos(d*x + c)^3)/d","A",0
54,1,70,0,0.340088," ","integrate(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{10 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{2} + 2 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 5 \, \tan\left(d x + c\right)^{3}\right)} b^{2} + \frac{15 \, a b}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{30 \, d}"," ",0,"1/30*(10*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^2 + 2*(3*tan(d*x + c)^5 + 5*tan(d*x + c)^3)*b^2 + 15*a*b/(sin(d*x + c)^2 - 1)^2)/d","A",0
55,1,180,0,0.339890," ","integrate(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{5 \, b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 8 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{192 \, a b}{\cos\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"1/480*(5*b^2*(2*(3*sin(d*x + c)^5 - 8*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 30*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + 192*a*b/cos(d*x + c)^5)/d","A",0
56,1,91,0,0.341588," ","integrate(sec(d*x+c)^8*(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{7 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} a^{2} + {\left(15 \, \tan\left(d x + c\right)^{7} + 42 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3}\right)} b^{2} - \frac{35 \, a b}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{3}}}{105 \, d}"," ",0,"1/105*(7*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^2 + (15*tan(d*x + c)^7 + 42*tan(d*x + c)^5 + 35*tan(d*x + c)^3)*b^2 - 35*a*b/(sin(d*x + c)^2 - 1)^3)/d","A",0
57,1,163,0,0.340169," ","integrate(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{1152 \, a^{2} b \cos\left(d x + c\right)^{8} + {\left(128 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 840 \, d x - 840 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 168 \, \sin\left(4 \, d x + 4 \, c\right) - 768 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 3 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a b^{2} - 128 \, {\left(3 \, \sin\left(d x + c\right)^{8} - 8 \, \sin\left(d x + c\right)^{6} + 6 \, \sin\left(d x + c\right)^{4}\right)} b^{3}}{3072 \, d}"," ",0,"-1/3072*(1152*a^2*b*cos(d*x + c)^8 + (128*sin(2*d*x + 2*c)^3 - 840*d*x - 840*c - 3*sin(8*d*x + 8*c) - 168*sin(4*d*x + 4*c) - 768*sin(2*d*x + 2*c))*a^3 - 3*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*a*b^2 - 128*(3*sin(d*x + c)^8 - 8*sin(d*x + c)^6 + 6*sin(d*x + c)^4)*b^3)/d","A",0
58,1,126,0,0.321107," ","integrate(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{15 \, a^{2} b \cos\left(d x + c\right)^{7} + {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} a^{3} - {\left(15 \, \sin\left(d x + c\right)^{7} - 42 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3}\right)} a b^{2} - {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} b^{3}}{35 \, d}"," ",0,"-1/35*(15*a^2*b*cos(d*x + c)^7 + (5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*a^3 - (15*sin(d*x + c)^7 - 42*sin(d*x + c)^5 + 35*sin(d*x + c)^3)*a*b^2 - (5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*b^3)/d","A",0
59,1,131,0,0.335880," ","integrate(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{96 \, a^{2} b \cos\left(d x + c\right)^{6} + {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 3 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a b^{2} + 16 \, {\left(2 \, \sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4}\right)} b^{3}}{192 \, d}"," ",0,"-1/192*(96*a^2*b*cos(d*x + c)^6 + (4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^3 - 3*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a*b^2 + 16*(2*sin(d*x + c)^6 - 3*sin(d*x + c)^4)*b^3)/d","A",0
60,1,107,0,0.320144," ","integrate(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{9 \, a^{2} b \cos\left(d x + c\right)^{5} - {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{3} + 3 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 5 \, \sin\left(d x + c\right)^{3}\right)} a b^{2} - {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} b^{3}}{15 \, d}"," ",0,"-1/15*(9*a^2*b*cos(d*x + c)^5 - (3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^3 + 3*(3*sin(d*x + c)^5 - 5*sin(d*x + c)^3)*a*b^2 - (3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*b^3)/d","A",0
61,1,91,0,0.329633," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{24 \, a^{2} b \cos\left(d x + c\right)^{4} - 8 \, b^{3} \sin\left(d x + c\right)^{4} - {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 3 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a b^{2}}{32 \, d}"," ",0,"-1/32*(24*a^2*b*cos(d*x + c)^4 - 8*b^3*sin(d*x + c)^4 - (12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^3 - 3*(4*d*x + 4*c - sin(4*d*x + 4*c))*a*b^2)/d","A",0
62,1,84,0,0.321778," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{a^{2} b \cos\left(d x + c\right)^{3}}{d} + \frac{a b^{2} \sin\left(d x + c\right)^{3}}{d} - \frac{{\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{3}}{3 \, d} + \frac{{\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} b^{3}}{3 \, d}"," ",0,"-a^2*b*cos(d*x + c)^3/d + a*b^2*sin(d*x + c)^3/d - 1/3*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^3/d + 1/3*(cos(d*x + c)^3 - 3*cos(d*x + c))*b^3/d","A",0
63,1,91,0,0.336433," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{6 \, a^{2} b \sin\left(d x + c\right)^{2} + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} + 3 \, {\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} a b^{2} - 2 \, {\left(\sin\left(d x + c\right)^{2} + \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)} b^{3}}{4 \, d}"," ",0,"1/4*(6*a^2*b*sin(d*x + c)^2 + (2*d*x + 2*c + sin(2*d*x + 2*c))*a^3 + 3*(2*d*x + 2*c - sin(2*d*x + 2*c))*a*b^2 - 2*(sin(d*x + c)^2 + log(sin(d*x + c)^2 - 1))*b^3)/d","A",0
64,1,84,0,0.330155," ","integrate(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, b^{3} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} + 3 \, a b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)} - 6 \, a^{2} b \cos\left(d x + c\right) + 2 \, a^{3} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*b^3*(1/cos(d*x + c) + cos(d*x + c)) + 3*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)) - 6*a^2*b*cos(d*x + c) + 2*a^3*sin(d*x + c))/d","A",0
65,1,85,0,0.421339," ","integrate(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} a^{3} - 6 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a b^{2} - b^{3} {\left(\frac{1}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)} - 3 \, a^{2} b \log\left(-\sin\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*a^3 - 6*(d*x + c - tan(d*x + c))*a*b^2 - b^3*(1/(sin(d*x + c)^2 - 1) - log(sin(d*x + c)^2 - 1)) - 3*a^2*b*log(-sin(d*x + c)^2 + 1))/d","A",0
66,1,118,0,0.328871," ","integrate(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{9 \, a b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 6 \, a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - \frac{36 \, a^{2} b}{\cos\left(d x + c\right)} + \frac{4 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} b^{3}}{\cos\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"-1/12*(9*a*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 6*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 36*a^2*b/cos(d*x + c) + 4*(3*cos(d*x + c)^2 - 1)*b^3/cos(d*x + c)^3)/d","A",0
67,1,87,0,0.342174," ","integrate(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 \, a b^{2} \tan\left(d x + c\right)^{3} + 4 \, a^{3} \tan\left(d x + c\right) + \frac{{\left(2 \, \sin\left(d x + c\right)^{2} - 1\right)} b^{3}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - \frac{6 \, a^{2} b}{\sin\left(d x + c\right)^{2} - 1}}{4 \, d}"," ",0,"1/4*(4*a*b^2*tan(d*x + c)^3 + 4*a^3*tan(d*x + c) + (2*sin(d*x + c)^2 - 1)*b^3/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 6*a^2*b/(sin(d*x + c)^2 - 1))/d","B",0
68,1,157,0,0.329737," ","integrate(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{45 \, a b^{2} {\left(\frac{2 \, {\left(\sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{240 \, a^{2} b}{\cos\left(d x + c\right)^{3}} - \frac{16 \, {\left(5 \, \cos\left(d x + c\right)^{2} - 3\right)} b^{3}}{\cos\left(d x + c\right)^{5}}}{240 \, d}"," ",0,"1/240*(45*a*b^2*(2*(sin(d*x + c)^3 + sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 60*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*a^2*b/cos(d*x + c)^3 - 16*(5*cos(d*x + c)^2 - 3)*b^3/cos(d*x + c)^5)/d","A",0
69,1,122,0,0.329373," ","integrate(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{20 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{3} + 12 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 5 \, \tan\left(d x + c\right)^{3}\right)} a b^{2} - \frac{5 \, {\left(3 \, \sin\left(d x + c\right)^{2} - 1\right)} b^{3}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} + \frac{45 \, a^{2} b}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{60 \, d}"," ",0,"1/60*(20*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^3 + 12*(3*tan(d*x + c)^5 + 5*tan(d*x + c)^3)*a*b^2 - 5*(3*sin(d*x + c)^2 - 1)*b^3/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) + 45*a^2*b/(sin(d*x + c)^2 - 1)^2)/d","A",0
70,1,208,0,0.332747," ","integrate(sec(d*x+c)^8*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{35 \, a b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 8 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 70 \, a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{672 \, a^{2} b}{\cos\left(d x + c\right)^{5}} - \frac{32 \, {\left(7 \, \cos\left(d x + c\right)^{2} - 5\right)} b^{3}}{\cos\left(d x + c\right)^{7}}}{1120 \, d}"," ",0,"1/1120*(35*a*b^2*(2*(3*sin(d*x + c)^5 - 8*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 70*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + 672*a^2*b/cos(d*x + c)^5 - 32*(7*cos(d*x + c)^2 - 5)*b^3/cos(d*x + c)^7)/d","A",0
71,1,154,0,0.333659," ","integrate(sec(d*x+c)^9*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{56 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} a^{3} + 24 \, {\left(15 \, \tan\left(d x + c\right)^{7} + 42 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3}\right)} a b^{2} + \frac{35 \, {\left(4 \, \sin\left(d x + c\right)^{2} - 1\right)} b^{3}}{\sin\left(d x + c\right)^{8} - 4 \, \sin\left(d x + c\right)^{6} + 6 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{2} + 1} - \frac{420 \, a^{2} b}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{3}}}{840 \, d}"," ",0,"1/840*(56*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^3 + 24*(15*tan(d*x + c)^7 + 42*tan(d*x + c)^5 + 35*tan(d*x + c)^3)*a*b^2 + 35*(4*sin(d*x + c)^2 - 1)*b^3/(sin(d*x + c)^8 - 4*sin(d*x + c)^6 + 6*sin(d*x + c)^4 - 4*sin(d*x + c)^2 + 1) - 420*a^2*b/(sin(d*x + c)^2 - 1)^3)/d","A",0
72,1,248,0,0.338750," ","integrate(sec(d*x+c)^10*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{63 \, a b^{2} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{7} - 55 \, \sin\left(d x + c\right)^{5} + 73 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{8} - 4 \, \sin\left(d x + c\right)^{6} + 6 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{2} + 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 168 \, a^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{6912 \, a^{2} b}{\cos\left(d x + c\right)^{7}} - \frac{256 \, {\left(9 \, \cos\left(d x + c\right)^{2} - 7\right)} b^{3}}{\cos\left(d x + c\right)^{9}}}{16128 \, d}"," ",0,"1/16128*(63*a*b^2*(2*(15*sin(d*x + c)^7 - 55*sin(d*x + c)^5 + 73*sin(d*x + c)^3 + 15*sin(d*x + c))/(sin(d*x + c)^8 - 4*sin(d*x + c)^6 + 6*sin(d*x + c)^4 - 4*sin(d*x + c)^2 + 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 168*a^3*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) + 6912*a^2*b/cos(d*x + c)^7 - 256*(9*cos(d*x + c)^2 - 7)*b^3/cos(d*x + c)^9)/d","A",0
73,1,184,0,0.332895," ","integrate(sec(d*x+c)^11*(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{24 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} a^{3} + 8 \, {\left(35 \, \tan\left(d x + c\right)^{9} + 135 \, \tan\left(d x + c\right)^{7} + 189 \, \tan\left(d x + c\right)^{5} + 105 \, \tan\left(d x + c\right)^{3}\right)} a b^{2} - \frac{21 \, {\left(5 \, \sin\left(d x + c\right)^{2} - 1\right)} b^{3}}{\sin\left(d x + c\right)^{10} - 5 \, \sin\left(d x + c\right)^{8} + 10 \, \sin\left(d x + c\right)^{6} - 10 \, \sin\left(d x + c\right)^{4} + 5 \, \sin\left(d x + c\right)^{2} - 1} + \frac{315 \, a^{2} b}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{4}}}{840 \, d}"," ",0,"1/840*(24*(5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*a^3 + 8*(35*tan(d*x + c)^9 + 135*tan(d*x + c)^7 + 189*tan(d*x + c)^5 + 105*tan(d*x + c)^3)*a*b^2 - 21*(5*sin(d*x + c)^2 - 1)*b^3/(sin(d*x + c)^10 - 5*sin(d*x + c)^8 + 10*sin(d*x + c)^6 - 10*sin(d*x + c)^4 + 5*sin(d*x + c)^2 - 1) + 315*a^2*b/(sin(d*x + c)^2 - 1)^4)/d","A",0
74,1,186,0,0.329997," ","integrate(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{140 \, a^{3} b \cos\left(d x + c\right)^{9} - {\left(35 \, \sin\left(d x + c\right)^{9} - 180 \, \sin\left(d x + c\right)^{7} + 378 \, \sin\left(d x + c\right)^{5} - 420 \, \sin\left(d x + c\right)^{3} + 315 \, \sin\left(d x + c\right)\right)} a^{4} + 6 \, {\left(35 \, \sin\left(d x + c\right)^{9} - 135 \, \sin\left(d x + c\right)^{7} + 189 \, \sin\left(d x + c\right)^{5} - 105 \, \sin\left(d x + c\right)^{3}\right)} a^{2} b^{2} - 20 \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} a b^{3} - {\left(35 \, \sin\left(d x + c\right)^{9} - 90 \, \sin\left(d x + c\right)^{7} + 63 \, \sin\left(d x + c\right)^{5}\right)} b^{4}}{315 \, d}"," ",0,"-1/315*(140*a^3*b*cos(d*x + c)^9 - (35*sin(d*x + c)^9 - 180*sin(d*x + c)^7 + 378*sin(d*x + c)^5 - 420*sin(d*x + c)^3 + 315*sin(d*x + c))*a^4 + 6*(35*sin(d*x + c)^9 - 135*sin(d*x + c)^7 + 189*sin(d*x + c)^5 - 105*sin(d*x + c)^3)*a^2*b^2 - 20*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*a*b^3 - (35*sin(d*x + c)^9 - 90*sin(d*x + c)^7 + 63*sin(d*x + c)^5)*b^4)/d","A",0
75,1,199,0,0.331522," ","integrate(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{1536 \, a^{3} b \cos\left(d x + c\right)^{8} + {\left(128 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 840 \, d x - 840 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 168 \, \sin\left(4 \, d x + 4 \, c\right) - 768 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} - 6 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} b^{2} - 512 \, {\left(3 \, \sin\left(d x + c\right)^{8} - 8 \, \sin\left(d x + c\right)^{6} + 6 \, \sin\left(d x + c\right)^{4}\right)} a b^{3} - 3 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} b^{4}}{3072 \, d}"," ",0,"-1/3072*(1536*a^3*b*cos(d*x + c)^8 + (128*sin(2*d*x + 2*c)^3 - 840*d*x - 840*c - 3*sin(8*d*x + 8*c) - 168*sin(4*d*x + 4*c) - 768*sin(2*d*x + 2*c))*a^4 - 6*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*a^2*b^2 - 512*(3*sin(d*x + c)^8 - 8*sin(d*x + c)^6 + 6*sin(d*x + c)^4)*a*b^3 - 3*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*b^4)/d","A",0
76,1,154,0,0.330235," ","integrate(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{20 \, a^{3} b \cos\left(d x + c\right)^{7} + {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} a^{4} - 2 \, {\left(15 \, \sin\left(d x + c\right)^{7} - 42 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3}\right)} a^{2} b^{2} - 4 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a b^{3} + {\left(5 \, \sin\left(d x + c\right)^{7} - 7 \, \sin\left(d x + c\right)^{5}\right)} b^{4}}{35 \, d}"," ",0,"-1/35*(20*a^3*b*cos(d*x + c)^7 + (5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*a^4 - 2*(15*sin(d*x + c)^7 - 42*sin(d*x + c)^5 + 35*sin(d*x + c)^3)*a^2*b^2 - 4*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a*b^3 + (5*sin(d*x + c)^7 - 7*sin(d*x + c)^5)*b^4)/d","A",0
77,1,170,0,0.341586," ","integrate(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{128 \, a^{3} b \cos\left(d x + c\right)^{6} + {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} - 6 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} b^{2} + 64 \, {\left(2 \, \sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4}\right)} a b^{3} + {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 12 \, d x - 12 \, c + 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} b^{4}}{192 \, d}"," ",0,"-1/192*(128*a^3*b*cos(d*x + c)^6 + (4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^4 - 6*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a^2*b^2 + 64*(2*sin(d*x + c)^6 - 3*sin(d*x + c)^4)*a*b^3 + (4*sin(2*d*x + 2*c)^3 - 12*d*x - 12*c + 3*sin(4*d*x + 4*c))*b^4)/d","A",0
78,1,123,0,0.331814," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{12 \, a^{3} b \cos\left(d x + c\right)^{5} - 3 \, b^{4} \sin\left(d x + c\right)^{5} - {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{4} + 6 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 5 \, \sin\left(d x + c\right)^{3}\right)} a^{2} b^{2} - 4 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a b^{3}}{15 \, d}"," ",0,"-1/15*(12*a^3*b*cos(d*x + c)^5 - 3*b^4*sin(d*x + c)^5 - (3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^4 + 6*(3*sin(d*x + c)^5 - 5*sin(d*x + c)^3)*a^2*b^2 - 4*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a*b^3)/d","A",0
79,1,136,0,0.336933," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{a^{3} b \cos\left(d x + c\right)^{4}}{d} + \frac{a b^{3} \sin\left(d x + c\right)^{4}}{d} + \frac{{\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4}}{32 \, d} + \frac{3 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} b^{2}}{16 \, d} + \frac{{\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) - 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} b^{4}}{32 \, d}"," ",0,"-a^3*b*cos(d*x + c)^4/d + a*b^3*sin(d*x + c)^4/d + 1/32*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^4/d + 3/16*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^2*b^2/d + 1/32*(12*d*x + 12*c + sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c))*b^4/d","A",0
80,1,126,0,0.342008," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{8 \, a^{3} b \cos\left(d x + c\right)^{3} - 12 \, a^{2} b^{2} \sin\left(d x + c\right)^{3} + 2 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{4} - 8 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a b^{3} + {\left(2 \, \sin\left(d x + c\right)^{3} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, \sin\left(d x + c\right)\right)} b^{4}}{6 \, d}"," ",0,"-1/6*(8*a^3*b*cos(d*x + c)^3 - 12*a^2*b^2*sin(d*x + c)^3 + 2*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^4 - 8*(cos(d*x + c)^3 - 3*cos(d*x + c))*a*b^3 + (2*sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1) + 6*sin(d*x + c))*b^4)/d","A",0
81,1,135,0,0.440256," ","integrate(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{8 \, a^{3} b \sin\left(d x + c\right)^{2} + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} + 6 \, {\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} b^{2} - 8 \, {\left(\sin\left(d x + c\right)^{2} + \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)} a b^{3} - 2 \, {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} b^{4}}{4 \, d}"," ",0,"1/4*(8*a^3*b*sin(d*x + c)^2 + (2*d*x + 2*c + sin(2*d*x + 2*c))*a^4 + 6*(2*d*x + 2*c - sin(2*d*x + 2*c))*a^2*b^2 - 8*(sin(d*x + c)^2 + log(sin(d*x + c)^2 - 1))*a*b^3 - 2*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*b^4)/d","A",0
82,1,142,0,0.349473," ","integrate(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{b^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + 3 \, \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, \log\left(\sin\left(d x + c\right) - 1\right) - 4 \, \sin\left(d x + c\right)\right)} - 16 \, a b^{3} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} - 12 \, a^{2} b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)} + 16 \, a^{3} b \cos\left(d x + c\right) - 4 \, a^{4} \sin\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(b^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1) - 4*sin(d*x + c)) - 16*a*b^3*(1/cos(d*x + c) + cos(d*x + c)) - 12*a^2*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)) + 16*a^3*b*cos(d*x + c) - 4*a^4*sin(d*x + c))/d","A",0
83,1,116,0,0.419943," ","integrate(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{3 \, {\left(d x + c\right)} a^{4} - 18 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{2} b^{2} + {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} b^{4} - 6 \, a b^{3} {\left(\frac{1}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)} - 6 \, a^{3} b \log\left(-\sin\left(d x + c\right)^{2} + 1\right)}{3 \, d}"," ",0,"1/3*(3*(d*x + c)*a^4 - 18*(d*x + c - tan(d*x + c))*a^2*b^2 + (tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*b^4 - 6*a*b^3*(1/(sin(d*x + c)^2 - 1) - log(sin(d*x + c)^2 - 1)) - 6*a^3*b*log(-sin(d*x + c)^2 + 1))/d","A",0
84,1,192,0,0.334731," ","integrate(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{3 \, b^{4} {\left(\frac{2 \, {\left(5 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 72 \, a^{2} b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{192 \, a^{3} b}{\cos\left(d x + c\right)} - \frac{64 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a b^{3}}{\cos\left(d x + c\right)^{3}}}{48 \, d}"," ",0,"1/48*(3*b^4*(2*(5*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1)) - 72*a^2*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 24*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 192*a^3*b/cos(d*x + c) - 64*(3*cos(d*x + c)^2 - 1)*a*b^3/cos(d*x + c)^3)/d","A",0
85,1,103,0,0.327726," ","integrate(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{b^{4} \tan\left(d x + c\right)^{5} + 10 \, a^{2} b^{2} \tan\left(d x + c\right)^{3} + 5 \, a^{4} \tan\left(d x + c\right) + \frac{5 \, {\left(2 \, \sin\left(d x + c\right)^{2} - 1\right)} a b^{3}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - \frac{10 \, a^{3} b}{\sin\left(d x + c\right)^{2} - 1}}{5 \, d}"," ",0,"1/5*(b^4*tan(d*x + c)^5 + 10*a^2*b^2*tan(d*x + c)^3 + 5*a^4*tan(d*x + c) + 5*(2*sin(d*x + c)^2 - 1)*a*b^3/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 10*a^3*b/(sin(d*x + c)^2 - 1))/d","B",0
86,1,251,0,0.333550," ","integrate(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{5 \, b^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{5} + 8 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, a^{2} b^{2} {\left(\frac{2 \, {\left(\sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 120 \, a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - \frac{640 \, a^{3} b}{\cos\left(d x + c\right)^{3}} + \frac{128 \, {\left(5 \, \cos\left(d x + c\right)^{2} - 3\right)} a b^{3}}{\cos\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"-1/480*(5*b^4*(2*(3*sin(d*x + c)^5 + 8*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 180*a^2*b^2*(2*(sin(d*x + c)^3 + sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 120*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 640*a^3*b/cos(d*x + c)^3 + 128*(5*cos(d*x + c)^2 - 3)*a*b^3/cos(d*x + c)^5)/d","A",0
87,1,151,0,0.327991," ","integrate(sec(d*x+c)^8*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{35 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{4} + 42 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 5 \, \tan\left(d x + c\right)^{3}\right)} a^{2} b^{2} + 3 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 7 \, \tan\left(d x + c\right)^{5}\right)} b^{4} - \frac{35 \, {\left(3 \, \sin\left(d x + c\right)^{2} - 1\right)} a b^{3}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} + \frac{105 \, a^{3} b}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{105 \, d}"," ",0,"1/105*(35*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^4 + 42*(3*tan(d*x + c)^5 + 5*tan(d*x + c)^3)*a^2*b^2 + 3*(5*tan(d*x + c)^7 + 7*tan(d*x + c)^5)*b^4 - 35*(3*sin(d*x + c)^2 - 1)*a*b^3/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) + 105*a^3*b/(sin(d*x + c)^2 - 1)^2)/d","A",0
88,1,322,0,0.335128," ","integrate(sec(d*x+c)^9*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{35 \, b^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{7} - 11 \, \sin\left(d x + c\right)^{5} - 11 \, \sin\left(d x + c\right)^{3} + 3 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{8} - 4 \, \sin\left(d x + c\right)^{6} + 6 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 560 \, a^{2} b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 8 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 560 \, a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - \frac{7168 \, a^{3} b}{\cos\left(d x + c\right)^{5}} + \frac{1024 \, {\left(7 \, \cos\left(d x + c\right)^{2} - 5\right)} a b^{3}}{\cos\left(d x + c\right)^{7}}}{8960 \, d}"," ",0,"-1/8960*(35*b^4*(2*(3*sin(d*x + c)^7 - 11*sin(d*x + c)^5 - 11*sin(d*x + c)^3 + 3*sin(d*x + c))/(sin(d*x + c)^8 - 4*sin(d*x + c)^6 + 6*sin(d*x + c)^4 - 4*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 560*a^2*b^2*(2*(3*sin(d*x + c)^5 - 8*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + 560*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 7168*a^3*b/cos(d*x + c)^5 + 1024*(7*cos(d*x + c)^2 - 5)*a*b^3/cos(d*x + c)^7)/d","A",0
89,1,193,0,0.330850," ","integrate(sec(d*x+c)^10*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{42 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} a^{4} + 36 \, {\left(15 \, \tan\left(d x + c\right)^{7} + 42 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3}\right)} a^{2} b^{2} + 2 \, {\left(35 \, \tan\left(d x + c\right)^{9} + 90 \, \tan\left(d x + c\right)^{7} + 63 \, \tan\left(d x + c\right)^{5}\right)} b^{4} + \frac{105 \, {\left(4 \, \sin\left(d x + c\right)^{2} - 1\right)} a b^{3}}{\sin\left(d x + c\right)^{8} - 4 \, \sin\left(d x + c\right)^{6} + 6 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{2} + 1} - \frac{420 \, a^{3} b}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{3}}}{630 \, d}"," ",0,"1/630*(42*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^4 + 36*(15*tan(d*x + c)^7 + 42*tan(d*x + c)^5 + 35*tan(d*x + c)^3)*a^2*b^2 + 2*(35*tan(d*x + c)^9 + 90*tan(d*x + c)^7 + 63*tan(d*x + c)^5)*b^4 + 105*(4*sin(d*x + c)^2 - 1)*a*b^3/(sin(d*x + c)^8 - 4*sin(d*x + c)^6 + 6*sin(d*x + c)^4 - 4*sin(d*x + c)^2 + 1) - 420*a^3*b/(sin(d*x + c)^2 - 1)^3)/d","A",0
