1,1,31,0,0.178522," ","integrate(sin(x)^6/(a-a*cos(x)^2),x, algorithm=""giac"")","\frac{3 \, x}{8 \, a} - \frac{5 \, \tan\left(x\right)^{3} + 3 \, \tan\left(x\right)}{8 \, {\left(\tan\left(x\right)^{2} + 1\right)}^{2} a}"," ",0,"3/8*x/a - 1/8*(5*tan(x)^3 + 3*tan(x))/((tan(x)^2 + 1)^2*a)","A",0
2,1,14,0,0.198363," ","integrate(sin(x)^5/(a-a*cos(x)^2),x, algorithm=""giac"")","\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
3,1,22,0,0.172862," ","integrate(sin(x)^4/(a-a*cos(x)^2),x, algorithm=""giac"")","\frac{x}{2 \, a} - \frac{\tan\left(x\right)}{2 \, {\left(\tan\left(x\right)^{2} + 1\right)} a}"," ",0,"1/2*x/a - 1/2*tan(x)/((tan(x)^2 + 1)*a)","A",0
4,1,7,0,0.158017," ","integrate(sin(x)^3/(a-a*cos(x)^2),x, algorithm=""giac"")","-\frac{\cos\left(x\right)}{a}"," ",0,"-cos(x)/a","A",0
5,1,5,0,0.217174," ","integrate(sin(x)^2/(a-a*cos(x)^2),x, algorithm=""giac"")","\frac{x}{a}"," ",0,"x/a","A",0
6,1,23,0,0.156131," ","integrate(sin(x)/(a-a*cos(x)^2),x, algorithm=""giac"")","-\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
7,1,38,0,0.146847," ","integrate(csc(x)/(a-a*cos(x)^2),x, algorithm=""giac"")","-\frac{\log\left(\cos\left(x\right) + 1\right)}{4 \, a} + \frac{\log\left(-\cos\left(x\right) + 1\right)}{4 \, a} + \frac{\cos\left(x\right)}{2 \, {\left(\cos\left(x\right)^{2} - 1\right)} a}"," ",0,"-1/4*log(cos(x) + 1)/a + 1/4*log(-cos(x) + 1)/a + 1/2*cos(x)/((cos(x)^2 - 1)*a)","B",0
8,1,17,0,0.317167," ","integrate(csc(x)^2/(a-a*cos(x)^2),x, algorithm=""giac"")","-\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
9,1,47,0,0.825417," ","integrate(csc(x)^3/(a-a*cos(x)^2),x, algorithm=""giac"")","-\frac{3 \, \log\left(\cos\left(x\right) + 1\right)}{16 \, a} + \frac{3 \, \log\left(-\cos\left(x\right) + 1\right)}{16 \, a} + \frac{3 \, \cos\left(x\right)^{3} - 5 \, \cos\left(x\right)}{8 \, {\left(\cos\left(x\right)^{2} - 1\right)}^{2} a}"," ",0,"-3/16*log(cos(x) + 1)/a + 3/16*log(-cos(x) + 1)/a + 1/8*(3*cos(x)^3 - 5*cos(x))/((cos(x)^2 - 1)^2*a)","A",0
10,1,99,0,0.151521," ","integrate(sin(x)^7/(a+b*cos(x)^2),x, algorithm=""giac"")","-\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^{4} \cos\left(x\right)^{5} - 5 \, a b^{3} \cos\left(x\right)^{3} - 15 \, b^{4} \cos\left(x\right)^{3} + 15 \, a^{2} b^{2} \cos\left(x\right) + 45 \, a b^{3} \cos\left(x\right) + 45 \, b^{4} \cos\left(x\right)}{15 \, b^{5}}"," ",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^4*cos(x)^5 - 5*a*b^3*cos(x)^3 - 15*b^4*cos(x)^3 + 15*a^2*b^2*cos(x) + 45*a*b^3*cos(x) + 45*b^4*cos(x))/b^5","A",0
11,1,59,0,0.165574," ","integrate(sin(x)^5/(a+b*cos(x)^2),x, algorithm=""giac"")","-\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^{2} \cos\left(x\right)^{3} - 3 \, a b \cos\left(x\right) - 6 \, b^{2} \cos\left(x\right)}{3 \, b^{3}}"," ",0,"-(a^2 + 2*a*b + b^2)*arctan(b*cos(x)/sqrt(a*b))/(sqrt(a*b)*b^2) - 1/3*(b^2*cos(x)^3 - 3*a*b*cos(x) - 6*b^2*cos(x))/b^3","A",0
12,1,30,0,0.177379," ","integrate(sin(x)^3/(a+b*cos(x)^2),x, algorithm=""giac"")","-\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
13,1,17,0,0.181816," ","integrate(sin(x)/(a+b*cos(x)^2),x, algorithm=""giac"")","-\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
14,1,50,0,0.219607," ","integrate(csc(x)/(a+b*cos(x)^2),x, algorithm=""giac"")","-\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
15,1,103,0,0.174812," ","integrate(csc(x)^3/(a+b*cos(x)^2),x, algorithm=""giac"")","-\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(\cos\left(x\right)^{2} - 1\right)} {\left(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)/((cos(x)^2 - 1)*(a + b))","B",0
16,1,178,0,0.193963," ","integrate(csc(x)^5/(a+b*cos(x)^2),x, algorithm=""giac"")","-\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{3 \, a \cos\left(x\right)^{3} + 7 \, b \cos\left(x\right)^{3} - 5 \, a \cos\left(x\right) - 9 \, b \cos\left(x\right)}{8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(\cos\left(x\right)^{2} - 1\right)}^{2}}"," ",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*cos(x)^3 + 7*b*cos(x)^3 - 5*a*cos(x) - 9*b*cos(x))/((a^2 + 2*a*b + b^2)*(cos(x)^2 - 1)^2)","B",0
17,1,119,0,1.614403," ","integrate(sin(x)^6/(a+b*cos(x)^2),x, algorithm=""giac"")","-\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)} {\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{a^{2} + a b}}\right)\right)}}{\sqrt{a^{2} + a b} b^{3}} + \frac{4 \, a \tan\left(x\right)^{3} + 9 \, b \tan\left(x\right)^{3} + 4 \, a \tan\left(x\right) + 7 \, b \tan\left(x\right)}{8 \, {\left(\tan\left(x\right)^{2} + 1\right)}^{2} b^{2}}"," ",0,"-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)*(pi*floor(x/pi + 1/2)*sgn(a) + arctan(a*tan(x)/sqrt(a^2 + a*b)))/(sqrt(a^2 + a*b)*b^3) + 1/8*(4*a*tan(x)^3 + 9*b*tan(x)^3 + 4*a*tan(x) + 7*b*tan(x))/((tan(x)^2 + 1)^2*b^2)","A",0
