1,1,37,0,0.853825," ","integrate(sin(x)^6/(a-a*cos(x)^2),x, algorithm=""maxima"")","-\frac{5 \, \tan\left(x\right)^{3} + 3 \, \tan\left(x\right)}{8 \, {\left(a \tan\left(x\right)^{4} + 2 \, a \tan\left(x\right)^{2} + a\right)}} + \frac{3 \, x}{8 \, a}"," ",0,"-1/8*(5*tan(x)^3 + 3*tan(x))/(a*tan(x)^4 + 2*a*tan(x)^2 + a) + 3/8*x/a","A",0
2,1,14,0,0.574461," ","integrate(sin(x)^5/(a-a*cos(x)^2),x, algorithm=""maxima"")","\frac{\cos\left(x\right)^{3} - 3 \, \cos\left(x\right)}{3 \, a}"," ",0,"1/3*(cos(x)^3 - 3*cos(x))/a","A",0
3,1,21,0,0.862300," ","integrate(sin(x)^4/(a-a*cos(x)^2),x, algorithm=""maxima"")","\frac{x}{2 \, a} - \frac{\tan\left(x\right)}{2 \, {\left(a \tan\left(x\right)^{2} + a\right)}}"," ",0,"1/2*x/a - 1/2*tan(x)/(a*tan(x)^2 + a)","A",0
4,1,7,0,0.659223," ","integrate(sin(x)^3/(a-a*cos(x)^2),x, algorithm=""maxima"")","-\frac{\cos\left(x\right)}{a}"," ",0,"-cos(x)/a","A",0
5,1,5,0,0.883536," ","integrate(sin(x)^2/(a-a*cos(x)^2),x, algorithm=""maxima"")","\frac{x}{a}"," ",0,"x/a","A",0
6,1,21,0,0.311921," ","integrate(sin(x)/(a-a*cos(x)^2),x, algorithm=""maxima"")","-\frac{\log\left(\cos\left(x\right) + 1\right)}{2 \, a} + \frac{\log\left(\cos\left(x\right) - 1\right)}{2 \, a}"," ",0,"-1/2*log(cos(x) + 1)/a + 1/2*log(cos(x) - 1)/a","B",0
7,1,37,0,0.483774," ","integrate(csc(x)/(a-a*cos(x)^2),x, algorithm=""maxima"")","\frac{\cos\left(x\right)}{2 \, {\left(a \cos\left(x\right)^{2} - a\right)}} - \frac{\log\left(\cos\left(x\right) + 1\right)}{4 \, a} + \frac{\log\left(\cos\left(x\right) - 1\right)}{4 \, a}"," ",0,"1/2*cos(x)/(a*cos(x)^2 - a) - 1/4*log(cos(x) + 1)/a + 1/4*log(cos(x) - 1)/a","B",0
8,1,17,0,0.321277," ","integrate(csc(x)^2/(a-a*cos(x)^2),x, algorithm=""maxima"")","-\frac{3 \, \tan\left(x\right)^{2} + 1}{3 \, a \tan\left(x\right)^{3}}"," ",0,"-1/3*(3*tan(x)^2 + 1)/(a*tan(x)^3)","A",0
9,1,51,0,0.703080," ","integrate(csc(x)^3/(a-a*cos(x)^2),x, algorithm=""maxima"")","\frac{3 \, \cos\left(x\right)^{3} - 5 \, \cos\left(x\right)}{8 \, {\left(a \cos\left(x\right)^{4} - 2 \, a \cos\left(x\right)^{2} + a\right)}} - \frac{3 \, \log\left(\cos\left(x\right) + 1\right)}{16 \, a} + \frac{3 \, \log\left(\cos\left(x\right) - 1\right)}{16 \, a}"," ",0,"1/8*(3*cos(x)^3 - 5*cos(x))/(a*cos(x)^4 - 2*a*cos(x)^2 + a) - 3/16*log(cos(x) + 1)/a + 3/16*log(cos(x) - 1)/a","A",0
10,1,87,0,0.880592," ","integrate(sin(x)^7/(a+b*cos(x)^2),x, algorithm=""maxima"")","-\frac{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{b \cos\left(x\right)}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} + \frac{3 \, b^{2} \cos\left(x\right)^{5} - 5 \, {\left(a b + 3 \, b^{2}\right)} \cos\left(x\right)^{3} + 15 \, {\left(a^{2} + 3 \, a b + 3 \, b^{2}\right)} \cos\left(x\right)}{15 \, b^{3}}"," ",0,"-(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*arctan(b*cos(x)/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/15*(3*b^2*cos(x)^5 - 5*(a*b + 3*b^2)*cos(x)^3 + 15*(a^2 + 3*a*b + 3*b^2)*cos(x))/b^3","A",0
11,1,53,0,0.826118," ","integrate(sin(x)^5/(a+b*cos(x)^2),x, algorithm=""maxima"")","-\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \arctan\left(\frac{b \cos\left(x\right)}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} - \frac{b \cos\left(x\right)^{3} - 3 \, {\left(a + 2 \, b\right)} \cos\left(x\right)}{3 \, b^{2}}"," ",0,"-(a^2 + 2*a*b + b^2)*arctan(b*cos(x)/sqrt(a*b))/(sqrt(a*b)*b^2) - 1/3*(b*cos(x)^3 - 3*(a + 2*b)*cos(x))/b^2","A",0
12,1,30,0,2.343357," ","integrate(sin(x)^3/(a+b*cos(x)^2),x, algorithm=""maxima"")","-\frac{{\left(a + b\right)} \arctan\left(\frac{b \cos\left(x\right)}{\sqrt{a b}}\right)}{\sqrt{a b} b} + \frac{\cos\left(x\right)}{b}"," ",0,"-(a + b)*arctan(b*cos(x)/sqrt(a*b))/(sqrt(a*b)*b) + cos(x)/b","A",0
13,1,17,0,0.922849," ","integrate(sin(x)/(a+b*cos(x)^2),x, algorithm=""maxima"")","-\frac{\arctan\left(\frac{b \cos\left(x\right)}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"-arctan(b*cos(x)/sqrt(a*b))/sqrt(a*b)","A",0
14,1,48,0,1.719716," ","integrate(csc(x)/(a+b*cos(x)^2),x, algorithm=""maxima"")","-\frac{b \arctan\left(\frac{b \cos\left(x\right)}{\sqrt{a b}}\right)}{\sqrt{a b} {\left(a + b\right)}} - \frac{\log\left(\cos\left(x\right) + 1\right)}{2 \, {\left(a + b\right)}} + \frac{\log\left(\cos\left(x\right) - 1\right)}{2 \, {\left(a + b\right)}}"," ",0,"-b*arctan(b*cos(x)/sqrt(a*b))/(sqrt(a*b)*(a + b)) - 1/2*log(cos(x) + 1)/(a + b) + 1/2*log(cos(x) - 1)/(a + b)","A",0
15,1,105,0,1.182517," ","integrate(csc(x)^3/(a+b*cos(x)^2),x, algorithm=""maxima"")","-\frac{b^{2} \arctan\left(\frac{b \cos\left(x\right)}{\sqrt{a b}}\right)}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a b}} - \frac{{\left(a + 3 \, b\right)} \log\left(\cos\left(x\right) + 1\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)}} + \frac{{\left(a + 3 \, b\right)} \log\left(\cos\left(x\right) - 1\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)}} + \frac{\cos\left(x\right)}{2 \, {\left({\left(a + b\right)} \cos\left(x\right)^{2} - a - b\right)}}"," ",0,"-b^2*arctan(b*cos(x)/sqrt(a*b))/((a^2 + 2*a*b + b^2)*sqrt(a*b)) - 1/4*(a + 3*b)*log(cos(x) + 1)/(a^2 + 2*a*b + b^2) + 1/4*(a + 3*b)*log(cos(x) - 1)/(a^2 + 2*a*b + b^2) + 1/2*cos(x)/((a + b)*cos(x)^2 - a - b)","B",0
16,1,200,0,0.725575," ","integrate(csc(x)^5/(a+b*cos(x)^2),x, algorithm=""maxima"")","-\frac{b^{3} \arctan\left(\frac{b \cos\left(x\right)}{\sqrt{a b}}\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{a b}} - \frac{{\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \log\left(\cos\left(x\right) + 1\right)}{16 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)}} + \frac{{\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \log\left(\cos\left(x\right) - 1\right)}{16 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)}} + \frac{{\left(3 \, a + 7 \, b\right)} \cos\left(x\right)^{3} - {\left(5 \, a + 9 \, b\right)} \cos\left(x\right)}{8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cos\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)}}"," ",0,"-b^3*arctan(b*cos(x)/sqrt(a*b))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt(a*b)) - 1/16*(3*a^2 + 10*a*b + 15*b^2)*log(cos(x) + 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 1/16*(3*a^2 + 10*a*b + 15*b^2)*log(cos(x) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 1/8*((3*a + 7*b)*cos(x)^3 - (5*a + 9*b)*cos(x))/((a^2 + 2*a*b + b^2)*cos(x)^4 - 2*(a^2 + 2*a*b + b^2)*cos(x)^2 + a^2 + 2*a*b + b^2)","B",0
17,1,112,0,1.025501," ","integrate(sin(x)^6/(a+b*cos(x)^2),x, algorithm=""maxima"")","\frac{{\left(4 \, a + 9 \, b\right)} \tan\left(x\right)^{3} + {\left(4 \, a + 7 \, b\right)} \tan\left(x\right)}{8 \, {\left(b^{2} \tan\left(x\right)^{4} + 2 \, b^{2} \tan\left(x\right)^{2} + b^{2}\right)}} - \frac{{\left(8 \, a^{2} + 20 \, a b + 15 \, b^{2}\right)} x}{8 \, b^{3}} + \frac{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} b^{3}}"," ",0,"1/8*((4*a + 9*b)*tan(x)^3 + (4*a + 7*b)*tan(x))/(b^2*tan(x)^4 + 2*b^2*tan(x)^2 + b^2) - 1/8*(8*a^2 + 20*a*b + 15*b^2)*x/b^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*arctan(a*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*b^3)","A",0
18,1,62,0,0.772214," ","integrate(sin(x)^4/(a+b*cos(x)^2),x, algorithm=""maxima"")","-\frac{{\left(2 \, a + 3 \, b\right)} x}{2 \, b^{2}} + \frac{\tan\left(x\right)}{2 \, {\left(b \tan\left(x\right)^{2} + b\right)}} + \frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} b^{2}}"," ",0,"-1/2*(2*a + 3*b)*x/b^2 + 1/2*tan(x)/(b*tan(x)^2 + b) + (a^2 + 2*a*b + b^2)*arctan(a*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*b^2)","A",0