90,1,382,0,0.344053," ","integrate(sec(d*x+c)^11*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{63 \, b^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{9} - 70 \, \sin\left(d x + c\right)^{7} + 128 \, \sin\left(d x + c\right)^{5} + 70 \, \sin\left(d x + c\right)^{3} - 15 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{10} - 5 \, \sin\left(d x + c\right)^{8} + 10 \, \sin\left(d x + c\right)^{6} - 10 \, \sin\left(d x + c\right)^{4} + 5 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 1260 \, a^{2} b^{2} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{7} - 55 \, \sin\left(d x + c\right)^{5} + 73 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{8} - 4 \, \sin\left(d x + c\right)^{6} + 6 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{2} + 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 1680 \, a^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - \frac{92160 \, a^{3} b}{\cos\left(d x + c\right)^{7}} + \frac{10240 \, {\left(9 \, \cos\left(d x + c\right)^{2} - 7\right)} a b^{3}}{\cos\left(d x + c\right)^{9}}}{161280 \, d}"," ",0,"-1/161280*(63*b^4*(2*(15*sin(d*x + c)^9 - 70*sin(d*x + c)^7 + 128*sin(d*x + c)^5 + 70*sin(d*x + c)^3 - 15*sin(d*x + c))/(sin(d*x + c)^10 - 5*sin(d*x + c)^8 + 10*sin(d*x + c)^6 - 10*sin(d*x + c)^4 + 5*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 1260*a^2*b^2*(2*(15*sin(d*x + c)^7 - 55*sin(d*x + c)^5 + 73*sin(d*x + c)^3 + 15*sin(d*x + c))/(sin(d*x + c)^8 - 4*sin(d*x + c)^6 + 6*sin(d*x + c)^4 - 4*sin(d*x + c)^2 + 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) + 1680*a^4*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 92160*a^3*b/cos(d*x + c)^7 + 10240*(9*cos(d*x + c)^2 - 7)*a*b^3/cos(d*x + c)^9)/d","A",0
91,1,233,0,0.333244," ","integrate(sec(d*x+c)^12*(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{66 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} a^{4} + 44 \, {\left(35 \, \tan\left(d x + c\right)^{9} + 135 \, \tan\left(d x + c\right)^{7} + 189 \, \tan\left(d x + c\right)^{5} + 105 \, \tan\left(d x + c\right)^{3}\right)} a^{2} b^{2} + 2 \, {\left(105 \, \tan\left(d x + c\right)^{11} + 385 \, \tan\left(d x + c\right)^{9} + 495 \, \tan\left(d x + c\right)^{7} + 231 \, \tan\left(d x + c\right)^{5}\right)} b^{4} - \frac{231 \, {\left(5 \, \sin\left(d x + c\right)^{2} - 1\right)} a b^{3}}{\sin\left(d x + c\right)^{10} - 5 \, \sin\left(d x + c\right)^{8} + 10 \, \sin\left(d x + c\right)^{6} - 10 \, \sin\left(d x + c\right)^{4} + 5 \, \sin\left(d x + c\right)^{2} - 1} + \frac{1155 \, a^{3} b}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{4}}}{2310 \, d}"," ",0,"1/2310*(66*(5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*a^4 + 44*(35*tan(d*x + c)^9 + 135*tan(d*x + c)^7 + 189*tan(d*x + c)^5 + 105*tan(d*x + c)^3)*a^2*b^2 + 2*(105*tan(d*x + c)^11 + 385*tan(d*x + c)^9 + 495*tan(d*x + c)^7 + 231*tan(d*x + c)^5)*b^4 - 231*(5*sin(d*x + c)^2 - 1)*a*b^3/(sin(d*x + c)^10 - 5*sin(d*x + c)^8 + 10*sin(d*x + c)^6 - 10*sin(d*x + c)^4 + 5*sin(d*x + c)^2 - 1) + 1155*a^3*b/(sin(d*x + c)^2 - 1)^4)/d","A",0
92,1,290,0,0.340028," ","integrate(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","-\frac{15360 \, a^{4} b \cos\left(d x + c\right)^{10} - 3 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} - 640 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 2520 \, d x + 2520 \, c + 25 \, \sin\left(8 \, d x + 8 \, c\right) + 600 \, \sin\left(4 \, d x + 4 \, c\right) + 2560 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{5} + 10 \, {\left(96 \, \sin\left(2 \, d x + 2 \, c\right)^{5} - 640 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 840 \, d x - 840 \, c + 45 \, \sin\left(8 \, d x + 8 \, c\right) + 120 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} b^{2} + 7680 \, {\left(4 \, \sin\left(d x + c\right)^{10} - 15 \, \sin\left(d x + c\right)^{8} + 20 \, \sin\left(d x + c\right)^{6} - 10 \, \sin\left(d x + c\right)^{4}\right)} a^{2} b^{3} - 15 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} + 120 \, d x + 120 \, c + 5 \, \sin\left(8 \, d x + 8 \, c\right) - 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a b^{4} - 512 \, {\left(6 \, \sin\left(d x + c\right)^{10} - 15 \, \sin\left(d x + c\right)^{8} + 10 \, \sin\left(d x + c\right)^{6}\right)} b^{5}}{30720 \, d}"," ",0,"-1/30720*(15360*a^4*b*cos(d*x + c)^10 - 3*(32*sin(2*d*x + 2*c)^5 - 640*sin(2*d*x + 2*c)^3 + 2520*d*x + 2520*c + 25*sin(8*d*x + 8*c) + 600*sin(4*d*x + 4*c) + 2560*sin(2*d*x + 2*c))*a^5 + 10*(96*sin(2*d*x + 2*c)^5 - 640*sin(2*d*x + 2*c)^3 - 840*d*x - 840*c + 45*sin(8*d*x + 8*c) + 120*sin(4*d*x + 4*c))*a^3*b^2 + 7680*(4*sin(d*x + c)^10 - 15*sin(d*x + c)^8 + 20*sin(d*x + c)^6 - 10*sin(d*x + c)^4)*a^2*b^3 - 15*(32*sin(2*d*x + 2*c)^5 + 120*d*x + 120*c + 5*sin(8*d*x + 8*c) - 40*sin(4*d*x + 4*c))*a*b^4 - 512*(6*sin(d*x + c)^10 - 15*sin(d*x + c)^8 + 10*sin(d*x + c)^6)*b^5)/d","A",0
93,1,224,0,0.330994," ","integrate(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","-\frac{175 \, a^{4} b \cos\left(d x + c\right)^{9} - {\left(35 \, \sin\left(d x + c\right)^{9} - 180 \, \sin\left(d x + c\right)^{7} + 378 \, \sin\left(d x + c\right)^{5} - 420 \, \sin\left(d x + c\right)^{3} + 315 \, \sin\left(d x + c\right)\right)} a^{5} + 10 \, {\left(35 \, \sin\left(d x + c\right)^{9} - 135 \, \sin\left(d x + c\right)^{7} + 189 \, \sin\left(d x + c\right)^{5} - 105 \, \sin\left(d x + c\right)^{3}\right)} a^{3} b^{2} - 50 \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} a^{2} b^{3} - 5 \, {\left(35 \, \sin\left(d x + c\right)^{9} - 90 \, \sin\left(d x + c\right)^{7} + 63 \, \sin\left(d x + c\right)^{5}\right)} a b^{4} + {\left(35 \, \cos\left(d x + c\right)^{9} - 90 \, \cos\left(d x + c\right)^{7} + 63 \, \cos\left(d x + c\right)^{5}\right)} b^{5}}{315 \, d}"," ",0,"-1/315*(175*a^4*b*cos(d*x + c)^9 - (35*sin(d*x + c)^9 - 180*sin(d*x + c)^7 + 378*sin(d*x + c)^5 - 420*sin(d*x + c)^3 + 315*sin(d*x + c))*a^5 + 10*(35*sin(d*x + c)^9 - 135*sin(d*x + c)^7 + 189*sin(d*x + c)^5 - 105*sin(d*x + c)^3)*a^3*b^2 - 50*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*a^2*b^3 - 5*(35*sin(d*x + c)^9 - 90*sin(d*x + c)^7 + 63*sin(d*x + c)^5)*a*b^4 + (35*cos(d*x + c)^9 - 90*cos(d*x + c)^7 + 63*cos(d*x + c)^5)*b^5)/d","A",0
94,1,228,0,0.327998," ","integrate(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","-\frac{1920 \, a^{4} b \cos\left(d x + c\right)^{8} + {\left(128 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 840 \, d x - 840 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 168 \, \sin\left(4 \, d x + 4 \, c\right) - 768 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{5} - 10 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} b^{2} - 1280 \, {\left(3 \, \sin\left(d x + c\right)^{8} - 8 \, \sin\left(d x + c\right)^{6} + 6 \, \sin\left(d x + c\right)^{4}\right)} a^{2} b^{3} - 15 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a b^{4} + 128 \, {\left(3 \, \sin\left(d x + c\right)^{8} - 4 \, \sin\left(d x + c\right)^{6}\right)} b^{5}}{3072 \, d}"," ",0,"-1/3072*(1920*a^4*b*cos(d*x + c)^8 + (128*sin(2*d*x + 2*c)^3 - 840*d*x - 840*c - 3*sin(8*d*x + 8*c) - 168*sin(4*d*x + 4*c) - 768*sin(2*d*x + 2*c))*a^5 - 10*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*a^3*b^2 - 1280*(3*sin(d*x + c)^8 - 8*sin(d*x + c)^6 + 6*sin(d*x + c)^4)*a^2*b^3 - 15*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*a*b^4 + 128*(3*sin(d*x + c)^8 - 4*sin(d*x + c)^6)*b^5)/d","A",0
95,1,194,0,0.328237," ","integrate(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","-\frac{75 \, a^{4} b \cos\left(d x + c\right)^{7} + 3 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} a^{5} - 10 \, {\left(15 \, \sin\left(d x + c\right)^{7} - 42 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3}\right)} a^{3} b^{2} - 30 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a^{2} b^{3} + 15 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 7 \, \sin\left(d x + c\right)^{5}\right)} a b^{4} + {\left(15 \, \cos\left(d x + c\right)^{7} - 42 \, \cos\left(d x + c\right)^{5} + 35 \, \cos\left(d x + c\right)^{3}\right)} b^{5}}{105 \, d}"," ",0,"-1/105*(75*a^4*b*cos(d*x + c)^7 + 3*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*a^5 - 10*(15*sin(d*x + c)^7 - 42*sin(d*x + c)^5 + 35*sin(d*x + c)^3)*a^3*b^2 - 30*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a^2*b^3 + 15*(5*sin(d*x + c)^7 - 7*sin(d*x + c)^5)*a*b^4 + (15*cos(d*x + c)^7 - 42*cos(d*x + c)^5 + 35*cos(d*x + c)^3)*b^5)/d","A",0
96,1,187,0,0.328308," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","-\frac{160 \, a^{4} b \cos\left(d x + c\right)^{6} - 32 \, b^{5} \sin\left(d x + c\right)^{6} + {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{5} - 10 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} b^{2} + 160 \, {\left(2 \, \sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4}\right)} a^{2} b^{3} + 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 12 \, d x - 12 \, c + 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a b^{4}}{192 \, d}"," ",0,"-1/192*(160*a^4*b*cos(d*x + c)^6 - 32*b^5*sin(d*x + c)^6 + (4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^5 - 10*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a^3*b^2 + 160*(2*sin(d*x + c)^6 - 3*sin(d*x + c)^4)*a^2*b^3 + 5*(4*sin(2*d*x + 2*c)^3 - 12*d*x - 12*c + 3*sin(4*d*x + 4*c))*a*b^4)/d","A",0
97,1,172,0,0.327804," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","-\frac{a^{4} b \cos\left(d x + c\right)^{5}}{d} + \frac{a b^{4} \sin\left(d x + c\right)^{5}}{d} + \frac{{\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{5}}{15 \, d} - \frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 5 \, \sin\left(d x + c\right)^{3}\right)} a^{3} b^{2}}{3 \, d} + \frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{2} b^{3}}{3 \, d} - \frac{{\left(3 \, \cos\left(d x + c\right)^{5} - 10 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} b^{5}}{15 \, d}"," ",0,"-a^4*b*cos(d*x + c)^5/d + a*b^4*sin(d*x + c)^5/d + 1/15*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^5/d - 2/3*(3*sin(d*x + c)^5 - 5*sin(d*x + c)^3)*a^3*b^2/d + 2/3*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^2*b^3/d - 1/15*(3*cos(d*x + c)^5 - 10*cos(d*x + c)^3 + 15*cos(d*x + c))*b^5/d","A",0
98,1,170,0,0.327311," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","\frac{80 \, a^{2} b^{3} \sin\left(d x + c\right)^{4} - 40 \, {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2} a^{4} b + {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{5} + 10 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} b^{2} + 5 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) - 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a b^{4} - 8 \, {\left(\sin\left(d x + c\right)^{4} + 2 \, \sin\left(d x + c\right)^{2} + 2 \, \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)} b^{5}}{32 \, d}"," ",0,"1/32*(80*a^2*b^3*sin(d*x + c)^4 - 40*(sin(d*x + c)^2 - 1)^2*a^4*b + (12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^5 + 10*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^3*b^2 + 5*(12*d*x + 12*c + sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c))*a*b^4 - 8*(sin(d*x + c)^4 + 2*sin(d*x + c)^2 + 2*log(sin(d*x + c)^2 - 1))*b^5)/d","A",0
99,1,162,0,0.331466," ","integrate(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","-\frac{10 \, a^{4} b \cos\left(d x + c\right)^{3} - 20 \, a^{3} b^{2} \sin\left(d x + c\right)^{3} + 2 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{5} - 20 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a^{2} b^{3} + 5 \, {\left(2 \, \sin\left(d x + c\right)^{3} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, \sin\left(d x + c\right)\right)} a b^{4} + 2 \, {\left(\cos\left(d x + c\right)^{3} - \frac{3}{\cos\left(d x + c\right)} - 6 \, \cos\left(d x + c\right)\right)} b^{5}}{6 \, d}"," ",0,"-1/6*(10*a^4*b*cos(d*x + c)^3 - 20*a^3*b^2*sin(d*x + c)^3 + 2*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^5 - 20*(cos(d*x + c)^3 - 3*cos(d*x + c))*a^2*b^3 + 5*(2*sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1) + 6*sin(d*x + c))*a*b^4 + 2*(cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*b^5)/d","A",0
100,1,179,0,0.425858," ","integrate(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","\frac{10 \, a^{4} b \sin\left(d x + c\right)^{2} + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{5} + 10 \, {\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} b^{2} - 20 \, {\left(\sin\left(d x + c\right)^{2} + \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)} a^{2} b^{3} - 10 \, {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a b^{4} + 2 \, {\left(\sin\left(d x + c\right)^{2} - \frac{1}{\sin\left(d x + c\right)^{2} - 1} + 2 \, \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)} b^{5}}{4 \, d}"," ",0,"1/4*(10*a^4*b*sin(d*x + c)^2 + (2*d*x + 2*c + sin(2*d*x + 2*c))*a^5 + 10*(2*d*x + 2*c - sin(2*d*x + 2*c))*a^3*b^2 - 20*(sin(d*x + c)^2 + log(sin(d*x + c)^2 - 1))*a^2*b^3 - 10*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a*b^4 + 2*(sin(d*x + c)^2 - 1/(sin(d*x + c)^2 - 1) + 2*log(sin(d*x + c)^2 - 1))*b^5)/d","A",0
101,1,181,0,0.334538," ","integrate(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","-\frac{15 \, a b^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + 3 \, \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, \log\left(\sin\left(d x + c\right) - 1\right) - 4 \, \sin\left(d x + c\right)\right)} - 120 \, a^{2} b^{3} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} + 4 \, b^{5} {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)} - 60 \, a^{3} b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)} + 60 \, a^{4} b \cos\left(d x + c\right) - 12 \, a^{5} \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(15*a*b^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1) - 4*sin(d*x + c)) - 120*a^2*b^3*(1/cos(d*x + c) + cos(d*x + c)) + 4*b^5*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)) - 60*a^3*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)) + 60*a^4*b*cos(d*x + c) - 12*a^5*sin(d*x + c))/d","A",0
102,1,174,0,0.421645," ","integrate(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} a^{5} - 120 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{3} b^{2} + 20 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a b^{4} + 3 \, b^{5} {\left(\frac{4 \, \sin\left(d x + c\right)^{2} - 3}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 2 \, \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)} - 60 \, a^{2} b^{3} {\left(\frac{1}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)} - 30 \, a^{4} b \log\left(-\sin\left(d x + c\right)^{2} + 1\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*a^5 - 120*(d*x + c - tan(d*x + c))*a^3*b^2 + 20*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a*b^4 + 3*b^5*((4*sin(d*x + c)^2 - 3)/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 2*log(sin(d*x + c)^2 - 1)) - 60*a^2*b^3*(1/(sin(d*x + c)^2 - 1) - log(sin(d*x + c)^2 - 1)) - 30*a^4*b*log(-sin(d*x + c)^2 + 1))/d","A",0
103,1,230,0,0.337135," ","integrate(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","\frac{75 \, a b^{4} {\left(\frac{2 \, {\left(5 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 600 \, a^{3} b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 120 \, a^{5} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{1200 \, a^{4} b}{\cos\left(d x + c\right)} - \frac{800 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a^{2} b^{3}}{\cos\left(d x + c\right)^{3}} + \frac{16 \, {\left(15 \, \cos\left(d x + c\right)^{4} - 10 \, \cos\left(d x + c\right)^{2} + 3\right)} b^{5}}{\cos\left(d x + c\right)^{5}}}{240 \, d}"," ",0,"1/240*(75*a*b^4*(2*(5*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1)) - 600*a^3*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 120*a^5*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 1200*a^4*b/cos(d*x + c) - 800*(3*cos(d*x + c)^2 - 1)*a^2*b^3/cos(d*x + c)^3 + 16*(15*cos(d*x + c)^4 - 10*cos(d*x + c)^2 + 3)*b^5/cos(d*x + c)^5)/d","A",0
104,1,166,0,0.346518," ","integrate(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","\frac{6 \, a b^{4} \tan\left(d x + c\right)^{5} + 20 \, a^{3} b^{2} \tan\left(d x + c\right)^{3} + 6 \, a^{5} \tan\left(d x + c\right) + \frac{15 \, {\left(2 \, \sin\left(d x + c\right)^{2} - 1\right)} a^{2} b^{3}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - \frac{{\left(3 \, \sin\left(d x + c\right)^{4} - 3 \, \sin\left(d x + c\right)^{2} + 1\right)} b^{5}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - \frac{15 \, a^{4} b}{\sin\left(d x + c\right)^{2} - 1}}{6 \, d}"," ",0,"1/6*(6*a*b^4*tan(d*x + c)^5 + 20*a^3*b^2*tan(d*x + c)^3 + 6*a^5*tan(d*x + c) + 15*(2*sin(d*x + c)^2 - 1)*a^2*b^3/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - (3*sin(d*x + c)^4 - 3*sin(d*x + c)^2 + 1)*b^5/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*a^4*b/(sin(d*x + c)^2 - 1))/d","B",0
105,1,289,0,0.341121," ","integrate(sec(d*x+c)^8*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","-\frac{175 \, a b^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{5} + 8 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 2100 \, a^{3} b^{2} {\left(\frac{2 \, {\left(\sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 840 \, a^{5} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - \frac{5600 \, a^{4} b}{\cos\left(d x + c\right)^{3}} + \frac{2240 \, {\left(5 \, \cos\left(d x + c\right)^{2} - 3\right)} a^{2} b^{3}}{\cos\left(d x + c\right)^{5}} - \frac{32 \, {\left(35 \, \cos\left(d x + c\right)^{4} - 42 \, \cos\left(d x + c\right)^{2} + 15\right)} b^{5}}{\cos\left(d x + c\right)^{7}}}{3360 \, d}"," ",0,"-1/3360*(175*a*b^4*(2*(3*sin(d*x + c)^5 + 8*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 2100*a^3*b^2*(2*(sin(d*x + c)^3 + sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 840*a^5*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 5600*a^4*b/cos(d*x + c)^3 + 2240*(5*cos(d*x + c)^2 - 3)*a^2*b^3/cos(d*x + c)^5 - 32*(35*cos(d*x + c)^4 - 42*cos(d*x + c)^2 + 15)*b^5/cos(d*x + c)^7)/d","A",0
106,1,223,0,0.956712," ","integrate(sec(d*x+c)^9*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","\frac{56 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{5} + 112 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 5 \, \tan\left(d x + c\right)^{3}\right)} a^{3} b^{2} + 24 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 7 \, \tan\left(d x + c\right)^{5}\right)} a b^{4} - \frac{140 \, {\left(3 \, \sin\left(d x + c\right)^{2} - 1\right)} a^{2} b^{3}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} + \frac{7 \, {\left(6 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{2} + 1\right)} b^{5}}{\sin\left(d x + c\right)^{8} - 4 \, \sin\left(d x + c\right)^{6} + 6 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{2} + 1} + \frac{210 \, a^{4} b}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{168 \, d}"," ",0,"1/168*(56*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^5 + 112*(3*tan(d*x + c)^5 + 5*tan(d*x + c)^3)*a^3*b^2 + 24*(5*tan(d*x + c)^7 + 7*tan(d*x + c)^5)*a*b^4 - 140*(3*sin(d*x + c)^2 - 1)*a^2*b^3/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) + 7*(6*sin(d*x + c)^4 - 4*sin(d*x + c)^2 + 1)*b^5/(sin(d*x + c)^8 - 4*sin(d*x + c)^6 + 6*sin(d*x + c)^4 - 4*sin(d*x + c)^2 + 1) + 210*a^4*b/(sin(d*x + c)^2 - 1)^2)/d","A",0
107,1,360,0,1.008828," ","integrate(sec(d*x+c)^10*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","-\frac{1575 \, a b^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{7} - 11 \, \sin\left(d x + c\right)^{5} - 11 \, \sin\left(d x + c\right)^{3} + 3 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{8} - 4 \, \sin\left(d x + c\right)^{6} + 6 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 8400 \, a^{3} b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 8 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 5040 \, a^{5} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - \frac{80640 \, a^{4} b}{\cos\left(d x + c\right)^{5}} + \frac{23040 \, {\left(7 \, \cos\left(d x + c\right)^{2} - 5\right)} a^{2} b^{3}}{\cos\left(d x + c\right)^{7}} - \frac{256 \, {\left(63 \, \cos\left(d x + c\right)^{4} - 90 \, \cos\left(d x + c\right)^{2} + 35\right)} b^{5}}{\cos\left(d x + c\right)^{9}}}{80640 \, d}"," ",0,"-1/80640*(1575*a*b^4*(2*(3*sin(d*x + c)^7 - 11*sin(d*x + c)^5 - 11*sin(d*x + c)^3 + 3*sin(d*x + c))/(sin(d*x + c)^8 - 4*sin(d*x + c)^6 + 6*sin(d*x + c)^4 - 4*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 8400*a^3*b^2*(2*(3*sin(d*x + c)^5 - 8*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + 5040*a^5*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 80640*a^4*b/cos(d*x + c)^5 + 23040*(7*cos(d*x + c)^2 - 5)*a^2*b^3/cos(d*x + c)^7 - 256*(63*cos(d*x + c)^4 - 90*cos(d*x + c)^2 + 35)*b^5/cos(d*x + c)^9)/d","A",0
108,1,275,0,0.784583," ","integrate(sec(d*x+c)^11*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","\frac{84 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} a^{5} + 120 \, {\left(15 \, \tan\left(d x + c\right)^{7} + 42 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3}\right)} a^{3} b^{2} + 20 \, {\left(35 \, \tan\left(d x + c\right)^{9} + 90 \, \tan\left(d x + c\right)^{7} + 63 \, \tan\left(d x + c\right)^{5}\right)} a b^{4} + \frac{525 \, {\left(4 \, \sin\left(d x + c\right)^{2} - 1\right)} a^{2} b^{3}}{\sin\left(d x + c\right)^{8} - 4 \, \sin\left(d x + c\right)^{6} + 6 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{2} + 1} - \frac{21 \, {\left(10 \, \sin\left(d x + c\right)^{4} - 5 \, \sin\left(d x + c\right)^{2} + 1\right)} b^{5}}{\sin\left(d x + c\right)^{10} - 5 \, \sin\left(d x + c\right)^{8} + 10 \, \sin\left(d x + c\right)^{6} - 10 \, \sin\left(d x + c\right)^{4} + 5 \, \sin\left(d x + c\right)^{2} - 1} - \frac{1050 \, a^{4} b}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{3}}}{1260 \, d}"," ",0,"1/1260*(84*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^5 + 120*(15*tan(d*x + c)^7 + 42*tan(d*x + c)^5 + 35*tan(d*x + c)^3)*a^3*b^2 + 20*(35*tan(d*x + c)^9 + 90*tan(d*x + c)^7 + 63*tan(d*x + c)^5)*a*b^4 + 525*(4*sin(d*x + c)^2 - 1)*a^2*b^3/(sin(d*x + c)^8 - 4*sin(d*x + c)^6 + 6*sin(d*x + c)^4 - 4*sin(d*x + c)^2 + 1) - 21*(10*sin(d*x + c)^4 - 5*sin(d*x + c)^2 + 1)*b^5/(sin(d*x + c)^10 - 5*sin(d*x + c)^8 + 10*sin(d*x + c)^6 - 10*sin(d*x + c)^4 + 5*sin(d*x + c)^2 - 1) - 1050*a^4*b/(sin(d*x + c)^2 - 1)^3)/d","A",0
109,1,420,0,0.541532," ","integrate(sec(d*x+c)^12*(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","-\frac{693 \, a b^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{9} - 70 \, \sin\left(d x + c\right)^{7} + 128 \, \sin\left(d x + c\right)^{5} + 70 \, \sin\left(d x + c\right)^{3} - 15 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{10} - 5 \, \sin\left(d x + c\right)^{8} + 10 \, \sin\left(d x + c\right)^{6} - 10 \, \sin\left(d x + c\right)^{4} + 5 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 4620 \, a^{3} b^{2} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{7} - 55 \, \sin\left(d x + c\right)^{5} + 73 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{8} - 4 \, \sin\left(d x + c\right)^{6} + 6 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{2} + 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 3696 \, a^{5} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - \frac{253440 \, a^{4} b}{\cos\left(d x + c\right)^{7}} + \frac{56320 \, {\left(9 \, \cos\left(d x + c\right)^{2} - 7\right)} a^{2} b^{3}}{\cos\left(d x + c\right)^{9}} - \frac{512 \, {\left(99 \, \cos\left(d x + c\right)^{4} - 154 \, \cos\left(d x + c\right)^{2} + 63\right)} b^{5}}{\cos\left(d x + c\right)^{11}}}{354816 \, d}"," ",0,"-1/354816*(693*a*b^4*(2*(15*sin(d*x + c)^9 - 70*sin(d*x + c)^7 + 128*sin(d*x + c)^5 + 70*sin(d*x + c)^3 - 15*sin(d*x + c))/(sin(d*x + c)^10 - 5*sin(d*x + c)^8 + 10*sin(d*x + c)^6 - 10*sin(d*x + c)^4 + 5*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 4620*a^3*b^2*(2*(15*sin(d*x + c)^7 - 55*sin(d*x + c)^5 + 73*sin(d*x + c)^3 + 15*sin(d*x + c))/(sin(d*x + c)^8 - 4*sin(d*x + c)^6 + 6*sin(d*x + c)^4 - 4*sin(d*x + c)^2 + 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) + 3696*a^5*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 253440*a^4*b/cos(d*x + c)^7 + 56320*(9*cos(d*x + c)^2 - 7)*a^2*b^3/cos(d*x + c)^9 - 512*(99*cos(d*x + c)^4 - 154*cos(d*x + c)^2 + 63)*b^5/cos(d*x + c)^11)/d","A",0
110,1,564,0,1.667469," ","integrate(cos(d*x+c)^5/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{4 \, b^{5} \log\left(-a - \frac{2 \, b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{4 \, b^{5} \log\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(3 \, a^{5} + 10 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{\frac{16 \, b^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{{\left(5 \, a^{3} + 9 \, a b^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{8 \, {\left(a^{2} b + 2 \, b^{3}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{{\left(3 \, a^{3} - a b^{2}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{{\left(3 \, a^{3} - a b^{2}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{8 \, {\left(a^{2} b + 2 \, b^{3}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{{\left(5 \, a^{3} + 9 \, a b^{2}\right)} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4} + 2 \, a^{2} b^{2} + b^{4} + \frac{4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}}}{4 \, d}"," ",0,"1/4*(4*b^5*log(-a - 2*b*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 4*b^5*log(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (3*a^5 + 10*a^3*b^2 + 15*a*b^4)*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (16*b^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - (5*a^3 + 9*a*b^2)*sin(d*x + c)/(cos(d*x + c) + 1) + 8*(a^2*b + 2*b^3)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + (3*a^3 - a*b^2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - (3*a^3 - a*b^2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 8*(a^2*b + 2*b^3)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + (5*a^3 + 9*a*b^2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a^4 + 2*a^2*b^2 + b^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*(a^4 + 2*a^2*b^2 + b^4)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + (a^4 + 2*a^2*b^2 + b^4)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8))/d","B",0