18,1,80,0,0.189877," ","integrate(sin(x)^4/(a+b*cos(x)^2),x, algorithm=""giac"")","-\frac{{\left(2 \, a + 3 \, b\right)} x}{2 \, b^{2}} + \frac{{\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{a^{2} + a b}}\right)\right)} {\left(a^{2} + 2 \, a b + b^{2}\right)}}{\sqrt{a^{2} + a b} b^{2}} + \frac{\tan\left(x\right)}{2 \, {\left(\tan\left(x\right)^{2} + 1\right)} b}"," ",0,"-1/2*(2*a + 3*b)*x/b^2 + (pi*floor(x/pi + 1/2)*sgn(a) + arctan(a*tan(x)/sqrt(a^2 + a*b)))*(a^2 + 2*a*b + b^2)/(sqrt(a^2 + a*b)*b^2) + 1/2*tan(x)/((tan(x)^2 + 1)*b)","A",0
19,1,50,0,0.193117," ","integrate(sin(x)^2/(a+b*cos(x)^2),x, algorithm=""giac"")","\frac{{\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{a^{2} + a b}}\right)\right)} {\left(a + b\right)}}{\sqrt{a^{2} + a b} b} - \frac{x}{b}"," ",0,"(pi*floor(x/pi + 1/2)*sgn(a) + arctan(a*tan(x)/sqrt(a^2 + a*b)))*(a + b)/(sqrt(a^2 + a*b)*b) - x/b","A",0
20,1,37,0,0.161814," ","integrate(1/(a+b*cos(x)^2),x, algorithm=""giac"")","\frac{\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{a^{2} + a b}}\right)}{\sqrt{a^{2} + a b}}"," ",0,"(pi*floor(x/pi + 1/2)*sgn(a) + arctan(a*tan(x)/sqrt(a^2 + a*b)))/sqrt(a^2 + a*b)","A",0
21,1,55,0,0.342644," ","integrate(csc(x)^2/(a+b*cos(x)^2),x, algorithm=""giac"")","\frac{{\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{a^{2} + a b}}\right)\right)} b}{\sqrt{a^{2} + a b} {\left(a + b\right)}} - \frac{1}{{\left(a + b\right)} \tan\left(x\right)}"," ",0,"(pi*floor(x/pi + 1/2)*sgn(a) + arctan(a*tan(x)/sqrt(a^2 + a*b)))*b/(sqrt(a^2 + a*b)*(a + b)) - 1/((a + b)*tan(x))","A",0
22,1,90,0,0.869048," ","integrate(csc(x)^4/(a+b*cos(x)^2),x, algorithm=""giac"")","\frac{{\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{a^{2} + a b}}\right)\right)} b^{2}}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a^{2} + a b}} - \frac{3 \, a \tan\left(x\right)^{2} + 6 \, b \tan\left(x\right)^{2} + a + b}{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \tan\left(x\right)^{3}}"," ",0,"(pi*floor(x/pi + 1/2)*sgn(a) + arctan(a*tan(x)/sqrt(a^2 + a*b)))*b^2/((a^2 + 2*a*b + b^2)*sqrt(a^2 + a*b)) - 1/3*(3*a*tan(x)^2 + 6*b*tan(x)^2 + a + b)/((a^2 + 2*a*b + b^2)*tan(x)^3)","A",0
23,1,156,0,0.598828," ","integrate(csc(x)^6/(a+b*cos(x)^2),x, algorithm=""giac"")","\frac{{\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{a^{2} + a b}}\right)\right)} b^{3}}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{a^{2} + a b}} - \frac{15 \, a^{2} \tan\left(x\right)^{4} + 45 \, a b \tan\left(x\right)^{4} + 45 \, b^{2} \tan\left(x\right)^{4} + 10 \, a^{2} \tan\left(x\right)^{2} + 25 \, a b \tan\left(x\right)^{2} + 15 \, b^{2} \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,"(pi*floor(x/pi + 1/2)*sgn(a) + arctan(a*tan(x)/sqrt(a^2 + a*b)))*b^3/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt(a^2 + a*b)) - 1/15*(15*a^2*tan(x)^4 + 45*a*b*tan(x)^4 + 45*b^2*tan(x)^4 + 10*a^2*tan(x)^2 + 25*a*b*tan(x)^2 + 15*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)","B",0
24,1,60,0,0.198453," ","integrate(sin(x)/(4-3*cos(x)^3),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{3} \left(\frac{4}{3}\right)^{\frac{1}{3}} \arctan\left(\frac{1}{4} \, \sqrt{3} \left(\frac{4}{3}\right)^{\frac{2}{3}} {\left(\left(\frac{4}{3}\right)^{\frac{1}{3}} + 2 \, \cos\left(x\right)\right)}\right) - \frac{1}{72} \cdot 36^{\frac{1}{3}} \log\left(\cos\left(x\right)^{2} + \left(\frac{4}{3}\right)^{\frac{1}{3}} \cos\left(x\right) + \left(\frac{4}{3}\right)^{\frac{2}{3}}\right) + \frac{1}{12} \, \left(\frac{4}{3}\right)^{\frac{1}{3}} \log\left(\left(\frac{4}{3}\right)^{\frac{1}{3}} - \cos\left(x\right)\right)"," ",0,"-1/12*sqrt(3)*(4/3)^(1/3)*arctan(1/4*sqrt(3)*(4/3)^(2/3)*((4/3)^(1/3) + 2*cos(x))) - 1/72*36^(1/3)*log(cos(x)^2 + (4/3)^(1/3)*cos(x) + (4/3)^(2/3)) + 1/12*(4/3)^(1/3)*log((4/3)^(1/3) - cos(x))","A",0
25,1,6,0,0.268845," ","integrate(1/(1-cos(x)^2),x, algorithm=""giac"")","-\frac{1}{\tan\left(x\right)}"," ",0,"-1/tan(x)","A",0
26,1,14,0,0.167845," ","integrate(1/(1-cos(x)^2)^2,x, algorithm=""giac"")","-\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
27,1,20,0,0.587375," ","integrate(1/(1-cos(x)^2)^3,x, algorithm=""giac"")","-\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