19,1,33,0,1.735248," ","integrate(sin(x)^2/(a+b*cos(x)^2),x, algorithm=""maxima"")","\frac{{\left(a + b\right)} \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} b} - \frac{x}{b}"," ",0,"(a + b)*arctan(a*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*b) - x/b","A",0
20,1,20,0,0.953234," ","integrate(1/(a+b*cos(x)^2),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{a \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a}}"," ",0,"arctan(a*tan(x)/sqrt((a + b)*a))/sqrt((a + b)*a)","A",0
21,1,38,0,0.738701," ","integrate(csc(x)^2/(a+b*cos(x)^2),x, algorithm=""maxima"")","\frac{b \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} {\left(a + b\right)}} - \frac{1}{{\left(a + b\right)} \tan\left(x\right)}"," ",0,"b*arctan(a*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*(a + b)) - 1/((a + b)*tan(x))","A",0
22,1,70,0,1.091661," ","integrate(csc(x)^4/(a+b*cos(x)^2),x, algorithm=""maxima"")","\frac{b^{2} \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} {\left(a^{2} + 2 \, a b + b^{2}\right)}} - \frac{3 \, {\left(a + 2 \, b\right)} \tan\left(x\right)^{2} + a + b}{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \tan\left(x\right)^{3}}"," ",0,"b^2*arctan(a*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*(a^2 + 2*a*b + b^2)) - 1/3*(3*(a + 2*b)*tan(x)^2 + a + b)/((a^2 + 2*a*b + b^2)*tan(x)^3)","A",0
23,1,127,0,0.846901," ","integrate(csc(x)^6/(a+b*cos(x)^2),x, algorithm=""maxima"")","\frac{b^{3} \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} a}} - \frac{15 \, {\left(a^{2} + 3 \, a b + 3 \, b^{2}\right)} \tan\left(x\right)^{4} + 5 \, {\left(2 \, a^{2} + 5 \, a b + 3 \, b^{2}\right)} \tan\left(x\right)^{2} + 3 \, a^{2} + 6 \, a b + 3 \, b^{2}}{15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \tan\left(x\right)^{5}}"," ",0,"b^3*arctan(a*tan(x)/sqrt((a + b)*a))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt((a + b)*a)) - 1/15*(15*(a^2 + 3*a*b + 3*b^2)*tan(x)^4 + 5*(2*a^2 + 5*a*b + 3*b^2)*tan(x)^2 + 3*a^2 + 6*a*b + 3*b^2)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*tan(x)^5)","A",0
24,1,89,0,0.917026," ","integrate(sin(x)/(4-3*cos(x)^3),x, algorithm=""maxima"")","-\frac{1}{72} \cdot 4^{\frac{1}{3}} 3^{\frac{2}{3}} \log\left(3^{\frac{2}{3}} \cos\left(x\right)^{2} + 4^{\frac{1}{3}} 3^{\frac{1}{3}} \cos\left(x\right) + 4^{\frac{2}{3}}\right) + \frac{1}{36} \cdot 4^{\frac{1}{3}} 3^{\frac{2}{3}} \log\left(\frac{1}{3} \cdot 3^{\frac{2}{3}} {\left(3^{\frac{1}{3}} \cos\left(x\right) - 4^{\frac{1}{3}}\right)}\right) - \frac{1}{12} \cdot 4^{\frac{1}{3}} 3^{\frac{1}{6}} \arctan\left(\frac{1}{12} \cdot 4^{\frac{2}{3}} 3^{\frac{1}{6}} {\left(2 \cdot 3^{\frac{2}{3}} \cos\left(x\right) + 4^{\frac{1}{3}} 3^{\frac{1}{3}}\right)}\right)"," ",0,"-1/72*4^(1/3)*3^(2/3)*log(3^(2/3)*cos(x)^2 + 4^(1/3)*3^(1/3)*cos(x) + 4^(2/3)) + 1/36*4^(1/3)*3^(2/3)*log(1/3*3^(2/3)*(3^(1/3)*cos(x) - 4^(1/3))) - 1/12*4^(1/3)*3^(1/6)*arctan(1/12*4^(2/3)*3^(1/6)*(2*3^(2/3)*cos(x) + 4^(1/3)*3^(1/3)))","A",0
25,1,6,0,0.497539," ","integrate(1/(1-cos(x)^2),x, algorithm=""maxima"")","-\frac{1}{\tan\left(x\right)}"," ",0,"-1/tan(x)","A",0
26,1,14,0,0.865554," ","integrate(1/(1-cos(x)^2)^2,x, algorithm=""maxima"")","-\frac{3 \, \tan\left(x\right)^{2} + 1}{3 \, \tan\left(x\right)^{3}}"," ",0,"-1/3*(3*tan(x)^2 + 1)/tan(x)^3","A",0
27,1,20,0,0.306460," ","integrate(1/(1-cos(x)^2)^3,x, algorithm=""maxima"")","-\frac{15 \, \tan\left(x\right)^{4} + 10 \, \tan\left(x\right)^{2} + 3}{15 \, \tan\left(x\right)^{5}}"," ",0,"-1/15*(15*tan(x)^4 + 10*tan(x)^2 + 3)/tan(x)^5","A",0
28,1,91,0,1.081246," ","integrate(cos(x)^7/(a+b*cos(x)^2),x, algorithm=""maxima"")","\frac{a^{3} \log\left(\frac{b \sin\left(x\right) - \sqrt{{\left(a + b\right)} b}}{b \sin\left(x\right) + \sqrt{{\left(a + b\right)} b}}\right)}{2 \, \sqrt{{\left(a + b\right)} b} b^{3}} + \frac{3 \, b^{2} \sin\left(x\right)^{5} + 5 \, {\left(a b - 2 \, b^{2}\right)} \sin\left(x\right)^{3} + 15 \, {\left(a^{2} - a b + b^{2}\right)} \sin\left(x\right)}{15 \, b^{3}}"," ",0,"1/2*a^3*log((b*sin(x) - sqrt((a + b)*b))/(b*sin(x) + sqrt((a + b)*b)))/(sqrt((a + b)*b)*b^3) + 1/15*(3*b^2*sin(x)^5 + 5*(a*b - 2*b^2)*sin(x)^3 + 15*(a^2 - a*b + b^2)*sin(x))/b^3","A",0
29,1,67,0,0.692733," ","integrate(cos(x)^5/(a+b*cos(x)^2),x, algorithm=""maxima"")","-\frac{a^{2} \log\left(\frac{b \sin\left(x\right) - \sqrt{{\left(a + b\right)} b}}{b \sin\left(x\right) + \sqrt{{\left(a + b\right)} b}}\right)}{2 \, \sqrt{{\left(a + b\right)} b} b^{2}} - \frac{b \sin\left(x\right)^{3} + 3 \, {\left(a - b\right)} \sin\left(x\right)}{3 \, b^{2}}"," ",0,"-1/2*a^2*log((b*sin(x) - sqrt((a + b)*b))/(b*sin(x) + sqrt((a + b)*b)))/(sqrt((a + b)*b)*b^2) - 1/3*(b*sin(x)^3 + 3*(a - b)*sin(x))/b^2","A",0
30,1,50,0,0.543229," ","integrate(cos(x)^3/(a+b*cos(x)^2),x, algorithm=""maxima"")","\frac{a \log\left(\frac{b \sin\left(x\right) - \sqrt{{\left(a + b\right)} b}}{b \sin\left(x\right) + \sqrt{{\left(a + b\right)} b}}\right)}{2 \, \sqrt{{\left(a + b\right)} b} b} + \frac{\sin\left(x\right)}{b}"," ",0,"1/2*a*log((b*sin(x) - sqrt((a + b)*b))/(b*sin(x) + sqrt((a + b)*b)))/(sqrt((a + b)*b)*b) + sin(x)/b","A",0
31,1,39,0,0.850445," ","integrate(cos(x)/(a+b*cos(x)^2),x, algorithm=""maxima"")","-\frac{\log\left(\frac{b \sin\left(x\right) - \sqrt{{\left(a + b\right)} b}}{b \sin\left(x\right) + \sqrt{{\left(a + b\right)} b}}\right)}{2 \, \sqrt{{\left(a + b\right)} b}}"," ",0,"-1/2*log((b*sin(x) - sqrt((a + b)*b))/(b*sin(x) + sqrt((a + b)*b)))/sqrt((a + b)*b)","A",0
32,1,64,0,0.924308," ","integrate(sec(x)/(a+b*cos(x)^2),x, algorithm=""maxima"")","\frac{b \log\left(\frac{b \sin\left(x\right) - \sqrt{{\left(a + b\right)} b}}{b \sin\left(x\right) + \sqrt{{\left(a + b\right)} b}}\right)}{2 \, \sqrt{{\left(a + b\right)} b} a} + \frac{\log\left(\sin\left(x\right) + 1\right)}{2 \, a} - \frac{\log\left(\sin\left(x\right) - 1\right)}{2 \, a}"," ",0,"1/2*b*log((b*sin(x) - sqrt((a + b)*b))/(b*sin(x) + sqrt((a + b)*b)))/(sqrt((a + b)*b)*a) + 1/2*log(sin(x) + 1)/a - 1/2*log(sin(x) - 1)/a","A",0
33,1,92,0,1.260694," ","integrate(sec(x)^3/(a+b*cos(x)^2),x, algorithm=""maxima"")","-\frac{b^{2} \log\left(\frac{b \sin\left(x\right) - \sqrt{{\left(a + b\right)} b}}{b \sin\left(x\right) + \sqrt{{\left(a + b\right)} b}}\right)}{2 \, \sqrt{{\left(a + b\right)} b} a^{2}} + \frac{{\left(a - 2 \, b\right)} \log\left(\sin\left(x\right) + 1\right)}{4 \, a^{2}} - \frac{{\left(a - 2 \, b\right)} \log\left(\sin\left(x\right) - 1\right)}{4 \, a^{2}} - \frac{\sin\left(x\right)}{2 \, {\left(a \sin\left(x\right)^{2} - a\right)}}"," ",0,"-1/2*b^2*log((b*sin(x) - sqrt((a + b)*b))/(b*sin(x) + sqrt((a + b)*b)))/(sqrt((a + b)*b)*a^2) + 1/4*(a - 2*b)*log(sin(x) + 1)/a^2 - 1/4*(a - 2*b)*log(sin(x) - 1)/a^2 - 1/2*sin(x)/(a*sin(x)^2 - a)","A",0
34,1,145,0,1.994113," ","integrate(sec(x)^5/(a+b*cos(x)^2),x, algorithm=""maxima"")","\frac{b^{3} \log\left(\frac{b \sin\left(x\right) - \sqrt{{\left(a + b\right)} b}}{b \sin\left(x\right) + \sqrt{{\left(a + b\right)} b}}\right)}{2 \, \sqrt{{\left(a + b\right)} b} a^{3}} - \frac{{\left(3 \, a - 4 \, b\right)} \sin\left(x\right)^{3} - {\left(5 \, a - 4 \, b\right)} \sin\left(x\right)}{8 \, {\left(a^{2} \sin\left(x\right)^{4} - 2 \, a^{2} \sin\left(x\right)^{2} + a^{2}\right)}} + \frac{{\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \log\left(\sin\left(x\right) + 1\right)}{16 \, a^{3}} - \frac{{\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \log\left(\sin\left(x\right) - 1\right)}{16 \, a^{3}}"," ",0,"1/2*b^3*log((b*sin(x) - sqrt((a + b)*b))/(b*sin(x) + sqrt((a + b)*b)))/(sqrt((a + b)*b)*a^3) - 1/8*((3*a - 4*b)*sin(x)^3 - (5*a - 4*b)*sin(x))/(a^2*sin(x)^4 - 2*a^2*sin(x)^2 + a^2) + 1/16*(3*a^2 - 4*a*b + 8*b^2)*log(sin(x) + 1)/a^3 - 1/16*(3*a^2 - 4*a*b + 8*b^2)*log(sin(x) - 1)/a^3","A",0