111,1,379,0,0.533720," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{3 \, b^{4} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(a^{2} b + 4 \, b^{3} + \frac{6 \, b^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, {\left(a^{3} + 2 \, a b^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2 \, {\left(a^{3} + 4 \, a b^{2}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, {\left(a^{2} b + 2 \, b^{3}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{3 \, {\left(a^{3} + 2 \, a b^{2}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4} + \frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}}}{3 \, d}"," ",0,"-1/3*(3*b^4*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2*(a^2*b + 4*b^3 + 6*b^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*(a^3 + 2*a*b^2)*sin(d*x + c)/(cos(d*x + c) + 1) + 2*(a^3 + 4*a*b^2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*(a^2*b + 2*b^3)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3*(a^3 + 2*a*b^2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^4 + 2*a^2*b^2 + b^4 + 3*(a^4 + 2*a^2*b^2 + b^4)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6))/d","B",0
112,1,284,0,2.007575," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{b^{3} \log\left(-a - \frac{2 \, b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{b^{3} \log\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{3} + 3 \, a b^{2}\right)} \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{\frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, b \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2} + b^{2} + \frac{2 \, {\left(a^{2} + b^{2}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{{\left(a^{2} + b^{2}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}}{d}"," ",0,"(b^3*log(-a - 2*b*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^4 + 2*a^2*b^2 + b^4) - b^3*log(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (a^3 + 3*a*b^2)*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(a^4 + 2*a^2*b^2 + b^4) + (a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*b*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 + b^2 + 2*(a^2 + b^2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + (a^2 + b^2)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4))/d","B",0
113,1,142,0,0.569762," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{b^{2} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(b + \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}}{a^{2} + b^{2} + \frac{{\left(a^{2} + b^{2}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}}{d}"," ",0,"-(b^2*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) - 2*(b + a*sin(d*x + c)/(cos(d*x + c) + 1))/(a^2 + b^2 + (a^2 + b^2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2))/d","A",0
114,1,124,0,0.604782," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, a \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2} + b^{2}} + \frac{b \log\left(-a - \frac{2 \, b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{2} + b^{2}} - \frac{b \log\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}{a^{2} + b^{2}}}{d}"," ",0,"(2*a*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(a^2 + b^2) + b*log(-a - 2*b*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^2 + b^2) - b*log(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/(a^2 + b^2))/d","B",0
115,1,80,0,0.730673," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} d}"," ",0,"-log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*d)","A",0
116,1,103,0,2.216301," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\log\left(-a - \frac{2 \, b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{b} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b}}{d}"," ",0,"(log(-a - 2*b*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/b - log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b)/d","B",0
117,1,163,0,1.693226," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{a \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{2}} - \frac{a \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{2}} + \frac{\sqrt{a^{2} + b^{2}} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{b^{2}} - \frac{2}{b - \frac{b \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}}{d}"," ",0,"-(a*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^2 - a*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^2 + sqrt(a^2 + b^2)*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/b^2 - 2/(b - b*sin(d*x + c)^2/(cos(d*x + c) + 1)^2))/d","B",0
118,1,238,0,0.600395," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(\frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{b \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{b^{2} - \frac{2 \, b^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{b^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{{\left(a^{2} + b^{2}\right)} \log\left(-a - \frac{2 \, b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{b^{3}} + \frac{{\left(a^{2} + b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{3}} + \frac{{\left(a^{2} + b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{3}}}{d}"," ",0,"-(2*(a*sin(d*x + c)/(cos(d*x + c) + 1) - b*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(b^2 - 2*b^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + b^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - (a^2 + b^2)*log(-a - 2*b*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/b^3 + (a^2 + b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^3 + (a^2 + b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^3)/d","B",0
119,1,361,0,0.419347," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(6 \, a^{2} + 8 \, b^{2} - \frac{3 \, a b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a b \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{12 \, {\left(a^{2} + b^{2}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, {\left(a^{2} + 2 \, b^{2}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)}}{b^{3} - \frac{3 \, b^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, b^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{b^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{4}} + \frac{3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{4}} - \frac{6 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} b^{4}}}{6 \, d}"," ",0,"1/6*(2*(6*a^2 + 8*b^2 - 3*a*b*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a*b*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 12*(a^2 + b^2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*(a^2 + 2*b^2)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/(b^3 - 3*b^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*b^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - b^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 3*(2*a^3 + 3*a*b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^4 + 3*(2*a^3 + 3*a*b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^4 - 6*(a^4 + 2*a^2*b^2 + b^4)*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^4))/d","B",0
120,1,462,0,0.344806," ","integrate(sec(d*x+c)^5/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(\frac{3 \, {\left(a^{3} + 2 \, a b^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, {\left(a^{2} b + 2 \, b^{3}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{{\left(9 \, a^{3} + 14 \, a b^{2}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{6 \, {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(9 \, a^{3} + 14 \, a b^{2}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3 \, {\left(a^{2} b + 2 \, b^{3}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{3 \, {\left(a^{3} + 2 \, a b^{2}\right)} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{b^{4} - \frac{4 \, b^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, b^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, b^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{b^{4} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(-a - \frac{2 \, b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{b^{5}} + \frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{5}} + \frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{5}}}{3 \, d}"," ",0,"-1/3*(2*(3*(a^3 + 2*a*b^2)*sin(d*x + c)/(cos(d*x + c) + 1) - 3*(a^2*b + 2*b^3)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - (9*a^3 + 14*a*b^2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 6*(a^2*b + b^3)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (9*a^3 + 14*a*b^2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3*(a^2*b + 2*b^3)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 3*(a^3 + 2*a*b^2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(b^4 - 4*b^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*b^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*b^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + b^4*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 3*(a^4 + 2*a^2*b^2 + b^4)*log(-a - 2*b*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/b^5 + 3*(a^4 + 2*a^2*b^2 + b^4)*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^5 + 3*(a^4 + 2*a^2*b^2 + b^4)*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^5)/d","B",0
121,1,625,0,0.439268," ","integrate(sec(d*x+c)^6/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(120 \, a^{4} + 280 \, a^{2} b^{2} + 184 \, b^{4} - \frac{15 \, {\left(4 \, a^{3} b + 9 \, a b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{80 \, {\left(6 \, a^{4} + 13 \, a^{2} b^{2} + 7 \, b^{4}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{30 \, {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{80 \, {\left(9 \, a^{4} + 20 \, a^{2} b^{2} + 14 \, b^{4}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{240 \, {\left(2 \, a^{4} + 5 \, a^{2} b^{2} + 3 \, b^{4}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{30 \, {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{120 \, {\left(a^{4} + 3 \, a^{2} b^{2} + 3 \, b^{4}\right)} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{15 \, {\left(4 \, a^{3} b + 9 \, a b^{3}\right)} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)}}{b^{5} - \frac{5 \, b^{5} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, b^{5} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{10 \, b^{5} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, b^{5} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{b^{5} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} - \frac{15 \, {\left(8 \, a^{5} + 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{6}} + \frac{15 \, {\left(8 \, a^{5} + 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{6}} - \frac{120 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} b^{6}}}{120 \, d}"," ",0,"1/120*(2*(120*a^4 + 280*a^2*b^2 + 184*b^4 - 15*(4*a^3*b + 9*a*b^3)*sin(d*x + c)/(cos(d*x + c) + 1) - 80*(6*a^4 + 13*a^2*b^2 + 7*b^4)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 30*(4*a^3*b + 5*a*b^3)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 80*(9*a^4 + 20*a^2*b^2 + 14*b^4)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 240*(2*a^4 + 5*a^2*b^2 + 3*b^4)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 30*(4*a^3*b + 5*a*b^3)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 120*(a^4 + 3*a^2*b^2 + 3*b^4)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 15*(4*a^3*b + 9*a*b^3)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/(b^5 - 5*b^5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*b^5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 10*b^5*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*b^5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - b^5*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) - 15*(8*a^5 + 20*a^3*b^2 + 15*a*b^4)*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^6 + 15*(8*a^5 + 20*a^3*b^2 + 15*a*b^4)*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^6 - 120*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^6))/d","B",0
122,1,282,0,0.553386," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{8 \, a b^{3} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{4 \, a b^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(a^{4} + 6 \, a^{2} b^{2} - 3 \, b^{4}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, a^{2} b - 2 \, b^{3} + {\left(a^{2} b - 3 \, b^{3}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{3} + a b^{2}\right)} \tan\left(d x + c\right)}{a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \tan\left(d x + c\right)^{3} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(8*a*b^3*log(b*tan(d*x + c) + a)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 4*a*b^3*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (a^4 + 6*a^2*b^2 - 3*b^4)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (2*a^2*b - 2*b^3 + (a^2*b - 3*b^3)*tan(d*x + c)^2 + (a^3 + a*b^2)*tan(d*x + c))/(a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*tan(d*x + c)^3 + (a^5 + 2*a^3*b^2 + a*b^4)*tan(d*x + c)^2 + (a^4*b + 2*a^2*b^3 + b^5)*tan(d*x + c)))/d","A",0
123,1,348,0,2.551150," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, a b^{2} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(2 \, a^{3} b - a b^{3} - \frac{3 \, a b^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{{\left(a^{4} + 3 \, a^{2} b^{2} - b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{{\left(a^{4} - a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4} + \frac{2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{{\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}}{d}"," ",0,"-(3*a*b^2*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2*(2*a^3*b - a*b^3 - 3*a*b^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + (a^4 + 3*a^2*b^2 - b^4)*sin(d*x + c)/(cos(d*x + c) + 1) - (a^4 - a^2*b^2 + b^4)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^6 + 2*a^4*b^2 + a^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*sin(d*x + c)/(cos(d*x + c) + 1) + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - (a^6 + 2*a^4*b^2 + a^2*b^4)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4))/d","B",0
124,1,131,0,0.431684," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, a b \log\left(b \tan\left(d x + c\right) + a\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{a b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{2} - b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{b}{a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} \tan\left(d x + c\right)}}{d}"," ",0,"(2*a*b*log(b*tan(d*x + c) + a)/(a^4 + 2*a^2*b^2 + b^4) - a*b*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (a^2 - b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - b/(a^3 + a*b^2 + (a^2*b + b^3)*tan(d*x + c)))/d","A",0
125,1,182,0,0.440540," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{a \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(a b + \frac{b^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}}{a^{4} + a^{2} b^{2} + \frac{2 \, {\left(a^{3} b + a b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{{\left(a^{4} + a^{2} b^{2}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}}{d}"," ",0,"-(a*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) + 2*(a*b + b^2*sin(d*x + c)/(cos(d*x + c) + 1))/(a^4 + a^2*b^2 + 2*(a^3*b + a*b^3)*sin(d*x + c)/(cos(d*x + c) + 1) - (a^4 + a^2*b^2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2))/d","B",0
126,1,21,0,0.340308," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{1}{{\left(b^{2} \tan\left(d x + c\right) + a b\right)} d}"," ",0,"-1/((b^2*tan(d*x + c) + a*b)*d)","A",0
127,1,212,0,0.426150," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(a + \frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}}{a^{2} b + \frac{2 \, a b^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{a^{2} b \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}} - \frac{a \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} b^{2}} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{2}} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{2}}}{d}"," ",0,"-(2*(a + b*sin(d*x + c)/(cos(d*x + c) + 1))/(a^2*b + 2*a*b^2*sin(d*x + c)/(cos(d*x + c) + 1) - a^2*b*sin(d*x + c)^2/(cos(d*x + c) + 1)^2) - a*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^2) - log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^2 + log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^2)/d","B",0
128,1,60,0,0.329640," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{a^{2} + b^{2}}{b^{4} \tan\left(d x + c\right) + a b^{3}} + \frac{2 \, a \log\left(b \tan\left(d x + c\right) + a\right)}{b^{3}} - \frac{\tan\left(d x + c\right)}{b^{2}}}{d}"," ",0,"-((a^2 + b^2)/(b^4*tan(d*x + c) + a*b^3) + 2*a*log(b*tan(d*x + c) + a)/b^3 - tan(d*x + c)/b^2)/d","A",0
129,1,471,0,0.437928," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(6 \, a^{3} + 2 \, a b^{2} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(9 \, a^{2} b + 2 \, b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{6 \, {\left(2 \, a^{3} + a b^{2}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, {\left(3 \, a^{2} b + b^{3}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{{\left(3 \, a^{2} b + 2 \, b^{3}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{2} b^{3} + \frac{2 \, a b^{4} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, a^{2} b^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, a b^{4} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, a^{2} b^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{2 \, a b^{4} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{a^{2} b^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{6 \, \sqrt{a^{2} + b^{2}} a \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{b^{4}} - \frac{3 \, {\left(2 \, a^{2} + b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{4}} + \frac{3 \, {\left(2 \, a^{2} + b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{4}}}{2 \, d}"," ",0,"-1/2*(2*(6*a^3 + 2*a*b^2 + 6*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (9*a^2*b + 2*b^3)*sin(d*x + c)/(cos(d*x + c) + 1) - 6*(2*a^3 + a*b^2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*(3*a^2*b + b^3)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + (3*a^2*b + 2*b^3)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^2*b^3 + 2*a*b^4*sin(d*x + c)/(cos(d*x + c) + 1) - 3*a^2*b^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*a*b^4*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*a^2*b^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 2*a*b^4*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - a^2*b^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 6*sqrt(a^2 + b^2)*a*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/b^4 - 3*(2*a^2 + b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^4 + 3*(2*a^2 + b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^4)/d","B",0
130,1,115,0,0.329660," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}{b^{6} \tan\left(d x + c\right) + a b^{5}} - \frac{b^{2} \tan\left(d x + c\right)^{3} - 3 \, a b \tan\left(d x + c\right)^{2} + 3 \, {\left(3 \, a^{2} + 2 \, b^{2}\right)} \tan\left(d x + c\right)}{b^{4}} + \frac{12 \, {\left(a^{3} + a b^{2}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{b^{5}}}{3 \, d}"," ",0,"-1/3*(3*(a^4 + 2*a^2*b^2 + b^4)/(b^6*tan(d*x + c) + a*b^5) - (b^2*tan(d*x + c)^3 - 3*a*b*tan(d*x + c)^2 + 3*(3*a^2 + 2*b^2)*tan(d*x + c))/b^4 + 12*(a^3 + a*b^2)*log(b*tan(d*x + c) + a)/b^5)/d","A",0
131,1,658,0,0.442728," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(4 \, a^{2} b^{2} - b^{4}\right)} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(6 \, a^{6} b - 10 \, a^{4} b^{3} - a^{2} b^{5} + \frac{{\left(2 \, a^{7} + 18 \, a^{5} b^{2} - 31 \, a^{3} b^{4} - 2 \, a b^{6}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, {\left(2 \, a^{6} b - 2 \, a^{4} b^{3} + 12 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, {\left(2 \, a^{7} + 2 \, a^{5} b^{2} + 15 \, a^{3} b^{4}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{{\left(2 \, a^{6} b - 30 \, a^{4} b^{3} + 15 \, a^{2} b^{5} + 2 \, b^{7}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(2 \, a^{7} - 6 \, a^{5} b^{2} + 9 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{10} + 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} + a^{4} b^{6} + \frac{4 \, {\left(a^{9} b + 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} + a^{3} b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{{\left(a^{10} - a^{8} b^{2} - 9 \, a^{6} b^{4} - 11 \, a^{4} b^{6} - 4 \, a^{2} b^{8}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{{\left(a^{10} - a^{8} b^{2} - 9 \, a^{6} b^{4} - 11 \, a^{4} b^{6} - 4 \, a^{2} b^{8}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, {\left(a^{9} b + 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} + a^{3} b^{7}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{{\left(a^{10} + 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} + a^{4} b^{6}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}}}{2 \, d}"," ",0,"-1/2*(3*(4*a^2*b^2 - b^4)*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a^2 + b^2)) - 2*(6*a^6*b - 10*a^4*b^3 - a^2*b^5 + (2*a^7 + 18*a^5*b^2 - 31*a^3*b^4 - 2*a*b^6)*sin(d*x + c)/(cos(d*x + c) + 1) - 2*(2*a^6*b - 2*a^4*b^3 + 12*a^2*b^5 + b^7)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*(2*a^7 + 2*a^5*b^2 + 15*a^3*b^4)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - (2*a^6*b - 30*a^4*b^3 + 15*a^2*b^5 + 2*b^7)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (2*a^7 - 6*a^5*b^2 + 9*a^3*b^4 + 2*a*b^6)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^10 + 3*a^8*b^2 + 3*a^6*b^4 + a^4*b^6 + 4*(a^9*b + 3*a^7*b^3 + 3*a^5*b^5 + a^3*b^7)*sin(d*x + c)/(cos(d*x + c) + 1) - (a^10 - a^8*b^2 - 9*a^6*b^4 - 11*a^4*b^6 - 4*a^2*b^8)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - (a^10 - a^8*b^2 - 9*a^6*b^4 - 11*a^4*b^6 - 4*a^2*b^8)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*(a^9*b + 3*a^7*b^3 + 3*a^5*b^5 + a^3*b^7)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + (a^10 + 3*a^8*b^2 + 3*a^6*b^4 + a^4*b^6)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6))/d","B",0
132,1,481,0,0.463744," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(3 \, a^{2} b - b^{3}\right)} \log\left(-a - \frac{2 \, b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(3 \, a^{2} b - b^{3}\right)} \log\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(\frac{{\left(3 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{{\left(5 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{{\left(3 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4} + \frac{4 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, {\left(a^{8} - 3 \, a^{4} b^{4} - 2 \, a^{2} b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{{\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}}{d}"," ",0,"(2*(a^3 - 3*a*b^2)*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (3*a^2*b - b^3)*log(-a - 2*b*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (3*a^2*b - b^3)*log(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*((3*a^3*b^2 + a*b^4)*sin(d*x + c)/(cos(d*x + c) + 1) + (5*a^2*b^3 + b^5)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - (3*a^3*b^2 + a*b^4)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^8 + 2*a^6*b^2 + a^4*b^4 + 4*(a^7*b + 2*a^5*b^3 + a^3*b^5)*sin(d*x + c)/(cos(d*x + c) + 1) - 2*(a^8 - 3*a^4*b^4 - 2*a^2*b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*(a^7*b + 2*a^5*b^3 + a^3*b^5)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + (a^8 + 2*a^6*b^2 + a^4*b^4)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4))/d","B",0
133,1,412,0,0.436925," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(2 \, a^{2} - b^{2}\right)} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} + \frac{2 \, {\left(4 \, a^{4} b + a^{2} b^{3} + \frac{{\left(11 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{{\left(4 \, a^{4} b - 7 \, a^{2} b^{3} - 2 \, b^{5}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{{\left(5 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4} + \frac{4 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, {\left(a^{8} - 3 \, a^{4} b^{4} - 2 \, a^{2} b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{{\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}}{2 \, d}"," ",0,"-1/2*((2*a^2 - b^2)*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) + 2*(4*a^4*b + a^2*b^3 + (11*a^3*b^2 + 2*a*b^4)*sin(d*x + c)/(cos(d*x + c) + 1) - (4*a^4*b - 7*a^2*b^3 - 2*b^5)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - (5*a^3*b^2 + 2*a*b^4)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^8 + 2*a^6*b^2 + a^4*b^4 + 4*(a^7*b + 2*a^5*b^3 + a^3*b^5)*sin(d*x + c)/(cos(d*x + c) + 1) - 2*(a^8 - 3*a^4*b^4 - 2*a^2*b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*(a^7*b + 2*a^5*b^3 + a^3*b^5)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + (a^8 + 2*a^6*b^2 + a^4*b^4)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4))/d","B",0