28,1,96,0,0.180308," ","integrate(cos(x)^7/(a+b*cos(x)^2),x, algorithm=""giac"")","\frac{a^{3} \arctan\left(\frac{b \sin\left(x\right)}{\sqrt{-a b - b^{2}}}\right)}{\sqrt{-a b - b^{2}} b^{3}} + \frac{3 \, b^{4} \sin\left(x\right)^{5} + 5 \, a b^{3} \sin\left(x\right)^{3} - 10 \, b^{4} \sin\left(x\right)^{3} + 15 \, a^{2} b^{2} \sin\left(x\right) - 15 \, a b^{3} \sin\left(x\right) + 15 \, b^{4} \sin\left(x\right)}{15 \, b^{5}}"," ",0,"a^3*arctan(b*sin(x)/sqrt(-a*b - b^2))/(sqrt(-a*b - b^2)*b^3) + 1/15*(3*b^4*sin(x)^5 + 5*a*b^3*sin(x)^3 - 10*b^4*sin(x)^3 + 15*a^2*b^2*sin(x) - 15*a*b^3*sin(x) + 15*b^4*sin(x))/b^5","A",0
29,1,65,0,0.161870," ","integrate(cos(x)^5/(a+b*cos(x)^2),x, algorithm=""giac"")","-\frac{a^{2} \arctan\left(\frac{b \sin\left(x\right)}{\sqrt{-a b - b^{2}}}\right)}{\sqrt{-a b - b^{2}} b^{2}} - \frac{b^{2} \sin\left(x\right)^{3} + 3 \, a b \sin\left(x\right) - 3 \, b^{2} \sin\left(x\right)}{3 \, b^{3}}"," ",0,"-a^2*arctan(b*sin(x)/sqrt(-a*b - b^2))/(sqrt(-a*b - b^2)*b^2) - 1/3*(b^2*sin(x)^3 + 3*a*b*sin(x) - 3*b^2*sin(x))/b^3","A",0
30,1,41,0,0.175913," ","integrate(cos(x)^3/(a+b*cos(x)^2),x, algorithm=""giac"")","\frac{a \arctan\left(\frac{b \sin\left(x\right)}{\sqrt{-a b - b^{2}}}\right)}{\sqrt{-a b - b^{2}} b} + \frac{\sin\left(x\right)}{b}"," ",0,"a*arctan(b*sin(x)/sqrt(-a*b - b^2))/(sqrt(-a*b - b^2)*b) + sin(x)/b","A",0
31,1,31,0,0.181546," ","integrate(cos(x)/(a+b*cos(x)^2),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{b \sin\left(x\right)}{\sqrt{-a b - b^{2}}}\right)}{\sqrt{-a b - b^{2}}}"," ",0,"-arctan(b*sin(x)/sqrt(-a*b - b^2))/sqrt(-a*b - b^2)","A",0
32,1,57,0,0.186554," ","integrate(sec(x)/(a+b*cos(x)^2),x, algorithm=""giac"")","\frac{b \arctan\left(\frac{b \sin\left(x\right)}{\sqrt{-a b - b^{2}}}\right)}{\sqrt{-a b - b^{2}} a} + \frac{\log\left(\sin\left(x\right) + 1\right)}{2 \, a} - \frac{\log\left(-\sin\left(x\right) + 1\right)}{2 \, a}"," ",0,"b*arctan(b*sin(x)/sqrt(-a*b - b^2))/(sqrt(-a*b - b^2)*a) + 1/2*log(sin(x) + 1)/a - 1/2*log(-sin(x) + 1)/a","A",0
33,1,85,0,0.190862," ","integrate(sec(x)^3/(a+b*cos(x)^2),x, algorithm=""giac"")","-\frac{b^{2} \arctan\left(\frac{b \sin\left(x\right)}{\sqrt{-a b - b^{2}}}\right)}{\sqrt{-a b - b^{2}} 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(\sin\left(x\right)^{2} - 1\right)} a}"," ",0,"-b^2*arctan(b*sin(x)/sqrt(-a*b - b^2))/(sqrt(-a*b - b^2)*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)/((sin(x)^2 - 1)*a)","A",0
34,1,127,0,0.193670," ","integrate(sec(x)^5/(a+b*cos(x)^2),x, algorithm=""giac"")","\frac{b^{3} \arctan\left(\frac{b \sin\left(x\right)}{\sqrt{-a b - b^{2}}}\right)}{\sqrt{-a b - b^{2}} 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}} - \frac{{\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \log\left(-\sin\left(x\right) + 1\right)}{16 \, a^{3}} - \frac{3 \, a \sin\left(x\right)^{3} - 4 \, b \sin\left(x\right)^{3} - 5 \, a \sin\left(x\right) + 4 \, b \sin\left(x\right)}{8 \, {\left(\sin\left(x\right)^{2} - 1\right)}^{2} a^{2}}"," ",0,"b^3*arctan(b*sin(x)/sqrt(-a*b - b^2))/(sqrt(-a*b - b^2)*a^3) + 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 - 1/8*(3*a*sin(x)^3 - 4*b*sin(x)^3 - 5*a*sin(x) + 4*b*sin(x))/((sin(x)^2 - 1)^2*a^2)","A",0
35,1,104,0,0.187296," ","integrate(cos(x)^6/(a+b*cos(x)^2),x, algorithm=""giac"")","-\frac{{\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{a^{2} + a b}}\right)\right)} a^{3}}{\sqrt{a^{2} + a b} b^{3}} + \frac{{\left(8 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} x}{8 \, b^{3}} - \frac{4 \, a \tan\left(x\right)^{3} - 3 \, b \tan\left(x\right)^{3} + 4 \, a \tan\left(x\right) - 5 \, b \tan\left(x\right)}{8 \, {\left(\tan\left(x\right)^{2} + 1\right)}^{2} b^{2}}"," ",0,"-(pi*floor(x/pi + 1/2)*sgn(a) + arctan(a*tan(x)/sqrt(a^2 + a*b)))*a^3/(sqrt(a^2 + a*b)*b^3) + 1/8*(8*a^2 - 4*a*b + 3*b^2)*x/b^3 - 1/8*(4*a*tan(x)^3 - 3*b*tan(x)^3 + 4*a*tan(x) - 5*b*tan(x))/((tan(x)^2 + 1)^2*b^2)","A",0
36,1,72,0,0.219078," ","integrate(cos(x)^4/(a+b*cos(x)^2),x, algorithm=""giac"")","\frac{{\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{a^{2} + a b}}\right)\right)} a^{2}}{\sqrt{a^{2} + a b} b^{2}} - \frac{{\left(2 \, a - b\right)} x}{2 \, b^{2}} + \frac{\tan\left(x\right)}{2 \, {\left(\tan\left(x\right)^{2} + 1\right)} b}"," ",0,"(pi*floor(x/pi + 1/2)*sgn(a) + arctan(a*tan(x)/sqrt(a^2 + a*b)))*a^2/(sqrt(a^2 + a*b)*b^2) - 1/2*(2*a - b)*x/b^2 + 1/2*tan(x)/((tan(x)^2 + 1)*b)","A",0
37,1,48,0,1.175796," ","integrate(cos(x)^2/(a+b*cos(x)^2),x, algorithm=""giac"")","-\frac{{\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{a^{2} + a b}}\right)\right)} a}{\sqrt{a^{2} + a b} b} + \frac{x}{b}"," ",0,"-(pi*floor(x/pi + 1/2)*sgn(a) + arctan(a*tan(x)/sqrt(a^2 + a*b)))*a/(sqrt(a^2 + a*b)*b) + x/b","A",0