35,1,97,0,1.048879," ","integrate(cos(x)^6/(a+b*cos(x)^2),x, algorithm=""maxima"")","-\frac{a^{3} \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} b^{3}} - \frac{{\left(4 \, a - 3 \, b\right)} \tan\left(x\right)^{3} + {\left(4 \, a - 5 \, b\right)} \tan\left(x\right)}{8 \, {\left(b^{2} \tan\left(x\right)^{4} + 2 \, b^{2} \tan\left(x\right)^{2} + b^{2}\right)}} + \frac{{\left(8 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} x}{8 \, b^{3}}"," ",0,"-a^3*arctan(a*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*b^3) - 1/8*((4*a - 3*b)*tan(x)^3 + (4*a - 5*b)*tan(x))/(b^2*tan(x)^4 + 2*b^2*tan(x)^2 + b^2) + 1/8*(8*a^2 - 4*a*b + 3*b^2)*x/b^3","A",0
36,1,54,0,0.909631," ","integrate(cos(x)^4/(a+b*cos(x)^2),x, algorithm=""maxima"")","\frac{a^{2} \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} b^{2}} - \frac{{\left(2 \, a - b\right)} x}{2 \, b^{2}} + \frac{\tan\left(x\right)}{2 \, {\left(b \tan\left(x\right)^{2} + b\right)}}"," ",0,"a^2*arctan(a*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*b^2) - 1/2*(2*a - b)*x/b^2 + 1/2*tan(x)/(b*tan(x)^2 + b)","A",0
37,1,31,0,1.394624," ","integrate(cos(x)^2/(a+b*cos(x)^2),x, algorithm=""maxima"")","-\frac{a \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} b} + \frac{x}{b}"," ",0,"-a*arctan(a*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*b) + x/b","A",0
38,1,20,0,1.431400," ","integrate(1/(a+b*cos(x)^2),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{a \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a}}"," ",0,"arctan(a*tan(x)/sqrt((a + b)*a))/sqrt((a + b)*a)","A",0
39,1,32,0,0.888245," ","integrate(sec(x)^2/(a+b*cos(x)^2),x, algorithm=""maxima"")","-\frac{b \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} a} + \frac{\tan\left(x\right)}{a}"," ",0,"-b*arctan(a*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*a) + tan(x)/a","A",0
40,1,48,0,0.869810," ","integrate(sec(x)^4/(a+b*cos(x)^2),x, algorithm=""maxima"")","\frac{b^{2} \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} a^{2}} + \frac{a \tan\left(x\right)^{3} + 3 \, {\left(a - b\right)} \tan\left(x\right)}{3 \, a^{2}}"," ",0,"b^2*arctan(a*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*a^2) + 1/3*(a*tan(x)^3 + 3*(a - b)*tan(x))/a^2","A",0
41,1,74,0,0.861952," ","integrate(sec(x)^6/(a+b*cos(x)^2),x, algorithm=""maxima"")","-\frac{b^{3} \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} a^{3}} + \frac{3 \, a^{2} \tan\left(x\right)^{5} + 5 \, {\left(2 \, a^{2} - a b\right)} \tan\left(x\right)^{3} + 15 \, {\left(a^{2} - a b + b^{2}\right)} \tan\left(x\right)}{15 \, a^{3}}"," ",0,"-b^3*arctan(a*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*a^3) + 1/15*(3*a^2*tan(x)^5 + 5*(2*a^2 - a*b)*tan(x)^3 + 15*(a^2 - a*b + b^2)*tan(x))/a^3","A",0
42,1,72,0,1.090127," ","integrate(1/(a+b*cos(x)^2)^2,x, algorithm=""maxima"")","-\frac{b \tan\left(x\right)}{2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} + {\left(a^{3} + a^{2} b\right)} \tan\left(x\right)^{2}\right)}} + \frac{{\left(2 \, a + b\right)} \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{2 \, \sqrt{{\left(a + b\right)} a} {\left(a^{2} + a b\right)}}"," ",0,"-1/2*b*tan(x)/(a^3 + 2*a^2*b + a*b^2 + (a^3 + a^2*b)*tan(x)^2) + 1/2*(2*a + b)*arctan(a*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*(a^2 + a*b))","A",0
43,1,186,0,1.132201," ","integrate(1/(a+b*cos(x)^2)^3,x, algorithm=""maxima"")","\frac{{\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{8 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sqrt{{\left(a + b\right)} a}} - \frac{{\left(8 \, a^{2} b + 5 \, a b^{2}\right)} \tan\left(x\right)^{3} + {\left(8 \, a^{2} b + 11 \, a b^{2} + 3 \, b^{3}\right)} \tan\left(x\right)}{8 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4} + {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} \tan\left(x\right)^{4} + 2 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \tan\left(x\right)^{2}\right)}}"," ",0,"1/8*(8*a^2 + 8*a*b + 3*b^2)*arctan(a*tan(x)/sqrt((a + b)*a))/((a^4 + 2*a^3*b + a^2*b^2)*sqrt((a + b)*a)) - 1/8*((8*a^2*b + 5*a*b^2)*tan(x)^3 + (8*a^2*b + 11*a*b^2 + 3*b^3)*tan(x))/(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4 + (a^6 + 2*a^5*b + a^4*b^2)*tan(x)^4 + 2*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*tan(x)^2)","A",0
44,1,13,0,0.820188," ","integrate(1/(1+cos(x)^2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \tan\left(x\right)\right)"," ",0,"1/2*sqrt(2)*arctan(1/2*sqrt(2)*tan(x))","A",0
45,1,26,0,0.959747," ","integrate(1/(1+cos(x)^2)^2,x, algorithm=""maxima"")","\frac{3}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \tan\left(x\right)\right) - \frac{\tan\left(x\right)}{4 \, {\left(\tan\left(x\right)^{2} + 2\right)}}"," ",0,"3/8*sqrt(2)*arctan(1/2*sqrt(2)*tan(x)) - 1/4*tan(x)/(tan(x)^2 + 2)","A",0
46,1,41,0,1.569289," ","integrate(1/(1+cos(x)^2)^3,x, algorithm=""maxima"")","\frac{19}{64} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \tan\left(x\right)\right) - \frac{13 \, \tan\left(x\right)^{3} + 22 \, \tan\left(x\right)}{32 \, {\left(\tan\left(x\right)^{4} + 4 \, \tan\left(x\right)^{2} + 4\right)}}"," ",0,"19/64*sqrt(2)*arctan(1/2*sqrt(2)*tan(x)) - 1/32*(13*tan(x)^3 + 22*tan(x))/(tan(x)^4 + 4*tan(x)^2 + 4)","A",0
47,1,10,0,0.885967," ","integrate((1-cos(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{\sqrt{\tan\left(x\right)^{2} + 1}}"," ",0,"-1/sqrt(tan(x)^2 + 1)","A",0
48,1,12,0,0.877075," ","integrate((-1+cos(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{\sqrt{-\tan\left(x\right)^{2} - 1}}"," ",0,"-1/sqrt(-tan(x)^2 - 1)","A",0
49,1,11,0,0.976907," ","integrate((1-cos(x)^2)^(3/2),x, algorithm=""maxima"")","-\frac{1}{12} \, \cos\left(3 \, x\right) + \frac{3}{4} \, \cos\left(x\right)"," ",0,"-1/12*cos(3*x) + 3/4*cos(x)","A",0
50,0,0,0,0.000000," ","integrate((-1+cos(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(\cos\left(x\right)^{2} - 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((cos(x)^2 - 1)^(3/2), x)","F",0
51,1,35,0,1.129403," ","integrate(1/(1-cos(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) - \frac{1}{2} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)"," ",0,"1/2*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - 1/2*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","B",0
52,1,17,0,0.899625," ","integrate(1/(-1+cos(x)^2)^(1/2),x, algorithm=""maxima"")","-\arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) + \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)"," ",0,"-arctan2(sin(x), cos(x) + 1) + arctan2(sin(x), cos(x) - 1)","A",0
53,1,300,0,1.835281," ","integrate(1/(1-cos(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\cos\left(3 \, x\right) + \cos\left(x\right)\right)} \cos\left(4 \, x\right) - 4 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(3 \, x\right) - 8 \, \cos\left(2 \, x\right) \cos\left(x\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) - 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) - 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) + 4 \, {\left(\sin\left(3 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) - 8 \, \sin\left(3 \, x\right) \sin\left(2 \, x\right) - 8 \, \sin\left(2 \, x\right) \sin\left(x\right) + 4 \, \cos\left(x\right)}{4 \, {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) - 1\right)}}"," ",0,"1/4*(4*(cos(3*x) + cos(x))*cos(4*x) - 4*(2*cos(2*x) - 1)*cos(3*x) - 8*cos(2*x)*cos(x) + (2*(2*cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - 4*cos(2*x)^2 - sin(4*x)^2 + 4*sin(4*x)*sin(2*x) - 4*sin(2*x)^2 + 4*cos(2*x) - 1)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - (2*(2*cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - 4*cos(2*x)^2 - sin(4*x)^2 + 4*sin(4*x)*sin(2*x) - 4*sin(2*x)^2 + 4*cos(2*x) - 1)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) + 4*(sin(3*x) + sin(x))*sin(4*x) - 8*sin(3*x)*sin(2*x) - 8*sin(2*x)*sin(x) + 4*cos(x))/(2*(2*cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - 4*cos(2*x)^2 - sin(4*x)^2 + 4*sin(4*x)*sin(2*x) - 4*sin(2*x)^2 + 4*cos(2*x) - 1)","B",0