134,1,171,0,0.356192," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{b \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{{\left(a^{4} + \frac{4 \, a^{3} b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 \, a^{3} b \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{2 \, {\left(a^{4} - 2 \, a^{2} b^{2}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} d}"," ",0,"2*(a*sin(d*x + c)/(cos(d*x + c) + 1) + b*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/((a^4 + 4*a^3*b*sin(d*x + c)/(cos(d*x + c) + 1) - 4*a^3*b*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 2*(a^4 - 2*a^2*b^2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*d)","B",0
135,1,326,0,0.455144," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(a^{2} b - \frac{{\left(a^{3} - 2 \, a b^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{{\left(a^{2} b - 2 \, b^{3}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{{\left(a^{3} + 2 \, a b^{2}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{6} + a^{4} b^{2} + \frac{4 \, {\left(a^{5} b + a^{3} b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, {\left(a^{6} - a^{4} b^{2} - 2 \, a^{2} b^{4}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, {\left(a^{5} b + a^{3} b^{3}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{{\left(a^{6} + a^{4} b^{2}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}}}{2 \, d}"," ",0,"-1/2*(2*(a^2*b - (a^3 - 2*a*b^2)*sin(d*x + c)/(cos(d*x + c) + 1) - (a^2*b - 2*b^3)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - (a^3 + 2*a*b^2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^6 + a^4*b^2 + 4*(a^5*b + a^3*b^3)*sin(d*x + c)/(cos(d*x + c) + 1) - 2*(a^6 - a^4*b^2 - 2*a^2*b^4)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*(a^5*b + a^3*b^3)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + (a^6 + a^4*b^2)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2))/d","B",0
136,1,315,0,0.337883," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(\frac{{\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{{\left(3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{{\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{4} b^{2} + \frac{4 \, a^{3} b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 \, a^{3} b^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{a^{4} b^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{2 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}} - \frac{\log\left(-a - \frac{2 \, b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{b^{3}} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{3}} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{3}}}{d}"," ",0,"-(2*((a^3 - a*b^2)*sin(d*x + c)/(cos(d*x + c) + 1) + (3*a^2*b - b^3)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - (a^3 - a*b^2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^4*b^2 + 4*a^3*b^3*sin(d*x + c)/(cos(d*x + c) + 1) - 4*a^3*b^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + a^4*b^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 2*(a^4*b^2 - 2*a^2*b^4)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2) - log(-a - 2*b*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/b^3 + log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^3 + log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^3)/d","B",0
137,1,518,0,0.456833," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(6 \, a^{4} - a^{2} b^{2} + \frac{{\left(21 \, a^{3} b - 2 \, a b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, {\left(6 \, a^{4} - 9 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, {\left(6 \, a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{{\left(6 \, a^{4} - 9 \, a^{2} b^{2} + 2 \, b^{4}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(3 \, a^{3} b - 2 \, a b^{3}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{4} b^{3} + \frac{4 \, a^{3} b^{4} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{8 \, a^{3} b^{4} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{4 \, a^{3} b^{4} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{a^{4} b^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{{\left(3 \, a^{4} b^{3} - 4 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{{\left(3 \, a^{4} b^{3} - 4 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{6 \, a \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{4}} + \frac{6 \, a \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{4}} - \frac{3 \, {\left(2 \, a^{2} + b^{2}\right)} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} b^{4}}}{2 \, d}"," ",0,"1/2*(2*(6*a^4 - a^2*b^2 + (21*a^3*b - 2*a*b^3)*sin(d*x + c)/(cos(d*x + c) + 1) - 2*(6*a^4 - 9*a^2*b^2 + b^4)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*(6*a^3*b - a*b^3)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + (6*a^4 - 9*a^2*b^2 + 2*b^4)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (3*a^3*b - 2*a*b^3)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^4*b^3 + 4*a^3*b^4*sin(d*x + c)/(cos(d*x + c) + 1) - 8*a^3*b^4*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 4*a^3*b^4*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - a^4*b^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - (3*a^4*b^3 - 4*a^2*b^5)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + (3*a^4*b^3 - 4*a^2*b^5)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 6*a*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^4 + 6*a*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^4 - 3*(2*a^2 + b^2)*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^4))/d","B",0
138,1,652,0,0.373293," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{\frac{{\left(6 \, a^{5} + 2 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{{\left(18 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{{\left(18 \, a^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{2 \, {\left(18 \, a^{4} b + 8 \, a^{2} b^{3} - b^{5}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(18 \, a^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{{\left(18 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{{\left(6 \, a^{5} + 2 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4} b^{4} + \frac{4 \, a^{3} b^{5} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{12 \, a^{3} b^{5} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{12 \, a^{3} b^{5} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{4 \, a^{3} b^{5} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{a^{4} b^{4} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{4 \, {\left(a^{4} b^{4} - a^{2} b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, {\left(3 \, a^{4} b^{4} - 4 \, a^{2} b^{6}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, {\left(a^{4} b^{4} - a^{2} b^{6}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{{\left(3 \, a^{2} + b^{2}\right)} \log\left(-a - \frac{2 \, b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{b^{5}} + \frac{{\left(3 \, a^{2} + b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{5}} + \frac{{\left(3 \, a^{2} + b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{5}}\right)}}{d}"," ",0,"-2*(((6*a^5 + 2*a^3*b^2 - a*b^4)*sin(d*x + c)/(cos(d*x + c) + 1) + (18*a^4*b + 6*a^2*b^3 - b^5)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - (18*a^5 - 2*a^3*b^2 - 3*a*b^4)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 2*(18*a^4*b + 8*a^2*b^3 - b^5)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (18*a^5 - 2*a^3*b^2 - 3*a*b^4)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + (18*a^4*b + 6*a^2*b^3 - b^5)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - (6*a^5 + 2*a^3*b^2 - a*b^4)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a^4*b^4 + 4*a^3*b^5*sin(d*x + c)/(cos(d*x + c) + 1) - 12*a^3*b^5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 12*a^3*b^5*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 4*a^3*b^5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + a^4*b^4*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 4*(a^4*b^4 - a^2*b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*(3*a^4*b^4 - 4*a^2*b^6)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*(a^4*b^4 - a^2*b^6)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - (3*a^2 + b^2)*log(-a - 2*b*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/b^5 + (3*a^2 + b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^5 + (3*a^2 + b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^5)/d","B",0
139,1,902,0,0.523414," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(60 \, a^{6} + 35 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + \frac{{\left(210 \, a^{5} b + 125 \, a^{3} b^{3} - 6 \, a b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, {\left(120 \, a^{6} - 10 \, a^{4} b^{2} - 55 \, a^{2} b^{4} + 3 \, b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, {\left(330 \, a^{5} b + 205 \, a^{3} b^{3} - 12 \, a b^{5}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2 \, {\left(180 \, a^{6} - 95 \, a^{4} b^{2} - 120 \, a^{2} b^{4} + 9 \, b^{6}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{12 \, {\left(60 \, a^{5} b + 35 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{6 \, {\left(40 \, a^{6} - 30 \, a^{4} b^{2} - 35 \, a^{2} b^{4} + 3 \, b^{6}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{6 \, {\left(50 \, a^{5} b + 25 \, a^{3} b^{3} - 4 \, a b^{5}\right)} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{3 \, {\left(20 \, a^{6} - 15 \, a^{4} b^{2} - 15 \, a^{2} b^{4} + 2 \, b^{6}\right)} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{3 \, {\left(10 \, a^{5} b + 5 \, a^{3} b^{3} - 2 \, a b^{5}\right)} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)}}{a^{4} b^{5} + \frac{4 \, a^{3} b^{6} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{16 \, a^{3} b^{6} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{24 \, a^{3} b^{6} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{16 \, a^{3} b^{6} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{4 \, a^{3} b^{6} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{a^{4} b^{5} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{{\left(5 \, a^{4} b^{5} - 4 \, a^{2} b^{7}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, {\left(5 \, a^{4} b^{5} - 6 \, a^{2} b^{7}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{2 \, {\left(5 \, a^{4} b^{5} - 6 \, a^{2} b^{7}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{{\left(5 \, a^{4} b^{5} - 4 \, a^{2} b^{7}\right)} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{15 \, {\left(4 \, a^{3} + 3 \, a b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{6}} + \frac{15 \, {\left(4 \, a^{3} + 3 \, a b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{6}} - \frac{15 \, {\left(4 \, a^{4} + 5 \, a^{2} b^{2} + b^{4}\right)} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} b^{6}}}{6 \, d}"," ",0,"1/6*(2*(60*a^6 + 35*a^4*b^2 - 3*a^2*b^4 + (210*a^5*b + 125*a^3*b^3 - 6*a*b^5)*sin(d*x + c)/(cos(d*x + c) + 1) - 2*(120*a^6 - 10*a^4*b^2 - 55*a^2*b^4 + 3*b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*(330*a^5*b + 205*a^3*b^3 - 12*a*b^5)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2*(180*a^6 - 95*a^4*b^2 - 120*a^2*b^4 + 9*b^6)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 12*(60*a^5*b + 35*a^3*b^3 - 3*a*b^5)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 6*(40*a^6 - 30*a^4*b^2 - 35*a^2*b^4 + 3*b^6)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 6*(50*a^5*b + 25*a^3*b^3 - 4*a*b^5)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 3*(20*a^6 - 15*a^4*b^2 - 15*a^2*b^4 + 2*b^6)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 3*(10*a^5*b + 5*a^3*b^3 - 2*a*b^5)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/(a^4*b^5 + 4*a^3*b^6*sin(d*x + c)/(cos(d*x + c) + 1) - 16*a^3*b^6*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 24*a^3*b^6*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 16*a^3*b^6*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 4*a^3*b^6*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - a^4*b^5*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - (5*a^4*b^5 - 4*a^2*b^7)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*(5*a^4*b^5 - 6*a^2*b^7)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 2*(5*a^4*b^5 - 6*a^2*b^7)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + (5*a^4*b^5 - 4*a^2*b^7)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 15*(4*a^3 + 3*a*b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^6 + 15*(4*a^3 + 3*a*b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^6 - 15*(4*a^4 + 5*a^2*b^2 + b^4)*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^6))/d","B",0
140,1,1053,0,0.389370," ","integrate(sec(d*x+c)^5/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(\frac{{\left(15 \, a^{7} + 18 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{{\left(45 \, a^{6} b + 54 \, a^{4} b^{3} + 9 \, a^{2} b^{5} - b^{7}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{{\left(75 \, a^{7} + 70 \, a^{5} b^{2} - 9 \, a^{3} b^{4} - 5 \, a b^{6}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{2 \, {\left(90 \, a^{6} b + 113 \, a^{4} b^{3} + 24 \, a^{2} b^{5} - 2 \, b^{7}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{2 \, {\left(75 \, a^{7} + 60 \, a^{5} b^{2} - 17 \, a^{3} b^{4} - 5 \, a b^{6}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2 \, {\left(135 \, a^{6} b + 172 \, a^{4} b^{3} + 35 \, a^{2} b^{5} - 3 \, b^{7}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{2 \, {\left(75 \, a^{7} + 60 \, a^{5} b^{2} - 17 \, a^{3} b^{4} - 5 \, a b^{6}\right)} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{2 \, {\left(90 \, a^{6} b + 113 \, a^{4} b^{3} + 24 \, a^{2} b^{5} - 2 \, b^{7}\right)} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{{\left(75 \, a^{7} + 70 \, a^{5} b^{2} - 9 \, a^{3} b^{4} - 5 \, a b^{6}\right)} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{{\left(45 \, a^{6} b + 54 \, a^{4} b^{3} + 9 \, a^{2} b^{5} - b^{7}\right)} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{{\left(15 \, a^{7} + 18 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)}}{a^{4} b^{6} + \frac{4 \, a^{3} b^{7} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, a^{3} b^{7} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{40 \, a^{3} b^{7} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{40 \, a^{3} b^{7} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{20 \, a^{3} b^{7} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{4 \, a^{3} b^{7} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{a^{4} b^{6} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{2 \, {\left(3 \, a^{4} b^{6} - 2 \, a^{2} b^{8}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{{\left(15 \, a^{4} b^{6} - 16 \, a^{2} b^{8}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, {\left(5 \, a^{4} b^{6} - 6 \, a^{2} b^{8}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{{\left(15 \, a^{4} b^{6} - 16 \, a^{2} b^{8}\right)} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{2 \, {\left(3 \, a^{4} b^{6} - 2 \, a^{2} b^{8}\right)} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} - \frac{3 \, {\left(5 \, a^{4} + 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(-a - \frac{2 \, b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{b^{7}} + \frac{3 \, {\left(5 \, a^{4} + 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{7}} + \frac{3 \, {\left(5 \, a^{4} + 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{7}}}{d}"," ",0,"-(2*((15*a^7 + 18*a^5*b^2 + 3*a^3*b^4 - a*b^6)*sin(d*x + c)/(cos(d*x + c) + 1) + (45*a^6*b + 54*a^4*b^3 + 9*a^2*b^5 - b^7)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - (75*a^7 + 70*a^5*b^2 - 9*a^3*b^4 - 5*a*b^6)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 2*(90*a^6*b + 113*a^4*b^3 + 24*a^2*b^5 - 2*b^7)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 2*(75*a^7 + 60*a^5*b^2 - 17*a^3*b^4 - 5*a*b^6)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2*(135*a^6*b + 172*a^4*b^3 + 35*a^2*b^5 - 3*b^7)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 2*(75*a^7 + 60*a^5*b^2 - 17*a^3*b^4 - 5*a*b^6)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 2*(90*a^6*b + 113*a^4*b^3 + 24*a^2*b^5 - 2*b^7)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + (75*a^7 + 70*a^5*b^2 - 9*a^3*b^4 - 5*a*b^6)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + (45*a^6*b + 54*a^4*b^3 + 9*a^2*b^5 - b^7)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - (15*a^7 + 18*a^5*b^2 + 3*a^3*b^4 - a*b^6)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)/(a^4*b^6 + 4*a^3*b^7*sin(d*x + c)/(cos(d*x + c) + 1) - 20*a^3*b^7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 40*a^3*b^7*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 40*a^3*b^7*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 20*a^3*b^7*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 4*a^3*b^7*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + a^4*b^6*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 2*(3*a^4*b^6 - 2*a^2*b^8)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + (15*a^4*b^6 - 16*a^2*b^8)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*(5*a^4*b^6 - 6*a^2*b^8)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + (15*a^4*b^6 - 16*a^2*b^8)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 2*(3*a^4*b^6 - 2*a^2*b^8)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) - 3*(5*a^4 + 6*a^2*b^2 + b^4)*log(-a - 2*b*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/b^7 + 3*(5*a^4 + 6*a^2*b^2 + b^4)*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^7 + 3*(5*a^4 + 6*a^2*b^2 + b^4)*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^7)/d","B",0
141,1,385,0,0.430165," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{12 \, {\left(a^{3} b - a b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{6 \, {\left(a^{3} b - a b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{13 \, a^{4} b + 2 \, a^{2} b^{3} + b^{5} + 3 \, {\left(3 \, a^{2} b^{3} - b^{5}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(7 \, a^{3} b^{2} - a b^{4}\right)} \tan\left(d x + c\right)}{a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6} + {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} \tan\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)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{8} b + 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} + a^{2} b^{7}\right)} \tan\left(d x + c\right)}}{3 \, d}"," ",0,"1/3*(3*(a^4 - 6*a^2*b^2 + b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 12*(a^3*b - a*b^3)*log(b*tan(d*x + c) + a)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 6*(a^3*b - a*b^3)*log(tan(d*x + c)^2 + 1)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - (13*a^4*b + 2*a^2*b^3 + b^5 + 3*(3*a^2*b^3 - b^5)*tan(d*x + c)^2 + 3*(7*a^3*b^2 - a*b^4)*tan(d*x + c))/(a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6 + (a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*tan(d*x + c)^3 + 3*(a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*tan(d*x + c)^2 + 3*(a^8*b + 3*a^6*b^3 + 3*a^4*b^5 + a^2*b^7)*tan(d*x + c)))/d","B",0
142,1,724,0,0.445149," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(2 \, a^{2} - 3 \, b^{2}\right)} a \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} + b^{2}}} + \frac{2 \, {\left(18 \, a^{7} b + 5 \, a^{5} b^{3} + 2 \, a^{3} b^{5} + \frac{3 \, {\left(27 \, a^{6} b^{2} + 4 \, a^{4} b^{4} + 2 \, a^{2} b^{6}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{6 \, {\left(6 \, a^{7} b - 20 \, a^{5} b^{3} - 3 \, a^{3} b^{5} - 2 \, a b^{7}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, {\left(54 \, a^{6} b^{2} - 21 \, a^{4} b^{4} - 4 \, a^{2} b^{6} - 4 \, b^{8}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, {\left(6 \, a^{7} b - 27 \, a^{5} b^{3} - 12 \, a^{3} b^{5} - 4 \, a b^{7}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{3 \, {\left(9 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 2 \, a^{2} b^{6}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{12} + 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} + a^{6} b^{6} + \frac{6 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, {\left(a^{12} - a^{10} b^{2} - 9 \, a^{8} b^{4} - 11 \, a^{6} b^{6} - 4 \, a^{4} b^{8}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, {\left(3 \, a^{11} b + 7 \, a^{9} b^{3} + 3 \, a^{7} b^{5} - 3 \, a^{5} b^{7} - 2 \, a^{3} b^{9}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, {\left(a^{12} - a^{10} b^{2} - 9 \, a^{8} b^{4} - 11 \, a^{6} b^{6} - 4 \, a^{4} b^{8}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{6 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{{\left(a^{12} + 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} + a^{6} b^{6}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}}}{6 \, d}"," ",0,"-1/6*(3*(2*a^2 - 3*b^2)*a*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a^2 + b^2)) + 2*(18*a^7*b + 5*a^5*b^3 + 2*a^3*b^5 + 3*(27*a^6*b^2 + 4*a^4*b^4 + 2*a^2*b^6)*sin(d*x + c)/(cos(d*x + c) + 1) - 6*(6*a^7*b - 20*a^5*b^3 - 3*a^3*b^5 - 2*a*b^7)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*(54*a^6*b^2 - 21*a^4*b^4 - 4*a^2*b^6 - 4*b^8)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*(6*a^7*b - 27*a^5*b^3 - 12*a^3*b^5 - 4*a*b^7)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3*(9*a^6*b^2 + 6*a^4*b^4 + 2*a^2*b^6)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^12 + 3*a^10*b^2 + 3*a^8*b^4 + a^6*b^6 + 6*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*sin(d*x + c)/(cos(d*x + c) + 1) - 3*(a^12 - a^10*b^2 - 9*a^8*b^4 - 11*a^6*b^6 - 4*a^4*b^8)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*(3*a^11*b + 7*a^9*b^3 + 3*a^7*b^5 - 3*a^5*b^7 - 2*a^3*b^9)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*(a^12 - a^10*b^2 - 9*a^8*b^4 - 11*a^6*b^6 - 4*a^4*b^8)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 6*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - (a^12 + 3*a^10*b^2 + 3*a^8*b^4 + a^6*b^6)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6))/d","B",0
143,1,53,0,0.339387," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{1}{3 \, {\left(b^{4} \tan\left(d x + c\right)^{3} + 3 \, a b^{3} \tan\left(d x + c\right)^{2} + 3 \, a^{2} b^{2} \tan\left(d x + c\right) + a^{3} b\right)} d}"," ",0,"-1/3/((b^4*tan(d*x + c)^3 + 3*a*b^3*tan(d*x + c)^2 + 3*a^2*b^2*tan(d*x + c) + a^3*b)*d)","A",0
144,1,606,0,0.445648," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{3 \, a \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} + \frac{2 \, {\left(5 \, a^{5} b + 2 \, a^{3} b^{3} - \frac{3 \, {\left(a^{6} - 6 \, a^{4} b^{2} - 2 \, a^{2} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{6 \, {\left(2 \, a^{5} b - 5 \, a^{3} b^{3} - 2 \, a b^{5}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, {\left(15 \, a^{4} b^{2} - 4 \, a^{2} b^{4} - 4 \, b^{6}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, {\left(a^{5} b - 8 \, a^{3} b^{3} - 4 \, a b^{5}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{3 \, {\left(a^{6} + 4 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{10} + 2 \, a^{8} b^{2} + a^{6} b^{4} + \frac{6 \, {\left(a^{9} b + 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, {\left(a^{10} - 2 \, a^{8} b^{2} - 7 \, a^{6} b^{4} - 4 \, a^{4} b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, {\left(3 \, a^{9} b + 4 \, a^{7} b^{3} - a^{5} b^{5} - 2 \, a^{3} b^{7}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, {\left(a^{10} - 2 \, a^{8} b^{2} - 7 \, a^{6} b^{4} - 4 \, a^{4} b^{6}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{6 \, {\left(a^{9} b + 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{{\left(a^{10} + 2 \, a^{8} b^{2} + a^{6} b^{4}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}}}{6 \, d}"," ",0,"-1/6*(3*a*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) + 2*(5*a^5*b + 2*a^3*b^3 - 3*(a^6 - 6*a^4*b^2 - 2*a^2*b^4)*sin(d*x + c)/(cos(d*x + c) + 1) - 6*(2*a^5*b - 5*a^3*b^3 - 2*a*b^5)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*(15*a^4*b^2 - 4*a^2*b^4 - 4*b^6)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*(a^5*b - 8*a^3*b^3 - 4*a*b^5)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3*(a^6 + 4*a^4*b^2 + 2*a^2*b^4)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^10 + 2*a^8*b^2 + a^6*b^4 + 6*(a^9*b + 2*a^7*b^3 + a^5*b^5)*sin(d*x + c)/(cos(d*x + c) + 1) - 3*(a^10 - 2*a^8*b^2 - 7*a^6*b^4 - 4*a^4*b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*(3*a^9*b + 4*a^7*b^3 - a^5*b^5 - 2*a^3*b^7)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*(a^10 - 2*a^8*b^2 - 7*a^6*b^4 - 4*a^4*b^6)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 6*(a^9*b + 2*a^7*b^3 + a^5*b^5)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - (a^10 + 2*a^8*b^2 + a^6*b^4)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6))/d","B",0
145,1,85,0,0.345086," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{3 \, b^{2} \tan\left(d x + c\right)^{2} + 3 \, a b \tan\left(d x + c\right) + a^{2} + b^{2}}{3 \, {\left(b^{6} \tan\left(d x + c\right)^{3} + 3 \, a b^{5} \tan\left(d x + c\right)^{2} + 3 \, a^{2} b^{4} \tan\left(d x + c\right) + a^{3} b^{3}\right)} d}"," ",0,"-1/3*(3*b^2*tan(d*x + c)^2 + 3*a*b*tan(d*x + c) + a^2 + b^2)/((b^6*tan(d*x + c)^3 + 3*a*b^5*tan(d*x + c)^2 + 3*a^2*b^4*tan(d*x + c) + a^3*b^3)*d)","A",0