38,1,37,0,0.376319," ","integrate(1/(a+b*cos(x)^2),x, algorithm=""giac"")","\frac{\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{a^{2} + a b}}\right)}{\sqrt{a^{2} + a b}}"," ",0,"(pi*floor(x/pi + 1/2)*sgn(a) + arctan(a*tan(x)/sqrt(a^2 + a*b)))/sqrt(a^2 + a*b)","A",0
39,1,36,0,0.241527," ","integrate(sec(x)^2/(a+b*cos(x)^2),x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{a^{2} + a b}}\right)}{\sqrt{a^{2} + a b} a} + \frac{\tan\left(x\right)}{a}"," ",0,"-b*arctan(a*tan(x)/sqrt(a^2 + a*b))/(sqrt(a^2 + a*b)*a) + tan(x)/a","A",0
40,1,71,0,0.166307," ","integrate(sec(x)^4/(a+b*cos(x)^2),x, algorithm=""giac"")","\frac{{\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{a^{2} + a b}}\right)\right)} b^{2}}{\sqrt{a^{2} + a b} a^{2}} + \frac{a^{2} \tan\left(x\right)^{3} + 3 \, a^{2} \tan\left(x\right) - 3 \, a b \tan\left(x\right)}{3 \, a^{3}}"," ",0,"(pi*floor(x/pi + 1/2)*sgn(a) + arctan(a*tan(x)/sqrt(a^2 + a*b)))*b^2/(sqrt(a^2 + a*b)*a^2) + 1/3*(a^2*tan(x)^3 + 3*a^2*tan(x) - 3*a*b*tan(x))/a^3","A",0
41,1,104,0,0.181824," ","integrate(sec(x)^6/(a+b*cos(x)^2),x, algorithm=""giac"")","-\frac{{\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{a^{2} + a b}}\right)\right)} b^{3}}{\sqrt{a^{2} + a b} a^{3}} + \frac{3 \, a^{4} \tan\left(x\right)^{5} + 10 \, a^{4} \tan\left(x\right)^{3} - 5 \, a^{3} b \tan\left(x\right)^{3} + 15 \, a^{4} \tan\left(x\right) - 15 \, a^{3} b \tan\left(x\right) + 15 \, a^{2} b^{2} \tan\left(x\right)}{15 \, a^{5}}"," ",0,"-(pi*floor(x/pi + 1/2)*sgn(a) + arctan(a*tan(x)/sqrt(a^2 + a*b)))*b^3/(sqrt(a^2 + a*b)*a^3) + 1/15*(3*a^4*tan(x)^5 + 10*a^4*tan(x)^3 - 5*a^3*b*tan(x)^3 + 15*a^4*tan(x) - 15*a^3*b*tan(x) + 15*a^2*b^2*tan(x))/a^5","A",0
42,1,69,0,0.177892," ","integrate(1/(a+b*cos(x)^2)^2,x, algorithm=""giac"")","\frac{{\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{a^{2} + a b}}\right)\right)} {\left(2 \, a + b\right)}}{2 \, {\left(a^{2} + a b\right)}^{\frac{3}{2}}} - \frac{b \tan\left(x\right)}{2 \, {\left(a \tan\left(x\right)^{2} + a + b\right)} {\left(a^{2} + a b\right)}}"," ",0,"1/2*(pi*floor(x/pi + 1/2)*sgn(a) + arctan(a*tan(x)/sqrt(a^2 + a*b)))*(2*a + b)/(a^2 + a*b)^(3/2) - 1/2*b*tan(x)/((a*tan(x)^2 + a + b)*(a^2 + a*b))","A",0
43,1,149,0,0.158808," ","integrate(1/(a+b*cos(x)^2)^3,x, algorithm=""giac"")","\frac{{\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(x\right)}{\sqrt{a^{2} + a b}}\right)\right)} {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)}}{8 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sqrt{a^{2} + a b}} - \frac{8 \, a^{2} b \tan\left(x\right)^{3} + 5 \, a b^{2} \tan\left(x\right)^{3} + 8 \, a^{2} b \tan\left(x\right) + 11 \, a b^{2} \tan\left(x\right) + 3 \, b^{3} \tan\left(x\right)}{8 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} {\left(a \tan\left(x\right)^{2} + a + b\right)}^{2}}"," ",0,"1/8*(pi*floor(x/pi + 1/2)*sgn(a) + arctan(a*tan(x)/sqrt(a^2 + a*b)))*(8*a^2 + 8*a*b + 3*b^2)/((a^4 + 2*a^3*b + a^2*b^2)*sqrt(a^2 + a*b)) - 1/8*(8*a^2*b*tan(x)^3 + 5*a*b^2*tan(x)^3 + 8*a^2*b*tan(x) + 11*a*b^2*tan(x) + 3*b^3*tan(x))/((a^4 + 2*a^3*b + a^2*b^2)*(a*tan(x)^2 + a + b)^2)","A",0
44,1,46,0,0.192303," ","integrate(1/(1+cos(x)^2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} {\left(x + \arctan\left(-\frac{\sqrt{2} \sin\left(2 \, x\right) - \sin\left(2 \, x\right)}{\sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} - \cos\left(2 \, x\right) + 1}\right)\right)}"," ",0,"1/2*sqrt(2)*(x + arctan(-(sqrt(2)*sin(2*x) - sin(2*x))/(sqrt(2)*cos(2*x) + sqrt(2) - cos(2*x) + 1)))","A",0
45,1,59,0,1.294646," ","integrate(1/(1+cos(x)^2)^2,x, algorithm=""giac"")","\frac{3}{8} \, \sqrt{2} {\left(x + \arctan\left(-\frac{\sqrt{2} \sin\left(2 \, x\right) - \sin\left(2 \, x\right)}{\sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} - \cos\left(2 \, x\right) + 1}\right)\right)} - \frac{\tan\left(x\right)}{4 \, {\left(\tan\left(x\right)^{2} + 2\right)}}"," ",0,"3/8*sqrt(2)*(x + arctan(-(sqrt(2)*sin(2*x) - sin(2*x))/(sqrt(2)*cos(2*x) + sqrt(2) - cos(2*x) + 1))) - 1/4*tan(x)/(tan(x)^2 + 2)","A",0
46,1,68,0,0.145010," ","integrate(1/(1+cos(x)^2)^3,x, algorithm=""giac"")","\frac{19}{64} \, \sqrt{2} {\left(x + \arctan\left(-\frac{\sqrt{2} \sin\left(2 \, x\right) - \sin\left(2 \, x\right)}{\sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} - \cos\left(2 \, x\right) + 1}\right)\right)} - \frac{13 \, \tan\left(x\right)^{3} + 22 \, \tan\left(x\right)}{32 \, {\left(\tan\left(x\right)^{2} + 2\right)}^{2}}"," ",0,"19/64*sqrt(2)*(x + arctan(-(sqrt(2)*sin(2*x) - sin(2*x))/(sqrt(2)*cos(2*x) + sqrt(2) - cos(2*x) + 1))) - 1/32*(13*tan(x)^3 + 22*tan(x))/(tan(x)^2 + 2)^2","A",0