54,1,284,0,1.053261," ","integrate(1/(-1+cos(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{{\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) - 1\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) - 1\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right) + 2 \, {\left(\sin\left(3 \, x\right) + \sin\left(x\right)\right)} \cos\left(4 \, x\right) - 2 \, {\left(\cos\left(3 \, x\right) + \cos\left(x\right)\right)} \sin\left(4 \, x\right) - 2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \sin\left(3 \, x\right) + 4 \, \cos\left(3 \, x\right) \sin\left(2 \, x\right) + 4 \, \cos\left(x\right) \sin\left(2 \, x\right) - 4 \, \cos\left(2 \, x\right) \sin\left(x\right) + 2 \, \sin\left(x\right)}{2 \, {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) - 1\right)}}"," ",0,"1/2*((2*(2*cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - 4*cos(2*x)^2 - sin(4*x)^2 + 4*sin(4*x)*sin(2*x) - 4*sin(2*x)^2 + 4*cos(2*x) - 1)*arctan2(sin(x), cos(x) + 1) - (2*(2*cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - 4*cos(2*x)^2 - sin(4*x)^2 + 4*sin(4*x)*sin(2*x) - 4*sin(2*x)^2 + 4*cos(2*x) - 1)*arctan2(sin(x), cos(x) - 1) + 2*(sin(3*x) + sin(x))*cos(4*x) - 2*(cos(3*x) + cos(x))*sin(4*x) - 2*(2*cos(2*x) - 1)*sin(3*x) + 4*cos(3*x)*sin(2*x) + 4*cos(x)*sin(2*x) - 4*cos(2*x)*sin(x) + 2*sin(x))/(2*(2*cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - 4*cos(2*x)^2 - sin(4*x)^2 + 4*sin(4*x)*sin(2*x) - 4*sin(2*x)^2 + 4*cos(2*x) - 1)","B",0
55,0,0,0,0.000000," ","integrate((1+cos(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{\cos\left(x\right)^{2} + 1}\,{d x}"," ",0,"integrate(sqrt(cos(x)^2 + 1), x)","F",0
56,0,0,0,0.000000," ","integrate((-1-cos(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-\cos\left(x\right)^{2} - 1}\,{d x}"," ",0,"integrate(sqrt(-cos(x)^2 - 1), x)","F",0
57,0,0,0,0.000000," ","integrate((a+b*cos(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(x\right)^{2} + a}\,{d x}"," ",0,"integrate(sqrt(b*cos(x)^2 + a), x)","F",0
58,0,0,0,0.000000," ","integrate((1+cos(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(\cos\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((cos(x)^2 + 1)^(3/2), x)","F",0
59,0,0,0,0.000000," ","integrate((-1-cos(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(-\cos\left(x\right)^{2} - 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-cos(x)^2 - 1)^(3/2), x)","F",0
60,0,0,0,0.000000," ","integrate((a+b*cos(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(x\right)^{2} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*cos(x)^2 + a)^(3/2), x)","F",0
61,0,0,0,0.000000," ","integrate(1/(1+cos(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{\cos\left(x\right)^{2} + 1}}\,{d x}"," ",0,"integrate(1/sqrt(cos(x)^2 + 1), x)","F",0
62,0,0,0,0.000000," ","integrate(1/(-1-cos(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-\cos\left(x\right)^{2} - 1}}\,{d x}"," ",0,"integrate(1/sqrt(-cos(x)^2 - 1), x)","F",0
63,0,0,0,0.000000," ","integrate(1/(a+b*cos(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \cos\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*cos(x)^2 + a), x)","F",0
64,0,0,0,0.000000," ","integrate(1/(1+cos(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(\cos\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((cos(x)^2 + 1)^(-3/2), x)","F",0
65,0,0,0,0.000000," ","integrate(1/(-1-cos(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-\cos\left(x\right)^{2} - 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-cos(x)^2 - 1)^(-3/2), x)","F",0
66,0,0,0,0.000000," ","integrate(1/(a+b*cos(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*cos(x)^2 + a)^(-3/2), x)","F",0
67,1,8,0,1.608408," ","integrate(cos(x)/(1+cos(x)^2)^(1/2),x, algorithm=""maxima"")","\arcsin\left(\frac{1}{2} \, \sqrt{2} \sin\left(x\right)\right)"," ",0,"arcsin(1/2*sqrt(2)*sin(x))","A",0
68,1,11,0,0.698655," ","integrate(cos(5+3*x)/(3+cos(5+3*x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, \arcsin\left(\frac{1}{2} \, \sin\left(3 \, x + 5\right)\right)"," ",0,"1/3*arcsin(1/2*sin(3*x + 5))","A",0
69,1,8,0,1.740671," ","integrate(cos(x)/(4-cos(x)^2)^(1/2),x, algorithm=""maxima"")","\operatorname{arsinh}\left(\frac{1}{3} \, \sqrt{3} \sin\left(x\right)\right)"," ",0,"arcsinh(1/3*sqrt(3)*sin(x))","A",0
70,0,0,0,0.000000," ","integrate(1/(a+b*cos(x)^4),x, algorithm=""maxima"")","\int \frac{1}{b \cos\left(x\right)^{4} + a}\,{d x}"," ",0,"integrate(1/(b*cos(x)^4 + a), x)","F",0
71,0,0,0,0.000000," ","integrate(1/(a-b*cos(x)^4),x, algorithm=""maxima"")","-\int \frac{1}{b \cos\left(x\right)^{4} - a}\,{d x}"," ",0,"-integrate(1/(b*cos(x)^4 - a), x)","F",0
72,0,0,0,0.000000," ","integrate(1/(1+cos(x)^4),x, algorithm=""maxima"")","\int \frac{1}{\cos\left(x\right)^{4} + 1}\,{d x}"," ",0,"integrate(1/(cos(x)^4 + 1), x)","F",0
73,1,20,0,1.639414," ","integrate(1/(1-cos(x)^4),x, algorithm=""maxima"")","\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \tan\left(x\right)\right) - \frac{1}{2 \, \tan\left(x\right)}"," ",0,"1/4*sqrt(2)*arctan(1/2*sqrt(2)*tan(x)) - 1/2/tan(x)","A",0
74,0,0,0,0.000000," ","integrate(1/(a+b*cos(x)^5),x, algorithm=""maxima"")","\int \frac{1}{b \cos\left(x\right)^{5} + a}\,{d x}"," ",0,"integrate(1/(b*cos(x)^5 + a), x)","F",0
75,0,0,0,0.000000," ","integrate(1/(a+b*cos(x)^6),x, algorithm=""maxima"")","\int \frac{1}{b \cos\left(x\right)^{6} + a}\,{d x}"," ",0,"integrate(1/(b*cos(x)^6 + a), x)","F",0
76,0,0,0,0.000000," ","integrate(1/(a+b*cos(x)^8),x, algorithm=""maxima"")","\int \frac{1}{b \cos\left(x\right)^{8} + a}\,{d x}"," ",0,"integrate(1/(b*cos(x)^8 + a), x)","F",0
77,0,0,0,0.000000," ","integrate(1/(a-b*cos(x)^5),x, algorithm=""maxima"")","-\int \frac{1}{b \cos\left(x\right)^{5} - a}\,{d x}"," ",0,"-integrate(1/(b*cos(x)^5 - a), x)","F",0
78,0,0,0,0.000000," ","integrate(1/(a-b*cos(x)^6),x, algorithm=""maxima"")","-\int \frac{1}{b \cos\left(x\right)^{6} - a}\,{d x}"," ",0,"-integrate(1/(b*cos(x)^6 - a), x)","F",0
79,0,0,0,0.000000," ","integrate(1/(a-b*cos(x)^8),x, algorithm=""maxima"")","-\int \frac{1}{b \cos\left(x\right)^{8} - a}\,{d x}"," ",0,"-integrate(1/(b*cos(x)^8 - a), x)","F",0