146,1,661,0,0.469099," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(2 \, a^{2} + 3 \, b^{2}\right)} a \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(6 \, a^{7} + 5 \, a^{5} b^{2} + 2 \, a^{3} b^{4} + \frac{3 \, {\left(11 \, a^{6} b + 8 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{6 \, {\left(2 \, a^{7} - 8 \, a^{5} b^{2} - 7 \, a^{3} b^{4} - 2 \, a b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, {\left(18 \, a^{6} b + 3 \, a^{4} b^{3} - 4 \, a^{2} b^{5} - 4 \, b^{7}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, {\left(2 \, a^{7} - 3 \, a^{5} b^{2} - 4 \, a^{3} b^{4} - 4 \, a b^{6}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{3 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{8} b^{3} + a^{6} b^{5} + \frac{6 \, {\left(a^{7} b^{4} + a^{5} b^{6}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, {\left(a^{8} b^{3} - 3 \, a^{6} b^{5} - 4 \, a^{4} b^{7}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, {\left(3 \, a^{7} b^{4} + a^{5} b^{6} - 2 \, a^{3} b^{8}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, {\left(a^{8} b^{3} - 3 \, a^{6} b^{5} - 4 \, a^{4} b^{7}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{6 \, {\left(a^{7} b^{4} + a^{5} b^{6}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{{\left(a^{8} b^{3} + a^{6} b^{5}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{4}} - \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{4}}}{6 \, d}"," ",0,"1/6*(3*(2*a^2 + 3*b^2)*a*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/((a^2*b^4 + b^6)*sqrt(a^2 + b^2)) - 2*(6*a^7 + 5*a^5*b^2 + 2*a^3*b^4 + 3*(11*a^6*b + 8*a^4*b^3 + 2*a^2*b^5)*sin(d*x + c)/(cos(d*x + c) + 1) - 6*(2*a^7 - 8*a^5*b^2 - 7*a^3*b^4 - 2*a*b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*(18*a^6*b + 3*a^4*b^3 - 4*a^2*b^5 - 4*b^7)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*(2*a^7 - 3*a^5*b^2 - 4*a^3*b^4 - 4*a*b^6)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3*(a^6*b + 2*a^4*b^3 + 2*a^2*b^5)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^8*b^3 + a^6*b^5 + 6*(a^7*b^4 + a^5*b^6)*sin(d*x + c)/(cos(d*x + c) + 1) - 3*(a^8*b^3 - 3*a^6*b^5 - 4*a^4*b^7)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*(3*a^7*b^4 + a^5*b^6 - 2*a^3*b^8)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*(a^8*b^3 - 3*a^6*b^5 - 4*a^4*b^7)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 6*(a^7*b^4 + a^5*b^6)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - (a^8*b^3 + a^6*b^5)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + 6*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^4 - 6*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^4)/d","B",0
147,1,144,0,0.407662," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{13 \, a^{4} + 2 \, a^{2} b^{2} + b^{4} + 6 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)^{2} + 6 \, {\left(5 \, a^{3} b + a b^{3}\right)} \tan\left(d x + c\right)}{b^{8} \tan\left(d x + c\right)^{3} + 3 \, a b^{7} \tan\left(d x + c\right)^{2} + 3 \, a^{2} b^{6} \tan\left(d x + c\right) + a^{3} b^{5}} + \frac{12 \, a \log\left(b \tan\left(d x + c\right) + a\right)}{b^{5}} - \frac{3 \, \tan\left(d x + c\right)}{b^{4}}}{3 \, d}"," ",0,"-1/3*((13*a^4 + 2*a^2*b^2 + b^4 + 6*(3*a^2*b^2 + b^4)*tan(d*x + c)^2 + 6*(5*a^3*b + a*b^3)*tan(d*x + c))/(b^8*tan(d*x + c)^3 + 3*a*b^7*tan(d*x + c)^2 + 3*a^2*b^6*tan(d*x + c) + a^3*b^5) + 12*a*log(b*tan(d*x + c) + a)/b^5 - 3*tan(d*x + c)/b^4)/d","A",0
148,1,936,0,0.484326," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(60 \, a^{7} + 5 \, a^{5} b^{2} + 2 \, a^{3} b^{4} + \frac{6 \, {\left(55 \, a^{6} b + 5 \, a^{4} b^{3} + a^{2} b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, {\left(120 \, a^{7} - 280 \, a^{5} b^{2} - 25 \, a^{3} b^{4} - 6 \, a b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, {\left(510 \, a^{6} b - 105 \, a^{4} b^{3} + 2 \, a^{2} b^{5} - 4 \, b^{7}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2 \, {\left(180 \, a^{7} - 635 \, a^{5} b^{2} - 65 \, a^{3} b^{4} - 18 \, a b^{6}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{2 \, {\left(540 \, a^{6} b - 195 \, a^{4} b^{3} - 2 \, a^{2} b^{5} - 8 \, b^{7}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{6 \, {\left(40 \, a^{7} - 140 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 6 \, a b^{6}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{2 \, {\left(210 \, a^{6} b - 75 \, a^{4} b^{3} + 2 \, a^{2} b^{5} - 4 \, b^{7}\right)} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{3 \, {\left(20 \, a^{7} - 45 \, a^{5} b^{2} - 4 \, a b^{6}\right)} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{6 \, {\left(5 \, a^{6} b + a^{2} b^{5}\right)} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)}}{a^{6} b^{5} + \frac{6 \, a^{5} b^{6} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{6 \, a^{5} b^{6} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{a^{6} b^{5} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{{\left(5 \, a^{6} b^{5} - 12 \, a^{4} b^{7}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, {\left(3 \, a^{5} b^{6} - a^{3} b^{8}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2 \, {\left(5 \, a^{6} b^{5} - 18 \, a^{4} b^{7}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, {\left(9 \, a^{5} b^{6} - 4 \, a^{3} b^{8}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{2 \, {\left(5 \, a^{6} b^{5} - 18 \, a^{4} b^{7}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{8 \, {\left(3 \, a^{5} b^{6} - a^{3} b^{8}\right)} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{{\left(5 \, a^{6} b^{5} - 12 \, a^{4} b^{7}\right)} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{15 \, {\left(4 \, a^{2} + 3 \, b^{2}\right)} a \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} b^{6}} - \frac{15 \, {\left(4 \, a^{2} + b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{6}} + \frac{15 \, {\left(4 \, a^{2} + b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{6}}}{6 \, d}"," ",0,"-1/6*(2*(60*a^7 + 5*a^5*b^2 + 2*a^3*b^4 + 6*(55*a^6*b + 5*a^4*b^3 + a^2*b^5)*sin(d*x + c)/(cos(d*x + c) + 1) - 2*(120*a^7 - 280*a^5*b^2 - 25*a^3*b^4 - 6*a*b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*(510*a^6*b - 105*a^4*b^3 + 2*a^2*b^5 - 4*b^7)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2*(180*a^7 - 635*a^5*b^2 - 65*a^3*b^4 - 18*a*b^6)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 2*(540*a^6*b - 195*a^4*b^3 - 2*a^2*b^5 - 8*b^7)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 6*(40*a^7 - 140*a^5*b^2 - 5*a^3*b^4 - 6*a*b^6)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 2*(210*a^6*b - 75*a^4*b^3 + 2*a^2*b^5 - 4*b^7)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 3*(20*a^7 - 45*a^5*b^2 - 4*a*b^6)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 6*(5*a^6*b + a^2*b^5)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/(a^6*b^5 + 6*a^5*b^6*sin(d*x + c)/(cos(d*x + c) + 1) + 6*a^5*b^6*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - a^6*b^5*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - (5*a^6*b^5 - 12*a^4*b^7)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8*(3*a^5*b^6 - a^3*b^8)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2*(5*a^6*b^5 - 18*a^4*b^7)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*(9*a^5*b^6 - 4*a^3*b^8)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 2*(5*a^6*b^5 - 18*a^4*b^7)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 8*(3*a^5*b^6 - a^3*b^8)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + (5*a^6*b^5 - 12*a^4*b^7)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 15*(4*a^2 + 3*b^2)*a*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^6) - 15*(4*a^2 + b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^6 + 15*(4*a^2 + b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^6)/d","B",0
149,1,217,0,0.333775," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{37 \, a^{6} + 39 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + 9 \, {\left(5 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + b^{6}\right)} \tan\left(d x + c\right)^{2} + 9 \, {\left(9 \, a^{5} b + 10 \, a^{3} b^{3} + a b^{5}\right)} \tan\left(d x + c\right)}{b^{10} \tan\left(d x + c\right)^{3} + 3 \, a b^{9} \tan\left(d x + c\right)^{2} + 3 \, a^{2} b^{8} \tan\left(d x + c\right) + a^{3} b^{7}} - \frac{b^{2} \tan\left(d x + c\right)^{3} - 6 \, a b \tan\left(d x + c\right)^{2} + 3 \, {\left(10 \, a^{2} + 3 \, b^{2}\right)} \tan\left(d x + c\right)}{b^{6}} + \frac{12 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{b^{7}}}{3 \, d}"," ",0,"-1/3*((37*a^6 + 39*a^4*b^2 + 3*a^2*b^4 + b^6 + 9*(5*a^4*b^2 + 6*a^2*b^4 + b^6)*tan(d*x + c)^2 + 9*(9*a^5*b + 10*a^3*b^3 + a*b^5)*tan(d*x + c))/(b^10*tan(d*x + c)^3 + 3*a*b^9*tan(d*x + c)^2 + 3*a^2*b^8*tan(d*x + c) + a^3*b^7) - (b^2*tan(d*x + c)^3 - 6*a*b*tan(d*x + c)^2 + 3*(10*a^2 + 3*b^2)*tan(d*x + c))/b^6 + 12*(5*a^3 + 3*a*b^2)*log(b*tan(d*x + c) + a)/b^7)/d","A",0
150,-2,0,0,0.000000," ","integrate(cos(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
151,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
152,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
153,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
154,-2,0,0,0.000000," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
155,1,29,0,0.315981," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2}{{\left(-i \, a + \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)} d}"," ",0,"2/((-I*a + a*sin(d*x + c)/(cos(d*x + c) + 1))*d)","A",0
156,1,101,0,0.336499," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{-\frac{i \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{i \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{i \, \log\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}{a}}{d}"," ",0,"-(-I*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - I*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + I*log(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)/a)/d","B",0
157,1,83,0,0.417380," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{2}{-i \, a + \frac{i \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}}{d}"," ",0,"(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - 2/(-I*a + I*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2))/d","B",0
158,1,108,0,0.346396," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{i \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{{\left(a - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} d}"," ",0,"2*(sin(d*x + c)/(cos(d*x + c) + 1) - I*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/((a - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*d)","B",0
159,1,186,0,0.330984," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(\frac{3 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{3 i \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + 2\right)}}{6 i \, a - \frac{18 i \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{18 i \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{6 i \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a}}{2 \, d}"," ",0,"1/2*(4*(3*I*sin(d*x + c)/(cos(d*x + c) + 1) + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3*I*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2)/(6*I*a - 18*I*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 18*I*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 6*I*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a)/d","B",0
160,1,211,0,0.346409," ","integrate(sec(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 i \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3 i \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{3 \, {\left(a - \frac{4 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d}"," ",0,"2/3*(3*sin(d*x + c)/(cos(d*x + c) + 1) - 3*I*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3*I*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/((a - 4*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d)","B",0
161,1,289,0,0.352655," ","integrate(sec(d*x+c)^6/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{16 \, {\left(-\frac{75 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{30 i \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{240 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{30 i \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{120 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{75 i \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - 24\right)}}{-120 i \, a + \frac{600 i \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1200 i \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1200 i \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{600 i \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{120 i \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a}}{8 \, d}"," ",0,"1/8*(16*(-75*I*sin(d*x + c)/(cos(d*x + c) + 1) + 30*I*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 240*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 30*I*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 120*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 75*I*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 24)/(-120*I*a + 600*I*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1200*I*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1200*I*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 600*I*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 120*I*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a)/d","B",0
162,1,313,0,0.358098," ","integrate(sec(d*x+c)^7/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{15 i \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{78 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{50 i \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{78 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{35 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{15 i \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{15 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)}}{15 \, {\left(a - \frac{6 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{20 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{6 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}\right)} d}"," ",0,"2/15*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 15*I*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 78*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 50*I*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 78*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 35*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 15*I*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 15*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)/((a - 6*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 20*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 6*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12)*d)","B",0
163,-2,0,0,0.000000," ","integrate(cos(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
164,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
165,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
166,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
167,1,45,0,0.328337," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{i \, \cos\left(3 \, d x + 3 \, c\right) + 3 i \, \cos\left(d x + c\right) + \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(d x + c\right)}{6 \, a^{2} d}"," ",0,"1/6*(I*cos(3*d*x + 3*c) + 3*I*cos(d*x + c) + sin(3*d*x + 3*c) + 3*sin(d*x + c))/(a^2*d)","A",0
168,1,22,0,0.316174," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{{\left(a^{2} \tan\left(d x + c\right) - i \, a^{2}\right)} d}"," ",0,"1/((a^2*tan(d*x + c) - I*a^2)*d)","A",0
169,1,117,0,0.425135," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{-2 i \, \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) - 2 i \, \arctan\left(\cos\left(d x + c\right), -\sin\left(d x + c\right) + 1\right) - 4 i \, \cos\left(d x + c\right) + \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right) - 4 \, \sin\left(d x + c\right)}{2 \, a^{2} d}"," ",0,"-1/2*(-2*I*arctan2(cos(d*x + c), sin(d*x + c) + 1) - 2*I*arctan2(cos(d*x + c), -sin(d*x + c) + 1) - 4*I*cos(d*x + c) + log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) - 4*sin(d*x + c))/(a^2*d)","B",0
170,1,30,0,0.332831," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{-\frac{2 i \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{2}} - \frac{\tan\left(d x + c\right)}{a^{2}}}{d}"," ",0,"(-2*I*log(tan(d*x + c) - I)/a^2 - tan(d*x + c)/a^2)/d","A",0
171,1,167,0,0.333006," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 i \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + 4 i\right)}}{a^{2} - \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}}{2 \, d}"," ",0,"-1/2*(2*(sin(d*x + c)/(cos(d*x + c) + 1) - 4*I*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 4*I)/(a^2 - 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2)/d","B",0
172,1,35,0,0.514125," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\tan\left(d x + c\right)^{3} + 3 i \, \tan\left(d x + c\right)^{2} - 3 \, \tan\left(d x + c\right)}{3 \, a^{2} d}"," ",0,"-1/3*(tan(d*x + c)^3 + 3*I*tan(d*x + c)^2 - 3*tan(d*x + c))/(a^2*d)","A",0
173,1,295,0,0.343601," ","integrate(sec(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{16 i \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{33 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{48 i \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{33 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{48 i \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{9 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - 16 i\right)}}{a^{2} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} + \frac{15 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} - \frac{15 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}}{24 \, d}"," ",0,"1/24*(2*(9*sin(d*x + c)/(cos(d*x + c) + 1) + 16*I*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 33*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 48*I*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 33*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 48*I*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 9*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 16*I)/(a^2 - 4*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) + 15*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 - 15*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2)/d","B",0
174,1,47,0,0.336050," ","integrate(sec(d*x+c)^6/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{6 \, \tan\left(d x + c\right)^{5} + 15 i \, \tan\left(d x + c\right)^{4} + 30 i \, \tan\left(d x + c\right)^{2} - 30 \, \tan\left(d x + c\right)}{30 \, a^{2} d}"," ",0,"-1/30*(6*tan(d*x + c)^5 + 15*I*tan(d*x + c)^4 + 30*I*tan(d*x + c)^2 - 30*tan(d*x + c))/(a^2*d)","A",0
175,-2,0,0,0.000000," ","integrate(cos(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
176,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
177,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
178,1,69,0,0.526373," ","integrate(cos(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 i \, \cos\left(5 \, d x + 5 \, c\right) + 10 i \, \cos\left(3 \, d x + 3 \, c\right) + 15 i \, \cos\left(d x + c\right) + 3 \, \sin\left(5 \, d x + 5 \, c\right) + 10 \, \sin\left(3 \, d x + 3 \, c\right) + 15 \, \sin\left(d x + c\right)}{60 \, a^{3} d}"," ",0,"1/60*(3*I*cos(5*d*x + 5*c) + 10*I*cos(3*d*x + 3*c) + 15*I*cos(d*x + c) + 3*sin(5*d*x + 5*c) + 10*sin(3*d*x + 3*c) + 15*sin(d*x + c))/(a^3*d)","A",0
179,1,51,0,0.366698," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{i \, \cos\left(4 \, d x + 4 \, c\right) + 2 i \, \cos\left(2 \, d x + 2 \, c\right) + \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)}{8 \, a^{3} d}"," ",0,"1/8*(I*cos(4*d*x + 4*c) + 2*I*cos(2*d*x + 2*c) + sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))/(a^3*d)","A",0
180,1,29,0,0.557305," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{i \, \cos\left(3 \, d x + 3 \, c\right) + \sin\left(3 \, d x + 3 \, c\right)}{3 \, a^{3} d}"," ",0,"1/3*(I*cos(3*d*x + 3*c) + sin(3*d*x + 3*c))/(a^3*d)","A",0
181,1,99,0,0.791417," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{4 \, d x + 4 \, c - 2 \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right) - 2 i \, \cos\left(2 \, d x + 2 \, c\right) + i \, \log\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right) - 2 \, \sin\left(2 \, d x + 2 \, c\right)}{2 \, a^{3} d}"," ",0,"-1/2*(4*d*x + 4*c - 2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1) - 2*I*cos(2*d*x + 2*c) + I*log(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) - 2*sin(2*d*x + 2*c))/(a^3*d)","A",0
182,1,329,0,0.739913," ","integrate(sec(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(6 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(d x + c\right) + 6 i \, \sin\left(3 \, d x + 3 \, c\right) + 6 i \, \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) + {\left(6 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(d x + c\right) + 6 i \, \sin\left(3 \, d x + 3 \, c\right) + 6 i \, \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), -\sin\left(d x + c\right) + 1\right) - {\left(-3 i \, \cos\left(3 \, d x + 3 \, c\right) - 3 i \, \cos\left(d x + c\right) + 3 \, \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - {\left(3 i \, \cos\left(3 \, d x + 3 \, c\right) + 3 i \, \cos\left(d x + c\right) - 3 \, \sin\left(3 \, d x + 3 \, c\right) - 3 \, \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right) + 12 \, \cos\left(2 \, d x + 2 \, c\right) + 12 i \, \sin\left(2 \, d x + 2 \, c\right) + 8}{{\left(-2 i \, a^{3} \cos\left(3 \, d x + 3 \, c\right) - 2 i \, a^{3} \cos\left(d x + c\right) + 2 \, a^{3} \sin\left(3 \, d x + 3 \, c\right) + 2 \, a^{3} \sin\left(d x + c\right)\right)} d}"," ",0,"((6*cos(3*d*x + 3*c) + 6*cos(d*x + c) + 6*I*sin(3*d*x + 3*c) + 6*I*sin(d*x + c))*arctan2(cos(d*x + c), sin(d*x + c) + 1) + (6*cos(3*d*x + 3*c) + 6*cos(d*x + c) + 6*I*sin(3*d*x + 3*c) + 6*I*sin(d*x + c))*arctan2(cos(d*x + c), -sin(d*x + c) + 1) - (-3*I*cos(3*d*x + 3*c) - 3*I*cos(d*x + c) + 3*sin(3*d*x + 3*c) + 3*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - (3*I*cos(3*d*x + 3*c) + 3*I*cos(d*x + c) - 3*sin(3*d*x + 3*c) - 3*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) + 12*cos(2*d*x + 2*c) + 12*I*sin(2*d*x + 2*c) + 8)/((-2*I*a^3*cos(3*d*x + 3*c) - 2*I*a^3*cos(d*x + c) + 2*a^3*sin(3*d*x + 3*c) + 2*a^3*sin(d*x + c))*d)","B",0
183,1,299,0,0.503714," ","integrate(sec(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{-8 i \, d x + {\left(4 i \, \cos\left(4 \, d x + 4 \, c\right) + 8 i \, \cos\left(2 \, d x + 2 \, c\right) - 4 \, \sin\left(4 \, d x + 4 \, c\right) - 8 \, \sin\left(2 \, d x + 2 \, c\right) + 4 i\right)} \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right) + {\left(-8 i \, d x - 8 i \, c\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(-16 i \, d x - 16 i \, c - 4\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(2 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 2 i \, \sin\left(4 \, d x + 4 \, c\right) + 4 i \, \sin\left(2 \, d x + 2 \, c\right) + 2\right)} \log\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right) + 8 \, {\left(d x + c\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(16 \, d x + 16 \, c - 4 i\right)} \sin\left(2 \, d x + 2 \, c\right) - 8 i \, c - 6}{{\left(-i \, a^{3} \cos\left(4 \, d x + 4 \, c\right) - 2 i \, a^{3} \cos\left(2 \, d x + 2 \, c\right) + a^{3} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{3} \sin\left(2 \, d x + 2 \, c\right) - i \, a^{3}\right)} d}"," ",0,"(-8*I*d*x + (4*I*cos(4*d*x + 4*c) + 8*I*cos(2*d*x + 2*c) - 4*sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c) + 4*I)*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1) + (-8*I*d*x - 8*I*c)*cos(4*d*x + 4*c) + (-16*I*d*x - 16*I*c - 4)*cos(2*d*x + 2*c) + (2*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 2*I*sin(4*d*x + 4*c) + 4*I*sin(2*d*x + 2*c) + 2)*log(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) + 8*(d*x + c)*sin(4*d*x + 4*c) + (16*d*x + 16*c - 4*I)*sin(2*d*x + 2*c) - 8*I*c - 6)/((-I*a^3*cos(4*d*x + 4*c) - 2*I*a^3*cos(2*d*x + 2*c) + a^3*sin(4*d*x + 4*c) + 2*a^3*sin(2*d*x + 2*c) - I*a^3)*d)","B",0
184,1,215,0,0.368783," ","integrate(sec(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(-\frac{9 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{48 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{18 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{9 i \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + 22\right)}}{6 i \, a^{3} - \frac{18 i \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{18 i \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{6 i \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{5 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} - \frac{5 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}}{2 \, d}"," ",0,"1/2*(4*(-9*I*sin(d*x + c)/(cos(d*x + c) + 1) - 48*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 18*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 9*I*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 22)/(6*I*a^3 - 18*I*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 18*I*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 6*I*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + 5*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 - 5*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3)/d","B",0
185,1,240,0,0.379225," ","integrate(sec(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 i \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{8 i \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{7 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3 i \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{\sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{{\left(a^{3} - \frac{4 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d}"," ",0,"2*(sin(d*x + c)/(cos(d*x + c) + 1) - 3*I*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 8*I*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 7*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3*I*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/((a^3 - 4*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d)","B",0