47,1,24,0,1.710169," ","integrate((1-cos(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2} \, x\right)\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}"," ",0,"-2*sgn(tan(1/2*x)^3 + tan(1/2*x))/(tan(1/2*x)^2 + 1)","B",0
48,1,28,0,1.247006," ","integrate((-1+cos(x)^2)^(1/2),x, algorithm=""giac"")","\frac{2 i \, \mathrm{sgn}\left(-\tan\left(\frac{1}{2} \, x\right)^{3} - \tan\left(\frac{1}{2} \, x\right)\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}"," ",0,"2*I*sgn(-tan(1/2*x)^3 - tan(1/2*x))/(tan(1/2*x)^2 + 1)","C",0
49,1,45,0,0.228060," ","integrate((1-cos(x)^2)^(3/2),x, algorithm=""giac"")","-\frac{4 \, {\left(3 \, \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2} \, x\right)\right) \tan\left(\frac{1}{2} \, x\right)^{2} + \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2} \, x\right)\right)\right)}}{3 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{3}}"," ",0,"-4/3*(3*sgn(tan(1/2*x)^3 + tan(1/2*x))*tan(1/2*x)^2 + sgn(tan(1/2*x)^3 + tan(1/2*x)))/(tan(1/2*x)^2 + 1)^3","B",0
50,1,55,0,0.647053," ","integrate((-1+cos(x)^2)^(3/2),x, algorithm=""giac"")","-\frac{12 i \, \mathrm{sgn}\left(-\tan\left(\frac{1}{2} \, x\right)^{3} - \tan\left(\frac{1}{2} \, x\right)\right) \tan\left(\frac{1}{2} \, x\right)^{2} + 4 i \, \mathrm{sgn}\left(-\tan\left(\frac{1}{2} \, x\right)^{3} - \tan\left(\frac{1}{2} \, x\right)\right)}{3 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{3}}"," ",0,"-1/3*(12*I*sgn(-tan(1/2*x)^3 - tan(1/2*x))*tan(1/2*x)^2 + 4*I*sgn(-tan(1/2*x)^3 - tan(1/2*x)))/(tan(1/2*x)^2 + 1)^3","C",0
51,0,0,0,0.000000," ","integrate(1/(1-cos(x)^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-\cos\left(x\right)^{2} + 1}}\,{d x}"," ",0,"integrate(1/sqrt(-cos(x)^2 + 1), x)","F",0
52,0,0,0,0.000000," ","integrate(1/(-1+cos(x)^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\cos\left(x\right)^{2} - 1}}\,{d x}"," ",0,"integrate(1/sqrt(cos(x)^2 - 1), x)","F",0
53,1,78,0,0.256069," ","integrate(1/(1-cos(x)^2)^(3/2),x, algorithm=""giac"")","\frac{\tan\left(\frac{1}{2} \, x\right)^{2}}{8 \, \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2} \, x\right)\right)} + \frac{\log\left(\tan\left(\frac{1}{2} \, x\right)^{2}\right)}{4 \, \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2} \, x\right)\right)} - \frac{2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}{8 \, \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2} \, x\right)\right) \tan\left(\frac{1}{2} \, x\right)^{2}}"," ",0,"1/8*tan(1/2*x)^2/sgn(tan(1/2*x)^3 + tan(1/2*x)) + 1/4*log(tan(1/2*x)^2)/sgn(tan(1/2*x)^3 + tan(1/2*x)) - 1/8*(2*tan(1/2*x)^2 + 1)/(sgn(tan(1/2*x)^3 + tan(1/2*x))*tan(1/2*x)^2)","B",0
54,1,90,0,0.686424," ","integrate(1/(-1+cos(x)^2)^(3/2),x, algorithm=""giac"")","-\frac{i \, \tan\left(\frac{1}{2} \, x\right)^{2}}{8 \, \mathrm{sgn}\left(-\tan\left(\frac{1}{2} \, x\right)^{3} - \tan\left(\frac{1}{2} \, x\right)\right)} - \frac{i \, \log\left(\tan\left(\frac{1}{2} \, x\right)^{2}\right)}{4 \, \mathrm{sgn}\left(-\tan\left(\frac{1}{2} \, x\right)^{3} - \tan\left(\frac{1}{2} \, x\right)\right)} + \frac{2 i \, \tan\left(\frac{1}{2} \, x\right)^{2} + i}{8 \, \mathrm{sgn}\left(-\tan\left(\frac{1}{2} \, x\right)^{3} - \tan\left(\frac{1}{2} \, x\right)\right) \tan\left(\frac{1}{2} \, x\right)^{2}}"," ",0,"-1/8*I*tan(1/2*x)^2/sgn(-tan(1/2*x)^3 - tan(1/2*x)) - 1/4*I*log(tan(1/2*x)^2)/sgn(-tan(1/2*x)^3 - tan(1/2*x)) + 1/8*(2*I*tan(1/2*x)^2 + I)/(sgn(-tan(1/2*x)^3 - tan(1/2*x))*tan(1/2*x)^2)","C",0
55,0,0,0,0.000000," ","integrate((1+cos(x)^2)^(1/2),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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
67,1,8,0,0.233862," ","integrate(cos(x)/(1+cos(x)^2)^(1/2),x, algorithm=""giac"")","\arcsin\left(\frac{1}{2} \, \sqrt{2} \sin\left(x\right)\right)"," ",0,"arcsin(1/2*sqrt(2)*sin(x))","A",0
68,1,11,0,0.423845," ","integrate(cos(5+3*x)/(3+cos(5+3*x)^2)^(1/2),x, algorithm=""giac"")","\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
69,1,16,0,1.422327," ","integrate(cos(x)/(4-cos(x)^2)^(1/2),x, algorithm=""giac"")","-\log\left(\sqrt{\sin\left(x\right)^{2} + 3} - \sin\left(x\right)\right)"," ",0,"-log(sqrt(sin(x)^2 + 3) - sin(x))","A",0