80,0,0,0,0.000000," ","integrate(1/(1+cos(x)^5),x, algorithm=""maxima"")","-\frac{-2 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)} \int \frac{{\left(\cos\left(7 \, x\right) - 4 \, \cos\left(6 \, x\right) + 15 \, \cos\left(5 \, x\right) - 40 \, \cos\left(4 \, x\right) + 15 \, \cos\left(3 \, x\right) - 4 \, \cos\left(2 \, x\right) + \cos\left(x\right)\right)} \cos\left(8 \, x\right) + {\left(16 \, \cos\left(6 \, x\right) - 44 \, \cos\left(5 \, x\right) + 110 \, \cos\left(4 \, x\right) - 44 \, \cos\left(3 \, x\right) + 16 \, \cos\left(2 \, x\right) - 4 \, \cos\left(x\right) + 1\right)} \cos\left(7 \, x\right) - 2 \, \cos\left(7 \, x\right)^{2} + 4 \, {\left(44 \, \cos\left(5 \, x\right) - 110 \, \cos\left(4 \, x\right) + 44 \, \cos\left(3 \, x\right) - 16 \, \cos\left(2 \, x\right) + 4 \, \cos\left(x\right) - 1\right)} \cos\left(6 \, x\right) - 32 \, \cos\left(6 \, x\right)^{2} + {\left(1010 \, \cos\left(4 \, x\right) - 420 \, \cos\left(3 \, x\right) + 176 \, \cos\left(2 \, x\right) - 44 \, \cos\left(x\right) + 15\right)} \cos\left(5 \, x\right) - 210 \, \cos\left(5 \, x\right)^{2} + 10 \, {\left(101 \, \cos\left(3 \, x\right) - 44 \, \cos\left(2 \, x\right) + 11 \, \cos\left(x\right) - 4\right)} \cos\left(4 \, x\right) - 1200 \, \cos\left(4 \, x\right)^{2} + {\left(176 \, \cos\left(2 \, x\right) - 44 \, \cos\left(x\right) + 15\right)} \cos\left(3 \, x\right) - 210 \, \cos\left(3 \, x\right)^{2} + 4 \, {\left(4 \, \cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) - 32 \, \cos\left(2 \, x\right)^{2} - 2 \, \cos\left(x\right)^{2} + {\left(\sin\left(7 \, x\right) - 4 \, \sin\left(6 \, x\right) + 15 \, \sin\left(5 \, x\right) - 40 \, \sin\left(4 \, x\right) + 15 \, \sin\left(3 \, x\right) - 4 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(8 \, x\right) + 2 \, {\left(8 \, \sin\left(6 \, x\right) - 22 \, \sin\left(5 \, x\right) + 55 \, \sin\left(4 \, x\right) - 22 \, \sin\left(3 \, x\right) + 8 \, \sin\left(2 \, x\right) - 2 \, \sin\left(x\right)\right)} \sin\left(7 \, x\right) - 2 \, \sin\left(7 \, x\right)^{2} + 8 \, {\left(22 \, \sin\left(5 \, x\right) - 55 \, \sin\left(4 \, x\right) + 22 \, \sin\left(3 \, x\right) - 8 \, \sin\left(2 \, x\right) + 2 \, \sin\left(x\right)\right)} \sin\left(6 \, x\right) - 32 \, \sin\left(6 \, x\right)^{2} + 2 \, {\left(505 \, \sin\left(4 \, x\right) - 210 \, \sin\left(3 \, x\right) + 88 \, \sin\left(2 \, x\right) - 22 \, \sin\left(x\right)\right)} \sin\left(5 \, x\right) - 210 \, \sin\left(5 \, x\right)^{2} + 10 \, {\left(101 \, \sin\left(3 \, x\right) - 44 \, \sin\left(2 \, x\right) + 11 \, \sin\left(x\right)\right)} \sin\left(4 \, x\right) - 1200 \, \sin\left(4 \, x\right)^{2} + 44 \, {\left(4 \, \sin\left(2 \, x\right) - \sin\left(x\right)\right)} \sin\left(3 \, x\right) - 210 \, \sin\left(3 \, x\right)^{2} - 32 \, \sin\left(2 \, x\right)^{2} + 16 \, \sin\left(2 \, x\right) \sin\left(x\right) - 2 \, \sin\left(x\right)^{2} + \cos\left(x\right)}{2 \, {\left(2 \, \cos\left(7 \, x\right) - 8 \, \cos\left(6 \, x\right) + 14 \, \cos\left(5 \, x\right) - 30 \, \cos\left(4 \, x\right) + 14 \, \cos\left(3 \, x\right) - 8 \, \cos\left(2 \, x\right) + 2 \, \cos\left(x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} + 4 \, {\left(8 \, \cos\left(6 \, x\right) - 14 \, \cos\left(5 \, x\right) + 30 \, \cos\left(4 \, x\right) - 14 \, \cos\left(3 \, x\right) + 8 \, \cos\left(2 \, x\right) - 2 \, \cos\left(x\right) + 1\right)} \cos\left(7 \, x\right) - 4 \, \cos\left(7 \, x\right)^{2} + 16 \, {\left(14 \, \cos\left(5 \, x\right) - 30 \, \cos\left(4 \, x\right) + 14 \, \cos\left(3 \, x\right) - 8 \, \cos\left(2 \, x\right) + 2 \, \cos\left(x\right) - 1\right)} \cos\left(6 \, x\right) - 64 \, \cos\left(6 \, x\right)^{2} + 28 \, {\left(30 \, \cos\left(4 \, x\right) - 14 \, \cos\left(3 \, x\right) + 8 \, \cos\left(2 \, x\right) - 2 \, \cos\left(x\right) + 1\right)} \cos\left(5 \, x\right) - 196 \, \cos\left(5 \, x\right)^{2} + 60 \, {\left(14 \, \cos\left(3 \, x\right) - 8 \, \cos\left(2 \, x\right) + 2 \, \cos\left(x\right) - 1\right)} \cos\left(4 \, x\right) - 900 \, \cos\left(4 \, x\right)^{2} + 28 \, {\left(8 \, \cos\left(2 \, x\right) - 2 \, \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) - 196 \, \cos\left(3 \, x\right)^{2} + 16 \, {\left(2 \, \cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) - 64 \, \cos\left(2 \, x\right)^{2} - 4 \, \cos\left(x\right)^{2} + 4 \, {\left(\sin\left(7 \, x\right) - 4 \, \sin\left(6 \, x\right) + 7 \, \sin\left(5 \, x\right) - 15 \, \sin\left(4 \, x\right) + 7 \, \sin\left(3 \, x\right) - 4 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(8 \, x\right) - \sin\left(8 \, x\right)^{2} + 8 \, {\left(4 \, \sin\left(6 \, x\right) - 7 \, \sin\left(5 \, x\right) + 15 \, \sin\left(4 \, x\right) - 7 \, \sin\left(3 \, x\right) + 4 \, \sin\left(2 \, x\right) - \sin\left(x\right)\right)} \sin\left(7 \, x\right) - 4 \, \sin\left(7 \, x\right)^{2} + 32 \, {\left(7 \, \sin\left(5 \, x\right) - 15 \, \sin\left(4 \, x\right) + 7 \, \sin\left(3 \, x\right) - 4 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(6 \, x\right) - 64 \, \sin\left(6 \, x\right)^{2} + 56 \, {\left(15 \, \sin\left(4 \, x\right) - 7 \, \sin\left(3 \, x\right) + 4 \, \sin\left(2 \, x\right) - \sin\left(x\right)\right)} \sin\left(5 \, x\right) - 196 \, \sin\left(5 \, x\right)^{2} + 120 \, {\left(7 \, \sin\left(3 \, x\right) - 4 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) - 900 \, \sin\left(4 \, x\right)^{2} + 56 \, {\left(4 \, \sin\left(2 \, x\right) - \sin\left(x\right)\right)} \sin\left(3 \, x\right) - 196 \, \sin\left(3 \, x\right)^{2} - 64 \, \sin\left(2 \, x\right)^{2} + 32 \, \sin\left(2 \, x\right) \sin\left(x\right) - 4 \, \sin\left(x\right)^{2} + 4 \, \cos\left(x\right) - 1}\,{d x} - 2 \, \sin\left(x\right)}{5 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)}}"," ",0,"-1/5*(5*(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)*integrate(-2/5*((cos(7*x) - 4*cos(6*x) + 15*cos(5*x) - 40*cos(4*x) + 15*cos(3*x) - 4*cos(2*x) + cos(x))*cos(8*x) + (16*cos(6*x) - 44*cos(5*x) + 110*cos(4*x) - 44*cos(3*x) + 16*cos(2*x) - 4*cos(x) + 1)*cos(7*x) - 2*cos(7*x)^2 + 4*(44*cos(5*x) - 110*cos(4*x) + 44*cos(3*x) - 16*cos(2*x) + 4*cos(x) - 1)*cos(6*x) - 32*cos(6*x)^2 + (1010*cos(4*x) - 420*cos(3*x) + 176*cos(2*x) - 44*cos(x) + 15)*cos(5*x) - 210*cos(5*x)^2 + 10*(101*cos(3*x) - 44*cos(2*x) + 11*cos(x) - 4)*cos(4*x) - 1200*cos(4*x)^2 + (176*cos(2*x) - 44*cos(x) + 15)*cos(3*x) - 210*cos(3*x)^2 + 4*(4*cos(x) - 1)*cos(2*x) - 32*cos(2*x)^2 - 2*cos(x)^2 + (sin(7*x) - 4*sin(6*x) + 15*sin(5*x) - 40*sin(4*x) + 15*sin(3*x) - 4*sin(2*x) + sin(x))*sin(8*x) + 2*(8*sin(6*x) - 22*sin(5*x) + 55*sin(4*x) - 22*sin(3*x) + 8*sin(2*x) - 2*sin(x))*sin(7*x) - 2*sin(7*x)^2 + 8*(22*sin(5*x) - 55*sin(4*x) + 22*sin(3*x) - 8*sin(2*x) + 2*sin(x))*sin(6*x) - 32*sin(6*x)^2 + 2*(505*sin(4*x) - 210*sin(3*x) + 88*sin(2*x) - 22*sin(x))*sin(5*x) - 210*sin(5*x)^2 + 10*(101*sin(3*x) - 44*sin(2*x) + 11*sin(x))*sin(4*x) - 1200*sin(4*x)^2 + 44*(4*sin(2*x) - sin(x))*sin(3*x) - 210*sin(3*x)^2 - 32*sin(2*x)^2 + 16*sin(2*x)*sin(x) - 2*sin(x)^2 + cos(x))/(2*(2*cos(7*x) - 8*cos(6*x) + 14*cos(5*x) - 30*cos(4*x) + 14*cos(3*x) - 8*cos(2*x) + 2*cos(x) - 1)*cos(8*x) - cos(8*x)^2 + 4*(8*cos(6*x) - 14*cos(5*x) + 30*cos(4*x) - 14*cos(3*x) + 8*cos(2*x) - 2*cos(x) + 1)*cos(7*x) - 4*cos(7*x)^2 + 16*(14*cos(5*x) - 30*cos(4*x) + 14*cos(3*x) - 8*cos(2*x) + 2*cos(x) - 1)*cos(6*x) - 64*cos(6*x)^2 + 28*(30*cos(4*x) - 14*cos(3*x) + 8*cos(2*x) - 2*cos(x) + 1)*cos(5*x) - 196*cos(5*x)^2 + 60*(14*cos(3*x) - 8*cos(2*x) + 2*cos(x) - 1)*cos(4*x) - 900*cos(4*x)^2 + 28*(8*cos(2*x) - 2*cos(x) + 1)*cos(3*x) - 196*cos(3*x)^2 + 16*(2*cos(x) - 1)*cos(2*x) - 64*cos(2*x)^2 - 4*cos(x)^2 + 4*(sin(7*x) - 4*sin(6*x) + 7*sin(5*x) - 15*sin(4*x) + 7*sin(3*x) - 4*sin(2*x) + sin(x))*sin(8*x) - sin(8*x)^2 + 8*(4*sin(6*x) - 7*sin(5*x) + 15*sin(4*x) - 7*sin(3*x) + 4*sin(2*x) - sin(x))*sin(7*x) - 4*sin(7*x)^2 + 32*(7*sin(5*x) - 15*sin(4*x) + 7*sin(3*x) - 4*sin(2*x) + sin(x))*sin(6*x) - 64*sin(6*x)^2 + 56*(15*sin(4*x) - 7*sin(3*x) + 4*sin(2*x) - sin(x))*sin(5*x) - 196*sin(5*x)^2 + 120*(7*sin(3*x) - 4*sin(2*x) + sin(x))*sin(4*x) - 900*sin(4*x)^2 + 56*(4*sin(2*x) - sin(x))*sin(3*x) - 196*sin(3*x)^2 - 64*sin(2*x)^2 + 32*sin(2*x)*sin(x) - 4*sin(x)^2 + 4*cos(x) - 1), x) - 2*sin(x))/(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)","F",0
81,1,72,0,0.775081," ","integrate(1/(1+cos(x)^6),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \tan\left(x\right) + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \tan\left(x\right) - 1\right)}\right) + \frac{1}{6} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \tan\left(x\right)\right) - \frac{1}{12} \, \log\left(\tan\left(x\right)^{2} + \tan\left(x\right) + 1\right) + \frac{1}{12} \, \log\left(\tan\left(x\right)^{2} - \tan\left(x\right) + 1\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*tan(x) + 1)) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*tan(x) - 1)) + 1/6*sqrt(2)*arctan(1/2*sqrt(2)*tan(x)) - 1/12*log(tan(x)^2 + tan(x) + 1) + 1/12*log(tan(x)^2 - tan(x) + 1)","A",0