186,1,341,0,0.350348," ","integrate(sec(d*x+c)^6/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{16 \, {\left(-\frac{15 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{320 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{390 i \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{400 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{960 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{390 i \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{360 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{15 i \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - 136\right)}}{-120 i \, a^{3} + \frac{600 i \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1200 i \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1200 i \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{600 i \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{120 i \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} + \frac{7 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} - \frac{7 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}}{8 \, d}"," ",0,"1/8*(16*(-15*I*sin(d*x + c)/(cos(d*x + c) + 1) + 320*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 390*I*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 400*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 960*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 390*I*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 360*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 15*I*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 136)/(-120*I*a^3 + 600*I*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1200*I*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1200*I*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 600*I*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 120*I*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) + 7*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 - 7*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3)/d","B",0
187,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^n/(cos(d*x+c)^n),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right)\right)}^{n} \cos\left(d x + c\right)^{-n}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + I*a*sin(d*x + c))^n*cos(d*x + c)^(-n), x)","F",0
188,1,31,0,0.320853," ","integrate(1/(sec(x)+tan(x)),x, algorithm=""maxima"")","2 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right) - \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)"," ",0,"2*log(sin(x)/(cos(x) + 1) + 1) - log(sin(x)^2/(cos(x) + 1)^2 + 1)","B",0
189,1,54,0,0.413161," ","integrate(sin(x)/(sec(x)+tan(x)),x, algorithm=""maxima"")","\frac{2 \, \sin\left(x\right)}{{\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)} {\left(\cos\left(x\right) + 1\right)}} - 2 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right) + \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)"," ",0,"2*sin(x)/((sin(x)^2/(cos(x) + 1)^2 + 1)*(cos(x) + 1)) - 2*log(sin(x)/(cos(x) + 1) + 1) + log(sin(x)^2/(cos(x) + 1)^2 + 1)","B",0
190,1,30,0,0.423576," ","integrate(cos(x)/(sec(x)+tan(x)),x, algorithm=""maxima"")","\frac{2}{\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1} + 2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"2/(sin(x)^2/(cos(x) + 1)^2 + 1) + 2*arctan(sin(x)/(cos(x) + 1))","B",0
191,1,28,0,0.429090," ","integrate(tan(x)/(sec(x)+tan(x)),x, algorithm=""maxima"")","\frac{2}{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1} + 2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"2/(sin(x)/(cos(x) + 1) + 1) + 2*arctan(sin(x)/(cos(x) + 1))","B",0
192,1,23,0,0.490536," ","integrate(cot(x)/(sec(x)+tan(x)),x, algorithm=""maxima"")","-2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right) + \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-2*arctan(sin(x)/(cos(x) + 1)) + log(sin(x)/(cos(x) + 1))","B",0
193,1,15,0,0.426406," ","integrate(sec(x)/(sec(x)+tan(x)),x, algorithm=""maxima"")","-\frac{2}{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1}"," ",0,"-2/(sin(x)/(cos(x) + 1) + 1)","A",0
194,1,25,0,0.569578," ","integrate(csc(x)/(sec(x)+tan(x)),x, algorithm=""maxima"")","-2 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right) + \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-2*log(sin(x)/(cos(x) + 1) + 1) + log(sin(x)/(cos(x) + 1))","B",0
195,1,29,0,0.340875," ","integrate(1/(sec(x)-tan(x)),x, algorithm=""maxima"")","-2 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right) + \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)"," ",0,"-2*log(sin(x)/(cos(x) + 1) - 1) + log(sin(x)^2/(cos(x) + 1)^2 + 1)","B",0
196,1,54,0,1.026679," ","integrate(sin(x)/(sec(x)-tan(x)),x, algorithm=""maxima"")","-\frac{2 \, \sin\left(x\right)}{{\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)} {\left(\cos\left(x\right) + 1\right)}} - 2 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right) + \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)"," ",0,"-2*sin(x)/((sin(x)^2/(cos(x) + 1)^2 + 1)*(cos(x) + 1)) - 2*log(sin(x)/(cos(x) + 1) - 1) + log(sin(x)^2/(cos(x) + 1)^2 + 1)","B",0
197,1,30,0,0.490734," ","integrate(cos(x)/(sec(x)-tan(x)),x, algorithm=""maxima"")","-\frac{2}{\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1} + 2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-2/(sin(x)^2/(cos(x) + 1)^2 + 1) + 2*arctan(sin(x)/(cos(x) + 1))","B",0
198,1,28,0,1.340453," ","integrate(tan(x)/(sec(x)-tan(x)),x, algorithm=""maxima"")","-\frac{2}{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1} - 2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-2/(sin(x)/(cos(x) + 1) - 1) - 2*arctan(sin(x)/(cos(x) + 1))","A",0
199,1,23,0,0.442641," ","integrate(cot(x)/(sec(x)-tan(x)),x, algorithm=""maxima"")","2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right) + \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"2*arctan(sin(x)/(cos(x) + 1)) + log(sin(x)/(cos(x) + 1))","B",0
200,1,15,0,0.328410," ","integrate(sec(x)/(sec(x)-tan(x)),x, algorithm=""maxima"")","-\frac{2}{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1}"," ",0,"-2/(sin(x)/(cos(x) + 1) - 1)","A",0
201,1,25,0,0.335194," ","integrate(csc(x)/(sec(x)-tan(x)),x, algorithm=""maxima"")","-2 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right) + \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-2*log(sin(x)/(cos(x) + 1) - 1) + log(sin(x)/(cos(x) + 1))","A",0
202,1,22,0,0.338245," ","integrate(csc(d*x+c)*(cot(d*x+c)+csc(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{1}{\sin\left(d x + c\right)} + \frac{1}{\tan\left(d x + c\right)}}{d}"," ",0,"-(1/sin(d*x + c) + 1/tan(d*x + c))/d","A",0
203,1,38,0,0.655857," ","integrate(sin(x)/(cot(x)+csc(x)),x, algorithm=""maxima"")","-\frac{2 \, \sin\left(x\right)}{{\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)} {\left(\cos\left(x\right) + 1\right)}} + 2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-2*sin(x)/((sin(x)^2/(cos(x) + 1)^2 + 1)*(cos(x) + 1)) + 2*arctan(sin(x)/(cos(x) + 1))","B",0
204,1,34,0,0.430919," ","integrate(cos(x)/(cot(x)+csc(x)),x, algorithm=""maxima"")","-\frac{2}{\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1} - \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)"," ",0,"-2/(sin(x)^2/(cos(x) + 1)^2 + 1) - log(sin(x)^2/(cos(x) + 1)^2 + 1)","B",0
205,1,39,0,0.433264," ","integrate(tan(x)/(cot(x)+csc(x)),x, algorithm=""maxima"")","-2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right) + \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right) - \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)"," ",0,"-2*arctan(sin(x)/(cos(x) + 1)) + log(sin(x)/(cos(x) + 1) + 1) - log(sin(x)/(cos(x) + 1) - 1)","B",0
206,1,23,0,0.430006," ","integrate(cot(x)/(cot(x)+csc(x)),x, algorithm=""maxima"")","-\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-sin(x)/(cos(x) + 1) + 2*arctan(sin(x)/(cos(x) + 1))","A",0
207,1,29,0,0.330258," ","integrate(sec(x)/(cot(x)+csc(x)),x, algorithm=""maxima"")","-\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right) - \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)"," ",0,"-log(sin(x)/(cos(x) + 1) + 1) - log(sin(x)/(cos(x) + 1) - 1)","B",0
208,1,9,0,0.329703," ","integrate(csc(x)/(cot(x)+csc(x)),x, algorithm=""maxima"")","\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}"," ",0,"sin(x)/(cos(x) + 1)","A",0
209,1,38,0,0.446893," ","integrate(sin(x)/(-cot(x)+csc(x)),x, algorithm=""maxima"")","\frac{2 \, \sin\left(x\right)}{{\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)} {\left(\cos\left(x\right) + 1\right)}} + 2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"2*sin(x)/((sin(x)^2/(cos(x) + 1)^2 + 1)*(cos(x) + 1)) + 2*arctan(sin(x)/(cos(x) + 1))","B",0
210,1,46,0,0.651521," ","integrate(cos(x)/(-cot(x)+csc(x)),x, algorithm=""maxima"")","\frac{2}{\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1} + 2 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right) - \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)"," ",0,"2/(sin(x)^2/(cos(x) + 1)^2 + 1) + 2*log(sin(x)/(cos(x) + 1)) - log(sin(x)^2/(cos(x) + 1)^2 + 1)","B",0
211,1,39,0,0.428588," ","integrate(tan(x)/(-cot(x)+csc(x)),x, algorithm=""maxima"")","2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right) + \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right) - \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)"," ",0,"2*arctan(sin(x)/(cos(x) + 1)) + log(sin(x)/(cos(x) + 1) + 1) - log(sin(x)/(cos(x) + 1) - 1)","B",0
212,1,23,0,0.448993," ","integrate(cot(x)/(-cot(x)+csc(x)),x, algorithm=""maxima"")","-\frac{\cos\left(x\right) + 1}{\sin\left(x\right)} - 2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-(cos(x) + 1)/sin(x) - 2*arctan(sin(x)/(cos(x) + 1))","A",0
213,1,41,0,0.341072," ","integrate(sec(x)/(-cot(x)+csc(x)),x, algorithm=""maxima"")","-\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right) - \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right) + 2 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-log(sin(x)/(cos(x) + 1) + 1) - log(sin(x)/(cos(x) + 1) - 1) + 2*log(sin(x)/(cos(x) + 1))","B",0
214,1,10,0,0.338555," ","integrate(csc(x)/(-cot(x)+csc(x)),x, algorithm=""maxima"")","-\frac{\cos\left(x\right) + 1}{\sin\left(x\right)}"," ",0,"-(cos(x) + 1)/sin(x)","A",0
215,1,176,0,0.573828," ","integrate(1/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""maxima"")","\frac{\sqrt{2} \log\left(-\frac{2 \, {\left(\sqrt{2} + 1\right)} \cos\left(d x + c\right) - \cos\left(d x + c\right)^{2} - \sin\left(d x + c\right)^{2} - 2 \, \sqrt{2} - 3}{2 \, {\left(\sqrt{2} - 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sqrt{2} + 3}\right) + \sqrt{2} \log\left(-\frac{2 \, {\left(\sqrt{2} - 1\right)} \cos\left(d x + c\right) - \cos\left(d x + c\right)^{2} - \sin\left(d x + c\right)^{2} + 2 \, \sqrt{2} - 3}{2 \, {\left(\sqrt{2} + 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sqrt{2} + 3}\right)}{8 \, d}"," ",0,"1/8*(sqrt(2)*log(-(2*(sqrt(2) + 1)*cos(d*x + c) - cos(d*x + c)^2 - sin(d*x + c)^2 - 2*sqrt(2) - 3)/(2*(sqrt(2) - 1)*cos(d*x + c) + cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sqrt(2) + 3)) + sqrt(2)*log(-(2*(sqrt(2) - 1)*cos(d*x + c) - cos(d*x + c)^2 - sin(d*x + c)^2 + 2*sqrt(2) - 3)/(2*(sqrt(2) + 1)*cos(d*x + c) + cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sqrt(2) + 3)))/d","B",0
216,1,252,0,0.575578," ","integrate(sin(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, d x - \sqrt{2} \arctan\left(\frac{2 \, \sqrt{2} \sin\left(d x + c\right)}{2 \, {\left(\sqrt{2} + 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sqrt{2} + 3}, \frac{\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) - 1}{2 \, {\left(\sqrt{2} + 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sqrt{2} + 3}\right) + \sqrt{2} \arctan\left(\frac{2 \, \sqrt{2} \sin\left(d x + c\right)}{2 \, {\left(\sqrt{2} - 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sqrt{2} + 3}, \frac{\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) - 1}{2 \, {\left(\sqrt{2} - 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sqrt{2} + 3}\right) + 4 \, c}{4 \, d}"," ",0,"1/4*(4*d*x - sqrt(2)*arctan2(2*sqrt(2)*sin(d*x + c)/(2*(sqrt(2) + 1)*cos(d*x + c) + cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sqrt(2) + 3), (cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) - 1)/(2*(sqrt(2) + 1)*cos(d*x + c) + cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sqrt(2) + 3)) + sqrt(2)*arctan2(2*sqrt(2)*sin(d*x + c)/(2*(sqrt(2) - 1)*cos(d*x + c) + cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sqrt(2) + 3), (cos(d*x + c)^2 + sin(d*x + c)^2 - 2*cos(d*x + c) - 1)/(2*(sqrt(2) - 1)*cos(d*x + c) + cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sqrt(2) + 3)) + 4*c)/d","B",0
217,1,16,0,0.468582," ","integrate(cos(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""maxima"")","\frac{\log\left(\sin\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*log(sin(d*x + c)^2 + 1)/d","A",0
218,1,35,0,0.550862," ","integrate(tan(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""maxima"")","-\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
219,1,11,0,0.644779," ","integrate(cot(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""maxima"")","\frac{\arctan\left(\sin\left(d x + c\right)\right)}{d}"," ",0,"arctan(sin(d*x + c))/d","A",0
220,1,39,0,0.471837," ","integrate(sec(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""maxima"")","\frac{\log\left(\sin\left(d x + c\right)^{2} + 1\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*(log(sin(d*x + c)^2 + 1) - log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1))/d","B",0
221,1,245,0,0.476750," ","integrate(csc(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x, algorithm=""maxima"")","\frac{\sqrt{2} \arctan\left(\frac{2 \, \sqrt{2} \sin\left(d x + c\right)}{2 \, {\left(\sqrt{2} + 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sqrt{2} + 3}, \frac{\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) - 1}{2 \, {\left(\sqrt{2} + 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sqrt{2} + 3}\right) - \sqrt{2} \arctan\left(\frac{2 \, \sqrt{2} \sin\left(d x + c\right)}{2 \, {\left(\sqrt{2} - 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sqrt{2} + 3}, \frac{\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) - 1}{2 \, {\left(\sqrt{2} - 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sqrt{2} + 3}\right)}{4 \, d}"," ",0,"1/4*(sqrt(2)*arctan2(2*sqrt(2)*sin(d*x + c)/(2*(sqrt(2) + 1)*cos(d*x + c) + cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sqrt(2) + 3), (cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) - 1)/(2*(sqrt(2) + 1)*cos(d*x + c) + cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sqrt(2) + 3)) - sqrt(2)*arctan2(2*sqrt(2)*sin(d*x + c)/(2*(sqrt(2) - 1)*cos(d*x + c) + cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sqrt(2) + 3), (cos(d*x + c)^2 + sin(d*x + c)^2 - 2*cos(d*x + c) - 1)/(2*(sqrt(2) - 1)*cos(d*x + c) + cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sqrt(2) + 3)))/d","B",0
222,1,28,0,0.418863," ","integrate(1/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2}{d {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}}"," ",0,"-2/(d*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1))","B",0
223,1,64,0,0.437118," ","integrate(sin(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{{\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)\right)}}{d}"," ",0,"-2*(sin(d*x + c)/((sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)*(cos(d*x + c) + 1)) + arctan(sin(d*x + c)/(cos(d*x + c) + 1)))/d","B",0
224,1,24,0,0.336691," ","integrate(cos(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""maxima"")","-\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","A",0
225,1,46,0,0.342749," ","integrate(tan(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \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*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1))/d","A",0
226,1,26,0,0.327821," ","integrate(cot(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""maxima"")","\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
227,1,17,0,0.349297," ","integrate(sec(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(\sin\left(d x + c\right)^{2} - 1\right)} d}"," ",0,"-1/2/((sin(d*x + c)^2 - 1)*d)","A",0
228,1,44,0,0.335353," ","integrate(csc(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, \sin\left(d x + c\right)}{d {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}}"," ",0,"-2*sin(d*x + c)/(d*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)*(cos(d*x + c) + 1))","B",0
229,1,28,0,0.343664," ","integrate(cos(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""maxima"")","-\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
230,1,28,0,0.339485," ","integrate(cos(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, a \cos\left(d x + c\right)^{3} - 3 \, b \sin\left(d x + c\right)^{2}}{6 \, d}"," ",0,"-1/6*(2*a*cos(d*x + c)^3 - 3*b*sin(d*x + c)^2)/d","A",0
231,1,25,0,0.412469," ","integrate(cos(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""maxima"")","-\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
232,1,25,0,0.353892," ","integrate(a*sin(d*x+c)+b*tan(d*x+c),x, algorithm=""maxima"")","-\frac{a \cos\left(d x + c\right)}{d} + \frac{b \log\left(\sec\left(d x + c\right)\right)}{d}"," ",0,"-a*cos(d*x + c)/d + b*log(sec(d*x + c))/d","A",0
233,1,32,0,0.325132," ","integrate(sec(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{a \log\left(-\sin\left(d x + c\right)^{2} + 1\right) - \frac{2 \, b}{\cos\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(a*log(-sin(d*x + c)^2 + 1) - 2*b/cos(d*x + c))/d","A",0
234,1,27,0,0.331894," ","integrate(sec(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{b \tan\left(d x + c\right)^{2} + \frac{2 \, a}{\cos\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(b*tan(d*x + c)^2 + 2*a/cos(d*x + c))/d","A",0
235,1,32,0,0.332395," ","integrate(sec(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{3 \, a}{\sin\left(d x + c\right)^{2} - 1} - \frac{2 \, b}{\cos\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"-1/6*(3*a/(sin(d*x + c)^2 - 1) - 2*b/cos(d*x + c)^3)/d","A",0
236,1,68,0,0.369659," ","integrate(cos(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{80 \, b^{2} \sin\left(d x + c\right)^{3} - 16 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 5 \, \sin\left(d x + c\right)^{3}\right)} a^{2} + 15 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a b}{240 \, d}"," ",0,"1/240*(80*b^2*sin(d*x + c)^3 - 16*(3*sin(d*x + c)^5 - 5*sin(d*x + c)^3)*a^2 + 15*(4*d*x + 4*c - sin(4*d*x + 4*c))*a*b)/d","A",0
237,1,66,0,0.333765," ","integrate(cos(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{64 \, a b \sin\left(d x + c\right)^{3} + 3 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} + 24 \, {\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} b^{2}}{96 \, d}"," ",0,"1/96*(64*a*b*sin(d*x + c)^3 + 3*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^2 + 24*(2*d*x + 2*c - sin(2*d*x + 2*c))*b^2)/d","A",0
238,1,76,0,0.339489," ","integrate(cos(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, a^{2} \sin\left(d x + c\right)^{3} + 3 \, {\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} a b + 3 \, b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)}}{6 \, d}"," ",0,"1/6*(2*a^2*sin(d*x + c)^3 + 3*(2*d*x + 2*c - sin(2*d*x + 2*c))*a*b + 3*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)))/d","A",0
239,1,84,0,0.687365," ","integrate((a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2}}{4 \, d} - \frac{{\left(d x + c - \tan\left(d x + c\right)\right)} b^{2}}{d} + \frac{a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)}}{d}"," ",0,"1/4*(2*d*x + 2*c - sin(2*d*x + 2*c))*a^2/d - (d*x + c - tan(d*x + c))*b^2/d + a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c))/d","A",0
240,1,102,0,0.461259," ","integrate(sec(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{8 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a b + b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 2 \, a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)}}{4 \, d}"," ",0,"-1/4*(8*(d*x + c - tan(d*x + c))*a*b + b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 2*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)))/d","A",0
241,1,82,0,0.435611," ","integrate(sec(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, b^{2} \tan\left(d x + c\right)^{3} - 6 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{2} - 3 \, a b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{6 \, d}"," ",0,"1/6*(2*b^2*tan(d*x + c)^3 - 6*(d*x + c - tan(d*x + c))*a^2 - 3*a*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)))/d","A",0
242,1,129,0,0.387098," ","integrate(sec(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{32 \, a b \tan\left(d x + c\right)^{3} + 3 \, b^{2} {\left(\frac{2 \, {\left(\sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(32*a*b*tan(d*x + c)^3 + 3*b^2*(2*(sin(d*x + c)^3 + sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)))/d","A",0
243,1,95,0,0.376758," ","integrate(cos(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{45 \, a b^{2} \sin\left(d x + c\right)^{4} - 5 \, {\left(2 \, \sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4}\right)} a^{3} + 12 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{2} b + 20 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} b^{3}}{60 \, d}"," ",0,"1/60*(45*a*b^2*sin(d*x + c)^4 - 5*(2*sin(d*x + c)^6 - 3*sin(d*x + c)^4)*a^3 + 12*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^2*b + 20*(cos(d*x + c)^3 - 3*cos(d*x + c))*b^3)/d","A",0
244,1,94,0,0.456710," ","integrate(cos(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{45 \, a^{2} b \sin\left(d x + c\right)^{4} + 4 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{3} + 60 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a b^{2} - 30 \, {\left(\sin\left(d x + c\right)^{2} + \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)} b^{3}}{60 \, d}"," ",0,"1/60*(45*a^2*b*sin(d*x + c)^4 + 4*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^3 + 60*(cos(d*x + c)^3 - 3*cos(d*x + c))*a*b^2 - 30*(sin(d*x + c)^2 + log(sin(d*x + c)^2 - 1))*b^3)/d","A",0
245,1,87,0,0.352471," ","integrate(cos(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{a^{3} \sin\left(d x + c\right)^{4} + 4 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a^{2} b - 6 \, {\left(\sin\left(d x + c\right)^{2} + \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)} a b^{2} + 4 \, b^{3} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{4 \, d}"," ",0,"1/4*(a^3*sin(d*x + c)^4 + 4*(cos(d*x + c)^3 - 3*cos(d*x + c))*a^2*b - 6*(sin(d*x + c)^2 + log(sin(d*x + c)^2 - 1))*a*b^2 + 4*b^3*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
246,1,113,0,0.420929," ","integrate((a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a^{3}}{3 \, d} - \frac{3 \, {\left(\sin\left(d x + c\right)^{2} + \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)} a^{2} b}{2 \, d} - \frac{b^{3} {\left(\frac{1}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)}}{2 \, d} + \frac{3 \, a b^{2} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{d}"," ",0,"1/3*(cos(d*x + c)^3 - 3*cos(d*x + c))*a^3/d - 3/2*(sin(d*x + c)^2 + log(sin(d*x + c)^2 - 1))*a^2*b/d - 1/2*b^3*(1/(sin(d*x + c)^2 - 1) - log(sin(d*x + c)^2 - 1))/d + 3*a*b^2*(1/cos(d*x + c) + cos(d*x + c))/d","A",0
247,1,109,0,0.352622," ","integrate(sec(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{3 \, {\left(\sin\left(d x + c\right)^{2} + \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)} a^{3} + 9 \, a b^{2} {\left(\frac{1}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)} - 18 \, a^{2} b {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} + \frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} b^{3}}{\cos\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"-1/6*(3*(sin(d*x + c)^2 + log(sin(d*x + c)^2 - 1))*a^3 + 9*a*b^2*(1/(sin(d*x + c)^2 - 1) - log(sin(d*x + c)^2 - 1)) - 18*a^2*b*(1/cos(d*x + c) + cos(d*x + c)) + 2*(3*cos(d*x + c)^2 - 1)*b^3/cos(d*x + c)^3)/d","A",0
248,1,96,0,0.356664," ","integrate(sec(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{b^{3} \tan\left(d x + c\right)^{4} - 6 \, a^{2} b {\left(\frac{1}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)} + 4 \, a^{3} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} - \frac{4 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a b^{2}}{\cos\left(d x + c\right)^{3}}}{4 \, d}"," ",0,"1/4*(b^3*tan(d*x + c)^4 - 6*a^2*b*(1/(sin(d*x + c)^2 - 1) - log(sin(d*x + c)^2 - 1)) + 4*a^3*(1/cos(d*x + c) + cos(d*x + c)) - 4*(3*cos(d*x + c)^2 - 1)*a*b^2/cos(d*x + c)^3)/d","A",0
249,1,128,0,0.363906," ","integrate(sec(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{30 \, a^{3} {\left(\frac{1}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)} - \frac{45 \, {\left(2 \, \sin\left(d x + c\right)^{2} - 1\right)} a b^{2}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} + \frac{60 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a^{2} b}{\cos\left(d x + c\right)^{3}} + \frac{4 \, {\left(5 \, \cos\left(d x + c\right)^{2} - 3\right)} b^{3}}{\cos\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(30*a^3*(1/(sin(d*x + c)^2 - 1) - log(sin(d*x + c)^2 - 1)) - 45*(2*sin(d*x + c)^2 - 1)*a*b^2/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) + 60*(3*cos(d*x + c)^2 - 1)*a^2*b/cos(d*x + c)^3 + 4*(5*cos(d*x + c)^2 - 3)*b^3/cos(d*x + c)^5)/d","A",0
250,1,188,0,0.427732," ","integrate(cos(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{b^{4} \log\left(a + b - \frac{{\left(a - b\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{5} - a^{3} b^{2}} + \frac{2 \, {\left(b + \frac{{\left(a + b\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{a^{2} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a + b} + \frac{{\left(a^{2} + b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}{a^{3}}}{d}"," ",0,"-(b^4*log(a + b - (a - b)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^5 - a^3*b^2) + 2*(b + (a + b)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^2 + 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - log(sin(d*x + c)/(cos(d*x + c) + 1))/(a + b) + (a^2 + b^2)*log(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/a^3)/d","A",0