70,1,307,0,1.025395," ","integrate(1/(a+b*cos(x)^4),x, algorithm=""giac"")","\frac{{\left(3 \, \sqrt{a^{2} + \sqrt{-a b} a} a^{2} + 4 \, \sqrt{a^{2} + \sqrt{-a b} a} a b - 3 \, \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} a - 4 \, \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} b\right)} {\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(x\right)}{\sqrt{\frac{4 \, a + \sqrt{-16 \, {\left(a + b\right)} a + 16 \, a^{2}}}{a}}}\right)\right)} {\left| a \right|}}{2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 4 \, a^{3} b^{2}\right)}} + \frac{{\left(3 \, \sqrt{a^{2} - \sqrt{-a b} a} a^{2} + 4 \, \sqrt{a^{2} - \sqrt{-a b} a} a b + 3 \, \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} a + 4 \, \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} b\right)} {\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(x\right)}{\sqrt{\frac{4 \, a - \sqrt{-16 \, {\left(a + b\right)} a + 16 \, a^{2}}}{a}}}\right)\right)} {\left| a \right|}}{2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 4 \, a^{3} b^{2}\right)}}"," ",0,"1/2*(3*sqrt(a^2 + sqrt(-a*b)*a)*a^2 + 4*sqrt(a^2 + sqrt(-a*b)*a)*a*b - 3*sqrt(a^2 + sqrt(-a*b)*a)*sqrt(-a*b)*a - 4*sqrt(a^2 + sqrt(-a*b)*a)*sqrt(-a*b)*b)*(pi*floor(x/pi + 1/2) + arctan(2*tan(x)/sqrt((4*a + sqrt(-16*(a + b)*a + 16*a^2))/a)))*abs(a)/(3*a^5 + 7*a^4*b + 4*a^3*b^2) + 1/2*(3*sqrt(a^2 - sqrt(-a*b)*a)*a^2 + 4*sqrt(a^2 - sqrt(-a*b)*a)*a*b + 3*sqrt(a^2 - sqrt(-a*b)*a)*sqrt(-a*b)*a + 4*sqrt(a^2 - sqrt(-a*b)*a)*sqrt(-a*b)*b)*(pi*floor(x/pi + 1/2) + arctan(2*tan(x)/sqrt((4*a - sqrt(-16*(a + b)*a + 16*a^2))/a)))*abs(a)/(3*a^5 + 7*a^4*b + 4*a^3*b^2)","A",0
71,1,299,0,1.127453," ","integrate(1/(a-b*cos(x)^4),x, algorithm=""giac"")","\frac{{\left(3 \, \sqrt{a^{2} + \sqrt{a b} a} a^{2} - 4 \, \sqrt{a^{2} + \sqrt{a b} a} a b - 3 \, \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} a + 4 \, \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} b\right)} {\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(x\right)}{\sqrt{\frac{4 \, a + \sqrt{-16 \, {\left(a - b\right)} a + 16 \, a^{2}}}{a}}}\right)\right)} {\left| a \right|}}{2 \, {\left(3 \, a^{5} - 7 \, a^{4} b + 4 \, a^{3} b^{2}\right)}} + \frac{{\left(3 \, \sqrt{a^{2} - \sqrt{a b} a} a^{2} - 4 \, \sqrt{a^{2} - \sqrt{a b} a} a b + 3 \, \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} a - 4 \, \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} b\right)} {\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(x\right)}{\sqrt{\frac{4 \, a - \sqrt{-16 \, {\left(a - b\right)} a + 16 \, a^{2}}}{a}}}\right)\right)} {\left| a \right|}}{2 \, {\left(3 \, a^{5} - 7 \, a^{4} b + 4 \, a^{3} b^{2}\right)}}"," ",0,"1/2*(3*sqrt(a^2 + sqrt(a*b)*a)*a^2 - 4*sqrt(a^2 + sqrt(a*b)*a)*a*b - 3*sqrt(a^2 + sqrt(a*b)*a)*sqrt(a*b)*a + 4*sqrt(a^2 + sqrt(a*b)*a)*sqrt(a*b)*b)*(pi*floor(x/pi + 1/2) + arctan(2*tan(x)/sqrt((4*a + sqrt(-16*(a - b)*a + 16*a^2))/a)))*abs(a)/(3*a^5 - 7*a^4*b + 4*a^3*b^2) + 1/2*(3*sqrt(a^2 - sqrt(a*b)*a)*a^2 - 4*sqrt(a^2 - sqrt(a*b)*a)*a*b + 3*sqrt(a^2 - sqrt(a*b)*a)*sqrt(a*b)*a - 4*sqrt(a^2 - sqrt(a*b)*a)*sqrt(a*b)*b)*(pi*floor(x/pi + 1/2) + arctan(2*tan(x)/sqrt((4*a - sqrt(-16*(a - b)*a + 16*a^2))/a)))*abs(a)/(3*a^5 - 7*a^4*b + 4*a^3*b^2)","B",0
72,1,170,0,0.665346," ","integrate(1/(1+cos(x)^4),x, algorithm=""giac"")","\frac{1}{4} \, {\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} + \frac{1}{4} \, {\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} - \frac{1}{8} \, \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) + \frac{1}{8} \, \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)"," ",0,"1/4*(pi*floor(x/pi + 1/2) + arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(-sqrt(2) + 2) + 2*tan(x))/sqrt(sqrt(2) + 2)))*sqrt(sqrt(2) + 1) + 1/4*(pi*floor(x/pi + 1/2) + arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(-sqrt(2) + 2) - 2*tan(x))/sqrt(sqrt(2) + 2)))*sqrt(sqrt(2) + 1) - 1/8*sqrt(sqrt(2) - 1)*log(tan(x)^2 + 2^(1/4)*sqrt(-sqrt(2) + 2)*tan(x) + sqrt(2)) + 1/8*sqrt(sqrt(2) - 1)*log(tan(x)^2 - 2^(1/4)*sqrt(-sqrt(2) + 2)*tan(x) + sqrt(2))","A",0
73,1,53,0,0.558964," ","integrate(1/(1-cos(x)^4),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} {\left(x + \arctan\left(-\frac{\sqrt{2} \sin\left(2 \, x\right) - \sin\left(2 \, x\right)}{\sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} - \cos\left(2 \, x\right) + 1}\right)\right)} - \frac{1}{2 \, \tan\left(x\right)}"," ",0,"1/4*sqrt(2)*(x + arctan(-(sqrt(2)*sin(2*x) - sin(2*x))/(sqrt(2)*cos(2*x) + sqrt(2) - cos(2*x) + 1))) - 1/2/tan(x)","A",0
74,0,0,0,0.000000," ","integrate(1/(a+b*cos(x)^5),x, algorithm=""giac"")","\int \frac{1}{b \cos\left(x\right)^{5} + a}\,{d x}"," ",0,"integrate(1/(b*cos(x)^5 + a), x)","F",0
75,-1,0,0,0.000000," ","integrate(1/(a+b*cos(x)^6),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,0,0,0,0.000000," ","integrate(1/(a+b*cos(x)^8),x, algorithm=""giac"")","\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=""giac"")","\int -\frac{1}{b \cos\left(x\right)^{5} - a}\,{d x}"," ",0,"integrate(-1/(b*cos(x)^5 - a), x)","F",0