82,0,0,0,0.000000," ","integrate(1/(1+cos(x)^8),x, algorithm=""maxima"")","\int \frac{1}{\cos\left(x\right)^{8} + 1}\,{d x}"," ",0,"integrate(1/(cos(x)^8 + 1), x)","F",0
83,0,0,0,0.000000," ","integrate(1/(1-cos(x)^5),x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)} \int \frac{{\left(\cos\left(7 \, x\right) + 4 \, \cos\left(6 \, x\right) + 15 \, \cos\left(5 \, x\right) + 40 \, \cos\left(4 \, x\right) + 15 \, \cos\left(3 \, x\right) + 4 \, \cos\left(2 \, x\right) + \cos\left(x\right)\right)} \cos\left(8 \, x\right) + {\left(16 \, \cos\left(6 \, x\right) + 44 \, \cos\left(5 \, x\right) + 110 \, \cos\left(4 \, x\right) + 44 \, \cos\left(3 \, x\right) + 16 \, \cos\left(2 \, x\right) + 4 \, \cos\left(x\right) + 1\right)} \cos\left(7 \, x\right) + 2 \, \cos\left(7 \, x\right)^{2} + 4 \, {\left(44 \, \cos\left(5 \, x\right) + 110 \, \cos\left(4 \, x\right) + 44 \, \cos\left(3 \, x\right) + 16 \, \cos\left(2 \, x\right) + 4 \, \cos\left(x\right) + 1\right)} \cos\left(6 \, x\right) + 32 \, \cos\left(6 \, x\right)^{2} + {\left(1010 \, \cos\left(4 \, x\right) + 420 \, \cos\left(3 \, x\right) + 176 \, \cos\left(2 \, x\right) + 44 \, \cos\left(x\right) + 15\right)} \cos\left(5 \, x\right) + 210 \, \cos\left(5 \, x\right)^{2} + 10 \, {\left(101 \, \cos\left(3 \, x\right) + 44 \, \cos\left(2 \, x\right) + 11 \, \cos\left(x\right) + 4\right)} \cos\left(4 \, x\right) + 1200 \, \cos\left(4 \, x\right)^{2} + {\left(176 \, \cos\left(2 \, x\right) + 44 \, \cos\left(x\right) + 15\right)} \cos\left(3 \, x\right) + 210 \, \cos\left(3 \, x\right)^{2} + 4 \, {\left(4 \, \cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + 32 \, \cos\left(2 \, x\right)^{2} + 2 \, \cos\left(x\right)^{2} + {\left(\sin\left(7 \, x\right) + 4 \, \sin\left(6 \, x\right) + 15 \, \sin\left(5 \, x\right) + 40 \, \sin\left(4 \, x\right) + 15 \, \sin\left(3 \, x\right) + 4 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(8 \, x\right) + 2 \, {\left(8 \, \sin\left(6 \, x\right) + 22 \, \sin\left(5 \, x\right) + 55 \, \sin\left(4 \, x\right) + 22 \, \sin\left(3 \, x\right) + 8 \, \sin\left(2 \, x\right) + 2 \, \sin\left(x\right)\right)} \sin\left(7 \, x\right) + 2 \, \sin\left(7 \, x\right)^{2} + 8 \, {\left(22 \, \sin\left(5 \, x\right) + 55 \, \sin\left(4 \, x\right) + 22 \, \sin\left(3 \, x\right) + 8 \, \sin\left(2 \, x\right) + 2 \, \sin\left(x\right)\right)} \sin\left(6 \, x\right) + 32 \, \sin\left(6 \, x\right)^{2} + 2 \, {\left(505 \, \sin\left(4 \, x\right) + 210 \, \sin\left(3 \, x\right) + 88 \, \sin\left(2 \, x\right) + 22 \, \sin\left(x\right)\right)} \sin\left(5 \, x\right) + 210 \, \sin\left(5 \, x\right)^{2} + 10 \, {\left(101 \, \sin\left(3 \, x\right) + 44 \, \sin\left(2 \, x\right) + 11 \, \sin\left(x\right)\right)} \sin\left(4 \, x\right) + 1200 \, \sin\left(4 \, x\right)^{2} + 44 \, {\left(4 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(3 \, x\right) + 210 \, \sin\left(3 \, x\right)^{2} + 32 \, \sin\left(2 \, x\right)^{2} + 16 \, \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, \sin\left(x\right)^{2} + \cos\left(x\right)}{2 \, {\left(2 \, \cos\left(7 \, x\right) + 8 \, \cos\left(6 \, x\right) + 14 \, \cos\left(5 \, x\right) + 30 \, \cos\left(4 \, x\right) + 14 \, \cos\left(3 \, x\right) + 8 \, \cos\left(2 \, x\right) + 2 \, \cos\left(x\right) + 1\right)} \cos\left(8 \, x\right) + \cos\left(8 \, x\right)^{2} + 4 \, {\left(8 \, \cos\left(6 \, x\right) + 14 \, \cos\left(5 \, x\right) + 30 \, \cos\left(4 \, x\right) + 14 \, \cos\left(3 \, x\right) + 8 \, \cos\left(2 \, x\right) + 2 \, \cos\left(x\right) + 1\right)} \cos\left(7 \, x\right) + 4 \, \cos\left(7 \, x\right)^{2} + 16 \, {\left(14 \, \cos\left(5 \, x\right) + 30 \, \cos\left(4 \, x\right) + 14 \, \cos\left(3 \, x\right) + 8 \, \cos\left(2 \, x\right) + 2 \, \cos\left(x\right) + 1\right)} \cos\left(6 \, x\right) + 64 \, \cos\left(6 \, x\right)^{2} + 28 \, {\left(30 \, \cos\left(4 \, x\right) + 14 \, \cos\left(3 \, x\right) + 8 \, \cos\left(2 \, x\right) + 2 \, \cos\left(x\right) + 1\right)} \cos\left(5 \, x\right) + 196 \, \cos\left(5 \, x\right)^{2} + 60 \, {\left(14 \, \cos\left(3 \, x\right) + 8 \, \cos\left(2 \, x\right) + 2 \, \cos\left(x\right) + 1\right)} \cos\left(4 \, x\right) + 900 \, \cos\left(4 \, x\right)^{2} + 28 \, {\left(8 \, \cos\left(2 \, x\right) + 2 \, \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) + 196 \, \cos\left(3 \, x\right)^{2} + 16 \, {\left(2 \, \cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + 64 \, \cos\left(2 \, x\right)^{2} + 4 \, \cos\left(x\right)^{2} + 4 \, {\left(\sin\left(7 \, x\right) + 4 \, \sin\left(6 \, x\right) + 7 \, \sin\left(5 \, x\right) + 15 \, \sin\left(4 \, x\right) + 7 \, \sin\left(3 \, x\right) + 4 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(8 \, x\right) + \sin\left(8 \, x\right)^{2} + 8 \, {\left(4 \, \sin\left(6 \, x\right) + 7 \, \sin\left(5 \, x\right) + 15 \, \sin\left(4 \, x\right) + 7 \, \sin\left(3 \, x\right) + 4 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(7 \, x\right) + 4 \, \sin\left(7 \, x\right)^{2} + 32 \, {\left(7 \, \sin\left(5 \, x\right) + 15 \, \sin\left(4 \, x\right) + 7 \, \sin\left(3 \, x\right) + 4 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(6 \, x\right) + 64 \, \sin\left(6 \, x\right)^{2} + 56 \, {\left(15 \, \sin\left(4 \, x\right) + 7 \, \sin\left(3 \, x\right) + 4 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(5 \, x\right) + 196 \, \sin\left(5 \, x\right)^{2} + 120 \, {\left(7 \, \sin\left(3 \, x\right) + 4 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) + 900 \, \sin\left(4 \, x\right)^{2} + 56 \, {\left(4 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(3 \, x\right) + 196 \, \sin\left(3 \, x\right)^{2} + 64 \, \sin\left(2 \, x\right)^{2} + 32 \, \sin\left(2 \, x\right) \sin\left(x\right) + 4 \, \sin\left(x\right)^{2} + 4 \, \cos\left(x\right) + 1}\,{d x} - 2 \, \sin\left(x\right)}{5 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)}}"," ",0,"1/5*(5*(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)*integrate(2/5*((cos(7*x) + 4*cos(6*x) + 15*cos(5*x) + 40*cos(4*x) + 15*cos(3*x) + 4*cos(2*x) + cos(x))*cos(8*x) + (16*cos(6*x) + 44*cos(5*x) + 110*cos(4*x) + 44*cos(3*x) + 16*cos(2*x) + 4*cos(x) + 1)*cos(7*x) + 2*cos(7*x)^2 + 4*(44*cos(5*x) + 110*cos(4*x) + 44*cos(3*x) + 16*cos(2*x) + 4*cos(x) + 1)*cos(6*x) + 32*cos(6*x)^2 + (1010*cos(4*x) + 420*cos(3*x) + 176*cos(2*x) + 44*cos(x) + 15)*cos(5*x) + 210*cos(5*x)^2 + 10*(101*cos(3*x) + 44*cos(2*x) + 11*cos(x) + 4)*cos(4*x) + 1200*cos(4*x)^2 + (176*cos(2*x) + 44*cos(x) + 15)*cos(3*x) + 210*cos(3*x)^2 + 4*(4*cos(x) + 1)*cos(2*x) + 32*cos(2*x)^2 + 2*cos(x)^2 + (sin(7*x) + 4*sin(6*x) + 15*sin(5*x) + 40*sin(4*x) + 15*sin(3*x) + 4*sin(2*x) + sin(x))*sin(8*x) + 2*(8*sin(6*x) + 22*sin(5*x) + 55*sin(4*x) + 22*sin(3*x) + 8*sin(2*x) + 2*sin(x))*sin(7*x) + 2*sin(7*x)^2 + 8*(22*sin(5*x) + 55*sin(4*x) + 22*sin(3*x) + 8*sin(2*x) + 2*sin(x))*sin(6*x) + 32*sin(6*x)^2 + 2*(505*sin(4*x) + 210*sin(3*x) + 88*sin(2*x) + 22*sin(x))*sin(5*x) + 210*sin(5*x)^2 + 10*(101*sin(3*x) + 44*sin(2*x) + 11*sin(x))*sin(4*x) + 1200*sin(4*x)^2 + 44*(4*sin(2*x) + sin(x))*sin(3*x) + 210*sin(3*x)^2 + 32*sin(2*x)^2 + 16*sin(2*x)*sin(x) + 2*sin(x)^2 + cos(x))/(2*(2*cos(7*x) + 8*cos(6*x) + 14*cos(5*x) + 30*cos(4*x) + 14*cos(3*x) + 8*cos(2*x) + 