251,1,129,0,0.445323," ","integrate(cos(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{b^{3} \log\left(a + b - \frac{{\left(a - b\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{4} - a^{2} b^{2}} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a + b} + \frac{b \log\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}{a^{2}} + \frac{2}{a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}}{d}"," ",0,"(b^3*log(a + b - (a - b)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^4 - a^2*b^2) + log(sin(d*x + c)/(cos(d*x + c) + 1))/(a + b) + b*log(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/a^2 + 2/(a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2))/d","A",0
252,1,102,0,0.424382," ","integrate(cos(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{b^{2} \log\left(a + b - \frac{{\left(a - b\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{3} - a b^{2}} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a + b} + \frac{\log\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}{a}}{d}"," ",0,"-(b^2*log(a + b - (a - b)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^3 - a*b^2) - log(sin(d*x + c)/(cos(d*x + c) + 1))/(a + b) + log(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/a)/d","A",0
253,1,71,0,0.327468," ","integrate(1/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{b \log\left(a + b - \frac{{\left(a - b\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{2} - b^{2}} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a + b}}{d}"," ",0,"(b*log(a + b - (a - b)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^2 - b^2) + log(sin(d*x + c)/(cos(d*x + c) + 1))/(a + b))/d","A",0
254,1,73,0,0.360378," ","integrate(sec(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{a \log\left(a + b - \frac{{\left(a - b\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{2} - b^{2}} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a + b}}{d}"," ",0,"-(a*log(a + b - (a - b)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^2 - b^2) - log(sin(d*x + c)/(cos(d*x + c) + 1))/(a + b))/d","A",0
255,1,125,0,0.374390," ","integrate(sec(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{a^{2} \log\left(a + b - \frac{{\left(a - b\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{2} b - b^{3}} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a + b}}{d}"," ",0,"(a^2*log(a + b - (a - b)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^2*b - b^3) - log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b + log(sin(d*x + c)/(cos(d*x + c) + 1))/(a + b))/d","A",0
256,1,158,0,0.438329," ","integrate(sec(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{a^{3} \log\left(a + b - \frac{{\left(a - b\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{2} b^{2} - b^{4}} - \frac{a \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{2}} - \frac{a \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{2}} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a + b} - \frac{2}{b - \frac{b \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}}{d}"," ",0,"-(a^3*log(a + b - (a - b)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^2*b^2 - b^4) - a*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^2 - a*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^2 - log(sin(d*x + c)/(cos(d*x + c) + 1))/(a + b) - 2/(b - b*sin(d*x + c)^2/(cos(d*x + c) + 1)^2))/d","A",0
257,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
258,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
259,-2,0,0,0.000000," ","integrate(cos(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
260,-2,0,0,0.000000," ","integrate(1/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
261,-2,0,0,0.000000," ","integrate(sec(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
262,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
263,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
264,1,684,0,0.476715," ","integrate(cos(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(15 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} \log\left(a + b - \frac{{\left(a - b\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}} + \frac{4 \, {\left(2 \, a + 5 \, b\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{a^{8} - 2 \, a^{7} b - a^{6} b^{2} + 4 \, a^{5} b^{3} - a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6} - \frac{2 \, {\left(a^{8} - 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 44 \, a^{3} b^{5} - 49 \, a^{2} b^{6} + 8 \, a b^{7} + 8 \, b^{8}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{{\left(a^{8} - 6 \, a^{7} b + 15 \, a^{6} b^{2} - 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} - 102 \, a^{3} b^{5} + 81 \, a^{2} b^{6} + 32 \, a b^{7} - 16 \, b^{8}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{\frac{{\left(a^{11} + a^{10} b - 4 \, a^{9} b^{2} - 4 \, a^{8} b^{3} + 6 \, a^{7} b^{4} + 6 \, a^{6} b^{5} - 4 \, a^{5} b^{6} - 4 \, a^{4} b^{7} + a^{3} b^{8} + a^{2} b^{9}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, {\left(a^{11} - a^{10} b - 4 \, a^{9} b^{2} + 4 \, a^{8} b^{3} + 6 \, a^{7} b^{4} - 6 \, a^{6} b^{5} - 4 \, a^{5} b^{6} + 4 \, a^{4} b^{7} + a^{3} b^{8} - a^{2} b^{9}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(a^{11} - 3 \, a^{10} b + 8 \, a^{8} b^{3} - 6 \, a^{7} b^{4} - 6 \, a^{6} b^{5} + 8 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a^{2} b^{9}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\sin\left(d x + c\right)^{2}}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, \log\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}{a^{3}}}{8 \, d}"," ",0,"-1/8*(8*(15*a^4*b^4 - 4*a^2*b^6 + b^8)*log(a + b - (a - b)*sin(d*x + c)^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) + 4*(2*a + 5*b)*log(sin(d*x + c)/(cos(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + (a^8 - 2*a^7*b - a^6*b^2 + 4*a^5*b^3 - a^4*b^4 - 2*a^3*b^5 + a^2*b^6 - 2*(a^8 - 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 44*a^3*b^5 - 49*a^2*b^6 + 8*a*b^7 + 8*b^8)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + (a^8 - 6*a^7*b + 15*a^6*b^2 - 20*a^5*b^3 + 15*a^4*b^4 - 102*a^3*b^5 + 81*a^2*b^6 + 32*a*b^7 - 16*b^8)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/((a^11 + a^10*b - 4*a^9*b^2 - 4*a^8*b^3 + 6*a^7*b^4 + 6*a^6*b^5 - 4*a^5*b^6 - 4*a^4*b^7 + a^3*b^8 + a^2*b^9)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*(a^11 - a^10*b - 4*a^9*b^2 + 4*a^8*b^3 + 6*a^7*b^4 - 6*a^6*b^5 - 4*a^5*b^6 + 4*a^4*b^7 + a^3*b^8 - a^2*b^9)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (a^11 - 3*a^10*b + 8*a^8*b^3 - 6*a^7*b^4 - 6*a^6*b^5 + 8*a^5*b^6 - 3*a^3*b^8 + a^2*b^9)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + sin(d*x + c)^2/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(cos(d*x + c) + 1)^2) - 8*log(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/a^3)/d","B",0
265,1,589,0,0.882617," ","integrate(cos(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{16 \, {\left(5 \, a^{2} b^{3} + b^{5}\right)} \log\left(a + b - \frac{{\left(a - b\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} - \frac{4 \, {\left(a + 4 \, b\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{a^{6} - 2 \, a^{5} b - a^{4} b^{2} + 4 \, a^{3} b^{3} - a^{2} b^{4} - 2 \, a b^{5} + b^{6} - \frac{2 \, {\left(a^{6} - 4 \, a^{5} b + 5 \, a^{4} b^{2} + 35 \, a^{2} b^{4} + 44 \, a b^{5} - b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{{\left(a^{6} - 6 \, a^{5} b + 15 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 95 \, a^{2} b^{4} - 70 \, a b^{5} - 15 \, b^{6}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{\frac{{\left(a^{9} + a^{8} b - 4 \, a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} + 6 \, a^{4} b^{5} - 4 \, a^{3} b^{6} - 4 \, a^{2} b^{7} + a b^{8} + b^{9}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, {\left(a^{9} - a^{8} b - 4 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 6 \, a^{4} b^{5} - 4 \, a^{3} b^{6} + 4 \, a^{2} b^{7} + a b^{8} - b^{9}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(a^{9} - 3 \, a^{8} b + 8 \, a^{6} b^{3} - 6 \, a^{5} b^{4} - 6 \, a^{4} b^{5} + 8 \, a^{3} b^{6} - 3 \, a b^{8} + b^{9}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\sin\left(d x + c\right)^{2}}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{8 \, d}"," ",0,"1/8*(16*(5*a^2*b^3 + b^5)*log(a + b - (a - b)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) - 4*(a + 4*b)*log(sin(d*x + c)/(cos(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - (a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*(a^6 - 4*a^5*b + 5*a^4*b^2 + 35*a^2*b^4 + 44*a*b^5 - b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + (a^6 - 6*a^5*b + 15*a^4*b^2 - 20*a^3*b^3 + 95*a^2*b^4 - 70*a*b^5 - 15*b^6)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/((a^9 + a^8*b - 4*a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 + 6*a^4*b^5 - 4*a^3*b^6 - 4*a^2*b^7 + a*b^8 + b^9)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*(a^9 - a^8*b - 4*a^7*b^2 + 4*a^6*b^3 + 6*a^5*b^4 - 6*a^4*b^5 - 4*a^3*b^6 + 4*a^2*b^7 + a*b^8 - b^9)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (a^9 - 3*a^8*b + 8*a^6*b^3 - 6*a^5*b^4 - 6*a^4*b^5 + 8*a^3*b^6 - 3*a*b^8 + b^9)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + sin(d*x + c)^2/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(cos(d*x + c) + 1)^2))/d","B",0
266,1,593,0,0.621195," ","integrate(cos(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{48 \, {\left(a^{3} b^{2} + a b^{4}\right)} \log\left(a + b - \frac{{\left(a - b\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} + \frac{12 \, b \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{a^{6} - 2 \, a^{5} b - a^{4} b^{2} + 4 \, a^{3} b^{3} - a^{2} b^{4} - 2 \, a b^{5} + b^{6} - \frac{2 \, {\left(a^{6} - 4 \, a^{5} b + 5 \, a^{4} b^{2} - 32 \, a^{3} b^{3} - 37 \, a^{2} b^{4} - 4 \, a b^{5} - 9 \, b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{{\left(a^{6} - 6 \, a^{5} b + 15 \, a^{4} b^{2} - 84 \, a^{3} b^{3} + 63 \, a^{2} b^{4} - 6 \, a b^{5} + 17 \, b^{6}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{\frac{{\left(a^{9} + a^{8} b - 4 \, a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} + 6 \, a^{4} b^{5} - 4 \, a^{3} b^{6} - 4 \, a^{2} b^{7} + a b^{8} + b^{9}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, {\left(a^{9} - a^{8} b - 4 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 6 \, a^{4} b^{5} - 4 \, a^{3} b^{6} + 4 \, a^{2} b^{7} + a b^{8} - b^{9}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(a^{9} - 3 \, a^{8} b + 8 \, a^{6} b^{3} - 6 \, a^{5} b^{4} - 6 \, a^{4} b^{5} + 8 \, a^{3} b^{6} - 3 \, a b^{8} + b^{9}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\sin\left(d x + c\right)^{2}}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{8 \, d}"," ",0,"-1/8*(48*(a^3*b^2 + a*b^4)*log(a + b - (a - b)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) + 12*b*log(sin(d*x + c)/(cos(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + (a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*(a^6 - 4*a^5*b + 5*a^4*b^2 - 32*a^3*b^3 - 37*a^2*b^4 - 4*a*b^5 - 9*b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + (a^6 - 6*a^5*b + 15*a^4*b^2 - 84*a^3*b^3 + 63*a^2*b^4 - 6*a*b^5 + 17*b^6)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/((a^9 + a^8*b - 4*a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 + 6*a^4*b^5 - 4*a^3*b^6 - 4*a^2*b^7 + a*b^8 + b^9)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*(a^9 - a^8*b - 4*a^7*b^2 + 4*a^6*b^3 + 6*a^5*b^4 - 6*a^4*b^5 - 4*a^3*b^6 + 4*a^2*b^7 + a*b^8 - b^9)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (a^9 - 3*a^8*b + 8*a^6*b^3 - 6*a^5*b^4 - 6*a^4*b^5 + 8*a^3*b^6 - 3*a*b^8 + b^9)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + sin(d*x + c)^2/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(cos(d*x + c) + 1)^2))/d","B",0
267,1,601,0,0.415373," ","integrate(1/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(3 \, a^{4} b + 8 \, a^{2} b^{3} + b^{5}\right)} \log\left(a + b - \frac{{\left(a - b\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} + \frac{4 \, {\left(a - 2 \, b\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{a^{6} - 2 \, a^{5} b - a^{4} b^{2} + 4 \, a^{3} b^{3} - a^{2} b^{4} - 2 \, a b^{5} + b^{6} - \frac{2 \, {\left(a^{6} - 4 \, a^{5} b + 29 \, a^{4} b^{2} + 24 \, a^{3} b^{3} + 11 \, a^{2} b^{4} + 20 \, a b^{5} - b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{{\left(a^{6} - 6 \, a^{5} b + 63 \, a^{4} b^{2} - 52 \, a^{3} b^{3} + 31 \, a^{2} b^{4} - 38 \, a b^{5} + b^{6}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{\frac{{\left(a^{9} + a^{8} b - 4 \, a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} + 6 \, a^{4} b^{5} - 4 \, a^{3} b^{6} - 4 \, a^{2} b^{7} + a b^{8} + b^{9}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, {\left(a^{9} - a^{8} b - 4 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 6 \, a^{4} b^{5} - 4 \, a^{3} b^{6} + 4 \, a^{2} b^{7} + a b^{8} - b^{9}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(a^{9} - 3 \, a^{8} b + 8 \, a^{6} b^{3} - 6 \, a^{5} b^{4} - 6 \, a^{4} b^{5} + 8 \, a^{3} b^{6} - 3 \, a b^{8} + b^{9}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\sin\left(d x + c\right)^{2}}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{8 \, d}"," ",0,"1/8*(8*(3*a^4*b + 8*a^2*b^3 + b^5)*log(a + b - (a - b)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) + 4*(a - 2*b)*log(sin(d*x + c)/(cos(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - (a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*(a^6 - 4*a^5*b + 29*a^4*b^2 + 24*a^3*b^3 + 11*a^2*b^4 + 20*a*b^5 - b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + (a^6 - 6*a^5*b + 63*a^4*b^2 - 52*a^3*b^3 + 31*a^2*b^4 - 38*a*b^5 + b^6)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/((a^9 + a^8*b - 4*a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 + 6*a^4*b^5 - 4*a^3*b^6 - 4*a^2*b^7 + a*b^8 + b^9)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*(a^9 - a^8*b - 4*a^7*b^2 + 4*a^6*b^3 + 6*a^5*b^4 - 6*a^4*b^5 - 4*a^3*b^6 + 4*a^2*b^7 + a*b^8 - b^9)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (a^9 - 3*a^8*b + 8*a^6*b^3 - 6*a^5*b^4 - 6*a^4*b^5 + 8*a^3*b^6 - 3*a*b^8 + b^9)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + sin(d*x + c)^2/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(cos(d*x + c) + 1)^2))/d","B",0
268,1,602,0,0.375609," ","integrate(sec(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(a^{5} + 8 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \log\left(a + b - \frac{{\left(a - b\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} - \frac{4 \, {\left(2 \, a - b\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{a^{6} - 2 \, a^{5} b - a^{4} b^{2} + 4 \, a^{3} b^{3} - a^{2} b^{4} - 2 \, a b^{5} + b^{6} - \frac{2 \, {\left(a^{6} - 20 \, a^{5} b - 11 \, a^{4} b^{2} - 24 \, a^{3} b^{3} - 29 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{{\left(a^{6} - 38 \, a^{5} b + 31 \, a^{4} b^{2} - 52 \, a^{3} b^{3} + 63 \, a^{2} b^{4} - 6 \, a b^{5} + b^{6}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{\frac{{\left(a^{9} + a^{8} b - 4 \, a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} + 6 \, a^{4} b^{5} - 4 \, a^{3} b^{6} - 4 \, a^{2} b^{7} + a b^{8} + b^{9}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, {\left(a^{9} - a^{8} b - 4 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 6 \, a^{4} b^{5} - 4 \, a^{3} b^{6} + 4 \, a^{2} b^{7} + a b^{8} - b^{9}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(a^{9} - 3 \, a^{8} b + 8 \, a^{6} b^{3} - 6 \, a^{5} b^{4} - 6 \, a^{4} b^{5} + 8 \, a^{3} b^{6} - 3 \, a b^{8} + b^{9}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\sin\left(d x + c\right)^{2}}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{8 \, d}"," ",0,"-1/8*(8*(a^5 + 8*a^3*b^2 + 3*a*b^4)*log(a + b - (a - b)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) - 4*(2*a - b)*log(sin(d*x + c)/(cos(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + (a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*(a^6 - 20*a^5*b - 11*a^4*b^2 - 24*a^3*b^3 - 29*a^2*b^4 + 4*a*b^5 - b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + (a^6 - 38*a^5*b + 31*a^4*b^2 - 52*a^3*b^3 + 63*a^2*b^4 - 6*a*b^5 + b^6)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/((a^9 + a^8*b - 4*a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 + 6*a^4*b^5 - 4*a^3*b^6 - 4*a^2*b^7 + a*b^8 + b^9)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*(a^9 - a^8*b - 4*a^7*b^2 + 4*a^6*b^3 + 6*a^5*b^4 - 6*a^4*b^5 - 4*a^3*b^6 + 4*a^2*b^7 + a*b^8 - b^9)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (a^9 - 3*a^8*b + 8*a^6*b^3 - 6*a^5*b^4 - 6*a^4*b^5 + 8*a^3*b^6 - 3*a*b^8 + b^9)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + sin(d*x + c)^2/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(cos(d*x + c) + 1)^2))/d","B",0
269,1,596,0,0.385860," ","integrate(sec(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{48 \, {\left(a^{4} b + a^{2} b^{3}\right)} \log\left(a + b - \frac{{\left(a - b\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} + \frac{12 \, a \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{a^{6} - 2 \, a^{5} b - a^{4} b^{2} + 4 \, a^{3} b^{3} - a^{2} b^{4} - 2 \, a b^{5} + b^{6} - \frac{2 \, {\left(9 \, a^{6} + 4 \, a^{5} b + 37 \, a^{4} b^{2} + 32 \, a^{3} b^{3} - 5 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{{\left(17 \, a^{6} - 6 \, a^{5} b + 63 \, a^{4} b^{2} - 84 \, a^{3} b^{3} + 15 \, a^{2} b^{4} - 6 \, a b^{5} + b^{6}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{\frac{{\left(a^{9} + a^{8} b - 4 \, a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} + 6 \, a^{4} b^{5} - 4 \, a^{3} b^{6} - 4 \, a^{2} b^{7} + a b^{8} + b^{9}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, {\left(a^{9} - a^{8} b - 4 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 6 \, a^{4} b^{5} - 4 \, a^{3} b^{6} + 4 \, a^{2} b^{7} + a b^{8} - b^{9}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(a^{9} - 3 \, a^{8} b + 8 \, a^{6} b^{3} - 6 \, a^{5} b^{4} - 6 \, a^{4} b^{5} + 8 \, a^{3} b^{6} - 3 \, a b^{8} + b^{9}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\sin\left(d x + c\right)^{2}}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{8 \, d}"," ",0,"1/8*(48*(a^4*b + a^2*b^3)*log(a + b - (a - b)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) + 12*a*log(sin(d*x + c)/(cos(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - (a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*(9*a^6 + 4*a^5*b + 37*a^4*b^2 + 32*a^3*b^3 - 5*a^2*b^4 + 4*a*b^5 - b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + (17*a^6 - 6*a^5*b + 63*a^4*b^2 - 84*a^3*b^3 + 15*a^2*b^4 - 6*a*b^5 + b^6)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/((a^9 + a^8*b - 4*a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 + 6*a^4*b^5 - 4*a^3*b^6 - 4*a^2*b^7 + a*b^8 + b^9)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*(a^9 - a^8*b - 4*a^7*b^2 + 4*a^6*b^3 + 6*a^5*b^4 - 6*a^4*b^5 - 4*a^3*b^6 + 4*a^2*b^7 + a*b^8 - b^9)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (a^9 - 3*a^8*b + 8*a^6*b^3 - 6*a^5*b^4 - 6*a^4*b^5 + 8*a^3*b^6 - 3*a*b^8 + b^9)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + sin(d*x + c)^2/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(cos(d*x + c) + 1)^2))/d","B",0
270,1,591,0,0.374920," ","integrate(sec(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{16 \, {\left(a^{5} + 5 \, a^{3} b^{2}\right)} \log\left(a + b - \frac{{\left(a - b\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} - \frac{4 \, {\left(4 \, a + b\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{a^{6} - 2 \, a^{5} b - a^{4} b^{2} + 4 \, a^{3} b^{3} - a^{2} b^{4} - 2 \, a b^{5} + b^{6} - \frac{2 \, {\left(a^{6} - 44 \, a^{5} b - 35 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{{\left(15 \, a^{6} + 70 \, a^{5} b - 95 \, a^{4} b^{2} + 20 \, a^{3} b^{3} - 15 \, a^{2} b^{4} + 6 \, a b^{5} - b^{6}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{\frac{{\left(a^{9} + a^{8} b - 4 \, a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} + 6 \, a^{4} b^{5} - 4 \, a^{3} b^{6} - 4 \, a^{2} b^{7} + a b^{8} + b^{9}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, {\left(a^{9} - a^{8} b - 4 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 6 \, a^{4} b^{5} - 4 \, a^{3} b^{6} + 4 \, a^{2} b^{7} + a b^{8} - b^{9}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(a^{9} - 3 \, a^{8} b + 8 \, a^{6} b^{3} - 6 \, a^{5} b^{4} - 6 \, a^{4} b^{5} + 8 \, a^{3} b^{6} - 3 \, a b^{8} + b^{9}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\sin\left(d x + c\right)^{2}}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{8 \, d}"," ",0,"-1/8*(16*(a^5 + 5*a^3*b^2)*log(a + b - (a - b)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) - 4*(4*a + b)*log(sin(d*x + c)/(cos(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + (a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*(a^6 - 44*a^5*b - 35*a^4*b^2 - 5*a^2*b^4 + 4*a*b^5 - b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - (15*a^6 + 70*a^5*b - 95*a^4*b^2 + 20*a^3*b^3 - 15*a^2*b^4 + 6*a*b^5 - b^6)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/((a^9 + a^8*b - 4*a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 + 6*a^4*b^5 - 4*a^3*b^6 - 4*a^2*b^7 + a*b^8 + b^9)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*(a^9 - a^8*b - 4*a^7*b^2 + 4*a^6*b^3 + 6*a^5*b^4 - 6*a^4*b^5 - 4*a^3*b^6 + 4*a^2*b^7 + a*b^8 - b^9)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (a^9 - 3*a^8*b + 8*a^6*b^3 - 6*a^5*b^4 - 6*a^4*b^5 + 8*a^3*b^6 - 3*a*b^8 + b^9)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + sin(d*x + c)^2/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(cos(d*x + c) + 1)^2))/d","B",0
271,1,180,0,0.361506," ","integrate(cos(d*x+c)^m*(a*sin(d*x+c)+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{{\left({\left(m + 1\right)} \cos\left(d x + c\right)^{3} - {\left(m + 3\right)} \cos\left(d x + c\right)\right)} a^{3} \cos\left(d x + c\right)^{m}}{m^{2} + 4 \, m + 3} + \frac{3 \, {\left(m \cos\left(d x + c\right)^{2} - m - 2\right)} a^{2} b \cos\left(d x + c\right)^{m}}{m^{2} + 2 \, m} + \frac{3 \, {\left({\left(m - 1\right)} \cos\left(d x + c\right)^{2} - m - 1\right)} a b^{2} \cos\left(d x + c\right)^{m}}{{\left(m^{2} - 1\right)} \cos\left(d x + c\right)} + \frac{{\left({\left(m - 2\right)} \cos\left(d x + c\right)^{2} - m\right)} b^{3} \cos\left(d x + c\right)^{m}}{{\left(m^{2} - 2 \, m\right)} \cos\left(d x + c\right)^{2}}}{d}"," ",0,"(((m + 1)*cos(d*x + c)^3 - (m + 3)*cos(d*x + c))*a^3*cos(d*x + c)^m/(m^2 + 4*m + 3) + 3*(m*cos(d*x + c)^2 - m - 2)*a^2*b*cos(d*x + c)^m/(m^2 + 2*m) + 3*((m - 1)*cos(d*x + c)^2 - m - 1)*a*b^2*cos(d*x + c)^m/((m^2 - 1)*cos(d*x + c)) + ((m - 2)*cos(d*x + c)^2 - m)*b^3*cos(d*x + c)^m/((m^2 - 2*m)*cos(d*x + c)^2))/d","A",0
272,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a*sin(d*x+c)+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + b \tan\left(d x + c\right)\right)}^{2} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + b*tan(d*x + c))^2*cos(d*x + c)^m, x)","F",0
273,1,36,0,0.343784," ","integrate(cos(d*x+c)^m*(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{a \cos\left(d x + c\right)^{m + 1}}{m + 1} + \frac{b \cos\left(d x + c\right)^{m}}{m}}{d}"," ",0,"-(a*cos(d*x + c)^(m + 1)/(m + 1) + b*cos(d*x + c)^m/m)/d","A",0
274,0,0,0,0.000000," ","integrate(cos(d*x+c)^m/(a*sin(d*x+c)+b*tan(d*x+c)),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{m}}{a \sin\left(d x + c\right) + b \tan\left(d x + c\right)}\,{d x}"," ",0,"integrate(cos(d*x + c)^m/(a*sin(d*x + c) + b*tan(d*x + c)), x)","F",0
275,1,105,0,0.447717," ","integrate(cos(x)*sin(x)/(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","\frac{a b \log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(a - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1}\right)}}{a^{2} + b^{2} + \frac{{\left(a^{2} + b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}"," ",0,"a*b*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) - 2*(a - b*sin(x)/(cos(x) + 1))/(a^2 + b^2 + (a^2 + b^2)*sin(x)^2/(cos(x) + 1)^2)","A",0
276,1,211,0,0.462651," ","integrate(cos(x)*sin(x)^2/(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","\frac{a^{2} b \log\left(-a - \frac{2 \, b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{a^{2} b \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{3} - a b^{2}\right)} \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{\frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{2 \, b \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{a \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}}{a^{2} + b^{2} + \frac{2 \, {\left(a^{2} + b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{{\left(a^{2} + b^{2}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}}"," ",0,"a^2*b*log(-a - 2*b*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2)/(a^4 + 2*a^2*b^2 + b^4) - a^2*b*log(sin(x)^2/(cos(x) + 1)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (a^3 - a*b^2)*arctan(sin(x)/(cos(x) + 1))/(a^4 + 2*a^2*b^2 + b^4) - (a*sin(x)/(cos(x) + 1) - 2*b*sin(x)^2/(cos(x) + 1)^2 - a*sin(x)^3/(cos(x) + 1)^3)/(a^2 + b^2 + 2*(a^2 + b^2)*sin(x)^2/(cos(x) + 1)^2 + (a^2 + b^2)*sin(x)^4/(cos(x) + 1)^4)","B",0