78,-1,0,0,0.000000," ","integrate(1/(a-b*cos(x)^6),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,0,0,0,0.000000," ","integrate(1/(a-b*cos(x)^8),x, algorithm=""giac"")","\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=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
81,1,185,0,0.378663," ","integrate(1/(1+cos(x)^6),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} {\left(x + \arctan\left(-\frac{\sqrt{3} \sin\left(2 \, x\right) + \cos\left(2 \, x\right) - 2 \, \sin\left(2 \, x\right) + 1}{\sqrt{3} \cos\left(2 \, x\right) + \sqrt{3} - 2 \, \cos\left(2 \, x\right) - \sin\left(2 \, x\right) + 2}\right)\right)} + \frac{1}{6} \, \sqrt{3} {\left(x + \arctan\left(-\frac{\sqrt{3} \sin\left(2 \, x\right) - \cos\left(2 \, x\right) - 2 \, \sin\left(2 \, x\right) - 1}{\sqrt{3} \cos\left(2 \, x\right) + \sqrt{3} - 2 \, \cos\left(2 \, x\right) + \sin\left(2 \, x\right) + 2}\right)\right)} + \frac{1}{6} \, \sqrt{2} {\left(x + \arctan\left(-\frac{\sqrt{2} \sin\left(2 \, x\right) - \sin\left(2 \, x\right)}{\sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} - \cos\left(2 \, x\right) + 1}\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)*(x + arctan(-(sqrt(3)*sin(2*x) + cos(2*x) - 2*sin(2*x) + 1)/(sqrt(3)*cos(2*x) + sqrt(3) - 2*cos(2*x) - sin(2*x) + 2))) + 1/6*sqrt(3)*(x + arctan(-(sqrt(3)*sin(2*x) - cos(2*x) - 2*sin(2*x) - 1)/(sqrt(3)*cos(2*x) + sqrt(3) - 2*cos(2*x) + sin(2*x) + 2))) + 1/6*sqrt(2)*(x + arctan(-(sqrt(2)*sin(2*x) - sin(2*x))/(sqrt(2)*cos(2*x) + sqrt(2) - cos(2*x) + 1))) - 1/12*log(tan(x)^2 + tan(x) + 1) + 1/12*log(tan(x)^2 - tan(x) + 1)","B",0
82,0,0,0,0.000000," ","integrate(1/(1+cos(x)^8),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
83,0,0,0,0.000000," ","integrate(1/(1-cos(x)^5),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
84,1,199,0,0.542907," ","integrate(1/(1-cos(x)^6),x, algorithm=""giac"")","\frac{1}{18} \, {\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor - \arctan\left(-\frac{3^{\frac{3}{4}} {\left(3^{\frac{1}{4}} {\left(\sqrt{6} - \sqrt{2}\right)} + 4 \, \tan\left(x\right)\right)}}{3 \, {\left(\sqrt{6} + \sqrt{2}\right)}}\right)\right)} \sqrt{6 \, \sqrt{3} + 9} + \frac{1}{18} \, {\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor + \arctan\left(-\frac{3^{\frac{3}{4}} {\left(3^{\frac{1}{4}} {\left(\sqrt{6} - \sqrt{2}\right)} - 4 \, \tan\left(x\right)\right)}}{3 \, {\left(\sqrt{6} + \sqrt{2}\right)}}\right)\right)} \sqrt{6 \, \sqrt{3} + 9} - \frac{1}{36} \, \sqrt{6 \, \sqrt{3} - 9} \log\left(\frac{1}{2} \, {\left(\sqrt{6} 3^{\frac{1}{4}} - 3^{\frac{1}{4}} \sqrt{2}\right)} \tan\left(x\right) + \tan\left(x\right)^{2} + \sqrt{3}\right) + \frac{1}{36} \, \sqrt{6 \, \sqrt{3} - 9} \log\left(-\frac{1}{2} \, {\left(\sqrt{6} 3^{\frac{1}{4}} - 3^{\frac{1}{4}} \sqrt{2}\right)} \tan\left(x\right) + \tan\left(x\right)^{2} + \sqrt{3}\right) - \frac{1}{3 \, \tan\left(x\right)}"," ",0,"1/18*(pi*floor(x/pi + 1/2) - arctan(-1/3*3^(3/4)*(3^(1/4)*(sqrt(6) - sqrt(2)) + 4*tan(x))/(sqrt(6) + sqrt(2))))*sqrt(6*sqrt(3) + 9) + 1/18*(pi*floor(x/pi + 1/2) + arctan(-1/3*3^(3/4)*(3^(1/4)*(sqrt(6) - sqrt(2)) - 4*tan(x))/(sqrt(6) + sqrt(2))))*sqrt(6*sqrt(3) + 9) - 1/36*sqrt(6*sqrt(3) - 9)*log(1/2*(sqrt(6)*3^(1/4) - 3^(1/4)*sqrt(2))*tan(x) + tan(x)^2 + sqrt(3)) + 1/36*sqrt(6*sqrt(3) - 9)*log(-1/2*(sqrt(6)*3^(1/4) - 3^(1/4)*sqrt(2))*tan(x) + tan(x)^2 + sqrt(3)) - 1/3/tan(x)","B",0
85,1,222,0,0.881114," ","integrate(1/(1-cos(x)^8),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2} {\left(x + \arctan\left(-\frac{\sqrt{2} \sin\left(2 \, x\right) - \sin\left(2 \, x\right)}{\sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} - \cos\left(2 \, x\right) + 1}\right)\right)} + \frac{1}{8} \, {\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} + \frac{1}{8} \, {\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} - \frac{1}{16} \, \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) + \frac{1}{16} \, \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) - \frac{1}{4 \, \tan\left(x\right)}"," ",0,"1/8*sqrt(2)*(x + arctan(-(sqrt(2)*sin(2*x) - sin(2*x))/(sqrt(2)*cos(2*x) + sqrt(2) - cos(2*x) + 1))) + 1/8*(pi*floor(x/pi + 1/2) + arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(-sqrt(2) + 2) + 2*tan(x))/sqrt(sqrt(2) + 2)))*sqrt(sqrt(2) + 1) + 1/8*(pi*floor(x/pi + 1/2) + arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(-sqrt(2) + 2) - 2*tan(x))/sqrt(sqrt(2) + 2)))*sqrt(sqrt(2) + 1) - 1/16*sqrt(sqrt(2) - 1)*log(tan(x)^2 + 2^(1/4)*sqrt(-sqrt(2) + 2)*tan(x) + sqrt(2)) + 1/16*sqrt(sqrt(2) - 1)*log(tan(x)^2 - 2^(1/4)*sqrt(-sqrt(2) + 2)*tan(x) + sqrt(2)) - 1/4/tan(x)","B",0