2*cos(x) + 1)*cos(8*x) + cos(8*x)^2 + 4*(8*cos(6*x) + 14*cos(5*x) + 30*cos(4*x) + 14*cos(3*x) + 8*cos(2*x) + 2*cos(x) + 1)*cos(7*x) + 4*cos(7*x)^2 + 16*(14*cos(5*x) + 30*cos(4*x) + 14*cos(3*x) + 8*cos(2*x) + 2*cos(x) + 1)*cos(6*x) + 64*cos(6*x)^2 + 28*(30*cos(4*x) + 14*cos(3*x) + 8*cos(2*x) + 2*cos(x) + 1)*cos(5*x) + 196*cos(5*x)^2 + 60*(14*cos(3*x) + 8*cos(2*x) + 2*cos(x) + 1)*cos(4*x) + 900*cos(4*x)^2 + 28*(8*cos(2*x) + 2*cos(x) + 1)*cos(3*x) + 196*cos(3*x)^2 + 16*(2*cos(x) + 1)*cos(2*x) + 64*cos(2*x)^2 + 4*cos(x)^2 + 4*(sin(7*x) + 4*sin(6*x) + 7*sin(5*x) + 15*sin(4*x) + 7*sin(3*x) + 4*sin(2*x) + sin(x))*sin(8*x) + sin(8*x)^2 + 8*(4*sin(6*x) + 7*sin(5*x) + 15*sin(4*x) + 7*sin(3*x) + 4*sin(2*x) + sin(x))*sin(7*x) + 4*sin(7*x)^2 + 32*(7*sin(5*x) + 15*sin(4*x) + 7*sin(3*x) + 4*sin(2*x) + sin(x))*sin(6*x) + 64*sin(6*x)^2 + 56*(15*sin(4*x) + 7*sin(3*x) + 4*sin(2*x) + sin(x))*sin(5*x) + 196*sin(5*x)^2 + 120*(7*sin(3*x) + 4*sin(2*x) + sin(x))*sin(4*x) + 900*sin(4*x)^2 + 56*(4*sin(2*x) + sin(x))*sin(3*x) + 196*sin(3*x)^2 + 64*sin(2*x)^2 + 32*sin(2*x)*sin(x) + 4*sin(x)^2 + 4*cos(x) + 1), x) - 2*sin(x))/(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","F",0
84,0,0,0,0.000000," ","integrate(1/(1-cos(x)^6),x, algorithm=""maxima"")","\frac{{\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} - 2 \, \cos\left(2 \, x\right) + 1\right)} \int \frac{{\left(\cos\left(3 \, x\right) + 4 \, \cos\left(2 \, x\right) + \cos\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(14 \, \cos\left(2 \, x\right) + 4 \, \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) + 2 \, \cos\left(3 \, x\right)^{2} + 2 \, {\left(7 \, \cos\left(x\right) + 2\right)} \cos\left(2 \, x\right) + 24 \, \cos\left(2 \, x\right)^{2} + 2 \, \cos\left(x\right)^{2} + {\left(\sin\left(3 \, x\right) + 4 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) + 2 \, {\left(7 \, \sin\left(2 \, x\right) + 2 \, \sin\left(x\right)\right)} \sin\left(3 \, x\right) + 2 \, \sin\left(3 \, x\right)^{2} + 24 \, \sin\left(2 \, x\right)^{2} + 14 \, \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, \sin\left(x\right)^{2} + \cos\left(x\right)}{2 \, {\left(2 \, \cos\left(3 \, x\right) + 6 \, \cos\left(2 \, x\right) + 2 \, \cos\left(x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 4 \, {\left(6 \, \cos\left(2 \, x\right) + 2 \, \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) + 4 \, \cos\left(3 \, x\right)^{2} + 12 \, {\left(2 \, \cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + 36 \, \cos\left(2 \, x\right)^{2} + 4 \, \cos\left(x\right)^{2} + 4 \, {\left(\sin\left(3 \, x\right) + 3 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) + \sin\left(4 \, x\right)^{2} + 8 \, {\left(3 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(3 \, x\right) + 4 \, \sin\left(3 \, x\right)^{2} + 36 \, \sin\left(2 \, x\right)^{2} + 24 \, \sin\left(2 \, x\right) \sin\left(x\right) + 4 \, \sin\left(x\right)^{2} + 4 \, \cos\left(x\right) + 1}\,{d x} + {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} - 2 \, \cos\left(2 \, x\right) + 1\right)} \int \frac{{\left(\cos\left(3 \, x\right) - 4 \, \cos\left(2 \, x\right) + \cos\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(14 \, \cos\left(2 \, x\right) - 4 \, \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) - 2 \, \cos\left(3 \, x\right)^{2} + 2 \, {\left(7 \, \cos\left(x\right) - 2\right)} \cos\left(2 \, x\right) - 24 \, \cos\left(2 \, x\right)^{2} - 2 \, \cos\left(x\right)^{2} + {\left(\sin\left(3 \, x\right) - 4 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) + 2 \, {\left(7 \, \sin\left(2 \, x\right) - 2 \, \sin\left(x\right)\right)} \sin\left(3 \, x\right) - 2 \, \sin\left(3 \, x\right)^{2} - 24 \, \sin\left(2 \, x\right)^{2} + 14 \, \sin\left(2 \, x\right) \sin\left(x\right) - 2 \, \sin\left(x\right)^{2} + \cos\left(x\right)}{2 \, {\left(2 \, \cos\left(3 \, x\right) - 6 \, \cos\left(2 \, x\right) + 2 \, \cos\left(x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} + 4 \, {\left(6 \, \cos\left(2 \, x\right) - 2 \, \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) - 4 \, \cos\left(3 \, x\right)^{2} + 12 \, {\left(2 \, \cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) - 36 \, \cos\left(2 \, x\right)^{2} - 4 \, \cos\left(x\right)^{2} + 4 \, {\left(\sin\left(3 \, x\right) - 3 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sin\left(4 \, x\right)^{2} + 8 \, {\left(3 \, \sin\left(2 \, x\right) - \sin\left(x\right)\right)} \sin\left(3 \, x\right) - 4 \, \sin\left(3 \, x\right)^{2} - 36 \, \sin\left(2 \, x\right)^{2} + 24 \, \sin\left(2 \, x\right) \sin\left(x\right) - 4 \, \sin\left(x\right)^{2} + 4 \, \cos\left(x\right) - 1}\,{d x} - 2 \, \sin\left(2 \, x\right)}{3 \, {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} - 2 \, \cos\left(2 \, x\right) + 1\right)}}"," ",0,"1/3*(3*(cos(2*x)^2 + sin(2*x)^2 - 2*cos(2*x) + 1)*integrate(1/3*((cos(3*x) + 4*cos(2*x) + cos(x))*cos(4*x) + (14*cos(2*x) + 4*cos(x) + 1)*cos(3*x) + 2*cos(3*x)^2 + 2*(7*cos(x) + 2)*cos(2*x) + 24*cos(2*x)^2 + 2*cos(x)^2 + (sin(3*x) + 4*sin(2*x) + sin(x))*sin(4*x) + 2*(7*sin(2*x) + 2*sin(x))*sin(3*x) + 2*sin(3*x)^2 + 24*sin(2*x)^2 + 14*sin(2*x)*sin(x) + 2*sin(x)^2 + cos(x))/(2*(2*cos(3*x) + 6*cos(2*x) + 2*cos(x) + 1)*cos(4*x) + cos(4*x)^2 + 4*(6*cos(2*x) + 2*cos(x) + 1)*cos(3*x) + 4*cos(3*x)^2 + 12*(2*cos(x) + 1)*cos(2*x) + 36*cos(2*x)^2 + 4*cos(x)^2 + 4*(sin(3*x) + 3*sin(2*x) + sin(x))*sin(4*x) + sin(4*x)^2 + 8*(3*sin(2*x) + sin(x))*sin(3*x) + 4*sin(3*x)^2 + 36*sin(2*x)^2 + 24*sin(2*x)*sin(x) + 4*sin(x)^2 + 4*cos(x) + 1), x) - 3*(cos(2*x)^2 + sin(2*x)^2 - 2*cos(2*x) + 1)*integrate(-1/3*((cos(3*x) - 4*cos(2*x) + cos(x))*cos(4*x) + (14*cos(2*x) - 4*cos(x) + 1)*cos(3*x) - 2*cos(3*x)^2 + 2*(7*cos(x) - 2)*cos(2*x) - 24*cos(2*x)^2 - 2*cos(x)^2 + (sin(3*x) - 4*sin(2*x) + sin(x))*sin(4*x) + 2*(7*sin(2*x) - 2*sin(x))*sin(3*x) - 2*sin(3*x)^2 - 24*sin(2*x)^2 + 14*sin(2*x)*sin(x) - 2*sin(x)^2 + cos(x))/(2*(2*cos(3*x) - 6*cos(2*x) + 2*cos(x) - 1)*cos(4*x) - cos(4*x)^2 + 4*(6*cos(2*x) - 2*cos(x) + 1)*cos(3*x) - 4*cos(3*x)^2 + 12*(2*cos(x) - 1)*cos(2*x) - 36*cos(2*x)^2 - 4*cos(x)^2 + 4*(sin(3*x) - 3*sin(2*x) + sin(x))*sin(4*x) - sin(4*x)^2 + 8*(3*sin(2*x) - sin(x))*sin(3*x) - 4*sin(3*x)^2 - 36*sin(2*x)^2 + 24*sin(2*x)*sin(x) - 4*sin(x)^2 + 4*cos(x) - 1), x) - 2*sin(2*x))/(cos(2*x)^2 + sin(2*x)^2 - 2*cos(2*x) + 1)","F",0
85,0,0,0,0.000000," ","integrate(1/(1-cos(x)^8),x, algorithm=""maxima"")","\frac{\frac{1}{2} \, {\left(\sqrt{2} \cos\left(2 \, x\right)^{2} + \sqrt{2} \sin\left(2 \, x\right)^{2} - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2}\right)} {\left(2 \, {\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{-\sqrt{2} + 2} + 2 \, \tan\left(x\right)\right)}}{2 \, \sqrt{\sqrt{2} + 2}}\right)\right)} \sqrt{\sqrt{2} + 1} + 2 \, {\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor + \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{-\sqrt{2} + 2} - 2 \, \tan\left(x\right)\right)}}{2 \, \sqrt{\sqrt{2} + 2}}\right)\right)} \sqrt{\sqrt{2} + 1} - \sqrt{\sqrt{2} - 1} \log\left(\tan\left(x\right)^{2} + 2^{\frac{1}{4}} \sqrt{-\sqrt{2} + 2} \tan\left(x\right) + \sqrt{2}\right) + \sqrt{\sqrt{2} - 1} \log\left(\tan\left(x\right)^{2} - 2^{\frac{1}{4}} \sqrt{-\sqrt{2} + 2} \tan\left(x\right) + \sqrt{2}\right)\right)} + {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} - 2 \, \cos\left(2 \, x\right) + 1\right)} \arctan\left(\frac{4 \, \sqrt{2} \sin\left(2 \, x\right)}{2 \, {\left(2 \, \sqrt{2} + 3\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 12 \, \sqrt{2} + 17}, \frac{\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 6 \, \cos\left(2 \, x\right) + 