277,1,278,0,0.446566," ","integrate(cos(x)*sin(x)^3/(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","\frac{a^{3} b \log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(2 \, a^{3} - a b^{2} - \frac{3 \, a^{2} b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{6 \, a^{3} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{3 \, a b^{2} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{3 \, a^{2} b \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{2 \, {\left(5 \, a^{2} b + 2 \, b^{3}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}}{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + \frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}}\right)}}"," ",0,"a^3*b*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2/3*(2*a^3 - a*b^2 - 3*a^2*b*sin(x)/(cos(x) + 1) + 6*a^3*sin(x)^2/(cos(x) + 1)^2 - 3*a*b^2*sin(x)^4/(cos(x) + 1)^4 - 3*a^2*b*sin(x)^5/(cos(x) + 1)^5 - 2*(5*a^2*b + 2*b^3)*sin(x)^3/(cos(x) + 1)^3)/(a^4 + 2*a^2*b^2 + b^4 + 3*(a^4 + 2*a^2*b^2 + b^4)*sin(x)^2/(cos(x) + 1)^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*sin(x)^4/(cos(x) + 1)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(x)^6/(cos(x) + 1)^6)","B",0
278,1,212,0,0.451105," ","integrate(cos(x)^2*sin(x)/(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","-\frac{a b^{2} \log\left(-a - \frac{2 \, b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{a b^{2} \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(a^{2} b - b^{3}\right)} \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{\frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{2 \, a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{b \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}}{a^{2} + b^{2} + \frac{2 \, {\left(a^{2} + b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{{\left(a^{2} + b^{2}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}}"," ",0,"-a*b^2*log(-a - 2*b*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2)/(a^4 + 2*a^2*b^2 + b^4) + a*b^2*log(sin(x)^2/(cos(x) + 1)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - (a^2*b - b^3)*arctan(sin(x)/(cos(x) + 1))/(a^4 + 2*a^2*b^2 + b^4) + (b*sin(x)/(cos(x) + 1) + 2*a*sin(x)^2/(cos(x) + 1)^2 - b*sin(x)^3/(cos(x) + 1)^3)/(a^2 + b^2 + 2*(a^2 + b^2)*sin(x)^2/(cos(x) + 1)^2 + (a^2 + b^2)*sin(x)^4/(cos(x) + 1)^4)","B",0
279,1,281,0,0.464691," ","integrate(cos(x)^2*sin(x)^2/(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","-\frac{a^{2} b^{2} \log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} + \frac{2 \, {\left(2 \, a^{2} b - b^{3} - \frac{3 \, a b^{2} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{6 \, a^{2} b \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{3 \, b^{3} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{3 \, a b^{2} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{2 \, {\left(2 \, a^{3} - a b^{2}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}}{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + \frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}}\right)}}"," ",0,"-a^2*b^2*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) + 2/3*(2*a^2*b - b^3 - 3*a*b^2*sin(x)/(cos(x) + 1) + 6*a^2*b*sin(x)^2/(cos(x) + 1)^2 - 3*b^3*sin(x)^4/(cos(x) + 1)^4 - 3*a*b^2*sin(x)^5/(cos(x) + 1)^5 + 2*(2*a^3 - a*b^2)*sin(x)^3/(cos(x) + 1)^3)/(a^4 + 2*a^2*b^2 + b^4 + 3*(a^4 + 2*a^2*b^2 + b^4)*sin(x)^2/(cos(x) + 1)^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*sin(x)^4/(cos(x) + 1)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(x)^6/(cos(x) + 1)^6)","B",0
280,1,431,0,0.451232," ","integrate(cos(x)^2*sin(x)^3/(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","-\frac{a^{3} b^{2} \log\left(-a - \frac{2 \, b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{a^{3} b^{2} \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(3 \, a^{4} b - 6 \, a^{2} b^{3} - b^{5}\right)} \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{4 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}} - \frac{\frac{8 \, a b^{2} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{16 \, a^{3} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{8 \, a b^{2} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - \frac{{\left(3 \, a^{2} b - b^{3}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{{\left(11 \, a^{2} b + 7 \, b^{3}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{{\left(11 \, a^{2} b + 7 \, b^{3}\right)} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{{\left(3 \, a^{2} b - b^{3}\right)} \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}}}{4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + \frac{4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{6 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}}\right)}}"," ",0,"-a^3*b^2*log(-a - 2*b*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + a^3*b^2*log(sin(x)^2/(cos(x) + 1)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 1/4*(3*a^4*b - 6*a^2*b^3 - b^5)*arctan(sin(x)/(cos(x) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 1/4*(8*a*b^2*sin(x)^2/(cos(x) + 1)^2 - 16*a^3*sin(x)^4/(cos(x) + 1)^4 + 8*a*b^2*sin(x)^6/(cos(x) + 1)^6 - (3*a^2*b - b^3)*sin(x)/(cos(x) + 1) - (11*a^2*b + 7*b^3)*sin(x)^3/(cos(x) + 1)^3 + (11*a^2*b + 7*b^3)*sin(x)^5/(cos(x) + 1)^5 + (3*a^2*b - b^3)*sin(x)^7/(cos(x) + 1)^7)/(a^4 + 2*a^2*b^2 + b^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*sin(x)^2/(cos(x) + 1)^2 + 6*(a^4 + 2*a^2*b^2 + b^4)*sin(x)^4/(cos(x) + 1)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*sin(x)^6/(cos(x) + 1)^6 + (a^4 + 2*a^2*b^2 + b^4)*sin(x)^8/(cos(x) + 1)^8)","B",0
281,1,281,0,0.433165," ","integrate(cos(x)^3*sin(x)/(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","\frac{a b^{3} \log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(a^{3} + 4 \, a b^{2} - \frac{3 \, b^{3} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{6 \, a b^{2} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{3 \, b^{3} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{2 \, {\left(2 \, a^{2} b - b^{3}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{3 \, {\left(a^{3} + 2 \, a b^{2}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}\right)}}{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + \frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}}\right)}}"," ",0,"a*b^3*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2/3*(a^3 + 4*a*b^2 - 3*b^3*sin(x)/(cos(x) + 1) + 6*a*b^2*sin(x)^2/(cos(x) + 1)^2 - 3*b^3*sin(x)^5/(cos(x) + 1)^5 + 2*(2*a^2*b - b^3)*sin(x)^3/(cos(x) + 1)^3 + 3*(a^3 + 2*a*b^2)*sin(x)^4/(cos(x) + 1)^4)/(a^4 + 2*a^2*b^2 + b^4 + 3*(a^4 + 2*a^2*b^2 + b^4)*sin(x)^2/(cos(x) + 1)^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*sin(x)^4/(cos(x) + 1)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(x)^6/(cos(x) + 1)^6)","B",0
282,1,424,0,0.453301," ","integrate(cos(x)^3*sin(x)^2/(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","\frac{a^{2} b^{3} \log\left(-a - \frac{2 \, b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{a^{2} b^{3} \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(a^{5} + 6 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{4 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}} + \frac{\frac{8 \, b^{3} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{16 \, a^{2} b \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{8 \, b^{3} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - \frac{{\left(a^{3} + 5 \, a b^{2}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{{\left(7 \, a^{3} + 3 \, a b^{2}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{{\left(7 \, a^{3} + 3 \, a b^{2}\right)} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{{\left(a^{3} + 5 \, a b^{2}\right)} \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}}}{4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + \frac{4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{6 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}}\right)}}"," ",0,"a^2*b^3*log(-a - 2*b*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - a^2*b^3*log(sin(x)^2/(cos(x) + 1)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 1/4*(a^5 + 6*a^3*b^2 - 3*a*b^4)*arctan(sin(x)/(cos(x) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 1/4*(8*b^3*sin(x)^2/(cos(x) + 1)^2 - 16*a^2*b*sin(x)^4/(cos(x) + 1)^4 + 8*b^3*sin(x)^6/(cos(x) + 1)^6 - (a^3 + 5*a*b^2)*sin(x)/(cos(x) + 1) + (7*a^3 + 3*a*b^2)*sin(x)^3/(cos(x) + 1)^3 - (7*a^3 + 3*a*b^2)*sin(x)^5/(cos(x) + 1)^5 + (a^3 + 5*a*b^2)*sin(x)^7/(cos(x) + 1)^7)/(a^4 + 2*a^2*b^2 + b^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*sin(x)^2/(cos(x) + 1)^2 + 6*(a^4 + 2*a^2*b^2 + b^4)*sin(x)^4/(cos(x) + 1)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*sin(x)^6/(cos(x) + 1)^6 + (a^4 + 2*a^2*b^2 + b^4)*sin(x)^8/(cos(x) + 1)^8)","B",0
283,1,521,0,0.450046," ","integrate(cos(x)^3*sin(x)^3/(a*cos(x)+b*sin(x)),x, algorithm=""maxima"")","\frac{a^{3} b^{3} \log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(2 \, a^{5} + 14 \, a^{3} b^{2} - 3 \, a b^{4} - \frac{15 \, a^{2} b^{3} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{15 \, a b^{4} \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} - \frac{15 \, a^{2} b^{3} \sin\left(x\right)^{9}}{{\left(\cos\left(x\right) + 1\right)}^{9}} + \frac{10 \, {\left(a^{5} + 7 \, a^{3} b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{20 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{10 \, {\left(a^{5} - 5 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{2 \, {\left(24 \, a^{4} b - 17 \, a^{2} b^{3} + 4 \, b^{5}\right)} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{30 \, {\left(a^{5} + 3 \, a^{3} b^{2}\right)} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - \frac{20 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}}\right)}}{15 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + \frac{5 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{10 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{10 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{5 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} + \frac{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sin\left(x\right)^{10}}{{\left(\cos\left(x\right) + 1\right)}^{10}}\right)}}"," ",0,"a^3*b^3*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a^2 + b^2)) - 2/15*(2*a^5 + 14*a^3*b^2 - 3*a*b^4 - 15*a^2*b^3*sin(x)/(cos(x) + 1) - 15*a*b^4*sin(x)^8/(cos(x) + 1)^8 - 15*a^2*b^3*sin(x)^9/(cos(x) + 1)^9 + 10*(a^5 + 7*a^3*b^2)*sin(x)^2/(cos(x) + 1)^2 - 20*(4*a^2*b^3 + b^5)*sin(x)^3/(cos(x) + 1)^3 - 10*(a^5 - 5*a^3*b^2 + 3*a*b^4)*sin(x)^4/(cos(x) + 1)^4 + 2*(24*a^4*b - 17*a^2*b^3 + 4*b^5)*sin(x)^5/(cos(x) + 1)^5 + 30*(a^5 + 3*a^3*b^2)*sin(x)^6/(cos(x) + 1)^6 - 20*(4*a^2*b^3 + b^5)*sin(x)^7/(cos(x) + 1)^7)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + 5*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sin(x)^2/(cos(x) + 1)^2 + 10*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sin(x)^4/(cos(x) + 1)^4 + 10*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sin(x)^6/(cos(x) + 1)^6 + 5*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sin(x)^8/(cos(x) + 1)^8 + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sin(x)^10/(cos(x) + 1)^10)","B",0
284,1,118,0,0.451929," ","integrate(cos(x)*sin(x)/(a*cos(x)+b*sin(x))^2,x, algorithm=""maxima"")","\frac{2 \, a b x}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(a^{2} - b^{2}\right)} \log\left(b \tan\left(x\right) + a\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{2} - b^{2}\right)} \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}} + \frac{a}{a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} \tan\left(x\right)}"," ",0,"2*a*b*x/(a^4 + 2*a^2*b^2 + b^4) - (a^2 - b^2)*log(b*tan(x) + a)/(a^4 + 2*a^2*b^2 + b^4) + 1/2*(a^2 - b^2)*log(tan(x)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + a/(a^3 + a*b^2 + (a^2*b + b^3)*tan(x))","A",0
285,1,265,0,0.459671," ","integrate(cos(x)*sin(x)^2/(a*cos(x)+b*sin(x))^2,x, algorithm=""maxima"")","-\frac{{\left(a^{2} - 2 \, b^{2}\right)} a \log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(3 \, a^{2} b + \frac{{\left(a^{3} + 4 \, a b^{2}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{{\left(a^{2} b - 2 \, b^{3}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{{\left(a^{3} - 2 \, a b^{2}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}}{a^{5} + 2 \, a^{3} b^{2} + a b^{4} + \frac{2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}}"," ",0,"-(a^2 - 2*b^2)*a*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2*(3*a^2*b + (a^3 + 4*a*b^2)*sin(x)/(cos(x) + 1) + (a^2*b - 2*b^3)*sin(x)^2/(cos(x) + 1)^2 - (a^3 - 2*a*b^2)*sin(x)^3/(cos(x) + 1)^3)/(a^5 + 2*a^3*b^2 + a*b^4 + 2*(a^4*b + 2*a^2*b^3 + b^5)*sin(x)/(cos(x) + 1) + 2*(a^4*b + 2*a^2*b^3 + b^5)*sin(x)^3/(cos(x) + 1)^3 - (a^5 + 2*a^3*b^2 + a*b^4)*sin(x)^4/(cos(x) + 1)^4)","B",0
286,1,259,0,0.458403," ","integrate(cos(x)*sin(x)^3/(a*cos(x)+b*sin(x))^2,x, algorithm=""maxima"")","\frac{{\left(3 \, a^{3} b - a b^{3}\right)} x}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(a^{4} - 3 \, a^{2} b^{2}\right)} \log\left(b \tan\left(x\right) + a\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(a^{4} - 3 \, a^{2} b^{2}\right)} \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}} + \frac{3 \, a^{3} - a b^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} \tan\left(x\right)^{2} - {\left(a^{2} b + b^{3}\right)} \tan\left(x\right)}{2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \tan\left(x\right)^{3} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \tan\left(x\right)^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \tan\left(x\right)\right)}}"," ",0,"(3*a^3*b - a*b^3)*x/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (a^4 - 3*a^2*b^2)*log(b*tan(x) + a)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 1/2*(a^4 - 3*a^2*b^2)*log(tan(x)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 1/2*(3*a^3 - a*b^2 + 2*(a^3 - a*b^2)*tan(x)^2 - (a^2*b + b^3)*tan(x))/(a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*tan(x)^3 + (a^5 + 2*a^3*b^2 + a*b^4)*tan(x)^2 + (a^4*b + 2*a^2*b^3 + b^5)*tan(x))","B",0
287,1,264,0,0.442574," ","integrate(cos(x)^2*sin(x)/(a*cos(x)+b*sin(x))^2,x, algorithm=""maxima"")","\frac{{\left(2 \, a^{2} b - b^{3}\right)} \log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(a^{3} - 2 \, a b^{2} - \frac{3 \, b^{3} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{{\left(a^{3} + 4 \, a b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{{\left(2 \, a^{2} b - b^{3}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}}{a^{5} + 2 \, a^{3} b^{2} + a b^{4} + \frac{2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}}"," ",0,"(2*a^2*b - b^3)*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2*(a^3 - 2*a*b^2 - 3*b^3*sin(x)/(cos(x) + 1) - (a^3 + 4*a*b^2)*sin(x)^2/(cos(x) + 1)^2 + (2*a^2*b - b^3)*sin(x)^3/(cos(x) + 1)^3)/(a^5 + 2*a^3*b^2 + a*b^4 + 2*(a^4*b + 2*a^2*b^3 + b^5)*sin(x)/(cos(x) + 1) + 2*(a^4*b + 2*a^2*b^3 + b^5)*sin(x)^3/(cos(x) + 1)^3 - (a^5 + 2*a^3*b^2 + a*b^4)*sin(x)^4/(cos(x) + 1)^4)","B",0
288,1,257,0,0.458834," ","integrate(cos(x)^2*sin(x)^2/(a*cos(x)+b*sin(x))^2,x, algorithm=""maxima"")","\frac{{\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} x}{2 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}} + \frac{2 \, {\left(a^{3} b - a b^{3}\right)} \log\left(b \tan\left(x\right) + a\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(a^{3} b - a b^{3}\right)} \log\left(\tan\left(x\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{4 \, a^{2} b + {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(x\right)^{2} + {\left(a^{3} + a b^{2}\right)} \tan\left(x\right)}{2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \tan\left(x\right)^{3} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \tan\left(x\right)^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \tan\left(x\right)\right)}}"," ",0,"1/2*(a^4 - 6*a^2*b^2 + b^4)*x/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(a^3*b - a*b^3)*log(b*tan(x) + a)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (a^3*b - a*b^3)*log(tan(x)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 1/2*(4*a^2*b + (3*a^2*b - b^3)*tan(x)^2 + (a^3 + a*b^2)*tan(x))/(a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*tan(x)^3 + (a^5 + 2*a^3*b^2 + a*b^4)*tan(x)^2 + (a^4*b + 2*a^2*b^3 + b^5)*tan(x))","B",0
289,1,611,0,0.481327," ","integrate(cos(x)^2*sin(x)^3/(a*cos(x)+b*sin(x))^2,x, algorithm=""maxima"")","\frac{{\left(2 \, a^{2} b - 3 \, b^{3}\right)} a^{2} \log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(2 \, a^{5} - 12 \, a^{3} b^{2} + a b^{4} - \frac{{\left(2 \, a^{4} b + 15 \, a^{2} b^{3} - 2 \, b^{5}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{{\left(4 \, a^{5} - 30 \, a^{3} b^{2} + 11 \, a b^{4}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{{\left(2 \, a^{4} b + 47 \, a^{2} b^{3}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{{\left(6 \, a^{5} + 40 \, a^{3} b^{2} - 11 \, a b^{4}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{{\left(14 \, a^{4} b - 25 \, a^{2} b^{3} + 6 \, b^{5}\right)} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{3 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{3 \, {\left(2 \, a^{4} b - 3 \, a^{2} b^{3}\right)} \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}}\right)}}{3 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6} + \frac{2 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{2 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{6 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{6 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{2 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{2 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} - \frac{{\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}}\right)}}"," ",0,"(2*a^2*b - 3*b^3)*a^2*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a^2 + b^2)) - 2/3*(2*a^5 - 12*a^3*b^2 + a*b^4 - (2*a^4*b + 15*a^2*b^3 - 2*b^5)*sin(x)/(cos(x) + 1) + (4*a^5 - 30*a^3*b^2 + 11*a*b^4)*sin(x)^2/(cos(x) + 1)^2 - (2*a^4*b + 47*a^2*b^3)*sin(x)^3/(cos(x) + 1)^3 - (6*a^5 + 40*a^3*b^2 - 11*a*b^4)*sin(x)^4/(cos(x) + 1)^4 + (14*a^4*b - 25*a^2*b^3 + 6*b^5)*sin(x)^5/(cos(x) + 1)^5 - 3*(2*a^3*b^2 - 3*a*b^4)*sin(x)^6/(cos(x) + 1)^6 + 3*(2*a^4*b - 3*a^2*b^3)*sin(x)^7/(cos(x) + 1)^7)/(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6 + 2*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sin(x)/(cos(x) + 1) + 2*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*sin(x)^2/(cos(x) + 1)^2 + 6*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sin(x)^3/(cos(x) + 1)^3 + 6*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sin(x)^5/(cos(x) + 1)^5 - 2*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*sin(x)^6/(cos(x) + 1)^6 + 2*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sin(x)^7/(cos(x) + 1)^7 - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*sin(x)^8/(cos(x) + 1)^8)","B",0
290,1,256,0,0.457160," ","integrate(cos(x)^3*sin(x)/(a*cos(x)+b*sin(x))^2,x, algorithm=""maxima"")","-\frac{{\left(a^{3} b - 3 \, a b^{3}\right)} x}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(3 \, a^{2} b^{2} - b^{4}\right)} \log\left(b \tan\left(x\right) + a\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(3 \, a^{2} b^{2} - b^{4}\right)} \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}} + \frac{4 \, a b^{2} \tan\left(x\right)^{2} - a^{3} + 3 \, a b^{2} + {\left(a^{2} b + b^{3}\right)} \tan\left(x\right)}{2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \tan\left(x\right)^{3} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \tan\left(x\right)^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \tan\left(x\right)\right)}}"," ",0,"-(a^3*b - 3*a*b^3)*x/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (3*a^2*b^2 - b^4)*log(b*tan(x) + a)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 1/2*(3*a^2*b^2 - b^4)*log(tan(x)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 1/2*(4*a*b^2*tan(x)^2 - a^3 + 3*a*b^2 + (a^2*b + b^3)*tan(x))/(a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*tan(x)^3 + (a^5 + 2*a^3*b^2 + a*b^4)*tan(x)^2 + (a^4*b + 2*a^2*b^3 + b^5)*tan(x))","B",0
291,1,606,0,0.484673," ","integrate(cos(x)^3*sin(x)^2/(a*cos(x)+b*sin(x))^2,x, algorithm=""maxima"")","-\frac{{\left(3 \, a^{2} b^{2} - 2 \, b^{4}\right)} a \log\left(\frac{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} + b^{2}}} + \frac{2 \, {\left(4 \, a^{4} b - 11 \, a^{2} b^{3} - \frac{{\left(a^{3} b^{2} + 16 \, a b^{4}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{{\left(8 \, a^{4} b - 31 \, a^{2} b^{3} + 6 \, b^{5}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{{\left(4 \, a^{5} + 15 \, a^{3} b^{2} - 34 \, a b^{4}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{{\left(4 \, a^{4} b + 45 \, a^{2} b^{3} - 4 \, b^{5}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{{\left(4 \, a^{5} - 9 \, a^{3} b^{2} + 32 \, a b^{4}\right)} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{3 \, {\left(3 \, a^{2} b^{3} - 2 \, b^{5}\right)} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{3 \, {\left(3 \, a^{3} b^{2} - 2 \, a b^{4}\right)} \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}}\right)}}{3 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6} + \frac{2 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{2 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{6 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{6 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{2 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{2 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} - \frac{{\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}}\right)}}"," ",0,"-(3*a^2*b^2 - 2*b^4)*a*log((b - a*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(b - a*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a^2 + b^2)) + 2/3*(4*a^4*b - 11*a^2*b^3 - (a^3*b^2 + 16*a*b^4)*sin(x)/(cos(x) + 1) + (8*a^4*b - 31*a^2*b^3 + 6*b^5)*sin(x)^2/(cos(x) + 1)^2 + (4*a^5 + 15*a^3*b^2 - 34*a*b^4)*sin(x)^3/(cos(x) + 1)^3 - (4*a^4*b + 45*a^2*b^3 - 4*b^5)*sin(x)^4/(cos(x) + 1)^4 - (4*a^5 - 9*a^3*b^2 + 32*a*b^4)*sin(x)^5/(cos(x) + 1)^5 - 3*(3*a^2*b^3 - 2*b^5)*sin(x)^6/(cos(x) + 1)^6 + 3*(3*a^3*b^2 - 2*a*b^4)*sin(x)^7/(cos(x) + 1)^7)/(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6 + 2*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sin(x)/(cos(x) + 1) + 2*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*sin(x)^2/(cos(x) + 1)^2 + 6*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sin(x)^3/(cos(x) + 1)^3 + 6*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sin(x)^5/(cos(x) + 1)^5 - 2*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*sin(x)^6/(cos(x) + 1)^6 + 2*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sin(x)^7/(cos(x) + 1)^7 - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*sin(x)^8/(cos(x) + 1)^8)","B",0
292,1,456,0,0.470248," ","integrate(cos(x)^3*sin(x)^3/(a*cos(x)+b*sin(x))^2,x, algorithm=""maxima"")","-\frac{3 \, {\left(a^{5} b - 6 \, a^{3} b^{3} + a b^{5}\right)} x}{4 \, {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)}} - \frac{3 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} \log\left(b \tan\left(x\right) + a\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{3 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)}} - \frac{a^{5} - 10 \, a^{3} b^{2} + a b^{4} - 3 \, {\left(3 \, a^{3} b^{2} - a b^{4}\right)} \tan\left(x\right)^{4} - 3 \, {\left(a^{4} b + a^{2} b^{3}\right)} \tan\left(x\right)^{3} + {\left(2 \, a^{5} - 17 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \tan\left(x\right)^{2} - {\left(2 \, a^{4} b + a^{2} b^{3} - b^{5}\right)} \tan\left(x\right)}{4 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \tan\left(x\right)^{5} + {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \tan\left(x\right)^{4} + 2 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \tan\left(x\right)^{3} + 2 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \tan\left(x\right)^{2} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \tan\left(x\right)\right)}}"," ",0,"-3/4*(a^5*b - 6*a^3*b^3 + a*b^5)*x/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 3*(a^4*b^2 - a^2*b^4)*log(b*tan(x) + a)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 3/2*(a^4*b^2 - a^2*b^4)*log(tan(x)^2 + 1)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 1/4*(a^5 - 10*a^3*b^2 + a*b^4 - 3*(3*a^3*b^2 - a*b^4)*tan(x)^4 - 3*(a^4*b + a^2*b^3)*tan(x)^3 + (2*a^5 - 17*a^3*b^2 + 5*a*b^4)*tan(x)^2 - (2*a^4*b + a^2*b^3 - b^5)*tan(x))/(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6 + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*tan(x)^5 + (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*tan(x)^4 + 2*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*tan(x)^3 + 2*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*tan(x)^2 + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*tan(x))","B",0
293,1,98,0,0.451787," ","integrate(tan(x)/(b*cos(x)+a*sin(x)),x, algorithm=""maxima"")","\frac{b \log\left(\frac{a - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{a - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} a} + \frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)}{a}"," ",0,"b*log((a - b*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(a - b*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*a) + log(sin(x)/(cos(x) + 1) + 1)/a - log(sin(x)/(cos(x) + 1) - 1)/a","B",0
294,1,79,0,0.458135," ","integrate(cot(x)/(b*cos(x)+a*sin(x)),x, algorithm=""maxima"")","\frac{a \log\left(\frac{a - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{a - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} b} + \frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{b}"," ",0,"a*log((a - b*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(a - b*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b) + log(sin(x)/(cos(x) + 1))/b","A",0