86,1,16,0,0.454347," ","integrate(tan(x)/(1+cos(x)^2),x, algorithm=""giac"")","\frac{1}{2} \, \log\left(\cos\left(x\right)^{2} + 1\right) - \log\left({\left| \cos\left(x\right) \right|}\right)"," ",0,"1/2*log(cos(x)^2 + 1) - log(abs(cos(x)))","A",0
87,1,38,0,0.400989," ","integrate((a+b*cos(x)^2)^(1/2)*tan(x),x, algorithm=""giac"")","-\frac{a \arctan\left(\frac{\sqrt{b \cos\left(x\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \sqrt{b \cos\left(x\right)^{2} + a}"," ",0,"-a*arctan(sqrt(b*cos(x)^2 + a)/sqrt(-a))/sqrt(-a) - sqrt(b*cos(x)^2 + a)","A",0
88,1,45,0,0.370389," ","integrate((1-cos(x)^2)^(1/2)*tan(x),x, algorithm=""giac"")","-\sqrt{-\cos\left(x\right)^{2} + 1} + \frac{1}{2} \, \log\left(\sqrt{-\cos\left(x\right)^{2} + 1} + 1\right) - \frac{1}{2} \, \log\left(-\sqrt{-\cos\left(x\right)^{2} + 1} + 1\right)"," ",0,"-sqrt(-cos(x)^2 + 1) + 1/2*log(sqrt(-cos(x)^2 + 1) + 1) - 1/2*log(-sqrt(-cos(x)^2 + 1) + 1)","B",0
89,1,24,0,0.310548," ","integrate(tan(x)/(a+b*cos(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{\sqrt{b \cos\left(x\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}}"," ",0,"-arctan(sqrt(b*cos(x)^2 + a)/sqrt(-a))/sqrt(-a)","A",0
90,1,27,0,0.365556," ","integrate(tan(x)/(1+cos(x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \log\left(\sqrt{\cos\left(x\right)^{2} + 1} + 1\right) - \frac{1}{2} \, \log\left(\sqrt{\cos\left(x\right)^{2} + 1} - 1\right)"," ",0,"1/2*log(sqrt(cos(x)^2 + 1) + 1) - 1/2*log(sqrt(cos(x)^2 + 1) - 1)","B",0
91,1,33,0,0.335239," ","integrate(tan(x)/(1-cos(x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \log\left(\sqrt{-\cos\left(x\right)^{2} + 1} + 1\right) - \frac{1}{2} \, \log\left(-\sqrt{-\cos\left(x\right)^{2} + 1} + 1\right)"," ",0,"1/2*log(sqrt(-cos(x)^2 + 1) + 1) - 1/2*log(-sqrt(-cos(x)^2 + 1) + 1)","B",0
92,1,143,0,2.134338," ","integrate(tan(x)^3/(a+b*cos(x)^3),x, algorithm=""giac"")","-\frac{b \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| -\left(-\frac{a}{b}\right)^{\frac{1}{3}} + \cos\left(x\right) \right|}\right)}{3 \, a^{2}} - \frac{\log\left({\left| b \cos\left(x\right)^{3} + a \right|}\right)}{3 \, a} + \frac{\log\left({\left| \cos\left(x\right) \right|}\right)}{a} + \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} \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)}{3 \, a^{2}} + \frac{\left(-a b^{2}\right)^{\frac{1}{3}} \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^{2}} + \frac{1}{2 \, a \cos\left(x\right)^{2}}"," ",0,"-1/3*b*(-a/b)^(1/3)*log(abs(-(-a/b)^(1/3) + cos(x)))/a^2 - 1/3*log(abs(b*cos(x)^3 + a))/a + log(abs(cos(x)))/a + 1/3*sqrt(3)*(-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*((-a/b)^(1/3) + 2*cos(x))/(-a/b)^(1/3))/a^2 + 1/6*(-a*b^2)^(1/3)*log(cos(x)^2 + (-a/b)^(1/3)*cos(x) + (-a/b)^(2/3))/a^2 + 1/2/(a*cos(x)^2)","A",0
93,1,38,0,0.511083," ","integrate((a+b*cos(x)^3)^(1/2)*tan(x),x, algorithm=""giac"")","-\frac{2 \, a \arctan\left(\frac{\sqrt{b \cos\left(x\right)^{3} + a}}{\sqrt{-a}}\right)}{3 \, \sqrt{-a}} - \frac{2}{3} \, \sqrt{b \cos\left(x\right)^{3} + a}"," ",0,"-2/3*a*arctan(sqrt(b*cos(x)^3 + a)/sqrt(-a))/sqrt(-a) - 2/3*sqrt(b*cos(x)^3 + a)","A",0
94,1,24,0,0.409241," ","integrate(tan(x)/(a+b*cos(x)^3)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \arctan\left(\frac{\sqrt{b \cos\left(x\right)^{3} + a}}{\sqrt{-a}}\right)}{3 \, \sqrt{-a}}"," ",0,"-2/3*arctan(sqrt(b*cos(x)^3 + a)/sqrt(-a))/sqrt(-a)","A",0
95,1,38,0,0.467465," ","integrate((a+b*cos(x)^4)^(1/2)*tan(x),x, algorithm=""giac"")","-\frac{a \arctan\left(\frac{\sqrt{b \cos\left(x\right)^{4} + a}}{\sqrt{-a}}\right)}{2 \, \sqrt{-a}} - \frac{1}{2} \, \sqrt{b \cos\left(x\right)^{4} + a}"," ",0,"-1/2*a*arctan(sqrt(b*cos(x)^4 + a)/sqrt(-a))/sqrt(-a) - 1/2*sqrt(b*cos(x)^4 + a)","A",0
96,1,24,0,0.423064," ","integrate(tan(x)/(a+b*cos(x)^4)^(1/2),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{\sqrt{b \cos\left(x\right)^{4} + a}}{\sqrt{-a}}\right)}{2 \, \sqrt{-a}}"," ",0,"-1/2*arctan(sqrt(b*cos(x)^4 + a)/sqrt(-a))/sqrt(-a)","A",0
97,1,46,0,0.562591," ","integrate((a+b*cos(x)^n)^(1/2)*tan(x),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{a b \arctan\left(\frac{\sqrt{b \cos\left(x\right)^{n} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} + \sqrt{b \cos\left(x\right)^{n} + a} b\right)}}{b n}"," ",0,"-2*(a*b*arctan(sqrt(b*cos(x)^n + a)/sqrt(-a))/sqrt(-a) + sqrt(b*cos(x)^n + a)*b)/(b*n)","A",0
98,1,27,0,0.559736," ","integrate(tan(x)/(a+b*cos(x)^n)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \arctan\left(\frac{\sqrt{b \cos\left(x\right)^{n} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} n}"," ",0,"-2*arctan(sqrt(b*cos(x)^n + a)/sqrt(-a))/(sqrt(-a)*n)","A",0