1}{2 \, {\left(2 \, \sqrt{2} + 3\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 12 \, \sqrt{2} + 17}\right) - 4 \, \sqrt{2} \sin\left(2 \, x\right)}{8 \, {\left(\sqrt{2} \cos\left(2 \, x\right)^{2} + \sqrt{2} \sin\left(2 \, x\right)^{2} - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2}\right)}}"," ",0,"1/8*((cos(2*x)^2 + sin(2*x)^2 - 2*cos(2*x) + 1)*arctan2(4*sqrt(2)*sin(2*x)/(2*(2*sqrt(2) + 3)*cos(2*x) + cos(2*x)^2 + sin(2*x)^2 + 12*sqrt(2) + 17), (cos(2*x)^2 + sin(2*x)^2 + 6*cos(2*x) + 1)/(2*(2*sqrt(2) + 3)*cos(2*x) + cos(2*x)^2 + sin(2*x)^2 + 12*sqrt(2) + 17)) + 64*(sqrt(2)*cos(2*x)^2 + sqrt(2)*sin(2*x)^2 - 2*sqrt(2)*cos(2*x) + sqrt(2))*integrate(((4*cos(2*x) + 1)*cos(4*x) + cos(8*x)*cos(4*x) + 4*cos(6*x)*cos(4*x) + 22*cos(4*x)^2 + sin(8*x)*sin(4*x) + 4*sin(6*x)*sin(4*x) + 22*sin(4*x)^2 + 4*sin(4*x)*sin(2*x))/(2*(4*cos(6*x) + 22*cos(4*x) + 4*cos(2*x) + 1)*cos(8*x) + cos(8*x)^2 + 8*(22*cos(4*x) + 4*cos(2*x) + 1)*cos(6*x) + 16*cos(6*x)^2 + 44*(4*cos(2*x) + 1)*cos(4*x) + 484*cos(4*x)^2 + 16*cos(2*x)^2 + 4*(2*sin(6*x) + 11*sin(4*x) + 2*sin(2*x))*sin(8*x) + sin(8*x)^2 + 16*(11*sin(4*x) + 2*sin(2*x))*sin(6*x) + 16*sin(6*x)^2 + 484*sin(4*x)^2 + 176*sin(4*x)*sin(2*x) + 16*sin(2*x)^2 + 8*cos(2*x) + 1), x) - 4*sqrt(2)*sin(2*x))/(sqrt(2)*cos(2*x)^2 + sqrt(2)*sin(2*x)^2 - 2*sqrt(2)*cos(2*x) + sqrt(2))","F",0
86,1,19,0,0.303099," ","integrate(tan(x)/(1+cos(x)^2),x, algorithm=""maxima"")","-\frac{1}{2} \, \log\left(\sin\left(x\right)^{2} - 1\right) + \frac{1}{2} \, \log\left(\sin\left(x\right)^{2} - 2\right)"," ",0,"-1/2*log(sin(x)^2 - 1) + 1/2*log(sin(x)^2 - 2)","A",0
87,1,95,0,1.138524," ","integrate((a+b*cos(x)^2)^(1/2)*tan(x),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{a} \log\left(b - \frac{\sqrt{-b \sin\left(x\right)^{2} + a + b} \sqrt{a}}{\sin\left(x\right) - 1} - \frac{a}{\sin\left(x\right) - 1}\right) + \frac{1}{2} \, \sqrt{a} \log\left(-b + \frac{\sqrt{-b \sin\left(x\right)^{2} + a + b} \sqrt{a}}{\sin\left(x\right) + 1} + \frac{a}{\sin\left(x\right) + 1}\right) - \sqrt{-b \sin\left(x\right)^{2} + a + b}"," ",0,"1/2*sqrt(a)*log(b - sqrt(-b*sin(x)^2 + a + b)*sqrt(a)/(sin(x) - 1) - a/(sin(x) - 1)) + 1/2*sqrt(a)*log(-b + sqrt(-b*sin(x)^2 + a + b)*sqrt(a)/(sin(x) + 1) + a/(sin(x) + 1)) - sqrt(-b*sin(x)^2 + a + b)","B",0
88,1,47,0,0.959497," ","integrate((1-cos(x)^2)^(1/2)*tan(x),x, algorithm=""maxima"")","\frac{1}{2} \, \left(-1\right)^{2 \, \sin\left(x\right)} \log\left(-\frac{\sin\left(x\right)}{\sin\left(x\right) + 1}\right) + \frac{1}{2} \, \left(-1\right)^{2 \, \sin\left(x\right)} \log\left(-\frac{\sin\left(x\right)}{\sin\left(x\right) - 1}\right) - \sqrt{\sin\left(x\right)^{2}}"," ",0,"1/2*(-1)^(2*sin(x))*log(-sin(x)/(sin(x) + 1)) + 1/2*(-1)^(2*sin(x))*log(-sin(x)/(sin(x) - 1)) - sqrt(sin(x)^2)","B",0
89,1,81,0,0.892870," ","integrate(tan(x)/(a+b*cos(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{\log\left(b - \frac{\sqrt{-b \sin\left(x\right)^{2} + a + b} \sqrt{a}}{\sin\left(x\right) - 1} - \frac{a}{\sin\left(x\right) - 1}\right)}{2 \, \sqrt{a}} + \frac{\log\left(-b + \frac{\sqrt{-b \sin\left(x\right)^{2} + a + b} \sqrt{a}}{\sin\left(x\right) + 1} + \frac{a}{\sin\left(x\right) + 1}\right)}{2 \, \sqrt{a}}"," ",0,"1/2*log(b - sqrt(-b*sin(x)^2 + a + b)*sqrt(a)/(sin(x) - 1) - a/(sin(x) - 1))/sqrt(a) + 1/2*log(-b + sqrt(-b*sin(x)^2 + a + b)*sqrt(a)/(sin(x) + 1) + a/(sin(x) + 1))/sqrt(a)","B",0
90,1,60,0,0.883634," ","integrate(tan(x)/(1+cos(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \log\left(\frac{\sqrt{-\sin\left(x\right)^{2} + 2}}{\sin\left(x\right) + 1} + \frac{1}{\sin\left(x\right) + 1} - 1\right) + \frac{1}{2} \, \log\left(-\frac{\sqrt{-\sin\left(x\right)^{2} + 2}}{\sin\left(x\right) - 1} - \frac{1}{\sin\left(x\right) - 1} + 1\right)"," ",0,"1/2*log(sqrt(-sin(x)^2 + 2)/(sin(x) + 1) + 1/(sin(x) + 1) - 1) + 1/2*log(-sqrt(-sin(x)^2 + 2)/(sin(x) - 1) - 1/(sin(x) - 1) + 1)","B",0
91,1,39,0,0.582336," ","integrate(tan(x)/(1-cos(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \left(-1\right)^{2 \, \sin\left(x\right)} \log\left(-\frac{\sin\left(x\right)}{\sin\left(x\right) + 1}\right) + \frac{1}{2} \, \left(-1\right)^{2 \, \sin\left(x\right)} \log\left(-\frac{\sin\left(x\right)}{\sin\left(x\right) - 1}\right)"," ",0,"1/2*(-1)^(2*sin(x))*log(-sin(x)/(sin(x) + 1)) + 1/2*(-1)^(2*sin(x))*log(-sin(x)/(sin(x) - 1))","B",0
92,1,151,0,1.592781," ","integrate(tan(x)^3/(a+b*cos(x)^3),x, algorithm=""maxima"")","\frac{\sqrt{3} {\left(b {\left(3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}} - \frac{2 \, a}{b}\right)} + 2 \, a\right)} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, \cos\left(x\right)\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a^{2}} - \frac{{\left(2 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} + 1\right)} \log\left(\cos\left(x\right)^{2} - \left(\frac{a}{b}\right)^{\frac{1}{3}} \cos\left(x\right) + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(\left(\frac{a}{b}\right)^{\frac{2}{3}} - 1\right)} \log\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} + \cos\left(x\right)\right)}{3 \, a \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{\log\left(\cos\left(x\right)\right)}{a} + \frac{1}{2 \, a \cos\left(x\right)^{2}}"," ",0,"1/9*sqrt(3)*(b*(3*(a/b)^(1/3) - 2*a/b) + 2*a)*arctan(-1/3*sqrt(3)*((a/b)^(1/3) - 2*cos(x))/(a/b)^(1/3))/a^2 - 1/6*(2*(a/b)^(2/3) + 1)*log(cos(x)^2 - (a/b)^(1/3)*cos(x) + (a/b)^(2/3))/(a*(a/b)^(2/3)) - 1/3*((a/b)^(2/3) - 1)*log((a/b)^(1/3) + cos(x))/(a*(a/b)^(2/3)) + log(cos(x))/a + 1/2/(a*cos(x)^2)","A",0
93,1,52,0,0.768821," ","integrate((a+b*cos(x)^3)^(1/2)*tan(x),x, algorithm=""maxima"")","-\frac{1}{3} \, \sqrt{a} \log\left(\frac{\sqrt{b \cos\left(x\right)^{3} + a} - \sqrt{a}}{\sqrt{b \cos\left(x\right)^{3} + a} + \sqrt{a}}\right) - \frac{2}{3} \, \sqrt{b \cos\left(x\right)^{3} + a}"," ",0,"-1/3*sqrt(a)*log((sqrt(b*cos(x)^3 + a) - sqrt(a))/(sqrt(b*cos(x)^3 + a) + sqrt(a))) - 2/3*sqrt(b*cos(x)^3 + a)","A",0
94,1,39,0,1.760135," ","integrate(tan(x)/(a+b*cos(x)^3)^(1/2),x, algorithm=""maxima"")","-\frac{\log\left(\frac{\sqrt{b \cos\left(x\right)^{3} + a} - \sqrt{a}}{\sqrt{b \cos\left(x\right)^{3} + a} + \sqrt{a}}\right)}{3 \, \sqrt{a}}"," ",0,"-1/3*log((sqrt(b*cos(x)^3 + a) - sqrt(a))/(sqrt(b*cos(x)^3 + a) + sqrt(a)))/sqrt(a)","A",0
95,1,43,0,2.064124," ","integrate((a+b*cos(x)^4)^(1/2)*tan(x),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{a} \operatorname{arsinh}\left(-\frac{a}{\sqrt{a b} {\left(\sin\left(x\right)^{2} - 1\right)}}\right) - \frac{1}{2} \, \sqrt{b \sin\left(x\right)^{4} - 2 \, b \sin\left(x\right)^{2} + a + b}"," ",0,"1/2*sqrt(a)*arcsinh(-a/(sqrt(a*b)*(sin(x)^2 - 1))) - 1/2*sqrt(b*sin(x)^4 - 2*b*sin(x)^2 + a + b)","A",0
96,0,0,0,0.000000," ","integrate(tan(x)/(a+b*cos(x)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right)}{\sqrt{b \cos\left(x\right)^{4} + a}}\,{d x}"," ",0,"integrate(tan(x)/sqrt(b*cos(x)^4 + a), x)","F",0
97,1,58,0,0.805678," ","integrate((a+b*cos(x)^n)^(1/2)*tan(x),x, algorithm=""maxima"")","-\frac{\sqrt{a} \log\left(\frac{\sqrt{b \cos\left(x\right)^{n} + a} - \sqrt{a}}{\sqrt{b \cos\left(x\right)^{n} + a} + \sqrt{a}}\right)}{n} - \frac{2 \, \sqrt{b \cos\left(x\right)^{n} + a}}{n}"," ",0,"-sqrt(a)*log((sqrt(b*cos(x)^n + a) - sqrt(a))/(sqrt(b*cos(x)^n + a) + sqrt(a)))/n - 2*sqrt(b*cos(x)^n + a)/n","A",0
98,1,42,0,1.038992," ","integrate(tan(x)/(a+b*cos(x)^n)^(1/2),x, algorithm=""maxima"")","-\frac{\log\left(\frac{\sqrt{b \cos\left(x\right)^{n} + a} - \sqrt{a}}{\sqrt{b \cos\left(x\right)^{n} + a} + \sqrt{a}}\right)}{\sqrt{a} n}"," ",0,"-log((sqrt(b*cos(x)^n + a) - sqrt(a))/(sqrt(b*cos(x)^n + a) + sqrt(a)))/(sqrt(a)*n)","A",0
